Models of Cellular Regulation

by Baltazar Aguda, Avner Friedman

Overview

The human genome of three billion letters has been sequenced. So have the genomes of thousands of other organisms. With unprecedented resolution, modern technologies are allowing us to peek into the world of genes, biomolecules, and cells-and flooding us with data of immense complexity that we are just barely beginning to understand. A huge gap separates our knowledge of the components of a cell and what is known from our observations of its physiology. The authors have written this graduate textbook to explore what has been done to close this gap of understanding between the realms of molecules and biological processes. They have gathered together illustrative mechanisms and models of gene regulatory networks, DNA replication, the cell cycle, cell death, differentiation, cell senescence, and the abnormal state of cancer cells. The mechanisms are biomolecular in detail, and the models are mathematical in nature. The interdisciplinary presentation will be of interest to both biologists and mathematicians, and every discipline in between.

Product Details

ISBN-13:	9780199657506
Publisher:	Oxford University Press, USA
Publication date:	10/12/2012
Series:	Oxford Graduate Texts
Edition description:	Reprint
Pages:	200
Product dimensions:	6.70(w) x 9.60(h) x 0.50(d)

About the Author

Baltazar Aguda is currently associate professor of Genetics & Genomics at the Boston University
School of Medicine. He holds joint appointments in Biomedical Engineering, in the Bioinformatics
& Systems Biology program at Boston University, and a membership in the Center for Biodynamics in the same university. Recently, he was appointed member of the National Science
Foundation's (NSF, USA) research proposal review panel in molecular & cellular biosciences
(2004-7). He was a visiting faculty at the Mathematical Biosciences Institute at Ohio State University
(2003), at the Weizmann Institute of Science in Israel (2000), and a visiting associate at the California Institute of Technology (2000-2001). Dr. Aguda obtained his PhD in Chemistry
(Chemical Physics Program) from the University of Alberta in Canada (1986), and was a tenured faculty member of the Department of Chemistry & Biochemistry at Laurentian University in
Canada (1994-2002) before moving to Boston. Avner Friedman is a Distinguished Professor of Mathematics and Physical Sciences at the Ohio State University, where he also serves as the Director of the Mathematical Biosciences
Institute. He received his Ph.D. degree in 1956 from the Hebrew University.
He was Professor of Mathematics at Northwestern University (1962-1985), and a Duncan
Distinguished Professor of Mathematics at Purdue University (1985-1987).

Table of Contents

1 General introduction 1

1.1 Goals 1

1.2 Intracellular processes, cell states and cell fate: overview of the chapters 2

1.3 On mathematical modelling of biological phenomena 3

1.4 A brief note on the organization and use of the book 5

References 5

2 From molecules to a living cell 6

2.1 Cell compartments and organelles 6

2.2 The molecular machinery of gene expression 9

2.3 Molecular pathways and networks 12

2.4 The omics revolution 15

References & further readings 16

3 Mathematical and computational modelling tools 18

3.1 Chemical kinetics 18

3.2 Ordinary differential equations (ODEs) 22

3.2.1 Theorems on uniqueness of solutions 22

3.2.2 Vector fields, phase space, and trajectories 23

3.2.3 Stability of steady states 24

3.3 Phase portraits on the plane 25

3.4 Bifurcations 27

3.5 Bistability and hysteresis 29

3.6 Hopf bifurcation 30

3.7 Singular perturbations 32

3.8 Partial differential equations (PDEs) 33

3.8.1 Reaction-diffusion equations 33

3.8.2 Cauchy problem 34

3.8.3 Dirichlet, Neumann and third-boundary-value problems 35

3.9 Well posed and ill posed problems 36

3.10 Conservation laws 37

3.10.1 Conservation of mass equation 37

3.10.2 Method of characteristics 38

3.11 Stochastic simulations 40

3.12 Computer software platforms for cell modelling 41

References 42

Exercises 42

4 Gene-regulatory networks: from DNA to metabolites and back 44

4.1 Genome structure of Escherichia coli 44

4.2 The Trp operon 45

4.3 A model of the Trp operon 47

4.4 Roles of the negative feedbacks in the Trp operon 50

4.5 The lac operon 52

4.6 Experimental evidence and modelling of bistable behavior of the lac operon54

4.7 A reduced model derived from the detailed lac operon network 55

4.8 The challenge ahead: complexity of the global transcriptional network 61

References 62

Exercises 63

5 Control of DNA replication in a prokaryote 65

5.1 The cell cycle of E. coli 65

5.2 Overlapping cell cycles: coordinating growth and DNA replication 67

5.3 The oriC and the initiation of DNA replication 67

5.4 The initiation-titration-activation model of replication initiation 69

5.4.1 DnaA protein synthesis 70

5.4.2 DnaA binding to boxes and initiation of replication 71

5.4.3 Changing numbers of oriCs and dnaA boxes during chromosome replication 73

5.4.4 Death and birth of oriCs 74

5.4.5 Inactivation of dnaA-ATP 74

5.5 Model dynamics 74

5.6 Robustness of initiation control 75

References 77

Exercises 78

6 The eukaryotic cell-cycle engine 79

6.1 Physiology of the eukaryotic cell cycle 79

6.2 The biochemistry of the cell-cycle engine 80

6.3 Embryonic cell cycles 82

6.4 Control of MPF activity in embryonic cell cycles 85

6.5 Essential elements of the basic eukaryotic cell-cycle engine 87

6.6 Summary 93

References 95

Exercises 95

7 Cell-cycle control 96

7.1 Cell-cycle checkpoints 96

7.2 The restriction point 97

7.3 Modelling the restriction point 98

7.3.1 The G1-S regulatory network 98

7.3.2 A switching module 100

7.4 The G2 DNA damage checkpoint 101

7.5 The mitotic spindle checkpoint 104

References 106

Exercises 107

8 Cell death 108

8.1 Background on the biology of apoptosis 108

8.2 Intrinsic and extrinsic caspase pathways 109

8.3 A bistable model for caspase-3 activation 111

8.4 DISC formation and caspase-8 activation 115

8.5 Combined intrinsic and extrinsic apoptosis pathways 120

8.6 Summary and future modelling 122

References 124

Exercises 124

9 Cell differentiation 125

9.1 Cell differentiation in the hematopoietic system 126

9.2 Modelling the differentiation of Th lymphocytes 127

9.3 Cytokine memory in single cells 130

9.4 Population of differentiating Th lymphocytes 131

9.4.1 Equation for population density [Phi] 131

9.4.2 Determining the population density [Phi] 133

9.5 High-dimensional switches in cellular differentiation 134

9.6 Summary 136

References 137

Exercises 137

10 Cell aging and renewal 139

10.1 Cellular senescence and telomeres 139

10.2 Models of tissue aging and maintenance 140

10.2.1 The probabilistic model of Op den Buijs et al. 140

10.2.2 A continuum model 142

10.3 Asymmetric stem-cell division 145

10.4 Maintaining the stem-cell reservoir 148

10.4.1 The Roeder-Loeffler model 148

10.4.2 A deterministic model 151

References 153

Exercises 153

11 Multiscale modelling of cancer 155

11.1 Attributes of cancer 155

11.2 A multiscale model of avascular tumor growth 156

11.2.1 Cellular scale 157

11.2.2 Extracellular scale 158

11.2.3 Subcellular scale 159

11.3 A multiscale model of colorectal cancer 160

11.3.1 Gene level: a Boolean network 161

11.3.2 Cell level: a discrete cell-cycle model 163

11.3.3 Tissue level: colonies of cells and oxygen supply 164

11.4 Continuum models of solid tumor growth 167

11.4.1 Three types of cells 167

11.4.2 One type of cells 172

References 174

Exercises 174

Glossary 176

Index 181