Models of Cellular Regulation

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.

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).

General introduction	p. 1
Goals	p. 1
Intracellular processes, cell states and cell fate: overview of the chapters	p. 2
On mathematical modelling of biological phenomena	p. 3
A brief note on the organization and use of the book	p. 5
References	p. 5
From molecules to a living cell	p. 6
Cell compartments and organelles	p. 6
The molecular machinery of gene expression	p. 9
Molecular pathways and networks	p. 12
The omics revolution	p. 15
References & further readings	p. 16
Mathematical and computational modelling tools	p. 18
Chemical kinetics	p. 18
Ordinary differential equations (ODEs)	p. 22
Theorems on uniqueness of solutions	p. 22
Vector fields, phase space, and trajectories	p. 23
Stability of steady states	p. 24
Phase portraits on the plane	p. 25
Bifurcations	p. 27
Bistability and hysteresis	p. 29
Hopf bifurcation	p. 30
Singular perturbations	p. 32
Partial differential equations (PDEs)	p. 33
Reaction-diffusion equations	p. 33
Cauchy problem	p. 34
Dirichlet, Neumann and third-boundary-value problems	p. 35
Well posed and ill posed problems	p. 36
Conservation laws	p. 37
Conservation of mass equation	p. 37
Method of characteristics	p. 38
Stochastic simulations	p. 40
Computer software platforms for cell modelling	p. 41
References	p. 42
Exercises	p. 42
Gene-regulatory networks: from DNA to metabolites and back	p. 44
Genome structure of Escherichia coli	p. 44
The Trp operon	p. 45
A model of the Trp operon	p. 47
Roles of the negative feedbacks in the Trp operon	p. 50
The lac operon	p. 52
Experimental evidence and modelling of bistable behavior of the lac operon	p. 54
A reduced model derived from the detailed lac operon network	p. 55
The challenge ahead: complexity of the global transcriptional network	p. 61
References	p. 62
Exercises	p. 63
Control of DNA replication in a prokaryote	p. 65
The cell cycle of E. coli	p. 65
Overlapping cell cycles: coordinating growth and DNA replication	p. 67
The oriC and the initiation of DNA replication	p. 67
The initiation-titration-activation model of replication initiation	p. 69
DnaA protein synthesis	p. 70
DnaA binding to boxes and initiation of replication	p. 71
Changing numbers of oriCs and dnaA boxes during chromosome replication	p. 73
Death and birth of oriCs	p. 74
Inactivation of dnaA-ATP	p. 74
Model dynamics	p. 74
Robustness of initiation control	p. 75
References	p. 77
Exercises	p. 78
The eukaryotic cell-cycle engine	p. 79
Physiology of the eukaryotic cell cycle	p. 79
The biochemistry of the cell-cycle engine	p. 80
Embryonic cell cycles	p. 82
Control of MPF activity in embryonic cell cycles	p. 85
Essential elements of the basic eukaryotic cell-cycle engine	p. 87
Summary	p. 93
References	p. 95
Exercises	p. 95
Cell-cycle control	p. 96
Cell-cycle checkpoints	p. 96
The restriction point	p. 97
Modelling the restriction point	p. 98
The G1-S regulatory network	p. 98
A switching module	p. 100
The G2 DNA damage checkpoint	p. 101
The mitotic spindle checkpoint	p. 104
References	p. 106
Exercises	p. 107
Cell death	p. 108
Background on the biology of apoptosis	p. 108
Intrinsic and extrinsic caspase pathways	p. 109
A bistable model for caspase-3 activation	p. 111
DISC formation and caspase-8 activation	p. 115
Combined intrinsic and extrinsic apoptosis pathways	p. 120
Summary and future modelling	p. 122
References	p. 124
Exercises	p. 124
Cell differentiation	p. 125
Cell differentiation in the hematopoietic system	p. 126
Modelling the differentiation of Th lymphocytes	p. 127
Cytokine memory in single cells	p. 130
Population of differentiating Th lymphocytes	p. 131
Equation for population density [Phi]	p. 131
Determining the population density [Phi]	p. 133
High-dimensional switches in cellular differentiation	p. 134
Summary	p. 136
References	p. 137
Exercises	p. 137
Cell aging and renewal	p. 139
Cellular senescence and telomeres	p. 139
Models of tissue aging and maintenance	p. 140
The probabilistic model of Op den Buijs et al.	p. 140
A continuum model	p. 142
Asymmetric stem-cell division	p. 145
Maintaining the stem-cell reservoir	p. 148
The Roeder-Loeffler model	p. 148
A deterministic model	p. 151
References	p. 153
Exercises	p. 153
Multiscale modelling of cancer	p. 155
Attributes of cancer	p. 155
A multiscale model of avascular tumor growth	p. 156
Cellular scale	p. 157
Extracellular scale	p. 158
Subcellular scale	p. 159
A multiscale model of colorectal cancer	p. 160
Gene level: a Boolean network	p. 161
Cell level: a discrete cell-cycle model	p. 163
Tissue level: colonies of cells and oxygen supply	p. 164
Continuum models of solid tumor growth	p. 167
Three types of cells	p. 167
One type of cells	p. 172
References	p. 174
Exercises	p. 174
Glossary	p. 176
Index	p. 181
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Models of Cellular Regulation

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