{"Affiliation":[{"label":"Affiliation","value":"Applied Science, Faculty of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."},{"label":"Affiliation","value":"Chemical and Biological Engineering, Department of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."}],"AggregatedSourceRepository":[{"label":"AggregatedSourceRepository","value":"DSpace","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","classmap":"ore:Aggregation","property":"edm:dataProvider"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","explain":"A Europeana Data Model Property; The name or identifier of the organization who contributes data indirectly to an aggregation service (e.g. Europeana)"}],"Campus":[{"label":"Campus","value":"UBCV","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","classmap":"oc:ThesisDescription","property":"oc:degreeCampus"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","explain":"UBC Open Collections Metadata Components; Local Field; Identifies the name of the campus from which the graduate completed their degree."}],"Creator":[{"label":"Creator","value":"Goudar, Chetan T.","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/creator","classmap":"dpla:SourceResource","property":"dcterms:creator"},"iri":"http:\/\/purl.org\/dc\/terms\/creator","explain":"A Dublin Core Terms Property; An entity primarily responsible for making the resource.; Examples of a Contributor include a person, an organization, or a service."}],"DateAvailable":[{"label":"DateAvailable","value":"2010-01-16T21:49:05Z","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"edm:WebResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"DateIssued":[{"label":"DateIssued","value":"2006","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"oc:SourceResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"Degree":[{"label":"Degree","value":"Doctor of Philosophy - PhD","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","classmap":"vivo:ThesisDegree","property":"vivo:relatedDegree"},"iri":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","explain":"VIVO-ISF Ontology V1.6 Property; The thesis degree; Extended Property specified by UBC, as per https:\/\/wiki.duraspace.org\/display\/VIVO\/Ontology+Editor%27s+Guide"}],"DegreeGrantor":[{"label":"DegreeGrantor","value":"University of British Columbia","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","classmap":"oc:ThesisDescription","property":"oc:degreeGrantor"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","explain":"UBC Open Collections Metadata Components; Local Field; Indicates the institution where thesis was granted."}],"Description":[{"label":"Description","value":"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 quantification and monitoring of cell metabolism were investigated in this study. Recognizing the adverse effect of high PCO\u2082 on cell growth, metabolism and protein productivity, a novel PCO\u2082 reduction strategy based on NaHCO\u2083 elimination was investigated that decreased PCO\u2082 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 kinetics 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 coefficient. 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 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.","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/description","classmap":"dpla:SourceResource","property":"dcterms:description"},"iri":"http:\/\/purl.org\/dc\/terms\/description","explain":"A Dublin Core Terms Property; An account of the resource.; Description may include but is not limited to: an abstract, a table of contents, a graphical representation, or a free-text account of the resource."}],"DigitalResourceOriginalRecord":[{"label":"DigitalResourceOriginalRecord","value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/18537?expand=metadata","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","classmap":"ore:Aggregation","property":"edm:aggregatedCHO"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","explain":"A Europeana Data Model Property; The identifier of the source object, e.g. the Mona Lisa itself. This could be a full linked open date URI or an internal identifier"}],"FullText":[{"label":"FullText","value":"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 \u00a9 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 \u2022 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 . : \u2022 . 19 2.8.4 pH 21 2.8.5 Dissolved Oxygen . . . . \u2022 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 \u2022 \u2022 \u2022 \u2022 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 \u2022 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 \u2022 \u2022 \u2022 114 6.4.1 Biological Significance.of the Logistic Parameters . . . . . . . . . . . .114 6.4.2 Description of Experimental Data from Batch Cultures . . \u2022'. . . . ' . 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 .. \u2022. . , ., \u201e , . . . . . . . 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 . \u2022. ': . . . . . . . . . 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 \u2022 \u2022 \u2022 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 \u2022 \u2022 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 . '\"\u2022 ' \" *. 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 \u2022 \u2022 \u2022 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 \u2022 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 \u2014 me), 5 measured extracellular rates (rmi,rm3 \u2014 rmQ) and 5 unknown intracellular fluxes (vi \u2014 ^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 \u00b1 standard deviation for the steady-state phase of the cultivation. . . .\u2022 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 \u00b1 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. >\u2022 \u2022. \u2022 79 4.11 Time profiles of pCG\"2 ( O ) a n d viable cell density (\u2022) 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 \u00b0C 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 \u00b0C 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 (\u2022\u2022\u2022\u2022\u2022) ; 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; (\u2014.. \u2014 ..) polynomial fit with one additional parameter (The two polynomial fits in panel c overlap). 122 7.1 Viable cell concentration ( O ) and viability (\u2022) time profiles over the 12 conditions examined in this study. Under standard conditions, D O = 50%, T = 36.5 \u00b0C, 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 \u00b1 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 \u2014 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\u00ae = 0 - 20 %). Xtf error legend for panel c: .(\u2022) 0 %; (o) 5 %; (\u2022) 10 %; (\u2022) 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: (\u2022) 0 %; (o)5 %; (\u2022) 10 %; (\u2022) 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 \u2014> SuCoA and Val \u2014> 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 (\u2022) and viability (O) for C H O cells in perfusion culture 158 8.2 Time profiles of bioreactor glucose (\u2022) 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 (\u2022) 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. [(\u2022) bioreactor cell density; (o) glucose; (\u2022) 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 ' \u2022 - xxii J.3 Time courses of bioreactor viable cell concentration (0) and viability (\u2022) for conditions A - I in the 38 day perfusion cultivation 322 J.4 Time courses of bioreactor. glucose (Q) and lactate concnetrations (\u2022) 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 (\u2022) 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 (\u2022) 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 (\u2022) 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. \u2022 327 J..8 Effect of DO increase on cell metabolism. Time profiles of of glycolytic (O); lactate (\u2022) 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 \u00a5\/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; \u2014> 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 \u2022 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 \u2022. 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 \u2022 Phosphogtycerate kinase \u2022 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 + \u2014> 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 \u2014 \u00bb 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 + \u2014> 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 \u2014 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 \u2014> 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 + \u2014> 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 \u2014 \u2022 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 \u2022H,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 \u2022 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 + . \u2014 \u2022 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 \u2014> 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 ^ \u2014> 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 \" \u2014 \u2022 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 \u00bb Pi + G D P V G T P + C o A succinate dehydrogenase fumarase malic enzyme Succinate . F A D S\u00bb. 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 \u2014 \u2022 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 ) + \u2014 \u2022 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 ) + \u2014 \u2022 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- \u2014 \u2022 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 \u00b1 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 \u00b1 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. ' . \u2022 - .\u2022 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 \u2014\u2022 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 \u00b0C. 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 \u00b0G [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 \u00b1 0.003 h \" 1 at 37 \u00b0C; 0.016 \u00b1 0.001 h r 1 at 33\u00b0C) [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 \u00b0C, 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 \u00b1 0.003 h 1 at 37\u00b0C to 0.014 \u00b1 0.004 h _ 1 at 33 \u00b0C 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 \u00b0C, 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 \u00b0C compared to 37 \u00b0C [19] while a 2-5 fold decrease was observed for hybridoma cells for temperature reduction from 39 to 33 \u00b0C [71]. For BHK-21 cells in batch culture, the specific, glucose uptake rate decreased from 0.58 ng\/cell-d at 37 \u00b0C to 0.45 ng\/cell-d when the temperature was lowered to 33\u00b0C [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 \u00b0C [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 \u00b0C [65] and similar observations were made for glutamine consumption and ammonium production. However, when the temperature was further lowered to 30 \u00b0C, glucose uptake and lactate production rates decreased by 44 and 56%, respectively (as compared to 37 \u00b0C) 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 \u00b0C range [80]. At temperatures close to 37 \u00b0C, every 1 \u00b0C 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 \u00b0C. 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 \u00b0C [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 \u00b0C [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 \u00b0C 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 \u00b0C 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 \u00b0C. 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. \u2022 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 \u2014\u2022> B \u2014> C where B is the intracellular metabolite. The mass balance expression for B can be written as \u2014 = 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& \u2014 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 \u2014 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 \u2014 me) and 5 measured extracellular rates ( r m i , r m 3 \u2014 r m g ) that have been arbitrarily selected to have enough measurements to solve for the 5 unknown intracellular fluxes (v\\ \u2014 vs.). Applying CHAPTER 3. METHODS FOR METABOLIC FLUX ESTIMATION 38 Eq.(3.5) around metabolites mi \u2014 TTIQ results in the following mass balance expressions 777,1 rmi-vi-v3 = 0 (3.6) 777,2 V\\ \u2014 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\\ \u2014 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) \u2022 \u2022 ' 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 \u2014 vi \u2014 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 \u2014 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, \\ + \u2022 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] \/ \u00ab1 \\ 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 \u2022 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, G^ T depending upon the number of metabolite mass balances (m) and reactions (r) and three scenarios are possible 1. Determined system (m = r) \u2022>\u2022 . \u2022'' 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 7^ 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\u201e,} -o . (3.26) V,\u201e{GL- G, \/(G;O#G\/,;}-O (3.27) which can be rewritten as , . Rv,\u201e - 0 (3,28) where R == G ^ \u2014 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 \u2014 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),
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 \u2014\u2022 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 ; \u2014-> 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 \u2014> Pyruvate: flux v c l ) as have those for the T C A cycle (Pyruvate \u2014> 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 \u2022 o 1 \u2022 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), \u2022 (c \/ -1 0 0 0 \/ - 1 0 0 0 0 0 0 \u2022 -1 o' 0 ' ( V m ) o 1 0 0 ' , 0 0 0 0 - 1 0 \/ \" m i \\ 0 0 3 \u2022\u2022 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 \u20141 A - 1 0 0 \u2022 o p ' 0 , 0 0 0 X ,0 - 1 0 V o . 0 \u2022 \u2022 o : ;o \u2022 \/ V 2 0 1 \u2022 2.5 ' 1.5 - 1 \/ K ) \/ Vcl \\ VC2 VC3 VC4 Vc5 \/ o \\ 0 0 0 0 0 0 v \u00b0 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\u2014 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 \u2022 0 0 0.3403 0 \\ \u2022 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 \u2022 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\u201e 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 ^ \u2014 G^ 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,
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 \u2014 o \u2022 \u2014 o O \u2014 O \u2014 \u2022 o \u2014 \u2022 \u2014 o o \u2014 \u2022 \u2014 \u2022 \u2022 \u2014 o \u2014 o \u2022 \u2014 o \u2014 \u2022 \u2022 \u2014 \u2022 \u2014 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 \u2014 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