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Bioprocess optimization for recombinant protein production from mammalian cells 2006

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B I O P R O C E S S O P T I M I Z A T I O N F O R R E C O M B I N A N T P R O T E I N P R O D U C T I O N F R O M M A M M A L I A N C E L L S by C H E T A N T. G O U D A R B.Tech., Regional Engineering College Trichy, 1995 M . S . , University of Oklahoma, 1998 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y l n T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Chemical and Biological Engineering) T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A August 2006 © Chetan T . Goudar, 2006 Abstract Mammalian cells are being increasingly used to manufacture complex therapeutic proteins given their ability to properly fold and glycosylate these proteins. However, protein yields are low and process enhancements are necessary to ensure economically viable processes. Methods for yield improvement, bioprocess development acceleration and rapid quantifica- tion and monitoring of cell metabolism were investigated in this study. Recognizing the adverse effect of high pCC>2 on cell growth, metabolism and protein productivity, a novel P C O 2 reduction strategy based on NaHC03 elimination was investigated that decreased .pC02 by 65 - 72%. This was accompanied by 68 - 123% increases in growth rate and 58 - 92% increases in productivity. To enable rapid and robust data analysis from early stage process development experiments, logistic equations were used to effectively describe the k i - netics of batch and fed-batch cultures. Substantially improved specific rate estimates were obtained from the logistic equations when compared with current modeling approaches. Metabolic flux analysis was used to.obtain quantitative information on cellular metabolism and the validity of using the balancing method for flux estimation was verified with data from isotope tracer studies. Error propagation from prime variables into specific rates and metabolic fluxes was quantified using Monte-Carlo analysis which indicated 8 - 22% specific rate error for 5 - 15% error in prime variable measurement. While errors in greater metabolic fluxes were similar to those in the corresponding specific rates, errors in the lesser metabolic fluxes were extremely sensitive to greater specific rate errors such that lesser fluxes were no longer representative of cellular metabolism. The specific rate to metabolic flux error relationship could be accurately described by the corresponding normalized sensitivity co- efficient. A framework for quasi-real-time estimation of metabolic fluxes was proposed and implemented to serve as a bioprocess monitoring and early warning system. Methods for real-time oxygen uptake and carbon dioxide production rate estimation were developed that enabled, rapid flux estimation. This framework was used to- characterize cellular response to pH and dissolved oxygen changes in a process development experiment and can readily be applied to a manufacturing bioreactor. Overall, the approaches for protein productivity ii ABSTRACT i i i enhancement and rapid metabolism monitoring developed in this study are' general with potential for widespread application to laboratory and manufacturing-scale perfusion and fed-batch mammalian cell cultivations. Contents Abstract ii Contents iv List of Tables xii i List of Figures xv Acknowledgements xxii i Dedicat ion xxv I Introduction and Literature Review 1 1 Introduction 2 2 Overview of Cel lular Metabo l i sm 5 2.1 Introduction • 5 2.2 Glycolysis 5 2.2.1 Overview of Glycolysis 5 2.2.2 Energetics of Glycolysis 6 2.2.3 Regeneration of N A D + Consumed during Glycolysis 7 2.2.4 Regulation of Glycolysis 7 2.3 Pentose Phosphate Pathway (PPP) 9 2.3.1 Overview of PPP 9. 2.3.2 Regulation of PPP 9 2.4 Tricarboxylic Acid (TCA) Cycle 10 2.4.1 Overview of the TCA Cycle . 10. iv CONTENTS v 2.4.2 Energetics of the T C A Cycle 11 2.4.3 Regulation of the T C A Cycle 11 2.5 Glutamine Metabolism . . 13 2.5.1 Overview of Glutamine Metabolism . . . 13 2.5.2 Catabolism of Glutamine . . . 14 2.6 Oxidative Phosphorylation 15 2.7 A n Integrated View of Cellular Metabolism 16 2.8 Environmental Effects on Cellular Metabolism 16 2.8.1 Nutrients 16 2.8.2 Metabolites . , . . . 17 2.8.3 Amino Acids . : • . 19 2.8.4 pH 21 2.8.5 Dissolved Oxygen . . . . • 22 2.8.6 Temperature 24 2.9 Conclusions 2.7 3 Methods for Metabol ic F l u x Est imat ion 35 3.1 Introduction. 35; 3.2 Flux Estimation from Metabolite Balancing ' . . 35 3.2.1 Theory 36 3.2.2 Flux Estimation Through Manual Substitution . 37 3.2.3 Flux.Estimation Through Linear Algebra 38 3.2.4 Application of the Matrix Approach for Flux Estimation 39 3.2.5 The Nature of Biochemical Networks . . . 40 3.2.6 Flux Determination in Overdetermined Systems 42 3.2.7 Flux Estimation in an Overdetermined System describing Mammalian Cell Metabolism . . . . 44 3.2.8 Summary of Flux Estimation in Overdetermined Systems . . . . . . 51 3.3 Flux Estimation Using Isotopic Tracers • • • • 52 3.3.1 Atom Mapping Matrices for Flux Estimation 53 3.3.2 Overview of Flux Estimation from Isotope Tracer Studies . 56 3.4 Summary . . . . . . . . . . . . . . ; . . . . . . . . . . 58 II p C 0 2 in High-Density Perfusion Culture 63 4 P C O 2 Reduct ion in Perfusion Systems 64 CONTENTS v i 4.1 Introduction 64 4.2 Theory 66 4.2.1 C O 2 Dynamics in a Mammalian Cell Bioreactor 66 4.2.2 Buffering Action of N a H C 0 3 and N a 2 C 0 3 67 4.2.3 Contributors to Bioreactor p C 0 2 68 4.3 Materials and Methods 69 4.3.1 Cell Line, Medium and Bioreactor System 69 4.3.2 Analytical Methods ; 69 4.3.3 Estimation of Specific Rates 70 4.4 Results ; 71 4.4.1 Bioreactor pCC>2 before NaHCC>3 Elimination from Medium and Base 71 4.4.2 p C 0 2 Reduction Strategy 71 4.4.3 Effect of Reduced p C 0 2 on Growth, Metabolism and Productivity . 74 4.5 Discussion 75 4.5.1 ' Comparison.of Growth, Productivity and Metabolism with Previous • Studies . 76 4.5.2 Impact of high pCC>2 on Osmolality 78 4.5.3 High p C 0 2 and Intracellular pH 79 4.5.4 Closed-loop p C 0 2 : C o n t r o l ' 80 4.6 Conclusions 81 5 O U R and C E R Estimation in Perfusion Systems 87 5.1 Introduction 87 5.2 Theory 89 5.2.1 O U R Estimation 89 5.2.2 C E R Estimation 89 5.3 Materials and Methods . 94 5.3.1 Cell Line, Medium and Cell Culture System 94 5.3.2 Analytical Methods 96 5.4 Results 97 5.4.1 Cell Density and Growth Rate 97 5.4.2 O U R and C E R Estimation . . . '. 98 5.5 Discussion 99 5.5.1 OUR, C E R and RQ Estimation 99 5.5.2 Comparison with Literature Data 100 5.6 Conclusions . . . . . . . . 101 CONTENTS , -,, vii III Robust Specific Rate and Metabolic Flux Estimation 105 6 Logis t ic M o d e l i n g of B a t c h and Fed-batch K i n e t i c s 106 6.1 Introduction : . ' . : - . ' 106 6.2 Theory 108 6.2.1 Calculation of Batch Culture Specific Rates 108 6.2.2 Calculation of Fed-batch Culture Specific Rates 109 6.2.3 A General Equation Describing the Dynamics of Batch and Fed-batch Cultures 109 6.3 Materials and Methods . 112 6.3.1 Cell Line, Medium and Cell Culture System 112 6.3.2 Analytical Methods . . . 113 6.3.3 Nonlinear Parameter Estimation 113 6.4 Results and Discussion • • • 114 6.4.1 Biological Significance.of the Logistic Parameters . . . . . . . . . . . .114 6.4.2 Description of Experimental Data from Batch Cultures . . •'. . . . ' . 115 6.4.3 Description of Experimental Data from Fed-Batch Cultures 117 6.4.4 Comparison with Other Modeling Approaches 119 6.4.5 Computation of Integral Quantities 123 6.4.6 Data for Estimation of Metabolic Fluxes 123 6.5 Conclusions 123 7 E r r o r i n Specific Rates and M e t a b o l i c F luxes 128 7.1 Introduction . . 128 7.2 Materials and Methods 129 7.2.1 Cell Line, Medium and Cell Culture System 129 7.2.2 Analytical Methods 130 7.2.3 Prime Variables and Specific Rates 130 7.2.4 Metabolic Fluxes 131 7.3 Results and Discussion 132 7.3.1 Perfusion Cultivation . 132 7.3.2 Prime Variable Error 133 7.3.3 Specific Rate Error 134 7.3.4 Error in Metabolic Fluxes r . . . . . . . . 140 7.4 Conclusions-'; '. 150 CONTENTS vi i i I V Metabo l i c F l u x Ana lys is 153 8 Metabol ic F l u x Analysis using Isotope Tracers 154 8.1 Introduction 154 8.2 Materials and Methods .' . 155 8.2.1 Cell Line Culture Medium and Bioreactor Operation 155 8.2.2 Analytical Methods 156 8.2.3 Sample Preparation for N M R Analysis 156 8.2.4 2 D - N M R Analysis . . . . 157 8.2.5 Biochemical Network 157 8.2.6 Metabolic Flux Analysis . . 158 8.3 Results 159 8.3.1 Cell Density and Viability 159 8.3.2 Glucose and Lactate Metabolism 160 8.3.3 . Glutamine and Ammonium Metabolism . 161 8.3.4 Metabolic Fluxes 162 8.4 Discussion 163 8.4.1 Pentose Phosphate Pathway 163 8.4.2 Pyruvate Carboxylase Flux 164 8.4.3 Implications for Bioprocess Development 164 8.5 Conclusions '. 165 9 Quas i -Real -Time Metabol ic F l u x Analysis 170 9.1 Introduction . ..: 170 9.2 Framework for Q R T - M F A 171 9.3 Materials and Methods . . 173 9.3.1 Cell Line.. Culture Medium and Bioreactor Operation . . . . . . . . 173 9.3.2 Analytical Methods 173 9.3.3 Estimation of Specific Rates ; 174 9.3.4 Estimation of Metabolic Fluxes . 174 9.3.5 Computer Implementation ; 175 9.4 Results . . . . . . . ; . . 176 9.4.1 Cell Density, Glucose, and Lactate Concentrations 177 9.4.2 Metabolic Fluxes at States A through F ; 177 9.4.3 Sensitivity Analysis for the Practical Realization of Q R T - M F A . '. . 179 9.5 Discussion . . . . . . . . . . . . i . . i 180 CONTENTS ix 9.5.1 Steady State Multiplicity 180 9.5.2 Quasi-Real-Time Metabolic Flux Analysis 181 9.5.3 Sensors for R T - M F A . 181 9.5.4 Metabolite Balancing and Isotope Tracer Approaches as Applied to Q R T - M F A 182 9.5.5 Implementation of Q R T - M F A in this Study . 183 9.5.6 Practical Implications of Q R T - M F A . . . . . . . . 184 9.6 Conclusions 186 V Conclusions and Future Work 190 10 Conclusions 191 10.1 Extensions of This Study .. •. . , ., „ , . . . . . . . 193 10.1.1 M F A Application to a Licensed Manufacturing Process . . . . . . . . 193 10.1.2 Metabolite Profiling . ; .' . . . . . . . . . . . . . ,". . . . . . 193 V 10.1.3 GS-MS for Isotope Tracer Studies . •. ': . . . . . . . . . 194 10.1.4 Flux Analysis from Transient Data . . . . . . . . . .-. . . , . . . . . . 194 10.1.5 Low C S P R Cultivation . . .". . . 195 A Computer P r o g r a m for F l u x Est imat ion 197 B Solution Chemistry in a Perfusion Bioreactor 200 B . l Computer Porgrams for Solution Chemistry Calculations . . . . 200 B . l . l Temperature Correction for Equilibrium Constants . . . . . . . . . . . . 201 B . l .2 Ionic Strength Calculation . ,203 B. l .3 Activity Coefficient Calculation , 204 B. l .4 Ionization Fractions 210 B. 1.5 pC-pH Diagrams . . . . . . . 216 C pCC<2 Contributors in a Perfusion System 231 C. l Acids, Bases and Buffering Action '231 C. l . l Carbon dioxide . . . 231 C.1.2 Lactic Acid . . . . . . 232 C. l .3 Ammonia . . . . . . '232 C.1.4. Base Addition .; . 233 CONTENTS x D Closed Loop p C 0 2 Control 234 D . l p C 0 2 Control Strategy 234 D. 2 Results from p C 0 2 Control . : 235 E R Q Estimation in Perfusion Systems 236 E . l Liquid Stream Contributions to O U R 236 E.2 k L a Estimation from O U R Data . . . 237 E.3 Effect of Medium and Base Composition on the Exit Gas Flow Rate . . . . 238 E.3.1 Medium with 2 g /L N a H C 0 3 and 6% N a H C 0 3 as Base 238 E. 3.2 Bicarbonate-free Medium and 6% N a 2 C 0 3 as Base 239 E. 4 Computer Programs for O U R and C E R Estimation 240 F Logistic Equation Modeling 246 F. l Logistic Equation Simulation : 246 F. l . l Generalized Logistic Equation . . . 246 F . l . 2 Logistic Growth Equation 248 F . l . 3 Logistic Decline Equation 249 F.2 Polynomial Fitting of Batch Culture Data 250 F.2.1 Fermentor Viable Cell Density 250 F.2.2 Glucose . . . 253 F.2.3 Glutamine 255 F.2.4 Lactate : 257 F.2.5 Ammonium 259 F.2.6 Product 261 F.3 Nonlinear Parameter Estimation in Logistic Models v . . . . . . . 263 F.3.1 . Generalized Logistic Equation . . . 263 F. 4 Integral Viable Cell Density . 267 G Parameter Estimation in Logistic Equations 268 G. l Initial Parameter Estimates 268 G.2 Final Parameter Estimation . . . 270 G.3 Generalized Logistic Equation ; 271 G.4 Logistic Growth Equation . . . ; 272 G.5 Logistic Decline Equation 274 G.6 Conclusions 275 CONTENTS ,.s x i H E r r o r in Specific Rates and Metabol ic Fluxes 284 H . l Specific Growth Rate 284 H . l . l Mass Balance on Viable Cells in the Bioreactor 285 H. l .2 Mass Balances on Viable Cells in the Cell Retention Device 286 H.1.3 Expression for Apparent Specific Growth Rate 286 H.2 Specific Glucose Consumption 287 H.3 Specific Glutamine Consumption 287 H.4 Specific Lactate Production 288 H.5 Specific Ammonium Production 288 H.6 Specific Productivity 288 H.7 Gaussian Method of Error Estimation 289 H.7.1 General Expression for Error 289 H.7.2 Error Estimation in Specific Growth Rate 289 H.8 Computer Programs for Specific Rate Error Estimation 290 H.8.1 Comparison of'Gaussian and. Monte-Carlo Methods 290 H.8.2 Specific Rate Error Estimation by the Monte-Carlo Method 299 H . 9 Computer Programs for Metabolic Flux Error Estimation 307 I T h e r m o d y n a m i c Analysis of Metabol ic Pathways 310 I. 1 Theory of Thermodynamic Feasibility 311 1.2 Steps for Determining Reaction Thermodynamic Feasibility 313 1.3 Application to Glycolysis 314 1.4 Bioprocess Implications 316 J F l u x Analysis for Bioprocess Development 317 J . l Introduction. 317 J.2 Materials and Methods 319 J.2.1 Cell Line, Medium and Cell Culture System 319 J.2.2 Analytical Methods 321 J.2.3 Specific Rate Estimation 321 J.2.4 Metabolic Flux Estimation 322 J.3 Results 323 J.3.1 Cell Growth and Viability 323 J.3.2 Residual Glucose and Lactate Concentrations 323 j.3.3 Effect of pH Changes on Metabolic Fluxes 324 J.3.4 Effect of DO Changes on Metabolic Fluxes 325 CONTENTS x i i J.3.5 Cell Size Variation 327 J.3.6 Specific Productivity and Protein Quality 328 J.4 Discussion • • • 330 J.4.1 Effect of pH on Metabolism.. 330 J.4.2 Effect of DO on Metabolism . . . . 331 J.4.3 Q R T - M F A Application to Bioprocess Development 332 J.5 Conclusions : 334 List of Tables 2.1 Essential and Nonessential.Amino Acids for Mammalian Cell Metabolism '. 20 3.1 Reactions in the simplified bioreaction network of Figure 3.2 44 3.2 Values of the chi 2 Distribution at varying Degrees of Freedom and Confidence Levels ; 49 3.3 Values of h after Sequential Elimination of the Measured Rates 51 3.4 Isotopomer distribution for a 3-carbon molecule along with their binary and decimal indexes • • 54 5.1 Published O U R values for mammalian cells 100 6.1 Previously-published batch and fed-batch studies used to test the logistic modeling approach presented in this study 117 7.1 Expressions for growth rate, specific productivity and specific uptake/production rates of key nutrients and metabolites in a perfusion system 133 7.2 Error in Prime Variable Measurements 134 7.3 Consistency index values for the 12 experimental conditions examined in this study . . 140 8.1 Comparison of Glycolytic Fluxes from the Isotope Tracer and Metabolite Balancing Methods . . 162 .8.2 Comparison of T C A Cycle Fluxes from the Isotope Tracer and Metabolite Balancing Methods--.. . .. 163 8.3 Comparison of P P P , Lactate Production, Malic Enzyme and Oxidative Phos- phorylation Fluxes, from the Isotope Tracer and Metabolite Balancing Methods 164 8.4 Comparison of Amino Acid fluxes from the Isotope Tracer and Metabolite Balancing Methods . . 165 . '"• ' " *. xii i LIST OF TABLES xiv 9.1 Medium composition and dilution rate for the six operating conditions ex- amined in this study 173 E . l Carbon dioxide contributions from the inlet and outlet streams when both medium and base streams contain sodium bicarbonate 239 E.2 Carbon dioxide contributions from the inlet and outlet streams with bicarbonate- free medium and sodium carbonate as base 239 G . l Comparison of G L E Parameter Estimates for Cell Density Data from Linear and Nonlinear Parameter Estimation 276 G.2 Comparison of G L E Parameter Estimates for Cell Density Data from Linear and Nonlinear Parameter Estimation 277 G.3 Comparison of G L E Parameter Estimates for Cell Density Data from Linear and Nonlinear Parameter Estimation . 278 . G.4 Comparison of L G E Parameters for Ammonium Concentration Data from Linear and Nonlinear Parameter Estimation 279 G.5 Comparison of L G E Parameters for Lactate Concentration Data from Linear and Nonlinear Parameter Estimation . 280 G.6 Comparison of L G E Parameters for Product Concentration Data from Linear and Nonlinear Parameter Estimation • • • 281 G.7 Comparison of L D E Parameter Estimates from Linear and Nonlinear Para- meter Estimation for Glucose Concentration Data 282 G.8 Comparison of L D E Parameter Estimates from Linear and Nonlinear Para- meter Estimation for Glutamine Concentration Data '. 283 • 1.1 Glycolytic Reactions and their Standard Free Energies . . . 314 1.2 Intracellular Metabolite and Cofactor Concentrations in the Glycolytic Path- way for Human Erythrocyte 315 1.3 Results from Thermodynamics Feasibility Analysis on the Glycolytic Reactions316 List of Figures 2.1 Conversion of glucose to pyruvate via the glycolytic pathway in mammalian cells 6 2.2 The oxidative branch of the pentose phosphate pathway 10 2.3 The nonoxidative branch of the pentose phosphate pathway 11 2.4 Reactions of the T C A cycle. 12 2.5 Reactions involved in glutamine catabolism 14 2.6 A n overview of amino acid catabolism in mammalian cells 21 3.1 A . simplified bioreaction network consisting of 6 intracelllular metabolies (mi — me), 5 measured extracellular rates (rmi,rm3 — rmQ) and 5 unknown intracellular fluxes (vi — ^5) . . . 37 3.2 A simplified network for mammalian cell metabolism with lumped reactions for glycolysis and T C A cycle and those for lactate production and oxidative phosphorylation [37]. The network consists of 5 unknown intracellular fluxes (v c i -v c 5) and 4 extracellular measured rates ( v m i - v m 4 ) . Fluxes vCA and vC5 involve N A D H and F A D H 2 , respectively (Table 3.1) 45 3.3 A n illustration of the steps involved in overdetermined system flux estimation using the metabolite balancing approach 53 3.4 A simple reaction network where molecule C is formed from molecules A and B 55 3.5 A n overview of the flux estimation process for the isotope tracer approach. 57 4.1 Bioreactor p C 0 2 time' profiles for mammalian cell cultivation in perfusion and fed-batch bioreactors. Perfusion p C 0 2 remains high throughout steady- state operation while high p C 0 2 can be a problem in late stages of fed-batch cultivation. 65 xv LIST OF FIGURES : , xvi 4.2 Calculated contributions from biotic (cellular respiration) and abiotic (medium and base N a H C 0 3 ) sources to bioreactor pC02 during perfusion cultivation of B H K cells 68 4.3 Time profiles of bioreactor pCC>2 and viable cell density for B H K and C H O cells in manufacturing-scale perfusion bioreactors. Bioreactor medium in both cases contained 23.8 m M NaHC03 as the buffer. Base usage was 0.71 M N a H C 0 3 for the B H K cultivation and 0.3 M NaOH for the C H O cultivation. 72 4.4 Influence of M O P S and histidine concentrations on cell growth and precipi- tation in the medium feed line. Histidine in the 10-20 m M range and M O P S in the 10-30 m M range did not adversely influence cell growth and prevented precipitation in the medium feed line 73 4.5 Average bioreactor P.CO2 for B H K cells in perfusion culture at 20 x 106 cells/mL. N a H C 0 3 was present both in the medium and base for phase A and was replaced with N a 2 C 0 3 as the base for phase B . Phase C was N a H C 0 3 - free with MOPS-Histidine mixture,,replacing it in the medium and N a 2 C 0 3 replacing it as the base. Bioreactor p C 0 2 reductions were 34.5 and 58.1% for phases B and C, respectively, when compared with phase A 74 4.6 Time profiles of p C 0 2 and viable cell density for B H K cells in 15 L perfusion bioreactors when medium containing MOPS-histidine buffer (NaHC0 3-free) was used along with 0.57 M N a 2 C 0 3 as the base for pH control. Bioreactor P C O 2 and cell density values are shown are mean ± standard deviation for the steady-state phase of the cultivation. . . .• 75 4.7 Time profiles of p C 0 2 and viable cell density for B H K cells in a manufacturing- scale perfusion bioreactor when medium containing MOPS-histidine buffer (NaHC0 3-free) was used along with 0.57 M N a 2 C 0 3 as the base for pH con- trol. Cell density and p C 0 2 values are shown are mean ± standard deviation for the steady-state phase of the cultivation. Bioreactor p C 0 2 and viable cell density for N a H C 0 3 containing medium and base in an identical bioreactor are shown in Figure 4.3. 76 4.8 Comparison of normalized growth rate and specific productivity under ref- erence (NaHC0 3-containing) conditions with NaHC0 3 -free perfusion culti- vations. Time profiles of bioreactor p C 0 2 for the a to d 15 L bioreactors are shown in Figure 4.6 while that for the manufacturing-scale bioreactor is shown in Figure 4.7. There was a significant (p<0.005) increase in growth rate and specific productivity upon N a H C 0 3 elimination in all cases 77 LIST OF FIGURES xvii 4.9 Comparison of normalized glucose consumption and lactate production rates under reference (NaHCG"3-containing) conditions with NaHC03-free perfu- sion cultivations. Time profiles of bioreactor pCC>2 for the a to d 15 L bioreac- tors are shown in Figure 4.6 while that for the manufacturing-scale bioreactor is shown in Figure 4.7. There was a significant (p<0.005) increase in glucose consumption and lactate production upon NaHCC>3 elimination in all cases. 78 4.10 Effect of bioreactor pCG"2 on key metabolic fluxes. The presentation is similar to that in Figures 4.8 and 4.9. The reference condition indicates high pCC>2, conditions 1 - 4 are for low pCC>2 in 15 L bioreactors and condition 5 is low pCC>2 in a manufacturing-scale bioreactor. >• •. • 79 4.11 Time profiles of pCG"2 ( O ) a n d viable cell density (•) for B H K cells in a manufacturing-scale perfusion bioreactor when medium containing M O P S - histidine buffer (NaHCC>3-free) was used along with 0.57 M Na2CC>3 as the base for pH control and oxygen sparged at 0.015 vessel volumes/minute. These p C 0 2 values can be directly compared with those in Figure 4.7 despite differences in cell density since both reactors were operated at identical cell specific perfusion rates . . 80 5.1 The steps involved in perfusion system C E R estimation. 90 5.2 Cell density averages for the different experimental conditions during the course of the perfusion cultivation. For standard conditions, D O = 50%, T = 36.5 °C and pH = 6.8 92 5.3 Growth rate averages for the different experimental conditions during the course of the perfusion cultivation. For standard conditions, D O = 50%, T = 36.5 °C and pH = 6.8. 94 5.4 O U R estimation in the 2 L. reactor by the dynamic method. D O data follow- ing inoculation with cells from the 15 L perfusion bioreactor were used for O U R estimation by the dynamic method 95 5.5 Comparison of O U R estimates from the dynamic method (external 2 L biore- actor) with those from the global mass balance method (in-situ estimation in the 15 L perfusion bioreactor) ' . . . . 96 5.6 Average OUR estimates from the mass balance method for the 12 experi- mental conditions in the perfusion cultivation. . ; 97 5.7 Average C E R estimates for the 12 experimental conditions in the perfusion cultivation. . , 98 LIST OF FIGURES xviii 5.8 Respiratory quotient (RQ) estimates for the 12 experimental conditions in the perfusion cultivation 99 6.1 Sensitivity of the viable cell.density curve to the logistic parameters D (/Jm a x) and B (kdmax). Successive curves are for 25% decreased parameters compared to the previous curve. . . I l l 6.2 Illustration of the biological significance of the logistic parameters using 8 batch and 7 fed-batch cell density data sets [1, 14, 33, 34] 114 6.3 Time profiles of cell density, nutrient and metabolite concentrations for C H O cells in 15 L batch culture. Experimental data (•••••) ; Logistic ( G L E for cell density, L D E for glucose and glutamine and L G E for lactate and ammonium) fit ( ); Logistic specific rate ( ); Discrete derivative specific rate ( ) 115 6.4 Viable cell density, IgG, glutamine and ammonium concentrations for hy- bridoma cells in 300 L batch culture [1]. The points are experimental data and the solid lines are fits by the logistic equations ( G L E for cell density. L D E " for glutamine and L G E for IgG and ammonium). Specific rates calculated from the logistic fits are shown as dashed lines. 116 6.5 Viable cell density, nutrient and metabolite concentrations for B H K cells in 500 mL batch culture [14]. The points are experimental data and the solid lines are fits by the logistic equations ( G L E for cell density, L D E for glucose and glutamine and L G E for lactate and ammonium). Specific rates calculated from the logistic fits are shown as dashed lines. . . . . . . . . . . 118 6.6 Viable cell density, nutrient and metabolite concentrations for hybridoma cells in glutamine limited 2.4 L fed-batch culture [15]. The points are exper- imental data and the solid lines are fits by the logistic equations ( G L E for cell density, L D E for glucose and glutamine and L G E for lactate and ammo- nium). Specific rates calculated from the logistic fits are shown as dashed lines. . . . 119 6.7 Viable cell density and t-PA concentration for C H O cells in 0.7 L fed-batch culture under two different feeding conditions [34]. Glucose was fed at 4 pmol/cell-day for panels a and b while amino acids we're also fed for panels c and d. The points are experimental data and the solid lines are fits by the logistic equations ( G L E for; both cell density and t-PA). Specific rates calculated from the logistic fits are shown as dashed lines 120 LIST OF FIGURES xix 6.8 Comparison of qcin values from logistic (LDE) and polynomial fits for C H O cells in 15 L batch culture. The polynomial fit to glutamine depletion data was statistically superior than the logistic fit for this data set 121 6.9 Comparison of logistic ( G L E for cell density, L G E for IgG and L D E for glutamine) and polynomial fits for batch cultivation of hybridoma cells in 100 mL T-flasks [33]. (; ) logistic fit; ( ) polynomial fit with . the same number of parameters as the logistic fit; (—.. — ..) polynomial fit with one additional parameter (The two polynomial fits in panel c overlap). 122 7.1 Viable cell concentration ( O ) and viability (•) time profiles over the 12 conditions examined in this study. Under standard conditions, D O = 50%, T = 36.5 °C, pH = 6.8 and the target cell concentration was 20 x 10 6 cells/mL for all conditions. . . ' . .- 132 7.2 Average specific glucose consumption rates (mean ± standard deviation) for the 12 experimental conditions in this study. More information about condi- tions A - L is in Figure 7.1, 134 7.3 Flux map for experimental condition E using the network of Nyberg et al [8]. Reaction numbers (1 — 33) and flux values (in parenthesis as pmol/cell-d) are also shown 135 7.4 Comparison of Gaussian and Monte-Carlo qc error estimates at 10% glucose error and 0 -20% Xy error. Both the first and second order Gaussian qc errror estimates were lower than the Monte-Carlo error at higher Xy errors. 136 7.5 Error in ii as a function of error in the 5 associated prime variables. Panel (a) is for V, Fj and F^ while panel (b) is for Xy and Xy. Panel (c) is when all prime variables are simultaneously in error (V, F'd and F^ at 5%; Xy = 5 - 20 %; X® = 0 - 20 %). Xtf error legend for panel c: .(•) 0 %; (o) 5 %; (•) 10 %; (•) 15 %; (A)'20 % 137 7.6 Errors in qc, qL, QGin and qo2 as functions of error in Xy and the corre- sponding prime variable. Xy error Legend: (•) 0 %; (o)5 %; (•) 10 %; (•) 15 %; (A) 20 %. . . . : 138 7.7 Effect of specific rate error on the error in lower metabolic fluxes. Panels (a)-(d) are for errors in the 5 greater specific rates while (e)-(h) are for errors in lower specific rates (amino acid metabolism) 141 7.8 Effect of specific rate error (shown in each frame) on the error in 4 greater metabolic fluxes. Panels (a)-(d) are-for errors in:5 larger specific rates while (e)-(h) are for errors in lower specific rates (amino acid metabolism), . . . . 142 LIST OF FIGURES : ,. xx 7.9 Flux error for greater (panel a) and lesser (panel b) fluxes when all specific rates in the bioreaction network have errors in the 5 - 25% range. The Thr —> SuCoA and Val —> SuCoA error profiles overlap in panel b 144 7.10 Absolute values of the maximum and minimum sensitivity coefficients for the metabolic model used in this study. For each of the 35 specific rates, there were 33 sensitivity coefficients corresponding to the 33 fluxes (Figure 7.3) in the bioreaction network 145 7.11 Normalized sensitivity coefficients for the greater fluxes in the bioreaction network for both greater (panels a-d) and lesser (panels e-h) specific rates. . 146 7.12 NSC variation with respect to glucose uptake rate during the course of an experiment. Data from this study are shown in panel a and those from Follstad et al. [6] in panel b 148 8.1 Time profiles of viable cell density (•) and viability (O) for C H O cells in perfusion culture 158 8.2 Time profiles of bioreactor glucose (•) and lactate (O) concentrations along with their respective specific uptake and production rates over the course of the perfusion cultivation ; 159 8.3 Time profiles of bioreactor glutamine (•) and ammonium (0) concentrations along with their respective specific uptake and production rates over the course of the perfusion cultivation 160 8.4 Metabolic fluxes estimated from analysis of N M R data. 161 9.1 Evolution of bioreactor monitoring and physiological state identification strate- gies from environment to intracellular fluxes 172 9.2 Illustration of the framework for quasi real-time metabolic flux estimation . 176 9.3 Bioreactor viable cell density and glucose and lactate concentrations over the course of the experiment. Medium composition and perfusion rates of states A through F are defined in Table 8.1. [(•) bioreactor cell density; (o) glucose; (•) lactate] 177 9.4 Profile of the two pyruvate fluxes at states A through F 178 9.5 Metabolic flux distribution, around the pyruvate branch point during the course of the experiment. Higher values are indicative of waste metabolism while low values correspond to increased carbon flux through the T C A cycle 179 LIST OF FIGURES xxi 9.6 Relative sensitivities of the calculated pyruvate kinase, pyruvate dehydro- genase, and citrate synthase fluxes with respect to measured specific rates. Only those specific rates with relative sensitivities greater than 0.05 are shown!80 9.7 Graphical representation of the results of metabolic flux analysis. Distinction is made between experimentally measured and calculated fluxes through use of color and the thickness of the flux lines correspond to the magnitude of the respective fluxes . . 184 C . l pC-pH diagram for the bicarbonate system 231 C.2 pC-pH diagram for lactic acid 232 C. 3 pC-pH diagram for ammonia 233 D. l Illustration of the pC02 control strategy proposed in this study 235 G . l Parameter estimation by the linear and nonlinear methods for cell density data of Bree et al., (1988). 270 G.2 Comparison of linear and 2 nonlinear fits to batch C H O cell density data. . 271 G.3 Initial parameter estimation (panel a) and comparison of linear and nonlinear fits (panel b) to ammonium concentration data for C H O cells in batch culture. 272 G.4 Initial parameter estimation (panel a) and comparison of linear and nonlinear fits (panel b) for lactate concentration data of Linz et al., (1997) 273 G.5 Initial parameter estimation (panel a) and comparison of linear and nonlinear fits (panel b) for product concentration data of Dalili et al., (1990) 273 G.6 Initial parameter estimation (panel a) and comparison of linear and nonlinear fits (panel b) for glucose concentration data of Ljumggren and Haggstrom (1994) 274 G. 7 Initial parameter estimation (panel a) and comparison of linear and nonlinear fits (panel b) for glutamine concentration data of Bree et al., (1988) 275 H . l Schematic of a perfusion system with the various flow streams and their respective viable cell concentrations 285 J . l Ranges of variables such as pH and dissolved oxygen in a perfusion bioreactor. Adapted from [3j. 318 J.2 Sequencing and sampling of the experimental procedure in this study. A total of 4 set point changes (pH = 6.6 and 7.0; DO = 0 and 150%) were examined in a 38 day perfusion cultivation 320 LIST OF FIGURES ' • - xxii J.3 Time courses of bioreactor viable cell concentration (0) and viability (•) for conditions A - I in the 38 day perfusion cultivation 322 J.4 Time courses of bioreactor. glucose (Q) and lactate concnetrations (•) for conditions A - T i n the 38 day perfusion cultivation; 323 J.5 Effect of pH reduction on cell metabolism. Panel (a) contains time profiles of glycolytic (Q), lactate (•) and T C A cycled A) fluxes for conditions A - C. Average flux values over, the last 4 data points of each condition are shown in panel (b) along with their standard deviations 325 J.6 Effect of pH increase on cell metabolism. Time profiles of of glycolytic (0)> lactate (•) and T C A cycle (A) fluxes are shown in panel (a) for conditions C - E . Average flux values over the last 4 data points of each condition are shown in panel (b) along with their standard deviations. . 326 J.7 Effect of DO decrease on cell metabolism. Time profiles of of glycolytic (O): lactate (•) and T C A cycle (A) fluxes are shown in panel (a) for conditions E - G. Average flux values over the last 4 data points of each condition are shown in panel (b) along with their standard deviations. • 327 J..8 Effect of DO increase on cell metabolism. Time profiles of of glycolytic (O); lactate (•) and T C A cycle (A) fluxes are shown in panel (a) for conditions G - I. Average flux values over the last 4 data points of each condition are shown in panel (b) along with their standard deviations. . 328 J.9 Effect of pH and D O changes on cell diameter 329 J.10 Time profile of product concentration 330 J . H Western blot for experimental conditions A - D. The last 2 samples from each experimental condition were analyzed such that the two standard condition samples ( A l , A2 or 01, C2) were 116 and 120 hours after set point change while those for the test conditions ( B l , B2 or D I , D2) were after 44 and 48 hours '. , - 331 J.12 Western blot for experimental conditions E and F. The last 2 samples from each experimental condition were analyzed such that the two standard con- dition samples ( E l and E2) were 116 and 120 hours after set point change while those for the test conditions ( F l and F2) were after 44 and 48 hours. 332 J.13 Western blot for experimental conditions G - I. The last 2 samples from each . experimental condition ¥/ere analyzed such that the two standard condition samples ( G l , G2 or II, 12) were 116 and 120 hours after set point change while those for the test conditions (HI, H2) were after 44 and 48 hours. . . 333 Acknowledgements I express my deepest gratitude and appreciation to Konstantin, whose vision, support and encouragement made this possible. He has been a great role model and has touched my life in many ways for which I will forever be grateful. I sincerely thank Jamie for his outstanding guidance and for believing this was possible. I am especially appreciative of his insistence on rigor and hope to write as well as him some day. M y committee members, Douglas Kilburn and Charles Haynes provided valuable feedback that has greatly enhanced the presentation in Chapter 7 and Appendix I. I thank them for very productive progress update meetings. I am grateful.to Bruce Bowen and Ross MacGillivray for their insightful feedback during the final exam. Richard Biener helped program early versions of the Q R T - M F A software. Our cell metabolism and computer programming discussions have always been very productive and his advice has been invaluable on multiple occasions. N M R flux analysis was performed in collaboration with METabolic EXplorer, especially Albert de Graaf, whose expertise enabled effective application of this technique to mammalian cells in perfusion culture I have benefitted immensely, from interactions with my Bayer colleagues. Chun Zhang provided the flexible and open environment that was so vital to bring this to fruition. I thank Jim Michaels for his friendship, support and consistent demonstration that operation outside the realm of the second law of themodynamics was possible. Cary Matanguihan was involved with early work on pC02 reduction and has taught many of us the nuances of operating a manufacturng-scale bioreactor in a process development laboratory. Rudiger Heidemann introduced me to mammalian cell culture and more importantly to the microbreweries in Berkeley. His friendship over all these years is greatly appreciated. Demonstrating pC02 reduction' at manufacturing-scale would not have been possible without assistance from Edward Long and Chris Cruz. I thank them for their outstanding commitment and for putting up with me. Mehdi Saghafi, Doan Tran, Meile L iu , Ricardo Ibarra and David Hou are continuing on that path and.we collectively hope to develop a process that, will result in an improved product for our patients. xxiii ACKNOWLEDGEMENTS xxiv Keith Strevett, Joseph Suflita, Michael Mclnerney and Mark Nanny have played a piv- otal role in my development as a researcher. I have benefitted from my interactions with Gregory Stephanopoulos and from the Metabolic Engineering research from his laboratory. I thank him for his insight and kindness. Donald Knuth's T ^ X and Leslie Lamport's I M E X helped make this dissertation Microsoft Office-free, What I am today is in large part due to my parents effort and sacrifice. I thank Harpreet for her unconditional love and unwavering support. While I tried hard to ensure A G < 0 for thesis completion, I had much reduced impact on the rate of progress. The kinetics improved substantially with Niah's arrival and I look forward to introducing her to Metabolic Engineering in the coming months. Timely completion of this dissertation would not have been possible without help from Harpreet's parents over the last six months. Finally, I thank my employer, Bayer HealthCare, for letting me pursue my Ph.D. while working full-time and for the opportunity to make products that dramatically improve patient quality of life. Dedicat ion To action alone hast thou a right and never at all to its fruits. Let not the fruits of action be thy motive. Neither let there be in thee any attachment to inaction. Bhagavad G i t a To my Teachers, Parents, Harpreet and Niah xxv Part I Introduction and Literature Review i Chapter 1 Introduction Protein biopharmaceuticals that are manufactured through modern molecular biology tech- niques have, revolutionized the way many life threatening illnesses are treated. These prod- ucts comprise a global annual market of $30 billion and this number is expected to increase exponentially in the future with about 500 products currently undergoing clinical evaluation [1] and thousands more being actively researched. The first biopharmaceutical to be ap- proved was recombinant insulin in 1982 [2] and since then a total of 84 biopharmaceuticals were approved in the United States and the European Union by the year 2000 [3]. The most rapid increase was during the 2000 - 2003 period with a total of 64 products receiving regulatory approval [1]. Mammalian cells have played an increasingly important role in the development of new biopharmaceuticals over the past decade. For instance, 64% (21 out of 33) of the biopharma- ceuticals that were approved between January 1996 and November 2000 were manufactured by mammalian cells [4]. This number is likely to increase in the future as mammalian cells have the ability to perform complex post-translational modifications which enable them to produce proteins that have the desired biological activity for therapeutic and diagnostic ap- plications. Current products of mammalian cell culture include therapeutics in the form of recombinant proteins or antibodies, vaccines, tissue-replacement products, and diagnostic products such as monoclonal antibodies. Despite the advantages of post-translational modifications, mammalian cell culture has several challenges. Mammalian cell growth rates are typically an order of magnitude lower than bacterial cells and protein productivity is also low, typically; less than 0.1% of the total protein concentration in the cell [5]. This places an enormous burden on downstream protein concentration and purification steps. In addition to lower growth and productivity, mammalian cells have complex nutritional requirements and are sensitive to shear during 2 CHAPTER 1. INTRODUCTION 3 bioreactor cultivation. Significant progress has been made over the last two decades to address these limitations resulting in suspension cultivation using serum-free media. It is the general perception that the low hanging fruits in mammalian cell culture have been gathered. These include products with low dosage and high market value such as Erythropoietin (EPO) which generated worldwide annual revenues of $7 billion in 2002 [6]. Products of the future are likely to have dosage requirements that are orders of magnitude higher than those for E P O with substantially smaller revenues. Thus protein productivity increase along with reduction in the cost of goods will be an underlying theme for manu- facturing the next generation of biopharmaceuticals. Robust cell line engineering coupled with bioprocess improvements can provide economically feasible manufacturing options. The first section of this study is introductory and presents an overview of mammalian cell metabolism (Chapter 2) and the methods used to determine intracellular fluxes from bioreactor experiments (Chapter 3). While metabolic flux analysis essentially involves the solution of mass balance expressions, a formal method of flux estimation was proposed only 15 years ago while methods of flux estimation from labeled substrates, albeit mature, are still in late stages of development. The important features of both these flux estimation methods have been reviewed with an emphasis on error identification in input data and robust flux estimation. Each of the following chapters, structured like an article, includes an introductory review. The second section presents a detailed description of the dynamics of dissolved carbon dioxide in mammalian cell perfusion bioreactors. High values of dissolved carbon dioxide (pC02 > 200 mm Hg) are commonly encountered in high-density perfusion bioreactors and have been shown to adversely affect growth, metabolism, productivity and protein glycosylation. A robust method of reducing bioreactor pC02 by ~70% (final values close to 70 mm Hg) has been proposed by eliminating NaHCOs from the medium and for bioreactor pH control (Chapter 4). This pC02 reduction was achieved with no changes to bioreactor operation and only a marginal increase in raw material cost while resulting in substantially increased specific protein productivity. Detailed oxygen and carbon dioxide mass balances were developed for a perfusion system that enabled the determination of oxygen uptake and carbon dioxide evolution rates (OUR and C E R , respectively) from which the respiratory quotient (RQ) was estimated (Chapter 5). While mammalian cell RQ's are typically close to unity, O U R and C E R are affected by bioreactor operating conditions and are also necessary for metabolic flux estimation. Robust methods of batch and fed-batch culture specific rate estimation along with a detailed analysis of error propagation during specific, rate and metabolic flux estimation in perfusion systems are presented in Section 3. Analytically differentiable logistic equa- BIBLIOGRAPHY 4 tions were used to describe time profiles of cell density, nutrient, metabolite, and product concentrations in batch and fed-batch cultures resulting in robust specific rate estimates which were in most instances statistically superior to current specific rate estimation meth- ods (Chapter 6). Error propagation from experimental measurements into specific rates and subsequently into metabolic fluxes was quantified using Monte-Carlo analysis (Chapter 7). This analysis helped quantify the uncertainty inherent in metabolic flux estimates due to experimental measurement errors. This information was critical to meaningfully com- pare flux data across different experimental conditions and for decoupling the effect on flux estimates of measurement error and cell physiology. Application of metabolic flux analysis to mammalian cell cultivation is presented in Sec- tion 4. The use of 1 3 C labeled glucose for detailed flux estimation in a C H O perfusion culture is described in Chapter 8. The biomass hydrolysates from these experiments were analyzed by 2 D - N M R which allowed flux estimation in reversible and cyclical reactions, something not possible using the metabolite balancing approach. Besides providing a comprehensive description of C H O cell metabolism, the extended flux data set allowed validation of flux data obtained using the metabolite balancing approach. A framework for quasi-real-time metabolic flux estimation is presented in Chapter 9 that provides rapid quantification of cell physiology and metabolism in both process development and commercial bioreactors. Bibliography [1] Walsh, G . Biopharmaceutical- benchmarks - 2003. Nat. Biotechnol, 2003, 21(8), 865- 870. [2] Gosse, M . ; Manocchia, M . The first biopharmaceuticals approved in the United States: 1980-1994. Drug Inf. J., 1996 , 30, 991-1001. [3] Walsh, G. Biopharmaceutical benchmarks. Nat. Biotechnol, 2000, 18, 831-833. [4] Chu, L . ; Robinson, D. Industrial choices for protein production by large-scale cell culture. Curr. Opin. Biotechnol, 2001, 12, 180-187. [5] Nyberg, G. B. ; Balcarcel, R. R.; Follstad, B . D.;. Stephanopoulos, G.; Wang, D. I. Metabolism of peptide amino acids by Chinese hamster ovary cells grown in a complex medium. Biotechnol Bioeng, 1999 , 62(3), 324-35. [6] Stix, G. Making'Proteins.without D N A . Sci.Am., 2004, 290, 38-40. Chapter 2 Overview of Cel lular Metabo l ism 2.1 I n t r o d u c t i o n Before analyzing the fluxes through a metabolic network, the biochemical reactions that make up the metabolic pathway of interest must be identified. A recombinant mammalian cell converts nutrients (primarily glucose and glutamine) into energy, biomass and waste products along with production of the therapeutic protein of interest. Energy in a cell is present primarily in the form of adenosine tri-phosphate (ATP), while reducing power is,pro- vided by the reduced forms of nicotinamide adenine dinucleotide (NADH) and nicotinamide adenine dinucleotide phosphate (NADPH) . Biosynthetic reactions use N A D P H while N A D H is used primarily for the production of ATP . Mammalian cell biochemistry has been the sub- ject of extensive research and detailed information on cellular metabolism can be found in standard biochemistry textbooks [1]. Only a brief summary of the primary pathways of mammalian cells metabolism will be presented here along with the effect of environmental conditions on cell growth, metabolism and protein productivity. 2.2 G l y c o l y s i s 2.2.1 Overview of Glycolysis Glycolysis involves the degradation of a molecule of glucose through a series of enzyme- catalyzed reaction resulting in two molecules of pyruvate Glucose + 2NAD++ 2ADP + 2P; —> 2Pyruvate + 2NADH + 2ATP + 2H + + 2H 2 0 (2-1) 5 CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 6 This conversion of glucose to pyruvate occurs in ten steps (Figure 2.1), the first five of which constitute the preparatory phase where 2 molecules of A T P are used to convert 1 molecule of glucose into 2 molecules of glyceraldehyde 3-phosphate. In the payoff phase that comprises the latter five reactions, 2 molecules of glyceraldehyde 3-phosphate are converted to 2 molecules of pyruvate resulting in the formation of 4 molecules of A T P and 2 molecules of N A D H . Since 2 molecules of A T P are used in the preparatory phase, the net A T P yield in glycolysis per molecule of glucose is 2. Glucose - A T P • A D P Glucose 6-phosphate Phosphoglucose isomerase Fructose 6-phosphate Phosphofructo- y~ kinase | ^ A T P A D P Dihydroxyacetone . phosphate Fructose 1.6-diphosphate : i •. Triose.phosphate \ ; isomerase Gtyceraldenyde 3-phosphate dehydrogenase Glyceraldehyde 3-phosphate N A D * + P. C N A D H + H* 1,3-Diphosphoglycerate - A D P • Phosphogtycerate kinase • A T P 3-Phosphoglycerate Phosphoglycero- mutase 2-Phosphoglycerate Phosphoenolpyruvate I ^ A D P Pyruvate kinase L A Pyruvate Figure 2,1: Conversion of glucose to pyruvate via the glycolytic pathway in mammalian cells. 2.2.2 Energetics of Glycolysis The overall glycolytic reaction presented as Eq.(2..1) can be split into the exergonic and endergonic components which are the conversion of glucose to pyruvate and the formation CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 7 of A T P from A D P and P;, respectively Glucose + 2 N A D + —> 2Pyruvate + 2 N A D H + 2 H + ; AG?=-146 kJ /mol (2.2) 2ADP + 2P; >2ATP + 2 H 2 0 ; AG^=61 kJ /mol ' ( 2 . 3 ) " It follows from Eqs. (2.2) and (2.3) that the overall standard free-energy change for glycol- ysis is -85 kJ/mol . This large decrease in net free energy makes glycolysis in the cell an essentially irreversible process and the energy released in glycolysis is recovered as A T P with efficiencies greater than 60%. It is also important to note that only a small portion of the total available energy from glucose is released during glycolysis. The total standard free-energy changefor complete oxidation of glucose to C O 2 and H 2 O is -2,480 kJ /mol while that for the degradation of glucose to pyruvate is only -146 k J/mol. Thus only about 5% of the energy available from glucose is released during glycolysis. Pyruvate retains most of the chemical potential energy from glucose which is subsequently extracted by the oxidative reactions of the citric acid cycle and by oxidative phosphorylation. 2.2.3 Regeneration of N A D + Consumed during Glycolysis It follows from Eq.(2.1) that glycolysis involves consumption of N A D + for the production of ' N A D H . Thus regeneration of N A D + is necessary to sustain glycolysis and this can happen in several ways in mammalian cells. One mechanism is the reoxidation of N A D H to N A D + by electron transfer through the respiratory chain located in the mitochondria. These electrons are then passed on through the respiratory chain to oxygen, the terminal electron acceptor 2 N A D H + 2 H + + 0 2 — » 2 N A D + + 2 H 2 0 (2.4) Alternatively, the production of lactate from pyruvate can also serve as a mechanism for the production of N A D + Pyruvate + N A D H + H + —> Lactate + NAD+ , (2.5) 2.2.4 Regulation of Glycolysis Glucose flux through glycolysis'^ regulated to achieve constant A T P levels and to maintain adequate amounts of glycolytic intermediates that are used for biosynthesis. Three enzymes - hexokinase (HK), phosphofructokinase (PFK) and pyruvate kinase (PK) are are considered to play a key role in controlling the glycolytic flux by regulating metabolite concentrations CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 8 such that balance between A T P production and consumption is maintained. 2.2.4.1 Hexokinase Hexokinase catalyzes the first step of glycolysis where glucose is phosphorylated to glucose 6-phosphate Glucose + A T P — G l u c o s e 6-phosphate + A D P + H + (2.6) Mammalian cells have several forms of hexokinase, all of which catalyze the above reac- tion. Muscle hexokinase is allosterically inhibited by glucose 6-phosphate such that high, concentrations of glucose 6-phosphate temporarily and reversibly inhibit hexokinase. This reduces the rate of formation of glucose 6-phosphate from glucose and helps reestablish a steady state for the glycolytic flux. The hexokinase found in the liver is also referred to as glucokinase and is not inhibited by glucose 6-phosphate but instead is inhibited by fructose 6-phosphate. 2.2.4.2 Phosphofructokinase Phosphofructokinase (PFK) catalyzes the phosphorylation of fructose 6-phosphate to fruc- tose 1,6-diphosphate. Fructose 6-phosphate + A T P —> Fructose 1,6-bisphosphate + A D P (2.7) This is often considered as the step that commits the cell to channeling glucose into gly- colysis. P F K has in addition to its substrate binding sites, several regulatory sites where allosteric activators or inhibitors can bind. The activity of P F K is influenced by the con- centrations of A T P , A M P , citrate, fructose 1,6-bihosphate and fructose 2,6-biphosphate. High A T P concentrations inhibit P F K by binding to an allosteric site thereby lowering the affinity of P F K for fructose 6-phosphate. This inhibition is relieved by an increase in the concentration of A D P and A M P which results from consumption of A T P . Citrate also serves as an allosteric regulator for P F K with high citrate concentration increasing the inhibitory effect of A T P . The most significant allosteric regulator of P F K is fructose 1,6-bihosphate which is not an intermediate in glycolysis. CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 9 2.2.4.3 Pyruvate Kinase Pyruvate kinase catalyzes the conversion of phosphoenolpyruvate (PEP) to pyruvate and is the last step in glycolysis P E P + A D P + H + —> Pyruvate + A T P (2.8) High A T P concentrations allosterically inhibit P K by decreasing its affinity for P E P as well as acetyl-CoA and long-chain fatty acids. Both acetyl-CoA and long-chain fatty acids are important fuels for the citric acid cycle and when these are present in high concentrations, A T P is readily produced by the citric acid cycle. Low A T P concentrations increase the affinity of P K for P E P resulting in the formation of A T P through substrate-level phospho- rylation, thereby maintaining the steady-state concentration of ATP . 2.3 Pentose Phosphate Pathway (PPP) 2.3.1 Overview of PPP The primary function of the P P P is the generation of N A D P H and five carbon sugars. The P P P consists of an oxidative branch which produces N A D P H (Figure 2.2) and a nonox- idative branch (Figure 2.3) that interconverts various sugars and connects the P P P to glycolysis. The overall reaction through the oxidative branch of the P P P is G6P + 2NADP+ + H 2 0 — • Ribose 6-phosphate + C 0 2 + 2 N A D P H + 2H+ (2.9) which results in the production of N A D P H , a reductant for biosynthetic reactions and ribose 5-phosphate which is a precursor for nucleotide synthesis. 2.3.2 Regulation of PPP The first step in the oxidative branch of the P P P is the dehydrogenation of glucose 6- phosphate (Figure 2.2) and this reaction is essentially irreversible under physiological con- ditions. Also, this reaction is frequently limiting and serves as the main control point in the P P P . In the nonoxidative branch of the P P P , all the reactions are readily reversible (Figure 2.3) and the direction and magnitude of their fluxes are likely to be determined by simple mass action. The control of this branch however, is not explicitly known. It is likely that cellular demand for N A D P H and ribose 5-phosphate will determine the flux through the pentose phosphate pathway. CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 10 Glucose 6-phosphate glucose 6-phosphate .--NADP* dehydrogenase . f NADPH + H* 6-Phosphoglucono-8-lactone Lactonase 6-phosphogluconate dehydrogenase •H,0 6-Phosphogluconate ^-NADP* y NADPH + H* + CO, D-Ribulose 5-phosphate phosphopentose isomerase D-Ribose 5-phosphate Figure 2.2: The oxidative branch of the pentose phosphate pathway. 2.4 Tricarboxylic Acid (TCA) Cycle 2.4.1 Overview of the T C A Cycle The T C A cycle (Figure 2.4) has the dual role of generating energy in the form of A T P from the oxidation of carbon compounds and also of generating biosynthetic precursors for a wide variety of products. The pyruvate produced during glycolysis is converted to acetyl-CoA and CO2 through an oxidative decarboxylation reaction that is catalyzed by the pyruvate dehydrogenase complex which is made up of three distinct enzymes - pyruvate dehydro- genase, dihydrolipoly transacetylase, and dihydrolipoly dehydrogenase. This conversion of pyruvate to acetyl-CoA and CO2 is an irreversible reaction. The acetyl-CoA formed above enters the T C A cycle where the first of eight reactions is the condensation of acetyl-CoA with oxaloacetate to form citrate under the action of citrate synthase (Figure 2.4). The overall reaction of the T C A cycle can be written as Acetyl-CoA + 2NAD+ + F A D + G D P + P ; + 2 H 2 0 -* 2 C 0 2 + 3 N A D H + F A D H 2 + G T P + 2H+ + CoA (2.10) CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 11 oxidative reactions of pentose phosphate pathway D-Ribose 5-phosphate Sedoheptulose 7-phosphate Fructose 6-phosphate Glucose 6-phosphate epimerase transketolase transaldolase phosphohexose isomerase Xylulose 5-phosphate Glyceraldehyde 3-phosphate Erythrose 4-phosphate Fructose 6-phosphate Xylulose 5-phosphate Glyceraldehyde 3-phosphate Figure 2.3: The nonoxidative branch of the pentose phosphate pathway. 2.4.2 Energetics of the T C A Cycle For one turn of the T C A cycle, two molecules of C O 2 are formed from the oxidation of isocitrate and a-ketoglutarate. The energy from these oxidation reactions is conserved in the reduction of three N A D + and one F A D molecule coupled with the production of one G T P molecule. While only one molecule of G T P is generated per turn of the T C A cycle, the oxidation steps of the T C A cycle (four in all) are electron sources. These electrons are transported to the respiratory chain via N A D H and F A D H 2 where additional A T P molecules are formed during oxidative phosphorylation. When coupled with glycolysis and assuming that both the pyruvate molecules are oxidized to C O 2 via the citric acid cycle, about 32 A T P molecules are generated per molecule of glucose. 2.4.3 Regulation of the T C A Cycle The T C A cycle is controlled to meet the energetic needs of the cell in addition to precursors for biosynthesis. The most important regulation is via the N A D + / N A D H ratio with many reactions requiring N A D + as an electron acceptor and other being allosterically regulated by N A D + or N A D H . Concentrations of other substrates such as succinyl-CoA, oxaloacetate, A T P and A D P also serve to control the activity of the T C A cycle. The key enzymes that CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 12 Pyruvate . CoA + NAD* Malate H,0 -A NAD' NADH + H* malate dehydrogenase Fumarate succinate dehydrogenase • Succinate actionase actionase c/'s-Actionate H,0 Isocitrate. NAD* isocitrate dehydrogenase Succinyl CoA + NADH GTP+CoA P^+GDP C0 3+NADI succinyl CoA synthetase r :i r \ V .̂ C 0 2 + I a-Ketoglutarate CoA + NAD* a-ketoglutarate dehydriogenase complex F i g u r e 2 .4 : R e a c t i o n s o f t h e T C A c y c l e . control T C A cycle activity are pyruvate dehydrogenase complex (PDC), citrate synthase (CS), isocitrate dehydrogenase (ID) and a-ketoglutarate dehydrogenase. ' 2.4.3.1 Pyruvate Dehydrogenase Complex The P D C catalyzes conversion of pyruvate into acetyl-CoA Pyruvate + CoA + N A D + . — • Acetyl-CoA + C 0 2 + N A D H + H + (2.11) ' The products of the above reaction, acetyl-CoA and N A D H are inhibitory to P D C and this inhibition is relieved by CoA and NAD+. Also, G T P inhibits P D C activity while A M P ac- tivates it. P D C is also activated by phosphorylation which is simulated by high A T P / A D P , acetyl-Co A / C o A , and N A D H / N A D 4 " ratios. Dephosphorylation however increases the ac- tivity of P D C . It appears that P D C is active when there is a need for acetyl-CoA, either for biosynthesis, or for the production of N A D H . CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 13 2.4.3.2 Citrate Synthase Citrate synthase (CS) catalyzes the first step of the T C A cycle where oxaloacetate and acetyl-CoA are converted to citrate Acetyl-CoA + oxaloacetate —> citrate + CoA (2-12) Activity of CS is strongly influenced by the concentrations of oxaloacetate and acetyl-CoA which are the reactants in the above reaction. The concentrations of these substrates vary with the metabolic state of the cell and hence affect the rate of citrate production. Succinyl- CoA, N A D H , and N A D P H act as inhibitors by decreasing the affinity of CS for acetyl-CoA 2.4.3.3 IsoCitrate Dehydrogenase Isocitrate dehydrogenase catalyzes the conversion of isocitrate to a-ketoglutarate Isocitrate + N A D ^ —> a-ketoglutarate + C 0 2 + N A D H + H + (2.13) The activity of isocitrate dehydrogenase is strongly affected by the N A D + / N A D H ratio and is allosterically activated by A D P . Increased A T P concentrations adversely affect the activity of isocitrate dehydrogenase. 2.4.3.4 a-Ketoglutarate Dehydrogenase Conversion of a-ketoglutarate to succinyl-CoA is catalyzed by a-ketoglutarate dehydroge- nase a-ketoglutarate + CoA + N A D 4 " — • Succinyl-CoA + N A D H + H + (2.14) The activity of this enzyme is inhibited by succinyl-CoA and N A D H , which are the products in the above reaction. A high A T P / A D P ratio is also known to inhibit a-ketoglutarate dehydrogenase. 2.5 Glutamine Metabolism 2.5.1 Overview of Glutamine Metabolism Glutamine is a major source of energy and nitrogen for mammalian cells. The anabolic reactions of glutamine typically take pace in the cytosol while the catabolism-of glutamine CHAPTER,2. OVERVIEW OF CELLULAR METABOLISM 14 occurs in the mitochondria. Detailed reviews on the metabolism of glutamine are available [2] and, given the dominant role that glutamine plays in catabolism, only this component will be discussed here. 2.5.2 Catabolism of Glutamine The use of glutamine for energy production is also referred to as glutaminolysis and results in the production of pyruvate with the concomitant production of N A D H (Figure 2.5). Glutamine glutaminase Glutamate NAD* Lactonase N H , + N A D H ^ R -OH glutamate transaminase ^ - R - N H , a-ketoglutarate dehydrogenase complex succinly CoA synthetase a-Ketoglutarate N A D * + C o A i V N A D P H + C O , Succinyl CoA » Pi + G D P V G T P + C o A succinate dehydrogenase fumarase malic enzyme Succinate . F A D S». F A D H , Fumarate ,H,0 Malate ^ - NAD(P)* ,V NAD(P)H + C 0 2 Pyruvate Figure 2.5: Reactions involved in glutamine catabolism. Glutamine is first converted to glutamate which subsequently is converted to a-ketoglutarate and enters the T C A cycle. While five carbon atoms enter the T C A cycle through a- ketoglutarate, only two are removed as C 0 2 for each turn of the T C A cycle. The remaining carbon atoms are removed by the conversion of malate to pyruvate; a reaction that is catalyzed by the malic enzyme. The pyruvate formed can either be converted to lactate or it can enter the T C A cycle via acetyl-CoA. CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 15 Glutamine is first converted to glutamate in the following reaction Glutamine + H 2 0 — • Glutamate + N H j (2.15) Subsequent conversion of glutamate to a-ketoglutarate can occur through either glutamate dehydrogenase (GLDH) or via a transaminase reaction (Figure 2.5). Alanine transaminase and aspartate transaminase are abundant in most cells and are likely to be major contribu- tors for the conversion of glutamate to a-ketoglutarate. In addition to the transamination reaction, glutamate can also be deaminated by G L D H as Glutamate + N A D ( P ) + — • a-ketoglutarate + N H j + N A D ( P ) H (2.16) and the a-ketoglutarate formed in the above reaction enters the T C A cycle. Of special interest is the conversion of malate to pyruvate through the action of the malic enzyme . Malate + N A D ( P ) + — • Pyruvate .+ C 0 2 + N A D ( P ) H (2.17) This action of the malic enzyme serves fo remove the excess carbons from the T C A cycle and also allows for complete oxidation of glutamine. 2.6 Oxidative Phosphorylation In aerobic metabolism, oxidative phosphorylation is the final step in the energy production process. The electrons released during the T C A cycle are carried by the energy rich mole- cules N A D H and F A D H 2 and are subsequently transferred to oxygen, the terminal electron acceptor. In mammalian cells, this process occurs in the mitochondria where the respiratory assemblies that carry out the electron transfer steps are located. The overall reaction can be written as N A D H + H+ + ~ 0 2 + (^j A D P + | ^ P- — • NAD+ + H 2 0 + (^j A T P (2.18) where ^ is the ratio of the number of A T P atoms formed per atom of oxygen. For mam- malian this ratio is usually between two and three. CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 16 2.7 A n Integrated View of Cellular Metabolism As the primary role of metabolism is to produce and maintain biomass, cells consume nutrients to produce energy, reducing power and biosynthetic precursors. The primary pathways that form the core of mammalian cell metabolism are glycolysis, T C A cycle, pentose phosphate cycle, glutaminolysis and oxidative phosphorylation. Having examined these pathways individually, it is important to view them in an integrated fashion as their numerous connections and interactions contribute to the overall behavior of the bioreaction network. Glycolysis and the P P P are connected by glucose-6-phosphate as well as several other glycolytic intermediates. Also, glycolysis is connected to the T C A cycle through pyruvate. Glutamine, which is first metabolized to glutamate, enters the T C A cycle as a- ketoglutarate. It is important to note that while the regulation of an individual enzyme can be evaluated fairly completely in vitro, understanding the role of regulation in the overall control of metabolism is extremely difficult. While significant progress has been made in trying to quantify the control of cellular metabolism through metabolic control analysis [3], much work still remains to be done. 2.8 Environmental Effects on Cellular Metabolism Bioreactor operating conditions have a significant effect on the growth and productivity of mammalian cells. The most commonly monitored parameters during routine cell cultivation include nutrient and metabolite concentration, pH, dissolved oxygen and temperature. A l l of these parameters have been known to have a significant influence on cellular metabolism and a summary is presented in the following sections. 2.8.1 Nutrients 2.8.1.1 Glucose Glucose is the primary source of energy and carbon for mammalian cells while glutamine is a source of both nitrogen and energy. A key observation in the metabolism of glucose and glutamine is that their uptake rates are highly concentration dependent. Early inves- tigations [2, 4, 5] have shown that at low glucose concentration, glutamine becomes the dominant source of energy. Also, glucose metabolism itself is a strong function of the glu- cose concentration in the bioreactor. At high glucose concentrations, specific glucose uptake rates are higher with a majority of glucose converted to lactate and only a small portion entering the T C A cycle [5-7]. At low glucose levels, a majority of the glucose enters the CHAPTER 2. OVERVIEW OF CELLIJLAR METABOLISM 17 T C A cycle where it is completely oxidized to C O 2 . . This difference in glucose utilization patterns has been, used to optimize the operation of fed-batch bioreactors where glucose concentration was maintained at a minimum level to minimize the production of lactate [8, 9]. However, it is important to note that a reversal of cellular metabolism can occur when cells are reintroduced into a high glucose environment. For instance, an increase in the molar stoichiometric ratio of lactate to glucose from 0.05 to 1.8 was observed within a few hours of reintroducing glucose starved cells into a glucose rich environment [6]. . 2.8.1.2 Glutamine Glutamine concentration also has an effect on the specific uptake rate of glutamine [10-13]. In continuous culture experiments with hybridoma cells, medium glutamine concentrations in the 0.5 - 2 m M range were limiting and were characterized by reduced rates of ammo- nium and alanine production [10]. Specific ammonium production rates were almost 2-fold higher at elevated glutamine concentrations when compared with those under glutamine- limiting conditions. Consumption rates of other amino acids decreased at higher glutamine concentration in the medium and it was hypothesized that their metabolic function was par- tially replaced by glutamine. Glutamine uptake rates exhibited a Michaelis-Menten type relationship with the glutamine concentration for B H K cells in batch culture and the ki- netic parameters were dependent on the glucose concentration in the medium as glutamine consumption rates were higher at low.glucose concentration [14]. However, no significant differences in the oligosaccharide structures of a human IgG-IL2 fusion protein were detected under glutamine limiting conditions [15]. . Metabolic flux analysis was used to investigate the metabolism of human 293 cells under low glutamine conditions [16]. At limiting amounts of glutamine, the consumption rates of other essential amino acids increased indicating that these could provide intermediates to the T C A cycle in the absence of glutamine. Replacement of glutamine with glutamate has also been proposed as a strategy to minimize ammonium accumulation [17] which is a consequence of both chemical decomposition of glutamine and the conversion of glutamine to glutamate. 2.8.2 Metabolites 2.8.2.1 Lactate A significant portion of glucose is converted to.lactate in cultured mammalian cells and high lactate concentrations are toxic to cells. Moreover, glucose conversion to lactate is energetically inefficient. A 20% reduction in hybridoma cell growth was observed at 10 m M CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 18 (0.9 g/L) lactate concentration [18] while a 50% reduction in hybridoma cell growth rate were observed at 22 m M [19], 40 m M [12, 20] and 55 m M [21] concentrations. As with other variables, the detrimental effects of lactate accumulation are cell line specific but concen- trations in excess of 1 g /L have the potential to adversely affect growth and metabolism. Uptake rates of glucose and glutamine also decreased with increase in bioreactor lactate concentration (20 - 70 mM) while death, oxygen uptake and specific antibody production rates were not affected [21]. For C H O cells in batch culture, lactate concentrations in excess of 30 m M inhibited cell growth with 25% growth rate reduction at 60 m M lactate while no reduction was seen in specific productivity and glucose and glutamine uptake [22]. 2.8.2.2 A m m o n i u m Ammonium in mammalian cell bioreactors is produced both from cellular metabolism and from the chemical decomposition of glutamine. Ammonium has significant effects on cellular metabolism [23] including reduction in cellular growth rates and decline in protein produc- tivity along with alteration of protein glycosylation [24-29]. Reviews on the mechanism of ammonium inhibition are available [30, 31]. In contrast to lactate, ammonium can inhibit cellular growth at much lower concentrations. Growth of several cell lines was inhibited at 2 m M ammonium concentration [18]. However, no inhibition was seen with hybridoma cells at 3 m M N H 4 C I concentration while significant growth inhibition was observed at 10 m M N H 4 C I [30]. As both lactate and ammonium can be toxic at elevated concentrations, it is desirable to keep their bioreactor concentrations as low as possible. 2.8.2.3 Disso lved C a r b o n Diox ide Carbon dioxide is a product of cellular respiration and indirect sources include NaHCOs which is typically a buffer in the cultivation medium. If NaHCOs or N a 2 C 0 3 are used as base to neutralize cellular lactate, these will be additional C O 2 sources. Bioreactor C O 2 concentration is measured as C 0 2 partial pressure ( p C 0 2 ) and the physiological range is 30 - 50 mm Hg. Cell growth can be inhibited at p C 0 2 < 30 mm Hg while elevated p C 0 2 has been implicated in reduced growth, metabolism and productivity in addition to adverse effects on glycosylation [32-43]. There is thus an optimial bioreactor p C 0 2 concentration close to the physiological range where bioreactor operation is desirable. For B H K cells in perfusion culture, a 40 to 280 mm Hg p C 0 2 increase resulted in 30% growth rate and specific productivity decreases [40]. A 57% growth rate decrease was observed for C H O cells in perfusion culture under high glucose concentrations when the p C 0 2 was increased from 53 to 228 mm Hg [44]. The specific antibody productivity, CHAPTER 2: OVERVIEW OF CELLULAR METABOLISM 19 however, was almost unchanged [44]. Increasing pC02 from 36 to 148 mm Hg during perfusion cultivation decreased C H O cell density by 33% (reflecting reduced growth rate) and specific productivity by 44% [37]. Under glucose limiting conditions, for a similar p C 0 2 increase the growth rate decreased by 38% along with a 15% reduction in specific antibody productivity. The growth rate of NS/0 cells decreased when p C 0 2 increased from 60 to 120 mm Hg [33]. Scale-up of a fed-batch process resulted in p C 0 2 values of 179 ± 9 mm Hg in a 1000 L bioreactor and a 40% decrease in specific productivity was seen under these conditions compared to a p C 0 2 value of 68 ± 13 mm Hg in a 1.5 L laboratory- scale bioreactor [41]. Glucose consumption rates decreased in a dose-dependent fashion for hybridoma cells in T-25 flasks [35] with a 40% decrease observed when p C 0 2 increased from 40 to 250 mm Hg. Similar observations were made for lactate production that decreased by 45% for the same p C 0 2 increase. Bioreactor pC02 control close to the physiological range is thus critical given the substantial impact on cell growth, metabolism and protein productivity. ' . • - .• 2.8.3 Amino Acids Amino acid metabolism in mammalian cell cultures is significantly different from that in microbial cultures as mammalian cells are incapable of synthesizing 10 of the 20 standard amino acids. These 10 are referred to as essential amino acids implying that they must be present in the culture medium to promote cell growth and function. A list of essential and non-essential amino acids is presented, in Table 2.1. This representation, however, is for classical human nutrition and all 20 amino acids are present in mammalian cell culture media to promote cell growth and productivity. Amino acid catabolism will be examined first followed by an examination of, the pathways through which the nonessential amino acids are synthesized. 2.8.3.1 A m i n o A c i d C a t a b o l i s m Only about 10 - 15% of energy is generated from amino acid catabolism (excluding gluta- mine) indicating that these pathways are significantly less active compared with glycolysis and fatty acid oxidation. A l l products of amino acid catabolism enter the T C A cycle and a summary of the pathways is shown in Figure 2.6. Arganine, glutamine, histidine and pro- line are first converted to glutamate through different pathways. Glutamate is subsequently converted to a-ketoglutarate either through transamination or deamination: Isoleucine, me- thionine, threonine and valine are all first converted to propionyl-CoA which is subsequently converted to succinyl-CoA by the action of methylmalonyl-CoA mutase. Phenylalanine and CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 20 Table 2.1:, Essential and Nonessential Amino Acids for Mammalian Cell Metabolism , Essent ia l amino acids Nonessent ia l amino acids Arginine Alanine Histidine Asparagine Isoleucine Aspartate Leucine Cysteine Lysine Glutamate Methionine Glutamine Phenylalanine Glycine Threonine Proline Tryptophan Serine Valine Tyrosine tyrosine can enter the T C A cycle either through fumarate or acetyl-CoA. Asparagine is converted to aspartate by the action of asparaginase and aspartate undergoes transami- nation with a-ketoglutarate yielding glutamate and oxaloacetate. A majority, (10) of the amino acids yield acetyl-CoA which subsequently enters the T C A cycle. Leucine, lysine, phenylalanine, tryptophan and tyrosine are first converted to acetoacetyl-CoA which is sub- sequently cleaved to acetyl-CoA. Alanine, cysteine, glycine, serine and tryptophan are first. converted to pyruvate and then to acetyl-CoA. 2.8.3.2 A m i n o A c i d Biosynthes is Of all the amino acids shown in Figure 2.6, the essential amino acids have to be supplied in the culture medium since they cannot be synthesized by the cells. Biosynthesis of only the non-essential amino acids is possible and an overview will be presented in this section. Alanine is produced by the transamination of pyruvate by alanine transaminase. The pro- duction of asparagine is catalyzed by asparagine synthetase and deamination of asparagine catalyzed by asparginase results in the formation of aspartate. The sulfur, for cysteine comes from methionine, an essential amino acid and homocysteine is first produced. Homo- cysteine condenses with serine to produce cystathionine, which is subsequently cleaved by cystathionase to produce cysteine and a-ketobutyrate. Glutamine is produced by amino- transferase reactions, with a number of amino acids donating the nitrogen atom (Figure 2.6). It can also be synthesized by the reductive animation of a-ketoglutarate catalyzed by glutamate dehydrogenase. Glutamine can be produced by the action of glutamine syn- thetase or from glutamate by the direct incorporation of ammonia. Glycine is produced from serine in a one-step reaction catalyzed by serine hydroxymethyltransferase. CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 21 Leucine Lysine Phenylalanine Tryptophan Tyrosine Acetoacetyl -CoA Glutamate Isocjtrate Citrate a-KetogJutarate Acetyl-CoA Succinyf-CoA Oxaloacetate W Arginine Glutamine Histidine Proline Isoleucine Methionine Threonine Valine Phenylalanine Tyrosine Fumajate Pyruvate Isoieucihe Leucine Tryptophan Alanine' Cysteine Glycine Serine Tryptophan Asparagine Aspartate Figure 2.6: An overview of amino acid catabolism in mammalian cells. Glutamate is the precursor for proline synthesis while serine is produced from the glycolytic intermediate 3-phosphoglycerate. A n NADH-linked dehydrogenase converts 3- phosphoglycerate into a keto acid, 3-phosphopyruvate, suitable for subsequent transami- nation. Aminotransferase activity with glutamate as a donor produces 3-phosphoserine, which is converted to serine by phosphoserine phosphatase. Tyrosine is produced in cells by hydroxylating the essential amino acid phenylalanine with approximately half of the phenylalanine required going into the production of tyrosine. 2.8.4 pH Bioreactor pH during mammalian cell cultivation is typically maintained close to neutral while optimal pH values for growth and protein production tend to be cell-line and product specific. For hybridoma cells in batch culture, maximum growth was seen at 7.4 and this CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 22 value decreased as the pH increased [45]. For hybridoma cells in batch culture, a decrease in bioreactor pH from 7.6 to 7.2 and subsequently to 6.8 decreased cell growth, glucose consumption and lactate production while glutamine uptake and ammonia production were not affected.by pH changes [30]. Similar reductions in glucose.uptake and lactate production rates at low bioreactor pH have been seen for hybridoma cells in batch and continuous culture [46] resulting in the substitution of glutamine for glucose .as the energy source. It has been shown that a decrease in bioreactor pH can reduce the intracellular pH (pHj) resulting in cytoplasmic acidification [47] which in turn is primarily responsible for the metabolism shifts in response to bioreactor p H changes. Changes to pFL; have significant implications for cell growth and,metabolism [48, 49]. Decrease in pEL; on the order of 0.2 units has been shown to significantly reduce the carbon flux through glycolysis [50-53]. One reason for this decrease is the strong dependence of the activity of the enzyme phosphofructokinase on pH^ [1]. Since changes to pH^ affect the ionization states of all peptides and proteins, pH^ is actively regulated [54, 55]. 2.8.5 Dissolved Oxygen The concentration of dissolved oxygen is a key variable in mammalian cell cultivation and is often controlled at,a constant value in the vicinity of 50% air saturation. Oxygen is essential for A T P production through oxidative phosphorylation and is typically provided to the bioreactor using,an air-oxygen mixture. Given the low solubility of oxygen in cell culture media, efficient aeration strategies need to be employed, especially in high-density cultivation. . It was observed early on that cell growth is sub-optimal in the absence of dissolved oxygen control and controlling p 0 2 in the 40 - 100 mm Hg range (25 - 63% air saturation) resulted in maximum viable cell densities during batch cultivation of mouse LS cells [56]: Cell growth and maximum cell density, however, were significantly reduced at low (1%) and high (200%) D O concentrations [57]: Oxygen uptake rate was also lower at D O = 1% and this was attributed to oxygen-limiting conditions in the bioreactor. Glucose metabolism was also significantly affected by bioreactor DO concentration. At DO = 200%, only 60% of the glucose was converted to lactate when compared with 90% conversion- for all other. DO concentrations investigated (7.5, 20, 25, 60, 100%). Thus more glucose was drawn into the T C A cycle at DO = 200% which was also characterized by higher oxygen uptake rates. The lactate production rate was the highest at D O = 1% and decreased at higher D O values. High lactate production at low DO values is necessary to generate A T P from the conversion of glucose to lactate since there is a reduction in A T P production through the CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 23 T C A cycle. A build-up of pyruvate was also seen at DO = 1% indicating that the pyruvate flux into lactate was slower than the conversion of glucose to pyruvate, A n analysis of the enzyme levels at various DO concentrations indicated low levels of isocitrate dehydrogenase and aldolase, and high levels of lactate dehydrogenase at low D O concentration [58]. Thus low DO concentration caused a reduction in the levels of enzymes involved in terminal respiration while the levels of those in glycolysis and the hexose-monophosphate pathway were increased. The effect of dissolved oxygen concentration in the 0.1 - 100% air saturation range on hybridoma cell metabolism was examined in continuous culture [59]. Oxygen uptake rate was constant for D O in the 10 - 100% range but decreased by more than 50% when the DO dropped below 10%, suggesting oxygen limitation. Lactate production from glucose was higher at low DO concentrations while glutamine consumption decreased. In another study on hybridoma cells in continuous culture, cell growth was reduced both at DO < 5% and DO —• 100% air saturation [60]. Glucose consumption and lactate production increased when the D O was < 5% while there was a significant reduction in the oxygen uptake rate and these findings are similar to those reported in earlier studies. Glutamine consumption and ammonium production rates were also higher under low DO conditions, in contrast to the observations in Miller et al. [59]. Amino acid consumption rates increased sharply at low DO concentration while the specific antibody production rate was DO independent. Metabolic flux analysis has been applied to characterize the influence of D O on cell metabolism [61, 62]. For hybridoma cells in continuous culture [62], growth rate was not affected at DO values as low as 1% but was significantly reduced at DO = 0.1%. Glucose consumption and lactate production rates were significantly higher at DO = 0.1% as with previous studies. Metabolic flux analysis indicated that the fluxes of NAD(P)H-producing dehydrogenase reactions decreased under hypoxic conditions (low N A D ( P ) + / N A D ( P ) H ra- tio) and increased at higher DO concentration (high N A D ( P ) + / N A D ( P ) H ratio). For hy- bridoma cells in batch culture [61] there was no significant effect on metabolism when the D O was varied between 5 and 60% air saturation. At DO values of 1% and 0%, both oxygen uptake and carbon dioxide production rates were lower while those for glucose consump- tion and lactate production increased. Glutamine consumption and ammonia production decreased at low D O while glutamate production was high. Metabolic flux analysis indi- cated that the pyruvate flux into the T C A cycle was non-existent at D O = 0% and the flux through glutamate dehydrogenase was reversed at low D O resulting in increased glutamate production. The fraction of A T P from glycolysis increased from 34% at DO = 60% to 69% when the D O was 0% reflective of the increased rates of glucose and lactate metabolism at low DO. .. CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 24 A l l the above studies suggest that there is a threshold DO concentration below which dramatic changes in growth and metabolism are seen. This value is typically 1% air sat- uration or lower for most cell lines studied to date. It must however be noted that it is not clear if the D O was actually controlled at 1 and 0.1% saturation. D O probes are not characterized by that level of accuracy and it is possible that the cultivations were actually at even lower D O levels. D O concentrations greater than 100% also have the potential to adversely impact cellular metabolism clearly highlighting the need to control bioreactor DO concentration at lower levels. It is nonetheless important to note that D O concentrations in the 1 0 - 9 0 % range have minimal impact on cell metabolism and protein productivity thereby minimizing the impact of D O excursions associated with operational error in a manufacturing scenario. Controlling DO at a defined set-point is rather straightforward and this is typically done using a PID controller that regulates the flow of a mixture of oxygen and nitrogen/air into the system. 2.8.6 Temperature Temperature is a key variable in mammalian cell cultivation and most bioreactors are typ- ically operated close to the physiological value of 37 °C. While reduction in cell growth and metabolism at lower temperatures have been long recognized [63, 64], manipulating temperature to improve protein productivity is relatively recent. Temperature effects on specific protein productivity are cell line-specific since observations to date include increased [65-70], decreased [19, 31, .71, 72] or unchanged productivity [31, 73-76] upon temperature reduction. While the advantages associated with increased specific productivity are obvious, even unchanged specific productivity can be beneficial in both fed-batch and perfusion sys- tems. Since lower temperatures are typically accompanied by reduced growth and metabolic rates, fed-batch cultivation times can be extended without large decreases in culture via- bility. Along similar lines, perfusion rates can be reduced in perfusion cultivation reducing both medium usage and the volume of harvest generated. This concentrated harvest stream can significantly reduce the cost associated with subsequent protein purification operations. 2.8.6.1 Effect of Temperature on Growth and Metabolism Both growth and metabolic rates are known to decrease sharply with temperature decreases. Reduction in growth rate is attributed to cell accumulation in the G0/G1 phase concomitant with a rapid reduction of cells in the S phase [66, 77, 78]. For B H K cells in batch culture, the growth rate was reduced by 25% when cultivation temperature was lowered from 37 to 33 °G [73] while a more'dramatic decrease was seen for EPO-producing C H O cells in batch CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 25 culture (0.029 ± 0.003 h " 1 at 37 °C; 0.016 ± 0.001 h r 1 at 33°C) [65]. Cell cycle analysis for C H O cells revealed that at 74 hours into the cultivation, the percentages of cells in the G0/G1 phase was 75.8, 62.8 and 47.3% at 30, 33 and 37 °C, respectively, while that, for the S phase were 11.6, 33.2 and 45.8%, respectively. Similar observations were made during batch cultivation of Ant i -4 - lBB producing C H O cells [79]. The growth rate decreased from 0.022 ± 0.003 h 1 at 37°C to 0.014 ± 0.004 h _ 1 at 33 °C and the percentages of cells in the G0/G1 phase 78 hours into the cultivation were 64.9, 59.1 and 36% at 30, 33 and 37 °C, respectively, while the S phase percentages were 17.4, 15.6 and 45.1%, respectively. Just as with growth rate, lower cultivation temperatures are associated with reduced glucose uptake and lactate production rates. For hybridoma cells in batch bioreactors, glucose uptake rate was reduced by 41% at 34 °C compared to 37 °C [19] while a 2-5 fold decrease was observed for hybridoma cells for temperature reduction from 39 to 33 °C [71]. For BHK-21 cells in batch culture, the specific, glucose uptake rate decreased from 0.58 ng/cell-d at 37 °C to 0.45 ng/cell-d when the temperature was lowered to 33°C [73] while a 50% reduction in both glucose uptake and lactate production rates was seen for C H O cells in a packed bed reactor for a temperature reduction from 37 to 32 °C [70]. For E P O - producing C H O cells in batch culture, there was no significant reduction in glucose uptake and lactate production rates for a temperature decrease from 37 to 33 °C [65] and similar observations were made for glutamine consumption and ammonium production. However, when the temperature was further lowered to 30 °C, glucose uptake and lactate production rates decreased by 44 and 56%, respectively (as compared to 37 °C) while the decreases in glutamine uptake and ammonium production were 47 and 36%, respectively. 2.8.6.2 Effect of Tempera ture on O x y g e n U p t a k e R a t e A n Arrhenius-type relationship has been proposed to describe the dependence of oxygen uptake rate on temperature in the 6 - 37 °C range [80]. At temperatures close to 37 °C, every 1 °C drop in temperature was accompanied by approximately 10% reduction in the oxygen uptake rate [74] and an order of magnitude decrease in the oxygen uptake rate was seen for temperatures below 15 °C. For C H O cells in a packed bed reactor, a 4 - 5 fold decrease in oxygen uptake rate was seen when the temperature was reduced from 37 to 32 °C [70]. For C H O cells in batch culture, a 50% reduction in oxygen uptake rate was seen when the temperature was reduced from 37 to 30 °C [77]. Temperature effects on oxygen consumption rate are thus consistent and follow an inverse relationship of the Arrhenius type. CHAPTER 2. OVERVIEW OF CELLULAR METABOLISM 26 2.8.6.3 Effect of Temperature on Cell Sensitivity to Shear There has been one report where the effect of temperature on shear sensitivity was studied for BHK-21 cells [81]: Cultivation temperatures in the 28 - 39 °C range were examined and an improvement in shear resistance was observed at lower temperatures. It was hypothesized that increased rigidity of the lipid bi-layer at reduced temperatures was contributing to the increased shear resistance. Cell morphology was also influenced by cultivation temperature and cells were more spherical at lower temperatures. However, temperature reduction is unlikely to be used with the sole objective of improving shear resistance properties in light of subsequent advances in the use of shear protectants [82]. Components such as pluronic F-68 are routinely used in current cell cultivation media and provide adequate shear protection in serum-free media under a variety of agitation and oxygenation conditions. 2.8.6.4 Implications for Bioprocess Optimization Reduced temperature cultivation has been suggested as a tool for increasing productivity in mammalian cell bioreactors. Higher productivity can be achieved rather easily when specific protein productivity is also higher at lower temperatures [65-70], and this has in one in- stance been linked.to.increased transcription level of the protein of interest [65]. A biphasic cultivation method has been proposed to maximize protein productivity which includes an initial phase of fast cell growth at 37 °C followed by cultivation at reduced temperatures where specific productivity is higher [66-70]. The shift in cultivation temperature has typ- ically been determined arbitrarily and a' model-based approach to cultivation temperature change has been proposed only recently [83]. Using simple Monod-type unstructured kinetic models to describe the dynamics of,cell growth and metabolism, a temperature shift after 3 days of growth was found to result in optimal volumetric productivity, a 90% increase when compared with cultivation at 37 °C. The lower rates of metabolite production at reduced temperatures allow perfusion cul- tivation at reduced perfusion rates since metabolite accumulation in the reactor is reduced. This lowers medium consumption thereby significantly reducing the cost of goods and also provides a harvest stream with increased product concentration that has positive implica- tions for downstream purification operations. However, temperature shifts can potentially affect product quality [84, 85] and this must be taken into account before temperature-based bioprocess optimization is considered in both fed-batch and perfusion cultivations. BIBLIOGRAPHY 27 2.9 Conclusions The primary pathways that form the core of mammalian cell metabolism are glycolysis, T C A cycle, pentose phosphate cycle, .glutaminolysis and oxidative phosphorylation, and an overview of. these pathways has been presented. 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Comparative analysis of two controlled proliferation strategies regarding product.quality, influence on tetracycline-regulated gene expression and productivity. Biotechnol. Bioeng., 2001, 72, 592-602. [85] Anderson, D.; Bridges, T.; Gawlitzek, M . ; Hoy, C. Multiple cell factors can affect the. glycosylation of.Asn-184 in CHO-produced tissue-type plasminogen activator. Biotech- nol. Bioeng., 2000, 70, 25-31. • Chapter 3 M e t h o d s f o r M e t a b o l i c F l u x E s t i m a t i o n 1 3.1 Introduction Flux is denned as the rate with which material is processed through a bioreactidn pathway [1]. While a reaction flux does not contain information on the activity of enzymes in that particular reaction, it does contain information on the extent of involvement of the enzymes in that reaction. For this reason, it has been argued that metabolic fluxes constitute a fundamental determinant of cell physiology and metabolic flux estimation is, therefore, the preferred method for characterizing the physiological state of a cell [2]. Metabolic fluxes can be estimated either by applying mass balances across intracellular metabolites or through isotope mass balances across every carbon atom in the metabolic network. A n overview of these two flux estimation methods is presented in this chapter. 3.2 Flux Estimation from Metabolite Balancing In the metabolite balancing approach, intracellular fluxes are estimated from experimentally measured extracellular rates [3-5]. Intracellular metabolites in the bioreaction network are identified and mass balance expressions are written around them resulting in a stoichiometric model of cellular metabolism. Specific uptake rates of key nutrients and specific production rates of some metabolites are experimentally measured and these constitute the input data 'A version of this chapter has been accepted for publication. Goudar, C.T., Biener, R., Piret, J.M. and Konstantinov, K.B. (2006) Metabolic Flux Estimation in Mammalian Cell Cultures, In R. Portner, (ed.), Animal Cell Biotechnology: Methods and Protocols, 2"d ed., Humana Press, Totowa, NJ. 35 CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION- 36 for flux estimation. Intracellular fluxes are subsequently computed from experimental data and the network stoichiometry using linear algebra. The earliest application of metabolite balancing to a fermentation process is for citric acid production by Candida lipolytica [6] and this approach was later used for validation of the bioreaction network of butyric acid bacteria [7, 8]. Metabolic flux analysis in its present form can be largely attributed to the seminal work on lysine fermentation [1] where metabolite balancing and extracellular fluxes were used to understand intracellular regu- latory mechanisms during lysine production by Corynebacterium glutamicum. Metabolite balancing has since seen widespread application for bacterial, yeast and mammalian cell cultures. Mammalian cell applications include B H K [9, 10], C H O [4, 11, 12], hybridoma [3, 13-20] and human [21] pells. 3.2.1 Theory Consider the reaction sequence A —•> B —> C where B is the intracellular metabolite. The mass balance expression for B can be written as — = rA - rc - fJ.B (3.1) where VA is the rate of formation of B from A, rc the rate of conversion of B to C and \iB the conversion of B to biomass. Substituting TB = r& — rc for the net formation rate of metabolite B, the above equation can be rewritten as ^ = r B - ^ B (3.2) At low intracellular metabolite concentrations, the p,B term is small and can be neglected. For aerobic chemostat cultivation of S. cerevisiae at a dilution rate of O.l h _ l , the intra- cellular concentrations of glycolytic pathway intermediates ranged between 0.05 - l.O /imol (g D W ) - 1 [22], resulting in 0.005 - 0.1 ^mol (g D W ) ~ 1 h ~ 1 fiB values. These values were much lower than the glycolytic fluxes that were ~1.1 mmol (g D W ) - 1 h - 1 , 4 - 6 orders of magnitude higher. A similar rationale can be applied to mammalian cells where intracel- lular metabolite concentrations are similar to those in yeast but with reduced growth and metabolic rates [2] such that -aH=TB (3-3) CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 37 Invoking the steady-state, hypothesis which suggests that the magnitude of change in intra- cellular, metabolite concentrations are negligible [20], we get rB,= 0 (34) which essentially states that the net rate of formation of intracellular metabolites in zero. For a bioreaction network with M intracellular metabolites we get r M = 0 (3.5) where T M is the vector of net metabolite formation rates. Mass transfer effects have not been included in the above derivation because substrate transfer from the cultivation medium into the celland availability of intracellular metabolites are not considered to be rate limiting. 3.2.2 Flux Estimation Through Manual Substitution ' m 4 'ml m. rrv m rrv ' m 3 r a ' m 5 ' m 6 Figure 3.1: A simplified bioreaction network consisting of 6 intracelllular metabolies (mi — ITIQ), 5 measured extracellular rates ( r m i , r T O 3 rme) and 5 unknown intracellular fluxes (vi -1'5). The application of Eq.(3.5) for flux estimation is illustrated using the reaction network shown, in Figure 3.1. This network consists of 6 intracellular metabolites --(mi — me) and 5 measured extracellular rates ( r m i , r m 3 — r m g ) that have been arbitrarily selected to have enough measurements to solve for the 5 unknown intracellular fluxes (v\ — vs.). Applying CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 38 Eq.(3.5) around metabolites mi — TTIQ results in the following mass balance expressions 777,1 rmi-vi-v3 = 0 (3.6) 777,2 V\ — V2 = 0. (3.7) 777 3 V2 - rm3 - f 4 = 0 (3,8) 777,4 ^ 3 - rmi - v5 = 0 (3.9) 777 5 (3.10) me VA - rm6 = 0 (3.11) Estimating the unknown fluxes v\ — v$ from the above equations is straightforward. From Eq.(3.10), v5 = rm5 and vA = rm6 from Eq.(3.11). Thus v3 = r m 4 + rm5 from Eq.(3.9) and V2 = v\ = rm3 + rme from Eqs.(3.7) and (3.8). The solution for the above bioreaction network can thus be summarized as vi=rm3+rm6 (3.12) V2 = vi (3.13) V3=rmi +rm5 (3.14) • • ' V4 = rm6 (3.15) v5 = rm5 (3.16) 3.2.3 Flux Estimation Through Linear Algebra The above approach of manual substitution works well for small bioreaction networks. For complicated networks that have multiple branch points and often include more than 30 metabolites and reactions, manual estimation of fluxes becomes cumbersome. A n elegant alternative is to use matrix notation and linear algebra techniques for flux estimation. Eq.(3.5) can be written as r M = G T v - - 0 (3.17) where G r is the matrix containing the stoichiometric coefficients for the intracellular metabo- lites and v is the vector of reaction rates that includes both the measured uptake and pro- duction rates as well as the unknown intracellular fluxes. To solve Eq.(3,17), it is convenient to split the reaction rate vector v into two components, v m and v c for the measured and cal- culated rates, respectively. If and are the corresponding splits in the stoichiometric CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 39 matrix, G, then Eq.(3.17) can be rewritten as G T v = Glvm + GTvc = 0 (3.18) from which v c can be estimated (assuming GT is a nonsingular square matrix) as . vc = - (Gjy1 Glvm (3.19) 3.2.4 Application of the Matrix Approach for Flux Estimation The first step in application of the matrix approach to the reaction network shown in Figure 3.1 involves construction of GT and v. The number of rows in G T equals the number of intracellular metabolites (6) and the number of columns equals the sum of the measured extracellular rates (5) and the number of unknown intracellular fluxes (5). G T is thus a 6 x 10 matrix while v is a 10 x 1 column vector whose elements include the measured extracellular rates and unknown intracellular fluxes. Eq.(3.17) can be written as / 1 0 0 0 0 0 0 0 0 ^ 1 0 0 0 0 - 1 0 0 0 0 - 1 ^ 0 - 0 0 0 Multiplying the first row of GT with the elements of v results in r m i — vi — v% = 0 which is identical to Eq.(3.6) and is the mass balance expression for metabolite m i . Multiplications of rows 2 - 6 of GT with v results in the mass balance expressions for metabolites m,2 — TUQ making the representation in Eq.(3.20) identical to Eqs.(3.6-3.11). The compact represen- tation in Eq.(3.20) becomes especially important for typical mammalian cell bioreaction networks that have more than 30 metabolites and reactions. . Eq.(3.20) can be split into the measured and unmeasured components according to ( G T ) 5 x l 0 0 0 0 0 1 0 0 0 0 0 - 1 1 0 0 0 - 1 0 0 1 0 0 0 0 - 1 0 0 1 o \ 0 0 - 1 1 0 / ( v ) l O x l ' T713 ' m6 Vl V2 V3 V ^ J / o \ 0 0 0 0 (3.20) CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION ' 4 0 Eq.(3.18) ) / 1 0 0 0 ' 0 \ 0 0 0 0 0 0 - 1 0 0 0 0 0 - 1 0 0 0 0 0 - 1 0 V 0 0 . 0 0 - 1 / ( v m ) rmi ( rm, \ + • V fm6 j ( - 1 0 - 1 0 0 \ 1 - 1 0 0 0 0 1 0 - 1 0 0 0 1 0 - 1 0 0 0 0 1 V 0 0 0 1 0 / (Vc] / «1 \ V2 V3 V4, W J The vector of unknown fluxes, v c,*can now be estimated from Eq.(3.19) V 0 0 0 0 \ 0 0 0 0 0 0 - 1 0 0 0 0 0 - 1 0 0 0 0 . o . - 1 0 0 0 o - 1 I ( v m ) r m 3 V rm6 / o \ 0 0 0 0 w (3.21 (3.22) 'c • When where (G^) ~ is the inverse (actually a pseudoinverse as G ^ is nonsquare) of experimentally measured extracellular rates are included in the v m vector, v c can.be readily calculated from the above equation. 3.2.5 The Nature of Biochemical Networks It follows from Eqs. (3.17 - 3.19) and the above example that intracellular flux estimation is a simple 3 step process that first involves formulation of the stoichiometric matrix, GT, from the reaction network, followed by separation of G T into G ^ and GT and subsequent estimation of v c by matrix inversion. However, computational complexities can arise due to singularities in, Ĝ T depending upon the number of metabolite mass balances (m) and reactions (r) and three scenarios are possible 1. Determined system (m = r) •>• . •'' 2. Underdetermined system (m < r) ' . . . 3. Overdetermined system (m > r) CHAPTER 3r METHODS FOR METABOLIC FLUX ESTIMATION 41 Determined systems are computationally the simplest (assuming G T i s square and non- singular) and usually have a unique solution that can be determined from Eq.(3.19). They have little practical utility since m 7̂  r for most biochemical networks. Underdetermined systems are more common because adequate experimental measure- ments can often not be made. These systems are formulated as linear programming (LP) problems [5, 23-34] and do not have unique solutions suggesting flexibility in the intracel- lular metabolic fluxes where Cj is the weight factor for flux v%. The choice of Cj determines the objective function to be minimized (or maximized) and it is critical that this be physiologically relevant. Choices can include maximization of growth rate or production of a particular metabolite and minimization of A T P production and nutrient uptake. Despite the possibility of an infinite number of solutions, the solution is confined to a feasible domain, a polyhedron, conceptualized as the metabolic genotype. The stoichiometric constraints of the system determine the feasible region and in two-dimensional space, these stoichiometric constraints are lines and are the boundaries of the feasible domain (plane). These systems are typically solved using the simplex method and the solutions occur at the extreme points of the feasible domain. Sensitivity analysis of the optimal solution can be analyzed using shadow prices where Z is the optimal value of the objective function and r-j the extracellular produc- tion/consumption of metabolite i. This quantity helps determine the contribution (or lack thereof) of to the stated objective function and provides useful information for designing rational metabolic engineering strategies for maximizing/minimizing Z. A major disadvan- tage of underdetermined systems is that the stated objective function may not reflect cell physiology. For instance, Bonarius et al, [3] used the minimum Euclidean norm constraint (minimize sum of flux values or the most efficient channeling of fluxes) for hybridoma cells in batch culture while experimental data indicated that cell physiology was more consistent with A T P and N A D H maximization constraints rather than the minimum Euclidean norm constraint. Nonetheless, this approach can provide very useful information helping target genetic engineering efforts to maximize the outcome of interest [5, 35]. Overdetermined systems have more metabolite mass balances than the number of re- actions (m > r) and are preferred over determined and underdetermined systems because excess experimental data can provide improved estimates of the metabolic fluxes and can (3.23) CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 42 also be used to check the validity of the assumed biochemistry. The stoichiometric matrix, G^T is non-square for overdetermined systems and a pseudoinverse must be computed to determine v c . Singularities can arise when one or more rows in GT can be expressed as a linear, combination of the other rows, a condition referred to as linear dependency. These often result from parallel pathways in the network such as the transhydrogenase reaction for the interconversion of N A D H and N A D P H where the balances of the two cofactors are coupled resulting in linearly dependent stoichiometries. Flux estimation in overdeter- mined systems along with methods of error analysis are presented in detail below since such systems usually provide the most robust flux estimates. 3.2.6 Flux Determination in Overdetermined Systems Overdetermined systems are those in which additional experimental measurements are avail- able and the degrees of freedom are > 0. For these systems, is not square and a pseudo-inverse of Gj is necessary to solve. Eq.(3.19) vc-~ (G '̂)* G^v,,, (3.25) where-(Gj?)* is the pseudo-inverse of GT. Substituting for v c from Eq.(3.25) in Eq.(3.18) results'in- ' v : ; - ' , : G ^ + G ; 7 { (G;O*G//,V„,} -o . (3.26) V,„{GL- G, /(G;O#G/,;}-O (3.27) which can be rewritten as , . Rv,„ - 0 (3,28) where R == G ^ — GT (GT)^ G ^ is called the redundancy matrix. The rank of R specifies the number of independent equations that must be satisfied by the measured and calculated rates.. As extra measurements are available in an overdetermined system, the matrix R has dependent rows. Eliminating the; dependent rows, Eq. (3.28) can be rewritten for only the independent .rows as R , . v m 0 (3.29) where R,. is referred to as the reduced redundancy matrix. In an ideal situation where experimental data are error free, the left hand side of Eq.(3,29) is exactly zero. However, all 1 experimental data are characterized by measurement error,- 8, which relates the measured CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 43 and actual vm values as v m = v m + r5 (3.30) where v m is the measured value and v m the actual value resulting in the following modifi- cation of Eq. (3.29) R r v m = e (3.31) where e is the residual vector. Substituting v m = v m + 5 from Eq.(3.30) into Eq.(3.29) results in Rr (v m + 5) = e (3.32) which simplifies to Kr6 = e (3.33) as R r v m = 0 (Eq.3.29). Under ideal conditions (with no error in the measured rates), 5 — 0, and Eq.(3.29) is valid. In the presence of measurement errors, however, the residual is not zero and it is possible to improve the measured rates such that the residual is minimized. The variance covariance matrix of the measured rates (F) is first determined by assuming that the error vector is normally distributed with zero mean E(5) = 0 (3.34) F = E ((v m - v m ) (v m - v r o f ) = E (55T) (3.35) It has been shown that the residuals are also normally distributed with zero mean [36] such that E (e) = 0 ' (3.36) tp = E(eeT) (3.37) where tp is the covariance matrix of the residuals. Substituting e = IC-S from Eq.(3.33), <p can be expressed in terms of Rr and F ip = HrFB4r (3.38) The minimum variance estimate of S is obtained by minimizing the sum of squared errors [36] ' 6 = F R ^ - ! R,.v„, (3.39) CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 44 from which the improved v m estimates can be obtained v m = v m - 5 = ( I - F R * V - 1 R T . ) v m (3.40) where I is an identity matrix. Statistical hypothesis testing can be used to identify gross measurement errors by com- puting a consistency index, h h = eT<f-1e (3.41) It has been shown that h follows a x2 distribution with the degrees of freedom equal to the number of redundant equations [36]. Hence the h value computed from Eq.(3.41) for any bioreaction network can be used to check the quality of experimental measurements. If h > x2 at a desired confidence level, it is an indication that either the measured values are in gross error or the assumed system biochemistry is incorrect. If excess measurements are present, h can be recalculated by eliminating a single measurement from the mass balances. If a dramatic reduction in h value is observed, it is likely that the eliminated measurement contained error. This process can be repeated for all the measured rates in the bioreaction network. Confidence can be placed in the unknown flux estimates only when h < x2 at the desired confidence level (usually 90 or 95 %). The concepts presented above will be applied to a simplified biochemical network for mammalian cell metabolism. Table 3.1: Reactions in the simplified bioreaction network of Figure 3.2 G l c + 2 N A D + + 2 A D P + 2 P i —• 2Pyr+2NADH+2ATP+2H 2 0+2H+ Pyr+NADH+H+ -> Lac+NAD+ P y r + 4 N A D + + F A D + A D P + 3 H 2 0 + P 7 ; —-> 3 C 0 2 + 4 N A D H + F A D H 2 + A T P + 2 H + 0.5O-2+2.5 ADP+2.5P,+NADH+3.5 H+ -> 2 . 5 A T P + N A D + + 3 . 5 H 2 0 0.5O2+1.5 ADP.+1.5Pi+FADH"2+1.5 H+ --> 1 .5ATP+FAD + +2 .5H 2 0 3.2.7 Flux Estimation in an Overdetermined System describing Mam- malian Cell Metabolism Figure 3.2 shows a simplified bioreaction network that was originally proposed by Balcarcel and- Clark [37] for flux analysis from well plate cultivations where limited measurements were available and the corresponding reactions are shown in Table 3.1. Glycolytic reactions have been lumped into a single reaction (Glucose —> Pyruvate: flux v c l ) as have those for the T C A cycle (Pyruvate —> CO2; flux vC2)- Conversion of pyruvate to lactate is a dominant reaction in most mammalian cell culture and this has been included in the network (Flux CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 45 Glucose V m 1 V Lactate * m2 V m.4 Glucose v V c2 Glycolysis Lactate Pyruvate ATP v c3 TCA Cycle ATP C 0 2 V m3 CO. F i g u r e 3 . 2 : A simplified network for mammalian cell metabolism with lumped reactions for gly- colysis and T C A cycle and those for lactate production and oxidative phosphorylation [37]. The network consists of 5 unknown intracellular fluxes (v c i-v c 5 ) and 4 extra- cellular measured rates ( v m l - v m 4 ) . Fluxes v c 4 and v c 5 involve NADH and F A D H 2 , respectively (Table 3 .1 ) . CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 46 v C 3) along with the oxidative phosphorylation reactions (vC4 and v cs). Rates of glucose and oxygen consumption along with those for lactate and C O 2 production make up the measured extracellular rates. The network has a total of 4 measured extracellular rates ( v m i - v m 4 ) and 5 unknown intracellular fluxes that have to be estimated ( v c l - v C 5 ) . Balcarcel and Clark [37] also included total A T P production as another unknown flux (vcg) and considered the following 8 metabolites for writing the mass balance expressions: glucose, lactate, C O 2 , O2, pyruvate, N A D H , F A D H 2 and A T P resulting in a 8 x 10 stoichiometric matrix. The small size of this network makes it convenient for illustrating the concepts of consistency testing and gross error detection for overdetermined 3.2.7.1 Determination of Intracellular Eq.(3.17) can be written for the network in F \ /8xl0 / -1 0 0 0 - 1 • o 1 • 0 0 0 -1 0 0 0 1 0 0 0 0 -1 0 0 0 3 0 0 0 0 1 0 ., 0. 0 -0.5 0 0 0 0 2 -1 -1 0 0 0 0 0 2 -1 4 -1 0 0 0 0 0 0 1 0 v 0 0 0 0 2 0 1 2.5 where the 8 rows of GT'represent the mass balance expressions for glucose, lactate, C O 2 , O2, pyruvate, N A D H , F A D H 2 and ATP , respectively,- columns 1-4 represent the 4 extracellular reactions whose rates are measured ( v m i - v m 4 ) and columns 5 -10 represent the 6 unknown intracellular fluxes ( v c i - v C 6) . Examination of some basic properties of G T is the first step towards determining the'unknown fluxes. The rank of GT was estimated to be 8 indicating all the 8 metabolites balance equations in G T were independent and could not be expressed as a linear combination of the other mass balance expressions. The condition number of G T was estimated as 7.6 and this low value indicates that estimated flux values are not overly sensitive to errors in the measured extracellular rates. Condition numbers < 100 have been considered acceptable for metabolic flux analysis [2]. Eq.(3.42) can be split into the measured and unmeasured components according to systems. Fluxes 'igure 3.2 as 0 ' 0 0 -0.5- 0 0 0 0 0 - 1 0 1.5 0 \ 0 0 1 ( v ) l O x l / vmi \ Vm2 %3 Vm4 VC1 Vc2 Vc3 Vc4 Vc5 \ Vc6 J / o \ 0 0 0 0 0 0 (3.42) CHAPTERS. METHODS FOR METABOLIC FLUX ESTIMATION 47 Eq.(3.18), • (c / -1 0 0 0 / - 1 0 0 0 0 0 0 • -1 o' 0 ' ( V m ) o 1 0 0 ' , 0 0 0 0 - 1 0 / " m i \ 0 0 3 •• 0 0 0 Q 0' 0 - 1 Vm2 0 0 0 -0.5 -0.5 0 0 0 ? 0 0 '0 ; % 3 2 - 1 - 1 0 0 0 0, 0 V Vm4 J 2 —1 A - 1 0 0 • o p ' 0 , 0 0 0 X ,0 - 1 0 V o . 0 • • o : ;o • / V 2 0 1 • 2.5 ' 1.5 - 1 / K ) / Vcl \ VC2 VC3 VC4 Vc5 / o \ 0 0 0 0 0 0 v ° y (3.43) Using experimental'.values for the measured rates (CHO cells in perfusion culture), the vector of known rates is / -1.4788 A 1.7293 5.8333 y -5.1369 / and taking the pseudoinverse of results in (3.44) (. -0.3172 0.3414 0.0103 -0.1034 0.2897 0.0517 0.0517 0 -0,3414 0.8293 -0.0052 0.0517 -0.1448 ' -0.0259 -0.0259 0 -0.0034 -0.0017 0.2121 , -0.1207 -0.0621 0.0603 0.0603 0 -0.2552 -0.1276 0.6931 -0.9310. 0.4069 -0.5345 0.4655 0 0.0483 0.0241 . 0.0310 -0.3103 -0.1310 0.1552 -0.8448 0 \ -1.2034 0.3983 2.0121 -3.1207 1.3379 -0.9397 0.0603 - 1 ) (3.45) Once v m and ( G ^ ) * are known, the unknown fluxes can be estimated from Eq.(3.19) as / 1.6512 \ 1.6431 1.8592. 8.9824 1.7456 \ 30.2361 J (3.46) While this completes the flux analysis, it is perhaps just as important to analyze the biore- CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 48 action network for inconsistencies and to check for gross error in experimental data as shown in the subsequent sections. 3.2.7.2 R e d u n d a n c y Ana lys i s and Gross E r r o r De tec t ion The above system has a total of 10 reaction rates (4 measured, 6 unknown) and 8 balances on pathway intermediates making it overdetermined with 2 degrees of freedom (Degrees of freedom = number of reaction rates - r ank(G r ) ) . The redundancy matrix, R , is first calculated as R = G ^ \ R = G c { G c ) # G T m (. -0.6828 -0.3414 -0,0103 0.1034 -0.3414 -0.1707 -0.0052 0.0517 -0.0103 -0.0052 -0.3638 -0.3621 0.1034 0.0517 -0.3621 -0.3793 -0.2897 -0.1448 -0.1862 -0.1379 -0.0517 -0.0259 0.1810 .0.1897 -0.0517 -0.0259 0.1810 0.1897 V 0 .0 0 0 (3.47) and the rank of R was calculated to be 2 and the reduced redundancy matrix R r was obtained from singular value decomposition (SVD) of R It— 0.8099 0.4049 -0.3679 -0.1839 -0.2250 -0.3599 -0.6745 -0.6131 (3.48) Assuming 10% error in all the measured rates, the error vector, 5, can be written as / 0.1479 \ 0.1729 0.5833 0.5137 (3.49) from which the variance covariance matrix, F, is computed using Eq.(3.35) / 0.0219 0 0 " 0 \ 0 ( 0.0299 0 0 • 0 0 0.3403 0 \ • 0 .. O ' O 0.2639 J (3.50) CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 49 It must be noted that the off-diagonal elements of F have been set to zero indicating that the measurements are uncorrected. This assumption may not be valid under all experimental conditions and methods to obtain representative F estimates are available [2]. The variance covariance matrix of the residuals, cp, can now be calculated from Eq.(3.38) as if = 0.0707 -0.1011 -0.1011 0.2579 (3.51) Once cp is known, h can be estimated from Eq.(3.41) as 3.36. This h value must be compared with the x2 distribution with 2 degrees of freedom. From Table 3.2, the h value of 3.36 is lower than the x 2 distribution at a confidence level of 0.900 suggesting that the measured rates do not contain gross errors. . Table 3.2: Values of the chi 2 Distribution at varying Degrees of Freedom and Confidence Levels Degrees of freedom Confidence Level 0.500 0.750 0.900 0.950 0.990 1 0.46 1.32 2.71 3.84 6.63 • 2 1.39 2.77 4.61 5.99 9:21 3 2.37 4.11 6.25 7.81 11.3 . 4 3.36 5.39 7.78 9.49 13.3 5 4.35 6.63 9.24 11.10 15.1 Improved estimates of the measured rates can now be obtained from Eq.(3.40) V m = V„ 6 = ( -1.4788 \ 1.7293 5.8333 -5.1369 / 0.191 \ 0.1306 0.6090 \ 0.0882 J ( -1.6698 \ 1.5987 5.2243 \ -5.2251 j (3.52) It has been shown that the above v m estimates have a smaller standard deviation than the measured values (vm) and are hence more reliable [36]. The differences between these two measured rate vectors is not substantial suggesting that the experimentally measured values are reasonably accurate. The unknown intracellular flux vector, v c, corrresponding CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 50 to the improved specific rate vector, v m , can now be computed as 1.6701. \ 1.5986 1.7415 (3,53) 8.7078 1.7417 V 29.4638 J and the corresponding h value is 2.49 x 1 0 - 8 , significantly smaller than the 3.36 obtained using the experimentally measured rates. From a comparison of Eqs.(3.46) and (3.53), however, there is only a small change in the estimated intracellular fluxes after correcting the measured specific rates. This may not be the case when measured data are in considerable error. A computer program that performs the above calculations is presented in Appendix A. 3.2.7.3 Error Diagnosis If h values greater than the x2 distribution (for instance, a value >10 in the above example) are obtained, it could be due to either systematic or large random errors in the measured rates. It becomes important to identify the error source and an elegant method has been proposed for such an analysis in overdetermined systems with at least 2 degrees of freedom [36]. In this iterative approach, one of the measured rates is eliminated and the remaining are used to compute the consistency index which is subsequently compared with the x 2 distribution at one lower degrees of freedom. This process is repeated by sequentially elimi- nating all the measured rates and the corresponding h values are recorded. If elimination of any single measured rate results in! a dramatic decreases in the h value, that measurement is likely to contain systematic errors. Once the measured rate in error has been identified, it can be corrected as illustrated in the following example. Let us assume that due to a measurement error, the C E R has been inaccurately de- termined to be 7.2916 (25% error; actual value = 5.8333) and the other measurements are CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 51 (3.54) unaffected. The unknown flux vector is calculated from Eq.(3.19) as / 1.6663 \ 1.6355 2.1684 9.9932 1.7902 y 33.1703 J with a corresponding h value of 9.64 which is higher than the x 2 distribution even at a confidence level of 0.99. It is thus clear that errors exist in the measured rates. The h values obtained by eliminating one measured rate at a time are shown in Table 3.3. C E R elimination results in a significant reduction in h when compared with other specific rates indicating the presence of gross measurement error in C E R . This problem can be adressed by making additional (accurate) C E R measurements and if this not possible, experimental C E R data must not be used for flux estimation. T a b l e 3 . 3 : Values of h after Sequential Elimination of the Measured Rates Measurement E l i m i n a t e d h value None 9.64 Glucose uptake rate 5.87 Lactate production rate 5.87 C O 2 production rate 1.59 O2 consumption rate 8.21 3.2.8 Summary of Flux Estimation in Overdetermined Systems When overdetermined systems are characterized by at least two degrees of freedom, the consistency of experimental data and the presence of gross measurement errors can by ana- lyzed as illustrated in the above example. A schematic of this approach is shown in Figure 3.3. The bioreaction network is first defined from which the stoichiometric matrix, G T , and the rate vector, v, are derived. The unknown intracellular fluxes are then determined from Eq.(3.25) through matrix inversion. The redundancy matrix, R , is then calculated as R = G ^ — Ĝ T ( G ^ ) * G ^ from which the reduced redundancy matrix R,. is derived by eliminating the dependent rows. The residual vector, e, is subsequently determined using R r and the measured rates (Eq.3.31). The variance-covariance matrix of the measured rates, F , is then estimated from the measured rate errors (Eq.3.35) following which the covariance CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 52 matrix of the residuals, <p, is estimated from I L and F (Eq.3.38). Finally, the consistency index, h, is estimated from ip and e (Eq.3.41) and compared with the x 2 distribution at the appropriate degrees of freedom. . If h < x2, then, no gross measurement errors are present and the assumed biochemistry is consistent. While the resulting fluxes constitute an acceptable solution, further improve- ment in the flux estimates is possible by improving the measured rates (Eq.3.40) followed by flux estimation. In addition to improved flux estimates, this approach will also significantly reduce the h value as demonstrated in the above example. While flux improvements for an accurate data set may be marginal, it is still useful to refine the flux estimates as this step. requires minimal computational effort. For cases when h < x2, either the experimental data contain gross errors or the assumed biochemistry is incorrect. Presence of gross errors can be determined by sequentially eliminating a measurement followed by flux estimation and h determination. If elimination of any single measurement results in a significant decrease in h, then that measurement contains gross errors. If additional accurate measurements are not available for that specific rate, it must not be used for flux estimation. However, if this analysis indicates no. gross measurement error, then the likely source of high h is the bioreaction network. Appropriate.modification of the network can result in flux estimates such that h < x2- 3.3 Flux Estimation Using Isotopic Tracers In isotopic tracer experiments, the cultivation medium contains a labeled substrate (usually 1 3 C glucose) that is stable and can be detected by N M R or G C - M S . Distribution of the label among the metabolites can be measured using either N M R or G C - M S and is a function of the intracellular metabolic fluxes. For simple biochemical networks, unknown intracellular fluxes can be directly determined by examining the fractional label enrichment either from transient intensity measurements or from experiments where both metabolic and isotopic steady states are reached. A n elegant method to analyze data from complex metabolic networks is by using atom mapping matrices (AMMs) which describe the transfer of carbon atoms from reactants to products [19]. The primary advantage of the A M M approach is the decoupling of the steady-state isotope balance equations from the reactions in the biochemical network. Detailed information on the A M M approach is presented below while information on other related approaches can be found elsewhere [38-47]. CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 53 Define Bioreaction Network Formulate stoichiometric matrix Estimate intracellular Fluxes Determine reduced redundancy matrix and covariance matrix of residuals Estimate h h<x2 Solution obtained h>x2 Modify reactions in the Biochemical network No Gross error detection by sequential elimination of measured rates Yes Optional _ | Compute improved values! of measured rates Repeat measurements if Possible. Otherwise change experimental data Compute improved flux estimates (final solution) F i g u r e 3 . 3 : A n illustration.of the steps involved in overdetermined system flux estimation using the metabolite balancing approach. 3.3.1 Atom Mapping Matrices for Flux Estimation 1 3 C glucose is the. most commonly used labeled substrate in the investigation of mammalian cell metabolism. When cells consume glucose, the carbon label gets incorporated into the various metabolites and for a metabolite with n carbon atoms, 2 n isotope isomers (isotopomers) are possible. Table 3.4 shows the isotopomer distribution for a 3-carbon molecule along with their binary and decimal indexes. Information on the isotopomers is contained in the N M R spectrum from which it is possible to quantify their relative distribution. Consider a simple example where A and B (both 3-carbon molecules) react to form C (also a 3-carbon molecule) and xr, X2 and x% are the associated fluxes (Figure. 3.4). The mass balance expression for this simple reaction network is straightforward (x\ + X2 = X3) and isotopomer balances are necessary to determine the contributions from the isotopomers of A and B to the isotopomers of C. It follows from Table 3.4 that 8 isotopomers of A,B and C are possible since they all contain 3 carbon atoms. For instance, if the ith isotopomer of A and the jth isotopomer of B are transformed into the kth isotopopmer of C, the steady-state CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 54 T a b l e 3 . 4 : Isotopomer distribution for a 3-carbon molecule along with their binary and decimal indexes C a r b o n A t o m s o — o • — o O — O — • o — • — o o — • — • • — o — o • — o — • • — • — o B i n a r y Index 000 001 010 011 100 101 110 111 D e c i m a l Index Index Vec to r isotopomer balance is xiA(i)+x2B(j) = x3C{k) (3.55) from which C (k) can be determined only if the other quantities are known. In the above balance,, the relationship between i, j and k was assumed and for complex metabolic net- works, atom mapping matrices help define these relationships conveniently. A M M s describe the transfer of carbon items from the reactant to the product and are designated as [re- actant > product] with the number of columns and rows equal to the number of carbon atoms in the reactant arid product, respectively [19]. If the ith. carbon in the product is derived from the jth carbon of the reactant, the element in the ith row and the jth column is 1 (this value is 0 otherwise). For the reaction network in Figure 3.4, two A M M s ([A > C] and [B > G]) must be CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 55 Figure 3 . 4 : A simple reaction network where molecule C is formed from molecules A and B. used to relate the reactant and product isotopomers. If carbon 1 of A becomes carbon 3 of C, carbon 2 of A becomes carbon 1 of C and carbon 3 of A becomes carbon 2 of C, then [A > C] can be written as / 0 1 0 \ [A > C] = 0 0 1 (3.56) \ 1 o o ) and multiplying the A M M by a vector of the carbon atoms of A will result in the vector of carbon atoms for C ( CL \ 0 1 0 = | 0 0 1 1 0 0 fal \ U s / f a 2 \ A3 (3.57) It must be noted that the vector of carbon atoms in A is not unique and 8 combinations are possible (Table 3.4). Each of these 8 carbon, vectors of A will result in a corresponding carbon vector for C and this dependency is dictated by the A M M . If we consider the second index of A (i — 2), the index vector can be written as [i] = ( 1 ^ 0 (3.58) The product vector [k] corresponding to the reactant vector [i] can be easily determined from the A M M / 0 1 0 \ [k] = [A > C] [i] = (3.59) CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 56 indicating that A (1) = C (4). A complete mapping of k at all 8 values of i results in C(0) C(4) C ( l ) C(5) C(2) C(6) C(3) C(7) A(0) A ( l ) 4(2) A(3) A(4) A(5) A(6) A(7) (3.60) (3.61) (3.62) (3.63) (3.64) (3.65) (3.66) (3.67) and a similar exercise can be done to develop the relationships between the isotopomers of where <g> is a mapping operator that helps generate all possible isotopomers of C from A and B. As metabolic fluxes are functions of the bioreaction network and isotopomer distribution, solution of the above equation followed by comparison with experimental N M R or G C - M S data in an iterative fashion (nonlinear least squares optimization) provides the desired flux estimates.. A n alternative to A M M s is isotopomer distribution analysis where steady-state iso- topomer balances are formulated for every metabolite in the network which allows deter- mination of the metabolic fluxes as function of the isotopomer population. This has some advantages over the use of A M M s and detailed information is available [39, 44, 46-49]. 3.3.2 Overview of Flux Estimation from Isotope Tracer Studies For complex metabolic networks, flux estimation from N M R or G C - M S data is computation- ally intensive and iterative because of the nonlinear relationship between the isotopomer balances and the the metabolic fluxes. A n overview of the flux estimation procedure is shown in Figure 3.5. The bioreaction network is first defined from which the metabolite and isotope balance equations are obtained. Either A M M s as described in the previous section or isotopomer mapping matrices can be used to formulate these equations. Once these equations are defined, an initial set of fluxes is assumed from which the metabolite isotopomer pools are calculated. This distribution of metabolite isotopomers helps predict reactant B and product C. Eq.(3.55) can now be written as x i [ A > C] ® A + x2[B > C] <g> B = x3C (3.68) CHAPTER 3.. METHODS FOR METABOLIC FLUX ESTIMATION. 57 label enrichment, molecular weight distribution of the isotopomers (for G C - M S analysis) and the N M R fine structure. This theoretically predicted information (which is dependent on the assumed value of the fluxes) is subsequently compared with experimental G C - M S / N M R data and initial agreement is usually not satisfactory. The assumed flux values are refined and the calculation procedure is repeated until there is good agreement between theoretical and experimental data. Define Bioreaction Network Formulate 1. Metabolite balances 2. Isotope balances Assume fluxes and solve for metabolite Isotopomer pools Predict label enrichment, Isotopomer molecular weight distribution or fine structure of NMR Modify reactions in the Biochemical network No Gross error present in measurements Yes Repeat measurements if Possible. Otherwise change experimental data Compare with GC-MS / NMR data Good Agreement Gross error detection in measurements and assumed biochemistry Wo Solution obtained. Current] fluxes are the best-fit values Poor Agreement Refine initial flux estimates F i g u r e 3 . 5 : An overview of the flux estimation process for the isotope tracer approach. Error diagnosis is an important component of flux estimation from isotope tracer studies as for the metabolite balancing approach. If no gross errors are detected, the obtained flux values are reliable and can be considered representative of cell physiology. However, if gross errors are detected, they could either be due to measurement error or inappropriate assumptions regarding system biochemistry. Depending upon the source of gross error, the existing experimental data must be reviewed and new measurements should be made if possible or the biochemical network must be modified to reflect cell physiology. Once either of these adjustments is done, the entire process of flux estimation must be repeated. BIBLIOGRAPHY 58 3.4 Summary A n overview of the two methods of flux estimation has been presented. Metabolite bal- ancing is more commonly used because of experimental and computational simplicity. For mammalian cell culture, experimental data necessary for flux estimation by metabolite bal- ancing include cell growth, nutrient uptake and metabolite/product formation rates along with uptake/production rates,of amino acids. As these quantities are routinely measured in cell culture experiments, there is little need for additional measurements for flux es- timation. The computational component of the metabolite balancing approach is simple and basic matrix manipulations are adequate for flux estimation. Overdetermined systems are preferable over determined and underdetermined systems as robust error diagnosis is possible in these systems, increasing the reliability of the flux estimates. The use of isotope tracers helps determine fluxes in reversible and cyclical reactions which is not possible using metabolite balancing. This improved flux resolution is obtained at the expense of significantly increased experimental, analytical and computational effort which limits widespread application of this approach. Direct application to laboratory and manufacturing-scale perfusion systems is virtually impossible given the cost associated with using labeled substrates. Isotope tracer studies thus have to be performed in scaled-down systems which to the extent possible must be metabolically representative of the larger bioreactors. Comparison of flux estimates from these isotope tracer studies with those from metabolite balancing will help validate the metabolite balancing approach that can subsequently be directly applied to large-scale systems. 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Bioeng., 1997, 56, 831-840. [47] Wiechert, W.; de Graaf, A . A . Bidirectional reaction steps in metabolic networks: I. Modeling and simulation of carbon isotope labeling experiments. Biotechnol. Bioeng., 1997, 55, 101-117. [48] Wiechert, W.; Siefke, O ; de Graaf, A . A. ; Marx, A . Bidirectional reaction steps in metabolic networks: II. Flux estimation and stastical analysis. Biotechnol. Bioeng., 1997, 55, 118-135. [49] Wiechert, W.; Mollney, M . ; Isermann, N . ; Wurzel, M . ; de Graaf, A . A . Bidirectional steps in metabolic networks: III. Explicit solution and analysis of isotopomer labeling systems. Biotechnol. Bioeng., 1999, 66, 69-85. Part II p C C > 2 i n H i g h - D e n s i t y P e r f u s i o n C u l t u r e 63 Chapter 4 p C C > 2 R e d u c t i o n i n P e r f u s i o n S y s t e m s 1 4.1 Introduction Mammalian cells are being increasingly used to produce recombinant proteins, given their ability to properly fold and glycosylate these proteins. While the majority of current manufacturing-scale processes are fed-batch, perfusion cultures can be required, for in- stance, when the product of interest is relatively unstable. The continuous nature of the perfusion process allows higher cell density cultivation, since toxic metabolites, such as lac- tate and ammonium, do not accumulate in the bioreactor. Cell densities on the order of 20 x 106 cells/mL can be maintained in the steady-state phase of perfusion cultivation for 100 days or more [1, 2]. High cell density coupled with high perfusion rates yields high volumetric productivity from perfusion cultivation. High density perfusion cultivation, however, results in elevated bioreactor pC02, often on the order of 200 mm Hg [3, 4], significantly higher than physiological values (30 - 50 mm Hg). Elevated p C 0 2 has been implicated in reduced growth, metabolism and productivity in addition to adverse effects on glycosylation [3, 5-15]. As bioreactor pH during perfusion cultivation is controlled at a pre-defined set point, high p C 0 2 results in increased osmolality which can also negatively impact cell growth, metabolism and productivity [7, 8, 10, 16-21]. High p C 0 2 is a consequence of both the cellular metabolism and the NaHC03 that is widely used as a buffer in the medium. In addition, NaHC03 is often added as a base to neutralize ' A version of this manuscript has been accepted for publication. Goudar, C.T., Matanguihan, R., Long, E., Cruz, C , Zhang, C , Piret, J .M. and Konstantinov, K . B . (2006) Decreased p C 0 2 accumulation by eliminating bicarbonate addition to high-density cultures. Biotechnology & Bioengineering. 64 CHAPTER 4. PC02 REDUCTION IN.PERFUSION SYSTEMS 65 the lactate produced by the cells. High p C 0 2 can also be a concern in late stage fed-batch cultivation but the problem is greater in perfusion bioreactors, as high pCG"2 values are maintained over the entire length of the production phase due to the typically higher cell concentration (Figure 4.1). Perfusion P e r f u s i o n h i g h p C 0 2 r e g i o n (> 2 0 0 m m H g ) vFed-Batch j Fed j - ba t ch h i g h p C 0 2 r e g i o n ( > 1 0 0 m m H g ) Time (days) 100 F i g u r e 4 . 1 : Bioreactor pCC>2 time profiles for mammalian cell cultivation in perfusion and fed- batch bioreactors. Perfusion pCC>2 remains high throughout steady-state operation while high p C 0 2 can be a problem in late stages of fed-batch cultivation. There is clearly a need for bioreactor p C 0 2 reduction although there have been relatively few studies addressing p C 0 2 removal and control in mammalian cell bioreactors [3, 12, 13]. Stripping is an obvious p C 0 2 removal approach, but it has a limited impact in mammalian cell bioreactors. For C H O cells in a 500 L perfusion bioreactor, the ratio of oxygen and carbon dioxide transfer rates was 25:1 [3], thus much higher high gas flow rates would be necessary for adequate C O 2 stripping. There is an upper limit on sparging rates given the detrimental effects on cells [22, 23]. Macrosparging resulted in a significant p C 0 2 reduction for C H O cells in fed-batch culture [13], but the maximum cell density was not reported and it is unlikely that it was high enough to be relevant to perfusion cultivation. Changing an impeller position yielded a 2-fold increase in the p C 0 2 transfer rate [13], but such improvements cannot be expected in a well-mixed bioreactor. The inadequacy of stripping clearly indicates that a more attractive target to reduce bioreactor p C 0 2 could be reduction at the source rather than removal after p C 0 2 production and additions. Engineering cellular metabolism to reduce p C 0 2 production is not practical because cell lines are selected primarily on productivity and growth considerations. In fact, there are advantages to maintaining high rates of respiration to minimize lactic acid production. CHAPTER 4. PC02 REDUCTION INPERFUSION SYSTEMS 66 The buffering components, on the other hand, offer the most potential for pCC>2 reduction and were the target of changes in this study. There have been some reports where reduced NaHCOa or NaHCC>3-free medium was used for mammalian cell cultivation [24-29], but pCG"2 reduction was not the primary objective in these studies and none were performed at manufacturing-scale. This study evaluates the biotic and abiotic contributions to bioreactor pCC>2 in a per- fusion system, and from these results, derives a simple pCC>2 reduction strategy based on minimizing abiotic pCO"2 contribution. The validity of this approach was verified both in laboratory and manufacturing-scale perfusion systems. Changes in cell growth, metabolism and protein productivity associated with pC0"2 reduction were also evaluated. 4.2 T h e o r y 4.2.1 C 0 2 Dynamics in a Mammalian Cell Bioreactor Carbon dioxide produced by cells dissolves in the culture medium to form carbonic acid: C 0 2 ( g ) - C 0 2 ( a q ) (4.1) C 0 2 ( a q ) + H 2 0 - H 2 C O 3 (4.2) It is common practice [30] to combine the C 0 2 ( a q ) and H 2 C O 3 concentrations into H 2 C O 3 * (C0 2 (aq) ' + H2CO3' = H 2 C O 3 * ) . Further dissociation of H 2 C 0 3 * into H C O 3 and C O f can be written as: H 2 C O 3 * ^ H C O 3 + H+; Kx = IO" 6 ' 3 5 (4.3) H C O 3 ^ ' C O f + H + ; K2 = I O " 1 0 3 3 (4.4) where K\ and Ki are equilibrium constants under standard conditions (temperature = 25 °C, ionic strength = 0). These must, however, be corrected to reflect cultivation conditions and K\ and K% were estimated to be IO"6 0 7 and IO' 1 0 0 4 , respectively, at 37 °C and 0.1 M ionic strength using the vant-Hoff and : Davies equations [31. 32]. Carbon dioxide produced by the cells thus exists as combination of H 2 C 0 3 * , H C 0 3 and CO3" whose relative amounts CHAPTER 4. PC02 REDUCTION IN PERFUSION SYSTEMS 67 at the cultivation pH of 6.8 were determined as: r+l2 [ H + ] 2 + [H +] K{ + K\K\ H- l % o f H 2 C 0 3 * . = r , , 2 . L . „„„ 100 = 15.7% (4.5) % of H C O 3 = ( , 9 [ H ] K ° l ) 100 = 84.3% (4.6) \ J H + ] 2 + Kl + K\Kl ) . % of CO3 = [ K ° K * •• ) 100 = 5 x 10-4% (4.7) \[H+}2 + Kl + KIK§ J Thus H C O 3 is the dominant species at pH 6.8 followed by H 2 C O 3 * while CO3" is virtu- ally non-existent. Additional information on medium solution chemistry and associated computer programs are presented in Appendix B. 4.2.2 Buffering Action of NaHC0 3 and N a 2 C 0 3 The fate of added NaHC03, either through the medium or separately for pH control, is also governed by Eqs.(4.3) and (4.4). Complete dissociation of N a H C 0 3 results in the formation of N a + and H C 0 3 ions, of which a portion of the latter is converted to H 2 C O 3 * N a H C 0 3 -» Na+ + H C O 3 (4.8) H C 0 3 + H + <-» H 2 C O 3 * (4.9) The relative concentrations of H 2 C O 3 * and H C 0 3 at pH 6.8 are 15.7 and 84-3%, respectively (from Eqs. 4.5 and 4.6) such that 5.4 moles of N a H C 0 3 are required to neutralize 1 mole of H + in the bioreactor. If instead Na2C03 is used as the base for pH control, complete dissociation results in the formation of CO3", which is essentially all converted to HCO" 3 under culture conditions: N a 2 C 0 3 -» 2 N a + + C O | - (4.10) C O f + H + <-> HCO3 (4.11) The significantly enhanced buffering capacity of lNTa2Cd3 is due to Eq.(4.11) where 1 mole of N a 2 C 0 3 neutralizes 1 mole of H + . Futher conversion of HCO" 3 to H 2 C O 3 * proceeds according to Eq.(4.9) such that 0.85 moles of N a 2 C 0 3 are required to neutralize 1 mole of B.^ in the bioreactor. A 84% improvement in buffer capacity and a corresponding decrease in the abiotic contribution to bioreactor pCCh can thus be expected when N a H C 0 3 is replaced with N a 2 C 0 3 . CHAPTER 4. PC02 REDUCTION IN PERFUSION SYSTEMS 68 Medium with N a H C 0 3 buffer C 0 2 -> 3 4 % c o 2 - » Base 43 % or pH Control (NaHC0 3 ) t Headspace gas COo C O . Cellular Respiration BIOREACTOR (pC0 2 > 225 mm Hg) C 0 2 -> Harvest + Bleed F i g u r e 4 . 2 : Calculated contributions from biotic (cellular respiration) and abiotic (medium and base NaHCOs) sources to bioreactor pCC>2 during perfusion cultivation of B H K cells. 4.2.3 Contributors to Bioreactor p C 0 2 Cellular respiration makes up the biotic component of bioreactor p C 0 2 (abiotic contributors are NaHC03 and Na 2 C0a) . For B H K cells in a perfusion bioreactor at 20 x 10 6 cells/mL, the carbon dioxide evolution rate was 8 pmol/cell-day, contributing 1.92 moles/day from cellular respiration to bioreactor p C 0 2 . Daily addition of 0.71 M NaHC03 as a base for pH control was 5 L , from which the contribution of the base was estimated as 3.57 moles/day. Medium (with 23.8 m M NaHCOs) how rate was 120 L/day resulting in a daily medium contribution of 2.86 moles. From the above data, the percentage contributions of cellular respiration, base, and medium to bioreactor p C 0 2 were 23, 43 and 34%, respectively (Figure 4.2). Eliminating NaHC03 from the medium should thus reduce bioreactor p C 0 2 by 34% while replacing NaHCOs with N a 2 C 0 3 as the base should reduce bioreactor p C 0 2 by 36% (84% of 43). Overall, NaHCOs elimination from the medium and replacement with N a 2 C 0 3 as base are expected to lower bioreactor p C 0 2 by 70% bringing it in the 60 - 80 mm Hg range, much closer to physiological values of 30. - 50 mm Hg. CHAPTER 4. PC02 REDUCTION IN-PERFUSION SYSTEMS 69 4.3 Materials and Methods 4.3.1 Cell Line, Medium and Bioreactor System Multiple perfusion B H K cell cultivations were performed with glucose and glutamine. as the main carbon and energy sources in a proprietary, medium formulation with either 2 g /L NaHCC>3 or a.MOPS-Histidine mixture as the buffering component. Laboratory-scale experiments were conducted in 15 L bioreactors (Applikon, Foster City, CA) with a 12 L working volume. .The temperature was maintained at 35.5 °C and the agitation at 70 ' rpm. The dissolved oxygen (DO) concentration was maintained at 50%. air saturation using oxygen-nitrogen mixture aeration through a silicone membrane. Bioreactor pH was maintained at 6.8 by the addition of either 0.71 M N a H C 0 3 or 0.57 M N a 2 C 0 3 . The bioreactors were inoculated at an initial cell density of approximately 1 x 106 cells/mL and,' with perfusion, the cells were allowed to accumulate up to a density of 20 x 106 cells/mL. Steady-state bioreactor cell density was maintained at this level by automatically discarding cells from the bioreactor based on optical density measurements [1]. Similar operating protocols and identical set points were maintained in the manufacturing-scale bioreactor. The effect of macrosparging on C 0 2 stripping was also examined in the manufacturing-scale bioreactor. 4.3.2 Analytical Methods Samples from the bioreactor were taken daily for cell density and viability analysis using the C E D E X system (Innovatis, Bielefeld,'Germany). The samples were subsequently cen- trifuged (Beckman Coulter, Fullerton, CA) and the supernatants were analyzed for nutrient and metabolite concentrations. Glucose, lactate, glutamine and glutamate concentrations were determined using a YSI Model 2700 analyzer (Yellow Springs Instruments, Yellow Springs, OH) while ammonium was measured by an Ektachem DT60 analyzer (Eastman Kodak, Rochester, N Y ) . The pH and D O were measured online using retractable electrodes (Mettler-Toledo Inc., Columbus, OH) and their measurement accuracy was verified through off-line analysis in a Rapidlab 248 blood gas analyzer (Bayer HealthCare, Tarrytown, N Y ) . The same instrument also measured the dissolved CO2 concentration. On-line mea- surements of cell concentration were made with a retractable optical density probe (Aquas- ant Messtechnik, Bubendorf, Switzerland), calibrated with the C E D E X cell concentration estimates..- . •• CHAPTER 4. PCO2 REDUCTION IN PERFUSION SYSTEMS 70 4.3.3 Estimation of Specific Rates Growth rate, specific productivity, nutrient consumption and metabolite production rates were calculated from mass balance expressions across the bioreactor and cell retention device and details are presented in Appendix H . Since bioreactor cell density was held constant by bleeding cells from the bioreactor and death rates were not accounted for, the growth rate, \i (1/day), was a function of the bleed rate, Fb (L/day), and the viable cell density in the harvest stream, Xy (109 cells/L): n . fh fx»\ , i (dx$ where V is the bioreactor volume (L), Fh the harvest flow rate (L/day), Xy the bioreactor viable cell density (109 cells/L) and t the time (day). The specific consumption rates of glucose and glutamine were determined from the glucose and glutamine concentrations in the bioreactor: 1 /Fm (Gm -- G) dG\ Q G = X B { v dFj ( 4 1 3 ) 1 (Fm(Glnm-Gln) dGln . r i \ ( A . A s nam = J B { — - V a T ~ k G l n G l n ) { A M ) where Fm is the medium flow rate (L/day) qc and qain are the specific consumption rates of glucose and glutamine, respectively, (pmol/cell-day), Gm and Glnm their respective con- centrations in the fed medium (mM) and G and Gin their bioreactor concentrations (mM). The kinetics of abiotic glutamine degradation were assumed to be first-order with a rate constant kcin that was estimated as 8.94 x IO"4 h" 1 ' [33]. Assuming the incoming medium to be free of lactate and ammonium, the specific production rates of lactate qi and ammonium qA were estimated as: q L = _ i _ . ±2Z^ + ^ ± (4.15) "• X " V. V dt) CA = 4 n ( ^ r i + ^-kGbiGln) .(4.16) where L and A are the bioreactor lactate and ammonium concentrations, respectively (mM). The expression for specific protein productivity is analogous to that for lactate production. CHAPTER 4. PC02 REDUCTION IN PERFUSION SYSTEMS 71 4.4 R e s u l t s 4.4.1 Bioreactor pC0 2 before NaHC0 3 Elimination from Medium and " Base Figure 4.3 shows time profiles of viable cell density and bioreactor pC02 for B H K and C H O cells cultivated in manufacturing-scale perfusion reactors (100 - 500 L working volume). The medium for both cultivations contained 23.8 m M N a H C 0 3 while the base added to control pH was 0.71 M N a H C 0 3 for the B H K and 0.3 M NaOH for the C H O cultivation. In both cases, the bioreactors were inoculated at initial cell densities of ~1 x 106 cells/mL and the target steady-state cell density was 20 x 106 cells/mL (actual steady-state cell densities were 20.5 ± 1 . 6 x 106 cells/mL for the B H K and 21.2 ± 2.2 x 106 cells/mL for the C H O cultivation). Bioreactor pC02, in both cases, was ~70 mm Hg upon inoculation and this value increased over the cell accumulation phase, leveling out during steady-state cultivation. Average steady-state p C 0 2 values were 238 ± 16 for the B H K and 193 ± 13 mm Hg for the C H O cultivation. Higher p C 0 2 values would have resulted for the C H O cells if N a H C 0 3 had been used in place of 0.3 M NaOH to control pH. The Figure 4.3 data illustrate the need for p C 0 2 reduction during perfusion cultivation of mammalian cells at high densities. 4.4.2 pC0 2 Reduction Strategy A strategy that involved the alteration of medium and external base compositions was used for bioreactor p C 0 2 reduction. Candidates for N a H C 0 3 replacement included his- tidine and iminodiacetic acid as complexing agents and 3 (N-morpholino) propanesul- fonic acid (MOPS), N . N bis (2-hydroxyethyl) 2 aminoethanesulphonic acid (BES), N tris (hydroxymethyl) 2 aminoethanesulphonic acid (TES), tris (hydroxymethyl) aminoethane ( T R I Z M A ) , N (2-hydroxyethyl) piperazine N 2 ethanesulfonic acid (HEPES) and Piper- azine 1,4 bis(2-ethanesulfonic acid) (PIPES) as buffers [34]. Based on the favorable growth, viability and metabolism obtained with a MOPS-histidine mixture, this was selected as the replacement for N a H C 0 3 in the cultivation medium. The M O P S pKa of 7.2 suggested an effective pH buffering range of 6.5 - 7.9 to ensure robust buffering during B H K cultivation (pH set point = 6.8). Histidine also serves as a minor contributor to buffering under culture conditions (pKa = 6) but was primarily used to minimize precipitation in the medium feed line at the point of medium and base contact. This convergence of medium and base lines outside the bioreactor reduced localized areas of high pH in the bioreactor that result from direct base addition. Cell aggregation and death have been associated with direct base CHAPTER 4. PC02 REDUCTION IN PERFUSION SYSTEMS 72 Time (days) F i g u r e 4 . 3 : Time profiles of bioreactor pC02 and viable cell density for BHK and CHO cells in manufacturing-scale perfusion bioreactors. Bioreactor medium in both cases contained 23.8 mM NaHC0 3 as the buffer. Base usage was 0.71 M NaHC0 3 for the BHK cultivation and 0.3 M NaOH for the CHO cultivation. addition and these problems are especially severe for perfusion systems given their long- term operation [35]. The imidazole moiety in histidine is primarily responsible for metal ion binding with the unshared electron pair on N-3, the most energetically favored coordination site for metal ions [36, 37]. Multiple bioreactor experiments (data not shown) defined, for our cells, estimated concentration ranges for M O P S and histidine that provide the required buffering and complexing action without adversely affecting cell growth (Figure 4.4). Histi- dine concentrations >10 m M were necessary to eliminate precipitation while concentrations >20 m M inhibited growth. M O P S did not inhibit the growth of the cells tested as long as the concentration was <30 m M . Results from B H K cells in perfusion culture at 12 L working volume where sequential medium and base modifications were made are shown in Figure 4.5. The highest bioreactor P C O 2 levels were observed when NaHC03 was present both in the medium and base (229 ± 19 mm Hg) and these values decreased upon N a H C 0 3 elimination (Figure 4.5). Eliminating NaHC03 from the medium reduced bioreactor p C 0 2 to 150 ± 15 mm Hg, a 34.5% reduction close to the theoretically expected 34% reduction. When N a H C 0 3 was eliminated from both the medium and the base, the p C 0 2 was 96 ± 6 mm Hg, a 58.1% reduction, slightly lower than the expected 70%. This preliminary experiment confirmed that theoretically expected CHAPTER 4. PC02 REDUCTION IN.PERFUSION SYSTEMS 73 F i g u r e 4 . 4 : Influence of M O P S and histidine concentrations on cell growth and precipitation in the medium feed line. Histidine in the 10-20 m M range and M O P S in the 10-30 m M range did not adversely influence cell growth and prevented precipitation in the medium feed line. pCC>2 reductions could be substantial and readily attained. 4.4.2.1 Bioreac to r Ope ra t ion after N a H C O s E l i m i n a t i o n Additional experiments were performed to verify the extent of pC02 reduction that could be obtained by eliminating NaHC03 from the cultivation medium and base. Time profiles of bioreactor pC02 and viable cell density for 4. long-term B H K perfusion cultivations are shown in Figure 4.6. The MOPS-histidine mixture was used as the medium buffer while N a 2 C 0 3 was the external base. Overall, average pC02 values ranged from 68 - 85 mm Hg and were significantly lower than the ~230 mm Hg observed when N a H C 0 3 was present (Figures 4.3 and 4.5). Using a reference pC02 value of 229 mm Hg from phase A in Figure 4.5, bioreactor pC02 reductions were 63, 70, 69 and 66%, respectively, for Figures 4.6a, 4.6b, 4.6c and 4.6d, consistent with the theoretically expected 70% reduction. A 33-day manufacturing-scale experiment was also performed under NaHC03-free con- ditions to check the transferability of results from laboratory-scale bioreactors. Time pro- files of bioreactor p C 0 2 and viable cell density from the manufacturing-scale bioreactor are shown in Figure 4.7 along with their respective steady-state averages. The steady-state p C 0 2 average was 84 ± 7 mm Hg reflective of a 65% reduction compared to 238 ± 16 CHAPTER 4. PC02 REDUCTION IN.PERFUSION SYSTEMS 74 bo I E E • 250 200 o CD CN 150 100 50 1 1 1 1 1 1 1 1 m • 1 1 1 1 1 | 1 1 ! 1 d 1 D) TT rw B o c X " E ' A ml ( L • Km •RJL - • H C O . " Z E " CO -H " A CD z E i n 0 CO cn . ; M ed iu  B as e O" - O Q. O" _ o> CD 3. 8 m M  N a H C  71  M  N a H C O , 29  ±  1 9 m m  H  g o ' CD O ^ CD 2 z E 5 «? r- co cn 50  ±  1 5 m m  H  N • IN E ^ 0 £ c 1 ™ ° 1 1 O I m 1 • a. 1 , 40 60 80 100 120 Run T ime (days) F i g u r e 4 . 5 : Average bioreactor pC02 for B H K cells in perfusion culture at 20 x 106 cells/mL. NaHCOs was present both in the medium and base for phase A and was replaced with N a 2 C 0 3 as the base for phase B . Phase C was NaHC03-free with MOPS-Histidine mixture replacing it in the medium and NaoCOa replacing it as the base. Bioreactor pCC>2 reductions were 34.5 and 58.1% for phases B and C, respectively, when compared with phase A . mm Hg that was observed when NaHCG"3 was present in both the medium and external base (Figure 4.3). Laboratory-scale p C Q 2 reductions (Figure 4.6) were thus reproducible at manufacturing-scale (Figure 4.7), 4.4.3 Effect of Reduced pC0 2 on Growth, Metabolism and Productivity Figure 4.8 shows a comparison of normalized growth rate and specific protein productiv- ity between the reference condition (pC02 ~230 mm Hg) and the low p C 0 2 cultivations from Figures 4.6 and 4.7. While both the specific growth rate and productivity averages were characterized by high standard deviations, results from a t-test (two-sided, assuming independent groups and unequal variances) indicated that growth rate and productivity in- creases at reduced pCCh values were significant in all 5 cultivations (p<0.005). The growth rate increase ranged from 68 - 123% while that for productivity was 58 - 92% under reduced pCG-2. Glucose consumption and lactate production rates also increased (p<0.005) at reduced P C O 2 and ranged from 2 3 - 3 1 % and 39 - 69%, respectively (Figure 4.9). There were thus CHAPTER 4. PC02 REDUCTION INTERFUSION SYSTEMS 75 p C C y 68 ± 12 mm Hg (b) Cell Density 20.6 + 1.8 x 10 6 cells/mL T 50 - 40 s/ m  - 3 0 • 20 c - 10 Q - 0 <3 40 60 80 Time (days) 40 60 80 Time (days) 100 120 Cell Density 20.1 ±1 .2 x 10 6 cells/mL 1 _j 'bo 140 r - 40 _E X 120 (fc _t/J £ "53 E 100 : u : 30 ' O u 80 - 20 >. Q. 60 - en si  ac to  40 - • 10 ai 20 -— 0 U ia - 0 20 40 60 Time (days) 80 Cell Density 21.5 + 2.7 x 10 6 cells/mL 50 - 40 :e lls /m L;  • 3 0 0 • 20 > • 10 II D er  J 0 20 40 60 80 100 120 140 Time (days) F i g u r e 4 . 6 : Time profiles of pCC>2 and viable cell density for B H K cells in 15 L perfusion bioreactors when medium containing MOPS-histidine buffer (NaHCCvfree) was used along with 0.57 M N a 2 C 0 3 as the base for pH control. Bioreactor pC02 and cell density values are shown are mean ± standard deviation for the steady-state phase of the cultivation. increases in cell growth, metabolism and protein productivity at reduced bioreactor p C C V Metabolic flux analysis was performed using a reduced metabolic model [38] employing experimentally measured cell-specific rates for glucose, lactate and oxygen. A l l fluxes were higher at reduced pCC>2 indicating a general increase in metabolic activity at pCC>2 values closer to the physiological range. Increase in the glycolytic and lactate fluxes were 35 - 57% and 37 - 62%, respectively, while those for the T C A cycle and oxygen consumption fluxes were 35 - 55% and 34 - 52%, respectively (Figure 4.10). The consistency index, h, for these data sets was between 0.03 and 2.23 suggesting no gross error in experimental data. 4.5 Discussion We have demonstrated pCC>2 reduction on the order of 60 - 70% in high-density B H K cell perfusion cultures. This reduction was achieved by eliminating additions of NaHCOs from the medium and the pH control base. The robustness of this preventive approach was shown by the relatively stable steady-state pC02 profiles in perfusion runs (Figures 4.6 CHAPTER 4, PC02 REDUCTION INPERFUSION SYSTEMS 76 0 5 10 15 20 25 30 35 Time (days) F i g u r e 4 . 7 : Time profiles of pCC>2 and viable cell density for B H K cells in a manufacturing-scale perfusion bioreactor when-medium containing M O P S - h i s t i d i n e buffer (NaHCC>3 - f ree) was used along with 0 .57 M Na2C03 as the base for pH control. Cell density and PCO2 values are shown are mean ± standard deviation for the steady-state phase of the cultivation. Bioreactor pC02 and viable cell density for N a H C 0 3 containing medium and base in an identical bioreactor are shown in Figure 4 . 3 . and 4.7) that together included over 400 days of bioreactor operation. Laboratory results were reproduced at the manufacturing scale, a major advantage as development work at this scale was minimized; It should be noted that there was no direct closed loop control of pCC>2 in any of these experiments. There was only an indirect control of bioreactor pCC>2 since all bioreactors were operated at a constant cell specific perfusion rate. 4.5.1 Comparison of Growth, Productivity and Metabolism with Previ- ous Studies The general trends in growth rate and specific protein productivity upon pCC>2 reduction observed here are similar to reports for other cell lines in perfusion or fed-batch cultures, though with cell-to-cell variability. A B H K perfusion culture bioreactor with a 40 to 280 mm Hg p C 0 2 increase had both the growth rate' and the specific productivity decrease by 30% [12]. For C H O .cells in perfusion culture with a high glucose concentrations, the growth rate decreased by 57% when the p C 0 2 . was increased from 53 to 228 mm Hg, but the cell specific antibody productivity was almost unchanged [39]. Increasing pC02 from 36 to 148 CHAPTER 4. PC02 REDUCTION INTERFUSION SYSTEMS 77 F i g u r e 4 . 8 : Comparison of normalized growth rate and specific productivity under reference (NaHC03 - con t a in ing ) conditions with N a H C 0 3 - f r e e perfusion cultivations. Time pro- files of bioreactor pCC>2 for the a to d 15 L bioreactors are shown in Figure 4.6 while that for the manufacturing-scale bioreactor is shown in Figure 4.7.' There was a sig- nificant (p<0.005) increase in growth.rate and specific productivity upon NaHCOs elimination in all cases. mm Hg during perfusion cultivation decreased C H O cell density by 33% (reflecting reduced growth rate) and specific productivity by 44% [3]. Under glucose limiting conditions, for a similar p C 0 2 increase, the growth rate decreased.by 38% along with a 15% reduction in specific antibody productivity. The growth rate .of NS/0 cells decreased when p C 0 2 increased from 60 to 120 mm Hg [6]. Scale-up of a fed-batch process resulted in p C 0 2 values of 179 ± 9 mm Hg in a 1000 L bioreactor and a 40% decrease in specific productivity was seen under these conditions compared to a p C 0 2 value of 68 ± 13 mm Hg in a 1.5 L laboratory-scale bioreactor [13]. Glucose consumption rates decreased in a.dose-dependent fashion for hybridoma cells in T-25 flasks [8] with a 40% decrease observed when the p C 0 2 increased from 40 to 250 mm Hg (osmolality held constant at 320 mOsm/kg). Similar observations were, made for lactate production that decreased by 45% for the same p C 0 2 increase. We have also observed increases in glucose consumption and lactate production rates at reduced P C O 2 (Figure 4:9). CHAPTER 4. PCO2 REDUCTION INTERFUSION SYSTEMS 78 F i g u r e 4 . 9 : Comparison of normalized glucose consumption and lactate production rates under reference (NaHCCvcontaining) conditions with NaHCOa-free perfusion cultivations. Time profiles of bioreactor pCC-2 for the a to d 15 L bioreactors are shown in Figure 4.6 while that for the manufacturing-scale bioreactor is shown in Figure 4.7. There was a significant (p<0.005) increase in glucose consumption and lactate production upon NaHC03 elimination in all cases. 4.5.2 Impact of high pC0 2 on Osmolality High osmolality can be caused by high pC02 and while elevated osmolality has not been consistently shown to reduce growth rate and specific productivity, it has had a negative interaction effect when p C 0 2 values were also high [8, 10]. For C H O cell cultivation in 6-well plates [10], growth rate and specific tissue plasminogen activator (tPA) productivity decreased 31% and 42%, respectively, when the p C 0 2 increased from 36 to 250 mm Hg (constant osmolality at 310 mOsm/kg). A n increase in osmolality from 310 to 376 mOsm/kg had no adverse impact on growth rate and tPA production for p C 0 2 values in the 36 - 250 mm Hg range. The highest reduction in growth rate (53%) was seen when both p C 0 2 (250 mm Hg) and osmolality values (376 mOsm/kg) were high. For C H O cells cultivated in 2 L batch bioreactors [21], the growth rate decreased, but only by 9% when the p C 0 2 increased from 50 to 150 mm Hg (osmolality controlled at 350 mOsm/kg) while a 60% reduction was reported when the osmolality increased from 316 to 450 mOsm/kg ( p C 0 2 at 38 mm CHAPTER 4. PC02 REDUCTION INf PERFUSION SYSTEMS 79 12 xT 10 .0 8 O E 6 O. X £ 2 0 Ref 1 2 3 4 5 Experimental Condit ion F i g u r e 4.10: Effect of bioreactor pCC>2 on key metabolic fluxes. The presentation is similar to that in Figures 4.8 and 4.9. The reference condition indicates high pCC>2, conditions 1 - 4 are for low pCC>2 in 15 L bioreactors and condition 5 is low p C 0 2 in a manufacturing- scale bioreactor. Hg). For hybridoma cells cultivated in T-25 flasks [8], high pC02 and osmolality reduced growth rate in a dose-dependent fashion. The growth rate decreased by about 40% when pCC>2 increased from 40 to 250 mm Hg (osmolality constant at 320 mOsm/kg) and a similar decrease was seen when the osmolality increased to 435 mOsm/kg (pCCV constant at 40 mm Hg). Growth rate decreased by 84% for p C 0 2 and osmolality values of 195 mm Hg and 435 mOsm/kg, respectively, suggesting a negative interaction effect. By reducing'base addition, the pC02 reduction strategy proposed in this study also minimizes osmolality increases and the adverse effects associated with combined high pC02 and osmolality. • 4.5.3 H i g h p C 0 2 and Intracel lular p H High pC02 has been reported to decrease intracellular pH (pHj) with significant implications for cell growth and metabolism [40, 41]. For hybridoma cells cultivated in T-25 flasks, a 0.1 - 0.2 unit pHi reduction was observed at pC02 values higher than 140 mm Hg when compared with a 40 mm Hg control [8]. While pHj was not measured in this study, earlier . work from our laboratory with B H K cells in perfusion culture observed a 0.2 unit reduction in pHj when pC02 increased from 40 to 250 mm Hg [4]. Decreases in pH; on the order of 0.2 units have been shown to significantly reduce the carbon flux through glycolysis [42-45]. One mechanism for this decrease is the strong dependence of phosphofructokinase activity. CHAPTER 4. PC02 REDUCTION ^PERFUSION SYSTEMS 80 on pH [46]. This is consistent with the 2 3 - 3 1 % increase in glucose consumption rates that were observed in this study at reduced p C 0 2 values. Since changes to pH^ affect the ionization states of all peptides and proteins, it is actively regulated [47, 48]. Under conditions of high external P C O 2 , diffusion into the cell followed by rapid conversion to H 2 C O 3 through the action of carbonic anhydrase can cause a decrease in pHj [49-51]. Cells try to maintain pH homeostasis through the action of acid extruders which include the vacuolar-type H + pump [41], the N a + / H + exchanger [52], the N a + driven C T / H C O 3 exchanger [51] and the electrogenic N a + / H C 0 3 cotransporter [53]. The extrusion of H + from cells and the intake of H C 0 3 require energy [47] resulting in an increased energy demand for maintenance. This could be partially responsible for the reduced growth rate at elevated p C 0 2 reported by most studies. 100 bo X E ^E O U Q. 00 20 30 40 T ime (days) Figure 4.11: Time profiles of pCQ2 (Q) a n ( f viable cell density (•) for BHK cells in a manufacturing-scale perfusion bioreactor when medium containing MOPS-histidine buffer (NaHC0 3-free) was used along with 0.57 M Na 2C03 as the base for pH control and oxygen sparged at 0.015 vessel volumes/minute. These pC02 values can be di- rectly compared with those in Figure 4.7 despite differences in cell density since both reactors were operated at identical cell specific perfusion rates. 4.5.4 Closed-loop p C Q 2 Control , Figures 4.6 and 4.7 show pCC>2 spikes in the beginning of the experiments when cell con- centrations were increasing from initial cell densities. Use of NaHC0 3 -free medium results BIBLIOGRAPHY 81 in low bioreactor p C 0 2 values, often less than 15 mm Hg. This will severely inhibit cell growth unless C O 2 is added to increase bioreactor pCG"2 to 40 mm Hg or higher. Since closed loop pCG"2 control was not employed, manual C O 2 addition was responsible for the variability in bioreactor pC02 during the cell scale-up phase. Closed loop pCG"2 control is currently being tested. Despite ~70% reduction in bioreactor p C 0 2 after medium and base changes (Figures 4.6 and 4.7), the average values ranged from 68 to 85 mm Hg, still higher than the physiological range (30 - 50 mm Hg). While additional reduction is possible through NaOH pH control, medium precipitation and cell death associated with its use do not make this an attractive option for long-term cultivation. Stripping C O 2 with macrosparging reduced p C 0 2 in a manufacturing-scale bioreactor to 60 mm Hg (Figure 4.11), a 29% reduction when compared to non-sparged conditions (84 mm Hg in Figure 4.7). Thus, additional p C 0 2 reduction is possible with macrosparging and this approach is being investigated with the closed-loop bioreactor p C 0 2 control 4.6 C o n c l u s i o n s We have presented a practical strategy for p C 0 2 reduction in high-density perfusion biore- actors by eliminating NaHC03 from the medium and base used for pH control. This method reduces p C 0 2 at the source in contrast to stripping techniques that rely on C O 2 removal after it has been produced. By minimizing the indirect contributions to bioreactor P C O 2 , a 63 - 70% pC02 reduction was achieved in laboratory-scale bioreactors and the results were reproduced at manufacturing-scale. Significant increases in cell growth, metabolism and protein productivity were obtained upon p C 0 2 reduction and these trends were consistent with other published studies. This approach can be readily implemented in established manufacturing processes since no changes to the bioreactor physical configuration or op- erational parameters are necessary. It is robust because p C 0 2 reductions are guaranteed once medium and base changes are made. The general nature of this approach makes it an attractive option for P C O 2 reduction in fed-batch cultivations as well. B i b l i o g r a p h y [1] Chuppa, S.; Tsai. S.; Yoon, S.; Shackelford, S.; Rozales, C ; Bhat, R.; Tsay, G.; Matanguihan, R:; Konstantinov, K.;' Naveh, D. Fermentor temperature as a tool for control of high-density-perfusion cultures of mammalian cells. Biotechnol. Bioeng., 1997, 55, 328-338. BIBLIOGRAPHY 82 .[2] Konstantinov, K . B. ; Tsai, Y . ; Moles, D.; Matanguihan, R. Control of long-term perfusion Chinese hamster ovary cell culture by glucose auxostat. Biotechnol Prog, 1996, 12(1), 100-109. [3] Gray, D.; Chen, S.; Howarth, W.; Inlow, D.; Maiorella, B . C 0 2 in large-scale and high-density C H O cell perfusion culture. Cytotechnology, 1996, 22, 65-78. [4] Taticek, R.; Petersen, S.; Konstantinov, K . ; Naveh, D. Effect of dissolved carbon dioxide and bicarbonate on mammalian cell metabolism and recombinant protein pro- ductivity in high density perfusion culture, in Cell Culture Engineering VI, San Diego, C A , 1998. [5] Anderson, D.; Goochee, C. The effect of cell culture conditions on the oligosaccharide structures of secreted glycoproteins. Curr. Opin. Biotechnol., 1994, 5, 546-549. [6] Aunins, J.; Henzler, H.-J . in Biotechnology: A multi-volume comprehensive treatise, Stephanopoulos, G.; Rehm, H.-J. ; Reed, G.; Puhler, A . ; Stadler, P., Eds., volume 3, p 817p. V C H Verlag, Weinheim, 1993. [7] deZengotita, V . ; Kimura, G.; Miller, W . Effects of C 0 2 and osmolality on hybridoma cells: Growth, metabolism and monoclonal antibody production. Cytotechnology, 1998, 28, 213-227. [8] deZengotita, V . ; Schmeizer, A . ; Miller, W. 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Prog., 2005, 21, 70-77. [22] Michaels, J . ; Nowak, J . E. ; Mallik, A- K . ; Koczo, K . ; Wasan, D. T.; Papoutsakis, E . Analysis of cell-to-bubble attachment in sparged bioreactors in the presence of cell-protecting additives. Biotechnol Bioeng., 1995, ^7, 407-419. [23] Michaels, J.; Nowak, J.; Mallik, A . ; Koczo, K . ; Wasan, D. T.; Papoutsakis, E . Interfa- cial properties of cell culture media with cell-protecting additives. Biotechnol. Bioeng., 1995,^7,420-430. BIBLIOGRAPHY 84 [24] Barngrover, D.; Thilly, T. High density mammalian cell growth in Leibovitz bicarbonate-free medium: effects of fructose and galactose on culture biochemistry. J. Cell Sci., 1985 , 78, 173-189. " [25] Bertheussen, K . Growth :of cells in a hew defined protein-free medium. Cytotechnology, 1993, 11, 219-231. • . [26] Itagaki, A . ; Kimura, G . ' T E S and H E P E S buffers in mammalian cell cultures and viral studies: problem of carbon dioxide requirement. Exp. Cell Res., 1974, 83, 351-361. [27] Leibovitz, A . The growth and maintenance of tissue-cell cultures in free gas exchange with the atmosphere. Am. J. Hyg., 1963, 78, 173-180. [28] Schmid, G.; Blanch, H. ; Wilke, C. Hybridoma growth, metabolism and product forma- tion in HEPES-buffered medium: Effect of pH. Biotechnol. Lett, 1990, 12, 633-638. [29] Swim, H. ; Parker, R. Nonbicarbonate buffers in cell culture media. Science, 1955, 122, 466. [30] Morel, F.; Hering, J . Principles and Applications of Aquatic Chemistry. John Wiley and Sons, New York, 1993. [31] Goudar, C ; Nanny, M . A M A T L A B toolbox for solving acid-base chemistry problems in Environmental Engineering Applications. Computer Applications in Engineering Education, 2005, i5 , 257-265. [32] Stumm, W.; Morgan, J . Aquatic Chemistry. John Wiley and Sons,: New York, 3rd edition edition, 1996. [33] Ozturk, S.; Palsson, B . Chemical decomposition of glutamine in cell culture media: Effect of media type, pH, and serum concentration. Biotechnol. 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Metabolic screening of mammalian cell cultures using well- plates. Biotechnol. Prog., 2003, 19, 98-108. [39] Takuma, S.; Hirashima, C ; Piret, J . in Animal Cell Technology: Basic and Applied Aspects, Yagasaki, K . ; Miura, Y . ; Hatori, M . ; Nomura, Y . , Eds., pp 99-103. Kluwer Academic Publishers, Netherlands, 2004. [40] Gillies, R.; Martinez-Zaguilan, R.; Peterson, E. ; Perona, R. Role of intracellular pH in mammalian cell proliferation. Cell Physiol. Biochem., 1992, 2, 159-179. [41] Roos, A . ; Boron, W . Intracellular pH. Physiol. Rev., 1981, 61, 296-434. [42] Busa, W . in Na+/H+-exchange, intracellular pH and cell function, Aronson, P.; Boron, W., Eds., p 291. Academic Press, New York, 1986. [43] Fidelman, M . ; Seeholzer, S.; Walsh, K . ; Moore, R. Intracellular pH mediates action of insulin on glycosysis in frog skeletal muscle. Am. J. Physiol, 1982, 242, C87-C93. [44] McQueen, A. ; Bailey, J . E . Effect of ammonium ion and extracellular pH on hybridoma cell metabolism amd antibody production. Biotechnol. Bioeng., 1990, 35, 1067-1077. [45] Moore, R.; Fidelman, M . ; Hansen, J . ; Otis, J . in Intracellular pH: Its measurement, regulation and utilization in cellular function, Nuccitelli, R.; Deamer, D. , Eds., p 385. John Wiley and Sons Inc., New York, 1982. [46] Stryer, L . Biochemistry. W . H . Freeman and Company, San Francisco, 4th edition, 1995. [47] Boron, W . Regulation of intracellular pH. Adv. Physiol. Educ, 2004, 28, 160-179. [48] Madshus, H . Regulation of intracellular pH in eukaryotic cells. Biochem. J., 1988, 250, 1-8. BIBLIOGRAPHY 86 [49] Bouyer, P.; Bradley, S.; Zhao, J.; Wang, W.; Richerson, G.; Boron, W . Effect of extracellular acid-base disturbances on the intracellular pH of neurones cultured from rat medullary raphe or hippocampus. J. Physiol. (Lond)'., 2004, 559, .85-101. [50] Buckler, K . ; Vaughan-Jones, R.; Peers, C ; Lagadic-Gossmann, D.; Nye, P. Effects of extracellular pH, pC02 and H C 0 3 - on intracellular pH in isolated type-1 cells of the neonatal rat carotid body. J. Physiol. (Lond)., 1991, 444, 703-721. [51] Thomas, R. The role of bicarbonate, chloride and sodium ions in the regulation of intracellular pH in snail neurones. J. Physiol. (Lond)., 1977, 273, 317-338. [52] Murer, FL; Hopfer, U . ; Kinne, R. Sodium/proton antiport in brush-border-membrane vesicles isolated from rat small intestine and kidney. Biochem. J., 1976, 154, 597-604. [53] Boron, W.; Boulpaep, E . Intracellular pH regulation in the renal proximal tubule of the salamander: basolateral H C 0 3 - transport. J. Gen. Physiol., 1983, 81, 53-94. Chapter 5 O U R a n d C E R E s t i m a t i o n i n P e r f u s i o n S y s t e m s 1 5.1 Introduction Oxygen uptake and carbon dioxide evolution rates (OUR and C E R , respectively) provide useful information on cell metabolism and physiology. Reliable estimation of these rates is desirable as they are indicators of changes in cellular metabolic activity [1-8]. Oxygen up- take data are an indicator of cell density and metabolic rates such as glucose consumption and on-line O U R measurements have been used to design feeding strategies and control bioreactor operation [9, 10]. O U R information is also necessary for bioreactor design and scale-up given the low solubility of oxygen. This is especially important for high density per- fusion cultivations that have high oxygen transfer requirements. Moreover, O U R and C E R are required for metabolic flux analysis even in the simplest of mammalian cell bioreaction networks [11]. Robust O U R and C E R estimation is thus critical for bioprocess development and is also important for monitoring and diagnosing manufacturing bioreactors. The primary approaches that have been used for in-situ O U R estimation in mammalian cell cultures include the stationary liquid phase balance approach, the dynamic method, and the global mass balance (GMB) approach [6j. The stationary liquid phase balance approach requires knowledge of the volumetric oxygen transfer coefficient, k^a, for O U R estimation [1, 2]. However, for both sparged and membrane aerated bioreactors, kt,a can change over time making the stationary liquid-phase balance approach unsuitable for long 1 A version of this chapter wi l l be submitted for publication. Goudar, C . T . , Piret, J . M . and Konstantinov, K . B . (2006). Estimating O U R and C E R in perfusion,systems using global mass balances and novel off-gas analyzers. 87 CHAPTER 5. OUR AND CER ESTIMATION IN PERFUSION SYSTEMS 8 8 term perfusion cultivations. The dynamic method is the simplest and perhaps the most widely used method for estimating oxygen uptake rates [10, 12, 13]. This approach typically involves increasing the DO concentration in the bioreactor to 60% saturation and turning off the oxygen supply. The subsequent rate of DO decrease is a consequence of cellular consumption and provides the O U R estimate. Despite its simplicity, this method involves a perturbation that is undesirable. Moreover, for high cell density perfusion cultures, rapid oxygen consumption complicates application of this method. For B H K cells at densities of 20 x 10 6 cells/mL, the time required for complete oxygen depletion when all supplies are cut off is on the order of 40 seconds resulting in unreliable O U R estimates from the dynamic method (DO probe response times are typically greater than 40 seconds). To overcome these limitations, an alternate O U R estimation approach was proposed where reactor contents were continuously drawn into an external loop and D O measurements were made at the outlet of the loop [14]. The difference between the D O levels in the reactor and at the outlet of the external loop helped determine OUR. This method required only a single additional D O measurement while no gas phase oxygen measurements were necessary making the process simple and robust. The G M B approach becomes attractive for O U R estimation when reliable gas phase oxygen measurements can be made as it does not require k^a determination and bioreactor, perturbation. Information on the gas flow rates and oxygen concentrations in the inlet and outlet streams is adequate for O U R estimation.. C E R estimation is more difficult than O U R because of the reversible dissociation of C 0 2 into H 2 C O 3 , H C O 3 and C O 3 " in solution. The equilibria of these dissociation reactions are strong functions of pH, temperature and ionic strength that must be accounted for during C E R estimation. While there are several reports on C E R estimation in microbial systems [15-20], there are only a few in-mammalian cell chemostat and batch studies [1, 21, 22] and none in perfusion systems. The use of bicarbonate buffered medium in mammalian cells further complicates C E R estimation because this is a major additional abiotic C O 2 component. In this study, we present methods to estimate O U R and C E R in mammalian cell perfu- sion cultures using global mass balances. While measurement of oxygen and carbon dioxide concentrations in the inlet and outlet gas streams is necessary, k^a data are not required and no reactor perturbations are necessary. Our approach allows real-time O U R and C E R estimation that can also serve as indicators of cell density and nutrient consumption rates. Moreover, these data enable real-time estimation of metabolic fluxes providing useful in- sights into cell metabolism and physiology that can be used in advanced control strategies for optimal bioreactor operation. CHAPTER 5. OUR AND CER ESTIMATION IN PERFUSION SYSTEMS 8 9 5.2 Theory 5.2.1 OUR Estimation Under ideal conditions, both liquid and gas stream oxygen flows must be taken into account in the generalized mass balance approach. However, a combination of low oxygen solubility and high cell density make liquid stream oxygen contributions negligible (usually less than 1%; Appendix E) and only gas phase oxygen balance equations are necessary for O U R esti- mation. Under steady-state conditions, there is no accumulation of oxygen in the bioreactor and oxygen uptake by the cells is the difference between the oxygen concentrations in the inlet and outlet streams 0 U R = ^ | 2 i ( O m _ o o ^ 1 0 3 ( 5 1 ) XVV • where O U R is the'cell specific oxygen uptake rate (pmol/cell-d), Ftotai is the total gas flow rate (L/d) , Xy the bioreactor viable cell density (109 cells/L), V the bioreactor volume (L) and 0 2 n and O™1 the inlet and outlet oxygen concentrations (mol/L), respectively. 5.2.2 CER Estimation 5.2.2.1 Bica rbona te Sys tem D y n a m i c s i n a M a m m a l i a n C e l l B io reac to r Carbon dioxide sources in a perfusion system include cellular respiration, bicarbonate buffered medium and sodium bicarbonate when used as a base for pH control. Carbon dioxide produced by the cells dissolves in water to form carbonic acid , ' co2 ( g ) ~co 2 ( a q ) f - . ; • : •; (5.2) C 0 2 ( a q j +. H 2 0 <- H 2 C 0 3 (5:3) It is common practice in solution chemistry to combine the aqueous concentration of car- bon dioxide and carbonic acid such .that the above equation's can be replaced by a single expression . . . ' '••'062(g) + H 2 0 - ' ~ H2CO3*; • Kg = 10-1Ar. • / (5.4) where H 2 C 0 3 * = 'CO^aq) ' + H 2 C O 3 and Kg is the equilibrium constant under standard conditions (T — 25 °C and ionic strength' (I)' = 0). Further dissociation of H 2 C O 3 * to H C O 3 and subsequently to CO3" can be described as . H 2 C O 3 * ^ H C O 3 + H+; A"i = 10 ''• (5.5) CHAPTERS. OUR AND CER ESTIMATION IN PERFUSION SYSTEMS -10.33 H C 0 3 <-> C G f + H + ; K2 = 10- where K\ and K2 are the equilibrium constants under standard conditions. 90 (5.6) Estimate medium ionic strength and calculate activity coefficients Compute rate constants K, and K 2 Calculate Henry's constant for C 0 2 Calculate [C0 2 ] T from bioreactor p C 0 2 measurement Determine C 0 2 mass flow rates in liquid and gas streams Calculate C E R Figure 5.1: The steps involved in perfusion system CER estimation. For typical mammalian cell cultivations, however, the temperature is close to 37 °C and the ionic strength is ~0.1 M depending upon the composition of the medium. The rate constants must hence be corrected to reflect experimental conditions. The rate constants can be corrected for temperature using the Van't Hoff equation [23] K = Kr ,f exp (AH0 Tr ref 1_ .f (5.7) where K and Kref are the corrected and reference rate constants, respectively at temper- atures T and Tref, AH0 the standard enthalpy change for the reaction, and R, the gas constant. The corrected equilibrium constants Kg, K\ and if2 were 10~ 6 - 3 0 and I O - 1 0 4 8 , respectively, at 37 °C and calculation details have been presented "in Appendix B . To account for ionic strength effects, the activity.coefficients were calculated using the CHAPTER 5. OUR AND CER ESTIMATION IN PERFUSION SYSTEMS. 91 Davies equation which is valid for ionic strengths:<; 0.5 M log 7 ,= -Az2 11 - 0.2/1 (5.8) where 7 is the activity coefficient, A = 1.825 x 106 (eT)~3^2 is a'constant (e = 78.38 is the dielectric constant for water, T is the absolute temperature) and I the ionic strength. The ionic strength of the medium,used in this study was calculated as 0.115 M from,the Debye-Hiickei theory [24] i 2. where C\ and z\ are charge and concentration of species i, respectively. The activity coeffi- cients for / = 0.115 M were estimated from,Eq.(5.8) as 0.7747 and 0.3602, respectively, for species with charges 1 and 2. Incorporating the temperature corrected values of the equi- librium constants, Eqs.(5.4) - (5.6) can be rewritten in terms of the species concentrations and activity coefficients as R = [H 2 C0 3 *] 7 H 2 C Q 3 * = ^ c T H i C O i l = iQ- - 1 - 6 0 (5.10) 9 [•C°2(g)].7p0 2 ( g ! ' 9 7 C 0 2 ( g ) . . K l J £ ^ X r ! \ C ^ ] 7 H C ° 3 = ^ 7 H + ; y k C Q - ' = 1 0 - 6 - 3 0 •": ; (5.11) I . H 2 C O 3 J 7 H 2 C O 3 * 7 H 2 C O 3 * • • , • K ^ [Ht] 7 g , - [CO 2-] 7 c o j : - - = . 7H + 7coj: ^ 1 Q _ 1 0 , 4 8 [ H C 0 3 ] 7 H C o 3 - . 7 H C O 3 . . . . where Kg, K\ and K% are the concentration based equilibrium constants and 7 the activ- ity coefficients of the various species. Activity, coefficients for the charged species were calculated from the Davies equation (7g.+ ' = 7 H C 0 3 _ = 0.7746, 7co32- = 0.3602) and 7C02(g> = 7 H 2 C 0 3 *  w a s estimated as .1.03 as described in [25]. Substituting these values in Eqs.(5.10) - (5.12), the concentration based equilibrium constants Kg, K\ and K% were calculated as I O " 1 , 6 0 , 1 0 " 6 ' 0 7 and 1 0 ~ 1 0 : 0 4 , respectively. These values now incorporate both' temperature and ionic strength corrections and are representative of the system at 37 °C and 0.115 M ionic strength.'Temperature corrections alone resulted in-25.8, 12.2 and - 29.2% change in Kg, K{ and K^, respectively, while the combined effect of temperature and ionic strength were, -.25.8,, 90.5 and 96.8%, .respectively (Kg was not affected by ionic strength as seen from Eq.5.10.).' •.. ;. ,-. . It follows from the above discussion that the carbon dioxide produced by the cells does not exist just as a gas but also as H 2 C 0 3 * , HCO3 and CO|"- The relative concentrations CHAPTER 5. OUR AND CER ESTIMATION IN PERFUSION SYSTEMS 92 of these species are influenced primarily by bioreactor pH while temperature and medium ionic strength have minor effects as seen from the ionization fraction expressions % of H 2 C O 3 * . = % of HCOo = % of C O f = + 12 [H + 12 + 12 + [H +] K{ + K\K\ [H + ] K\ - ^ + [ H + ] K f + K\Kl J _Km___\ x 100 x 100 x 100 (5.13) (5.14) (5.15) At pH = 6.8, the cultivation pH in this study, the relative amounts of H 2 C O 3 * , H C 0 3 and COf in the medium were 15.69, 84.26 and 5 x 10" 4%, respectively. Thus H C 0 3 is the dominant species followed by H 2 C O 3 * while CO3" can be neglected. S t e a d y S t a t e s Figure 5.2: Cell density averages for the different experimental conditions during the course of the perfusion cultivation. For standard conditions, DO = 50%, T = 36.5 °C and pH = 6̂ 8. 5.2.2.2 C 0 2 M a s s Ba lance Equat ions In a perfusion system, bioreactor pCC>2 is relatively constant suggesting no C O 2 accumula- tion. The C O 2 produced by the cells is then simply the difference between the C O 2 leaving CHAPTER 5. OUR AND CER ESTIMATION IN PERFUSION SYSTEMS 9 3 and entering the system. C O 2 produced by cells = C 0 2 leaving the System - C 0 2 entering the System (5.16) with units of mol/d. Recognizing that C G 2 produced by the cells can exist as both H 2 CC>3* and HCO3, it is convenient to combine them while deriving mass balance expressions. The total C 0 2 concentration, [ C 0 2 ] T , is thus defined as [ C 0 2 ] T = [ H 2 C 0 3 * ] + [ H C 0 3 ] . Sources of [ C 0 2 ] T include bicarbonate-containing cultivation medium, base (NaHCOs or N a 2 C 0 3 ) or C 0 2 gas used for bioreactor.pH control, and cellular metabolism. Removal mechanisms for [ C 0 2 ] T include the harvest and cell bleed streams along with gaseous C 0 2 stripping, either through sparging or membrane aeration. Eq.(5.16) can be rewritten to include contributions of the individual components to the inlet and outlet streams CER = { ^ } { ^ M [ C 0 2 j ^ + F f e a s J C 0 2 ] ^ e + F C 0 2 ( i r t ) } • (5.17) - { F H [ C 0 2 ] ? + Fbl.ed{C02}h^ed + FCo2(out)} where CER is the carbon dioxide evolution rate (pmol/cell-d), V the reactor volume (L), Xy the viable cell density in the bioreactor (IO 9 cells/L), F M , Fbase, E'H, Fueed the medium, base, harvest and bleed flow rates (L/d), respectively, [ C 0 2 ] ^ , [ C 0 2 ] ^ a s e , [ C 0 2 ] T and [C0 2])p l e e d the total C 0 2 concentration (mol/L) in the medium, base, harvest and bleed streams, respectively, and Fco2{in) and Fco2fout) the molar flow rates of C 0 2 (mol/d) in the inlet and outlet steams, respectively. Quantifying contributions from the medium and base on a mol/day basis is straightfor- ward as their carbonate concentrations and flow rates are known. The flow rate of C 0 2 gas into the reactor will help determine the amount of C 0 2 gas added to the reactor (this is seldom done when bicarbonate-containing medium is used). To determine [ C 0 2 ] T removal from the harvest and cell bleed streams, the total C 0 2 concentration in the bioreactor must be known because C 0 2 concentrations in the harvest and bleed streams are similar to those in the bioreactor. Bioreactor C 0 2 concentration can be estimated from p C 0 2 measurements that are typically made using a blood gas analyzer rnr. 1 bioreactor J 1 , &l , K^K^ \ J pCQ2bioreactor \ ^ 1 8 ^ [ c ° 2 ] t - \ 1 + [ H V [ f T t j i ^ J - where [ C 0 2 J T ° R E A C T O R is the total C 0 2 concentration in the bioreactor (mol/L), pC02bioreactor the bioreactor p C 0 2 (mm Hg) and hco2 is the Henry's constant for C 0 2 (mm Hg-L/mol) •'•f. 5R'-r..,f-"' CHAPTER 5. O U R A M ) C E R ESTIMATION IN PERFUSION SYSTEMS 94 determined as 101:3 * 22.395 a 7.500617 a - a + bE+cT2 + dT3+ eT4 (5.19) (5.20) with a = 1.72, 6 = -6.689 x 10~ 2, c = 1.618 x I O - 3 , d = -2.284 x I O - 5 and e = 1.394 x I O - 7 [26]. Once [ C 0 2 ] x ° r e a c t o r is determined, the harvest and cell discard flow rates can be used to determine [C02]T removal on a mol/day basis. Finally, measuring C O 2 gas concentration in the outlet gas will help determine [C02]T-.removal by stripping. The C E R is then estimated by substituting these values in Eq.(5.17). This C E R estimation procedure is summarized in Figure 5.1. Steady States Figure 5.3: Growth rate averages for the different experimental conditions during the course of the perfusion cultivation. For standard conditions, D O = 50%, T = 36.5 °C and.pH = 6.8. 5.3 Materials and Methods 5.3.1 Cell Line, Medium and Cell Culture System C H O cells were cultivated in perfusion mode-with glucose and glutamine as the main carbon and energy sources. Experiments were conducted in a 15 L bioreactor (Applikon, Foster City, C A ) with a 12 L working volume. The temperature was maintained at 36.5 °C and CHAPTER 5. OUR AND CER ESTIMATION IN PERFUSION SYSTEMS 95 the agitation at 40 R P M . Under standard conditions, the dissolved oxygen (DO) concen- tration was maintained at 50% air saturation by sparging a mixture of oxygen and nitrogen (100 - 150 mL/min) through 0.5 spargers and the pH was maintained at 6.8 by the automatic addition of 0.3 M NaOH. The bioreactor was inoculated at an initial cell density of approximately 1.0 x 10 6 cells/mL and cells were allowed to accumulate to a steady- state concentration of 20 x 10 6 cells/mL. The steady-state cell density was maintained by automatic cell bleed from the bioreactor. Time (minutes) •Figure 5.4: OUR estimation in the 2 L reactor by the dynamic method. DO data following inocu- lation with cells from the 15 L perfusion bioreactor were used for OUR estimation by the dynamic method. Bioreactor DO, temperature and pH were varied during the course of the cultivation to determine the operating ranges for these variables. The low and high values for D O were 20% and 100%, respectively (set point = 50%) while those for pH were 6.6 and 7.0, respectively. The temperature set point was 36.5 °C and was varied between 30.5 - 37.5 °C during the course of the experiment. Bioreactor conditions were maintained at each of these altered conditions for 10 days and data from the last 4 days were considered representative of each experimental condition. O U R and C E R data presented in later sections are averages of these 4 days for each experimental condition. In addition to the above perfusion cultivation, a 2 L bioreactor was used for O U R estimation by the dynamic method. The reactor was initially filled with 1.9 L of fresh medium and was maintained at 36.5 °C, pH = 6.8, and D O concentration in the 75 - 85% range. The gas supply to the bioreactor was shut off and a 100 mL sample from the 15 L perfusion bioreactor (steady-state cell density of 20 x 10 6 cells/mL) was used to CHAPTER 5. OUR AND CER ESTIMATION IN PERFUSION SYSTEMS 96 inoculate the 2 L bioreactor at a cell density of ~1 x 10 6 cells/mL. The resulting decrease in D O concentration was monitored and this information was used to compute the OUR. A comparison was then made between O U R estimates from the mass balance method (in- situ estimation in the perfusion bioreactor) and the dynamic method (in the external 2 L bioreactor). The headspace volume was 100 mL such that surface aeration effects were minimal. I 5 8 4 -2= 3 a O 2 Dynamic Method Mass Balance Method A B C D E F Figure 5 . 5 : Comparison of O U R estimates from the dynamic method (external 2 L bioreactor) with those from the global mass balance method (in-situ estimation in the 15 L perfusion bioreactor). 5.3.2 Analytical Methods Samples from the bioreactor were taken daily for cell density and viability analysis using the C E D E X system (Innovatis, Bielefeld, Germany). The samples were subsequently cen- trifuged (Beckman Coulter, Fullerton, CA) and the supernatants were analyzed for nutrient and metabolite concentrations. Glucose, lactate, glutamine and glutamate concentrations were determined using a YSI Model 2700 analyzer (Yellow Springs Instruments, Yellow Springs, OH) while ammonium was- measured by an Ektachem DT60 analyzer (Eastman Kodak, Rochester, N Y ) . The pH and D O were measured online using retractable electrodes (Mettler-Toledo Inc., Columbus, OH) and their measurement accuracy was verified through off-line analysis in a Stat Profile 9 blood gas analyzer (Nova Biomedical, Waltham, M A ) . The same instrument also measured the'dissolved C O 2 concentration. On-line measurements of cell density were made with a' retractable optical density probe (Aquasant Messtechnik, Bubendorf, Switzerland), calibrated with C E D E X cell density measurements. Concentra- CHAPTER 5. OUR AND CER ESTIMATION IN PERFUSION SYSTEMS 97 tions of oxygen and carbon-dioxide in the exit gas were measured using a MGA-1200 Mass Spectrometer (Applied Instrument Technologies, Pomona, C A ) . O 4 O 2 rri di o "D O "O S= •<- i= CO ^ O CD CO CO CO o D Steady States Figure 5 . 6 : Average OUR estimates from the mass balance method for the 12 experimental con- ditions in the perfusion cultivation. 5.4 Results 5.4.1 Cell Density and Growth Rate The perfusion cultivation comprised of 12 experimental conditions each of 10 day duration and average cell densities for each of these steady states are shown in Figure 5.2. The target cell density was 20 x 10 6 cells/mL with most values'very close to the target. The exceptions- were the T = 30.5 °C and pH = 6.6 steady states where growth rates were much lower than at the other conditions (Figure 5.3). Temperature reduction caused an expected decline in growth rate as did pH reduction. No change in growth rate was seen when the DO was varied between 20 and 100%. Cell viability was greater than 95% in all cases (not shown). CHAPTER 5. OUR AND CER ESTIMATION IN PERFUSION SYSTEMS 98 f 5 O 4 B 3 a: W o 2 ill O Q co co co O Steady States F i g u r e 5.7: Average C E R estimates for the 12 experimental conditions in the perfusion cultivation. 5.4.2 OUR and CER Estimation 5.4.2.1 Comparison of Mass Balance and Dynamic O U R Estimates Two independent techniques were used for O U R estimation. In the M B approach, O U R was determined using Eq.(5.1) from the inlet and outlet gas stream oxygen concentrations. O U R estimation by the dynamic method was done off-line in a 2 L batch bioreactor using a sample from the perfusion bioreactor. A representative DO time profile in the 2 L batch reactor is shown in Figure 5.4 and DO data in the 60 - 30% range were used for O U R estimation. A comparison of O U R estimates from these two methods for six different samples is shown in Figure 5.5. O U R estimates from both methods were comparable with the maxi- mum difference being 13.4%. Percentage differences in O U R estimates from these methods were computed based on the assumption that dynamic method estimates were accurate while those from the G M B were in error. This is a reasonable assumption given the sim- plicity of the dynamic method. The mass balance approach requires accurate measurement of gas flow rates and gas phase oxygen concentrations that can introduce error in the O U R estimation process. However, despite these limitations, O U R estimates from the mass bal- ance method were in close agreement with those from the dynamic method. CHAPTER 5. OUR AND CER ESTIMATION IN PERFUSION SYSTEMS 99 1.4 r : 1 1.2 j - • _ ' Z • 1.01- rn r—i' r—j 0 . 8 - J a CC. 0 . 6 r - 0 . 4 ; ' -_ 0 . 2 ; . . '• •' o.o r I I I I I I I i I I I I I I I I I I I I I I I I - w o w 0 i - i - i n i n i n w i n <o h - "O C\t T> O X> C\i O T3 h~' " " I « T « f f s 7 ^ ^ ? Q E O ? I - I - I - ? I - ro O TO ro 55 co 55 55 Steady States Figure 5.8: Respiratory quotient (RQ) estimates for the 12 experimental conditions in the perfusion cultivation. 5.4.2.2 O U R , C E R and R Q at Varying Operating Conditions O U R values at different DO, temperature and pH set points are shown in Figure 5,6. The values are averages over their respective experimental conditions along with their'associated standard deviations. While O U R values were, mostly unchanged across most experimental conditions, they were lower at T = 30.5 °C and pH = 6.6 where an overall reduction in growth (Figure 5.3) and metabolism (not shown) were observed. The lowest C E R values of 4.02 and 4.15 pmol/cell-d were also observed at T = 30.5 °C and pH = 6.6, respectively, while those at otlier set points were relatively similar (Figure 5.7). RQ values estimated from the average O U R and C E R values ranged from 0.96 - 1.18 (Figure 5.8) suggesting minimal impact of DO, temperature and pH set point changes on' RQ. 5.5 Discussion 5.5.1 OUR, CER and RQ Estimation We have presented methods to estimate O U R and C E R in mammalian cell perfusion systems using the global mass balance method. This approach does not require k^a data and no reactor perturbations are necessary. Composition and flow rates of the inlet and exit gas streams along with other routinely measured quantities are adequate for O U R and C E R CHAPTER 5. OUR AND CER ESTIMATION IN PERFUSION SYSTEMS 100 Table 5 . 1 : Published OUR values for mammalian cells O U R (pmol /ce l l -d) C e l l L i n e Reference 3.6-8.64 Hybridoma [27] 5.62 Hybridoma [28] 1.2. Human diploid cells [29] 4.56 - 9.6 Hybridoma • [2, 30-32] 0.55 - 2.09 Hybridoma [4] 7.92 - 8.88 Hybridoma [33] 3.6 Hybridoma [13] 5.26 - 9.74 Myeloma [14] 11.04 Hybridoma [10] 5.52-10.08 Hybridoma •[34]. 10.1 •- 10.7 . Hybridoma [1] 3.97 - 5.77 C H O This Study estimation. Real-time OUR, C E R and RQ estimations are possible (data could be generated every second if desired) because the required measurements and calculations can be rapidly performed. In addition to providing valuable information on cell metabolism, this enables real-time determination of metabolic fluxes providing additional insights into cell physiology. 5.5.2 Comparison with Literature Data Changes to temperature and pH had the most effect on O U R and C E R while D O in the 20 - 100% range had minimal effect (Figures 5.6 and 5.7). O U R values ranged from 3.97 - 5.77 pmol/cell-d and the low values of 3.97 and 4.07 were at T = 30.5 °C and pH = 6.6, respectively. Similar C E R trends were seen with values of 4.02 and 4.15 pmol/cell- d at T = 30.5 °C and pH = 6.6, respectively (CER range was 4.02 - 6.36 pmol/cell-d). Published O U R values for mammalian cells are shown in Table 5.1 and are in the 0.55 - 10.7 pmol/cell-d range. Values for C H O cells obtained in this study were clustered in the middle of this range. C E R values for hybridoma cells in chemostat culture were in the 9.9 - 11.1 pmol/cell-d range [1] while those in batch culture varied between 1.2 and 8.4 pmol/cell-d [21]. Our values for C H O cells were lower than the hybridoma chemostat data and closer to those observed in the batch hybridoma cultivations. Despite significant changes to O U R and C E R at low temperature and pH, they were correlated such that RQ values-were relatively unchanged. R Q values were close to unity (0.96 - 1.18, Figure 5.8) under all experimental conditions and part of the variation was likely due to error in O U R and C E R estimates. For instance, a 10% error in O U R can cause BIBLIOGRAPHY 101 RQ to vary between 0.9 and 1.1 (neglecting C E R error). The maximum difference between mass balance and dynamic O U R estimates was 13.4% (Figure 5.5) indicating that O U R estimates could be associated with ~10% error. It is likely that errors of similar magnitude were associated with the C E R values and a combination of these errors could be responsible for RQ variation in the 0.96 - 1.18 range. It is unlikely that cell metabolism was responsible for RQ changes because 1 mol of N A D H accompanies 0.5 mol of C 0 2 production and this N A D H is oxidized by 0.5 mol of oxygen. While fatty acid synthesis can result in R Q values greater than unity [1], it is unlikely that fluxes through these reactions are significant enough to cause an RQ increase on the order of 20%. 5.6 Conclusions We have presented methods to estimate OUR, C E R and RQ from mammalian cells in perfusion culture. These are based on global mass balance expressions and do not require k^a information and bioreactor perturbations. They are especially suited for perfusion systems where k^a values change over the course of the cultivation and the dynamic method is not applicable. O U R estimates from the global mass balance method were in good agreement with estimates from the dynamic method and the maximum difference was 13.4%. Accurate C E R estimation was possible by accounting for the dissociation of cellular C O 2 into H 2 C 0 3 , HCO3 and CO3" and the effect of temperature and ionic strength on the equilibria of the dissociation reactions. This C E R estimation method is general and works when bicarbonate is present both in the medium and base. Since all necessary measurements can be made on-line, real time O U R and C E R estimation is possible. 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' BIBLIOGRAPHY 103 [14] Yoon, S.; Konstantinov, K . Continuous, real-time monitoring of the oxygen uptake rate (OUR) in animal cell bioreactors. Biotechnol. Bioeng., 1994, 44, 983-990. [15] Aiba, S.; FUruse, H . Some comments on respiratory quotient (RQ) determination from the analysis of exit gas from a fermentor. Biotechnol. Bioeng., 1990, 36, 534-538. [16] Ho, O ; Smith, M . ; Shanahan, J . Carbon dioxide transfer in biochemical reactors. Advances in Biochemical Engineering, 1987, 35, 83-125. [17] Minkevich, I.; Neubert, M . Influence of carbon dioxide solubility on the acuracy of mea- surements of carbon dioxide production rate by gas balance technique. Acta Biotech- nology, 1985, 5, 137-143. [18] Royce, P. Effect of changes in the pH and carbon dioxide evolution rate on the measured respiratory quotient of fermentations. Biotechnol. Bioeng., 1992, 40, 1129-1138. [19] Royce, P.; Thornhill, N . Estimation of dissolved carbon dioxide concentrations in aerobic fermentations. 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[26] Schumpe, A . ; Quicker, G.; Deckwer, W . D. Gas solubilities in microbial culture media. Adv. Biochem. Eng. Biotechnol, 1982 , 24, 1-38. BIBLIOGRAPHY 104 [27] Backer, M . ; Metzger, L . ; Slab.er, P.; Nevitt, K . ; Boder, G. Large-scale production of monoclonal antibodies in suspension culture. Biotechnol. Bioeng., 1988, 32, 993-1000. [28] Dorresteijn, R. C ; Numan, K . H . ; D., .d. G. ('.: Tramper, J.; Beuvery, E . C. On-line estimation of the biomass activity during animal-cell cultivations, Biotechnol. Bioeng.; 1996, 50, 206-214. [29] Fleischaker, R.; Sinskey, A . J . Oxygen demand and supply in cell culture. Appl. Microbiol. Biotechnol, 1981, 12. 193 197. '. [30] Miller, W.; Blanch, H. ; Wilke, C. A kinetic analysis of hybridoma growth and metabolism in batch and continuous suspension culture: Effect of nutrient concen- tration, dilution rate and pH. Biotechnol. Bioeng., 1987, 32, 947-965. [31] Miller, W.; Wilke, C ; Blanch, H . 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Part III Robust Specific Ra te and Metabo l ic F l u x Es t imat ion 105 C h a p t e r 6 L o g i s t i c M o d e l i n g o f B a t c h a n d F e d - b a t c h K i n e t i c s 1 6.1 Introduction There has been an increasing use of mammalian cell cultures for the manufacture of com- plex therapeutic proteins. However, protein yields from mammalian culture are relatively low, requiring the optimization of cell lines, medium formulations and bioprocesses. These optimization efforts typically first involve evaluating non-instrumented batch cultivations (typically <100 mL working volume) in T-flasks, spinners or roller bottles where cell growth, metabolism and protein productivity are monitored over the course of the experiment. This provides information used, to select the cell lines and medium components that maximize protein yields. Further bioprocess optimization, in either fed-batch or continuous perfu- sion cultivations, is mainly performed using laboratory-scale (>1 L) bioreactors. While maximizing specific protein productivity is often the primary, objective in laboratory-scale experiments, ensuring robust cell growth and metabolism are also important. All these vari- ables^ of interest are quantified using cell specific rates that;, enable comparison of cell lines and cultivation conditions. Accurate estimation of specific rates is thus vital to meaningfully interpret results from bioprocess .optimization experiments. While specific rates for steady-state perfusion cultures are readily computed because of their' relatively time-invariant nature, analyzing the dynamic kinetics of batch and.fed- batch cultures is more challenging. A conventional approach to model mammalian cells in .-A version of this/chapter h a s ' b e e n published: Goudar, C:T., Joeris, K. , Konstantinov, K. and Piret, J.M. (2005) Logistic equations effectively,model mammalian ceil batch and fed:batch kinetics by logically constraining the fit. Biotechnology, Progress, 21, 1109-1118. 106 CHAPTER 6. LOGISTIC MODELINQ, OF BATCH AND FED-BATCH KINETICS 107 batch and fed-batch cultures has been through the use of unstructured kinetic models or variations of the classical Monod equation [1-5], and reviews of these models are available [6, 7]. While unstructured kinetic models have adequately described experimental data, they are computationally not practical to implement as they involve nonlinear estimation of a large number of kinetic parameters from a system of differential equations. Unique estimation of the kinetic parameters in such systems is not always possible. Moreover, given the variety of unstructured kinetic models that have been used to describe mammalian cell cultures, comparisons between studies is complicated. Analytical solutions of the differential equations describing the state variables have also been used to estimate specific rates [8- 11]. These solutions, however, are derived under the assumption that the specific rates are constant as can be expected during the exponential growth phase. These have limited applicability to the other phases of batch and fed-batch cultures where specific rates are not constant. Specific rates in fed-batch cultures have also been estimated from the slope on plots of cumulative state variables (nutrient, metabolite or product) versus integral viable cell density [12, 13]. This approach provides an average estimate of the specific rate of interest over the exponential growth phase but additional linear or nonlinear fits need to be used for other cultivation phases. This need for multiple fits to describe the time course of a single variable makes this approach cumbersome and prone to error. A general approach that is applicable over the entire time course of cultures, is fitting polynomials to the data [14, 15]. This approach has been used both for batch and fed-batch cultivations and is attractive because it allows simplified computation of the time derivatives necessary to estimate cell specific rates. However, as time profiles of cellular, nutrient and product concentrations exhibit exponential behavior, they are difficult to describe by polynomials [16]. For instance, two polynomial functions were necessary to describe the time course of some state variables [14]. Moreover, polynomial fits are known to yield unrealistic trends, especially when the data include even a few outliers. Logistic equations have been successfully used to describe population dynamics in a variety of applications [17-23] but have not been reported to model experimental data from mammalian cell batch or fed-batch cultures. Most reported applications involve bacterial growth curves characterized by lag, exponential and stationary phases that are adequately described by the logistic growth equation. Mammalian cells in batch and fed-batch cultiva- tions also exhibit, a sharp decline in cell density following the stationary phase, a behavior that cannot be described by the standard logistic growth equation. In addition, a decline in lactate concentration during later stages of fed-batch cultivation is also frequently observed [13, 24]. Alternate logistic formulations that incorporate both the ascending and descending components of cell growth are available [25]. CHAPTER 6. LOGISTIC MODELING OF BATCH AND FED-BATCH KINETICS 108 This study presents a method for modeling batch and fed-batch mammalian cell culture data using logistic equations. A n alternate logistic formulation was applied to cases where variables had both increasing and decreasing phases. Cell specific rates were readily obtained from the analytically differentiable logistic equations. A comparison was made between this logistic modeling approach and the polynomial fitting or the unstructured kinetic modeling approaches that are commonly used to describe batch and fed-batch data. 6.2 Theory 6.2.1 Calculation of Batch Culture Specific Rates Most batch kinetic studies have used discrete forms to compute specific rates. The wide- spread use of this approach is primarily due to its simplicity as seen from the specific growth rate expression A Y where /J,' is the apparent specific growth rate (l/day) over an interval from t\ to t2, \i the actual specific growth rate (l /day), ko the specific death rate, (l /day), Xv the viable cell density (x 10 6 cells/mL), AXV = XV2 -XVl, t is time (day), A t = t2 — t\ and Xv = "2 2 V l . Thus AXV and A i represent the difference between successive viable cell density and time points-, respectively, while Xv is the arithmetic average of the consecutive cell density data points. A log-normal average can also be used for Xv during the exponential growth phase but this provides a. poor estimate for the average Xv in the decline phase. For intervals of constant apparent growth rate, a more accurate estimate of LL' can be obtained by combining multiple data points. However, when this constant growth rate ends and how the growth rate changes beyond that point remain difficult to accurately compute. The primary sources of carbon and energy in a typical mammalian cell culture medium are glucose and glutamine. The specific consumption rate of glucose can be calculated from Q C = _ J ^ L (6.2) ^ XyAt ^ ' where qc is the specific glucose consumption rate (pmol/cell-day) and A G = G2 — G\ is the difference in glucose concentration over consecutive data points (mol/L). The primary known toxic metabolites of glucose and glutamine metabolism are lactate and ammonium, CHAPTER 6. LOGISTIC MODELING- OF BATCH AND FED-BATCH KINETICS 109 respectively. These metabolite as well as protein production rates can be calculated from where qp is the specific production rate (pg/cell-day) and A P = P2•— Pi is the change in metabolite/product concentration over consecutive data points (g/L). 6.2.2 Calculation of Fed-batch Culture Specific Rates Fed-batch cultivations typically, involve the periodic feeding of glucose, glutamine and other medium components. Hence nutrient mass balance expressions are modified to take the feeding into account while the expressions for Cell density, metabolites and products are essentially identical to those in a simple batch cultivation (when dilution effects can be neglected). For example, specific glutamine uptake rate in a continuously fed batch reactor can be described by AG In FGlnt , Gin ,n-tS • . • q a h ! ---x^Ai+V-x7 ' • : • (6;4). where..qcin is the specific glutamine uptake rate (pmol/cell-day), AGlh—.Gln2 — Gln\ the. change in glutamine concentration over consecutive data points (mol/L), F the glutamine feed rate (L/day), V the bioreactor working volume (L), Glnf the glutamine concentration in the feed (mol/L) and koin the first-order abiotic degradation constant for glutamine with values depending on the medium composition, temperature and culture pH [26], The last term in the right hand side of Eq.( 6.4) accounts for abiotic glutamine .degradation at cultivation temperature. 6.2.3 A General Equation Describing the Dynamics of Batch and Fed- batch Cultures The selection of final process parameters from optimization experiments' is derived mainly from comparisons of cell specific productivity and growth rate. Therefore; it is important to reliably estimate these rates'from sequential data points and Eqs.(6.1) - (6.4). However, this typically yields erratic time profiles since this method is sensitive to the measurement errors common in biological systems. Mathematical models that. describe the dynamics of cellular growth and protein production according to expected trends can provide more robust estimates of the cell specific variables of interest. Such models should more smoothly and logically fit the experimental data. For instance, to describe viable cell density (X) in batch and fed-batch systems requires initially, increasing and subsequently decreasing levels. CHAPTER 6. LOGISTIC MODELING OF BATCH AND FED-BATCH KINETICS 110 This cannot be fit by a simple exponential growth model (Eq.6.1) or by the commonly used logistic growth equation. It is proposed that a four-parameter generalized logistic equation (GLE) should be used to describe viable cell concentration [25]. • A exp (Bi) + C exp (-£>*). V ' J where A , B, C and D are non-negative model parameters that are specific to the data set being modeled. It is informative to relate the logistic equation parameters to correspond- ing biological process parameters. The contribution of exp (Bt) is minimal in the growth phase and when set to zero, Eq.(6.5) reduces to an exponential growth equation with D as the specific growth rate. Similarly, neglecting contributions of C exp (—Dt) during the cell death phase reduces Eq.(6l5) to an exponential decay expression with B as the death rate. The parameters D and B thus represent the maximum growth rate, ^ m a x , and the maxi- mum death rate, fcrfmax, respectively. These would be constant in the exponential growth and corresponding decline phases, respectively. Simulations were performed to test this hypothesis and Figure 6.1 illustrates sensitivity of the cell density curve to D and B and hence Mmax a n d kdm3uX values. As expected, changes to n m a x affect the exponential growth phase while the influence is negligible in the decay phase, especially for t > 1.5t m a x (Figure 6.1a). Sensitivity to ^ m a x is minimal for t < 0 .5 t m a x while later portions of the cell density curve are significantly affected (Figure 6.1b). Eq.(6.5) can thus be written in terms of / i m a x and k.i ,. as A . (6 6) • e X P ( f a m „ * ) + C e X P (-^max*) •• The initial cell density, XQ, can be expressed in terms of A and C by setting t — 0 in Eq.(6.6). Setting the derivative of Eq.(6.6), ^ = 0 provides an equation for i m a x ! the time corre- sponding to the maximum, cell density imax =- 7 ]• -An(^A (6,8) ^ d m a x + Mmax V Kdma.x / A n estimate for X m a x , the maximum cell density attained during the cultivation, can be obtained from substituting Eq. (6.8) into Eq.(6.6) It must be noted that Eq.(6.5) could also fit' the successive ascending and descending CHAPTER 6. LOGISTIC MODELING OF BATCH AND FED-BATCH KINETICS 111 30 >, 25 S E 20 o ^ " S O 1 5 o " ""o 10 ro 5 10 15 Time (days) 20 (b) Decreasing kd^ \ \ . \ \ \ /CL \ \ . \ 5 10 15 Time (days) F i g u r e 6 . 1 : Sensitivity of the viable cell density curve to the logistic parameters- D (£im a x) and B (fcdmax)- Successive curves are for 25% decreased parameters compared to the previ- ous curve. lactate concentrations often observed in fed-batch culture. Most other product and nutrient concentrations can be expected to monotonically increase or decrease, respectively, over the whole duration of the run (expect at times of fed-batch additions).' This suggests that simplified forms of Eq.(6.5) could effectively describe the concentrations of nutrients and products in batch or fed-batch cultivations. Setting B —> 0 in Eq.(6.5) results in the logistic growth equation (LGE) that can be used to describe a monotonically increasing product concentration, Pi . • • A . • " ' ' F ~ M - C e x p ( Dt) ( 6 ' 9 ) The parameter D is a rate constant for concentration increase and definitions of A and C can be obtained by setting ^ • = 0 and t -- 0 in Eq.(6.9), respectively . A = Prr C Pmax Pp Pn • (6.10) CHAPTER 6. LOGISTIC MODELING: OF BATCH AND FED-BATCH KINETICS 112 where Pmax is the maximum value of P and PQ the initial value at t = 0. Using these definitions, the L G E can be rewritten to be consistent with other presentations in the literature [27] . P = - P o j P m a x (6.11) P0 + (Pmax - P 0 ) exp {-Dt) Setting D —* 0 in Eq.(6.5) results in the logistic decline equation (LDE) that can be used to describe any monotonically decreasing nutrient concentration, N: where B is a rate constant for concentration decrease and A and C are related to the initial nutrient concentration, iVo, as: N° = TTc • (6'13) Specific rates could be readily estimated from the logistic models as Eqs. (6.5), (6.9) and (6.12) are analytically differentiable: dX _ f DC exp {-Dt) - B exp (Bt) \ dt \ exp (St)+ C exp (-£>*) J { ' 1 6.3 Materials and Methods 6.3.1 Cell Line, Medium and Cell Culture System C H O cells were cultivated in batch mode with glucose and glutamine as the main carbon and energy sources in a proprietary medium formulation. Experiments were conducted in three 15 L bioreactors (Applikon, Foster City, C A ) with a 10 L working volume. The temperature was maintained at 36.5 °C and the agitation at 40 R P M . The dissolved oxygen (DO) concentration was maintained at 50% air saturation by sparging a mixture of oxygen and nitrogen (100 - 150 mL/min) through 0.5 /im spargers. The bioreactor was inoculated at an initial cell density of approximately 1.0 x 106 cells/mL and the pH was maintained at 6.8 by the automatic addition of 0.3 M NaOH. CHAPTER 6. LOGISTIC MODELING: OF BATCH AND FED-BATCH KINETICS 113 6.3.2 Analytical Methods Samples from the bioreactor were taken daily for cell density and viability analyses using the C E D E X system (Innovatis, Bielefeld, Germany). The samples were subsequently cen- trifuged (Beckman Coulter, Fullerton, CA) and the supernatants were analyzed for nutrient and metabolite concentrations. Glucose, lactate, glutamine and glutamate concentrations were determined using a YSI Model 2700 analyzer (Yellow Springs Instruments, Yellow Springs, OH) while ammonium was measured by an Ektachem DT60 analyzer (Eastman Kodak, Rochester. N Y ) . The pH and DO were measured online using retractable electrodes (Mettler-Toledo Inc., Columbus, OH) and their measurement accuracy was verified through off-line analysis in a Stat Profile 9 blood gas analyzer (Nova Biomedical, Waltham, M A ) . The same instrument also measured the dissolved C O 2 concentration. On-line measurements of cell density were made with a retractable optical density probe (Aquasant Messtechnik, Bubendorf, Switzerland), calibrated with heamocytometer counts of cell concentrations. 6.3.3 Nonlinear Parameter Estimation The parameters A, B, C and D in Eqs.(6.5), (6.9) and (6.12) were estimated by minimizing the sum of squares error (SSE) between the experimental and model fit data. where (xmeas)i is the ith experimental x value and [xfit)i is the i model fitted x value in a total of j observations. Eq.(6.5) involved the sum of exponentials and was inherently unstable. Hence three different algorithms were used for nonlinear parameter estimation: the Levenberg-Marquardt method [28], the simplex approach [29] and the generalized re- duced gradient method [30, 31]. The parameters used were those that resulted in the lowest values of the SSE defined in Eq.(6.17). The parameter standard errors and the correlation between parameters were estimated from the covariance matrix to help evaluate the quality of the model fit to the experimental data. When multiple models with different degrees of freedom were fitted to the same data set, the F test [32] was used to discriminate among the models. Computer programs for logistic modeling are presented in Appendix F and nonlinear parameter estimation details are provided in Appendix G. 3 (6.17) CHAPTER 6. LOGISTIC MODELING,, OF BATCH AND FED-BATCH KINETICS 114 6.4 Results and Discussion 6.4.1 Biological Significance of the Logistic Parameters The exponential growth and death phases were defined as 0 < t < 0 . 5 £ m a x and 1.5£ m a x < t < 2 £ m a x , respectively, based on an examination of the cell density profiles from Figure 6.1. To verify these definitions, / i m a x and &d m a x were computed from all' the cell concentration data analyzed in this work and compared with the logistic parameters D and B. Excellent agreement between the maximum rates and the logistic parameters was seen in" all cases (Figure 6.2a, 6.2b) supporting the reformulation of Eq.(6.5) as Eq.(6.6). The utility of Eqs.(6.6) and (6.8) to predict the maximum cell density in batch and fed-batch cultures was verified by comparing Xmax values calculated from these equations with experimental data (Figure 6.2c). For all 15 data sets, experimentally observed maximum cell densities were accurately predicted by Eqs. (6.6) and (6.8) and the fitted logistic .parameters. (a) • / R 2 = 0.945 Umax (1/<0 2.0 . o.o I •— >—-J ' 1 ' ' • 1 0.0 0,4 0.8 1.2 1.6 2.0 0 2 4 f> £ 10 12 14 Experimental X m a x (106 cells/mL) Figure 6.2: Illustration, of the biological significance of the logistic parameters using 8 batch and 7 fed-batch cell density data sets [1, 14, 33, 34]. CHAPTER 6. LOGISTIC MODELING OF BATCH AND FED-BATCH KINETICS 115 6.4.2 Description of Experimental Data from Batch Cultures The time profiles of CHO. cell density, nutrient and metabolite concentrations along with the logistic model fits are shown in Figure 6.3. The G L E was first used to describe all the state variables measured in this experiment. Subsequently, the L D E was used to describe the monotonically decreasing glucose and glutamine concentrations while the L G E was used to describe the increasing lactate and ammonium concentrations. Model discrimination using the F test indicated that the L D E and L G E fits were statistically superior to the G L E at the 95% confidence level for the nutrient and metabolite concentrations, respectively, and hence results from these equations are presented in Figure 6.3. The experimental data were well fitted by the models and the corresponding specific rates were calculated from Eqs. (6.1) - (6,3) using analytical derivatives of the logistic equations (Eqs.6.14 - 6.16). 14 I • r -^ 1 ' 1 ' 1 ' 1 ' 1 0.6 T i m e (days) , T i m e (days) Figure 6.3: Time profiles of cell density, nutrient and'metabolite concentrations for CHO cells in 15 L batch culture. Experimental .data (•' • • o •); Logistic (GLE for cell density, LDE • for glucose and glutamine and LGE for lactate and ammonium) fit ( ); Logistic specific rate (—, — - — —): Discrete derivative-specific rate .(—•• •'— •'•). CHAPTER 6. LOGISTIC MODELING OF BATCH AND FED-BATCH KINETICS 116 It is remarkable that the model fit the data so well even though logistic models do not include independent terms for growth-related and maintenance-related metabolism. This could be in part due to the predominant effect of exponential cell growth compared to relatively gradual shifts over a batch culture of growth- or maintenance-related metabolic rates. From a practical standpoint, the use of a single equation and its reduced forms to describe all experimental measurements in batch (or fed-batch) cultivations adds to the simplicity of the proposed logistic approach. Time (days) Time (days) (C) 1 0 ? E Time (days) Figure 6 .4 : Viable cell density, IgG, glutamine and'ammonium concentrations for hybridoma cells in 300 L batch culture [l]:.- The points.are experimental data and the solid lines are fits by the logistic equations (GLE for cell density, LDE for glutamine and L G E for IgG and ammonium).- Specific rates calculated from the logistic fits are shown as.dashed lines. Experimental data from batch cultivations are obtained from periodic samples whose concentrations are analyzed and then the data are converted to the corresponding derivatives to obtain specific rates. The logistic equations provided smooth and close fits to all of the concentration data, thereby yielding smooth logistic specific rate profiles (Figure 6.3). In contrast, specific rates obtained using discrete derivatives of the state variables were not smooth and were highly sensitive to outliers in experimental measurements. Though the discretely derived qgin values were acceptable, those for glucose and ammonium were in CHAPTER 6. LOGISTIC MODELING. OF BATCH AND FED-BATCH KINETICS 117 gross error, primarily due to outliers in the experimental data. The ii' and specific lactate production rate, qit profiles were similar to those from the logistic fits, albeit not as smooth. In all cases besides qcin> physiologically' implausible oscillations were introduced by the discrete fit and not by the logistic fit. • . ' Table 6.1: Previously-published batch and fed-batch studies used to test the logistic modeling approach presented in this study Reference C e l l L i n e Bioreac tor T y p e M o d e l i n g A p p r o a c h [1] Hybridoma Stirred tank (300 L batch) Kinetic modeling [33] Hybridoma T-flask (100 mL batch) Kinetic modeling [14] B H K Spinner (500 mL batch) Polynomial fitting [15] Hybridoma Bench-top (2.4 L fed-batch) Polynomial fitting [34] C H O , Hybridoma Bench-top (0.7 L fed-batch) Discrete derivatives The more general utility of this logistic approach was further evaluated using data from published batch studies that investigated different cell lines (hybridoma and Baby Hamster Kidney) in bioreactors ranging from 150 cm 2 T-flasks to 300 L stirred tanks (Table 6.1). Two of these studies [1, 33] used Monod-type kinetics to describe the experimental data while experimental data were fitted by polynomial functions in the third [14]. Results from using the logistic equations to describe the data from two of these experiments are shown in Figures 6.4 and 6.5. The nutrient, metabolite and product concentrations were fit by the L D E and L G E models while the four-parameter G L E was necessary to describe the dynamics of viable cell concentration. In all cases, the experimental data were well described by the logistic equations and similar good fits were obtained for data from the third study (not shown). These results clearly indicate the applicability of the logistic models to describe experimental data obtained by multiple groups from batch reactors of varying sizes and cell types. • . . . 6.4.3 Description of Experimental Data from Fed-Batch Cultures These logistic methods would be much more useful if they could be applied to fed-batch cultures that become the focus of later stages of development and manufacturing. However, it was a concern that periodic feeding of nutrients would distort the resulting profiles so that the logistic approach might ;not be suitable. Fed-batch data from two studies [15, 34] (Table 6.1) were analyzed using the logistic, equations.. In the first study [15], hybridoma cells were cultivated in a 2.4 L bioreactor with the feeding of glucose or glutamine or both. The second involved cultivation of tissue plasminogen activator (t-PA) producing C H O cells CHAPTER 6. LOGISTIC MODELING OF BATCH AND FED-BATCH KINETICS 118 ™ ~ 1.5 1̂ •5 « 1.0 N \ • (a). -\ n' \ / \ / • 7 \ / x • / \ • Time (days) T i m e (days) T ime (days) T i m e (days) T i m e (days) Figure 6 .5 : Viable cell density, nutrient and metabolite concentrations for BHK cells in 500 mL batch culture [14]. The points are experimental data and the solid lines are fits'by the logistic equations (GLE for cell density, LDE for glucose and glutamine and LGE for lactate and ammonium). Specific rates calculated from the logistic fits are shown as dashed lines. in a 0.7 L bioreactor with glucose or amino acid feeding. Data from glutamine limited fed-batch hybridoma cultures are shown in Figure 6.6 along with corresponding logistic fits. A l l variables except glutamine (the nutrient that was fed) were fit well by the logistic equations. Time profiles of the-fed nutrient will depend strongly on the feeding strategy, often with concentrations at low values to minimize the production of metabolites [13, 35]. The logistic equations cannot be expected to effectively fit such fed- nutrient profiles. A total of 20 data sets were analyzed from the C H O fed-batch cultivations [34] and representative cell density and t-PA concentration data under two different feeding conditions are shown in Figure 6.7. The logistic equations fit the data well as was true for the remaining 16 data sets (not shown). It should be noted that the 4-parameter G L E was used to describe t-PA concentration due to the declining trend later in the culture. Similar CHAPTER 6. LOGISTIC MODELING, OF BATCH AND FED-BATCH KINETICS 119 1.4 I . 1 . 1 . 1 1 • 1 0.08 0.0 ' ' 1 ' ' ' 1 ' 1 ' ' -0.04 0 20 40 60 60 100 Time (h) 0 - 20 40 60 ' 80 • 100 0 20 40 60 80 100 Time (h) Time (h) F i g u r e 6 . 6 : Viable cell density, nutrient and metabolite concentrations for hybridoma cells.in glu- tamine limited 2A L fed-batch culture [15]. The points; are experimental data and the solid lines are fits by the logistic equations (GLE for cell density, LDE for glucose and glutamine and L G E for lactate and ammonium). Specific rates calculated from the logistic fits are shown as dashed lines. declines have been observed for lactate concentration in fed-batch cultures [24] and in such instances, the G L E (as opposed to the L G E ) more effectively fits those experimental data. 6.4.4 Comparison with Other Model ing Approaches Polynomial approximation and .unstructured. kinetic modeling are the primary methods currently used to fit data from batch and fed-batch experiments. Given the conceptual similarity between the logistic modeling approach presented in this study and polynomial approximation, it is important to compare their ability to describe mammalian cell culture data.. Polynomial approximation has limitations because exponential state variable time profiles are difficult to describe with polynomial functions [16]. The same 30 data sets from batch cultures were also analyzed using polynomial fitting and the inability to describe the CHAPTER 6. LOGISTIC MODELING OF BATCH AND FED-BATCH KINETICS 120 E, Time (days) = 1 1 9 1 - / ^ \ / \ X J \ N \ 9/ \ i 2 4 6 Time (days) 0.6 0.4 0.2 _ 0.0 5 -0.2 3 - -0.4 -0.6 Figure 6.7: Viable cell density and t-PA concentration for CHO cells in 0.7 L fed-batch culture under two different feeding conditions [34], Glucose was fed at 4 pmol/cell-day for panels a- and b while amino acids were also fed for panels c and d. . The points are experimental data and the solid lines are fits by the logistic equations (GLE for both cell density and t-PA). Specific rates calculated from the logistic fits are shown as dashed lines. experimental data was quantified by the Eq.(6.17) sum of squares errors to compare with logistic fitting. Since increasing, the order of a polynomial function could result in a better fit to experimental data, polynomial functions with one additional parameter than the corresponding logistic equation were also evaluated. For instance, the viable cell density description using Eq.(6.5) has 4 parameters and this was compared with polynomials of orders 3 (4 parameters) and 4 (5 parameters). Comparisons between logistic equations and polynomials of the same order used the SSE values while comparisons between logistic equations and higher order polynomials were done using the F-test. The F-test determined if the higher order polynomial fit was indeed a closer representation at the 95 % confidence level. Of the 30 batch data sets examined using both the logistic and polynomial approaches, the polynomial approach was statistically superior in only. 3 instances. It is important to note that even in the few cases of statistical superiority for the polynomial fit, these did CHAPTER 6. LOGISTIC MODELING, OF BATCH AND FED-BATCH KINETICS 121 0 2 4 . 6 8 10 12 T i m e (days) F i g u r e 6.8: Comparison of qcin values from logistic (LDE) and polynomial fits for C H O cells in 15 L batch culture. The polynomial fit to glutamine depletion data was statistically superior than the logistic fit for this data set. not necessarily yield improved specific rate estimates. Figure 6.8 shows specific glutamine consumption rates for C H O cells that was one of the above mentioned 3 cases where the polynomial fit was statistically superior to the logistic fit. A n examination of the specific rate data from the polynomial fit indicates that data after t = 9 days were negative, suggesting net glutamine production. This is not reflective of the biology and is an artifact due to an inflexion in the polynomial fit to the data at t = 9 days and beyond. The logistic modeling approach does not suffer from such errors. Instead the fits are constrained to the expected trends, monotonic in this case. Logistic and polynomial fits to the data from Dalili et al. [33] are shown in Figure 6.9 as examples of the data sets where the logistic approach was statistically superior. Both polynomials grossly misrepresented the time course of viable cell density and no improve- ment was obtained by increasing the order of the polynomial. Computation of growth rates from either of the polynomial fits would not be acceptable. Similar limitations, albeit to. a lesser extent, were seen for the IgG and glutamine data sets in Figure 6.9. The polynomial approach thus lacks generality and cannot be relied upon as a robust tool for specific rate estimation in batch cultures. Unstructured kinetic modeling involves the use of Monod-type equations and estimating a large number of kinetic parameters by nonlinear optimization in the system of differential equations. Two batch studies [1, 33], whose data were used in this study for verification CHAPTER 6. LOGISTIC MODELING OF BATCH AND FED-BATCH KINETICS 122 & 6 X'M 4 O w 4 > ° ' -2 0 2 <i 6 . 8 T i m e ( d a y s ) •J "B> 4 E. O 2 Oi -2 0 2 4 6 8 T i m e ( d a y s ) ' 0.6 ' 0.5 < £ 0.4 « 0.3 c E 0.2 re = 0.1 o 0.0 -0.1 • 0 2 ' ' 4 6 8 T i m e ( d a y s ) Figure 6.9: Comparison of logistic (GLE for cell density, L G E for IgG and LDE for glutamine) and polynomial fits for batch cultivation of hybridoma cells in 100 mL T-flasks [33]. (—: ) logistic fit; ( ) polynomial fit with the same number of parameters as the logistic fit; (—.. — ••) polynomial fit with one additional parameter (The two polynomial fits in panel c overlap). of the logistic approach, employed modified forms of the Monod equation in kinetic ex- pressions to describe their experimental data. One used simpler kinetic expressions for glutamine limited cultures [33], requiring 8 parameters to be estimated while 13 parame- ters were required for a more comprehensive kinetic model [1]. Estimating such a large number of kinetic parameters through nonlinear least squares from a system of nonlinear differential equations is not trivial and is unlikely to provide robust parameter estimates due to the strong correlation among the kinetic parameters. Moreover, the large variability in the kinetic models used [6, 7] makes it difficult to compare results from different studies employing this approach. CHAPTER 6. LOGISTIC MODELING, OF BATCH AND FED-BATCH KINETICS 123 6.4.5 Computation of Integral Quantities The integral viable cell density is an important parameter for the characterization of batch and fed-batch cultures [36]. Since it corresponds to the area under the curve in a plot of viable cell density versus time, it can be computed by integrating Eq.(6.5). However, Eq.(6.5) cannot be analytically integrated because of the sum of exponential terms in the denominator and an approximation to this integral is presented in Appendix F . Alterna- tively, a simple numerical technique, such as the trapezoidal or any higher-order quadrature rule [37], can be used to estimate the integral viable cell density from Eq.(6.5). 6.4.6 Data for Estimation of Metabolic Fluxes A n original motivation for this work was in the context of metabolic flux analysis that is increasingly used to characterize cellular metabolism and physiology by estimating fluxes through the pathways of central carbon metabolism [38]. Input data for metabolic flux analysis include specific uptake and production rates in addition to cellular growth rate. The logistic equations presented in this study provide a practical means of more reliable specific rate estimation that should enable more robust metabolic flux computation in batch and fed-batch cultures. 6.5 Conclusions The application of logistic equations for analyzing mammalian cell batch and fed-batch data has been illustrated. Though non-mechanistic in nature, these equations did provide a means to impose logical general constraints on the fitted profiles. Simplified logistic equa- tion forms were selected based on expected monotonic or increasing followed by decreasing trends. Time profiles of cell density, nutrients and metabolites were well fitted by the logistic equations and time derivatives of these variables were readily computed, resulting in rapid estimation of specific rates. Besides providing valuable information on cellular physiology and metabolism, specific rates are precursors for metabolic flux estimation, thereby allowing improved use of information collected in batch and fed-batch cultivations. This functional representation also allowed for computation of integral viable cell density, an indicator of batch and fed-batch process performance. Another advantage of the logistic approach is its. general nature thereby increasing its applicability to a wide variety of experimental systems as shown in this study. This general nature coupled with the ability to rapidly obtain more robust specific rate estimates should make it an attractive alternative for describing the dynamics of mammalian cell growth and protein production in batch and fed-batch culture. BIBLIOGRAPHY 124 This philosophy of empirical modeling based oh constraining fits to expected trends could be extended to the derivation of other useful models where the complexity of systems makes mechanistic models impractical. . .< Bibliography [1] Bree, M . ; Dhurjati, P.; Geoghegan, R.; Robnett, B . Kinetic modeling of hybridoma cell growth and immunoglobulin production in a large-scale suspension culture. Biotechnol. Bioeng., 1988, 32, 1067-1072. [2] Dhir, S.; Morrow, K . ; Rhinehart, R,; Wiesner, T. Dynamic optimization of hybridoma growth in a fed-batch bioreactor. 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Effect of various glucose/glutamine ratios on hybridoma growth, viability and monoclonal antibody production. Biotechnol. Lett., 1987, 5(8), 691-696. [37] Press, W.; Teukolsky, S.; Vellerling, W.; Flannery, B . Numerical Recipies in FOR- TRAN. The art of scientific computing. Cambridge University Press, Cambridge, 2nd edition, 1992. [38] Stephanopoulos, G.; Stafford, D. Metabolic Engineering: a new frontier of chemical reaction engineering. Chem. Eng. Sci., 2002, 57, 2595-2602. C h a p t e r 7 E r r o r i n Specific Rates and Metabo l ic F luxes 1 7.1 Introduction Metabolic fluxes are considered a fundamental determinant of cell physiology [1] and metabolic flux analysis has been increasingly used to characterize the metabolism of mammalian cell cultures [2-8]. Flux data provide a quantitative description of the cellular response to changing environmental conditions, such as those encountered during bioprocess develop- ment, and are hence useful for bioprocess optimization. The first step in metabolic flux estimation is the construction of a bioreaction network that describes the conversion of sub- strates to metabolites and biomass. These bioreaction networks are typically simplified to enable flux estimation from available experimental data. For mammalian cells, these include the main reactions of central carbon and amino acid metabolism [5, 6, 9]. The unknown fluxes in the bioreaction network are subsequently estimated either using metabolite bal- ancing [2, 3, 6, 8, 10-13] or isotope tracer techniques [9, 14-19]. In the metabolite balancing approach, fluxes are estimated by applying mass balances around the intracellular metabo- lites using the measured extracellular rates as input data. The analytical and computational techniques associated with the metabolite balancing approach are relatively simple [1] and can be readily applied to most experimental systems. This approach, however, cannot deter- mine fluxes in cyclic and bidirectional reactions. Additional shortcomings and approaches to overcome them have been discussed in detail [10, 20]. Despite these limitations, metabolite ' A version of this chapter will be-submitted for publication. Goudar, C.T., Biener, R., Konstantinov, K . B . and Piret. J .M. (2006). Error propagation from prime variables into specific rates and metabolic fluxes for mammalian cells in perfusion culture. 128 CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 129 balancing remains the method of choice for a majority of process development experiments and for all pilot and manufacturing-scale studies given the expense of the isotope tracing alternative. Information on the error associated with metabolic flux values obtained by the metabo- lite balancing approach is critical to meaningfully interpret changes in cellular metabolism. As cell specific rates including growth, nutrient consumption and metabolite production comprise the input data for flux estimation, flux values can be strongly influenced by spe- cific rate errors. Cell specific rates, however, are not experimentally measured but are calculated from measured prime variables including cell, nutrient, metabolite and product concentrations. Information on prime variable error is thus necessary to characterize their influence on specific rate error and ultimately on flux values. The need to have specific rate data with no gross measurement error has been long recognized and a framework has been proposed to check for the presence of gross errors [19, 21, 22]. However, error propagation from prime variables into metabolic fluxes has not been reported. This study is aimed at systematically characterizing error propagation from prime variables to metabolic fluxes for mammalian cells. Prime variable errors were first estimated and their propagation into specific rates and metabolic fluxes was quantified using a combination of experimental data and Monte-Carlo analysis. A n operating flux error region could be identified allowing more reliable interpretation of the calculated fluxes. 7.2 Ma te r i a l s and M e t h o d s 7.2.1 Cell Line, Medium and Cell Culture System C H O cells were cultivated in perfusion mode with glucose and glutamine as the main carbon and energy sources in a proprietary medium formulation. The bioreactor was inoculated at 0.92 x 10 6 cells/mL and cells were accumulated until the bioreactor reached 20 x 10 6 cells/mL at which point the cell concentration was maintained constant by controlling the bleed stream from the bioreactor. Experiments were conducted in a 15 L bioreactor (App- likon, Foster City, CA) with a 10 L working volume. Under standard operating conditions, the temperature was maintained at 36.5 °C and the agitation at 40 rpm. The dissolved oxygen (DO) concentration was maintained at 50% air, saturation by sparging a mixture of oxygen and nitrogen through 0.5 fim spargers. The bioreactor pH was maintained at 6.8 by the addition of 0.3 M NaOH. Temperature, DO and pH were varied during the course of the cultivation resulting in a total of 12 experimental conditions, each of 10 day duration to identify valid operating ranges for these variables. Data from the last 4 days of each ex- CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 130 perimental condition were considered representative (variation < 15%) and used for specific rate and metabolic flux calculations: 7.2.2 Analytical Methods Samples from the bioreactor were analyzed daily for cell concentration and viability using the Cedex system'(Innovatis, Bielefeld, Germany). The samples were subsequently cen- trifuged (Beckman Coulter, Fullerton, CA) and the supernatant was analyzed for nutrient and metabolite concentrations. Glucose, lactate, glutamine and glutamate concentrations were determined using a YSI Model 2700 analyzer (Yellow Springs Instruments, Yellow Springs, OH) while ammonium was measured using an Ektachem DT60 analyzer (Eastman Kodak, Rochester, N Y ) . The pH and D O were measured online using retractable electrodes (Mettler-Toledo Inc., Columbus, OH) and their measurement accuracy was verified through off-line analysis in a Stat Profile 9 blood gas analyzer (Nova Biomedical, Waltham, M A ) . The same instrument also measured the dissolved C 0 2 concentration. On-line measure- ments of cell concentration were made with a retractable optical density probe (Aquasant Messtechnik, Bubendorf, Switzerland) that was calibrated with cell concentrations esti- mated using the Cedex system. Oxygen and carbon-dioxide concentrations in the exit gas were determined using a MGA-1200 Mass Spectrometer (Applied Instrument Technologies, Pomona, CA) 7.2.3 Prime Variables and Specific Rates Errors in prime variable (cell concentration, product, glucose, glutamine, lactate, ammo- nium and oxygen) measurements were estimated by analyzing multiple bioreactor samples with replicate numbers determined by power analysis A significance level of 0.05 was as- sumed and the detectable difference was set equal to the assumed experimental error. The sample size was determined at a power value of 0.95. A total of 32 samples from 2 bioreac- tors (16/bioreactor) were used for error estimation from the mean and standard deviation of the 16 measurements. Specific rate expressions were derived from mass balance equations for all prime variables of interest. Error in specific rates calculated from these equations were determined using the Gaussian approach [23], retaining only the first-order term in the Taylor series expansion Af (x1,x2,...xn) » where Af (x\,x2, ...xn) is the error in the function / , x\. x2, -.xn are the true values of the df 0 / dx2 Ax2 + df dxn Axr, (7.1) CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 131 prime variables and A x i , Ax2, ..'.Axnthe measurement errors. Recognizing the truncation associated limitation of the Gaussian approach at high prime variable errors, a Monte-Carlo approach was also used for specific rate error estimation. Normally distributed noise with mean=0 and desired standard deviation was introduced in the prime variables and specific rates were computed. As most specific rates were functions of multiple prime variables, errors in each prime variable were changed one at a time to calculate the corresponding specific rate errors. This allowed comprehensive specific rate error characterization in a multidimensional grid over the desired range of prime variable errors. For each prime variable error value, 10,000 normally distributed random error values were generated and 10,000 specific rates calculated. Thus the specific rate data reported from Monte-Carlo analysis are an average of 10,000 estimates. This procedure was repeated when all associated prime variables were in error. Additional details and computer programs are presented in Appendix G . 7.2.4 M e t a b o l i c F l u x e s A biochemical network previously developed for C H O cells [8] was used in this study. This includes the major reactions of central carbon metabolism along with reactions for amino acid metabolism by an approach previously described in more detail [6, 8]. The stoichiomet- ric matrix for this reaction network was of full rank and had a low condition number (69) indicating that flux estimates were not overly sensitive to specific rate variations. Metabolic fluxes were estimated using weighted least squares x = ( A 1 <.; ' A ) ! A ' f - ' r (7.2) where x is the flux vector, A the stoichiometric matrix, r the rate vector and tp the variance- covariance matrix of r. The bioreaction network was characterized by two degrees of freedom and the two redundant measurements were used to test the consistency of the experimental data and the assumed biochemistry. The consistency index, h, was calculated for each of the 12 experimental conditions according to methods previously described [19, 21, 22] and was compared with y2 = 5.99 (95% confidence level for 2 degrees of freedom). To characterize error propagation from specific rates into metabolic fluxes, an initial metabolic flux vector was assumed and the corresponding specific rate vector was determined as r = A x . Subsequently, error was introduced in r using normally distributed noise with zero mean and standard deviation corresponding to the desired error level (0 - 25%). Initially, error was separately added to each element in r (10,000 points at each error magnitude) and the resulting flux vector was computed. The flux data were averaged CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 132 and compared with the error-free flux vector. The difference between these flux values was caused by the specific rate error and helped quantify error propagation from the specific rates into the metabolic fluxes. For a more realistic representation of experimental conditions, this procedure was repeated with all elements of the specific rate vector simultaneously in error. T i m e (Days ) Figure 7.1: Viable cell concentration ( O ) and viability (•) time profiles over the 12 conditions examined in this study. Under standard conditions, DO = 50%, T = 36.5 °C, pH = 6.8 and the target cell concentration was 20 x 106 cells/mL for all conditions. 7.3 Results and Discussion 7.3.1 Perfusion Cultivation DO, temperature and pH set points were varied during the course of the cultivation resulting in a total of 12 experimental phases, each of. 10 day duration. Time courses of viable cell concentration and cell viability are shown in Figure 7.1. While the target cell concentration throughout the cultivation was 20 x 10 6 cells/mL, cell concentrations for T = 30.5 °C and pH = 6.6 were significantly lower due to-reduced growth rates. Cell viability was greater than 90% throughout the experiment. Specific rates including growth, nutrient consumption and metabolite/product formation were calculated using the Table 7.1 equations. The average specific glucose consumption rates are shown in Figure 7.2. Changes to DO had no effect CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 133 on glucose consumption while temperature and pH reduction significantly lowered the cell specific glucose consumption rate. Glucose consumption increased at higher temperatures and pi I = 7. Table 7.1: Expressions for growth rate, specific productivity and specific uptake/production rates' of key nutrients and metabolites in a perfusion system • ' • • Specific Rate Expression specific growth rate u & + *k(*l\+ i ( dXv\ . » - v + v [xv) + xv \ dt ) specific productivity 0 - l (Fmr , dF\ qP ~ xB v v ^ dt) specific glucose consumption rate • .. 1 C) dG\ - X (' { V dt ) , specific glutamine consumption rate 1 (Fm{Glnm-Gln) . dGln u _,', r i n \ QGln = X B ( ^ v dt KGln^lnJ specific lactate production rate. 'II- \>! \ \- dt ) specific ammonium production rate specific oxygen uptake rate i f Fgas(02in-O2out)\ io2 - xi< y v J Metabolic fluxes were computed using the average specific rates as inputs from the steady-state portion of each of the 12 experimental conditions, and are shown in Figure 7.3 for experimental phase E (standard bioreactor conditions). The fluxes through glycolysis, the T C A cycle and oxidative phosphorylation were one to three orders of magnitude higher than those for amino acid biosynthesis and catabolism as were some fluxes for biomass synthesis. Similar observations on relative flux magnitudes were made for the 11 other experimental conditions (not shown). The actual flux values, however, did change between different experimental phases, especially when temperature and pH were varied. 7.3.2 Prime Variable Error Errors in prime variable measurements were determined by analyzing multiple samples and the results are shown in Table 7.2. ;Glucose, lactate and glutamine measurements had errors close to 5% of the measured value, among the. lowest. The highest errors were 12.2 and 10.4%, respectively, for ammonium and oxygen. Errors in the bioreactor volume and the harvest, cell discard and gas flow rates were assumed to be 5% based on manufacturer specifications. ;-'.• . - : » V ' ' • . " ' • • CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 134 A B C D E F G H I J K L E x p e r i m e n t a l C o n d i t i o n Figure 7.2: Average specific glucose consumption rates (mean ± standard deviation) for the 12 experimental conditions in this study. More information about conditions A - L is in Figure. 7.1. 7.3.3 Specific Rate E r r o r Mass balances around the bioreactor and cell retention device were used to obtain ex- pressions for growth rate, specific productivity and specific uptake/consumption rates for nutrients and metabolites (Table 7.1). Since perfusion systems are typically operated at constant cell concentration and perfusion rates, the prime variables, would ideally be time invariant. However, imperfect cell concentration control and shifts in cellular metabolism require retention of the accumulation terms in the mass balance expressions. Table 7.2: Error in Prime Variable Measurements P r i m e Var iab le E r r o r (%) Bioreactor viable cell concentration (Xy) 8.9 Harvest viable cell concentration (Xy) 7.9 Product concentration (P) 8 Glucose concentration (G) 4.9 Glutamine concentration (Gin) 5.1 Lactate concentration (L) 4.8 Ammonium concentration (A) 12.2 Oxygen concentration (O2) 10.4 CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 135 Lactate • 3 (2.852) .4 (1.719) Glucose 1 (1.499) I I 25 (0.039) B i o m a s s s G 6 P G 6 P I " „ . i «-. Biomass„«p 5(0.065) R 5 P 26 (-0.01Q) Biomassŝ .p G A p16(0.002J G |y L 15(0.000) Pyruvate Ser Asn - 12 (0.657) Lys He ' 18(0.028)^ 17(0.048)1 6(1.809) ^ A c C o A ^ 0 0 4 5 ) L e u • M^lBiomass ^23 (-0.024) 8(1.322) | Asp 24 (-0.011) OAA Pro 20 (0.002) | Glu Gin 7 (-0.003) Ala n ; „ „ „ . 29 (-0.009) T - BiomassOM-.—5 <_J ii(i.9n a-KG J 3(1.726) 13(0.225) - Biomasss. Fum. . SuCoA He 22(0.130)^ Val | 21 (-0.027) Thr CO, Biomass, C02 NADH NADH + 0 . 5 O 2 ^ ^ L 3 A T P FADH, + 0.5 O, 3 3 ( Z 1 2 1 ) . 3 ATP Figure 7.3: Flux map for experimental condition E using the network of Nyberg et al [8]. Reaction numbers ( 1 — 33) and flux values (in parenthesis as pmol/cell-d) are also shown. 7.3.3.1 Gaussian Error Estimation vs. Monte-Carlo Analysis Specific glucose consumption rate, qc, was used to compare the Gaussian and Monte-Carlo approaches for specific rate error estimation. The specific glucose consumption rate is a function of five prime variables, V, F'h,Gm,G, and Xy (Table 7.1) and is thus affected by error in all of them. For simplicity, however, the bioreactor volume, V, the harvest flow rate, Fh, and the glucose concentration in the medium, Gm, were assumed to be error-free for this comparison. The error in bioreactor glucose concentration was varied from 0 - 10% while that in bioreactor viable cell concentration, was varied from 0 - 20%. For each pair of G and Xy errors, the corresponding error in qc was calculated using both the Gaussian and Monte-Carlo approaches (Figure 7.4). For Xy error <8%, both the Gaussian and Monte- Carlo approaches resulted in similar qc errors while the Gaussian approach underpredicted qc error at Xy error >8% for all G errors (Error estimates from the Monte-Carlo method are representative since no assumptions and approximations are made). Since Xy errors of 8.9% (Table 7.2) and higher are commonly observed in practice, the Gaussian approach as CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 136 defined in Eq.(7.1) has limited utility. 0 5 10 15 20 25 X° E r r o r (%) Figure 7.4: Comparison of Gaussian and Monte-Carlo qg error estimates at 10% glucose error and 0 - 2 0 % Xy error. Both the first and second order Gaussian qc errror estimates were lower than the Monte-Carlo error at higher Xy errors. This limitation of.the Gaussian approach is due the lack of higher-order terms in Eq.(7.1) Inclusion of the second-order term considerably increased the complexity of the Gaussian error expression with only a minor improvement in error prediction (Figure.7.4). For exam- ple, a 10% error in G and a 20% error in Xy resulted in a 26.9% qc error by the Monte-Carlo. method while the corresponding Gaussian error estimates were 22.4 and 23.1%, respectively, using the first and second-order terms. While addition of third and higher order terms can further increase the accuracy of Gaussian error estimates, the resulting expressions are quite complex. The Monte-Carlo approach with its ability to accurately estimate error over any desired range without derivative computation is superior to the Gaussian approach and has been used to obtain the data presented in subsequent sections. 7.3.3.2 E r r o r i n Specific G r o w t h R a t e The apparent specific growth rate, fi,. is a function of five prime variables (Table 7.1) and using values from Condition E , the dominant contributor is the cell bleed stream, followed CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 137 Figure 7.5: Error in a as a function of error in the 5 associated prime variables. Panel (a) is for V, Fd and F^ while panel (b) is for Xy and Xy. Panel (c) is when all prime variables are simultaneously ir> error (V, Fd and Fh at 5%; Xtf = 5 - 20 %; = 0 - 20 %). error legend for panel c: (•) 0 %; (b) 5 %; (•) 10 %; (•) 15 %; (A) 20 %. by the cell loss in the harvest 0.60 The bleed stream term makes up 82% of the growth rate while the remaining 18% is from the harvest stream term. The dXy has been set to zero to reflect an ideal steady-state with perfect cell concentration control. It is common to observe ~10% variation in cell density that can be more due to sampling and instrument error than a true change in cell density. Including this variation in the above expression will misrepresent contributions of the cell 4.9 100/0.21 To+"irJv^o" = 0.49 + 0.11 + 0.0 •1 /o + 20 1 (7.3) (7.4) CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 138 bleed and harvest streams to growth rate. It is the term, however, that largely affects growth rate error as will be shown below. Figure 7.5 shows the error in JM as a function of errors in the 5 prime variables that make up the specific growth rate expression. The impacts of 0 - 10% error in V, Fb, and F^ are shown in Figure 7.5a (Xy and Xy were assumed error free) where the \x errors increased monotonically with those in V, Fb, or Fh- Errors in V had the highest impact on fj, and the average ^ error ratio was 1.03 (standard deviation of 0.01) suggesting a one-to-one relationship. The ^ a n d e r r o r ratios were 0.83 (SD = 3!3 x 10~3) and 0.17 (SD = 6.4 x 1 0 - 4 ) , respectively, indicating lower sensitivity of fi to Fb and F'h errors.. This difference in error sensitivity is consistent with the relative prime variable contributions to the [i value. The fermentor volume, V, is in both the terms that contribute to \i in Eq.(7.3) resulting in the one-to-one error dependence. The bleed rate is present only in the first term that contributes 82% to the /i value, consistent with the ^ error ratio of 0.83. Errors in the harvest flow rate have the least impact because Fh is present only in the second term with a 18% contribution to fi, consistent with the •#- error ratio of 0.17. Impacts on \i errors from errors in bioreactor and harvest cell concentrations are shown CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 139 in Figure 7.5b (V, Ft,, and Fh were assumed to be error free). Cell concentration estimates are more prone to error as manual cell counting techniques continue to be widespread. While this has been alleviated with the advent of reliable automated cell concentration estimators, viable cell concentration in the harvest stream, Xy , is especially susceptible to experimental error as there are relatively few cells. However, given the minor contribution of the harvest stream term to the growth rate, a 20% error in Xy results in only 3.3% error in the corresponding ii estimate (Figure 7.5b). Errors in Xy however have a dramatic effect on the error in ii with the third term in Eq.(7.3) largely responsible for the strong influence of Xy error on \i. This was primarily due to the error associated with derivative estimation that is typically done by finite forward differences using Xy values from two consecutive days. More accurate derivative estimation approaches should be used to minimize the error in ii. Derivative computation using central differences resulted in a 50% reduction in ti errors (data not shown) and techniques such a splining could provide improved derivative estimates as well. Figure 7.5c shows the calculated error in IL when all the five prime variables are in error, reflective of experimental conditions. For a 5% error in V, and Fh and a 10% error in Xy and Xy (approximate conditions in this study), the corresponding /x error was 24.4%, emphasizing the need for accurate cell concentration determination and subsequent derivative estimation. 7.3.3.3 Error in Specific Uptake and Production Rates The Monte-Carlo approach was used to estimate error in nutrient consumption and metabo- lite production rates from the Table 7.1 expressions. Wi th the exception of oxygen, these specific rates were functions of V, Fh, Xy and the corresponding nutrient/metabolite con- centration while the oxygen uptake rate expression had Fo2 in place of Fh- A 5% error was assumed for V, Fh and Fo2 while Xy and the nutrient/metabolite concentration were evaluated over a 2 - 20 % error range. For each combination of Xy and nutrient/metabolite error, 10,000 specific rates were calculated and average error values are shown in Figure 7.6. For 0% error in Xy, error in all specific rates increased monotonically with error in the corresponding prime variable. For instance, the qc error was 7.3% at a 2% G error (V and Fh error = 5%, Xy error = 0%) and this value increased to 19.5% at a 20% G error. Increases in the Xy error caused an upward shift in the error profile while maintaining the monotonic dependence on the corresponding prime variable error. There were slight differences in the specific rate errors for their corresponding prime variables and this is due to differences in the.specific rate expressions (Table 7.1). Error profiles iox.qp and qA were CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 140 identical to those for qi. T a b l e 7 . 3 : Consistency index values for the 12 experimental conditions examined in this study E x p e r i m e n t a l C o n d i t i o n Bioreac tor Set Po in t s h .. A , .Standard 5.93 • ,,. .- B . • • D O = 20% 2.54 C ' Standard 4.64 I) DO = 100% 3.08 E Standard 1.59 F T = 34.5°C 0.95 G ' ; .• • - T = 32.5°C 0.80 H T = 30.5°C 4.28 I Standard 0.89 T = 37.5°C 0.26 K pH = 6.6 4.84 L pH = 7.0 3.56 Of all specific rates for the approximate conditions in this study (Table 7.2), the specific growth rate was characterized by the highest error with 5% errors in V, Fd and Fh and 10% errors in Xy and Xy resulting in a 24.4% error in ii (Figure 7.5). For a 5% measurement errors in glucose, lactate and glutamine concentrations, errors in their respective specific rates at a 10% X$ error were in the 12 - 14% range (Figure 7.6). The estimated error in oxygen uptake rate at a 10% Xy and oxygen errors was 16.1% (Figure 7.6). Overall, specific rate errors are ~10% with 5% errors in prime variables and 20 - 25% with 15% prime variable errors. (Figure 7.6). Thus the specific rate errors in a perfusion system can be expected to span a 10 - 25% range depending upon the accuracy of prime variable measurements. 7.3.4 Error in Metabolic Fluxes Metabolic fluxes were computed for all 12 experimental conditions and the consistency of the experimental data was verified by calculating the consistency index, (h) values (Table 7.3) using methods described earlier [6, 21]. The h values for all steady states passed the %2 distribution test with a 95% confidence level (h < 5.99 for 2 degrees of freedom) indicating that the experimental data for all experimental conditions were consistent and unlikely to contain gross measurement errors. This observation coupled with the stoichiometirc matrix, A , being of full rank and having a low condition number clearly attest to the robustness of the bioreaction network and the quality of the experimental data. Experimental condition CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC,FLUXES 141 E , where the bioreactor was operated under standard conditions (Table 7.3) was arbitrarily chosen to quantify the effect of specific rate errors on those in the metabolic fluxes. 70 60 ' 50 O 40 fc m 30 X Fl u 20 10 0. 50 g 40 s LU 30 X 3 20 ' Li . 10 0 300 O fc 200 UJ X 3 LL 100 0 300 3" O 200 fc LU X Fl u 100. 0 . (a) Thr -> SucCoA —Glucose ' • • Lactate «̂ (e) Thr-> SucCdA . ..: —O— Ser ' (f) Val -> SuCoA^/* \ (c) l\e->?MdCo^ 1 2 ' 5 2.0 s? 1.5 o fc 1.0 LU X 3 LL : 0.5 - 0.0 : 1.0 : 0.8 • 0.6 g LU - 0.4 X ' 3 LL • 0.2 - 0.0 : 20 " 15 O fc - 10 LU X 3 U . • 5 : 0 • 0 8 : 0.6 ^o" O fc - 0.4 LU X . 3 - 0.2 LL - 0.0 0 5 10 15 20 25 0 5 10 15 20 25 S p e c i f i c R a t e E r r o r (%) S p e c i f i c R a t e E r r o r {%) Figure 7.7: Effect of specific rate error on the error in lower metabolic fluxes.. Panels (a)-(d) are for errors in the 5 greater specific rates while (e)-(h).are for errors'in lower specific rates (amino acid metabolism). : 7.3.4.1 Lower M e t a b o l i c F luxes The effect of specific rate errors on the lower metabolic fluxes is shown in Figure 7.7. Panels a-d are for relatively greater specific rates while e-h are for amino acid metabolism (lower specific rates). Despite all 4 metabolic fluxes in Figure 7.7 being associated with the T C A cycle (Figure 7.3: threonine, valine and isoleucine are catabolized to SuCoA, asparagine is produced from oxaloacetate), they were greatly affected by the glucose uptake rate error. A 25% error in glucose uptake rate resulted in 60, 18, 103 and 54% errors, respectively (Figure 7.7a-d). The lactate production rate had a similar effect resulting in errors of 34, CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 142 10, 59 and 31%, respectively, (Figure 7.7a-d) for a 25% lactate production rate error. As expected, the Figure 7.7a-d fluxes were affected by errors in the oxygen uptake and carbon dioxide production rates given their close relation to the T C A cycle (threonine catabolism was less affected since this reaction does not directly involve O2 or CO2). A 25% error in the oxygen uptake rate resulted in respective errors of 26, 54, 387 and 228% while that in the CO2 production rate caused 10, 49, 349 and 291% errors, respectively, in the Figure 7.7a-d fluxes. Thus errors in the greater specific rates very substantially influence the lower metabolic fluxes to the extent that the values are far from accurately representing cellular metabolism. 30 r 25 20 p fc 15 UJ X 3 10 IL 5 0 25 gS 20 0 t 15 LU X 3j 10 LL. 5 0 16 12 O fc UJ g X 3 UL 4 0 20 15 O t UJ 10 X 3 l i . 5 0 . (a) Glc -> G6P • Glucose . • Lactate — * - C02 - * - Bio_NAD>T • • 1 M 1 (e)Glc->G6P - O - Ser : - 0 - Giy - O — ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ •• (b) Pyr -»• Lac » (f) Pyr -> Lac (g) aKG -> SucCoA . (d)^Cv->3^^ # » t 1 i (h)0 2->3ATP 0.07 0.06 0.05 g 0.04 g 0.03 0.02 I 0.01 0.00 0.03 0.01 2 0.00 0.16 0.12 — g 0.08 iii K 0.04 0.00 • 0.04 S? 0.03 f o 0.02 \ 0.01 5 10 15 20 25 0 S p e c i f i c R a t e E r r o r (%) 5 10 15 20 25 S p e c i f i c R a t e E r r o r (%) F i g u r e 7 .8: Effect of specific rate error (shown in each frame) on the error in 4 greater metabolic fluxes. Panels (a)-(d) are for errors in 5 larger specific rates while (e)-(h) are for errors in lower specific rates (amino acid metabolism). With the exception of the He —> SucCoA flux, errors in amino acid metabolic rates did not significantly affect the metabolic fluxes. Overall, the maximum flux error was less than 2.5% even when the specific rate error was 25% (Figure 7.7e,f,h). As expected, the lie —> CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 143 SucCoA flux was influenced by errors in isoleucine catabolism with a 25% error resulting in a 20% error in the flux (Figure 7.7g) and this dependence was true in all instances where the specific rate and flux were closely related. 7.3.4.2 Grea te r M e t a b o l i c F luxes The effect of specific rate errors in the 5 - 25% range on the greater metabolic flux errors was examined for experimental condition E and data for four fluxes representing glycolysis, lactate production, the T C A cycle and oxidative phosphorylation are shown in Figure 7.8. While the influence of all 35 specific rates in the bioreaction network were examined, Figure 7.8 shows representative results for the 5 greater specific rates (glucose, lactate, oxygen, carbon dioxide, B i o _ N A D H ; panels a-d) and 5 lower specific rates representing amino acid metabolism (serine, glycine, lysine, isoleucine, aspartate; panels e-h). As expected, specific rates that were not closely related to the flux had a lower impact on the flux error. For instance, a 25% error in glucose uptake rate caused 0.7, 1.4 and 2.7% errors, respectively, in Figures 7.8b-c while the error in Figure 7.8a was 23.6%. Similarly, a 25% error in lactate production rate caused errors of 0.92, 0.81 and 1.54%, respectively, in Figure 7.8a,c,d while that in Figure 7.8b was 24.8%. . Thus, errors in the greater specific rates had a significant effect on the errors in the most closely related fluxes. For instance, a 25% error in glucose uptake resulted in a 23.6% error in the Glc —> G C P flux (Figure 7.8a) and a similar dependence was seen between the error in the lactate production rate and the Pyr —> Lac flux (Figure 7.8b). The error in the T C A cycle flux, Q K G —> SuCoA, was most influenced by error in C O 2 production and oxygen uptake (Figure 7.8c) while that for oxidative phosphorylation was primarily affected by error in the oxygen uptake rate (Figure 7.8d). Errors in the amino acid metabolic rates, however, had minimal impact on the flux errors even when they were related to the flux. For instance, the specific production rates of serine and glycine (both synthesized from. G A P (Figure 7.3)), had a negligible impact on the glycolytic fluxes. A 25% error in serine or glycine production rates resulted in 2.34 x 10~ 4 or 7.02 x 1 0 _ 4 % error, respectively, in the Glc -> G C P flux (Figure 7.8e). While lysine and isoleucine are catabolized to form AcCoA which enters the T C A cycle, their rate errors had little impact on the T C A cycle flux ( a K G —> SucCoA). A 25% error in their catabolic rates resulted in respective flux errors of 0.14 or 0.12% (Figure 7.8g). Aspartate is formed in the T C A cycle from oxaloacetate and a 25% error in aspartate production rate caused a 3.67 x 10~ 2% error in the cuKG —> SucCoA flux. Thus, errors from lower magnitude specific rates have negligible impact on the error in the greater metabolic fluxes even when CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 144 30 0 5 10 15 20 25 30 S p e c i f i c R a t e E r r o r (%) F i g u r e 7 . 9 : Flux error for greater (panel a) and lesser (panel b) fluxes when all specific rates in the bioreaction network have errors in the 5 - 25% range. The Thr —» SuCoA and Val —> SuCoA error profiles overlap in panel b. the specific rates and metabolic fluxes are related. . 7.3.4.3 Ove ra l l F l u x E r r o r s i n Perfusion C u l t i v a t i o n Figures 7.7 and 7.8 and show flux error data when only one specific rate is in error. In a typical experiment, all specific rates have error and their combined influences on the flux error are shown in Figure 7.9. Specific rate errors in the 5 - 25% range were examined and when all specific rate errors were 15%, the greater flux errors ranged from 12.3% for aKG —>• SuCoA to 14.7% for Pyr —> Lac (Figure 7.9a). For the lesser fluxes, when the specific rate errors were 15%, the flux errors were between 46.9% (Thr —> SuCoA) and 312.5% (He —> SuCoA) (Figure 7.9b). Hence lesser flux values can be extremely sensitive to specific rate errors making their accurate determination difficult even at relatively low prime variable and specific rate errors. This was despite using a robust bioreaction network with a stoichiometric matrix of full rank and low condition number. CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 145 10 0.001 t 0.0001 Maximum values of — 5r 10 20 30 S p e c i f i c R a t e s 40 F i g u r e 7.10: Absolute values of the maximum and minimum sensitivity coefficients for the metabolic model used in this study. For each of the 35 specific rates, there were 33 sensitivity coefficients corresponding to the 33 fluxes (Figure 7.3) in the bioreac- tion network. 7.3.4.4 N o r m a l i z e d Sens i t iv i ty Coefficients for A n a l y s i s of M e t a b o l i c F l u x E r - rors The flux error data in Figures 7.7 and 7.8 were obtained from multiple simulations using the Monte-Carlo method. Although comprehensive, this approach is cumbersome to apply to new metabolic models and a generalized approach to quantify the relationship between specific rate and metabolic flux errors is desirable. The sensitivity matrix, S, provides a framework for such quantification and can be readily estimated from the stoichiometric matrix of the metabolic network [1] as S = ( A T A ) _ 1 A T (7.5) and the individual elements of S can be written as -h3 dxj (7.6) where Sij is the sensitivity of the ith flux with respect to the jth rate. For the metabolic network examined in this study, S is a 33 x 35 matrix where the jth column contains CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 146 the sensitivities of the 33 fluxes to the jth rate. Figure 7.10 shows absolute values of the minimum and maximum flux sensitivities for each of the 35 specific rates. The minimum sensitivities ranged from 0.0009 - 0.0092 while the maximum values were in the 0.32 - 1.50 range. Low sensitivity coefficients are favorable from an error analysis standpoint as the influence of specific rate errors on flux estimates is minimal. Even the maximum sensitivities .obtained were quite low, consistent with the low condition number (69) of the stoichiometric matrix, A . c c o o « o 1.0 0.'8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0 .8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 ( a ) G / c - > G 6 P . I (e) Glc - > G6P (b) Pyr -> Lac (f) Pyr - > Lac JUL. . (c ) aKG - > SuCoA (g) aKG - > SuCoA mm "IT . ( d ) 0 2 - > 3 / < 7 Y > {b)02->3ATPm 1.0e-3 5 .0e -4 0.0 - 5 . 0 e - 4 - 1 . 0 e - 3 • - 1 . 5 e - 3 - 2 . 0 e - 3 - 2 . 5 e - 3 1 .2e-3 8 . 0 e - 4 4 .0e^t 0.0 ^t .Oe^t 2 e - 3 - • 0 - 2 e - 3 - 4 e - 3 1 e - 3 0 - 1 e - 3 - 2 e - 3 G l c L a c 0 2 C 0 2 B i o S e r G l y L y s lie A s p Speci f ic Rates Figure 7.11: Normalized sensitivity coefficients for the greater fluxes in the bioreaction network for .both greater (panels a-d) and lesser (panels e-h) specific rates. However, sensitivity coefficients as defined in Eq.(7.5) do not completely explain the relationship between specific rate and flux error. For instance, sensitivity coefficients for the O2 —> 3ATP flux are -1.354 and -0.587 for the oxygen uptake and glucose uptake rates, CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 147 respectively, a ratio of 2.3. Errors in the O2 —• 3ATP flux, however, are scaled differently since 25% errors in glucose and oxygen uptake rates result in flux errors of 21.39 and 2.7%, respectively, a ratio of 7.9. This discrepancy is due to the difference in the magnitudes of the oxygen and glucose uptake rates (-5.14 and -1.48 pmol/cell-d, respectively) which is not accounted for in Eq.(7.6). If the sensitivity coefficients -1.35 and -0.59 are multiplied by their respective specific rates of -5.14 and -1.48, the resulting values are 6.94 and 0.87 with a ratio of 7.9 that is consistent with the flux error ratio and the results of Monte-Carlo analysis (Figure 7.8). A normalization of the Eq.(7.6) sensitivity coefficients is thus necessary for the resulting value to be representative of the error relationship between the specific rate and metabolic flux pair. This can be done by multiplying the right hand side of Eq.(7.6) with a ratio of the specific rate and metabolic flux where sf^ is the normalized sensitivity coefficient (NSC) for flux X{ with respect to rate rj (A similar approach is used to define the flux control coefficients in metabolic control analysis that describe the change in steady-state flux due to a change in enzyme activity [24]). For the O2 —> 3ATP flux, the normalized sensitivity coefficients from Eq.(7.7) were 0.849 and 0.106 for oxygen uptake and glucose uptake, respectively. The ratio of these normalized sensitivity coefficients is 8 which is similar to the flux error ratio of 7.9 from Monte-Carlo analysis with a small difference due to round-off errors. Normalized sensitivity coefficients as defined in Eq.(7.7) thus provide accurate quantification of the dependence of metabolic flux error on specific rate error (this was verified for other flux-specific rate combinations). NSCs for the greater fluxes are shown for both greater and lesser specific rates in Figure 7.11. For the Glc —> G6P flux, the NSC with respect to the glucose uptake rate from Eq.(7.7) was 0.923 indicating that a 1% error in glucose uptake rate would result in a 0.923% error in the Glc —> G6P flux (Figure 7.11a). The flux to specific rate error ratio from Figure 7.8a was 0.940 ± 1.7 x 1 0 - 3 (average of 5 data points for the glucose uptake rate) verifying the ability of the NSC to accurately describe the specific rate and flux error relationship. NSCs for lactate, oxygen, C O 2 and biomass from Eq.(7.7) were 0.037, 0.027, 0.011 and 0.003, respectively (error ratios from Figure 7.8b-d were identical), suggestive of their much lower impact on the Glc —> G6P flux. The highest NSC for the Pyr —> Lac flux was for lactate (0.99) while both oxygen and C O 2 were characterized by high NSCs for the a K G -> SucCoA flux (0.416 and 0.691, respectively). The 0 2 -> 3ATP flux was most affected by errors in the.oxygen, uptake rate and this dependence was characterized by a (7.7) CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 148 normalized sensitivity coefficient of 0.849 (Figure 7.11d). Normalized sensitivity coefficients with respect to amino acid metabolism were much smaller (Figure 7.11e-h) reflecting their minimal impact on the greater flux errors. While both Figures 7.8 and 7.11 provide very similar information on the specific rate and flux error relationship, Figure 7.11 data are easier to generate and are a more compact representation of error dependence. The sensitivity matrix can be readily estimated from the stoichiometric matrix using Eq.('7.5) and once metabolic fluxes are calculated using the experimentally measured specific rates (Eq.7.2), NSCs can be determined from Eq.(7.7). Moreover, a single number completely characterizes the specific rate and flux error relation- ship. Figure 7.12: NSC variation with respect to glucose uptake rate during the course of an experiment. Data from this study are shown in panel a and those from Follstad et al. [6] in panel b. CHAPTER 7. ERROR IN SPECIFIC RATES AND METABOLIC FLUXES 149 7.3.4.5 V a r i a t i o n i n N o r m a l i z e d Sens i t iv i ty Coefficients It must be recognized that NSCs and hence specific rate-flux error relationships can change during the course of an experiment if either the specific rate or metabolic flux changes. This is not true of the conventional sensitivity coefficients that depend only upon the stoichiom- etry of the bioreaction network (Eq.7.6). Figure 7.12a shows variation in the normalized sensitivity coefficients for the O2 —> 2ATP and SuCoA —> Fum fluxes with respect to glucose uptake rate for the 12 experimental conditions in this study. For both fluxes, the lowest values of the normalized sensitivity coefficients (0.218 and 0.139, respectively) were at T = 30.5 °C (condition H), where the flux values were the highest and the rate values were among the lowest. The opposite was true at pH = 7 (condition L) where flux values were the lowest and rate values were the highest (NSCs of 0.949 and 0:481). Thus during the course of a single experiment, the NSC for the O2 —> 2ATP flux with respect to glucose uptake rate ranged from 0.218 - 0.949, a 4.4-fold variation while a 3.4 increase was observed for the SuCoA —> Fum flux. The value of the O2 —> 2ATP flux was 4.4 times more affected by errors in glucose uptake rate at pH — 7 than at T = 30.5 °C while the SuCoA —> Fum flux was 3.4 more affected. Eq.(7.7) was also used to calculate NSCs for hybridoma cell cultivation in chemostat culture reported by Follstad et al, [6] at different dilution rates (Figure 7.12b). The dilution rates corresponding to steady states A - E were 0.04, 0.03, 0.02, 0.01 and 0.04 h r - 1 , respec- tively, and significant changes in cellular metabolism were observed over the course of the experiment. The sensitivity coefficient for the Pyr —> AcCoA flux was 0.67 and the normal- ized sensitivity coefficient for steady state A was 6.57 reflecting the 10-fold higher value of glucose uptake when compared to this flux. For steady states B - D, the Pyr—> AcCoA flux increased while the glucose uptake rate decreased resulting in significant reduction in the NSC. A n increase in the glucose uptake rate for steady state E was responsible for the slight increase in the NSC. Thus the Pyr —> AcCoA flux was most sensitive to glucose uptake rate errors in steady state A and this decreased by 6.5-fold for steady state D. Variations in the SuCoA —> Fum flux were primarily due to changes in the glucose uptake rate since the SuCoA —> Fum flux did not change much over the course of the cultivation while those for the Gin —> Glu flux were due to changes in both the flux and glucose uptake rate. Thus the flux and specific rate error relationship can change during the course of an experiment and NSCs under all experimental conditions must be calculated to rationally interpret the metabolic flux data. BIBLIOGRAPHY 150 7.4 C o n c l u s i o n s We have characterized error propagation from prime variables into specific rates and sub- sequently into metabolic fluxes for mammalian cells in high cell concentration perfusion culture. Prime variable errors were in the 5 - 15% range resulting in a 10 - 25% error in specific rates. The effect of specific rate error on the flux error was a function of both the sensitivity of the flux with respect to the specific rate and relative magnitudes of the flux and the specific rate. The greater fluxes in the bioreaction network had errors that were comparable in magnitude to the related greater specific rate errors and were virtually unaffected by errors in the lower specific rates. Greater flux errors ranged from 12 - 15% for 15% error in the greater specific rates suggesting that the 30% increase in T C A cycle fluxes reported in Chapter 9 are indeed representative of changes in cell metabolism. The lower fluxes, however, were extremely sensitive to errors in the greater specific rates making their accurate estimation difficult given analytical limitations in prime variable measurements. Often, errors were so large that the flux values grossly misrepresented cellular metabolism. The relationship between specific rate and flux error was accurately described by the nor- malized sensitivity coefficient that could be readily calculated once the metabolic fluxes were estimated. We recommend normalized sensitivity coefficient calculation be an integral part of metabolic flux analysis as it describes the relationship between flux and specific rate error through a single numeric value. B i b l i o g r a p h y [1] Stephanopoulos, G.; Aristodou, A. ; Nielsen, J . Metabolic Engineering., Principles and Methodologies. Academic Press, San Diego, 1998. [2] Balcarcel, R. R.; Clark, L . Metabolic screening of mammalian cell cultures using well- plates. Biotechnol. Prog., 2003, 19, 98-108. [3] Bonarius, H. ; Hatzimanikatis, V . ; Meesters, K . ; de Gooijer, C. D.; Schmid, G. ; Tram- per, J . Metabolic flux analysis of hybridoma cells in different culture media using mass balances. Biotechnol. Bioeng., 1996, 50, 229-318. [4] Bonarius, H . ; Houtman, J. ; Schmid, G.; C D . , d. 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