Castilho Leda R., Moraes Angela Maria (Ed.) Animal Cell Technology: From Biopharmaceuticals to Gene Therapy

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Appendix

Case study: Mathematical modeling of the growth of a

hybridoma

From a set of three experiments (initial conditions in Table A1) conducted

in batch mode, employing a secreting monoclonal anti-TNP (trinitro-

phenyl) hybridoma, various phenomena were observed and detailed be-

low.

(i) The speciﬁc growth rate is limited by glutamine and inhibited by

secreted ammonium and lactate (Equation A.1).

(ii) The speciﬁc death rate is inhibited by glutamine and limited by

lactate and ammonium (Equation A.2).

(iii) The viable cell production rate is equal to the difference between the

growth rate of viable cells and the death rate (Equation A.3).

(iv) The glucose consumption rate is divided in cell growth, ﬁrst equation

term, and lactate formation (Equation A.5).

(v) The glutamine consumption rate is divided in a ﬁrst order chemical

decomposition, ﬁrst equation term, viable cell formation, second

equation term, and ammonium formation (Equation A.6).

(vi) The variation of monoclonal concentration is partially associated

with cellular growth (Equation A.7).

(vii) The lactate production rate is partially associated with cell growth

(Equation A.8).

(viii) The ammonium production rate is associated with cell growth (Equa-

tion A.9).

The proposed mathematical modeling to ﬁt the experimental data is

based on Bree et al. (1988), and is represented by a set of differential

Equations A.1 to A.9, consisting of seven state variables (Table A2) and 20

ﬁtted parameters (Table A3).

Table A1 Initial conditions for tests

Test X

V,0

(cel/ml) GLC

(g/L) GLN

(g/L) NH

4,0

(mg/L) LAC

(g/L)

1 4.5 0.58

2 1.0 3 10

5.6 1.45 0.0 0.0

3 11.3 2.90

Adapted from Lee, 2003.



¼ 

X,max

GLN

þ GLN



i,NH

þ NH

i,LAC

þ LAC

(A:1)

¼ k

d,max

þ NH

LAC

þ LAC

i,GLN

þ GLN

(A:2)

¼ 

 k

(A:3)

¼ k

(A:4)

Table A2 Model state variables

Viable cells concentration (cel/ml)

Non-viable concentration (cel/ml)

GLC Glucose concentration (g/L)

GLN Glutamine concentration (mg/L)

mAb Monoclonal antibody concentration (mg/L)

LAC Lactate concentration (g/L)

Ammonium concentration (mg/L)

Table A3 Fitted parameters

Parameters Description Fitted value



X,max

Maximum speciﬁc cell growth rate (h

–1

) 0.0630

GLN

Glutamine limitation constant for growth (mg/L) 2.65

i,NH

Ammonium inhibition constant for growth (mg/L) 65.73

i,LAC

Lactate inhibition constant for growth (g/L) 15.14

d,max

Maximum speciﬁc cell death rate (h

–1

) 0.0763

Ammonium limitation constant for death (mg/L) 21.86

LAC

Lactate limitation constant for death (g/L) 6.114

i,GLN

Glutamine inhibition constant for death (mg/L) 778.2

Xv=GLC

Glucose-to-viable cells yield coefﬁcient

(10

cell/10

–3

1.16

LAC=GLC

Glucose-to-lactate yield coefﬁcient (g/g) 1.00

Constant (10

–3

g/10

cell) 0.520

=GLN

Glutamine-to-viable cells yield coefﬁcient

(10

cell/10

–3

20.85

=GLN

Glutamine-to-ammonium yield coefﬁcient (mg/mg) 0.0210



Constant (10

mg/10

cell) 7.05

Constant (10

–3

g/10

cell) 8.67

Constant (10

–3

g/10

cell.h) 1.15

Constant (10

–3

mg/10

cell) 24.99

 Parameter no associated to growth (10

–3

g/10

cell.h) 0.389



Constant (10

–3

g/10

cell.h) 0.312 3 10

–3

K First order constant for glutamine decomposition

–1

)

0.334 3 10

–2

506 Animal Cell Technology

dGLC

¼



=GLC



:

LAC=GLC

(A:5)

dGLN

¼k:GLN 



=GLN





:

=GLN

(A:6)

dMAb

:

MAb=Xv

þ :X

(A:7)

dLAC

¼ Æ

:

þ 

(A:8)

dNH

¼ Æ

:

(A:9)

Figure A1 illustrates the model simulation results with the ﬁnal ﬁtted

parameters of one of the experiment 2. The proposed model represents

adequately the characteristic phenomena of the process.

0.0E 00⫹

4.0E 05⫹

8.0E 05⫹

1.2E 06⫹

1.6E 06⫹

2.0E 06⫹

2.4E 06⫹

2.8E 06⫹

X (cel/ml)

Xv Xd

100

120

mAb ( g/ml)µ

0.0

2.0

4.0

6.0

Time (h)

GLC ou LAC (g/L)

GLC LAC

0.0

0.4

0.8

1.2

1.6

GLN (g/L)

100

NH (mg/L)

⫹

GLN NH

100

120

0 20 40 60 80 100 120

Time (h)

0 20 40 60 80 100 120

Figure A1

Experimental data simulation: (symbols) experimentals data; (line) model simulation.

Appendix 507

Index

2-oxoglutarate 142

3T3 cells 4, 120

Abbokinase

398

Acetyl CoA 79, 81–82, 88

Acetylation 134

Acoustic separators 290

Acridine orange 157, 158

Activase

394, 402

Active transport 98, 100

Acute myocardial infarction 394, 398

Adeno-associated virus 492, 500, 503

Adenovirus 9, 31, 442, 452, 453, 492, 500, 501

Adherent cells 19–23, 27, 112, 118, 443, 444, 445

Adventitious agents (see Product contaminants)

Aeration (see also Oxygen supply) 26, 246, 261,

263, 265

Afﬁnity chromatography 301, 314–319, 323,

335, 418

Afﬁnity ligands 314–318

Biospeciﬁc 316

Matrix coupling 317–318

Pseudo-biospeciﬁc 316

Aggregation of product 330, 331, 336, 337, 338

Agitation 246

Alanine 76, 79, 82, 85–91, 94–95, 99, 101, 112,

114, 123 184, 186, 201, 429

Alemtuzumab 3

Allosteric regulation 75, 89

Allotransplants 475–476

Alpha-ketoglutarate 79, 82, 84, 86, 88, 97, 101

Amadori re-arrangement 140

Amino acid 75–78, 80–82, 84–90, 112, 114,

116–117, 118, 120, 122, 123, 124, 130,

133–134, 140, 351, 316, 366, 425

Sequence 331, 336–337, 339, 341, 423

Ammonia/Ammonium 76, 84–87, 91, 94–102,

116, 123, 138, 184, 186, 192, 200, 201, 203,

209, 214, 215, 428, 429, 500

Ammonium sulfate 302, 313

Amyloid 139

Anaplerotic reaction 82

Anchorage-dependent cells 20, 21

Anemia 392, 394

Angiogenesis 475

Anion exchangers 311–312

Annexin V 158

Antennarity 98–99, 133

Antibiotics 30, 114, 120

Antibodies 338, 339, 341, 343, 396, 399, 411–415

Afﬁnity 416, 419, 420, 422

Antigenic determinant 409, 412, 413, 422

Bi-functional 425

Bi-speciﬁc 425

Chimeric 420, 421

Domains 411, 412, 419, 422, 423, 425

Gene recombination 412, 413, 423, 427

Half life 423, 425

Humanized 420, 421

Speciﬁcity 409, 410, 415, 419, 420, 425

Variety 410, 412, 413

Antibody fragments 410, 420, 421, 422–425

Diabodies 421, 425

Tetrabodies 421, 425

Triabodies 421, 425

Antigen 6, 316, 374, 380, 381, 383, 435, 444, 448,

450, 451, 455

Antioxidant enzymes 102

Apligraf

Apoptosis 23, 27, 122, 124, 151, colour plate/

Fig. 7.3

Molecular aspects 159

Morphological characteristics 151, 156, 157,

160, 162, 168

Control 171

Deﬁnition 151

Detection 155

Induction 152

Apoptosome 167, 168, 169, 170, 171

Apoptotic pathways 160

Intrinsic mitochondrial pathway 162

Intrinsic ER stress-induced pathway 169

Extrinsic death receptor-induced

pathway 170

Aranesp

394, 406

Arginine 79, 88–89, 112, 139, 142

Ascorbate 142

Asparagine 84–85, 87–90, 130, 138, 142

ATP 10, 16, 75–80, 83, 89, 92, 102

Autoimmune diseases 389, 391, 399, 400, 475

Avastin

3, 396, 399, 419

Avonex

3, 391, 394, 402

B lymphocyte 409, 410, 412, 413, 414, 416, 419,

420, 422, 482–483

Baculovirus 6, 32, 135, 136, 300, 448, 449, 450,

451,455, 459–470

Baculovirus expression vector system 6

Baculovirus infection cycle 461–462, 463, 464,

468

Passage effect 467, 470

BAE-1 20

Balb/c 125 415

Basiliximab 3

Bcl-2 153, 154, 162, 164, 169, 171

Beneﬁx

3, 394, 399, 402

Betaferon

391

Beta-hydroxyaspartate 130

Beta-oxidation 92

Betaseron

391

Bevacizumab 3

Bexxar

419

BHK cells 2, 3, 4, 6, 10, 20, 30, 55, 81, 83, 86–90,

93, 95–96, 99, 103, 130, 141, 120, 125, 443,

427, 429

Bioassays 330, 331, 341–345

Bioballistics 494–495

Biogenerics 366–367

Bioinsecticide 459–474

Comparison to chemical pesticides 459–460

Comparison to in vivo production 460

Mechanism of action 460–463

Virulence 460, 463, 466–467

Biopesticide (see Bioinsecticide)

Biopharmaceuticals 1, 2, 3, 6, 30, 122, 383, 388,

389, 394, 400, 402, 404

Characterization 404

Formulation and delivery 402

Market 400

Second-generation molecules 405

Stability 402, 403

Bioreactors

Air-lift bioreactors 225, 227

Bioreactors for attached cell growth 225,

231

Cell concentration ranges 254

Classiﬁcation of bioreactors 225

Economic aspects 252

Fluidized-bed bioreactors 225, 231

Heterogeneous bioreactors 228

Hollow-ﬁber bioreactors 225, 231

Homogeneous bioreactors 225

Microcarrier-based systems 225, 229

Packed-bed bioreactors 225, 230

Roller bottles 225

Scale of operation 221, 225, 226, 230, 252

Small-scale culture systems 221, 223

Stirred-tank bioreactors 225

Types of bioreactors 224, 225

Wave bioreactors 225, 226

Biosafety 330, 331, 333, 335, 341, 342, 354

Blood coagulation 140

Blood coagulation factors 394, 398

Blood serum (see serum)

BSE (bovine spongiform encephalopathy) 357

Buffer exchange 305

By-product synthesis 185, 186, 188, 191, 192,

195, 199, 200, 201, 203, 208, 209, 210, 215,

426, 430

Caco-2 cells 4

Campath

3, 396, 419

Cancer 389, 391, 392, 396, 399

Capillary electrophoresis 362

Capsid 340, 341, 439, 448, 450, 454

Carbohydrate 76, 80, 83–84, 99, 115, 130, 136,

335, 340, 484

Carbon dioxide 26, 79, 101, 103–104, 111,

115, 116, 262, 485

Dissolved, 267

Carboxylation 103, 130, 141

Carcinogenicity 363–364

Carnitine 92

Carticel

Caspases 151, 160

Activation 160

Classiﬁcation 160, 161

Structure 161

Cation exchangers 311–312

CBER 352

CDER 352

CDR (Complementarity-determining regions)

411, 420, 422

Grafting 420, 421

Cell banks 4, 28, 29, 125, 332–333, 334, 355, 360,

501

Cell concentration measurement 23

Cell cycle 13, 77, 88, 96, 147, 148, 149, 150

Cell disruption (see cell lysis)

Cell factory 7, 8, 444

Cell growth phases 21–23

Death phase 23

Exponential or log phase 22

Lag phase 22

Stationary phase 23

Cell line storage 28–29

Cell lines 54

Cell lysis 298–299

Cell maintenance 20

Cell monitoring 263, 264, 265–267

Flow cytometry 217, 267

Image analysis 266, 267

Respiration 263, 264, 265

Size distribution 266, 267, 275, 276, 278

Cell morphology 20

510 Animal Cell Technology

Cell proliferation 147

Cell propagation 222

Adherent cells 224

Suspension cells 223

Cell structure

Cytosol 14–15

Endosome 14

Golgi complex 14, 16

Lysosome 14, 16

Mitochondria 14, 16, 17

Nucleous 14, 17

Peroxisome 14, 17

Plasma membrane 14

Polyribosome 14

Rough endoplasmic reticulum 14, 15

Cell therapy 4, 7, 8, 11, 475, 478–479, 484, 486,

489

CellCube

225, 231, 501

CellFactory

225, 231

Centrifugation 281

Multi-chamber centrifuges 281, 282

Disc centrifuges 281, 282

Tubular centrifuges 281, 282

Centritech

centrifuges 282

Cerezyme

394, 398

Chemostat 83, 85, 103

Chimeric antibodies 401, 419, 420

Chimeric viral particles 454

CHO cells 2, 3, 4, 6, 10, 20, 30, 54, 55, 83, 89, 93,

95, 99–102, 125, 129, 133–134, 138, 141,

320, 322, 358, 427, 428, 429, 443

Cholesterol 91, 118, 120

Chromatin 152, 155, 156, 157, 158

Chromosomal integration 41, 53

Positioning effect 41, 44, 53, 57

Random recombination 44, 53

Site-speciﬁc integration 57

Chromosome 17, 76, 493, 495

CHSE cells 81

Citrate 79, 81–82

Cleaning validation 359

Clinical trials 330, 344, 350, 352, 363–365

Clusters of differentiation (CDs) 480–483

CMP-NANA 99–100

Collagen 27, 117, 118, 119, 125, 142, 484

Collagenase 17, 21

Computational ﬂuid dynamics 288

Continuous cell lines 443

Control (process control) 259–270

Actuator 260, 269, 270

Adaptive 270

Cascade 262, 269

Loop 260, 269

On-off 261, 269

PID 260, 269, 270,

Strategies 268–270

Copper 139

Core-like particles 444

Cornea 486

CPMP 352

Cryopreservation 28, 355, 486

Cryoprotector 28

CultiSpher

230, 444

Culture conditions 152, 153, 154, 155

Culture media

Contaminants 29

Degradation by light 29

Culture media types

Basal media 111

Chemically deﬁned media 111, 124

Classical formulations 112

For insect cells 112, 463

For mammalian cells 112

Growth media 111

Maintenance media 111

Protein-free media 2, 4, 123

Serum-free media 2, 4, 32, 111, 112, 117,

122–125, 300, 464–465

Cut size 278

Reduced cut size 278

Cystathionine pathway 90

Cystine 87–90, 113

Cytochrome C 155, 156, 159, 166, 167, 168, 171

Cytodex

229, 230, 444

Cytokines 94, 352, 390, 392, 394, 400, 406,

484–485

Cytomegalovirus 357

Cytosol 14, 15, 77, 80–84, 87, 92, 94–95, 100,

496

DACS

SC 8

DAPI 157

Data treatment 186, 190–191, 192

Experimental error 190, 213

Rate estimation 180–191

Smoothing methods 190–191

Deamidation 138–140

Deamination 85, 139

Density gradient 304

Deoxyglucosone 139

Desalting 305, 309

Diabodies (see Antibody fragments)

Diaﬁltration 305, 306

Dialysis 301, 305

Dipeptides 86–87

DISC (death-inducing signaling complex) 170

Disulﬁde bonds 130, 132, 351, 362

DMSO 28

DNA ﬁngerprinting 356

DNA vaccines 9, 451–452

Index 511

Dolichol 130, 132, 137

Doubling time 22

Downstream processing 295–324, 445, 451

Dye exclusion 23

E. coli 49–51, 62, 134–135, 494

ECGF 118

Economic aspects 400

EDTA 17, 21, 299

Efﬁcacy of products 330, 331, 340, 342

EGF 118, 119, 120, 125

Eicosanoid 91

Elastin 484

Electrode (see Sensor)

Electrofocusing (see isoelectric focusing)

Electron microscopy 358, 496

Electrophoresis 156

Electrophoresis 310, 337–339, 341

Embryonated chicken eggs 357

Embryonic germ cells 478

Embryonic stem cells 7, 8

EMEA 350, 352, 366–367

Enbrel

396, 406

Endoplasmic reticulum 14, 15, 130–131

Endothelial cells 4, 119, 120, 125, 479–481, 485

Endotoxin 115, 120, 360, 362

Env gene 493

Epogen

3, 394, 402

Epstein-barr virus 5, 357, 375

Erbitux

419

Erythropoietin 3, 6, 83, 366–367, 384, 392, 394,

400, 402, 406

Ethidium bromide 157, 158

Expanded bed adsorption 319–321

Expression systems 44–48, 55, 61, 66, 404

Extracellular matrix 27, 118, 119, 125

Exubera

403

Fabrazyme

394, 398

FACS (see Flow cytometry)

Factor IX 3, 394, 399, 402

Factor VII/VIIa 394, 399

Factor VIII 3, 139, 394, 398, 402

Factor X 129, 140–141, 399

FAD 78–80, 92

Fatty acid 79, 80, 91–95, 114

FDA 122, 351–352, 355–363, 366–367, 501

Fed-batch cultures 83, 85–86, 90–91, 138, 237

FGF 118, 119, 125

FIA (see Flow Injection Analysis)

Fibra-Cel

501

Fibroblast 4, 10, 19, 20, 24, 30, 31, 119, 120, 125

Fibronectin 21, 27, 118, 119, 125, 484

Filtration 285

Dynamic ﬁlters 287

Filter medium 285, 287

Spin-ﬁlters 288

Tangential ﬂow ﬁltration 285

Rotating disc ﬁlters 288

Finite cells 4

Flavivirus 500

Flow cytometry 263, 267

Flow injection analysis (FIA) 267

Flow ratio 276

Fluorochrome 479

Follicle-stimulating hormone

Fructosamine 139–140

Fructose 77–78, 83, 116, 140

Fucosylation 133–135

Fungi 132, 136

Gag gene 493

Galactose 83, 101, 116, 131, 137

Galactosylation 99, 138

Galactosyltransferase 136

GalNac 100, 133–134, 136

Gamma-carboxylation 130, 140–141

G-CSF 366, 392, 394, 400, 402, 403

GDP 79, 89, 130

Gel ﬁltration (see molecular exclusion

chromatography)

Gel permeation chromatography (see molecular

exclusion chromatography)

Gendicine

498, 501

Gene expression 40

Gene gun 494–495, 500

Gene therapy 4, 9, 11, 31, 435, 489–493,

497–502

Genetic elements 40

39 untranslated region 42, 43

59 untranslated region 42, 43

Capping 40, 41

Codon usage 43

Chromosomal elements 40

Enhancer 40, 41, 43, 51

Introns 41, 42

Polyadenylation signals 41, 42, 48, 51

Promoter 40, 41, 50, 51, 52

Termination codon 43

Transcription-termination sequences 41,

42, 51

Genetic engineering 374, 375, 376

GlcNac 99–100, 130–138

Glucose 24, 76–106, 113, 115–116, 118, 122, 123,

131, 137–140

Glucose transporters 77, 107

Glucosidase 130–131

Glutamate 79, 84–90, 94, 107, 114

Glutamate dehydrogenase 79, 84, 89, 101

512 Animal Cell Technology

Glutamine 76, 81–84, 91, 94–105, 113, 114, 116,

123, 137–138

Glutamine thermal degradation 116

Glutaminolysis 76, 84, 94, 99, 103

Glutathione 102

Glycation 139–140

Glycerol 28

Glycine 85, 87–89, 101, 112, 140

Glycocalyx 22, 484

Glycolic acid 496

Glycolysis 22, 35, 76–77, 79–83, 85, 89, 94–95,

97–99, 102–103, 116

Glycoproteins 405

Glycosaminoglycans 484

Glycosylation 31, 83, 97, 99–100, 103, 116,

130–138, 142, 351, 339, 340, 390, 404, 406,

448, 450

Glycosyltransferase 134–137

GM-CSF 392, 400, 402, 404

GMOs 354

GMP 349–355, 358–359

Golgi 99, 129, 131–134, 136–137, 142, 328

Gonal-f

3, 393, 394

Granulocyte-colony stimulating factor 366, 392,

394, 400, 402, 403

Gravity settling 280

Lamella settlers 280

Vertical settlers 280

Growth factors 118–122, 124, 125, 149, 152, 153,

392

Growth hormone 138, 349, 366–367

Guinea pigs 357

HACA (see Human anti-chimeric antibody)

HAMA (see Human anti-murine antibody)

Hayﬂick limit 19, 150

HBsAg 303, 304, 448, 450

HBV 435, 441, 448, 450, 453, 454

Heart 91, 95, 475–476, 501

HEK-293 cells 4, 20, 30, 31, 141, 501

HeLa cells 20, 139, 443

Hematopoiesis 479, 484

Hematopoietic

Cascade 483

Growth factors 392

Stem cells 477, 479, 481, 483–485

Tissue 474

Hemoﬁlia 394, 398, 399

Hemolymph 116, 118, 124, 465, 466

HEPA ﬁlters 353–354

Hepatitis 366–367, 450

Hepatitis B vaccine 3, 448, 449, 450

Hepatitis virus 357, 440

Hepatocyte 84, 96

HEPG2 cells 20

Herceptin

3, 396, 419

Herpes virus 357, 442, 492, 500

Heterologous gene expression 44

Baculovirus 48

DNA virus 45

Expression vectors 44

Inducible promoters 50

Multiple gene expression 53

Plasmid vectors 50

Quantitation of recombinant proteins 66

RNA virus 47

Signal peptide 52

Stable expression 55, 56, 57

Tags 52

Transient expression 54, 55, 56, 57

Viral vectors 44

Hexanoic acid 93

Hexokinase 77–78, 81, 83, 100, 110

Hexose 83

High-Five

32, 124, 449

Histidine 79, 88–89, 113

HIV 133, 358, 360, 452

HL-60 cell 20, 86

Hollow ﬁber membrane modules 286, 287

Hormones 393, 394

Human anti-chimeric antibody (HACA) 420

Human anti-murine antibody (HAMA) 418

Human genome 489, 502

Human neurotropic virus 493

Human parvovirus B19 449

Humanized antibodies 401, 419, 420

Humatrope

402

Humira

419

Humulin

402

Hybridization 375

Hybridoma 2, 3, 5, 14, 30, 31, 83–86, 89–91, 93–

94, 96–97, 102, 104, 119, 120, 125, 319, 375,

380, 381, 383, 410, 414, 415–418

Hybridoma technology 410, 415–418, 420

Hydrocyclones 274, 283

Hydrodynamic stress 154

Hydrolysates 116, 123, 124

Hydrophobic interaction chromatography 301,

313–314

Hydroxyapatite 486

Hydroxylation 142

Hydroxyproline 142

Hyperglycemia 139

Hypoxia 102, 142

Hypoxia-inducible factor (HIF) 142

ICH 350, 352–353, 355

IGF-1 118, 119, 120

IGF-2 119, 120

IL-mu6 99

Index 513