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UBC Theses and Dissertations

Predictive control and optimization of bioprocesses for recombinant T-PA protein production by mammalian… Dowd, Jason Everett 2000

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PREDICTIVE CONTROL AND OPTIMIZATION OF BIOPROCESSES FOR RECOMBINANT T-PA PROTEIN PRODUCTION BY MAMMALIAN CELLS by Jason Everett Dowd B.A. Sc., University of Waterloo, ON, Canada, 1994 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES BIOTECHNOLOGY LABORATORY & DEPARTMENT OF CHEMICAL AND BIOLOGICAL ENGINEERING We accept this thesis as confirming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA 2000 © Jason Everett Dowd, 2000 In p r e s e n t i n g this thesis in partial fu l f i lment of the requ i rements fo r an a d v a n c e d d e g r e e at t h e Univers i ty of Brit ish C o l u m b i a , I agree that the Library shall m a k e it f reely avai lable for re fe rence and study. 1 further agree that p e r m i s s i o n for ex tens ive c o p y i n g of this thes is f o r scho lar ly p u r p o s e s may b e granted by the h e a d of my d e p a r t m e n t o r by his o r her representat ives. It is u n d e r s t o o d that c o p y i n g o r p u b l i c a t i o n o f this thesis for f inancial ga in shal l n o t b e a l l o w e d w i t h o u t m y w r i t t e n p e r m i s s i o n . D e p a r t m e n t of C rV, \ *-~J- ) 03 f ^ b ^ i - ^ e t r , T h e Un ivers i ty of Brit ish C o l u m b i a V a n c o u v e r , C a n a d a Date 2 000 D E - 6 (2/88) ABSTRACT Genetically engineered mammalian cells produce a large array of recombinant proteins for research, diagnostic and therapeutic applications. The relatively low cellular production rates in mammalian cells require intensification of the production methods to raise product concentrations and volumetric productivity. Recombinant human tissue plasminogen activator (t-PA) produced in Chinese Hamster Ovary (CHO) cells served as the basis for this investigation. Multiple model adaptive protocols were applied to control the extracellular environment with the goal of fed-batch and perfusion process optimization of protein titers and productivity. Fed-batch and perfusion bioreactors in various forms are widely used to produce recombinant proteins and monoclonal antibodies for therapeutic and diagnostic use. Better control of the cellular environment can lead to higher volumetric productivity, ensure product consistency and optimize medium utilization. The objective was to manipulate and control substrate concentrations in fed-batch and perfusion bioprocesses using predictive modeling and control. The goal of the predictive controller was to minimize future deviations from the set point concentration, by structuring the controller output. The appropriate structure for the future manipulated variable was specified using the selected model of uptake rate estimates. When there was a deviation from the set point value, the flow rates were adjusted to drive the process close to the set point value in a defined first order manner. The shape of the first order process response depended on the magnitude of the deviation from the set point value. With daily sampling, a feed rate profile (8 flow rates per day) was specified to control the bioprocess. The predictive control protocols have demonstrated glucose variation of less than 0.4 mM in transient conditions, and less than 0.2 mM in pseudo-steady-state conditions. The non-linear controller ii allows for rapid changes in set point concentrations (6 to 9 h) or a reference trajectory to be followed. Set point changes and reference trajectories were simulated and tested with real process data. Modeling error and measurement bias was simulated to have the greatest potential effect during exponential growth. With good model estimation of the process, predictive control was able to maintain the process at the set point with a level of variability approaching that of the glucose assay. Fed-batch operation for the production of t-PA using Chinese Hamster Ovary (CHO) cells was optimized using serial and parallel experimentation. The isotonic concentrate efficacy was improved to obtain 2- to 2.5-fold increases in integrated viable cell days versus batch. With a low glucose inoculum train, the viability index was increased up to 4.5-fold. Hydrolysates were substituted for the amino acid portion of the concentrate with no significant change in fed-batch results. The concentrate addition rate was based on a constant 4 pmol/cell-day glucose uptake rate that maintained relatively constant glucose concentrations (approximately 3 mM). Increased viable cell indices did not lead to concomitant increases in t-PA concentrations compared to batch. The fed-batch concentrate was tested in hybridoma culture, where a four-fold increase in viable cell index yielded a four-fold increase in antibody concentration. Instead, there appeared to be an extracellular t-PA concentration maximum at 30-35 mg/L. The half-life of t-PA decreased from 42 to 14 days with decreasing cell viability (> 90% to ~ 70%), but this was not sufficient to explain the apparent t-PA threshold. Analysis of both the total and t-PA mRNA levels in dose response experiments revealed no response to extracellular t-PA concentrations. Instead, increasing intracellular t-PA levels revealed a secretory pathway limitation. A new reactor configuration used an acoustic filter to retain the cells in the reactor and an ultrafiltration module to strip the t-PA from the clarified medium and returned the permeate back to the reactor. iii By adding this harvesting step, the t-PA fed-batch production was increased over 2-fold, up to a yield of80mg/L. Perfusion cultures of CHO cells producing t-PA were performed using an acoustic filter to retain cells in the bioreactor as spent medium was removed. A robust off-line glucose analysis and predictive control protocol was developed that maintained the process within approximately 0.5 mM of the glucose set point without the need for a more fallible on-line sensor. Earlier onset of perfusion with a ramping glucose set point (1 to 2 mM/day) resulted in improved growth and consistency in the perfusion culture start-up. A medium formulation with elevated levels of glutamine resulted in significant increases in glutamine consumption and ammonium production, along with reductions in consumption rates of glucose and several amino acids. In contrast, elevated levels of glucose had no significant impact on the cellular metabolism. Amino acid analysis of the initial batch and early perfusion culture resulted in an improved medium formulation which resulted in increased medium residence times and increased t-PA concentrations. Glucose depletion was used as an indicator of the extent of overall medium utilization, to map acceptable ranges of operation and the edge of failure. Peak t-PA concentrations of over 90 mg/L were obtained by controlling at a glucose depletion of approximately 25 mM, but were not sustainable for more than 3 days. A consistent t-PA concentration of 40 mg/L was obtained at a glucose depletion of 22.5 mM. The variability in the t-PA concentrations increased gradually with increasing glucose depletion up to approximately 23 mM, then increased 3-fold between a glucose depletion of 23 and 25 mM. iv T A B L E OF CONTENTS ABSTRACT ii TABLE OF CONTENTS v LIST OF TABLES x LIST OF FIGURES xi LIST OF ABBREVIATIONS xv LIST OF SYMBOLS AND UNITS xvii GLOSSARY OF TERMS xxi ACKNOWLEDGEMENTS xxii DEDICATION xxiii CHAPTER 1 INTRODUCTION : 1 1.1 Recombinant Protein Production in Bioreactors 1 1.1.1 Selection of Host 1 1.1.2 Selection of Process 2 1.1.3 Optimization of Bioreactors 5 1.2 Model System 6 1.2.1 Culture Modeling 6 1.2.2 t-PA As a Model Recombinant Protein 7 1.2.3 Bench-scale Reactors 7 1.2.4 Cell Retention 8 v 1.2.5 Identification of Limiting Factors 9 1.3 Thesis Objectives 10 CHAPTER 2 LITERATURE REVIEW 12 2.1 Modeling of Cells 12 2.1.1 Growth Modeling 13 2.1.2 Substrate Uptake and Metabolite Production Modeling 15 2.1.3 Microbial Culture Modeling 17 2.1.4 Animal Culture Modeling 17 2.1.5 Recombinant Protein Production Modeling 18 2.1.6 Mass Balance-based Modeling 19 2.2 High Cell Density Bioreactor Production of Recombinant Proteins 20 2.2.1 Rationale for Limiting Substrates 20 2.2.2 Predictive Control 22 2.2.3 Fed-batch Process 23 2.2.4 Perfusion Process 26 2.3 Summary 28 CHAPTER 3 MATERIALS AND METHODS 30 3.1 Cell Culture 30 3.1.1 Inoculum Train 30 3.1.2 Low Glucose Inoculum Train 31 3.1.3 Bioreactor Operation 31 3.2 Dose-Response and Survey Experimentation 33 3.2.1 Three-Day Experiment 33 vi 3.2.2 Survey Experimentation 33 3.3 t-PA Analysis 34 3.3.1 t-PA Activity Assay 34 3.3.2 t-PA Enzyme Linked Immunosorbent Assay 34 3.3.3 t-PA Concentration in Hollow Fibre Module 35 3.3.4 t-PA Stability 35 3.3.5 Intracellular t-PA Concentration 35 3.4 Concentrate Formulation 36 3.5 Total and t-PA Messenger R N A Analysis 36 3.6 Amino Acid Analysis 37 3.7 Competitive Binding with e-Aminocaproic Acid 37 3.8 Equations Used in Analysis 38 CHAPTER 4 MODELING AND PREDICTTVE CONTROL 40 4.1 Introduction 40 4.2 Identification 40 4.2.1 Glucose Uptake Estimate at Current Sampling >. 41 4.2.2 Model for the Prediction Horizon 42 4.3 Control Law Derivation 43 4.4 Base Case Simulation 46 4.5 Results and Discussion 48 4.5.1 Comparison of Operator and Computer Estimation of Feed Rates 48 4.5.2 Simulation Results of Perfusion Culture 49 4.5.3 Simulation of Noise Sources 52 vii 4.5.4 Estimation of Process Data 52 4.5.5 Experimental Results 57 4.6 Conclusions 63 CHAPTER 5 FED-BATCH EXPERIMENTATION 64 5.1 Introduction '. 64 5.2 Fed-batch Process Modification to Remove t-PA 64 5.3 Results and Discussion..: 65 5.3.1 Dose Response Analysis 65 5.3.2 Initial Concentrate Formulation 66 5.3.3 Feeding Strategy 69 5.3.4 Concentrate Formulation 71 5.3.5 Hybridoma Test Culture 76 5.3.6 Low Glucose Inoculum and t-PA Threshold 76 5.3.7 t-PA Binding and Stability 78 5.3.8 t-PA Dose Response 80 5.3.9 Formulation of Kinetic Model for Extracellular t-PA Concentrations 83 5.3.10 Fed-batch Protocol Modification.. 84 5.4 Conclusions 88 CHAPTER 6 PERFUSION EXPERIMENTATION 89 6.1 Introduction 89 6.2 Modeling and Predictive Control Protocols 89 6.3 Results and Discussion 91 6.3.1 Batch Culture 91 viii 6.3.2 Dose Response 92 6.3.3 Perfusion Initiation 96 6.3.4 Long-Term Perfusion Culture 96 6.3.5 Cell Specific Uptake and Production Rates as a Function of Medium Formulation 99 6.3.6 Glucose as Index of Medium Utilization and t-PA Concentrations 102 6.4 Conclusions 112 CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK. 113 7.1 Overall Review ."' • •• 113 7.2 Predictive Modeling and Control 113 7.3 Fed-batch Culture 114 7.4 Perfusion Culture 115 7.5 Combined Fed-batch and Perfusion Culture Process 116 7.6 Dose Response 116 7.7 Quality Specifications 116 7.8 Principal Component Analysis 117 CHAPTER 8 REFERENCES 118 APPENDIX 1 MANUSCRIPT OF PREVIOUS HOLLOW FIBRE WORK 135 APPENDED 2 COMPUTER CODE 169 A.2.1 Anglicon Datalog Program (Quick Basic) 169 A.2.2 Generic Pump Control Program (Quick Basic) 170 A.2.3 Predictive Modeling and Control Program (Matlab) 172 ix LIST OF TABLES Table 2.1. Different Perspectives of Cellular Kinetic and Metabolic Modeling 12 Table 2.2. Approaches to Model Estimation of Cell Growth 14 Table 2.3. Substrate Uptake and Metabolite Production Modeling 16 Table 4.1. Perfusion Simulation Parameters 47 Table 4.2. Comparison of Operator Versus Computer Estimation of Feed Rates 49 Table 4.3. Linear Approximation Errors in Exponential Growth 56 Table 5.1. Fed-batch Amino Acid Formulation 67 Table 5.2. Fed-batch Concentrate Components 72 Table 5.3. Dose Response with Hydrolysates 74 Table 6.1. Medium Formulations 100 Table 6.2. Cell Specific Rate Changes as a Function of Medium Formulation 101 x LIST O F FIGURES Figure 1.1. Bioprocess schematic alternatives for recombinant protein production 3 Figure 2.1. Simplified schematic for the utilization of glucose and glutamine in mammalian cells. . 21 Figure 4.1. Simplified block diagram of process 44 Figure 4.2. Control intervals every 3 h for a CHO culture. The onset of perfusion is indicated by the step increase in dilution rate from zero at day 4 50 Figure 4.3. Control intervals every 24 h for a CHO culture. The onset of perfusion is indicated by the step increase in dilution rate from zero at day 4 51 Figure 4.4. Estimating the glucose uptake rate at the current sampling. The data points (squares) are plotted in each window 53 Figure 4.5. Control protocol estimation for a bioreactor start-up, with an example of the graphical user interface plots. Perfusion was initiated on day 2. 55 Figure 4.6. Culture profile of 10 L hybridoma culture 58 Figure 4.7. Set point change in CHO culture 59 Figure 4.8. Maintenance of a constant glucose concentration in CHO culture under transient conditions 61 Figure 4.9. Reference trajectory of glucose in CHO culture. 62 Figure 5.1. Serial experimentation withHPLC analysis. The amino acid profiles for glutamine, aspartate, glutamate, glycine and asparagine for three bioreactor experiments are shown. The first, second and third iteration of experiment, followed by HPLC analysis, are shown in the top, middle and bottom panel, respectively 68 xi Figure 5.2. Magnitude of concentrate additions. The cell specific glucose uptake rate was specified at 3, 4 or 5 pmol/cell-day and multiplied by cell numbers in the reactor to obtain the addition volumes 70 Figure 5.3. Simplified versus complete concentrate. In the top panel, the activity assay was used with three concentrates compared to batch. In the bottom panel, the ELISA protein-based assay was used for concentrates A and C, compared to batch 73 Figure 5.4. Substituting hydrolysates for defined amino acids. The viability in fed-batch cultures was extended relative to batch, with three concentrates with different amino acid components 75 Figure 5.5. Hybridoma fed-batch results. Using the same feeding strategy as the fed-batch cultures involving CHO cells, the performance of Concentrate E on MAb production using hybridoma cells is illustrated 77 Figure 5.6. Degradation of t-PA in culture. Samples were taken from the reactor at days 2 and 6. The plotted values are normalized with respect to their maximum values to obtain percentage values. The fitted degradation curves of t-PA neglect the first point taken immediately after filtration 79 Figure 5.7. t-PA dose response with concentrated t-PA. The top panel shows the final viable cell concentration (squares) and the starting and final (circles) measured t-PA concentrations. The bottom panel shows the growth rate (squares) and the calculated cell specific productivity assuming a half-life of 40 days. The values are plotted versus the log mean t-PA concentration over the three day culture 81 Figure 5.8. Northern blot and intracellular t-PA concentration versus extracellular t-PA concentration 82 xii Figure 5.9. Fed-batch process modification schematic 86 Figure 5.10. Fed-batch culture with t-PA stripping. The process modification to strip t-PA from the fed-batch culture resulted in increased t-PA titers which are plotted as the cumulative concentration. The batch culture t-PA concentration reached approximately 32 mg/L 87 Figure 6.1. Batch profile of glucose concentration with growth and cell specific t-PA productivity 93 Figure 6.2. Dose response of glucose and glutamine. The cell specific uptake and production rates as a function of the log mean glucose and glutamine concentrations 94 Figure 6.3. Growth rate and t-PA cell specific productivity as a function of the log mean glucose or glutamine concentrations 95 Figure 6.4. In A the feeding was initiated at day 5 when the glucose set point of 8.5 mM was reached. In B, the feeding was initiated at day 3 and followed a glucose set point ramp to 8.5 mM by day 6. Calculation of the apparent growth rate neglects minor losses (generally < 5%) through the cell retention device 97 Figure 6.5. 52-Day perfusion culture profile. The dilution rate was changed as a result changing reactor conditions, glucose set point and the inlet glucose concentration. (Glc = glucose, Gin = glutamine, Glu = glutamic acid and Asp = aspartic acid) 98 Figure 6.6. Glucose, t-PA and amino acid concentrations in batch and early perfusion. Perfusion was initiated after 4 days of culture at a glucose concentration of 15 mM. The glucose concentration reaches approximately 5 mM at its nadir, while the t-PA concentration reaches approximately 60 mg/L at its peak. The t-PA concentrations are measured both with activity and ELISA (protein) assays 103 xiii Figure 6.7. Normalized cell specific rates of medium components in perfusion culture. The cell specific amino acid uptake rates were normalized using Equation 6.2. Increased uptake or production is indicated by larger (absolute value) positive or negative numbers, respectively. A large number of amino acids exhibit a decline in cell specific uptake rates (top panel), and a decline in cell specific production rates (bottom panel). Another subset of amino acids exhibit no significant trend (middle panel) 105 Figure 6.8. Depletion of amino acids along with concentrations of alanine and ammonium plotted as a function of glucose depletion 107 Figure 6.9. Glucose and t-PA concentrations in perfusion culture controlled at 6 mM glucose. 109 Figure 6.10. Glucose and t-PA concentrations for a perfusion culture controlled at 8.5 mM glucose 110 Figure 6.11. t-PA concentrations and variability as a function of glucose depletion. The reactor glucose set point concentration may be specified as a function of the expected t-PA concentration and variability Ill xiv LIST O F ABBREVIATIONS ATP adenosine triphosphate BHK baby hamster kidney cDNA complementary deoxyribonucleic acid CHO Chinese hamster ovary CNBr cyanogen bromide DEPC diethyl pyrocarbonate DHFR dihydrofolate reductase DMEM Dulbecco's Modified Eagle Medium DMSO dimethyl sulfoxide ECS extracapillary space EF-1 elongation factor 1 ELISA enzyme linked immunosorbent assay FBS fetal bovine serum FDA US Food and Drug Agency HFBR hollow fibre bioreactor HPLC high performance liquid chromatography ICS intracapillary space IMDM Iscove's Modified Dulbecco's Medium ln natural logarithm MEM Modifed Eagle Medium mRNA messenger ribonucleic acid MTX methotrexate NADH nicotinamide adenine dinucleotide (reduced form) PAI plasminogen activator inhibitor PBS phosphate balanced saline PID proportional + integral + derivative PITC phenylthiocarbamyl PTM post-translational modification RNA ribonucleic ccid TCA tricarboxylic acid t-PA tissue-type plasminogen activator xvi LIST O F SYMBOLS AND UNITS AV addition volume [L] Cconc glucose concentration in concentrate [mM] C e st ,Gic estimated glucose concentration [mM] CGIC glucose concentration [mM] Cp metabolite concentration [mM] CP, in inlet metabolite concentration [mM] Cp, out outlet metabolite concentration [mM] Cs substrate concentration [mM] Cs, in inlet substrate concentration [mM] Cs, out outlet substrate concentration [mM] CSP set point concentration [mM] C concentration deviation variable ( C = C F e e d - C R e a c t o r ) [mM] g average concentration deviation variable [mM] C s p difference between the inlet and set point glucose concentration [mM] °C degrees Celsius Da dalton [g/mol] exp exponential function F flow rate [L/day] F average flow rate [L/day] AF change in flow rate [L/day] xvii g gravitation acceleration [9.81 m/s2] GUR glucose uptake rate [mmol/L-day] GURest estimated glucose uptake rate [mmol/L-day] GURMax maximum expected glucose uptake rate [mmol/L-day] GUR predicted glucose uptake rate [mmol/L-day] H m minimum cost horizon Hp prediction horizon IVC integrated viable cells [cell-days/L] J error criterion function ka inactivation rate [1/day] Ki Monod inhibitor constant [mM] K s Monod substrate constant [mM] M molarity [mols/L] mp maintenance requirement for metabolite production [pmol/cell-day] ms maintenance requirement for substrate uptake [pmol/cell-day] qoic cell specific glucose uptake rate [pmol/cell-day] Qoic volumetric glucose uptake rate [mmol/L-day] QGIC, Max maximum expected volumetric glucose uptake rate [mmol/L-day] qP cell specific metabolite production rate [pmol/cell-day] qs cell specific substrate uptake rate [pmol/cell-day] t time [day] At change in time [day] U International unit, the amount of enzyme required to turn over 1 umol xviii substrate/min V reactor volume [L] v/v volume/volume W period of moving average filter w/v weight/volume X V viable cell concentration [cells/L] XV.LM log mean viable cell concentration [cells/L] y; normalized cell specific uptake/production rates Yxv/p yield of biomass from metabolite [cell/pmol] Yxv/s yield of biomass from substrate [cell/pmol] Ala alanine Amn ammonium Arg arginine Asn asparagine Asp aspartate Cys cysteine/cystine Glc glucose Gin glutamine Glu glutamate Gly glycine His histidine I inhibitor xix He isoleucine Leu leucine Lys lysine Met methionine P metabolite Phe phenylalanine Pro proline S substrate Ser serine Thr threonine Trp tryptophan Tyr tyrosine Val valine a regressed parameter estimate B regressed parameter estimate X controller tuning parameter u. specific growth rate [1/day] u-max maximum specific growth rate [1/day] xx GLOSSARY OF TERMS bolus addition cell specific cell viability data window glycosylation inferential estimation loose-loop metabolite period pinocytosis plant outputs reference trajectory spinner flask substrate T-flasks titer transcription translation volume added to reactor on a per cell basis measure of cell health by excluding Trypan blue dye last n data points post-translational step. involving the addition of large sugar complexes at specific amino acids in protein model-based estimation between data points operator-mediated dissolved medium component which is a byproduct of metabolism number of data points cell membrane engulfing extracellular volume set of manipulated variable (flow rate) values set of set point values suspension culture vessel with magnetically-driven impeller dissolved medium component which cells utilize stationary culture vessel in which cells settle onto bottom surface concentration mRNA copied from cDNA protein copied from mRNA xxi A C K N O W L E D G E M E N T S I would like to thank my supervisors, Jamie Piret and Ezra Kwok, for encouraging my thesis work and enabling my progress. I appreciate the trust that Jamie has shown by allowing me to mentor several students over the years. I especially appreciate the standard of excellence in research that Jamie has instilled in me to pursue. I would also like to thank my committee for fruitful discussions and important new perspectives. If I have grown as a researcher, it is through their guidance and enthusiasm. I would like to thank past members of the Biotechnology Lab, especially Eric Jervis, Peter Zandstra, Steve Woodside and Chorng-Hwa Fann, who I have sought to emulate and apprentice -Eric, for ideas, Peter, for pragmatic approach, Steve, for thoughtful appreciation, Chorng-Hwa, for thoroughness. If my desire to learn has increased, it is through being their student. I would like to thank the present members of the Biotechnology Lab, especially Gary Lesnicki, Yita Lee, and Chris Sherwood, for their camaraderie and partnership. I especially thank Gary for good discussions. If we have collaborated, I am better as a result. I would like to thank my friends, for providing avenues for discovery and renewal. I especially thank Kim Blouin and Amanda McGuire for philosophical, practical and metaphysical discussions, Mike Macklem and Taka Katsube for providing spiritual and physical outlets for renewal and rejuvenation. It is through their friendship that I have learned to appraise and strive for the important elements in my life. Finally, I would like to thank Christine Jarchow, my fiancee. If I am jubilant in my life, it is due to her presence. My hopes for a happy and thriving life are linked to our future together. xxii DEDICATION I would like to dedicate this thesis to my parents, brother and sister for their unflagging support. I owe them everything that I have become. xxiii C H A P T E R 1 INTRODUCTION 1.1 RECOMBINANT PROTEIN PRODUCTION IN BIOREACTORS BY MAMMALIAN CELLS As the production of recombinant proteins increases for therapeutic and diagnostic use, it becomes increasingly important to understand how bioreactor operation affects protein production. Mammalian cells have been widely used to produce recombinant proteins, especially those requiring complex post-translational modifications (Bially, 1987). Process optimization depends on consistent cellular protein production and reproducible process control of culture conditions. Reproducible control is complicated by the nature of biological systems, where complete models do not exist (Tzaimpazis and Sambanis, 1994). Modeling and predictive control protocols have been successfully applied to complex systems such as missile guidance systems and nuclear power plants (Seborg et al., 1986), and, if properly applied, should yield improved bioprocess control. 1.1.1 Selection of Host The selection of recombinant protein production begins with the choice of host organism, which may include bacteria, yeast, insect cells or mammalian cells. Considerations for the protein produced include fidelity of expression, correct post-translational modifications (PTM) including folding, di-sulphide bonding and the form of glycosylation. An example of a PTM is n-linked glycosylation occurring at asparagine residues in the protein, where the glycosyl moieties are large branched polymers of glucose and mannose derivatives (Warren, 1993). 1 However, many forms of glycosylation and other post-translational modifications are difficult or impossible to achieve in bacteria, yeast or insect cell culture (Griffiths, 1992). E. coli was used to produce tissue plasminogen activator (t-PA) (Cartwright and Crespo, 1991) to very high levels (700 mg/L), but the protein was insoluble and inactive. Yeast hosts also produce large quantities of recombinant proteins, but the product is often hyper-glycosylated, which affects its activity and clearance in vivo (Cartwright, 1992). High levels of t-PA production have been obtained in yeast (up to 100 mg/L), but the product was not secreted (). Insect cells also can produce to high levels (up to 160 mg/L) (Farrell et al., 1999), however t-PA produced in insect cells have similar problems of incorrect (Cartwright, 1992) or missing (Farrell et al., 1999) glycosylation. Many types of mammalian cells including Chinese hamster ovary (CHO), hybridoma and Bowes melanoma cells (Brenner and Hulser, 1996) have been used to produce t-PA. There is some heterogeneity in the glycosylation patterns between different mammalian cell types, but these patterns are much closer to human protein glycosylation and thus, therapeutic product. Chinese hamster ovary and baby hamster kidney (BHK) cell production of complex recombinant proteins are widely used in bioprocesses due to the fidelity of expression and the secretion of the product to the extracellular medium, with relatively few other proteins contaminating the culture supernatant. 1.1.2 Selection of Process In the production of the recombinant proteins, there are four general types of bioprocesses used: batch, (semi-) continuous, fed-batch and perfusion (Figure 1.1). Batch processes have predominantly been used due to their relative simplicity and ease of operation. The reasons for using batch culture are primarily historical due to the fact that (1) most cell culture was based on 2 Medium Feed Spent Medium, Cells & Product Batch Semi-continuous Concentrate Feed Medium Feed Cell Retention Spent Medium & Product Fed-batch Perfusion Figure 1.1. Bioprocess schematic alternatives for recombinant protein production. 3 vaccine manufacture (cell lytic process), (2) technology in the 1960's was not suited to continuous cultures, (3) original cell lines were human diploid cells (limited life span), (4) animal cell processes were adapted from bacterial systems (the main adaptation was for oxygenation at low impeller speeds) (Griffiths, 1992). In batch culture, cells may grow for 3 to 7 days and the entire culture is harvested, generally when cell viability starts to decline and protein titers (concentrations) are maximized. The production scale reactors may be as large as 106 L (Shuler and Kargi, 1992). As the cells grow in batch, the reactor environment changes, which may cause heterogeneity in the protein product (Hooker et al., 1995; Coppen et al., 1995). Substrates are consumed, while toxic byproducts tend to accumulate. If the culture progresses too far and the viability of the culture declines, then the protein product may be contaminated with cellular debris and protein from lysed cells. Semi-continuous processes have also been termed repeated-batch processes (Shuler and Kargi, 1992). The culture is allowed to grow to the same point as a batch culture, but a large fraction is harvested and replaced with fresh medium. The repeated harvesting may be more cost-effective than batch processes, but semi-continuous processes suffer from similar disadvantages, such as changing culture conditions and build-up of toxic byproducts in the growth phase (Griffiths, 1992). Continuous cultures are extensions of semi-continuous processes, with the culture approaching that of a continuous stirred tank reactor. The dilution rate sets the growth rate in the culture (Bailey and Ollis, 1983), ensuring relatively easy study of the cellular kinetics (Miller et al., 1988; Miller et al., 1989; Hiller et al., 1993). Continuous processes (also known as chemostats) have not been generally used for production, given the relatively low cell densities and product titers that are obtained (Hiller et al., 1993). 4 In fed-batch culture, a concentrate of nutrients (typically eliminating the salt content in the medium and to make a 5- to 10-fold concentrate of glucose, amino acids and other components) is fed to extend the culture viability. Fed-batch strategies have been applied successfully in hybridoma cultures, where order of magnitude improvements (relative to batch) in the antibody titer are possible (Xie and Wang, 1994b; Bibila et al., 1994; reviewed in Bibila and Robinson, 1995). The culture conditions in fed-batch cultures can change more than in batch, and variations in the post-translational modifications for the product protein have been described (Xie et al., 1997), including increased proportions of under- and non-glycosylated protein product (Robinson et al., 1994). In perfusion culture, a high cell concentration is maintained in the reactor, while fresh medium is added and spent medium is removed, allowing for a homogeneous environment and generally, a much greater volumetric productivity (Griffiths, 1992; Kadouri and Spier, 1997). Perfusion cultures require a cell retention device to sieve the relatively small and delicate animal cells from the extracellular medium, without exposing the cells to potentially damaging conditions (such as low oxygen tensions or the lack of pH control). The first FDA-approved perfusion process was relatively recently validated (Bodeker et al., 1994). 1.1.3 Optimization of Bioreactors The optimization of mammalian cultures has tended to be for either the protein product concentration (Bibila and Robinson, 1995; Grammatikos et al., 1999) or the volumetric protein productivity (Kadouri and Spier, 1997). Increasing protein yields from medium will maximize the use of medium components (Glacken et al., 1986) and facilitate downstream processing. Optimizing volumetric protein productivity will maximize the total amount of protein produced. The use of medium recirculation has been suggested in order to identify toxic metabolites 5 (Buntemeyer et al., 1992) or limiting factors. Identifying limiting factors is the focus of bioprocess simulation and optimization software (Petrides et al, 1995), and since t-PA has been extensively researched, software optimization for the overall cost of t-PA production has been performed (Datar et al., 1993; Rouf et al., 1998). 1.2 M O D E L S Y S T E M Tissue-type plasminogen activator (t-PA) production by CHO cells in serum-free medium was used to assess control protocols for fed-batch and perfusion cultures, as well as optimize the overall production of recombinant protein. Controlling a mammalian bioprocess is a challenge due to non-linear cellular growth and the lack of on-line sensors for the analytes of interest. Model-based predictive control protocols may be formulated with non-linear models and inferential estimation for periods between sampling (Soeterboek, 1992). Simpler process models may suffice for control purposes, as the model parameters can be updated with sampled data. 1.2.1 Culture Modeling Understanding recombinant protein production is well served through modeling (Bailey, 1998), with the system boundary being either the cell membrane or the bioreactor. With the system boundary being the cell wall, the modeling includes the assessment of growth and uptake rate kinetics, usually in response to either genetic changes (Dorner et al., 1992), medium formulation (Glacken et al., 1986) or glucose and glutamine concentrations (Ljunggren and Haggstrom, 1994; Zeng and Deckwer, 1995). With the system boundary being the bioreactor, the modeling includes volumetric uptake or production rates for the purposes of process control (Ozturk et al., 1997; Dowd et al., 1999) or observing correlations due to different operating conditions such as different cell concentrations (Banik and Heath, 1995). 6 1.2.2 t-PA As a Model Recombinant Protein T-PA is a serine protease in the fibrinolytic system which converts plasminogen to plasmin, which in turn, digests fibrin (blood clots). A naturally-occurring glycoprotein, t-PA can be used as a therapeutic drug for heart-attack and stroke victims. Glycosylation is important for the therapeutic function of the protein, as it may control biological activity and clearance from circulation in vivo (Wilhelm et al., 1990; Drickamer, 1991). Normal t-PA exists in two glycoforms, Type I and II, in which form I is glycosylated at three points and form II is glycosylated at two points (Pohl et al., 1987). The specific activity of Type II t-PA has been shown to be up to 50% greater than Type I (Einarsson et al., 1985). The single-chain amino acid sequence can be cleaved by plasmin to form a two-chain disulfide-linked molecule, consisting of an A chain and a B chain. The two-chain form of t-PA has similar biological function as the single-chain form, but is cleared in vivo at a higher rate (McKillip et al., 1991). The levels of Types I and II t-PA products varied with the type of bioprocess and medium components used (McKillip et al., 1991). Plasminogen activator inhibitors (PAT) are present in serum-containing medium (Sprengers and Kluft, 1987), thus the use of serum-free medium should prevent t-PA inactivation (Kadouri and Bohak, 1985). As a model recombinant protein, both activity and protein-based assays for t-PA are well characterized (Randy and Wallen, 1981; Harlow and Lane, 1988). 1.2.3 Bench-scale Reactors The bioreactors used in this study were of bench-scale, and were used due to the ease of setup and operation, while including temperature, pH, dissolved oxygen and level controls, which are also characteristic of larger reactors. Larger reactors potentially have greater problems in 7 cleaning and sterilization and may experience spatial- and temporal-inhomogeneities in oxygen concentrations due to mixing and measurement limitations (Nienow et al., 1996; Hatzimanikatis and Bailey, 1997). Cells were grown in T-flasks and spinner flasks (in incubators) to observe culture effects, under the assumption that these conditions approach that of the reactor environment (Humphrey, 1998). 1.2.4 Cell Retention As reviewed in Woodside et al. (1998), various cell retention strategies have been employed and these will impact the perfusion operation. One of the earliest studies for mammalian cells in suspension was performed with a spin filter (Himmelfarb et al., 1969). However, spin filters foul, with the majority of the cell fouling occurring initially with single-cell suspensions. Increased rotation speeds may reduce fouling, but the gradual growth of cells on the filter will cause the filter to fail (Deo et al., 1996). Microcarriers have been used at constant cell densities of 2 to 6 x 106cells/mL with CHO cells for over two months (Kong et al., 1998). Microcarriers may be useful for anchorage-dependent cell lines, but mass transfer gradients across the multi-layers of cells that grow may cause production inhibition of 1.9-fold, similar to what was observed in hollow fibre bioreactors (Kratje and Roland, 1992). Hollow fibre bioreactors have been used to produce recombinant proteins with mammalian cells, but with adherent BHK cells, large decreases in the protein production were observed. The cells may stick together and leave insufficient intercellular space for removal of the product, even with the use of protein-free medium (Ryll et al., 1990). Centrifuges have been reported to preferentially separate viable and nonviable cells (Johnson et al., 1996), but performance may depend on the feed rate, rotor speed, separation and discharge time. The operation of continuous centrifuges may be complicated by component durability and the negative effect of being in a cell pellet on the 8 culture viability (Johnson et al., 1996). Unassisted gravitational settling separation systems exploit sloped surfaces and quiescent regions in the reactor and may cause less physical damage to cells compared to filtration and centrifugation (Tokashiki and Takamatsu, 1993). Acoustic filtration (Pui et al., 1995) has been exploited for perfusion cell retention, and has many desirable characteristics, including non-fouling surfaces and ease of operation. Similar to an external vortex flow filtration (Roth et al., 1997), cells are pumped in a recirculation line to help aggregates settle back into the reactor. In serum-free and protein-free medium however, pumping of the cell suspension may negatively affect the culture viability (Merten, 1999). 1.2.5 Identification of Limiting Factors The process of identifying limiting factors may be applied to any process analysis (Bailey, 1998), with the recombinant protein production from mammalian cells being no different. A challenge in dose response analysis is to replicate the conditions to what is observed in the process. Extensive work has been done to examine the metabolic pathways in attempts to identify limitations and optimize the per cell protein production (Holms et al., 1991; Grampp et al., 1992; Varma and Palsson, 1994; Bonarius et al., 1995; Bonarius et al., 1996). Once limitations are identified, changes in process operation may improve cellular production and increase yields of protein from medium (Glacken et al., 1986). The cellular metabolism as measured via cell specific uptake or production rates, may be a sensitive function of the culture conditions (Zeng and Deckwer, 1995). The effects of cellular limitations may also be used in simulation work of the process (Williams et al., 1986; Ozturk, 1996; Zeng and Deckwer, 1999). 9 1.3 THESIS OBJECTIVES AND ORGANIZATION It is the hypothesis of this thesis that advanced predictive control strategies should be well suited to control substrate concentrations in biological systems that are inherently difficult to control due to noisy and infrequent measurements. The performance of modeling and predictive process control strategies will be evaluated for fed-batch and perfusion feed rate estimation, with the goal of reducing process variability. Once a well-controlled process is obtained, Chinese Hamster Ovary cell recombinant t-PA production in fed-batch and perfusion processes will be optimized. Fed-batch and perfusion process performance will be compared and any intracellular or process limitations analyzed. In fed-batch processes, the amino acid portion of the concentrate formulation will be optimized using models and measurements. The goals of fed-batch cultures are to extend culture viability to elevate protein titers, as well as analyze any cellular or process limitations. In perfusion processes, feed rate calculation based on daily glucose sampling and inferential glucose uptake rate estimation will be assessed, as well as long-term acoustic cell filter use. Consistent perfusion start-p will be desirable, as will medium optimization and assessing the process response to different glucose set points to map the optimal range of operation. To satisfy these overall objectives, there were several components of this research. A literature review of the topic of discussion, along with a materials and methods summary for the thesis work are presented in Chapters 2 and 3, respectively. Following these elements, the systematic modeling of the volumetric uptake and production rates used as a basis for predictive control protocols for perfusion and fed-batch cultures will be described in Chapter 4. Subsequent modeling will also be presented in Chapter 4, along with simulation of the processes to assess the importance of noise and model selection on the effectiveness of the process control. Fed-batch process development and results, along with t-PA dose response experimentation will be 10 discussed in Chapter 5. Perfusion process results and culture responses as a function of medium formulation and utilization will be described in Chapter 6. Finally, the conclusions of the research will be presented, along with directions for possible further research in Chapters 7 and 8, respectively. 11 C H A P T E R 2 LITERATURE REVIEW 2.1 MODELING OF CELLS In general, the modeling of cells is complicated due to the complex nature of cellular processes. Different perspectives of modeling cell population growth and metabolism have been taken (Table 2.1). Multi-component cell representations are termed structured models, whereas segregated models consider the cell population as a heterogeneous mixture. For example, a multi-component cell representation may distinguish between cellular DNA, RNA and protein levels and mechanistically describe intracellular processes. A segregated model considers the culture as a mixed population, for instance, cell diameters may be based on a Gaussian function. A further distinction that can be made in cell modeling is between stochastic (probabilistic) and deterministic models. Bastin and Dochain (1990) and Stephanopoulos and San (1983a), used stochastic estimators to model cell growth. Complete growth models for even a small portion of a biological process do not exist (Tzaimpazis and Sambanis, 1994). These models need to be able to describe what is observed experimentally in order to be used for control purposes. Table 2.1. Different Perspectives of Cellular Kinetic and Metabolic Modeling Unstructured Structured Multi-component average cell description Multi-component, heterogeneous cell population Adapted from Bailey and Ollis (1983). 12 A goal of modeling both the cell and bioreactor is to understand how the process may be manipulated in order to improve performance (Bailey, 1998). The majority of the cell modeling has been for growth, substrate uptake and protein production. Several groups used theoretical equations (Kyung et al., 1994; Pelletier et al., 1994) and/or an extended Kalman filter (Stephanopoulos and San, 1983a,b; Gudi et al., 1994), to estimate the state of the biological system. Modeling the cell includes kinetic models for the recombinant protein production (Bibila and Flickinger, 1992, Fann and Piret, 2000) or substrate uptake rates, usually in response to changes in the genetic makeup of the cells (Dorner et al., 1992). This can also include how the cells respond to different medium formulations (Bonarius et al., 1996) or to transient culture conditions, usually studied in continuous cultures (Miller et al., 1988; Miller et al., 1989; Hiller et al., 1993). The majority of modeling on a bioreactor scale is mass balance based and applied to correlating protein production to reactor concentrations, such as glucose and glutamine (Ljunggren and Haggstrom, 1994; Zeng and Deckwer, 1995). 2.1.1 Growth Modeling Cell growth and death depend, for example, on the substrate concentrations, extent of cell aggregation, etc. (Tzaimpazis and Sambanis, 1994). Typically, either the Monod equation (Equation 2.1) or a modified Monod equation (Equation 2.2) are used: C< H = m^ax H = Umax or 'S i Csi + K S i f C ^si V c s i + K s i V 'S2 C s 2 + K s 2 J K, f V 'SI V C S 1 + K s l y 'S2 V C I 1 + K H K 12 C j 2 +K I 2 V C n +K V M l K 12 II A ^ I 2 C„ +K 12 7 (2.1) (2.2) 13 where u, and |imax are the specific and maximum specific growth rates, respectively, the subscripts 1 and 2 refer to different specific substrates (S) or inhibitors (I), respectively, and K s. and Ki are the substrate and inhibitor constants, respectively. The modifications include additional substrate or inhibition terms either in additive or multiplicative forms (Shuler and Kargi, 1992). However, the Monod equation and its variants are not generally valid for transient conditions, (i.e. after a pulse or step concentration change), but several approaches have been used to attempt to solve time-varying or transient growth conditions (Table 2.2). Table 2 . 2 . Approaches to Model Estimation of Cell Growth Approach Comments Reference Growth rate assigned a priori and feed rate determined based on the feedback control of the growth rate Applicable only for microbial cultures of single limiting substrate Mou and Cooney, 1983; Williams et al., 1986 Treat the growth rate as a coloured noise term in an Extended Kalman Filter (EKF) technique to re-estimate the growth rate Adaptable, requires implementation of EKF estimation Stephanopoulos and San, 1983a,b Model growth as an a priori set value that could be adjusted by culture measurements Adaptable, growth rates were restricted to small range of values Bastin and Dochain, 1990; Cornet et al., 1993 Allow substrate concentration(s) to be time variant, and substitute into time-invariant growth equation Simple, but may be limited in transient conditions Pelletier et al., 1994 14 2.1.2 Substrate Uptake and Metabolite Production Modeling The quantitative description of substrate uptake or metabolite production starts with mass balance equations which can be prepared for specific reactor configurations. Yield and rate equations describe the cellular metabolism which is independent of reactor configuration. Yield equations are based on material and energy balances which require assumptions for simplification. Yields are often reported as ratios of rates, such as the ratio of lactate production to glucose consumption and assume invariant rates over the time interval. Rate equations describe the cellular kinetics that are functions of intracellular parameters and the extracellular medium. For instance, the rate of protein secretion to the extracellular medium may be expressed as a function of the intracellular protein level (Bibila and Flickinger, 1992). However these yield and rate equations tend to be empirical in nature (Andrews, 1993; Tzaimpazis and Sambanis, 1994). In general, the rate and mass balance equations are expressed as a function of the specific growth rate and yield coefficient. On occasion, an additional coefficient is included in the model (Table 2.3) to represent endogenous and/or maintenance metabolism. Endogenous metabolism refers to reactions which involve the breakdown of cell structure, while maintenance metabolism involves the consumption of substrate for other energetic cellular processes, unrelated to growth. Metabolite production modeling has been structured in an analogous manner to substrate uptake (Table 2.3). 15 Table 2.3. Substrate Uptake and Metabolite Production Modeling Equation Comments References 1^  <ls = v +ms Yxv/s q P = v ^ + m p YX V/P Maintenance (ms or mp) can be difficult to measure, and may not be included Leudeking and Piret, 1959; Mou and Cooney, 1983, Stephanopoulos and San, 1983; Wu et al., 1995; Kurokawa et al., 1994 „ v l r v-9 , .„ = q s x v - 1 0 + fit ^ L = q PX v .10- 9 + dt D(CP I n _ C P out) Basic mass balance used for almost all feed type bioreactor processes Ljunggren and Haggstrom, 1994; Ljunggren and Haggstrom, 1995 where the subscripts S and P refer to substrate and metabolite, respectively, q is the cell specific rate, (pmol/cell-day), m is the maintenance requirement (pmol/cell-day), C , C, in and C out are the general, feed and outlet concentrations; respectively (mM), t is time (day), X v is biomass concentration (cells/L), D is the dilution rate (day'1), Yyj. is the yield of biomass (cell/pmol substrate or pmol metabolite). -The biomass concentration may either be total or viable cell biomass (Ljunggren and Haggstrom, 1994; Ljunggren and Haggstrom, 1995). The cell specific rates are assumed to be linear functions of the growth rate and have constant maintenance requirements. Both assumptions may be problematic as culture conditions change (Zeng and Deckwer, 1995). Mass balance equations based on the volumetric uptake or production rates obviate the concerns for determining cellular maintenance coefficients. The mass balance equations can accurately describe process dynamics, however deviations can occur if the assumed flow patterns deviate 16 from actual, such as inhomogeneities in mixing for a continuous stirred tank reactor (Hatzimanikatis and Bailey, 1997). 2.1.3 Microbial Culture Modeling Mou and Cooney (1983) and Stephanopoulos and San (1983a,b) used elemental balances to partially specify a process model. The model system of equations was completed using measurement values for the rate kinetics. Their objectives were to implement the model, estimate parameters, verify estimates under different conditions and then use the model for prediction. Flux analysis of metabolic pathways using metabolic control theory has been used for microbial cultures (Holms, 1986; Holms et al., 1991; Regan and Gregory, 1995). The method by Regan and Gregory (1995) used measurement of substrates, biomass, metabolites and stoichiometric knowledge to form a basis for the system, which could then be integrated into a control strategy. In metabolic flux balancing, a metabolic quasi-steady state was assumed, based on the assumption that metabolic transients were typically rapid compared to cellular growth rates and environmental changes. The metabolic fluxes leading to the formation and degradation of any metabolite must balance, that is, S • v = b, (where S is the stoichiometry matrix, v is the metabolic reaction rate vector and b is the net metabolite uptake vector (Savinell and Palsson, 1992; Varma and Palsson, 1994)). The problem with this approach was that often complex matrix manipulations were required. 2.1.4 Animal Culture Modeling The knowledge and methods of microbial culture modeling can be applied in more complex animal culture processes. For example, Batt and Kompala (1989) used structural compartments of intracellular components to create a small number of metabolite pools for a 17 microbial culture in a structured model. In a similarly structured model, Ray and Shuler, 1987 developed a CHO model that takes into account glucose, glutamine, amino acids, metabolic by-products and chemical structures. The rate equations exhibited saturation-type kinetics with feedback control. The model could be quite accurate, but required a great deal of literature values and could not easily be made adaptable (due to lack of measurement) (Tzaimpazis and Sambanis, 1994), which is problematic if used for process control purposes. Glucose and glutamine are partially substitutable and partially complementary (Zielke et al., 1978). Mammalian cells can shift their metabolism in response to different conditions, for example, a modified Monod model may predict zero growth with low glucose and high glutamine concentrations. However, mammalian cells could shift their metabolism to utilize the glutamine and may have a non-zero growth rate (Jeong and Wang, 1995). Glutamine spontaneously decomposes at varying rates depending on temperature, pH and culture medium (Ozturk and Palsson, 1990). Its degradation can be modeled as a first order process and is sometimes included in substrate balance equations (Zeng and Deckwer, 1995). 2.1.5 Recombinant Protein Production Modeling The production of recombinant proteins begins with transcription from the cDNA, then by translation at the mRNA, followed by post-translational modifications and finally secretion. Bibila and Flickinger (1992a,b) proposed a kinetic model of hybridoma protein production that was modified by Fann et al. (2000) and the parameter values were obtained for a wide range of CHO cell clones producing t-PA (Fann et al., 2000) (including the CHO cells used in this study). The levels of cDNA, mRNA, intracellular protein and expected protein productivities of these CHO cells should be consistent, as these come from a cell clone. However, Fann et al. (2000) assumed that the time derivatives of these variables would be equal to zero. In batch and fed-18 batch cultures, the growth rate will be a function of time, as the culture progresses through exponential growth, stationary and death phases. Messenger RNA levels have been shown to vary with growth rate and over a batch culture (Dalili and Ollis, 1990; Bibila and Flickinger, 1991; Fann, 1999). Messenger RNA variation will affect other cellular parameters, such as intracellular protein content and secretion rates. Thus, the assumptions of the derivatives being equal to zero may not be valid in batch and fed-batch bioreactor studies. 2.1.6 Mass Balance-based Modeling Mass balance-based modeling of perfusion and fed-batch processes predict bioreactor changes in response to feed volumes of medium and formulated concentrates. This modeling can be used in the calculation of the feed rates for perfusion and fed-batch processes. In the control protocol, current and immediate future glucose uptake or lactate production rate estimates can be modeled in order to select the future feed rates (Ozturk et al., 1997; Dowd et al., 1999). The modeling of the volumetric glucose uptake rates was done instead of specifying a constant cell specific rate and multiplying by the cell number and reactor volume to obtain uptake rates. The mass balance approach was done to avoid estimation of the cell numbers, as it assumes that cell specific glucose uptake rates are known or deterministic and that cell volumes remain constant. These two assumptions may not be valid, as variations in the cell specific uptake/production rates are observed over batch culture (Zeng and Deckwer, 1999) and cell volumes may not remain constant even in perfusion culture (Seewoster and Lehmann, 1997). 19 2.2 HIGH C E L L DENSITY BIOREACTOR PRODUCTION OF RECOMBINANT PROTEINS Both fed-batch and perfusion processes are improvements on batch operation through increases in product and/or cell concentrations. Both processes involve a feed of media components, and require strict control of the feeding in order to realize improvements in performance. The supply of substrates will affect the cellular performance, which in turn, affects the process scale performance. A general approach to improving the process performance is to limit the supply of nutrients to the fed-batch and perfusion cultures, as well as through process control. 2.2.1 Rationale for Limiting Substrates Glucose and glutamine supply energy to the cell (Figure 2.1) in the form of ATP via their metabolic breakdown. Glucose and glutamine (substrates) are the primary carbon and energy sources for the cells, while glutamine is the primary nitrogen source (Zielke et al., 1978). Glucose can be metabolized either by the pentose phosphate pathway, the tricarboxylic acid (TCA) cycle or glycolysis to generate adenosine triphosphate (ATP). Glucose also forms the subunits which make up the ribose moieties for glycoproteins, as well as the ribosyl units for RNA and DNA. Glutamine is used for anabolic functions such as protein and nucleic acid biosynthesis, deamination to glutamate, oxidization via the TCA cycle to four carbon products, then to three carbon products and finally to CO2. 20 Glucose Pentose cycle NADH Lactate ^ . Biosynthesis Protein Biosynthesis << Asparagine ^ Aspartate Oxidative Phosphorylation Glutamate N H / < -4- Biosynthesis Glutamine Figure 2.1. Simplified schematic for the utilization of glucose and glutamine in mammalian cells. 21 As there is no outflow in a fed-batch process, reducing ammonium and lactate production rates are required for extending culture viability (Glacken et al., 1986; Kurokawa et al., 1994; Xie and Wang, 1994a,b). In a perfusion process, the flow rate will tend to flush inhibitory components from the reactor. Lower perfusion rates are desirable to increase product titers (Ozturk, 1996), however insufficient addition rates can cause potentially inhibitory levels of ammonium (Griffiths et al., 1992), which can affect product glycosylation (Jenkins and Hovey, 1993; Anderson and Goochee, 1995; Gawlitzek et al., 1995). Therefore, effective control of the metabolite and substrate concentrations in the bioreactor is needed so that the cells will produce a high quantity and quality of protein. 2.2.2 Predictive Control The application of standard control protocols is complicated by the nature of biological systems. The response of a biological system to changing conditions tends not to be as reproducible as responses in traditional chemical production processes. In addition, the sensors for molecules of interest often are not available. Off-line measurements are usually at a low frequency and the results are delayed. Partially for these reasons, pharmaceutical companies have used computers more for monitoring than for control purposes (Liidi et al., 1992; Schugerl et al., 1996). Predictive control belongs to a family of adaptive model-based controller protocols. A model of the process is a required element and is used to design the controller. The advantage of predictive controllers is that the relationship between the design parameters and the desired performance is easily observed. Model-based controllers such as linear quadratic or pole-placement require a translation between the design parameters (weighting matrices or closed-loop pole locations) and the desired performance (response time, overshoot, etc.) that is, in general, 22 highly non-linear (Soeterboek, 1992). There are several additional advantages for predictive control and the relevant ones for this work include the ability: (1) to be derived for non-linear processes, (2) for constraints to be handled in a systematic way in the design, and (3) for feed-forward action to be introduced for measurable disturbance compensation or tracking reference trajectories. The growth models used for both fed-batch and perfusion processes are highly non-linear and have constraints (i.e. maximal limits on cell growth, etc.). Model-based feed-forward action is advantageous as the bioprocess may respond differently at various culture stages (Meyer andBeyeler, 1984). 2.2.3 Fed-batch Process The operation of successful fed-batch cultures depends on feeding a nutrient concentrate to maintain cell viability and protein production. At higher than limiting glucose and glutamine concentrations, mammalian cells tend to produce higher levels of the inhibitory metabolites, lactate and ammonium. Accumulation of lactate and ammonium can be inhibitory to the cell growth (Glacken et al., 1986) and affect the protein production quantity (Xie and Wang, 1994) and quality (Anderson and Goochee, 1995). For ammonium-inhibited fed-batch cultures, Portner et al. (1996) utilized dialysis to remove ammonium from the extracellular medium, which resulted in increased antibody and cell concentrations. If the concentrations of glucose and glutamine are controlled at near-limiting levels, then there can be more efficient use of medium components (Glacken et al., 1986). Variations in limiting nutrient levels have been correlated with variable cell specific protein productivity and heterogeneous post-translational modifications (Van Erp et al., 1991). Fed-batch cultures are generally grown as a batch and then concentrate addition is initiated. Supplementing the culture with glucose and/or glutamine as the culture was near the 23 stationary phase resulted in 1.9- to 5-fold increases in monoclonal antibody titers relative to batch (Reuveny et al., 1986; Flickinger et al., 1990). More complex concentrate formulations have evolved, resulting in up to 11-fold increases in antibody concentrations relative to batch (Robinson et al., 1994). The timing for the start of feeding will depend on the initial conditions. Glacken et al. (1986) used bolus additions at the end of logarithmic growth, after the culture had grown for several days. However, Zhou et al. (1995) inoculated cultures at low glucose concentration which necessitated concentrate additions after 1 day. To control concentrations in fed-batch cultures, several types of controllers have been used including conventional PID-controllers (Kurokawa et al., 1994), model-based a priori control (de Tremblay et al., 1993), adaptive control (Wang et al., 1995) and on-line estimation of oxygen uptake rate (OUR) (Zhou and Hu, 1994). Conventional PID-controllers are not often applied to infrequently sampled glucose- and glutamine-limited cultures (Shimizu et al., 1988), due to lack of predictive ability. Instead, PID controllers are more suitable with flow injection analysis systems that frequently analyze samples (Kurokawa et al., 1994). A priori or open-loop model-based controllers do not adjust to actual culture conditions and need to have good predictive ability at near-limiting conditions (Schwabe et al., 1999), where growth or metabolism may be significantly impacted by small changes in substrate concentrations (Wang et al., 1995). With a priori feeding, de Tremblay et al. (1993) reported 3-fold higher antibody titers versus batch compared to under 2-fold higher for feedback control. Fike et al. (1993) based hourly additions on automated glucose analyzer results to lengthen culture viability and increase protein productivity. In addition, with constant, continuous feeding, a decreasing cell specific growth rate was observed, but when an exponentially increasing feed was applied, a constant cell specific growth rate was obtained (Ljunggren and Haggstrom, 1994). Adaptive control protocols update model parameters based on the measured values during the culture and controlled glucose 24 concentrations to less than 0.1 mM variation with an automated sampling and sensor system (Siegwart et al., 1999). Concentrate addition has also used on-line estimation of the oxygen uptake rate (Zhou and Hu, 1994) or carbon dioxide evolution rate (de Tremblay et al., 1993). These methods assumed either a stoichiometric relationship between oxygen and glucose (updated off-line) or a correlation between the rates of increase for carbon dioxide evolution and specific growth rates. Both strategies increased productivity and reduced lactate and ammonium accumulation. Accurate on-line measurement (~ 0.1 mM) of glucose and glutamine has been performed (Kurokawa et al., 1994; Wang et al., 1995), using a potentially fallible on-line HPLC system. More often, glucose has been used as the culture indicator to control, and other nutrients, such as glutamine, have been supplied in a constant ratio (Omasa et al., 1992; Ljunggren and Haggstrom, 1994) to maintain their levels. Unbalanced concentrate formulations (compared to the relative uptake rates) causes the surplus or shortage of certain substrate components (Fike et al., 1993; Schwabe et al., 1999). Fike et al. (1993) based concentrations in the supplement on batch culture prior to significant medium depletion. Xie and Wang (1994) based their formulation on a stoichiometric analysis of the cells, with assumptions about molecular formulas of cellular components and metabolic ratios. Even though the concentrations of many components increased several-fold over the culture period, 5-fold increases in viable cell indices and 10-fold increases in antibody titers were obtained relative to batch (Xie and Wang, 1994), as has been reported in other hybridoma cultures (Bibila et al., 1994). Step-wise improvements in the amino acid portion of the concentrate were based on subsequent fed-batch measured concentrations. The amount of concentrate fed at each interval was characterized (Xie and Wang, 1994) as a stoichiometric addition based on the change in cell number. Control of feeding based on cell 25 numbers is analogous to cell specific perfusion rate specification used to control perfusion cultures (Bodeker et al., 1994). In CHO cells, t-PA may be toxic to cells at 50 mg/L (Kaufman et al., 1985), but others have reported 65 mg/L t-PA concentrations with no apparent cytotoxic effects (Tung et al., 1988). Serum-containing medium may cause t-PA instability due to plasminogen activator inhibitors (Sprengers and Kluft, 1987). The use of aprotinin (Brouty-Boye et al., 1984) or serum-free medium has increased the half-life of t-PA in culture medium (Kadouri and Bohak, 1985). In serum-free medium, Cartwright (1992) reported that t-PA levels appear to plateau at 50 mg/L. In human fibroblast cultures where half of the supernatant was withdrawn and replaced with spent medium treated with silica (to adsorb and remove t-PA), t-PA production was increased up to 3-fold (Kadouri and Bohak, 1985). In addition, external additions of t-PA appeared to suppress de novo protein production (Kadouri and Bohak, 1985). These effects may be cell-line specific, as t-PA may be avidly bound and internalized by fibroblasts (Hoal et al., 1983). The adsorption of t-PA is also prevented through the use of Tween-80 at a concentration of 0.01% (Einarsson et al., 1985). 2.2.4 Perfusion Process The operation of high cell density perfusion cultures requires timely and appropriate feeding of nutrients to allow for cell growth and to maximize protein production. Chemostats operated at constant dilution rates readily attain steady-state cell and culture concentrations. In perfusion cultures with complete particle retention, dead cells and debris will tend to accumulate inside the bioreactor, so a cell bleed rate is required, which will affect the final cell density and culture performance (Zeng and Deckwer, 1999). Vits and Hu (1992) showed that perfusion systems operated at high dilution rate and high cell retention may experience large fluctuations in 26 biomass concentration. Changing cell concentrations complicate reliable control of feed rates to maintain optimal culture conditions. Often perfusion feeding has been based on off-line measurements and increasing the feed rate to maintain the glucose concentration or to limit the lactate accumulation (Handa-Corrigan et al., 1992). Alternatively, the required flow rates have been calculated by multiplying the viable cell number (obtained via hemocytometer counts or a viable cell probe) by a cell specific perfusion rate (Bodeker et al., 1994). The calculation of the flow rate is straightforward, however variability in the hemocytometer counts or probe calibration/noise may result in a changing bioreactor environment. The optimization of a process controlled in this manner is possible by manipulating the cell specific perfusion rate and observing the effect on bioreactor performance (Ozturk, 1996; Heidemann et al., 1999). Alternatively, oxygen uptake rate measurements were used (Kyung et al., 1994) to estimate the perfusion rate, assuming a constant stoichiometric coefficient between glucose and oxygen utilization. The maintenance of a constant glucose environment using either a viable cell probe or an oxygen probe depends on a constant relationship between cell number or oxygen utilization to glucose utilization. Banik and Heath (1995) described hybridoma perfusion cultures in which the specific glucose uptake rate was strongly correlated with specific growth rate and may be a function of viable cell density. Under low oxygen tensions (Lin et al., 1993), the ratio of oxygen to glucose consumption has been shown to change. More frequent sampling may be accomplished (Konstantinov et al., 1996; Ozturk et al., 1997) with a flow injection analysis system to automatically sample and control the process. Konstantinov et al. (1996) used a linear controller (with a dead zone and an activation time) to control the process within 0.66 to 0.72 mM of the set point concentration. Ozturk et al. (1997) used a simple feed-forward algorithm using glucose uptake rates and hourly sampling to control the process with low 27 variability when the viable cell density was increasing. However, these approaches require a dedicated analyzer with a complex automated flow injection analysis system that is potentially fallible. With medium fortification, the medium perfusion rates can be lowered, which reduces the cost of operation and increases the product titer (Ozturk, 1996). Higher glutamine concentrations have been reported to increase maximum cell concentrations, antibody titers and cell specific antibody productivity in hybridoma cells (Jeong and Wang, 1995), while Duval et al. (1991) reported the depletion of glutamine induced uptake arrest with other amino acids and negatively affected culture viability. Medium fortification with 2X and 3X basal medium has resulted in lower perfusion rates and higher product titers, but were unoptimized (Ozturk, 1996). Medium optimization may simply involve reducing or removing components, such as serum to facilitate downstream processing or lower costs (Ryll et al., 1990), or may be more sophisticated, as has been done with concentrates of fed-batch cultures (Bibila and Robinson, 1995). 2.3 S U M M A R Y As illustrated in the previous sections, there have been extensive efforts to model both the cellular and bioreactor processes. However, the use of simple, unstructured models in bioprocess control has not been well characterized and should satisfy the thesis objectives to maintain and/or manipulate the process environment. Once effective control is attained, then bioreactor operation can be optimized. It should be stressed that fed-batch processes have been studied predominantly for hybridoma cells producing monoclonal antibodies (see review in Bibila and Robinson (1995)). Optimizing fed-batch operation for CHO cells producing t-PA, a recombinant protein, has not been adequately reported. The optimization of perfusion processes has not been extensively studied (Ozturk, 1996), due to process complexity. A methodology for correlating 28 controlled variables with the perfusion process performance would be a useful optimization target. 29 CHAPTER 3 MATERIALS AND METHODS 3.1 CELL CULTURE Chinese hamster ovary (CHO) cells were transfected and amplified to produce t-PA (Fann, 1999). The cell clone used, unless otherwise noted, was SI5-12.23SFM23, initially supplied by Cangene Corporation (Winnipeg, MB). Briefly, the cell line was transfected with vector pSLl 1 which contains one t-PA cDNA cassette with a dihydrofolate reductase (DHFR) cDNA for methotrexate (MTX) selection, while production is controlled and enhanced by the elongation factor-1 (EF-1) promoter and EF-1 intron, respectively. The CHO cells were grown in a serum-free medium (CNJSFM 2.1, Cangene, Winnipeg, MB), a 1:1 formulation of Hamm's F12 and Iscove's Modified Dulbecco's Medium (JMDM) with a proprietary set of additives. A hybridoma cell line was used as a control for some CHO cell experimentation. The rat hybridoma cell line, TFL-P9, producing an IgGi monoclonal antibody (StemCell Technologies, Vancouver, BC) was grown in Dulbecco's Modified Eagle Medium (DMEM) supplemented with 5% fetal bovine serum (Life Technologies, Burlington, ON). Inoculum train and bioreactor operation was identical to CHO cell culture. 3.1.1 Inoculum Train The inoculum train forms the basis for the presented experimental results and was kept as consistent as possible for comparison purposes. The inoculum train begins with a 1 mL frozen vial of between 106 and 107 cells in 8% dimethyl sulphoxide (DMSO) in fetal bovine serum (FBS). The cells are resuspended in 20 mL of fresh medium in a T-flask (75 cm2). After viable cells adhere to the T-flask surface at 24 h, the supernatant is removed and 25 mL of fresh CNJ-30 SFM2.1 is added to flush the serum and DMSO (a cryo-protectant). Over the next couple of days, the cells tend to detach from the surface in this serum-free environment. Cells are transferred 4 days post-thaw to a larger T-flask (175 cm2) with a 1:3 split with fresh medium. The cells from the larger T-flask are then transferred after 3-4 days to spinner flasks for two subcultures (both 1:3 splits with fresh medium) before bioreactor inoculation. Inoculation was generally at 1.5xl05 cells/mL with at least 90% viability. 3.1.2 Low Glucose Inoculum Train Prior to inoculation in the bioreactor or set of parallel experiments, the culture was twice sub-cultured (1:3 splits) with fresh 8 mM glucose and 1.3 mM glutamine medium. This inoculum train was used in later fed-batch cultures to start at lower glucose and glutamine levels. 3.1.3 Bioreactor Operation A 0.6 L working volume Lh bioreactor (Slough, UK) was run in batch phase for 2 to 5 days prior to concentrate (fed-batch) or medium (perfusion) additions (unless otherwise indicated). The gas flow control protocols for the operation of high cell density reactors were harmonized for comparison between fed-batch and perfusion systems. The control of pH (in general, at approximately 7.2) was mediated through the addition of CO2 to the headspace via on/off control of a solenoid valve. The control of dissolved oxygen was mediated through the addition of pure oxygen (at low inlet pressure (< 25 kPA gauge)) through a solenoid valve and a point sparger (unless otherwise indicated) located below the impeller to maintain 60% of air saturation levels. A constant air overlay into the headspace (controlled manually with rotameter between 4 and 10 headspace volumes per hour), similar to Clapp and De Garrido (1996), prevented excessive CO2 and oxygen levels in the headspace and maintained a slight positive 31 pressure within the bioreactor. The gas exited through a heat exchanger which allowed condensed water to flow back into the reactor. The air flow rates were generally 4- and 8-fold higher than the maximum C O 2 and oxygen flow rates, respectively (when the solenoid valves were open). The temperature in all cultures was controlled at approximately 37 °C. Temperature, pH and dissolved oxygen probes (Westech, Calgary, AB) were monitored and culture conditions were controlled with Anglicon (Brighton Systems, New Haven, UK) digital controllers and data logged using a personal computer. A pitched-blade impeller (Lh Fermentation, Slough, UK) at approximately 75 RPM was used for agitation. A QuickBasic (Microsoft, WA) computer program was created to activate a solid-state relay for a pump (503S Watson-Marlow, Wilmington, MA) via the parallel port. The program calibrated and controlled the pump which added medium volumes corresponding to the required flow rates every hour. A conductance-based sensor triggered the outflow pump to maintain a constant liquid level in the perfusion bioprocess. The cells were retained by an acoustic filter (Trampler et al., 1993; Zhang et al., 1998; Woodside et al., 1998) using a Biosep 10L (PSI Systems, Coquitlam, BC) (unless otherwise indicated) for the CHO cell cultures. Briefly, the acoustic filter uses a high frequency resonance field to retain, aggregate and recycle cells to the bioreactor. Acoustic separation employs an acoustic field, rather than a physical filter, eliminating fouling problems that are a challenge for filter-based retention systems. Cellular aggregation in the acoustic field enhances sedimentation rates, eliminating the need for stagnant settling zones, inclined surfaces and large hold-up volumes. As a result of having no moving parts, acoustic filtration has been very reliable and efficacy has been widely demonstrated. The acoustic filter does not retain all sizes of cellular particles and has demonstrated selective retention for larger viable cells (Pui et al., 1995). A cell bleed is a required element in a perfusion process, as cellular debris will tend to accumulate. The cell bleed in the perfusion 32 bioreactor cultures was controlled by manipulating the acoustic filter duty (on : off ratio). Decreasing the duty allowed for more cells to leave the reactor. The cell bleed rate and resultant viable cell concentration was controlled by manipulating the acoustic filter duty from between 45 on : 6 off and 15 on : 45 off. The acoustic filter was operated in upflow mode with an automated 15 min backflush, similar to Merten (1999). This upflow orientation avoided pumping cells through the recirculation line. 3.2 DOSE-RESPONSE AND SURVEY EXPERIMENTATION 3.2.1 Three-Day Experiment Cells from an exponentially growing culture (between 5xl05 and 8xl05 cells/mL with a viability of greater than 90%) were centrifuged, used to inoculate T-flasks or spinners (as indicated) at 105 cells/mL and cultured for 72 h. Cells numbers and viability were determined using trypan blue exclusion and a hemocytometer. Supernatants were obtained through centrifugation (lOOOg, 15 min) and aliquoted and stored at -20°C for t-PA analysis. Glucose, lactate and ammonium concentrations were obtained using the NOVA Stat Profile 10 (Waltham, MA). The cell specific t-PA production, glucose uptake, lactate production and ammonium production rates were calculated based on the starting and final concentrations and the log-mean viable cell number during the 72 h culture period. 3.2.2 Survey Experimentation For survey fed-batch experimentation, cells and samples were handled and analyzed as described in the previous section. Different concentrates and components were tested in parallel from a common basis in these fed-batch cultures. 33 3.3 t-PA ANALYSIS 3.3.1 t-PA Activity Assay The enzymatic activity of t-PA was analyzed by a colorimetric assay (Randy and Wallen, 1981; Verheijen et al., 1982) with some modifications. The standards for the assay were serial dilutions of plasma t-PA (Calbiochem, La Jolla, CA) from 0.25 U/mL to 10 U/mL in 0.1 M TrisCl buffer, pH 8.0, containing 0.1% v/v Tween 80 and 1% w/v IMDM/10% v/v FBS medium. Supernatant samples were diluted with the 0.1 M TrisCl buffer. The t-PA standards and samples were loaded onto 96-well flat-bottomed microtiter plates (Dynatech, Burlinton, MA) at 50 uL/well, followed by the addition of plasminogen (0.13 uM, Boehringer Mannheim, Laval, PQ), CNBr-fragmented fibrinogen (0.12 mg/mL, Calbiochem, La Jolla, CA) and the substrate, D-Val-Leu-Lys-/)-Nitroanilide dihydrochloride (0.5 mM, Sigma Chemical Co., St. Louis, MO). The microtiter plates were incubated at 37°C for 2 h and the /7-nitroanilide cleaved from the substrate was detected at 405 nm using a microtiter plate reader (Molecular Devices, Sunnyvale, CA). 3.3.2 t-PA Enzyme Linked Immunosorbent Assay Concentrations of t-PA were analyzed by enzyme linked immunosorbent assay (ELISA) with HI72C anti-t-PA monoclonal antibody (Life Technologies, Burlington, ON) for plate-coating and rabbit anti-t-PA antiserum (Cangene, Winnipeg, MB) as the secondary antibody (described in Harlow and Lane, 1988). The immuno-complex formed by binding of t-PA with these antibodies was detected by alkaline phosphatase conjugated goat anti-rabbit antibody and alkaline phosphatase substrate (Sigma 104, Sigma Chemical Co., St. Louis, MO). Plasma t-PA 34 (Calbiochem, La Jolla, CA) served as the standard in the ELISA, diluted in the same medium/buffer (0.1 M TrisHCl, 0.1% v/v Tween 80, 1% w/v IMDM/10% v/v FBS, pH 8.0) as were the analyzed samples. All ELISA plates were analyzed at 405 nm for optical density with a microtiter reader (Molecular Devices, Sunnyvale, CA). 3 . 3 . 3 t -PA Concentration in Hollow Fibre Module Reactor outflow (from perfusion experiments) was centrifuged (lOOOg, 15 min) to remove cellular debris and sterile filtered (0.22 micron) if required. The conditioned medium was concentrated using a Unisyn hollow fibre module with a 30 kDa molecular weight cut-off. Medium was pumped through the inner capillary space (ICS) of the hollow fibre bioreactor (HFBR), while a pump connected to the extra-capillary space (ECS) was used to collect the permeate (low molecular weight conditioned medium with little or no t-PA). 3 . 3 . 4 t -PA Stability Reactor samples were centrifuged (lOOOg, 15 min), sterile filtered (0.22 micron) and placed in the 37°C incubator. Subsequent daily samples were analyzed with either the activity or ELISA t-PA assay. The first-order exponential decay of t-PA was obtained from the regression software routines in Microsoft Excel (Seattle, WA) or Microcal Origin (Northampton, MA). 3.3.5 Intracellular t-PA Concentration Reactor samples were centrifuged (lOOOg, 15 min) and the supernatants discarded. The cell pellet is resuspended with PBS and re-centrifuged twice. The cell pellet is resuspended with cell lysis buffer (10% v/v Nonidet P40 (Boehringer Mannheim, Laval, PQ), 50 mM TrisHCl, 150 mM NaCl, pH adjusted to 8.0) and stored at -20°C for later ELISA analysis. 35 3.4 CONCENTRATE FORMULATION The amino acid portion of the concentrate (including glutamine) was dissolved (at 50-fold basal concentrations) in 1 M hydrochloric acid for stability (Hagen et al., 1993). Protein hydrolysates (Sigma, Oakville, ON) that substituted for defined amino acid formulations were similarly dissolved at 5 g/L concentrations. Modified Eagle Medium (MEM) vitamin mixtures (Gibco Life Technologies, Burlington, ON) at approximately 5 x basal levels were dissolved in 1 M sodium hydroxide. Both were stored at -20°C until required. The glucose (600 mM), chemically defined lipid mixture (at approximately 5X basal) and trace salts (with proteins) (at approximately 5X basal) (Gibco Life Technologies, Burlington, ON) mixtures were made in water (NANOpure II, Barnstead, Boston, MA), and stored (in the dark for lipids) at 4°C until required. Upon combination, the pH would be close to 7.0, and little adjustment was generally required. 3.5 TOTAL AND t-PA MESSENGER RNA ANALYSIS Total cellular RNA was isolated based on the protocol described by Chomczynski and Sacchi, 1987. The cells were washed three times with DEPC-treated ice cold PBS, then resuspended in guanidinium thiocyanate solution then frozen at -70°C for total RNA and t-PA mRNA analysis. The purified RNA was quantified by optical absorbance at 260 nm and 280 nm, then analyzed by Northern hybridization (Maniatis et al., 1982). The t-PA mRNA level was analyzed by loading 5 mg RNA per clone onto the 1.2% v/v agarose gel containing formaldehyde. After gel electrophoresis, resolved RNA was transferred onto a positively-charge nylon membrane (Boehringer Mannheim, Laval, PQ) followed by hybridization with DNA probes in 50% v/v formamide at 50°C overnight. The luminescent bands were visualized by 36 exposure to Hyperfilm-ECL (Amsham, Oakville, ON) and analyzed with a laser densitometer (Molecular Dynamics, Sunnyvale, CA). The mRNA levels of the housekeeping gene 3-actin, were used to normalize the t-PA mRNA data. 3.6 A M I N O A C I D A N A L Y S I S Tissue culture samples were centrifuged (lOOOg, 15 min) and the supernatants stored at - 20°C. The amino acid concentrations were determined by phenylisothiocarbamyl (PTC) derivatization followed by separation on a C18 reverse phase HPLC column (Cohen and Strydom, 1988; Hagen et al., 1993). Initial drying removes solvents and volatile components such as hydrochloric acid. The redry step neutralizes any residual acid, while the coupling step forms the PITC derivatives that are analyzed. The net hydrophobicity of the PITC-amino acid derivative is a function of the amino acid siderchain and determines the relative retention time in the column. A gradient of increasing organic content or hydrophobicity during elution is applied to the column to facilitate separation. A set of physiologically relevant amino acids were made at 0.08, 0.2 and 0.8 mM, with an internal standard of 500 pmol norleucine per 10 uL injection. The slope of the standard curve is used to correct calculate the concentrations in the culture samples and the internal standard is used to normalize the concentrations. 3.7 C O M P E T I T I V E B I N D I N G W I T H e - A M I N O C A P R O I C A C I D e-Aminocaproic acid binds competitively to lysine residues with t-PA (Einarsson et al., 1985). A 0.2 M potassium phosphate and 0.1 M e-aminocaproic acid buffer was titrated to pH 7.4. In the analysis of culture samples, equal volumes of culture samples (prior to 37 centrifugation) and buffer were placed on ice for 30 minutes. The 2-fold diluted sample was centrifuged (lOOOg, 10 min) and the supernatant frozen (-20°C) for later t-PA analysis. 3.8 E Q U A T I O N S U S E D I N A N A L Y S I S The percent viability of the culture was computed using: Percent Viability = ^ 100 (3.1) Total Cell where X v is the viable cell concentration (cells/L). The log mean average of component z, between two sampled points at time points, 1 and 2, was computed as: _ (z2 ~ z i) 0 x LM 7 T T (3-2) In where ZLM is the log mean value of z and ln is the natural logarithm. The integrated viable cell days, IVC was used as a culture viability index and is defined as: I V C =r l l [(xv.w+Xv.iHvi-ti)] (3-3) 1 i=i where ti+i and t; correspond to time points i+1 and i, respectively. The cell specific t-PA production rates were corrected (as indicated) for inactivation using: CT-PA,2 C t _ P A , + kd • C L M • (t2 tj)^ q ; _ P A = i ^ i • IO"' (3.4) where q\.pA was the corrected t-PA production rate (pg/cell-day), CI-PA,I and Ct-PA,2 are t-PA concentrations (mg/L) at time points 1 and 2, respectively, CLM is the log mean t-PA 38 concentration (mg/L), kd is the inactivation rate (1/day), X V ,LM is the log mean viable cell concentration (cells/L). 39 C H A P T E R 4 MODELING AND PREDICTIVE C O N T R O L 4.1 INTRODUCTION The objective of this work was to develop a long-range predictive control protocol using multiple models in an adaptive framework. The protocol had to be applicable in loose-loop configuration, with non-constant sampling and, in some cases, few data points. Daily sampling of the bioreactor yielded glucose concentrations that were converted to glucose uptake rates. The glucose uptake rates were modeled and plotted via a graphical user interface to allow operator estimation of the current and future state of the culture. Process noise necessitating data filtering protocols. Model choice allowed inferential estimation of the process every 3 h, and calculation of the required flow rates in a predictive control protocol. A computer-controlled and calibrated pump performed the required additions based on the controller design to drive the process to the glucose set point within 6 to 12 h. Simulations were performed to assess the controller performance and perfusion culture concentrations were manipulated in order to track glucose set point changes and reference trajectories. 4.2 IDENTIFICATION The control protocol presented was based on a loose-loop configuration (i.e. operator mediation is required to close the loop). There were two stages in the identification of the process and both were operator-mediated. The operator observed the glucose uptake rate estimates and the filtered forms through the graphical user interface and decided whether the modeling parameters (i.e. period of moving average filter, data window size, etc.) needed to be 40 changed or outliers needed to be removed. The second stage involved the fitting of growth models to form the predictive horizon for the controller. 4.2.1 Glucose Uptake Estimate at Current Sampling The glucose uptake rate was estimated from past glucose measurements using the mass balance relationship describing the feed rate, F, reactor volume, V, the bioreactor glucose uptake rate, GUR, and the glucose concentration, C: d C . Z . C - G U R ( 4. 1 } dt V V where C was the concentration deviation variable C = C F e e d - C R e a c t o r . (The following development is for perfusion bioreactors, however, fed-batch equations can be similarly obtained with the simplifying assumption that there is no outflow.) The glucose uptake rate was estimated by discretizing the above equation and used the average flow rate over the previous time interval. These glucose uptake rate estimates were then plotted versus time, along with three filtered or modeled forms of the data. The first filtering technique was a moving average estimate of the GUR, typically with a period, W, of 2 or 3: GUR e s a = G U R ^ n +-J--(GURk -GUR k_ w) (4.2) w where GUR^k and GUR^ic-i were the filtered values at time index k and k-1, respectively, while GURk and GURk-w were the unfiltered values at time index k and k-W, respectively. The moving average filter was straightforward to implement and works robustly, but will under- or over-estimate monotonically increasing or decreasing data, respectively. The second filtering technique was an exponential growth/decline model: GUR t + A t - GURt exp(u • At) (4.3) 41 where GURI+AI and GURt were the glucose uptake rate estimates at time t+At and t, and u. was the specific growth/decline rate obtained from non-linear regression of the window of data points. The exponential growth/decline model was most applicable to the first 10 days of the culture (initial growth phase). The third filtering technique was a logistic growth model: G U R T = G U f M a x , (4.4) l + exp(a + p-t) where a and P were non-linearly regressed parameter estimates and GURMax was the maximum expected glucose uptake rate in the culture. With a larger number of parameters specified, the logistic growth model will tend to be valid for longer periods of time. The logistic growth form has a growth phase, followed by a steady-state, which will occur in an idealized perfusion culture. 4.2.2 Model for the Prediction Horizon A window of glucose uptake rate estimates (generally the last 3-7 data points) was specified based on the operator experience and graphical user interface confirmation to tune the model choices. The modeling of the immediate culture future could also be re-analyzed with improved model parameters. Once a model was chosen, the parameters obtained were used to estimate a set of glucose uptake rates for the next three days at three hour intervals. The exponential growth parameter, u., was applied to the most recent moving average and exponential estimates to project into the future. The logistic equation was similarly used to project the logistic current uptake estimate into the future (until the next sampling). 42 4.3 CONTROL LAW DERIVATION A challenge with Equation 4.1 was the non-linear term where: the flow rate (manipulated variable) and the deviation concentration variable (controlled variable), were multiplied together. Taking the Taylor series approximation for the FC term in the mass balance (Equation 4.1) equation yielded: dC = J _ dt V ( 5FC dC »\ arc .(c-e). ( F - F ) + F - C c=c GUR V (4.5) where F and C were the average flow rate and concentration deviation values over the last interval. Organizing terms, it followed that: _ d C _ ^ C = e . A F . G U R (4.6) dt V V V and the following transfer function representation was obtained: C( s ) = - ^ ^ . A F ( s ) + 7 ^ ^ (4.7) (V-s + F) (V-s + F) The process model was first order with a time constant that will decrease with increasing flow rate through the culture. A simplified block diagram for the process is illustrated in Figure 4.1. All the dotted lines indicate operator-mediated actions. Analyzed glucose concentrations were used to compare versus the reference trajectory (i.e. future set point values) and in the estimation of the glucose uptake rate (described in Section 4.2). 43 Reference trajectory CSP Model design Controller design o Set of flow rates Predictive F Control Bioprocess controller element w Estimated GUR GUR modeling Daily sampling •'Reactor Glucose analysis Legend Reference trajectory Model design Controller design Control element Set of glucose set point values, CSP Culture volume, data window size, specific growth rate limits, pump and process limits GUR model selection, form of criterion function, J, H m , H p, R and X. Computer automated pump Figure 4.1. Simplified block diagram of process. 44 In general use of predictive controllers, the process sampling and control intervals are the same, even though a future controller output sequence can be assumed in the calculation, only the first element is used (Soeterboek, 1992). In this work, the samples were taken daily, with the control interval specified at 3 h intervals. Therefore, the first 8 elements of the controller output sequence were used to control the process. If there was deviation, the first 4-5 elements of the output sequence were used to drive the process to the set point. The remaining elements were specified assuming no deviation from the set point. Using the predicted values of the glucose uptake rate estimates from the modeling portion, the required flow rates between sampling were inferentially estimated with the steady-state mass balance relationship: where GUR t + A t was the predicted glucose uptake rate at t+At from the last estimate and C S P was the difference between the inlet and set point glucose concentration. A future set point reference trajectory was specified as [Csp(t+j); j-1,2,...], which may or may not be constant. The future of the process was specified conceptually (Richalet et al., 1978) as a simple first-order model: where, Cest,Gic was the desired trajectory of the output variable (glucose concentration) and X was a specified value between 0 and 1. The objective of the predictive control protocol was to drive the future plant outputs "close" to the set point values. A criterion function, J, can be specified as: F = G U R T H t+At (4.8) Cest,Glc(t + j)=^-C e s t ) G l c(t + j) + (l-X)-CS P(t + j) (4.9) (4.10) i=H, m 45 where, CSP is the reactor glucose set point at time point t+At-i, H p is the prediction horizon (8 for daily sampling) and H m is the minimum-cost horizon (set to 1). A receding-horizon approach (Clarke et al., 1987) for sample-instant t, was taken, where (1) a set point sequence was specified, (2) the prediction model specified was used to generate a set of predicted process outputs, using the process and growth models available up to time point t, (3) the manipulated variable was specified to drive the predicted outputs to the desired process output, satisfying constraints, (4) the set of flow rates was calculated. The growth model constraints were specified as limits on the maximum specific growth rate (u. < l.l*umax). The maximum specific growth rate for the hybridoma cells was 0.86 l/day, while for the CHO cells it was 0.55 l/day and both were obtained from previous batch culture. 4.4 BASE CASE SIMULATION Glucose and glutamine supply energy to mammalian cells via their metabolic breakdown (Zielke et al., 1978) and produce lactate and ammonium as potential growth-inhibiting by-products (Omasa et al., 1992; Griffiths et al., 1992). A mammalian cell perfusion culture was simulated using a logistic growth function starting at 2xl05 cells/mL growing to a final cell concentration at steady-state of lxlO7 cells/mL. The assumed cell specific uptake and production rates were obtained from previous perfusion experiments. The glucose uptake, lactate production, glutamine uptake and ammonium production rates were 6, 9, 2.5 and 1 pmol/cell-day, respectively, while the protein production was 6 pg/cell-day. The process uptake and production rates were obtained by multiplying the cell number by the cell specific glucose uptake rate at each interval. The cell number was obtained using the following relation with the parameter values shown in Table 4.1: 46 where, Xv, t and Xv,Max are the viable cell concentrations in the reactor at time t and the maximum viable cell concentration attainable, respectively. Table 4.1. Perfusion Simulation Parameters Parameter Value Comment a ln(199) Set inoculum at 2x105 viable cells/mL Equation 4.12 Growth equation U-max ln(2) Doubling time of 1 day XV ; max 107 viable cells/mL Maximum viable cell concentration For the growth-substrate relationship, a Monod model is a saturation-type kinetic that has been successfully applied in a wide range of culture modeling (Bailey and Ollis, 1983; Shuler and Kargi, 1992). The form of the lactate and ammonium growth inhibition may be specified as competitive, non-competitive or mixed (Bailey and Ollis, 1983). From dose-response experimentation, ammonium was observed to be a non-competitive growth inhibitor with an inhibition value (KAmn) of 14 mM. Lactate did not exhibit a growth inhibition effect in the range tested (data not shown). These results were obtained from Linweaver-Burke plots (Bailey and Ollis, 1983) of dose response results and the following Monod form for the growth-substrate relationship was used: H _ C Glc C G l n KAmn (4.12) M-max (CG1C+ KG1C) (CGln+ K Gln) ( K Amn + CAmn) where u.max l s the maximum attainable growth rate for the culture (1/day). The KGI c and KGI„ values (0.1 mM) come from literature estimates of mammalian cell Monod constants (Frame and 47 Hu, 1991; Glacken et al., 1986; Ljunggren and Haggstrom, 1994). In general, reactor glutamine concentrations were between 5- and 40-fold higher than the chosen Kan value, while the glucose concentrations were between 20- and 200-fold higher than the chosen KGI c value. The controller simulation results have been based on instantaneous sampling and analysis, assuming no error in the analyzer output. The simulations do not assume any concentration dependence of the uptake/production rates which may be the case for very low substrate concentrations or very high metabolite concentrations. The form of the growth model assumed no negative growth rates at either very low substrate or very high metabolite concentrations. The values inside the reactor were updated every 10 minutes, while the control action occurred at specified time intervals. 4.5 RESULTS AND DISCUSSION 4.5.1 Comparison of Operator and Computer Estimation of Feed Rates Previous work using hollow fibre bioreactors (HFBR) illustrates the potential pitfalls of operator estimation of the feed rates compared to computer estimation of the feed rates (Dowd et al., 1999). The inclusion of perfusion HFBR culture results with a hybridoma cell line is relevant for illustrating the utility of the adaptive modeling and predictive control protocols described in the preceding sections. In operator estimation of the feed rates, both the magnitude and time schedule of the selected feed rates were inappropriate (Dowd et al., 1999). For operators, it is often difficult to predict, without systematic predictive calculations, how the feed rates should be manipulated over time to control the process. The control performance of the computer estimated feed rates exhibited very low glucose and lactate concentration variability compared with operator estimation, with fewer samples taken (Table 4.2). The results in Dowd et al. (1999) 48 compared well to a suspension perfusion culture system with similar glucose variability of between 0.61 and 0.78 mM (Konstantinov, 1996), but which used up to a 24-fold high frequency of sampling with a flow injection analysis system. Table 4.2. Comparison of Operator Versus Computer Estimation of Feed Rates Culture feed rate estimation method Average glucose concentration (mM) Average lactate concentration (mM) Average sampling rate (#/day) Operator 14.2 ±2.7 22.4 ± 7.4 1.3 Computer 13.1 ±0.66 18.4 ± 1.0 1.0 4.5.2 Simulation Results of Perfusion Culture With the control action updated at 3 hour intervals (Figure 4.2), the control of the process showed little perturbation due to the control action. However, with control intervals at 24 h (Figure 4.3), the process exhibited perturbation of the concentrations due to the stepping nature of the changes in flow rate. The glutamine concentrations approach 0.1 mM near the end of these steps in flow rate. These low concentrations could affect the performance of the perfusion bioreactor, as the cells would be transiently exposed to conditions that affect their growth. The challenge in attempting to control the concentration is that while the cellular uptake is a continuous function with time, the manipulated variable (change in feed rate) is a stepwise function. Therefore the step changes in the flow rate will only roughly approximate a continuously increasing/decreasing uptake rate. Step-wise changes in the feed rate will perturb the system from the set point concentration. 49 Time (days) Figure 4.2. Control intervals every 3 h for a CHO culture. The onset of perfusion is indicated by the step increase in dilution rate from zero at day 4. 50 Time (days) Figure 4.3. Control intervals every 24 h for a CHO culture. The onset of perfusion is indicated by the step increase in dilution rate from zero at day 4. 51 4.5.3 Simulation of Noise Sources An analysis of variance for the process control was performed including bias in the glucose uptake rate (GUR) estimation at the current sampling and divergence in the prediction horizon (growth model) estimation. Normally distributed errors in the GUR estimation at the current sampling and in the prediction horizon had a maximum range of 20% of the GUR value. These simulations were combined in order to estimate the normal variation which may be seen experimentally. The sum of the standard deviations in the resultant reactor glucose concentrations was 0.45 mM. If only the variation in modeling and prediction horizons were considered, the sum of the glucose standard deviations was 0.27 mM. The remaining amount of variation was approximately 0.18 mM and would be due to inherent error in the reactor setup (i.e. step increments in flow rate, non-constant inlet and outlet flows, etc.). From a standard solution in the 5 to 10 mM glucose concentration range, analyzer error is approximately 0.20 mM (NOVA Biomedical, Waltham, MA). These simulations indicate that with good model estimation of the glucose uptake rates, predictive control routines can control the reactor glucose concentrations at the expected measurement variance for the analyzer. 4.5.4 Estimation of Process Data In the estimation of process data, the following examples illustrate the potential pitfalls of poor estimation through the graphical user interface. In a 50-day CHO perfusion culture (Figure 4.4), the moving average filter robustly estimates the current glucose uptake rate, especially under pseudo-steady-state conditions. With monotonically increasing uptake rates, such as in bioreactor start-up, the moving average filter (Figure 4.4a) will tend to underestimate 52 40 Time (days) Figure 4.4. Estimating the glucose uptake rate at the current sampling. The data points (squares) are plotted in each window. 53 the current uptake rate, especially with a period of 5 (dashed line). A period of 2 (solid line) was generally used in the estimation of the glucose uptake rates. With the exponential growth/decline model (Figure 4.4b), using the entire data set (dashed line) will tend to overestimate the actual rates, especially in extended periods of pseudo-steady-state conditions. A window size of 6 data points (solid line), combined with a limit on the maximum specific growth rate (u. < l.l*LiMax) allowed for good estimation of the current uptake rate. With the logistic model (Figure 4.4c), the maximum glucose uptake rate value (GURMEX) was set to twice that of what was attained in the reactor (dashed line). With realistic estimation of the maximum glucose uptake rate (solid line), the logistic model fits the entire culture period with reasonable accuracy. The exponential and logistic estimation was used more often in the growth phase, while the moving average and logistic estimation was used more often in the pseudo-steady-state. An example of the graphical user interface plots is illustrated in Figure 4.5 with the glucose uptake rate estimates and example model prediction horizons for the start-up of a perfusion culture. The example model prediction horizons at days 2 and 4 were indicative of the predictions that occurred at every sampling. The logistic equation predictions on the second and fifth day overlap, indicating that the logistic growth function may have been the best predictor in this stage of the culture. Non-linear model predictions (exponential and logistic) were used because even if the data were noise-free, linear model projections of glucose uptake rate estimates in an exponentially growing culture would result in under-estimation errors that depend on both the sampling interval and the size of the data window. Table 4.3 compares the linear approximation errors in exponential growth for different sampling intervals and size of data window. The approximation error was calculated by comparison to the true value of 54 1 0 0 0 CD -#—< CO V CO co p -»—' ^ CD £ (/) s S o o o 100-J 1 0 0 -J • Data Moving Average Exponential Fit Logistic Fit A. Initial Estimates 1 1 B. Prediction Horizon • ' • 1 0 0 2 4 Time (days) T 6 Figure 4.5. Control protocol estimation for a bioreactor start-up, with an example of the graphical user interface plots. Perfusion was initiated on day 2. 55 Table 4.3. Linear Approximation Errors in Exponential Growth Interval Data window of 2 Data window of 4 Data window of 6 3 h 0.7% 1.3% 1.9% 6h 2.5% 4.6% 6.2% 12 h 8.6% 14% 18% 1 day 25% 36% 41% exponentially growing cells. At sufficiently small sampling intervals of less than 6 h, the inherent error in using a linear approximation would be in the range of 3% to 6% for small data windows (2 to 6 points), which may be acceptable for glucose concentration control. However, with daily sampling, linear projections result in errors in the range from 25% to 41%. Noise from the glucose concentration assay could add to estimation errors. At a simulated steady-state cell concentration of 10 x 106 cells/mL, the error criterion function, J, was calculated for a linear projection of feed rates used to manipulate the reactor glucose concentration. This criterion value was compared to specifying the reactor glucose trajectory (Equation 4.9) and using the non-linear predictive control protocol. The criterion value, J, was reduced up to 7-fold using the non-linear predictive control protocol compared to using a linear projection (based on daily samples). These simulations assumed no error in the glucose uptake rate estimation and were based on glucose set point changes. The reduction in the error criterion depended on the size of the set point change, but was simulated in the range of ± 4 mM to 6 mM. Larger set point changes resulted in larger reductions in error criterion. With a flow injection analysis system and automated sampling at high frequency (< 3 h), reasonable control of the perfusion bioreactor was possible with a simple feed-forward (linear) controller 56 (Ozturk et al., 1997). With non-linear estimation of the process and a predictive controller, good control of perfusion processes was possible with daily sampling. A dedicated glucose analyzer and the operation of a potentially fallible flow injection analysis system was not required. 4.5.5 Experimental Results A glucose set point of 10 mM was chosen for a 10 L bioreactor inoculated with 2.5xl05 cells/mL at 23 mM glucose and grown as a batch for 2 days. The modeling predicted that the glucose concentration would be less than the set point concentration six hours after the third sample and the computer-controlled feeding to the reactor was started (Figure 4.6). The GUR modeling and example prediction horizons were previously shown in Figure 4.5. The predictive non-linear modeling and daily sampling were able to maintain the process at the glucose set point with a standard deviation of 0.35 mM (Figure 4.6A). This compares favourably with a semi-on-line process sampling and analysis system with a linear controller and hourly sampling with a standard deviation of between 0.66 to 0.72 mM (Konstantinov, 1996). The cell growth was exponential in this phase of the culture (Figure 4.6C). The protocol specified flow rates every three hours (Figure 4.6B), to control the process between samples and to approximate the continuous function of the glucose uptake model. The graphical user interface, as part of the predictive control protocol was a useful tool to allow operators to select feed rates in perfusion systems (Dowd et al., 1999). In the design of the controller, the response to deviations from the set point was non-linear. If the concentrations were close to the set point value, then little adjustment was made. However, with larger deviations, the more active the controller becomes in terms of adjusting the flow rate. This can be observed in set point changes in a separate perfusion experiment from 10 mM to 57 25 s 5 g c o § o O 0) to C T J O ^ % 3 = 5 E O O 10 0 1(T 0 • • A Perfusion n n • n n 1—1 M 1—1 I I I I i B 1 1 r T C 1 1 —O— Total Cells —L>-Viable Cells 2 4 Time (days) Figure 4.6. Culture profile of 10 L hybridoma culture. 58 c o (0 -f-' C (D O c o O 0 (/> o o J3 CD 20 15H E 10 0 2.0H 0 | ~ 1.5 0 5 1 ^ 1.0 Q 0.5 0.0 B • Manual Samples Automated Samples Set Point 29 30 Time (days) Figure 4.7. Set point change in CHO culture. 59 6 mM glucose (more active control changes), compared with set point changes from 6 mM to 5 mM (less active control changes (Figure 4.7). The assay results from manual samples were used to calculate the feeding profile for the next day. The automated samples were collected using a fraction collector on the reactor outflow. The design of the controller was to manipulate the dilution rates to change the glucose concentration in a defined first-order manner. With good estimation of the immediate future glucose uptake rates, the process can be made to track set point changes within 6 to 9 hours. The process could also be maintained at a constant value, even in transient conditions (Figure 4.8). The viable cell numbers decreased 35% over the 5 day interval shown (Figure 4.8B) and the apparent ratio of lactate production to glucose consumption decreased 20% (Figure 4.8C). Even under these transient conditions with changing cell numbers and apparent changes in cell specific rates of glucose uptake and lactate production, the predictive control routines maintained process control with a variability of between 0.15 and 0.3 mM. As before, the daily samples were used to calculate the feeding profile until the next sampling. In perfusion culture, a reference trajectory was operationally advantageous, as it allows for cells to acclimatize to changing reactor conditions. This was the case in the transition from batch to perfusion (Grammatikos et al., 1999). A reference trajectory was introduced and the predicted glucose concentrations (Figure 4.9) used the selected model glucose uptake rates and the mass balance equation (Equation 4.1) to calculate the predicted reactor concentrations. The predictions converge better to the reference trajectory with a greater number of data points used in the estimation (day 4 and 5 predictions versus day 2 predictions in Figure 4.9). 60 c o CD CO CO O £= o c o o 15 10 5 • Manual Samples Automated Samples Set Point Time (days) Figure 4.8. Maintenance of a constant glucose concentration in CHO culture under transient conditions. 61 20 15T Data Reference Trajectory Predicted Glucose Concentrations c o '-+—> CO 1 10 o c o O CD tf) O O _3 (D 5 0 T 6 0 4 Time (days) Figure 4.9. Reference trajectory of glucose in CHO culture. 62 4.6 CONCLUSIONS With daily flow rate selection, substrate levels were simulated to be potentially limiting, especially in the growth phase. Non-linear modeling in an inferential predictive control framework has been effective to control substrate concentrations with daily sampling. The controller used a growth model to inferentially estimate the state of the process and change the manipulated variable every three hours. The process can be controlled at the level of the glucose variability inherent in the concentration measurement. The control protocol can cause reactor glucose concentrations to track set point changes within 6 to 9 h with good estimation of the immediate future uptake values. Even in transient conditions, the reactor concentrations may be maintained with glucose concentration variances of less than 0.3 mM. Reference trajectories may be followed closely, allowing for smooth transition between batch and perfusion culture. 63 C H A P T E R 5 FED-BATCH EXPERIMENTATION 5.1 INTRODUCTION Most fed-batch reports are of hybridoma cultures (see Bibila and Robinson (1995) for review). In this work, concentrate formulations and feed rates for CHO recombinant protein fed-batch production are reported. A stoichiometrically balanced formulation was obtained for the glucose and amino acid portion of the concentrate. Based on daily cell samples, the calculated addition rates maintained constant glucose concentrations. Hybridoma fed-batch cultures were performed to observe the concentrate feeding protocol effects on another cell line. The cell specific t-PA production was investigated as a function of extracellular t-PA concentration, as well as the t-PA stability at 37°C in serum-free medium. The intracellular t-PA concentrations were measured, along with the total and mRNA levels were analyzed to characterize potential limitations in the t-PA production. A kinetic model of the extracellular t-PA concentrations was formulated to describe the effects of production, inactivation and binding. Removal of t-PA from the culture supernatant was added to the fed-batch process protocol to increase t-PA yields. 5.2 FED-BATCH PROCESS MODIFICATION TO REMOVE t-PA The fed-batch process was modified to strip extracellular t-PA from the culture in a batchwise manner. An acoustic filter (PSI Systems, Coquitlam, BC) was used to retain cells (approximately 95% separation efficiency) in the reactor, while approximately 80% of the culture volume was removed. The clarified medium was pumped into an ultrafiltration circuit. The intracapillary space (ICS) of the 30 kDa UniSyn (Hopkinton, MA) hollow fibre module was previously flushed with approximately 1 L of sterile phosphate balanced saline (PBS). While an 64 additional 2 L of PBS was flowing through the ICS, using a syringe on the extracapillary space (ECS) port, at least 150 mL was pulled through the membrane to flush the ECS (10 mL volume). The ultrafiltration module was aseptically attached (SCD ITB Sterile Tubing Welder, Terumo, Elkton, MD) to the outflow of the acoustic filter. The medium containing t-PA was recirculated at approximately 500 mL/min through the ICS, while a pump (Masterflex, Cole-Parmer, Chicago, EL) on the ECS port pulled the permeate at approximately 5 mL/min through the ultrafiltration membranes. The permeate (approximately 90% of the harvested volume) was returned to the reactor within 2 to 4 h of its initial removal. The maximum pH shift was measured to be approximately 0.1 pH units higher. 5.3 R E S U L T S A N D DISCUSSION 5.3.1 Dose Response Analysis Medium concentrates can effectively improve fed-batch yields, however, there is a need to avoid increasing the osmolarity, medium components and/or growth by-products to inhibitory levels (Bibila et al., 1994). Ryu and Lee (1997) reported the adaptation of hybridoma cells to hypo-osmotic medium (approximately 220 mOsm/kg) and then feeding a medium concentrate (of approximately 770 mOsm/kg) to increase antibody production relative to standard fed-batch culture in isotonic medium. The effects of osmolarity on the CHO cell growth and specific t-PA productivity were tested. The highest growth rates were obtained between 320 mOsm/kg to 380 mOsm/kg, while the cell specific t-PA productivities showed no consistent pattern on repeated osmolar 3-day cultures between 200 mOsm/kg and 500 mOsm/kg (data not shown). This result was in contrast with hybridomas that can exhibit higher antibody productivity (and lower growth rates) in hyper-osmolar conditions (Ozturk and Palsson, 1991; Bibila et al., 1994; 65 Reddy and Miller, 1994). The formulation of all subsequent concentrates for these CHO cell cultures was approximately 350 mOsm/kg. 5.3.2 Initial Concentrate Formulation The exponential phase cell specific rates relative to glucose uptake (in batch culture) were used to select the concentrate amino acid concentrations relative to the concentrate glucose concentration of 125 mM (Table 5.1). For example, the glutamine uptake rate was 23% of the glucose uptake rate, so the concentrate glutamine concentration was set at 29 mM. For glutamate, glycine and proline, only the periods of consumption (days 3 to 7 in batch for glutamate and glycine, days 1 to 6 for proline) were considered for the calculation of formulation concentrations (Table 5.1). Alanine was not included in any of the concentrate formulations due to its production in batch culture. Medium proteins, lipids and vitamins were included in the concentrate at approximately basal levels. Serial fed-batch cultures were analyzed by H P L C to improve subsequent fed-batch formulations. The majority of the amino acid concentrations fluctuated within 0.5- to 2-fold of the starting concentration with predictive feeding based on glucose measurements. In the first iteration, glutamine, glutamate, asparagine, aspartate and glycine reached <0.1 m M concentrations (Figure 5.1). For hybridoma cells, Franek and Chladkova-Sramkova (1995) reported that apoptosis may be prevented with additions of glutamine, asparagine and glycine, (but not prevented by aspartate and glutamate additions) in cultures grown at low amino acid concentrations. However, the viability of the CHO cultures remained greater than 90% and the t-PA titers increased approximately 15%-30% relative to batch. The concentrations of several amino acids, including aspartate, glutamate, asparagine and glutamine (Table 5.1) were increased with subsequent iterations. Stoichiometric analysis can be sensitive to the assumptions of 66 Table 5 1. Fed-batch Amino Acid Formulation Amino Acid Based on Uptake Rates in Batch (mM) Second Iteration (mM) Third Iteration (mM) Aspartate 0.43 0.96 1.4 Glutamate 0.17 2.0 2.5 Serine 1.6 1.6 1.6 Asparagine 1.4 10 10 Glycine 0.44 0.80 0.80 Glutamine 29 40 40 Histidine 0.68 1.0 1.0 Threonine 1.4 2.3 2.3 Alanine 0 0 0 Arginine 1.5 4.2 4.2 Proline 0.48 0 0 Tyrosine 1.4 1.5 1.5 Valine 2.0 2.3 2.3 Methionine 0.43 0.58 0.58 Cysteine/Cystine N/A (0.95) 0.95 0.95 Isoleucine 2.0 2.1 2.1 Leucine 0.81 2.3 2.3 Phenylalanine 1.2 1.1 1.1 Tryptophan N/A (0.22) 0.22 0.22 Lysine N/A (3.1) 3.1 3.1 Glucose 125 125 125 67 ..„•—. Asp — - A — - Ser —-0---GIU —-v—-Asn Time (days) Figure 5.1. Serial experimentation with HPLC analysis. The amino acid profiles for glutamine, aspartate, glutamate, glycine and asparagine for three bioreactor experiments are shown. The first, second and third iteration of experiment, followed by HPLC analysis, are shown in the top, middle and bottom panel, respectively. 68 metabolic fluxes which may change over the fed-batch culture. The second fed-batch culture was inoculated higher at 4x10s cells/mL, so the culture duration was shorter (middle panel in Figure 5.1), but the increase in t-PA concentration was similar (data not shown). In the third iteration, HPLC analysis revealed no apparent limitations in any of the 17 measured amino acids, however, there were no increases in the change in t-PA concentrations (start versus finish) between the three cultures in Figure 5.1. 5.3.3 Feeding Strategy The uptake of glucose was used as an easily measured indicator of medium usage. All bioreactor cultures were inoculated at approximately 7 mM glucose. The additions were started when the viable cell numbers were between 0.7 to 1.0 xlO6 cells/mL. In an analogue to a per cell perfusion rate (Bodeker et al., 1994), a per cell fed-batch concentrate feeding was tested with different constant values of cell specific glucose uptake rates. The following equation was used: AV = i - - V - q G l c . A t (5.1) ^Conc where AV is the volume added (L), X v is the viable cell concentration (cells/L), Cconc is the glucose concentration in the concentrate (mM), V is the reactor volume (L), q^c is the cell specific glucose uptake rate (mmol/cell-day) and At is the change in time (days). Controlling the glucose concentration at low levels can reduce lactate production and increase cell specific productivities (Glacken et al., 1986). In the exponential phase of CHO batch cultures, the cell specific glucose uptake rate was 6 pmol/cell-day. In calculating the added concentrate volume based on Equation 5.1, constant cell specific glucose uptake rates of 3, 4 and 5 pmol/cell-day were tested. At 5 pmol/cell-day (and 6 pmol/cell-day, data not shown), the culture glucose concentrations increased (Figure 5.2), as did lactate concentrations (data not shown). At 69 - - A - • 3 pmol/cell day —O—4 pmol/cell day • • •• • 5 pmol/cell day — X — Batch Time (days) Figure 5.2. Magnitude of concentrate additions. The cell specific glucose uptake rate was specified at 3, 4 or 5 pmol/cell-day and multiplied by cell numbers in the reactor to obtain the addition volumes. 70 3 pmol/cell-day and in batch, the glucose concentration and the viability decreased (data not shown). Controlling the glucose concentration at approximately 4 mM with a 4 pmol/cell-day feed resulted in the highest t-PA concentration of 30 mg/L (Figure 5.2) and increased the viable cell index 2.5-fold compared to batch. 5.3.4 Concentrate Formulation Using a feed protocol based on a cell specific uptake rate of 4 pmol/cell-day, a concentrate formulation (A and C in Table 5.2) with selected amino acids (glutamate, aspartate, asparagine and glycine) were compared in duplicate to a concentrate formulation (B in Table 5.2) with a complete amino acid complement. The integrated viable cell days (in all fed-batch cultures) were extended between 2- and 2.6-fold, but the overall t-PA concentration was not significantly elevated according to either activity or ELISA protein-based assays (Figure 5.3). Concentrate A contained only the selected amino acids, while C had a soy enzymatic hydrolysate at 0.2 g/L levels. Dose response experimentation showed that an enzymatic soy hydrolysate (Sigma, Oakville, ON) exhibited better cell growth and increased t-PA titers in 3-day cultures (Table 5.3). Glutamine at 20 mM levels was included in the amino acid portion of concentrates containing hydrolysates. A second set of survey experiments (Figure 5.4) showed that the soy enzymatic hydrolysate (E in Table 5.2) could be successfully substituted for defined amino acids with similar 2- to 2.5-fold extensions in integrated viable cell days. 71 c <u B O a S o U CU « s I . c CU w S o o •a CU — « Glucose 125 mM 125 mM 125 mM 125 mM 125 mM 125 mM Enzymatic Hydrolysate 0.20 g/L 5 g/L CO Glutamine 40 mM 20 mM 40 mM 20 mM 20 mM 20 mM Amino Acid MEM Non-Essential S S MEM Essential S S S Selected Amino Acids 5 mM Glu, Asp, Asn, Ser 5 mM Glu, Asp, Asn, Ser Vitamins S s S S S s Salts S s S S s s Lipids s s s s s s Concentrate < CQ u w fa o CN r--50 Activity Onset of u -| 1 — i 1 1 0 2 4 6 8 Time (days) Figure 5.3. Simplified versus complete concentrate. In the top panel, the activity assay was used with three concentrates compared to batch. In the bottom panel, the ELISA protein-based assay was used for concentrates A and C, compared to batch. 73 Table 5.3. Dose Response with Hydrolysates Protein Additive Relative Effect on Specific Growth Rate Relative Effect on t-PA Titers Soy Protein Peptone Polypeptone BSA Fraction V 16 ± 2 % 6 ± 2% - 8 ± 3% - 22 ± 3% 11 ± 2% 6 ± 1% 3 ± 0 . 1 % -28 ± 1% The stated range represents results from duplicate experiments. 74 o 8 C o O D) E —•— Concentrate E —O— Concentrate F —A— Concentrate G —X— Batch Time (days) Figure 5.4. Substituting hydrolysates for defined amino acids. The viability in fed-batch cultures was extended relative to batch, with three concentrates with different amino acid components. 75 5 . 3 . 5 Hybridoma Test Culture Increased integrated viable cell days have been correlated with increased hybridoma antibody production (Renard et al., 1988). Concentrate E (Table 5.2) was tested on a hybridoma cell line to assess its ability to increase antibody production. The optimal CHO feeding protocol was based on 4 pmol/cell-day or 2/3 of the batch cell specific glucose uptake rate of 6 pmol/cell-day. For the hybridoma cells, the exponential phase glucose uptake was 9 pmol/cell-day, so the feeding protocol was based on 6 pmol/cell-day (2/3 of the batch rate). The fed-batch hybridoma culture showed approximately 4-fold increases in both antibody concentrations and viable cell indices (Figure 5.5). This result was obtained although the feeding was the first attempt and not optimized for fed-batch hybridoma culture. 5 . 3 . 6 Low Glucose Inoculum and t-PA Threshold In an effort to increase the t-PA concentrations and viable cell indices, the glucose and glutamine levels were reduced in the inoculum train. Using such a strategy, Zhou et al. (1997) had obtained 1.5-fold higher maximal cell concentrations and 7-fold higher antibody concentrations compared to previous fed-batch cultures. The CHO inoculum train was twice subcultured with low glucose (8 mM) and glutamine (1.3 mM) medium, prior to culture inoculation. Using a 4 pmol/cell-day feeding protocol with concentrate E (Table 5.2), the fed-batch culture from this low glucose inoculum train exhibited viable cell indices 4.5-fold greater than batch in similar conditions (data not shown). However, as before, there was little or no improvement in the t-PA titers (data not shown). 76 500 Time (days) Figure 5.5. Hybridoma fed-batch results. Using the same feeding strategy as the fed-batch cultures involving CHO cells, the performance of Concentrate E (see Table 5.2) on monoclonal antibody production using hybridoma cells is illustrated. 77 The extracellular t-PA concentration in any batch or fed-batch culture was not observed to increase above an apparent threshold between 30-35 mg/L. The t-PA concentrations did not increase beyond this threshold when the reactors were inoculated with higher cell concentrations (4-5xl05 cells/mL versus l-2xl05 cells/mL), lower starting glucose concentrations (2-7 mM versus 15-20 mM) and earlier concentrate additions (1 day versus 3-4 days). t-PA instability or binding to cells could help explain the t-PA threshold. 5.3.7 t-PA Stability and Binding To test the stability of t-PA samples from the reactor were filtered (0.22 micron) and placed in a 37 °C incubator. The day 2 medium had a t-PA half-life of 43 days (Figure 5.6). The day 6 medium exhibited a reduced t-PA half-life of 15 days. The day 2 and 6 viabilities were 92% and 71%, respectively. Protein-based ELISA assays exhibited little degradation (half lives of well over 200 days) indicating enzyme inactivation. The addition of 50 mg/L aprotinin (a serine protease inhibitor) resulted in greatly reduced loss of activity (data not shown). Thus, t-PA was being inactivated by a serine protease, even in serum-free medium. Equivalent rates of inactivation were observed over a range of t-PA concentrations of 5-80 mg/L, indicating no self-inactivation. However, the effects were not sufficient to explain the apparent t-PA threshold, as the expected losses associated with these effects would be less than 15%, within a 10 day fed-batch culture. Binding of t-PA to lysine residues is important for plasminogen activation in vivo (reviewed in Angles-Cano (1994)) and could potentially limit the harvest concentrations from the reactor. To detect and decrease this binding, e-aminocaproic acid (e-ACA), a lysine analog, was 78 110 70 H 1 1 1 1 1 0 2 4 6 8 10 Time (days) Figure 5.6. Degradation of t-PA in culture. Samples were taken from the reactor at days 2 and 6. The plotted values are normalized with respect to their maximum values to obtain percentage values. The fitted degradation curves of t-PA neglect the first point taken immediately after filtration. 79 used to treat samples for 30 min (on ice) before centrifugation of the cells. As a test of s-ACA treatment on cellular viability, lactate dehydrogenase activity in both the treated and non-treated samples over a 6 h period did not change (data not shown). Up to day 5 of a batch culture, the t-PA concentrations in the e-ACA-treated samples were equivalent to the reactor samples. After day 6, when the culture viability decreased below 90%, non-treated sample t-PA concentrations declined approximately 25%. The e-ACA-treated samples remained approximately constant at peak non-treated concentrations. The loss in t-PA activity at lower culture viability was not sufficient to explain the apparent limit in t-PA concentrations, as the apparent cell specific productivity was reduced up to 3-fold after day 4 in the culture. 5.3.8 t-PA Dose Response A dose response experiment with t-PA additions was performed to analyze the effect of extracellular t-PA concentration on CHO cell specific t-PA productivity (Kadouri and Bohak, 1985). There was no effect on the growth rate over the range of t-PA additions (Figure 5.7). However, there was a significant and reproducible (n = 8) reduction in the t-PA production at higher t-PA concentrations. Interestingly, the apparent t-PA productivity decreases almost to zero at a starting t-PA concentration of approximately 35 mg/L (Figure 5.7). These dose response experiments were repeated with reagent grade t-PA (data not shown). As before, there was no significant effect on the growth over the range of 0 to 200 mg/L, but a reproducible effect on the cell specific t-PA productivity. The t-PA mRNA (1.0 ± 0.13 arbitrary units) and the ratio of t-PA mRNA to total RNA (1.0 ± 0.077) were constant with increasing t-PA concentrations (Figure 5.8). Since the t-PA mRNA levels were invariant, 80 t-PA Concentration (mg/L) Figure 5.7. t-PA dose response with concentrated t-PA. The top panel shows the final viable cell concentration (squares) and the starting and final (circles) measured t-PA concentrations. The bottom panel shows the growth rate (squares) and the calculated cell specific productivity assuming a t-PA half-life of 40 days. The values are plotted versus the log mean t-PA concentration over the three day culture. 81 2.0 H Hi W^m w i s ?™ 0.0 < Q. 0) o CD c 0 o c o ~ O c o CU = o Q. ^5A 10J —•— Reagent —O— Concentrate 50 100 150 t-PA Concentration (mg/L) 200 Figure 5.8. Northern blot and intracellular t-PA concentration versus extracellular t-PA concentration. 82 the increased extracellular t-PA levels did not appear to regulate transcription. Instead, the intracellular t-PA concentration (measured by ELISA) showed a dose-dependent relationship with increasing extracellular t-PA concentration (Figure 5.8). Thus, the limitation at high extracellular t-PA concentrations was at a post-translational step. It is unlikely that there would be a specific ceil surface t-PA receptor on CHO cells that would suppress production. However, pinocytosis and inclusion were possible mechanisms proposed by (Kadouri and Bohak, 1985). t-PA is avidly bound and internalized by fibroblasts (Hoal et al., 1983) and the surface membrane protein actin serves as a binding site in endothelial cells (Dudani and Ganz, 1996). The t-PA may be bound to the surface of CHO cells and recycled as the cell membrane is renewed. 5.3.9 Formulation of Kinetic Model for Extracellular t-PA Concentrations Three effects on active t-PA concentrations in culture have been observed; production, inactivation and binding. These effects can be modeled as: where Pe is the active extracellular t-PA concentration (mg/L), t is time (days), qp is the cell specific t-PA productivity (pg/cell-day), X is the viable cell concentration (109 cells/L), kj is the inactivation constant (l/day), a is the cellular rate of t-PA adsorption (pg/cell-day) and XN is the nonviable cell concentration (109 cells/L). The effects of binding become apparent at culture viabilities of less than 90% and was ignored in further analysis. Inactivation rates were independent of concentration and reproducibly exhibited exponential decline. The cell specific productivity was expressed in Fann et al. (2000) as: dPe q p -X-kj Pe - a X N (5.2) dt q P = k s • p i (5.3) 83 where, ks is the secretion rate, (1/days) and Pi is the intracellular protein concentration, (pg/cell). However, in Fann et al. (2000), three-day cultures were used to assess productivity with extracellular concentrations reaching a maximum of approximately 20 mg/L. From the t-PA dose response, the cell specific productivity may be expressed as: q P = k s ( P i T - P i ) (5-4) where Pj is the threshold intracellular t-PA concentration, (pg/cell), where the cell specific productivity is zero. The threshold intracellular t-PA concentration corresponds to the threshold extracellular t-PA concentration. In Fann et al. (2000), a number of cell clones were created exhibiting a range of cell specific t-PA productivities. With an approximately 10-fold lower producing cell clone, the extracellular t-PA threshold concentration appeared to be approximately 2.5 mg/L. In fed-batch cultures with this low producing clone, the t-PA titers were elevated by approximately 15-20% compared to batch (data not shown). A threshold extracellular t-PA concentration appeared to be relative to a particular cell clone. The secretion rate, ks, was relatively constant for the high-producing and low-producing clone. The secretion rate was 3.4 ± 0.25 1/day with the high-producing cells in the t-PA dose response and 9.7 ±1.6 1/day in a batch experiment. With the low-producing clone in a batch experiment, the secretion rate was 8.1 ±3.1 1/day. The intracellular t-PA threshold for the high and low producing clones were approximately 2.5 ± 0.5 and 0.25 ± 0.05 pg/cell, respectively. The difference in cell specific productivities appeared to be the intracellular threshold levels. 5.3.10 Fed-batch Protocol Modification To increase the cell specific t-PA productivity, the extracellular t-PA was periodically removed. Approximately 80% of the culture volume was first clarified on days 3 and 5 (to less 84 than 104 cells/mL) using an acoustic filter (Pui et al., 1995). The clarified volume was then ultra-filtered through a 30 kDa UniSyn hollow fibre module to strip the t-PA from the medium (Figure 5.9). The permeate (-90% of harvested volume) was returned to the reactor. Each stripping procedure lowered the reactor t-PA concentrations by approximately 15 mg/L with minimal cell or culture volume loss. With lower extracellular t-PA concentrations, the cell specific t-PA productivities recovered to higher levels (Figure 5.10). Stripping the t-PA from the extracellular medium increased the yield on medium by 2-fold to 80 mg/L (Figure 5.10). 85 Harvest Recirculation Pump HF Ultrafiltration Module Permeate Return Pump Fed-batch Bioreactor Figure 5.9. Fed-batch process modification schematic. 86 •4-* > O T3 2 CL < CL I . 0 o CD Q_ 00 0) o E CD C o CD < CL CD CD O O) Q . E 20 15J 1 10H 80-60-40-20-- O - Fed-batch with UF Fed-batch Batch t-PA Stripping \ A - — A Onset of Feeding T 2 ~T~ 6 Time (days) Figure 5.10. Fed-batch culture with t-PA stripping. The process modification to strip t-PA from the fed-batch culture resulted in increased t-PA titers which are plotted as the cumulative concentration. The batch culture t-PA concentration reached approximately 32 mg/L. 87 5.4 CONCLUSIONS Isotonic concentrate formulation gave consistent results with hydrolysates or defined amino acid mixtures. Fed-batch concentrate additions based on cell numbers and a 4 pmol/cell-day cell specific glucose uptake rate maintained consistent reactor conditions. An apparent threshold of t-PA concentrations was reached at approximately 30-35 mg/L. Decreased t-PA half-lives in late phases of culture and t-PA lysine binding were not sufficient to explain the observed t-PA threshold. With increasing extracellular t-PA concentrations, increasing intracellular t-PA concentrations indicated a secretory pathway limitation. A fed-batch protocol with t-PA stripping increased protein yields compared to previous fed-batch cultures by approximately 2-fold to 80 mg/L. 88 CHAPTER 6 PERFUSION EXPERIMENTATION 6.1 INTRODUCTION In this work, without a dedicated glucose analyzer or a complex flow injection analysis system, a constant glucose environment was mediated through predictive control protocols that depended on daily samples to specify a flow rate profile until the next sampling. Glucose uptake rates were presented via a graphical user interface to allow the operator to better estimate the current and immediate future of the culture (Dowd et al., 1999). The current and immediate future glucose uptake rates could then be used in an adaptive predictive control protocol to move the process to a set point value in a robust and reproducible manner (regardless of the state of the process and the previous flow rates in the culture). The predictive control protocols were used as a tool to manipulate the reactor glucose concentration, while observing the protein concentrations (and the variability) as a function of both the feed medium formulation and the extent of medium utilization (glucose depletion). Using the results from several perfusion runs, optimal perfusion operation can be specified as a function of the glucose depletion. Implications for the definition of proven acceptable range of operation as well as the edge of failure are discussed. 6.2 MODELING AND PREDICTIVE CONTROL PROTOCOLS Daily perfusion bioreactor samples were taken and the metabolite (glucose, lactate and ammonium) concentrations were analyzed using a Stat 10 NOVA Blood/Gas Analyzer (NOVA Biomedical, Waltham, MA). Glucose depletion was defined as the difference between the feed and reactor glucose concentrations (mM units). Glucose depletion was used as the index for medium utilization, as glucose is the primary carbon and energy source for mammalian cells 89 (Zielke et al., 1978) and has often been used as the basis for modeling and controlling perfusion cultures (Handa-Corrigan et al., 1992; Hiller et al., 1993). Glucose depletion is differentiated from glucose uptake which is represented as either a volumetric or cell specific rate. The cell specific uptake/production rates were calculated from: (Cj,2-Cj,i) _F / _ T \ { ( t 2 - tQ ' y - l ^ - ^ J Q . = (6.1) A v , L M where, qi is the cell specific uptake/production rate for component i (pmol/cell day), Q i and Ci,2 are the component concentrations at time points 1 and 2 (mM), respectively, Ci,in and Q are the inlet and average component concentrations (mM), respectively, ti and t2 are time points 1 and 2 (days), respectively, F is the flow rate (L/day), V is the reactor volume (L) and XV,LM is the log mean cell concentration (cells/L). The cell specific rates were normalized by the following: where, yj are the normalized cell specific uptake/production rates, q"i is the average of the qi values, and SD(q;) is the standard deviation of the qi values. This transformation scales the values to be normally distributed (zero mean and standard deviation of 1) (Himmelblau, 1990). Decreased uptake rates are negative numbers, while elevated uptake rates are positive. On the other hand, decreased production rates are positive numbers, while elevated production rates are negative. In this way, the pattern of production and uptake rates tend to mirror each other. Substrate uptake and metabolite production rates were presented via a graphical user interface and modeled to assist in the selection of the perfusion feed rates (Dowd et al., 1999). Exponential growth models and a flat profile (for stationary phase) were used as growth models 90 for a predictive control protocol to maintain and/or manipulate the reactor glucose concentrations under changing operating conditions. A logistic growth model has been included as a potential modeling basis and may accurately indicate the dynamics of a perfusion culture with growth and stationary phases (Dowd et al., 2000). The form of the logistic growth model in the estimation procedures was: Glc,t = T~ / , Q A ( 6 - 3 ) l + exp(a + pt) where Qact is the volumetric glucose uptake rate at time t, QGic,Max is the maximum expected glucose uptake rate in the culture, a and P are regressed parameter estimates. The maximum expected glucose uptake rate was a user-specified variable that depended on the maximum viable cell concentration and assumed a cell specific glucose uptake rate of 6 pmol/cell-day. In the control protocol, a glucose set point or trajectory (i.e. ramp, etc.) was specified and the created control program (MATLAB, The MathWorks, Natick, MA) calculated the series of required hourly flow rates until the next sampling. A QuickBasic (Microsoft, WA) computer program was created to activate a solid-state relay for a pump (503 S Watson-Marlow, Wilmington, MA) via the parallel port. The program calibrated and controlled the pump which added medium volumes corresponding to the required flow rates every hour. 6.3 RESULTS AND DISCUSSION 6.3.1 Batch Culture In perfusion cultures, the medium feed is normally initiated after the cells are grown in batch for several days. In 20 mM glucose batch cultures, the growth and t-PA productivity were generally constant (at u = 0.57 ±0.11 l/day and qp = 9.2 ± 1.4 pg/cell-day, respectively) for 91 approximately 4 days, until glucose declined below 10 mM. The growth rate and t-PA productivity then fell rapidly (Figure 6.1). Interestingly, the viability of the batch culture remained above 90% until day 6. 6.3.2 Dose Response The effects of glucose or glutamine concentration on growth rate and t-PA productivity were tested in 3-day cultures. At 4 mM glucose, the glucose uptake was 3.5-fold lower than at 20 mM glucose, while the lactate production was only 1.5-fold lower (Figure 6.2). At 0.2 mM glutamine, the ammonium production was up to 35-fold lower than at 4 mM glutamine (Figure 6.2). The specific ammonium production increased with increasing glutamine concentrations, as observed by Glacken et al. (1986). There was no significant dose-dependent effect on the cell growth and protein productivity over these glucose and glutamine ranges (Figure 6.3). The specific rates of substrate uptake or metabolite production for these CHO cells were not directly proportional to the specific growth rate as originally proposed by Leudeking and Piret (1959) for Lactobacillus and as has been observed in some hybridoma cells (Goergen et al., 1992; Hiller et al., 1993). In a preliminary way, these results were used to gauge how glucose and glutamine concentrations affect the cell specific rates and to target set points to maximize growth and t-PA productivity, while minimizing the production of lactate and ammonium. 92 25 Time (days) Figure 6.1. Batch profile of glucose concentration with growth and cell specific t-PA productivity. 93 c o 20 15J 1 10H OL 5 H O IJ "O o s; o r f TO ° 1 CD O CO o Q. E . 3 3 4 o c^ o CD Q. CO "CD O 0 3 2 H 0 Lactate Production ..•10' Glucose . Q'' Uptake 5 - 1 -10 —J— 15 20 25 Glucose Concentration (mM) Ammonium Production ® Glutamine Degradation 0 1 2 3 4 5 Glutamine Concentration (mM) Figure 6.2. Dose response of glucose and glutamine. The cell specific uptake and production rates as a function of the log mean glucose and glutamine concentrations. 94 CD -4—' co or p CO g -'o CD Q . CO 0.8n 1 16 Growth Rate 12 8 4 0.0H , 1 1 1 IO _ 0 5 10 15 20 25 g Glucose Concentration (mM) 0 8 O <D O o-Productivity o CD 0.8 0.6-0.0 Growth Rate o o n o ° o o • - o —o o • • Productivity Q. 03 16 "< 12 8 4 0 O <p_ co •o CD O =ri O T l > —\ o CL c a <; 0 1 2 3 4 5 Glutamine Concentration (mM) Figure 6 . 3 . Growth rate and t-PA cell specific productivity as a function of the log mean glucose or glutamine concentrations. 95 6.3.3 Perfusion Initiation In perfusion culture, if the onset of perfusion was delayed until a glucose value of 8.5 mM was attained, the cell specific t-PA production declined 3-fold between days 5 and 10 (Figure 6.4A). The decline in t-PA production and, to a lesser extent, glucose uptake, was likely due to the cells being in the late exponential, or approaching the stationary, phase. Grammatikos et al. (1999) suggested that the intracellular nucleotide triphosphate pools can be depleted in the batch phase of perfusion start-up with negative effects on the culture growth and protein productivity. Thus, they recommended an earlier onset of perfusion. Instead of a simple glucose set point, a ramping of the glucose set point (with a negative slope of 1.5 mM/day) until 8.5 mM was followed by a constant set point. The cell specific growth and t-PA production rates were relatively constant through the initial stages of the perfusion culture with the glucose set point ramp (Figure 6.4B). For several inoculations at approximately 2xl05 cells/mL, the viable cell numbers obtained by day 6 were 2-fold higher (4x106 cells/mL) in these cultures. Thus, ramping the glucose set point accelerated perfusion culture start-up. 6.3.4 Perfusion Culture A 52-day perfusion culture was performed to determine the glucose and amino acid requirements and potential limitations in order to optimize the production of t-PA (Figure 6.5). The average dilution rate fluctuated due to changes in the glucose set point. After the initial ramping set point trajectories, the glucose set point was specified as a series of step changes between 5 and 10 mM glucose. At day 15, there was a process upset (loss in computer control of feed) resulting in losses in cell numbers (60%) and viability (30%). From day 17 to 20, the 96 A B c o 8 c o O co S = CL O £ 20 15H 10 5H S; 15H CO CL 5 A \ / A p-o. n r ,-o-, T r 1 r T r -o-oj — i 1 1 r 0 2 4 6 8 Time (days) Figure 6.4. In A, the feeding was initiated at day 5 when the glucose set point of 8.5 mM was reached. In B, the feeding was initiated at day 3 and followed a glucose set point ramp to 8.5 mM by day 6. Calculation of the apparent growth rate neglects minor losses (generally < 5%) through the cell retention device. 97 20 Time (days) Figure 6.5. 52-Day perfusion culture profile. The dilution rate was changed as a result changing reactor conditions, glucose set point and the inlet glucose concentration. (Glc = glucose, Gin = glutamine, Glu = glutamic acid and Asp = aspartic acid). 98 acoustic filter non-resonant time was increased to flush nonviable cells and debris from the reactor. The culture recovered within 4 days, and was maintained between 6 and 1 lxl06 cells/mL at greater than 85% viability for the remaining 32 days. For these cultures, the cell bleed and outflow streams were combined, as the non-resonant time of the acoustic filter was manipulated to control the cell concentration at approximately 107 cells/mL. 6.3.5 Cell Specific Uptake and Production Rates as a Function of Medium Formulation The basal medium contained 25 mM glucose and 4 mM glutamine. From day 27 to 36, the feed medium was supplemented with 2 mM glutamine. Elevated levels of glutamine have been reported (Jeong and Wang, 1995) to increase hybridoma cell concentrations and protein titers. From day 36 to 40, the medium was fortified with 5 mM glucose. Medium fortification will reduce perfusion rates and result in higher product titers (Ozturk, 1996). From day 40 to 52, the medium glucose level was increased by 5 mM, while both glutamate and aspartate were supplemented by 1 mM (A through D in Table 6.1). A paired Student's T-test was used to observe whether mean cell specific rates were significantly different due to the feed medium formulation. Supplementing the medium with 2 mM glutamine at day 27 resulted in significant (p<0.05) changes in the metabolic rates, including increased cell specific ammonium production and glutamine consumption, while reducing glucose uptake (A to B in Table 6.2). The increase in glutamine consumption and ammonium production confirmed the Figure 6.2 results and previous reports (Glacken et al., 1986; Omasa et al., 1992). The decrease in glucose consumption indicated that glutamine substituted for glucose in supplying the cellular energy requirements (Zielke et al., 1978). The increase in glutamine uptake was offset by a similar decrease in the glutamate uptake (Table 6.2). 99 Table 6.1. Medium Formulations Average t-PA Titer Designation Medium Formulation (mg/L) A 25 mM Glc, 4 mM Gin 40±4.3(n=17) B 25 mM Glc, 6 mM Gin 37 ± 2.6 (n=8) C 30 mM Glc, 4 mM Gin 40 ± 1.8 (n=4) D 30 mM Glc, 4 mM Gin, 1 mM Glu, 1 mM Asp 47±2.5(n=16) 100 Table 6.2. Cell Specific Rate Changes as a Function of Medium Formulation. Feed Medium Transition Cell Specific Rate Change P-value (A to B) Gin uptake increased 18% <0.05 Glc uptake decreased 16% O.05 Amm production increased 36% <0.05 t-PA production decreased 44% <0.05 (Bto C) t-PA production increased 30% <0.05 (AtoD) Lac production decreased 28% <0.01 Gin uptake decreased 21% <0.05 Intracellular amino acid pool depletion/formation have time scales on the order of an hour (Shotwell et al., 1980), so these effects were ignored when compared to daily cell specific rate calculations. The transient conditions between changes in medium formulation were also ignored in the analysis to allow for steady-state comparisons. 101 Increased glutamine flux through the TCA cycle would increase the amount of intracellular glutamate formed and lessen the requirement for extracellular glutamate. In the synthesis of nonessential amino acids, transamination from glutamate (to a-ketoglutarate) yields 3-phosphoserine, which is hydrolyzed to serine (Lehninger, 1986). Serine was consumed prior to the addition of glutamine to the feed, but was then produced (data not shown). There was also a decrease in the t-PA production rate (44%) and a decline in cell numbers (35%) though there were no changes in acoustic cell retention operation. As expected, there were no significant differences in the cell specific glucose uptake, lactate production or amino acid uptake when changing the medium from 25 mM glucose to 30 mM glucose at day 36 (A to C in Table 6.2). Upon 1 mM glutamate supplementation at day 40 (C to D in Table 6.2), the cell specific glutamate uptake increased 108% (p<0.01), likely due to higher supply concentration. Comparing the culture feed media (A to D in Table 6.2), the glutamine uptake decreased 21%, while the lactate production was reduced 34% (p<0.01), even though the reactor glucose concentration was similar (approximately 5 or 10 mM). 6.3.6 Glucose as Index of Medium Utilization and t-PA Concentrations As the reactor glucose concentration was manipulated to different set point concentrations, the glucose depletion (the difference between the fresh medium and reactor glucose concentration) was used to indicate overall medium utilization. To maximize the reactor t-PA concentrations, a larger difference may be desirable, but these may also cause toxic metabolite build-up or substrate limitation. In the early stages of the 52-day culture, the glucose concentration was brought close to 5 mM (Figure 6.6), and the t-PA concentration reached a peak of 60 mg/L. The glutamine and glucose concentration profiles were similar for the batch phase 102 - + - A l a - X - Gly - • - G i n — O — A s n O Asp — A — Glu T ime (days) Figure 6.6. Glucose, t-PA and amino acid concentrations in batch and early perfusion. Perfusion was initiated after 4 days of culture at a glucose concentration of 15 mM. The glucose concentration reaches approximately 5 mM at its nadir, while the t-PA concentration reaches approximately 60 mg/L at its peak. The t-PA concentrations are measured both with activity and ELISA (protein) assays. 103 and after approximately three days of perfusion (i.e. day 7 onward). Glutamine and asparagine were significantly depleted but did not appear to reach limiting levels upon perfusion, while alanine and glycine were produced. Both aspartate and glutamate reached less than 0.03 mM levels at day 5 (Figure 6.6), without apparent effect on the culture viability. The remainder of the amino acids exhibited little change in concentrations (data not shown). Analysis of the normalized cell specific uptake and production rates of several amino acids revealed significant trends with culture time (as the glucose depletion increased from approximately 10 mM to 20 mM) (Figure 6.7). The effect of normalization is to similarly scale the cell specific rates and it tends to improve pattern detection (Geladi and Kowalski, 1986). With increasing glucose depletion, the cell specific rates of glucose, glutamine and several amino acid uptake rates declined (p<0.01) (Figure 6.7), while the cell specific production rates of lactate, glycine, alanine, ammonium and t-PA also declined (p<0.01). In the calculation of cell specific rates, uptake rates were positive, while production rates were negative, thus the sign for the slope for the normalized rates (top and bottom panels in Figure 6.7) were opposite. Glucose may be used as an indicator (Wold et al., 1987) for the pattern of utilization/production rate for all these substrates and metabolites (top and bottom panel in Figure 6.7, respectively). Thus, process modeling based on measured glucose uptake rates can be used to predict how rates, such as t-PA productivity change. Culture conditions that maximize glucose uptake could be used to infer maximal t-PA productivity. Several medium components exhibit constant cell specific rates as a function of medium depletion (middle panel of Figure 6.7). If process modeling was treated as a stoichiometric equation, the coefficients would be constant, regardless of the extent of medium utilization. It 104 CO CD -•—< CO ct o «t 'o CD Q. GO "53 O T3 0 N ro E 2-0--2-2-0--2-2-0--2-x ? + I 0 T + v 8 0 8 TT' • • Glc o Asp A Glu V Asn O Gin + Val X lie * Leu Lys • Ser o His A Thr V Arg O Pro + Tyr X Met * Phe - Trp • o A V O Gly Ala Lac Amm t-PA ~ i 1 1 1 6 8 10 12 14 T ime (days) Figure 6.7. Normalized cell specific rates of medium components in perfusion culture. The cell specific amino acid uptake rates were normalized using Equation. 6.2. Increased uptake or production is indicated by larger (absolute value) positive or negative numbers, respectively. A large number of amino acids exhibit a decline in cell specific uptake rates (top panel), and a decline in cell specific production rates (bottom panel). Another subset of amino acids exhibit no significant trend (middle panel). 105 follows that the depletion of medium components was linear with respect to each other, as the cell specific rates would not change with respect to each other. However, this situation is not observed (Figure 6.7), so process modeling based on stoichiometry will need to include the significant effects of variable coefficients in an assumed stoichiometric relation being correlated with either medium or glucose depletion. With the 25 mM glucose and 4 mM glutamine medium (A), the depletion of medium components, plotted versus glucose depletion may indicate limitations and changes in metabolism. Glutamine and isoleucine are examples of the predominant pattern (that include arginine, leucine, valine, phenylalanine and threonine) of amino acid depletions that exhibit linear relationships with increasing glucose depletion (Figure 6.8). However, asparagine, aspartate and glutamate all indicate that no further consumption was possible (due to limitation in supply) after a glucose depletion of approximately 10 mM. The asparagine concentrations do not appear to be limiting (approximately 0.1 to 0.2 mM reactor concentration), yet no further depletion was observed. Both alanine and ammonium are produced in culture and exhibit maximum concentrations at glucose depletions of 17 and 9 mM, respectively. Ammonium and alanine are both by-products of glutamine metabolism, which indicates glutamine utilization becomes more efficient at greater glucose (and glutamine) depletions. The ammonium concentrations and the glutamine depletions follow similar patterns for the batch stage (<10 mM glucose depletions), but tend to diverge in the perfusion culture with higher glucose depletions. Similarly, Pelletier et al. (1994) illustrated that a batch culture model based on glucose measurements was not able to accurately predict ammonium concentrations in perfusion cultures. 106 Glucose Depletion (mM) Figure 6.8. Depletion of amino acids along with concentrations of alanine and ammonium plotted as a function of glucose depletion. 107 A decline in culture viability may be offset by increasing the non-resonant time of the acoustic filter (to allow for flushing of the cells), as discussed previously. In a perfusion culture in which the glucose depletion was brought to 24 mM, the non-resonant time of the acoustic filter was increased, in an attempt to maintain the culture viability. The t-PA concentrations reached over 90 mg/L on days 9 through 11, but declined to approximately 20 mg/L by day 19 (Figure 6.9). The peak in t-PA concentrations coincides with when the culture was initially brought to low glucose concentrations. Perfusion culture concentrations may be optimized by cycling through high and low glucose set points. The increase in the non-resonant time for the acoustic filter allowed the viability of the culture to be maintained generally above 80%, but was not sufficient for maintaining elevated t-PA titers. In a different culture controlled at a constant 21.5 mM glucose depletion, stable operation at 40 mg/L t-PA was obtained (Figure 6.10). The difference in the glucose set points (8.5 versus 6 mM) was not large, but it had a significant impact on the culture viability and t-PA titers in the culture. For perfusion cultures fed with medium D (Figures 6.4, 6.9 and 6.10), all the t-PA concentrations were plotted as a function of glucose depletion. The concentration-depletion data points were sorted by increasing glucose depletion and averaged (5 and 10 data points for below and above 22 mM glucose depletion, respectively). The average t-PA concentrations exhibited a saturation-type function of glucose depletion (Figure 6.11). The variability (standard deviation) exhibited a gradual increase with increasing glucose depletion, up to approximately 22 mM glucose depletion. Between 22 and 24 mM glucose depletions, the variance increases up to 3-fold. The operating point for the perfusion reactor may be specified from the average and variance in the t-PA concentrations as a function of glucose depletion. The optimal glucose set 108 25 c o '•*-> CO l_ "c CD i f CD (/> O O _=J C3 o CO I ? o £ o < 0-20 43 100 J ° oooxl D D D D n D r j D n 100 8 0 c? 60 = < 40 2! 20 Time (days) Figure 6.9. Glucose and t-PA concentrations in perfusion culture controlled at 6 mM glucose. 109 o TO CD §f O >E CD (/) o o O c o O O) O < CL 25 20-I 15->*><X>% sO<> '<xx>Q<r Oo Pa 10-5-o 50-40-30 20 10 0 0 / a o A / i o d 5 10 Time (days) - r — 15 100 80 "U CD — i 60 8 3 «—1-40 Viabil 20 0 20 Figure 6.10. Glucose and t-PA concentrations for a perfusion culture controlled at 8.5 mM glucose. 110 100 c o < CO c 8 c o o < Q_ E c o ' CO c 8 c o o < CL 20 H 0 0 dF • UJ©-. HP L • o I I 1 Average i ; i • • • • • Standard § § 9 Deviation 0 * M - - -/ - * V * - - - / 0 0 m m 0 0 * % % ft 1 ft ft 1 1 1 1 1 1 1 % 0 5 10 15 20 25 Glucose Depletion (mM) 30 Figure 6.11. t-PA concentrations and variability as a function of glucose depletion. The reactor glucose set point concentration may be specified as a function of the expected t-PA concentration and variability. I l l point would be specified based on the desired t-PA concentration and variation. A consistent concentration of 40 mg/L was obtained at a glucose depletion of 22.5 mM. The expected level of variability would be less than 15%. 6.4 CONCLUSIONS Earlier feeding of fresh medium resulted in improved growth and consistency for the transition between batch and perfusion cultures. Daily glucose measurements were used in modeling to maintain process control, as well as to indicate the level of medium usage. An optimized medium formulation led to approximately 7 mg/L higher t-PA titers and the culture exhibited significantly lower cell specific lactate production. A consistent t-PA yield of approximately 40 mg/L was obtained at a glucose depletion of 22 mM with a variability of less than 15%. Transient maxima of up to 90 mg/L t-PA were observed at glucose depletions of 25 mM, but did not appear to be sustainable for longer periods than three days. These transient increases in t-PA concentrations appear to be at the edge of failure as the culture viability is negatively affected. The average and variability in the t-PA concentrations, specified as a function of glucose depletion, may be used to specify range of operation. 112 C H A P T E R 7 CONCLUSIONS AND RECOMMENDATIONS FOR F U T U R E W ORK 7.1 OVERALL REVIEW Predictive control based on daily glucose measurements was effective in controlling and manipulating reactor concentrations. Fed-batch and perfusion process optimization became the thesis focus. Fed-batch culture viable cell indices were increased up to 4-fold versus batch. The CHO cell line exhibited a secretory pathway limitation, as t-PA intracellular levels increased with extracellular concentration. Stripping the product protein from the extracellular medium increased fed-batch t-PA yield on medium 2-fold to 80 mg/L. A controlled onset of perfusion feeding improved start-up consistency. Perfusion t-PA yields and optimal range of operation were mapped as a function of glucose depletion, an indicator of medium utilization. Perfusion processes exhibited 10-fold higher volumetric productivity with a stable 40 mg/L t-PA yield on medium. 7.2 PREDICTIVE MODELING AND CONTROL In this study, robust modeling and predictive control protocols were developed to control substrate concentrations for fed-batch and perfusion bioreactors. As a result, feed rate estimation was improved compared to operator estimation. As well, daily manual sampling was used, rather than an automated flow injection system that would be complex and potentially fallible. A graphical user interface of the up-to-date and future glucose uptake rates was correlated with an increased operator confidence that the process was being well controlled. The controller response to concentration deviations from the set point was designed to be independent of the 113 state of the culture, process flows, or sampling interval. As a result, fewer samples were taken, with a concomitant reduction in labour and analytical expense. With good model estimation, the process can be controlled at the set point with a level of variability approaching that of the glucose assay. The predictive process control protocols have been successfully applied to fed-batch and perfusion suspension bioreactors. This work, however, should be regarded as a preliminary step to improving the control of mammalian protein production processes. The presented predictive modeling and control protocols were generally based on one flow rate through a perfusion process. Further simulation and experimental work should be done with two or more separate feed streams. This mode of operation may be advantageous to change component concentrations without changing medium sources. The possibility of finely controlling reactor conditions, may be advantageous for cell products, such as hematopoietic cells, in which cytokine concentrations are changed with respect to time in order to control the level or type of cellular differentiation. 7.3 FED-BATCH CULTURE Fed-batch concentrates formulated using hydrolysates to substitute for defined amino acid mixtures resulted in similar 2.5-fold (and up to 4-fold) extensions in the viable cell indices relative to batch. Feeding of the concentrate was based on cell numbers and a 4 pmol/cell-day glucose uptake rate to control substrate concentrations. However, increased viable cell indices did not lead to increased t-PA titers. A secretory pathway limitation was confirmed with clinical grade and concentrated supernatants from perfusion cultures. In fed-batch reactors, proof-of-concept experiments demonstrated that when t-PA was stripped from the extracellular medium, t-PA cell specific productivity could be maintained at higher levels, resulting in higher yields on medium. 114 The fed-batch process modification could be further improved by continuous stripping of the t-PA from the reactor using a t-PA affinity column. The cell specific productivity would remain at high levels and the initial downstream purification steps would be combined. 7.4 PERFUSION CULTURE Glucose measurements were used to indicate medium utilization and specify the proven acceptable range of operation and edge of failure for operation in perfusion culture. At a glucose set point of 10 mM, consistent 40 mg/L yields may be expected with the SI5-23SFM23 cell clone. As the process approaches the edge of failure, peaks in protein production up to 90 mg/L are possible, but not sustainable. The variation in product concentrations increases dramatically at a glucose depletion of 22 mM. Optimized media formulations led to elevated t-PA titers. Perfusion processes exhibited up to 10-fold higher volumetric productivity compared to batch and fed-batch cultures. The production of t-PA may be maximized by periodically varying the set point concentration between high and low levels. For example, glucose levels at approximately 10 mM maintain culture viability, while 5 mM levels generate peak t-PA concentrations. By controlling the culture between these glucose set points (i.e. every 3-4 days), peak t-PA concentrations may be obtained, along with good culture viability. It is likely that the secretory pathway limitation in the t-PA producing CHO cells affected the yields obtained from perfusion culture. Stripping t-PA from the culture may be accomplished by adding a recirculation loop through the acoustic filter in the perfusion culture. A portion of the harvest stream would flow through an affinity separation column and returned to the reactor. As before, this would lower reactor concentrations (maintaining high cell specific productivity) and be the first stage in the downstream purification. 115 7.5 COMBINED FED-BATCH AND PERFUSION CULTURE PROCESS In a combined fed-batch and perfusion process, a culture may be grown to high cell densities in perfusion mode, at which point, fed-batch concentrates may be fed in order to obtain higher product titers. The fed-batch and perfusion portions of the culture may be alternated, in order to maintain long-term high viable cell concentrations, and periodic increases in protein titers. The advantages of a combined fed-batch and perfusion process would be identified in a cell system (i.e. a hybridoma cell line producing a monoclonal antibody) that does not exhibit secretory pathway limitations at high protein concentrations. 7.6 DOSE RESPONSE Dose response experimentation was useful in determining the effects of medium components on the culture performance. This approach may be used to determine the edge of failure in culture, especially with spent medium taken from either fed-batch or perfusion culture. If cells are grown on spent medium, the potential for further growth and/or t-PA productivity may be assessed. This may be used as an indication for the edge of failure and this may be restated in terms of more easily measured components, such as the glucose concentration. The spent medium, along with additions of test components, may be used to further improve the medium formulation for further utilization. With the addition of specific components, further growth and t-PA productivity may result and lead to higher t-PA titers. 7.7 QUALITY SPECIFICATIONS In perfusion bioreactors, the t-PA concentrations were specified as a function of the glucose depletion. In future work, specifications of the sialic acid content may be similarly specified as a 116 function of glucose depletion. These specifications would improve the estimation of the best reactor glucose concentration to operate at in order to obtain consistent results. Quantity and quality standards for the t-PA produced in fed-batch and perfusion processes could be performed. This work is still required in order to properly compare reactor configurations and decide on the preferred mode of operation. 7.8 PRINCIPAL COMPONENT ANALYSIS The application of principal component analysis to the characterization of the substrate and metabolite uptake and production rates within different cultures may yield useful correlations between process data. Throughout the presented work, there were observed differences in the pattern of uptake rates between different cultures. These may be further applied for use in validation of processes, even between different process scales, medium formulation and protein produced. Models based on macroscopic measurements would be easier to implement, as the data are more readily available. The principal component models are robust, measurement based and combine data into forms which describe the system. 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Physiol. 9 5 : 41-48. 134 APPENDIX 1 MANUSCRIPT OF PREVIOUS H O L L O W FIBRE W O R K A.l . PREDICTIVE CONTROL OF HOLLOW FD3RE BIOREACTORS FOR THE PRODUCTION OF MONOCLONAL ANTTJBODTJES Jason E. Dowd ', Ingrid Weber '' , Beatriz Rodriguez , James M. Piret' , K. Ezra Kwok Running Title: Predictive Control of Hollow Fibre Bioreactors for Antibody Production biotechnology Laboratory, University of British Columbia, Vancouver, BC, Canada V6T 1Z3; telephone: (604) 822-5835; fax: (604) 822-2114; e-mail: jpiret@chml.ubc.ca department of Chemical and Bio-Resource Engineering, University of British Columbia, Vancouver, BC, Canada V6T 1Z3 3Departement de Genie Biochimique et Alimentaire, INSA Toulouse, France 4StemCell Technologies Inc., Vancouver, BC, Canada V5Z 4J7 Keywords: predictive control, hollow fibre bioreactors, monoclonal antibodies, perfusion 135 ABSTRACT The selection of medium feed rates for perfusion bioreactors represents a challenge for process optimization, particularly in bioreactors which are sampled infrequently. When the present and immediate future of a bioprocess can be adequately described, predictive control can minimize deviations from set points in a manner to maximize process consistency. Predictive control of perfusion hollow fibre bioreactors was investigated in a series of hybridoma cell cultures which compared operator control to computer estimation of feed rates. Adaptive software routines were developed to estimate the current, and predict the future, glucose uptake and lactate production of the bioprocess at each sampling interval. The current and future glucose uptake rates were used to select the perfusion feed rate in a designed response to deviations from the set point values. The routines presented a graphical user interface through which the operator was able to view the up-to-date culture performance and assess the model description of the immediate future culture performance. In addition, fewer samples were taken in the computer-estimated cultures, reducing labour and analytical expense. The use of these predictive controller routines and the graphical user interface decreased the glucose and lactate concentration variances up to 7-fold and antibody yields increased 10% to 43%. 136 INTRODUCTION Hollow fibre bioreactors (HFBR) have been used extensively for the production of monoclonal antibodies (MAb) (Brotherton and Chau, 1996; Jackson et al., 1996). The process control of these bioreactors is often limited to operator adjustment of the medium feed to maintain a desired set point (usually a glucose concentration). Perfusion flow rates in suspension cultures can be set a priori (Pelletier et al., 1994; Banik and Heath, 1995), however, a priori perfusion flow rates are not likely to optimize the medium utilization, especially in dynamic and variable cultures. One approach to optimize stirred bioreactor medium usage has been to maintain a per viable cell perfusion rate (Bodeker et al., 1994; Konstantinov, 1996). However, in an HFBR, representative samples cannot be recovered to analyze the bioreactor cell concentration. In addition, the response of a biological system to changing conditions tends to be less reproducible than most traditional chemical engineering processes and the application of traditional control protocols (i.e. Proportional + Integral + Derivative) is complicated by the non-linear nature of biological systems. A given set of process control parameters may give an underdamped response at one stage of the process, while giving an overdamped response at another stage (Meyer and Beyeler, 1984). Industrial protein production processes typically involve relatively few analyses of indicative parameters to gauge the physiological state of the culture (Glacken, 1995). For instance, the bioreactor glucose uptake and lactate production rates have been used as indicators for the state of the culture (Evans and Miller, 1990). The process control of HFBR systems usually involve a priori or rule-based step increases of medium perfusion flow rate with time (Kurkela et al., 1993; Lowrey et al., 1994; Brotherton and Chau, 1995). Typically, (Handa et al., 1992) rule-based 137 algorithms require the feed rates to be increased if the glucose and glutamine levels become too low, or if the lactate and ammonium levels become too high (i.e., <8.3 mM for glucose and >16.7 mM for lactate). Liu et al. (1991) reported the use of the HFBR Acusoft-P software to control the pH, glucose and lactate levels. The set points for pH, glucose and lactate in the growth phase were 7.43, 18.6 mM, 8.7 mM, respectively, while in the production phase, these set points were 7.2, 9.8 mM, 15.0 mM. There were no indications of how the software was designed, or how well the software controlled the concentrations (Liu et al., 1991). Feed rate control by on-line sensors such as for glucose are not widely used, while off-line sampling is usually at a low frequency (i.e., daily) and there are often delays before measurement results are obtained. Due to bioprocess variability, using concentration measurements as the only guide can lead to under- or over-feeding of cultures. Under-feeding of cultures can result in substrate limitations or metabolite inhibitions, increasing cell death in HFBRs and reducing reactor productivity. Over-feeding of cultures can result in costly medium wastage. Predictive elements in the control scheme, not only can offset delays in analysis, but they also can provide appropriate control action between infrequent samples. The development of model-based process control protocols can describe the culture dynamics (Soderstrom and Stoica, 1989) and improve bioprocess repeatability (Soeterboek, 1992). The time-varying nature of bioprocess parameters complicates the estimation of model parameters and completely structured models for mammalian cell culture processes are not available (Tzaimpazis and Sambanis, 1994). However, for control purposes, simpler unstructured process models will often suffice, since control models need only accurately describe the process in the intervals between samples (Seborg et al., 1989). 138 The application of multiple models in predictive control can be used (He et al., 1986; Martin et al., 1987) in order to span the range of observable behaviour in a bioprocess. The objective of this work is to develop a predictive control protocol for calculating perfusion feed rates in order to effectively control the glucose concentrations. A loose loop control strategy based on glucose was developed which involved manual sampling and analysis, followed by modeling and implementing a predictive control scheme to select the feed rate of fresh medium to the HFBR recirculation loop. Different models were used in different culture phases to account for variable lag, exponential and stationary growth phases. Based on the assessment of the immediate culture future, the appropriate feed rates were calculated to maintain (or attain) the glucose set point concentration in the culture. The first two cultures were performed with operator control and operator estimation of feed rates, while the third and fourth cultures were performed with operator control and computer estimation of feed rates. The bioprocessing protocols, modeling methodology and culture results are described in the following sections. MATERIALS AND METHODS Cell Culture The mouse hybridoma cell line 341 G6 producing IgGi anti-dextran (DX1) monoclonal antibody (MAb) and the rat hybridoma cell line TFL-P9 producing IgGi anti-mouse (P9) MAb were provided by the Terry Fox Laboratory (Vancouver, BC). Frozen cells were thawed rapidly and cultured in Dulbecco's modified Eagles medium (DMEM) supplemented with 10% fetal bovine serum (FBS) for one week and then in DMEM with 5% FBS. The cells were maintained in 139 T-flasks for at least three weeks and then transferred to a 1.0 L spinner flask. Cell counts were performed using trypan blue exclusion and a hemocytometer. Approximately 7108 exponential growth phase cells, with greater than 90% viability, were spun down (800 g, 10 min). The pellet was resuspended and inoculated the extracapillary space (ECS) of the GFE-15 Gambro-Dialysatoren (Hechingen, Germany) HFBR with a 97.4 mL ECS volume (Labecki et al., 1998). After the first few days of culture, approximately 50 mL every two days was harvested from the ECS to recover the produced monoclonal antibody. Fresh medium was simultaneously added to the ECS as the harvested medium was removed. The Unisyn Technologies (Hopkinton, MA) Cell Pharm™ System perfusion feed rate was controlled manually by the operator via the feed pump control. A fixed 100 mL volume between two level controllers was automatically drained and the same volume of fresh medium was added in a sequence. The time interval between addition sequences was based on the set feed rate. Manual samples were taken daily from the intra-capillary space (ICS) using a syringe (Figure 1). The glucose and lactate concentrations of the samples were analyzed within 5 min using either a Stat 10 NOVA Blood/Gas Analyzer (Waltham, MA), or a YSI Glucose/Lactate Analyzer (Yellow Springs, IL). The control action was then taken approximately 10 min after analysis. Control Protocol The controlled variable in these cultures was the glucose concentration, while the manipulated variable was the addition of fresh medium to the ICS. The control of the glucose concentration was mediated via operator or computer estimation of the feed rates. For computer estimation of the feed rates, the data was entered into a computer spreadsheet. A MATLAB (The MathWorks, 140 Natick, MA) program extracted this spreadsheet data, modeled the process and implemented a predictive control scheme to calculate the required feed rates. These model predictions were studied via the graphical user interface, and, if required, rerun with different parameters. The addition rate of fresh medium to the ICS was implemented by the operator via the feed pump control. Initial glucose uptake and lactate production rate estimates were based on the number of cells inoculated multiplied by the batch specific rates (obtained during exponential growth). Modeling and Control Mass Balance Model For a hollow fibre culture system with a constant volume and variable perfusion flow, a general balance for glucose can be specified: ^ = - ( c F - c R ) - ^ (1) dt V V W where, CF and CR are the feed and HFBR ICS glucose concentrations (mM) respectively, t is the culture time (h), F is the ICS fresh medium addition rate (L/h), V is the ICS volume including the reservoir and recirculation loop (L), and GUR is the HFBR glucose uptake rate (mmol/h). This process model is different from typical process control systems, in that the controlled variable is the concentration and the manipulated variable is the feed rate. Typical concentration control for chemical flow processes involve varying the inlet concentration or reactor conditions (temperature and/or pressure) and maintaining a constant flow rate (Seborg et al., 1989). The multiplication of the flow rate and the reactor concentration makes the separation of variables required for straightforward process control more complex. A further difficulty is that the GUR 141 consumption term can increase exponentially with cell growth. The Taylor series expansion of Eqn. 1 generated the required separation of variables: V-# + F-C GUR AF = (2) C C where, C = C F - C R (3) is the deviation variable of the glucose concentration (mM), AF is the change in the feed rate, C and F are the previous average concentration deviation variable and feed rate, respectively. The key variable to be estimated in Eqn. 2 was the GUR at the current point and over the interval until the next sampling. Filtering for Estimation of Glucose Uptake Rate at Current Sampling Point Initial simulation studies for the controller design were performed with data from a previous operator-controlled HFBR experiment (Figure 2). The variability in the glucose measurements and the growth of the culture caused large variation in the calculation of the GUR (Figure 2). For the GUR to be reliably used in the calculation of the required feed rate, filtering was used to suitably smooth the data. Potentially significant offsets (bias) and filter effects needed to be understood and will be discussed in the following sections. Averaging Filters In the first technique, a simple arithmetic moving average (AMA) was applied to the measurement: yk = y k - i + V N - ( x k - x k - N ) ( 4 ) 142 where, yk, yic-i are the filtered values at time index k and k-1, Xk, Xk-N are the unfiltered values at time index k and k-N and N is the period of the filter. The AMA estimator (Eqn. 4), works robustly as there is no assumed model form. However, for an increasing glucose uptake rate, the AMA estimator tended to underestimate the uptake rates (i.e., from day 8 to day 13 in Figure 2). The AMA filter can be tuned by decreasing the period, but at the cost of increasing noise (filtering effect). Tuning a filter to balance between accuracy and the filtering effect can be assisted by statistics (Saucedo and Karim, 1997) and/or a graphical user interface. More complex averaging filters were used (data not shown), but these suffered from similar difficulties (Seborg etal., 1989). Model-Based Filters A linear growth model can be assumed using least squares (LS) estimation, while an exponential growth model can be assumed using linearized least squares (LLS) estimation. If the process conforms to a model, the estimates obtained will have less offset than moving average filters. The HFBR data in Figure 2 illustrates that a single model did not accurately describe the entire HFBR culture period without significant bias. A window of data (the last n data points) was used to obtain estimates with less bias. However, if the window was smaller, there was less likely to be a bias from the process data, but the estimates were more likely to be affected by measurement and/or process noise. Using an arbitrary fixed data window of 6 points, this problem of noise leading to over-estimation is illustrated on day 10 of Figure 2. Specific data points could be excluded from the analysis if they were deemed (based on operator experience) to be outliers. The outliers tended to occur if the time between sampling was small and the glucose analyzer was not properly calibrated. In total, 3 samples (taken over a 6 h interval for one of the presented 143 cultures) were deemed outliers as the apparent glucose concentration varied by as much as 7 mM. This observation was confirmed by performing a propagation of errors (Himmelblau, 1990) on Eqn. 1 (data not shown). Glucose measurement variability, combined with a 1 h sampling interval caused the maximum errors in GUR estimates to increase by up to 6-fold compared to daily sampling. A graphical user interface with a plot of different estimates helped in choosing the most accurate descriptor of the current state of the culture. Estimation of Prediction Horizon In addition to an estimate of the current state, the controller required a prediction profile of future GURs. Linear profiles have been used (Williams et al., 1986; Stoll et al., 1996), but tend to underestimate the future requirements in the initial stages, as in the first two LS projections of Figure 3. Linear control of the feed rates can lead to oscillatory concentration profiles (Shimizu et al., 1988; Kurokawa et al., 1994; Wang et al., 1995; Konstantinov, 1996). A linearized least squares (LLS) regression of the volumetric uptake over a window of data was used in this work to obtain the estimate for the specific rate of change in GUR. The current AMA or LLS estimates (Figure 2) were then iteratively multiplied by the specific rate of change in GUR to form the prediction horizon (Figure 3). These estimates gave more accurate predictions in the highly non-linear growth and death phases. The current AMA estimate was also utilized to create a flat (constant) prediction horizon (during stationary phase). The use of multiple models in the predictive control protocol has been used to describe other bioprocess dynamics and should help identify and respond to changing conditions (He et al., 1986; Martin et al., 1987; Yu et al., 1992). 144 Predictive Control Law The goal of the predictive controller was to model the dynamics of the process and, if required, add corrective measures to bring the system back to the set point concentration. The response of the bioprocess to an offset (deviation) from the set point was designed in order to give the desired result (Soeterboek, 1992). If the glucose concentration was at the set point, the required feed rate was matched to the predicted uptake rates until the next sampling interval. If the concentration was different from the set point, then the feed rate was adjusted from the current point. If the predicted uptake rates were matched in the future, then the error in the future would decrease in a first order manner (Soeterboek, 1992). The controller was designed to bring the process back into concentration range within 2 sampling intervals (minimum sampling interval of 12 h), with no overshoot and to asymptotically converge to the set point value. The stated minimum interval of 12 h was based on simulation of the designed controller. The controller could be designed to more rapidly return the process back into control, however, this may result in unstable operation. The control protocol was independent of the choice of model used to describe the bioprocess. This contrasts with the practice of using a single model (which may be inadequate in certain culture periods) and attempting to tune the control protocol. Rule-based criteria have been used to constrain the control protocol to consider only relevant model choices (Kwok et al., 1995). In this work, the models were selected for use based on their representation of the data via the graphical user interface. The performance of the predictive controller was designed to be independent of the state of the culture and the previous feed rates. The performance of the controller versus sampling interval can be gauged by whether the culture glucose concentration moved closer to the set point value (decreased offset) at the next sampling point. An offset 145 would likely be larger if the period between sampling was longer (Seborg et al., 1989) or only one model was used (He et al., 1986). RESULTS and DISCUSSION Operator Estimation of Feed Rates Figure 4 illustrates the challenges encountered by an HFBR culture operator adjusting the feed rate to maintain the set point concentration range between 13.5 and 16.5 mM. After the initial batch culture period, the perfusion flow was started too late and the size of the initial control action was too large, as indicated by the spike in the feed rate at day 2. Both the magnitude and time schedule of the selected feed rates was not appropriate. As well, there was a lack of appropriate control action from day 15 to 19 when, for no apparent reason, the GUR transiently decreased. The decrease of the glucose concentration below 8.5 mM should not be limiting, given the expected HFBR axial and radial mass transport gradients (Piret et al., 1991). However, the lactate concentrations increased up to 34 mM, which in batch cultures of the same cells was correlated with a drop to 32% viability (data not shown). Interestingly, there was not a clear indication of increased cell death in the HFBR during this period since the bioreactor nearly recovered its maximum GUR by day 19. Nonetheless, it is desirable to avoid such perturbations in medium conditions to maintain high HFBR performance, especially when process consistency is essential for FDA regulatory approval. 146 Initial Feed Rate Algorithm The second (72 day) HFBR culture involved the operator maintaining the set point glucose concentration in a range of between 11.5 and 14.5 mM (Figure 5). In this culture, the perfusion flow was started at 0.1 L/day. Subsequent flow rates were iteratively increased by the exponential of the specific growth rate multiplied by the time interval between sampling. From day 3 to 8, the specific growth rate used was 70% of u.max (obtained from batch cultures), while from day 9 to 13, the specific growth rate used was 35% of u,max. These flow rate estimates served as a guide. There was an undershoot of the glucose concentration as the starting point for the feed was slightly delayed. Guided by the algorithm, operator estimation was able to maintain the glucose concentration near the set point range between day 3 and day 13 (Figure 5). With no corrective measures to raise the concentration, the process concentration remained at the low end of the range during this initial stage. The GUR (data not shown) leveled off after day 13 and slowly declined after day 45. The glucose concentration was higher than the set point range between days 58 and 68. Medium overfeeding was calculated to be approximately 10-12 L in the final stage of the culture. Computer Estimation Using One Model of Glucose Uptake Rates The third HFBR culture initial control estimates were based on an AMA (Equation 3) with a period, in general, of three sampling points. The control profile was an exponential growth projection based on a window of measured glucose concentrations (Figure 6). Two Unisyn HFBR cartridges were cultivated with a common ICS medium reservoir in this 58 day HFBR culture (Figure 1). As a result, the glucose concentration decreased more rapidly than in the previous cultures. At day 2, the computer routine parameters were set 16-fold too high, resulting 147 in a large initial feed rate. The GUR increased rapidly after an initial lag period and then reached an apparent stationary state from day 12 to day 16 (Figure 6). Upon observing (through the graphical user interface) this apparent stationary state, the use of reduced serum in the culture was investigated. Serum is a major component of the cost of mammalian cell medium and may not be required in HFBR culture if cell growth is minimal (Ehrlich et al., 1978). The culture performance was tested with 1% FBS or 0.5% FBS + 5 mg/L insulin versus 2% FBS (Figure 6). Ehrlich et al. (1978) reported that the glucose uptake and lactate production decreased 50% in 0.1% or 1% FBS cultures compared to cultures with 5% FBS. In Figure 6, the feeding of 0.5% FBS + 5 mg/L insulin appears to cause a reduction in the GUR, however, this result was not conclusive, given the sequential experimental design and the variability of HFBR GURs. The glucose control was more challenging in this culture versus the first two cultures, since there was faster culture dynamics (2 parallel HFBRs), variable serum levels and much less sampling (0.57 day"1). When there was offset (at day 10, due to a long period without sampling between day 7 to 10), the predictive control elements brought the system back into control in 2 sampling intervals. In addition, the set point was maintained without overshoot (between day 10 to 14). When the GUR was decreasing (between days 18-23 and days 42-58), the predictive elements maintained the process in control, which probably prevented costly medium overfeeding. Computer Estimation Using Multiple Models The fourth HFBR culture used Computer routines to calculate the future feeding profiles from the last sampling point to a point up to three days in the future. As with the third culture, two HFBR cartridges were inoculated in parallel for this 92 day HFBR culture (Figure 7). Both LLS and 148 AMA estimation techniques were used to estimate the current point for control purposes, with the LLS specific rates of change iteratively multiplying the current estimates to form the prediction horizon (as in Figure 3). The operator chose a model form using the graphical user interface based on a window of measured concentrations. With previous culture information about simultaneous glucose and lactate ICS concentrations for a given feed medium, the glucose and lactate set point concentrations were specified at 13.0 and 18.5 mM, respectively. The actual average glucose and lactate concentrations were 13.1 mM (s.d. 0.66 mM) and 18.4 mM (s.d. 1.0 mM), respectively. These simultaneous glucose and lactate concentrations compared well to Kurkela et al. (1993), with glucose and lactate concentrations of 16.9 mM (s.d. 2.7 mM) and 13.2 mM (s.d. 5.7 mM), respectively. The lactate production rates were similarly filtered, modeled, presented via the graphical user interface and predictive controller feed rates calculated as discussed previously with glucose. The feed rates using glucose uptake rates were virtually identical to the feed rates predicted using lactate production rates (<3% variation). There was a high correlation (p<0.0001) between the lactate production rate and the glucose uptake rate throughout the culture (Figure 8). The yield of lactate from glucose was 1.71 (s.d. 0.02). The variability shown here was less than reported by others (Heifetz et al., 1989; Evans and Miller, 1990; Handa et al., 1992). These results illustrate the potential of using lactate production rates to provide an independent prediction of the required feed rates as a safeguard against failure of the glucose analysis. The control performance of the fourth culture exhibited very low glucose and lactate concentration variability compared to the previous runs. These results compared well to a suspension perfusion culture system with similar glucose variability of between 0.61 and 149 0.78 mM (Konstantinov 1996), but which used up to a 24-fold higher frequency of sampling with a flow injection analysis system. Comparison of Hollow Fiber Cultures The differences in cell line, number of perfusion modules and FBS addition should be negligible in terms of comparing the different control strategies. The modeling and predictive control algorithms are expected to be independent of these considerations. In the first two cultures, the calculated glucose uptake rate was not plotted or available to the operator, and both runs illustrated over- and under-feeding. For operators, it is often difficult to predict without systematic predictive calculations how the feed rates should be manipulated over time in order to control the process. A set of concentration values does not indicate to the operator the magnitude of how the process is changing, unless the process is well-established and understood. Systematic modeling as a basis for feed rate estimation can better indicate to an operator how to control an FfFBR culture, especially in the critical initial growth stages and for new cell lines. Several other cultures were performed with operator control (similar to the first culture), but were not included. The variation in the glucose and lactate concentrations were statistically similar (95% confidence). The second culture exhibited a significant (99% confidence) reduction in the variability of the glucose and lactate concentrations compared to the first culture (Table 1). The higher frequency of sampling in the second culture (1.6 day"1 versus 1.3 day'1) and the initial feed rate algorithm appeared to improve the estimation of feed rates and maintained more constant concentrations. 150 Despite no instructions to operators to take fewer samples, the average sampling rate was approximately 2-fold reduced for the last two computer estimated cultures versus the first two operator controlled cultures (Table 1). The information displayed via the graphical user interface increased the operator confidence that the culture was being well controlled, and thereby reduce the amount of sampling and labour performed. With reduced sampling, there was a reduction in both the labour and analytical expense. The variances of the glucose concentration of the second and third culture were not significantly different (99% confidence), while the sampling rate for the second culture was 2.8 times greater than the third culture. With a large reduction in sampling frequency and several medium changing challenges in the third culture, the predictive control routines were able to generate similar control performance in the second and third cultures. When comparing the second and fourth cultures (Table 1), there was a significant reduction (99% confidence) in the variance of the glucose concentration measurements, even with 1.6 times fewer samples. For the third culture, the choice of prediction horizon was limited to one modeling option. In the third culture, there was a trend (p<0.025) of increasing offset with longer periods between sampling. The fourth culture showed no trend of increasing offset with longer sampling intervals. This indicates that the choice of different models for control purposes has advantages in that a longer prediction period may be adequately described without increasing offset. As a result of modeling choices, there was a significant reduction (99% confidence) in the glucose concentration variability between the third (s.d. 2.08 mM) and fourth (s.d. 0.66 mM) cultures. Subsequent cultures using computer estimation of the feed rates had statistically similar (95% confidence) concentration variances. 151 The first and third cultures (producing DX1) shared similar glucose set points/ranges (13.5 mM to 16.5 mM). The first culture produced 3.2 g, while the third produced 7.9 g. The yield of antibody from the total ICS volume fed was 0.030 g/L for the first culture. The ECS fed medium was neglected as this represents <1% of the total ICS fed medium. The third culture with improved control resulted in a yield of 0.043 g/L. The second and fourth cultures (producing P9) shared similar glucose set points/ranges of 11.5 mM to 14.5 mM. The second and fourth cultures produced 5.7 g and 16.5 g, respectively. The yield in the second culture was 0.029 g/L, while the fourth culture yielded of 0.032 g/L (Table 1). CONCLUSIONS A robust predictive controller appeared to improve feed rate estimation compared to operator control. The controller response to concentration deviations from the set point was designed to be independent of the model, state of the culture, process flows or sampling interval. A graphical user interface of the up-to-date and future glucose uptake and lactate production rates was correlated with an increased operator confidence that the process was being well-controlled. As a result, fewer samples were taken, with a concomitant reduction in the labour and analytical expense. The operator has computer protocols to learn in order to use the presented control routines, however, the data was presented in either a tabular or graphical form that could be printed at any time and was useful for computer record-keeping purposes. Up to 4- and 7-fold smaller variances of the glucose and lactate concentrations, respectively, were obtained using a multiple-model adaptive predictive control protocol. Lactate production rate for glucose uptake rate gave virtually identical predictors of feed rate for the control of these cultures. The cultures 152 with predictive control routines generated 10% to 43% higher yields of antibody from medium. We are currently applying the predictive control protocols to suspension CHO bioprocesses. ACKNOWLEDGEMENTS This work was sponsored by the Natural Sciences and Engineering Research Council of Canada. The authors thank StemCell Technologies for generous gifts of medium and serum. J.E. Dowd holds a Natural Sciences and Engineering Research Council of Canada Postgraduate Fellowship. 153 REFERENCES Banik, G.G. and Heath, CA. 1995. "Hybridoma Growth and Antibody Production as a Function of Cell Density and Specific Growth Rate in Perfusion Culture." Biotechnol. Bioeng. 48: 289-300. Bodeker, B.G.D., Newcomb, R., Yuan, P., Braufman, A. and Kelsey, W. 1994. Production of Recombinant Factor VIII From Perfusion Cultures: 1. Large-Scale Fermentation, pp. 580-583. In: R.E. Spier, J.B. Griffiths, W. Berthold (eds.), ESACT - The 12th Meeting, Butterworth Heinemann, Oxford. Brotherton, J.D. and Chau, P.C. 1995. "Protein-free human-human hybridoma cultures in an intercalated-spiral alternate-dead-ended hollow fiber bioreactor." Biotechnol. Bioeng. 47: 384-400. Brotherton, J.D. and Chau, P.C. 1996. "Modeling of axial-flow hollow fiber cell culture bioreactors." Biotechnol. Prog. 12(5): 575-590. Ehrlich, K.C., Stewart, E. and Klein, E. 1978. "Artificial capillary perfusion cell culture: metabolic studies." In Vitro 14: 443. Evans, T.L. and Miller, R.A. 1990. "Evaluation of hollow-fiber bioreactor systems for large-scale production of murine monoclonal antibodies." Targeted Diagnosis and Therapy 3: 25-43. Glacken, M.W. 1995. "Instrumentation and Control Methods for Mammalian Cell Bioreactors." Gen. Eng. News August: 10-11. Handa, C.A., Nikolay, S., Jeffery, D., Heffernan, B. and Young, A. 1992. "Controlling and predicting monoclonal antibody production in hollow fiber bioreactors." Enzyme Microb. Technol. 14(1): 58-63. 154 He, W.G., Kaufman, H. and Roy, R. 1986. "Multiple Model Adaptive Control Procedure for Blood Pressure Control." IEEE Trans. Biomed. Eng. BME-33(n: 10-19. Heifetz, A.H., Braatz, J.A., Wolfe, R.A., Barry, R.M., Miller, DA. and Solomon, B.A. 1989. "Monoclonal Antibody Production in Hollow-Fiber Bioreactors Using Serum-Free Medium." BioTechniq. 7(2): 192-199. Himmelblau, DM. 1990. Process Analysis by Statistical Methods. Austin, TX, University of Texas. Jackson, L.R., Trudel, L.J., Fox, J.G. and Lipman, N.S. 1996. "Evaluation of Hollow Fiber Bioreactors as an Alternative to Murine Ascites Production for Small Scale Monoclonal Antibody Production." J. Immunol. Meth. 189: 217-231. Konstantinov, K.B. 1996. "Monitoring and control of the physiological state of cell cultures." Biotechnol. Bioeng. 52: 271-289. Kurkela, R., Fraune, E. and Vihko, P. 1993. "Pilot-Scale Production of Murine Monoclonal Antibodies in Agitated, Ceramic-Matrix or Hollow-Fiber Cell Culture Systems." BioTechniq. 15(4): 674-683. Kurokawa, H., Park, Y.S., Iijima, S. and Kobayashi, T. 1994. "Growth characteristics in fed batch culture of hybridoma cells with control of glucose and glutamine concentrations." Biotechnol. Bioeng. 44(1): 95-103. Kwok, K.E., Shah, S.L., Clanachan, AS. and Finegan, B.A. 1995. "Evaluation of a Long-Range Adaptive Predictive Controller from Computerized Drug Delivery Systems." IEEE Trans. Biomed. Eng. 42(1): 79-86. Labecki, M., Weber, I., Dudal, Y., Koska, J., Piret, J.M. and Bowen, BD. 1998. "Hindered Transmembrane Protein Transport in Hollow Fibre Devices." J. Memb. Sci. 146: 197-216 155 Liu, J.J., Chen, B.-S., Tsa, T.F., Wu, Y.-J., Pang, V.F., Hsieh, A., Hsieh, J.-H. and Chang, TH. 1991. "Long term and large-scale cultivation of human hepatoma Hep G2 cells in hollow fiber bioreactor." Cytotechnol. 5: 129-139. Lowrey, D., Murphy, S. and Goffe, R.A. 1994. "A Comparison of Monoclonal Antibody Productivity in Different Hollow Fiber bioreactors." J. Biotechnol. 36: 35-38. 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Process Dynamics and Control. New York, John Wiley & Sons. Shimizu, K., Morikawa, M., Mizutani, S., Iijima, S., Matsubar, M. and Kobayashi, T. 1988. "Comparison of Control Techniques for Baker's Yeast Culture Using an Automatic Glucose Analyzer." Journal of Chemical Engineering in Japan 21: 113. Soderstrom, T. and Stoica, P. 1989. System Identification. Toronto, Prentice Hall. Soeterboek, R. 1992. Predictive Control - A Unified Approach. Toronto, Prentice Hall. Stoll, T.S., Ruffieux, P.A., von Stockar, U. and Marison, I.W. 1996. "Development of an On-Line Control System for the Cultivation of Animal Cells in a Hollow-Fiber Reactor Using Flow Injection Analysis and a Visual Programming Language." J. Biotechnol. 51: 37-48. Tzaimpazis, E. and Sambanis, A. 1994. "Modeling of Cell Culture Processes." Cytotechnol. 14: 191-204. Wang, J., Honda, H., Lenas, P., Watanabe, H. and Kobayashi, T. 1995. "Effective t-PA Production by BHK Cells in Nutrients-Controlled Culture Using an On-line HPLC Measuring System." J. Ferm. Bioeng. 80(1): 107-110. Williams, D., Yousefpour, P. and Wellington, E.M.F. 1986. "On-line Adaptive Control of a Fed-Batch Fermentation of Saccharomyces cerevisiae." Biotechnol. Bioeng. 28: 631-645. Yu, C, Roy, R.J., Kaufman, H. and Bequette, B.W. 1992. "Multiple-Model Adaptive Predictive Control of Mean Arterial Pressure and Cardiac Output." IEEE Trans. Biomed. Eng. 39(8): 765-777. 157 Table I. Summary of Culture Performance Number of Culture and Culture Feed Rate Estimation Method Average Glucose Concentration (mM) Average Lactate Concentration (mM) Average Sampling Rate (#/day) Antibody Produced Yield (g/L ICS medium) 1) Operator 14.2 (s.d. 2.7) 22.4 (s.d. 7.4) 1.3 3.2gDXl 0.030 2) Initial Feed Rate Algorithm 12.6 (s.d. 1.6) 18.8 (s.d. 2.4) 1.6 5.7 gP9 0.029 3) One-Model GUR 14.5 (s.d. 2.1) N/A 0.57 7.9gDXl 0.043 4) Multiple Model GUR and LPR 13.1 (s.d. 0.66) 18.4 (s.d. 1.0) 1.0 16.5 gP9 0.032 158 Figure 1. Cell Pharm Reactor System. The medium was recirculated between a reservoir and the intra capillary spaces (ICS) of the hollow fiber bioreactor and oxygenator at 300-600 mL/min flow rates. Equivalent fresh medium addition and spent medium removal were controlled by the feed pump (from 0.0 to 9.9 L/day) and a solenoid valve, respectively. The ICS was sampled via a syringe and the 97.4 mL extracapillary space (ECS) was periodically harvested using a pump. Cultures #1 and #2 were performed with 1 HFBR, while cultures #3 and #4 were performed with 2 HFBRs. Figure 2. Effect of Filtering on the Estimation of Glucose Uptake Rate. The glucose uptake rate (GUR) data was filtered by: (1) an arithmetic moving average (A MA) filter, (2) a least squares (LS) filter with a linear growth model, (3) a linearized least squares (LLS) filter with an assumed exponential growth model. The A M A filter had a period of three, while both the LS and the LLS filters had a fixed data window of the last six GUR estimates (after day 5). Figure 3. Examples of the Estimation of Prediction Horizon. In the arithmetic moving average plus linearized least squares ( A M A & LLS) estimation of the prediction horizon, an A M A was used to obtain the initial estimate and a window of past data was used to estimate the future exponential growth profile. The least squares (LS) estimation of the prediction horizon used the linear model to estimate both the initial estimate and future profiles. Similarly, the L L S estimation used the exponential growth model to generate both the initial estimate and the future profiles. Al l the protocols used the same arbitrary data window of six glucose uptake rate estimates after day 5. The example predictions illustrated began on days 2, 7 and 15, but were representative of the modeling that was occurring at every sampling interval. Figure 4. Operator Estimation of Feed Rates. The ICS glucose concentrations, ICS lactate concentrations and the HFBR perfusion feed rate for the first (operator-controlled) culture are presented above. From day 2 when the perfusion was initiated, the feed rate was adjusted by the operator attempting to maintain the glucose concentration range of 13.5 and 16.5 mM. 159 Figure 5. Algorithm Estimation of Feed Rates. The ICS glucose concentrations, ICS lactate concentrations and the HFBR perfusion feed rate for the second (operator-controlled) culture are presented above. An exponential feeding profile was used from day 4 to 13, followed by constant feed rates until day 50, at which point the feed rates were reduced by the operator attempting to maintain the glucose concentration in the range of 11.5 and 14.5 mM. Figure 6. Single-Model Glucose-Based Computer Estimation of Feed Rates. The HFBR ICS glucose concentrations, calculated glucose uptake rates (GUR) via Eqn. 1 and the HFBR perfusion feed rate for the third (computer-estimated) culture are presented above. Feeding was initiated at day 2 to maintain the glucose concentration at the set point of 15 mM. The GUR (middle panel) was presented to the operator via the graphical user interface with a single AMA & LLS estimate of the prediction horizon. Different regimes for the ICS serum content are illustrated on the feed rate profile (bottom panel). Figure 7. Multiple-Model Glucose Based Computer Estimation of Feed Rates. The HFBR ICS glucose concentrations, calculated glucose uptake rates (GUR) via Eqn. 1 and the HFBR perfusion feed rate for the fourth (computer-estimated) culture are presented above. The GUR (middle panel) was presented to the operator via the graphical user interface with either LLS, AMA & LLS or a flat estimate of the prediction horizon. Both the glucose uptake rates (middle panel) and the lactate production rates (data not shown) were presented to the operator via the graphical user interface. The feed rate profile (bottom panel) was generated using the glucose uptake rate as the indicator of the state of the culture. Figure 8. Average Lactate Production Versus Average Glucose Uptake Rates. The average lactate production exhibited a linear trend with the average glucose uptake rate over the entire range of the fourth culture. The linearly regressed (solid) line, along with the 95% confidence intervals for the correlation (dashed lines) and prediction limits (dotted lines) are illustrated. 160 Medium Reservoir Oxygenator Recirculation Pump 95% Air 5% C 0 2 IHFBRI IHFBRi Solenoid ECS Harvest • Feed Pump (^^) Spent Medium Fresh Medium 161 Time (days) 162 163 164 165 166 40 60 Time (days) 167 1 1 1 1 1 1 0 20 40 60 80 100 Average Glucose Uptake Rate (mmol/day) 168 APPENDIX 2 COMPUTER CODE A.2.1 ANGLICON DATALOG PROGRAM (QUICKBASIC) CLS LINE INPUT "Enter f i l e name t o s t o r e d a t a : "; filenames OPEN filenames FOR OUTPUT AS #2 TIMER ON INPUT "Time sample i n t e r v a l (sec) ", t i n i e i n t PRINT —' PRINT "press any key t o begin , press s t o end" begins = INPUTS(1) t i m e i n i = TIMER j = 0 tcum = 0 z = 2 CLS PRINT " TIME TEMP pH D.O." PRINT " VIEW PRINT 23 TO 24 PRINT " 99 j - 0 DO OPEN ucoml:1200,n,8,2,rs,asc,ds0" FOR RANDOM AS #1 LEN -256 sendS - "101R1;" PRINT #1, sendS FOR x = 1 TO 1500 NEXT x r e t l S = INPUTS(LOC(l), #1) a l = ABS(LEN(retlS) - 4) FOR X = 1 TO 500 NEXT X sendS = "101RX23;" PRINT #1, sendS FOR x = 1 TO 1500 NEXT x r e t l c S = INPUTS(LOC(1), #1) a l e = ABS (LE N ( r e t l c S ) - 4) FOR x - 1 TO 500 NEXT x sendS = "!02R1;" PRINT Ml, sendS FOR x = 1 TO 1500 NEXT x ret2S = INPUTS(LOC(l), #1) a2 = ABS(LEN(ret2S) - 4) FOR x • 1 TO 500 NEXT x sendS = "102RX22;" PRINT #1, sendS FOR x = 1 TO 1500 NEXT x ret2cS = INPUTS(LOC(l), #1) a2c = ABS(LEN(ret2c$) - 4) FOR x = 1 TO 500 NEXT x sendS - "102R23;" PRINT #1, sendS FOR x = 1 TO 1500 NEXT x ret2aS - INPUTS(LOC(l) , #1) a2a = ABS(LEN(ret2aS) - 4) FOR x - 1 TO 500 NEXT x sendS - "I02R25;" PRINT #1, sendS FOR x = 1 TO 1500 NEXT X ret2bS = INPUTS(LOC(1), #1) a2b •= ABS (LEN (ret2bS) - 4) FOR x = 1 TO 500 NEXT x sendS = "!03R1;" PRINT #1, sendS FOR x - 1 TO 1500 NEXT x ret3S - INPUTS(LOC(l), #1) a3 - ABS(LEN(ret3S) - 4) FOR x •= 1 TO 500 NEXT x sendS - "103R25;" PRINT #1, sendS FOR x - 1 TO 1500 NEXT x ret3cS = INPUTS(LOC(l), #1) a3c - ABS(LEN(ret3cS) - 4) FOR x - 1 TO 500 NEXT X sendS = "I03R26;" PRINT #1, sendS FOR x = 1 TO 1500 NEXT x ret3aS - INPUTS(LOC(1), #1) a3a = ABS (LEN (ret3a$) - 4) FOR x = 1 TO 500 NEXT X CLOSE #1 Z = Z + 1 IF z > 22 THEN z = 3 VIEW PRINT 23 TO 24 PRINT " END IF VIEW PRINT z TO z + 2 PRINT USING " ###.###* "; tcum + (TIMER - t i m e i n i ) / 3600; PRINT TAB(17); L E F T S ( r e t I S , a l ) ; TAB(25); L E F T S ( r e t l c S , a l e ) ; TABI36); LEFTS(ret2S, a2); TAB(44); LEFTS(ret2c$, a2c); TAB(55); LEFTS(ret3S, a 3 ) ; TAB(63); LEFTS(ret3cS, a3c) PRINT " PRINT #2, DATES, TIMES, tcum + (TIMER - t i m e i n i ) / 3600, L E F T S ( r e t l S , a l ) , L E F T S ( r e t l c S , a l e ) , LEFTS(ret2S, a2), LEFTS(ret2cS, a2c), LEFTS(ret2aS, a2a), LEFTS(ret2bS, a2b), LEFTS(ret3S, a3), LEFTS(ret3cS, a3c), LEFTS(ret3aS, a3a) 3 = 3 + 1 DO IF (TIMER - t l a s t ) < 0 THEN j - o tcum = (86400 - t i m e i n i ) / 3600 + tcum t i m e i n i = 0 END IF IF INKEYS - " j " GOTO 99 VIEW PRINT 24 TO 25 PRINT " DATA FILE "; filenames." TAB(44); PRINT USING "RUN TIME ####.#### h r s " ; tcum + (TIMER -t i m e i n i ) / 3600 t l a s t - TIMER FOR b - 1 TO 5000 NEXT b IF INKEYS = " s " GOTO 999 LOOP UNTIL ((TIMER - t i m e i n i ) > j 4 t i m e i n t ) LOOP UNTIL INKEYS « " s " PRINT "stop" 999 CLOSE #2 END 169 A.2.2 GENERIC PUMP CONTROL PROGRAM (QUICK BASIC) DIM C V o l d TO 8, 1 TO 72), C o n l l TO 8, 1 TO 72) AS SINGLE DIM MFLOWfl TO 8), StartTime, S t o p T i m e d TO 8) AS SINGLE DIM flag<0 TO 8) AS INTEGER DECLARE SUB F i l t e r ( i n s t r i n g S ) DECLARE SUB S p e c i f i c ( f s t r i n g S , srch$, r e s u l t AS SINGLE) VIEW PRINT CLS : COLOR 0, 7: PRINT SPACES(80); ' re v e r s e v i d e o LOCATE 1, 20: PRINT " M u l t i p l e Pump C o n t r o l Program"; COLOR 7, 0: LOCATE 3, 1 PRINT " 1. C a l i b r a t e pump(s) " PRINT " 2. C o n t r o l pump(s) on a sequence " PRINT " 3. S t a r t / S t o p pump(s) " PRINT " 4. End." 10180 VIEW PRINT 7 TO 23 ' s e t p r i n t window LOCATE 8, 1: PRINT "Enter s e l e c t i o n (1-4) LOCATE 8, 24: INPUT iS VIEW PRINT 9 TO 23 1 save menu s e l e c t i o n on screen CLS IF ( i * < 1) OR (iS > 4) THEN SOUND 100, .5: GOTO 10180 10240 ON i S GOSUB 11275, 11370, 11620, 14000 10245 GOTO 10180 11275 C a l i b r a t i o n o f aux out pump 11280 LOCATE 10, 5: INPUT "How many pumps t o c a l i b r a t e (1-8) ?"; iS IF (iS < 1) OR (iS > 8) THEN SOUND 100, .5: GOTO 11280 FOR jS = 1 TO iS PRINT "Press any key t o s t a r t c a l i b r a t i o n pump # "; j S 11300 IF INKEY$ = "" THEN GOTO 11300 OUT SH378, 2 " (jS - 1) gtime = TIMER PRINT "Press any key t o stop pump # "; jS 11310 IF INKEY$ - "" THEN GOTO 11310 OUT SH378, 0 stime = TIMER INPUT "Enter measured volume [mL] "; MVOL(j S) MFLOW(jS) - MVOL(jS) / (stime - gtime): PRINT MFLOW(jS) NEXT jS RETURN 11370 * ** C o n t r o l pump on a sequence 11380 LOCATE 10, 5: INPUT "How many pumps t o c o n t r o l on sequence (1-8) "; iS IF (iS < 1) OR (iS > 8) THEN SOUND 100, .5: GOTO 11380 intnS = 0 INPUT "What i s the i n t e r v a l f o r r e g u l a r feeding? [sj "; C o n t l n t s FOR kS - 1 TO iS jS = 1 11400 PRINT "Input volume fed at i n t e r v a l "; j S ; " for pump "; kS; INPUT " [mL] [<0 t o end] ",- CVoKkS, jS) IF CVoKkS, jS) >= 0 THEN IF MFLOW(kS) = 0 THEN PRINT "ERROR - NO CALIBRATION FOR PUMP # "; kS RETURN END IF ConlkS, jS) = CVoKkS, jS) / MFLOW(kS) IF ConlkS, jS) > C o n t l n t s THEN PRINT "ERROR - PUMP FLOWRATE NOT SUFFICIENT ".- kS RETURN END IF jS - jS • 1 GOTO 11400 END IF IF jS > intnS THEN intnS - jS ' j8 i s the number o f i n t e r v a l s NEXT kS INPUT "Press e n t e r t o s t a r t at i n t e r v a l 1", inS StartTime = TIMER OUT SH378, (2 - iS) - 1: PRINT TIME$; "ON" CS = (2 - iS) - 1 FOR IS = 1 TO iS StopTime(lS) = StartTime + CondS, 1) GOSUB 12650 * check f o r past midnight f l a g ( l S ) = 0 NEXT IS kS - 2 fla g ( 0 ) = 0 numf = 0 DO IF numf = iS AND flag(O) « 0 THEN StartTime = StartTime + C o n t l n t s GOSUB 12710 * check f o r s t a r t past midnight f l a g ( 0 ) = 1 END IF IF TIMER > StartTime AND f l a g ( 0 ) = 1 THEN OUT SH378, (2 " iS) - 1: PRINT TIMES; k&; "ON" CS = (2 - iS ) - 1 kS = kS + 1 FOR nS = 0 TO iS flag(nS) = 0 NEXT nS numf = 0 END IF DO numf = 0 FOR IS = 1 TO iS StopTime(lS) =* StartTime + C o n d S , kS) GOSUB 12650 IF TIMER > StopTimedS) AND f l a g ( l S ) = 0 THEN OUT 5H378, CS - 2 - (IS - 1) PRINT TIMES; IS; "OFF"; StopTime(lS) - StartTime CS = CS - 2 " (IS - 1) f l a g ( I S ) = 1 END IF numf - numf + f l a g ( I S ) NEXT 18 LOOP WHILE numf < i8 LOOP WHILE k8 < intnS GOTO 10180 ' a f t e r i t ' s a l l over, go back t o menu 11620 '** Set aux out f o r pump u n i t s or '** alarm f o r mixer u n i t s . 11640 INPUT "Which pump do you want t o c o n t r o l ? "; nS IF (i8 < 1) OR (i8 > 8) THEN SOUND 100, .5: GOTO 11640 11680 INPUT "Enter pump s t a t u s ( 0 - o f f , l=on) "; OS8 IF OSS O 0 AND OSS <> 1 THEN GOTO 11680 IF OSS = 1 THEN OUT SH378, 2 " (nS - 1): PRINT TIMES; nS; "ON", IF OSS - 0 THEN OUT SH378, 0: PRINT TIMES; nS; "OFF" INPUT " C o n t r o l another pump ? [y / n ] " ; inS IF inS = "y" OR inS - "V" THEN GOTO 11640 GOTO 10180 ' r e t u r n t o menu *** Check f o r past midnight on stop time 12650 IF StopTimedS) > 86400 THEN StopTimedS) = StopTimedS) - 86400 'check f o r past midnight WHILE TIMER > 10 'keep pump on u n t i l past midnight WEND END IF RETURN '** Check f o r past midnight on s t a r t time ****** **************** ********* * * * * ******* 12710 IF StartTime > 86400 THEN StartTime = StartTime - 86400 ' che f o r past midnight WHILE TIMER > 10 'wait u n t i l t i m e r passes midnight WEND END IF RETURN 14000 END SUB F i l t e r ( i n s t r i n g S ) STATIC DO Backspace - INSTR(instringS, CHRS(8)) IF Backspace THEN MI D S ( i n s t r i n g S , Backspace) = CHRS(29) 170 LOOP WHILE Backspace DO Lnfd = INS T R ( i n s t r i n g S , CHRS(IO)) IF Lnfd THEN i n s t r i n g S - L E F T S ( i n s t r i n g $ , Lnfd - 1) MI D S ( i n s t r i n g S , L n f d + 1) LOOP WHILE L n f d ' going t o use l t r i r a and r t r i m t o get r i d of zeros •DO • Space - INS T R ( i n s t r i n g S , CHRS(32)) * IF Space THEN i n s t r i n g S = L E F T S ( i n s t r i n g S , Space -+ M I D S ( i n s t r i n g S , Space + 1) •LOOP WHILE Space 'DO • Pound - INS T R ( i n s t r i n g S , CHRS(35)) * IF Pound THEN i n s t r i n g S = L E F T S ( i n s t r i n g S , Pound -+ M I D S ( i n s t r i n g S , Pound + 3, L E N ( i n s t r i n g S ) - Pound + 3) •LOOP WHILE Pound vluS = vluS + •PRINT vluS END IF NEXT i r e s u l t = VAL(vluS) END SUB SUB GetNOVAdata ( g l u , l a c , bun, ph, po2, pco2, status) OPEN "com2:9600,n,7,2" FOR RANDOM AS #1 LEN - 16396 to t S - "" n - l DO IF NOT EOF(l) THEN retS - INPUTS(LOC(l) , 1) F i l t e r r e t S PRINT r e t S ; t o t S - t o t S + retS ELSEIF EOF(l) AND LEN(totS) > 1350 THEN n = n + 1 END IF LOOP WHILE n < 20 10 'PRINT " l e n g t h of t o t S "; LEN(totS} S p e c i f i c t o t S , "GL=", g l c PRINT "Glucose ", g l c S p e c i f i c t o t S , "LA=", l a c PRINT " L a c t a t e ", l a c S p e c i f i c t o t S , "UR=", bun PRINT "BUN ", bun S p e c i f i c t o t S , "YY=", year S p e c i f i c t o t S , "MM=", month S p e c i f i c t o t S , "DD=", day S p e c i f i c t o t S , "HH-", hour S p e c i f i c t o t S , "MI=", minute •minute = INT(minute / 10) PRINT "The time of sample i s "; month; "/"; day; "/"; year; " F r a c t i o n a l day "; (hour + minute / 60) / 24 ' A l t e r n a t e t h i n g s t o l o g S p e c i f i c t o t S , "PH=", ph: PRINT "pH ", ph S p e c i f i c t o t S , "PO=", po2: PRINT " P a r t i a l 02 ", po2 S p e c i f i c t o t S , "PO", pco2: PRINT " P a r t i a l C02 ", S p e c i f i c t o t S , "0M=", osmo: PRINT "Osmolarity ", S p e c i f i c t o t S , "BO", b i c a r b : PRINT "Bicarbonate ", pco2 osmo b i c a r b S p e c i f i c t o t S , "CC**", corpco2: PRINT "Corrected P a r t i a l C02 ", corpco2 S p e c i f i c t o t S , "CP-", corp02: PRINT "Corrected P a r t i a l 02 ", corpo2 S p e c i f i c t o t S , "TO", t o t c o 2 : PRINT " T o t a l Carbonate ", t o t c o 2 S p e c i f i c t o t S , "NA=", sodium: PRINT "Sodium ", sodium S p e c i f i c t o t S , "KK=", potas: PRINT "Potasium ", potas S p e c i f i c t o t $ , "CA=", calcium: PRINT "Calcium ", c a l c i u m S p e c i f i c t o t S , "CL=", c h l o r i n e : PRINT " C h l o r i n e ", c h l o r i n e END SUB SUB S p e c i f i c ( f s t r i n g S , srchS, r e s u l t AS SINGLE) STATIC p - I N S T R ( f s t r i n g S , srchS) ansS - M I D S ( f s t r i n g S , p + 3, 5) •PRINT ansS vluS - "" FOR i = 1 TO LEN(ansS) cS = MIDSIansS, i , 1) IF INSTR("0123456.789.-", cS) <> 0 THEN 171 A.2.3 PREDICTIVE MODELING AND CONTROL PROGRAM (MATLAB) I function[RqdFlows] = perfsn26(Inoc} % This f u n c t i o n takes care o f the input of the system f o r % Jason's S u p e r - I n c r e d i b l e P e r f u s i o n System % 1 runhl = [Time,Reactor_Volume,Flowrate,Glc,Lac,Vcsg] % % Inoc i s innoculum c o n c e n t r a t i o n , I Vcsg i s the Estimated s p e c i f i c growth r a t e I % Programmed by Jason Dowd, UBC Biotechnology I jdowd@chml.ubc.ca % 822-6986 % SAME as perfsn25 except d i f f e r e n t f i l e name function[RqdFlows] = perfsn25(Inoc) cd d:\ cd astudent cd jason cd psmtlb l o a d runp22.txt cd c:\ cd matlab Inoc = 4e5; runplO = runp22; for i = 2 : s i z e ( r u n p l O , 1 ) i f r u n p l 0 ( i , 4 ) = = r u n p l 0 ( i , 5 ) & r u n p l 0 ( i , 4 ) ==0 runplO = ru n p l O ( 1 : i - 1 , : ) ; b r e a k ; end end Time = r u n p l O ( : , 1 ) ; % days Vo l = runplO(:,2) ; % L Flow = runplO<:,3); % L/d Glc = r u n p l O ( : , 4 ) ; I mM Lac = r u n p l O ( : , 5 ) ; % mM Bun = r u n p l O ( : , 6 ) ; % mM Vcsg = l o g { 1 . 8 ) * o n e s ( s i z e ( T i m e , 1 ) ) ; % upper l i m i t on growth r a t e s n=length(Time) ; % number of data p o i n t s gu = 3e-9 ; % glucose uptake mmol/cell/d l p = 1.4* gu; % 18.3e-9 ; * l a c t a t e p r o d u c t i o n mmol/cell/d bp = 8e-10 ; % Bun p r o d u c t i o n mmol/cell/d G l c i n = 3 0 * o n e s ( s i z e ( T i m e ) ) ; % I n l e t g l u c o s e , l a c t a t e c o n c e n t r a t i o n s I at n= 5 G l c i n w i l l be 30 % G l c i n ( 5 : s i z e ( T i m e ) ) = 3 0 + o n e s ( s i z e ( 5 : s i z e ( T i m e ) ) ) ; L a c i n = 0 .* o n e s ( s i z e ( T i m e ) ) ; Bunin = 1.5 .* o n e s ( s i z e ( T i m e ) ) ; Eflow = Flow; * Eflow i s Out flow from r e a c t o r View = 3 ; % Aspect R a t i o f o r Output Graphs rgn = 1 9 ; % r e g r e s s i o n window s t a r t i n g n modln = 1 9 ; % model s t a r t i n g n (probably won't need) T = 3/24 ; % p r e d i c t i o n i n t e r v a l a v f l a g = 2; * moving average f l a g 2 p o i n t s , 4 p o i n t s , 8 p o i n t s mulim = log(2) / V c s g ( l ) ; I l i m i t on s p e c i f i c growth r a t e KupGlc - 10e6 * 1000 * Vol(1) * gu; KupLac - 10e6 * 1000 * V o l ( l ) * l p ; KupBun = 10e6 * 1000 * Vol(1) * bp; * SET POINTS G l c s p t = 1 0 * o n e s ( s i z e ( T i m e ) ) ; % mM Lacspt = 2 0 * o n e s ( s i z e ( T i m e ) ) ; % mM Bunspt = 4 * o n e s ( s i z e ( T i m e ) ) ; XmM Data = 'Glucose s e t p o i n t i s 10 mM* Data = 'Lactate s e t p o i n t i s 10 mM' Data = 'BUN s e t p o i n t i s 3.5 mM' Data=*The c e l l s p e c i f i c GURs are (mmol/cell/d)' gu Data='The c e l l s p e c i f i c LPRs are (mmol/cell/d)' l p Data='The c e l l s p e c i f i c BPRs are (mmol/cell/d)' bp * I n i t i a l i z i n g S e c t i o n GUR(l) =- V o l ( l ) "1000 *gu * Inoc ; 8 mmols/day A P r i o r i Modeling LPR(l) = V o l ( l ) *1000 * l p * Inoc ; 8 mmols/day BPR(l) = V o l ( l ) *1000 *bp * Inoc ; * mmols/day 8 V a r i a b l e s with 'Q' are based on Mass Balance t V a r i a b l e s with 'e' are moving averaged v a r i a b l e s Q G l c ( l ) =GUR(1); eGUR(l) - GURU); e Q G l c ( l ) = GUR(l); QLac(l) = L P R ( l ) ; eLPR(l) = L P R ( l ) ; eQLac(l) = L P R ( l ) ; QBun(l) =BPR(1); eBPR(l) - B P R ( l ) ; eQBun(l) =BPR(1); t V a r i a b l e s with ' f i t * are Non-Linear Regression V a r i a b l e s Q G f i t ( l ) - GUR(l); Q L f i t ( l ) - L P R ( l ) ; Q B f i t ( l ) - BPR(l) ; \ V a r i a b l e s of the form p_ pGUR(l) = (1 + 3/24) GUR(l) pLPR(l) = (1 + 3/24) .* LPR(l) pBPR(l) - (1 + 3/24) .* BPRfl pQGlc(l) - p G U R ( l ) ; peGUR(l) pGUR(l); pQLac(1) = pLPR(1) ; pLP R ( l ) ; pQBun(l) = pBPR(l); = pBPR(l); p Q G f i t ( I ) - pGUR(l); p Q L f i t ( l ) = p L P R ( l ) ; p Q B f i t ( l ) = pBPR(l); are p r e d i c t i o n v a r i a b l e s p eQGlc(l) -pGUR(1) ; peLPR(l) = p L P R ( l ) ; peBPR(l) = pBPR ( l ) ; peQBun(l) peQLac{1) = % 0 i s the order h o l d and 2 stn=2 ; oh=0; T G l c ( l ) = 0 ; TLac(l)=0; i s the s t a r t i n g n TBun(l)=0; f o r i = stn:n i f oh==0 QG l c ( i ) = (- ( G l c ( i ) - G l c ( i - l ) ) / ( T i m e d ) -Time(i-1)) + F l o w ( i - l ) / V o l ( i ) * G l c i n ( i ) - E f l o w ( i - 1 ) / V o l ( i ) ( G l c ( i ) *• G l c ( i - l ) ) / 2 ) * V o l ( i ) ; QLac(i) = (• ( L a c ( i ) - L a c ( i - l ) ) / (Time(i) -T i m e ( i - l ) ) - F l o w ( i - l ) / V o l ( i ) * L a c i n ( i ) + E f l o w ( i - l ) / V o l ( i ) ( L a c ( i ) + L a c ( i - l ) ) / 2 ) * V o l ( i ) ; QBun(i) = (+ (Bund) - B u n ( i - l ) ) / ( T i m e d ) -T i m e ( i - l ) ) - F l o w ( i - l ) / V o l ( i ) * B u n i n ( i ) + E f l o w ( i - l ) / V o l ( i ) (Bund) + B u n d - l ) ) / 2 ) * V o l ( i ) ; e l s e % assumed f i r s t order h o l d - onl y i f ramping flow r a t e s Q G l c ( i ) = (- ( G l c ( i ) - G l c ( i - l ) ) / (Time(i) -Time ) + ( F l o w ( i - l ) + (Time ( i ) - T i m e ( i - 1 ) ) / 2' ( F l o w d -1) -Flow(i-2)) / ( T i m e ( i - l ) - T i m e ( i - 2 ) ) ) / V o l ( i ) * G l c i n d ) ( E f l o w ( i - l ) + ( T i m e ( i ) - T i m e ( i - l ) ) / 2* ( E f l o w ( i - l ) - E f l o w d -2) ) / ( T i m e ( i - l ) - T i m e ( i - 2 ) ) ) / V o l ( i ) * ( G l c ( i ) + G l c d -l ) ) / 2 ) * V o l ( i ) ; QLac(i) - (t ( L a c ( i ) - L a c ( i - l ) ) / (Time(i) -T i m e d - D ) - ( F l o w ( i - l ) t (Time d ) - T i m e ( i - 1 ) ) / 2 * ( F l o w ( i -1) - F l o w ( i - 2 ) ) / ( T i m e ( i - l ) - T i m e ( i - 2 ) ) ) / V o l ( i ) * L a c i n ( i ) + ( E f l o w ( i - l ) + ( T i m e ( i ) - T i m e ( i - l ) ) / 2 * ( E f l o w ( i - 1 ) - E f l o w ( i -2) ) / ( T i m e ( i - l ) - T i m e ( i - 2 ) ) ) / V o l ( i ) M L a c d ) + L a c ( i -l ) ) / 2 ) * V o l ( i ) ; QBund) = (t (Bund) - B u n ( i - l ) ) / (Time(i) -T i m e ( i - l ) ) - ( F l o w ( i - l ) + ( T i m e d ) - T i m e ( i - 1 ) ) / 2 * ( F l o w ( i -1) - F l o w ( i - 2 ) ) / ( T i m e ( i - 1 ) - T i m e ( i - 2 ) ) ) / V o l ( i ) * B u n i n ( i ) + ( E f l o w ( i - l ) + ( T i m e ( i ) - T i m e ( i - l ) ) / 2* ( E f l o w ( i - l ) - E f l o w d -2) ) / ( T i m e ( i - l ) - T i m e ( i - 2 ) ) ) / V o i d ) M B u n ( i ) + B u n ( i -l ) ) / 2 ) * V o l ( i ) ; end T G l c ( i ) - T G l c ( i - l ) + Q G l c d ) * (Timed) - T i m e ( i - D ) T L a c ( i ) - T L a c ( i - l ) + QLac ( i ) * (Time ( i ) - T i m e ( i - D ) TBund) = T B u n d - l ) + QBun d ) * (Time ( i ) - T i m e ( i - D ) i f i > modln GUR(i) - gu* 1000* Inoc * e x p ( V c s g d ) • ( T i m e ( i ) -Time(modln) ) ) * V o i d ) • (.99 +. 0055*Flow(i-l) -0.00142*Flow(i-1)*Flow(i-1)); LPR(i) = l p * 1000* Inoc * e x p ( V c s g d ) • ( T i m e d ) -Time(modln))) * V o l ( i ) * (.99 +.0055*Flow(i-l) -0.00142*Flow(i-1)*Flow(i-1)); BPRd) - bp* 1000* Inoc * e x p ( V c s g d ) * ( T i m e ( i ) -Time(modln) ) ) * V o i d ) * (.99 +. 0055*Flow(i-l) -0.00142*Flow(i-1)'Flow(i-1)); e l s e GUR(i) = gu* 1000* Inoc * V o l ( i ) ; LPR(i) - l p * 1000* Inoc * V o l ( i ) ; BPRd) - bp* 1000* Inoc * V o i d ) ; end end t .9 i s the f o r g e t t i n g f a c t o r , n i s number of p o i n t s , 1 i s s t a r t i n g n * 2 i s r e g r e s s i o n s t a r t i n g n ff=.9; s t n = l ; 172 f o r i = s t n :n i f 1<3 S p g r d , 1:6) - log(2) .* [1,1,1,1,1,1); Q G f i t ( i ) = Q G l c ( i ) ; Q L f i t ( i ) = QLac(i) ; Q B f i t d ) = QBun(i) ; e l s e S p g r l i , 1 ) = l o g ( T G l c ( i ) / T G l c ( i - l ) ) / (Timed) -T i m e ( i - l ) ) ; S p g r l i , 2 ) = l o g ( T L a c ( i ) / T L a c ( i - D ) / (Timed) -T i m e ( i - l ) ) ; S p g r ( i , 3 ) = l o g ( T B u n ( i ) / T B u n ( i - 1 ) ) / (Timed) -T i m e ( i - l ) ) ; i f i<3 S p g r d , 4:6) = Spgr ( i , 1:3); S no r e g r e s s i o n * S p g r d , 5:6) = Spgr ( i , 1:2),- % e l s e % Double E x p o n e n t i a l Weighted Moving Average IS p g r ( i , 3 : 4 ) = ( f f * f f ) . * S p g r d , 1 : 2 ) + (2 M1-f f ) ) . * S p g r ( i - l , 3 : 4 ) + ( (1-f f) * d - f f) ) . "Spgr (i-2,3:4 ) ; end end % now f o r n o n - l i n e a r r e g r e s s i o n part I going t o use p o l y f i t with degree one f o r the equation of the form % l n ( x 2 / x l ) = p i * t , where p i w i l l be equal t o the s p e c i f i c growth r a t e , i f i>2 f o r j = 2: i y ( j , l ) = l o g ( Q G l c l j ) ) ; y 2 ( j , l ) = log(KupGlc / Q G l c ( j ) - 1); y ( j , 2 ) - l o g ( Q L a c l j ) ) ; y2(j,2) -log(KupLac / QLac(j) - 1); y ( j , 3 ) » l o g ( Q B u n ( j ) ) ; y2(j,3) = log(KupBun / QBun(j) - 1); end p2 - p o l y f i t ( T i m e ( 2 : i , l ) , y ( 2 : i , l ) , 1); pl2 « p o l y f i t ( T i m e ( 2 : i , 1 ) , y 2 ( 2 : i , l ) , 1); p3 = p o l y f i t ( T i m e ( 2 : i , l ) , y ( 2 : i , 2 ) , 1); p l 3 - p o l y f i t ( T i m e ( 2 : i , 1 ) , y 2 ( 2 : i , 2 ) , 1); p4 = p o l y f i t ( T i m e ( 2 : i , l ) , y ( 2 : i , 3 ) , 1); pl4 = p o l y f i t ( T i m e ( 2 : i , 1 ) , y 2 ( 2 : i , 3 ) , 1); i f rgn ~= 2 & i > rgn i Regression on s m a l l e r 'window of data p2 = p o l y f i t ( T i m e ( r g n : i , 1 ) , y ( r g n : i , l ) , 1) ; p3 = p o l y f i t ( T i m e ( r g n : i , 1 ) , y ( r g n : i , 2 ) , 1) 1) end i f modln 2 & i > modln % Regression on s m a l l e r 'window of data pl2 = p o l y f i t ( T i m e ( r g n : i , 1 ) , y 2 ( r g n : i , l ) , 1); p l 3 = p o l y f i t ( T i m e ( r g n : i , 1), y 2 ( r g n : i , 2 ) , 1); pl4 = p o l y f i t ( T i m e ( r g n : i , 1 ) , y 2 ( r g n : i , 3 ) , 1); end S p g r d , 4 ) = p 2 ( l , l ) ; S p g r d , 5 ) - p 3 ( l , l ) ; S p g r d , 6 ) = p 4 d , l ) ; Q G f i t ( i ) = exp(p2(l,2) + p 2 ( 1 , 1 ) ' T i m e ( i ) ) ; Q L f i t d ) = exp(p3(l,2) + p 3 ( 1 , 1 ) ' T i m e ( i ) ) ; Q B f i t ( i ) - exp(p4(l,2) + p 4 ( 1 , 1 ) ' T i m e ( i ) ) ; Q G l f i t ( i ) - K u p G l c / d + e x p ( p l 2 ( l , 2 ) + p l 2 ( l , l ) ' T i m e ( i ) ) ) ; Q L l f i t d ) =- KupLac/(l + e x p ( p l 3 ( l , 2 ) + p l 3 ( l , l ) * T i m e ( i ) ) ) ; Q B l f i t d ) - KupBun/(l + e x p ( p l 4 ( l , 2 ) + pl4 (1,1) - T imed) ) ) ; G l p - p l 2 ; L i p = p l 3 ; B l p = p l 4 ; end end p4 = p o l y f i t ( T i m e ( r g n : i , 1 ) , y ( r g n : i , 3 ) , s L l = LPR(l) ; sL - Q L a c d ) ; s B l SB -s G l - GUR(1); BPRd) ; sG - Q G l c ( 1 ) ; QBun(1); wg = 1; wl = 1; wb = 1; f o r i=2 : n i Average uptake or p r o d u c t i o n r a t e s i f i > a v f l a g SeGUR(i)= eGUR(i-l) t 1 / a v f l a g • (GUR(i) - GURd-a v f l a g ) ) ; l e L P R ( i ) - e L P R ( i - l ) * 1 / a v f l a g * (LPRd) -L P R ( i - a v f l a g ) ) ; l e B P R d ) - eBPRd-1) + 1 / a v f l a g ' (BPRd) - B P R d - a v f l a g ) ) ; e Q G l c d ) = e Q G l c ( i - l ) + 1 / a v f l a g * (OGlc(i) - QGlc ( i -a v f l a g ) ) ; e Q L a c (i)= e Q L a c ( i - l ) + 1 / a v f l a g * (QLac(i) - Q L a c d -a v f l a g ) ) ; eQBund)= eQBund-l) + 1 / a v f l a g * (QBun(i) - QBun(i-a v f l a g ) ) ; e l s e tsGl=sGl + GUR(i); % s L l = s L l + LPRd) ; »sBl= s B l + B P R d ) ; SeGURd) - s G l / i ; J e L P R d ) = s L l / i ; SeBPR(i) = s B l / i ; sG - sG + Q G l c ( i ) ; sL - sL + Q L a c d ) ; sB = sB + QBun(i); e Q G l c ( i ) =sG/i; eQLac(i) "=sL/i; eQBun(i) = s B / i ; end % now f o r the p r e d i c t i o n check i n d i c e f o r Spgr for j = l :24 % f o r the next t h r e e days peGURIi, j) = GUR(i) * e x p ( V c s g d ) 1 (j-1) *T) -G U R ( i ) * ( l - (.99 +.0055*Flow(i-l) - 0 . 0 0 1 4 2 * F l o w ( i - l ) * F l o w ( i -1))) ; peLPRd, j) - LPR(i) * e x p ( V c s g d ) * (j-1) *T) -L P R ( i ) * ( l - (.99 +.0055*Flow(i-l) - 0.00142*Flow(i-1)*Flow(i-1))) ; peBPRd, j ) = BPRd) * e x p ( V c s g d ) * (j-1) *T) -B P R ( i ) * ( l - (.99 +.0055*Flow(i-l) - 0.00142*Flow(i-1)*Flow(i-1))) ; i f S p g r d , 4 ) > mulim * V c s g ( i ) WarnG(wg) = i ; % Warning v a r i a b l e p e Q G l c d , j) = e Q G l c ( i ) * exp(mulim * V c s g d ) * (j-1) *T) ; p Q G f i t d , j ) = O G f i t ( i ) * exp(mulim * V c s g d ) * ( j -1) * T ) ; e l s e p e Q G l c d , j) = e Q G l c ( i ) * exp (Spgr ( i , 4) * (j-1) *T) p Q G f i t d , j ) = Q G f i t ( i ) * exp(Spgr(i,4) * (j-1) T ) ; end i f S p g r d , 5 ) > mulim * V c s g ( i ) WarnL(wl) = i ; p e Q L a c d , j) = eQLac(i) * exp(mulim*Vcsg(i) * ( j -1) *T) ; p Q L f i t d , j ) = Q L f i t d ) * exp(mulim * V c s g ( i ) * ( j -1) * T ) ; e l s e p e Q L a c d , j) = e Q L a c ( i ) * exp (Spgr ( i , 5) * (j-1) *T) T ) ; p Q L f i t d , j ) - Q L f i t d ) * exp(Spgr(i,5) * (j-1) * end i f S p g r d , 6 ) > mulim*Vcsgd) WarnB(wb) = i ; peQBund, j) = eQBun(i) * exp(mulim*Vcsg(i) * ( j -1) *T) ; p Q B f i t l i , j ) •= Q B f i t d ) * exp(mulim * V c s g ( i ) * ( j -1) * T ) ; e l s e peQBund, j) = eQBun(i) * exp (Spgr ( i , 6) * (j-1) *T) p Q B f i t d , j ) = Q B f i t d ) * e x p ( S p g r ( i , 6) * (j-1) * end p Q G l f i t d , j ) = K u p G l c / d + e x p ( G l p ( l , 2 ) + G l p ( l , l ) * ( T i m e ( i ) + (j-1) *T))).-p Q L l f i t d , j ) = K u p L a c / d + e x p ( L l p ( l , 2 ) + L l p ( l , l ) * ( T i m e ( i ) + (j-1) * T ) ) ) ; p Q B l f i t d , j ) - KupBun/d + e x p ( B l p ( l , 2 ) + B l p ( l , l ) * ( T i m e ( i ) + (j-1) * T ) ) ) ; end wg = wg + 1; wb = wb + 1; wl = wl + 1; end * P l o t t i n g S e c t i o n plot(Time,TGlc,'b-',Time, TGlc,*bo*,Time,TLac,'g-',Time,TLac,*g*',Time,TBun,'r:',Time,TBun,*r+ * ) ; x l a b e l ( ' T i m e ( d a y s ) ' ) ; y l a b e l ( ' G l u c o s e Consumed and Lactate/BUN Produced (mmol) ') ; S a x i s ( { 0 , Time(n) + 1, min(0, View*TGlc, View'TLac, View'TBun), max(View'TGlc, View*TLac, View'TBun)]); res - i n p u t ( ' P r e s s enter t o c o n t i n u e . o - Glucose, * -L a c t a t e , + - BUN','s');ipause; p l o t (Time,GUR, 'mx', Time,GUR, *m: ' ,Time,eQGlc, 'g* ', Time,eQGlc, 'g-' .Time,QGlc, *wo', Time,QGf i t , 'c+ *, Time.QGfit, 'c-',Time,QG1fit,'y.',Time,QG1fit,'y-');xlabel('Time ( d a y s ) * ) ; y l a b e l ( ' G l u c o s e Uptake R a t e s ' ) ; a x i s ( [ 0 , Time(n) + 1, min([0 V i e w * Q G l c l ) , max(View*QGlc)]); re3 = i n p u t ( ' P r e s s enter t o c o n t i n u e , o - Mass B a l . , x - A P r i o r i , * - M.A. of Mass B a l . , + - Exp. Reg., . - Log. Reg.','s *) ; l p a u s e ; 173 p l o t (Time,LPR, 'nw' ,Time, LPR, 'm: *,Time,eQLac, 'g* * ,Time,eQLac, 'g-',Time,QLac,'wo',Time,QLfit,*c+*,Time,QLfit,*c-•, T i m e , Q L l f i t , 'y. • , T i m e , Q L l f i t , *y-') ; x l a b e l ('Time (days) ') ; y l a b e l ( ' L a c t a t e P r o d u c t i o n R a t e s * ) ; a x i s ( ( 0 , Time(n) + 1, min([0 View*QLacJ), max(View*QLac)]J; res = i n p u t ( ' P r e s s e n t e r t o c o ntinue, o - Mass B a l . , x - A P r i o r i , * - M.A. of Mass B a l . , + - Exp. Reg., . - Log. Reg.*,*s');%pause; plot(Time,BPR,'mx',Time,BPR,'m:',Time,eQBun,'g*',Time, eQBun, *g-',Time,QBun,'wo',Time,QBfit,'c+*,Time,QBfit,*c-Ti m e , Q B 1 f i t , ' y . * , T i m e , Q B 1 f i t , * y - ' ) ; x l a b e l ( ' T i m e ( d a y s ) * ) ; ylabel('BUN P r o d u c t i o n R a t e s ' ) ; a x i s { [ 0 , Time{n) + 1, min([0 View*QBunJ), max(View*QBun)]); res = i n p u t ( ' P r e s s e n t e r t o c o ntinue, o - Mass B a l . , x - A P r i o r i , * - M.A. o f Mass B a l . , + - Exp. Reg., . - Log. Reg.','s *);%pause; plot(Time(2:n),TLac(2:n),/TGlc<2:n),*b-',Time(2:n>,TLac(2:n)./TGlc(2:n), 'bo',Time(2;n),TBun(2:n) ./T Glc(2:n) , 'r:',Time(2:n),TBun(2:n)./TGlc(2:n),'r+*);xlabel(*T ime ( d a y s ) * ) ; y l a b e l ( ' Y i e l d o f Lac/Glc and Bun/Glc'); res = i n p u t ( ' P r e s s e n t e r t o c a l c u l a t e c o n t r o l l e r a c t i o n , o -Lac/Glc, + - BUN/Glc ' , ' s ' ) ; RqdFlow3G(i,j) - l e - 9 ; end I Now f o r L a c t a t e C o n t r o l Estimates DLacl = DLacl + peLPR(i,j) *T / V o l ( i ) ; i f ( L a c ( i ) + DLacl) > L a c s p t ( i ) 8 i f j == 1 RqdFlowLPU,j) = - peLPRU, j) / ( L a c i n ( i ) • L a c s p t ( i ) + ( L a c ( i ) - L a c s p t ( i ) ) ); % L/d e l s e RqdFlowLPU, j) = - peLPR(i, j) / ( L a c i n ( i ) -L a c s p t ( i ) ) ; I end e l s e RqdFlowLPU, j ) - l e - 9 ; end DLac2 = DLac2 + p e Q L a c ( i . j ) *T / V o l ( i ) ; i f ( L a c ( i ) + DLac2) > L a c s p t ( i ) % i f j — 1 RqdFlowQLU, j) = - p e Q L a c f i , j) / ( L a c i n ( i ) L a c s p t ( i ) + (Lac U ) -Lacspt ( i ) ) ); * L/d e l s e RqdFlowQL(i,j) = - p e Q L ac(i, j) / ( L a c i n ( i ) » C o n t r o l P o r t i o n of program L a c s p t ( i ) ) ; 1 end f o r i= 2 n e l s e D G l c l = 0; DLacl = 0; DBunl = 0; RqdFlowQLd,j) = l e - 9 ; DGlc2 = 0; DLac2 - 0; DBun2 - 0; end DGlc3 - 0; DLac3 - 0; DBun3 - 0; DGlc4 = 0; DLac4 = 0; DBun4 - 0; DLac3 - DLac3 + p Q L f i t ( i , j ) *T / V o l ( i ) DGlc5 = 0; DLacS - 0; DBun5 = 0; i f ( L a c ( i ) + DLac3) > L a c s p t ( i ) S f o r j = l : 24 i f j =•= 1 D G l c l - D G l c l + peGUR(i.j) *T / V o l ( i ) ; i f ( G l c ( i ) - D G l c l ) < G l c s p t ( i ) I i f j == 1 RqdFlowGU(i,j) = peGUR(i, j) / ( G l c i n ( i ) -G l c s p t ( i ) + ( G l c ( i ) - G l c s p t ( i ) ) ); S L/d e l s e RqdFlowGUd, j ) - peGURd, j ) / ( G l c i n ( i ) -G l c s p t ( i ) ) ; » end e l s e RqdFlowGUd, j ) = l e - 9 ; end DGlc2 - DGlc2 + p e Q G l c d , j) * T / V o l ( i ) ; i f ( G l c ( i ) - DGlc2) < G l c s p t ( i ) I i f j — 1 RqdFlowQGIi, j) - p e Q G l c d , j) / ( G l c i n ( i ) G l c s p t ( i ) + ( G l c ( i ) - G l c s p t ( i ) ) ); I L/d e l s e RqdFlowQGd, j ) - p e Q G l c d , j ) / ( G l c i n ( i ) G l c s p t ( i ) ) ; I L / d end e l s e RqdFlowQGd,j) - l e - 9 ; end DGlc3 - DGlc3 + p Q G f i t d , j) * T / V o l l i ) ; i f ( G l c ( i ) - DG1C3) < G l c s p t ( i ) I i f j — 1 RqdFlowlGU, j ) - p O G f i t l i , j ) / ( G l c i n ( i ) G l c s p t l i ) • ( G l c ( i ) - G l c s p t ( i ) ) ); I L/d e l s e R qdFlowlGU, j ) - p O G f i t l i , j ) / ( G l c i n ( i ) G l c s p t l i ) ) ; S L / d end e l s e R qdFlowlGU, j ) - l e - 9 ; end DGlc4 = DGlc4 + Q G l c ( i ) * T / V o l l i ) ; i f ( G l c l i ) - DGlc4) < G l c s p t l i ) % i f j ™ 1 RqdFlow2G(i, j) = Q G l c ( i ) / ( G l c i n l i ) -G l c s p t l i ) t ( G l c ( i ) - G l c s p t ( i ) ) ); » L/d e l s e RqdFlow2G(i, j) - Q G l c ( i ) / ( G l c i n l i ) -G l c s p t l i ) ) ; * L / d end e l s e RqdFlow2G(i,j) = l e - 9 ; end DGlc5 = DGlc5 + p Q G l f i t d ) * T / V o i d ) ; i f ( G l c l i ) - DGlc5) < G l c s p t ( i ) % i f j — 1 RqdFlow3G(i, j ) •= p Q G l f i t ( i ) / ( G l c i n l i ) -G l c s p t l i ) + ( G l c l i ) - G l c s p t ( i ) ) ); I L/d e l s e RqdFlow3G(i, j) = p Q G l f i t ( i ) / ( G l c i n ( i ) -G l c s p t ( i ) ) ; % L / d RqdFlowlL(i, j) - - p Q L f i t d , j ) / ( L a c i n ( i ) L a c s p t ( i ) + ( L a c ( i ) - L a c s p t d ) ) ); S L/d e l s e R q d F l o w l L d , j) = - p Q L f i t d , j ) / ( L a c i n d ) L a c s p t ( i ) ) ; % end e l s e R q d F l o w l L d , j) - l e - 9 ; end DLac4 = DLacl • QXac(i) *T / V o l ( i ) ; i f ( L a c ( i ) + DLac4) > L a c s p t d ) 8 i f j -= 1 RqdFlow2L(i, j) = - Q L a c d ) / ( L a c i n d ) -L a c s p t ( i ) + ( L a c ( i ) - L a c s p t ( i ) ) ); ! L/d e l s e RqdFlow2L(i,j) = - Q L a c d ) / ( L a c i n d ) -L a c s p t ( i ) ) ; * end e l s e RqdFlow2L(i,j) » l e - 9 ; end DLac5 = DLac5 + p Q L l f i t d ) *T / V o l ( i ) ; i f ( L a c ( i ) + DLacS) > L a c s p t d ) » i f j -= 1 RqdFlow3L(i,j) - - p Q L l f i t d ) / ( L a c i n d ) -L a c s p t ( i ) * ( L a c ( i ) - L a c s p t ( i ) ) ); S L/d e l s e RqdFlow3L(i,j) - - p Q L l f i t d ) / ( L a c i n ( i ) -L a c s p t ( i ) ) ; I end e l s e RqdFlow3L(i,j) - l e - 9 ; end I Now f o r the BUN Estimates DBunl = DBunl • peBPRd.j) *T / V o l ( i ) ; i f (Bund) + DBunl) > Bunspt(i) S i f j — 1 RqdFlowBPd, j) = - peBPRIi, j) / ( B u n i n d ) B u n s p t l i ) + ( B u n ( i ) - B u n s p t ( i ) ) ); I L/d e l s e RqdFlowBPd,j) = - peBPRIi, j) / ( B u n i n d ) B u n s p t ( i ) ) ; 8 end e l s e RqdFlowBPd, j) = l e - 9 ; end DBun2 = DBun2 + peQBund, j) *T / V o l ( i ) ; i f (Bund) + DBun2) > B u n s p t d ) 8 i f j — 1 RqdFlowQB ( i , j ) = - peQBund, j ) / ( B u n i n d ) B u n s p t d ) + ( B u n d ) - B u n s p t d ) ) ); S L/d e l s e RqdFlowQB ( i , j ) = - peQBund, j) / ( B u n i n d ) B u n s p t d ) ) ; I end e l s e 174 end RqdFlowQB(i,j) - l e - 9 ; DBun3 - DBun3 t p Q B f i t ( i , j ) *T / V o l ( i ) ; i f (Bun(i) + DBun3) > B u n s p t d ) I i f j =- 1 R q d F l o w l B d . j ) - - p Q B f i t d , j ) / (Bunin(i) B u n s p t d ) + ( B u n ( i ) - B u n s p t ( i ) ) ); % L/d e l s e R q d F l o w l B l i , j ) = - p Q B f i t d , j ) / (Bunin(i) B u n s p t d ) ) ; * end e l s e R q d F l o w l B d , j ) - l e - 9 ; end DBun4 = DBun4 + QBun(i) *T / V o i d ) ; i f (Bun(i) + DBun4l > Bunspt(i) S i f j == 1 RqdFlow2B(i,j) = - QBun(i) / (Bunin(i) -B u n s p t d ) + ( B u n ( i ) - B u n s p t ( i ) ) ); % L/d e l s e RqdFlow2B(i,j) - - QBun(i) / (Bunin(i) -B u n s p t d ) ) ; % end e l s e RqdFlow2B(i,j) = l e - 9 ; end DBun5 = DBun5 + p Q B l f i t d ) *T / V o l ( i ) ; i f ( Bund) + DBunS) > Bunspt(i) % i f j — 1 RqdFlow3B(i, j) - - p Q B l f i t d ) / (Bunin(i) -B u n s p t d ) + ( B u n ( i ) - B u n s p t ( i ) ) I; I L/d e l s e RqdFlow3B(i, j) = - p Q B l f i t d ) / (Bunin(i) -B u n s p t d ) ) ; % end e l s e RqdFlow3B(i,j) » l e - 9 ; end * Now f o r the averages RqdFlowRd, j ) = (RqdFlowGUd, j RqdFlowBPd, j ) )/3 RqdFlowLP( (RqdFlowQGd, j) * RqdFlowQLI (RqdFlowlGd, j) + RqdFlowlLI (RqdFlow2G(i,j) + RqdFlow2L( • j) + .j) + • j) * • j) + - (RqdFlow3G(i,j) + RqdFlow3L(i,j) + RqdFlowQd, j RqdFlowQB(i,j))/3 R q d F l o w l d , j ) R q d F l o w l B d , j ) )/3 RqdFlow2(i,j) RqdFlow2Bd, j ) )/3 RqdFlow3d, j) RqdFlow3Bd, j ) )/3 end end GUR = GUR'; LPR = LPR' ; BPR = BPR'; pGUR = pGUR'; pLPR = pLPR'; pBPR = pBPR'; QGlc = QGlc'; QLac = QLac'; QBun = QBun'; pQglc = pQglc'; pQlac = pQlac'; pQbun = pQbun' eQGlc = eQGlc *; eQLac = eQLac'; eQBun = eQBun * eGUR = eGUR'; eLPR - eLPR'; eBPR = eBPR'; TGlc = T G l c ' ; TLac - TLac' ; TBun = TBun'; Eflow = Eflow'; Q G f i t = Q G f i t ' ; Q L f i t - Q L f i t ' ; Q B f i t = Q B f i t ' Q G l f i t = Q G l f i t ' Q L l f i t - Q L l f i t ' ; Q B l f i t = Q B l f i f res = i n p u t ( ' S a v e data t o d i s k i n f i l e named runpl 2 o . t x t ? l y / n ] ' , ' s ' ) ; i f ce3 B='y' t res=='Y' b i g - ( T i m e , T G l c , Q G l c , e Q G l c , Q G f i t , Q G l f i t ] ; t b i g • p Q G f i t ; save d:\astudent\jason\prmtlb\runpl2e.txt b i g -a s c i i -tabs big2 - [peQGlc,pQGfit,pQGlfit] ; save d : \ a s t u d e n t \ j a s o n \ p s m t l b \ r u n p l 2 f . t x t big2 -a s c i i -tabs end Data = 'Previous Data. Time and Flow* I n f o = [Time Flow] fo r j=0:23 t i ( j + l,l)=T*24'' j ; end I P l o t t i n g S e c t i o n f o r O b t a i n i n g Best Estimates plot(Time,QGlc,'wo',ti(1:24,1)/24 • Time(n),peQGlc(n,1:24)*,*g-*,ti(1:24,1)/24 + Time(n) , peGURfn, 1:24 ) ', 'm~ ' , t i (1:24 , 1)/24 + Time(n),pQGfit(n,1:24)',*c-',ti(1:24,1)/24 + Time(n),pQGlfit(n,1:24)*,'y-',ti(1:24,1)/24 + T i m e ( n ) , Q G l c ( n ) . ' o n e s ( s i z e ( t i ) ) , ' r : ' , t i ( 1 : 2 4 , 1 ) / 2 4 + T i m e ( n ) , e Q G l c ( n ) . * o n e s ( s i z e ( t i ) ) , ' g : ' ) ; x l a b e l ( ' T i m e (days)'); y l a b e l ( ' G l u c o s e Uptake Rates'); a x i s ( ( T i m e ( r g n ) , Time(n) + 1 + T*24, min((0 View*QGlc']), max(View*QGlc)]); res = i n p u t ( ' P r e s s enter t o c o n t i n u e . Green- Mass B a l . , Magenta - A P r i o r i , Cyan- Exp. Reg., Yellow- Log. Reg., Red-Constant ','s') ; plot(Time,QLac,'wo',ti(1:24,1)/24 + Time(n),peQLac(n,1:24)','g-',ti(1:24,1)/24 + Time(n) ,peLPR(n, 1:24 ) ', *m—', t i (1:24 , 1 )/24 + Time(n),pQLfit(n,1:24)*,'c-',ti(1:24,1)/24 + T i m e ( n ) , p Q L l f i t ( n , 1 : 2 4 ) ' , ' y - ' , t i ( 1 : 2 4 , 1 ) / 2 4 + T i m e ( n ) , Q L a c ( n ) . ' o n e s ( s i z e ( t i ) ) , ' r : ' , t i ( 1 : 2 4 , 1 ) / 2 4 + Time(n) , eQLac (n) . *ones ( s i z e ( t i ) ) , * g : ' ) ,-xlabel ( 'Time ( d a y s ) ' ) ; y l a b e l ( ' L a c t a t e P r o d u c t i o n Rates'); a x i s ( [ T i m e ( r g n ) , Time(n) + 1 + T*24, min((0 View*QLac']), max(View*QLac)]); res = i n p u t ( ' P r e s s enter t o c o n t i n u e . Green- Mass B a l . , Magenta - A P r i o r i , Cyan- Exp. Reg., Yellow- Log. Reg., Red-Constant ','s') ; plot(Time,QBun,'wo',ti(1:24,1)/24 + Time(n),peQBun(n,1:24)','g-',ti(1:24,1)/24 + Time (n),peBPR(n, 1:24) ','m—', t i (1:24 , 1)/24 + Time(n),pQBfit(n,1:24)','c-',ti(1:24,1)/24 + T i m e ( n ) , p Q B l f i t ( n , 1 : 2 4 ) ' , ' y - ' , t i ( 1 : 2 4 , 1 ) / 2 4 + T i m e ( n ) , Q B u n ( n ) . * o n e s ( s i z e ( t i ) ) , ' r : ' , t i ( l : 2 4 , l ) / 2 4 + T i m e ( n ) , e Q B u n ( n ) . * o n e s ( s i z e ( t i ) ) , * g : ' ) ; x l a b e l ( ' T i m e ( d a y s ) * ) ; ylabel('BUN P r o d u c t i o n Rates*); a x i s ( [ T i m e ( r g n ) , Time(n) + 1 + T*24, min([0 View*QBun']), max(View'QBun))); res = i n p u t ( ' P r e s s enter t o c o n t i n u e . Green- Mass B a l . , Magenta - A P r i o r i , Cyan- Exp. Reg., Yellow- Log. Reg., Red-Constant ','s') ; I These flows are converted t o volumes for my purposes. I However, f o r I n g r i d , these 3hould be flow r a t e s res = input('Do you want t o see the flow r a t e s based on Mass Balance ? [y/n] ' , ' s ' ) ; i f res=='y' I res=='Y' i f length(WarnG) > 0 Info = 'The c a l c u l a t e d growth rate from Glucose was l a r g e r than E s t . Max. f o r points',WarnG end i f length(WarnL) >0 Info = 'The c a l c u l a t e d growth rate from L a c t a t e was l a r g e r than E s t . Max. f o r points',WarnL end i f length(WarnB) >0 Info = 'The c a l c u l a t e d growth r a t e from BUN was l a r g e r than E s t . Max. f o r points',WarnB end Info = 'From Sample Time, Glc-Based, Lac-Based, BUN-Based, G l c , Lac and BUN Based [mL]' Info = [ t i ( : , l ) , 1000/24.* RqdFlowQG(n,:)',1000/24.* RqdFlowQLIn,:)', 1000/24.* RqdFlowQB(n,:)', 1000/24.* RqdFlowQ(n,:)'] end res a input('Do you want t o see the flow r a t e s based on L o g i s t i c Growth Model ? [y/n] ' , ' s ' ) ; i f res=='y' 1 res=='Y' Info = 'From Sample Time, Glc-Based, Lac-Based, BUN-Based, G l c , Lac and BUN Based [mL]' Info - [ t i ( : , D , 1000/24 .* RqdFlow3G (n, : ) ' , 1000/24 . ' RqdFlow3L(n,:)', 1000/24.' RqdFlow3B(n,:)', 1000/24.* RqdFlow3(n,:)'] end res *= input ('Do you want t o see the flow r a t e s based on Non-Linear Regression ? (y/n] ' , ' s ' ) ; i f res=='y' I res=='Y' i f length(WarnG) > 0 I n f o = 'The c a l c u l a t e d growth r a t e from Glucose was l a r g e r than 1.2 * E s t . Max. f o r points',WarnG end i f length(WarnL) >0 Info = 'The c a l c u l a t e d growth r a t e from L a c t a t e was l a r g e r than 1.2 * E s t . Max. f o r points',WarnL end i f length(WarnB) >0 Info = 'The c a l c u l a t e d growth r a t e from BUN was l a r g e r than 1.2 * E s t . Max. f o r points*,WarnB end Info = 'From Sample Time, Glc-Based, Lac-Based, BUN-Based, G l c , Lac and BUN Based [mL]' I n f o - [ t i ( : , l ) , 1 0 0 0 / 2 4 . * RqdFlowlGIn,:)',1000/24.' RqdFlowlL(n,:)', 1000/24.* RqdFlowlB(n,:)',1000/24.* RqdFlowl(n,:)'] end 175 res = input('Do you want t o see the flow r a t e s based on Change ? [y/n] ',*s * ) ; i f res=='y' I res=='Y' Info = 'From Sample Time, Glc-Based, Lac-Based, BUN Based, G l c , Lac and BUN Based [mL]' Info - [ t i ( : , 1), 1000/24.* RqdFlow2G(n,:)', 1000/24. RqdFlow2L(n,:)', 1000/24.* RqdFlow2B{n,:)',1000/24.* RqdFlow2(n,:)* J end 

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