Systems biology : mathematical modeling and model analysis

379 Pages·2014·3.138 MB·English

by  Kremling, Andreas

Biomedical Engineering
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Y
“Systems Biology: Mathematical Modeling and Model Analysis is S
SYSTEMS
a rich resource of mathematical methods and approaches that can be
utilized to analyze and understand biological systems. It will be particularly T
attractive to engineers and mathematicians who want to learn the basics
E
of modern biology in a condensed fashion and then apply the tools of
their trades to relevant biological questions. … Systems Biology devotes BIOLOGY
M
a good portion of the material to state-of-the-art model diagnostics and
engineering techniques, such as linear systems analysis and control
theory, which so far are rarely found in systems biology texts and are S
therefore a welcome addition to the repertoire of textbook literature.
… Laudably, all topics are illustrated with step-by-step examples, and Mathematical Modeling
many of them are reinforced with exercises.” B
—Eberhard Voit, Georgia Institute of Technology and Model Analysis
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“… a meticulous and far-reaching treatment of this critically important
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subject. … comprehensive without sacrificing depth … an exhaustive
survey of modeling approaches. Each chapter is thoughtfully crafted to
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draw in novices to the field while still engaging to experts. Additionally, a
number of well-designed exercises complement each chapter.”
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—Markus Covert, Stanford University
Drawing on the latest research in the field, this book presents many G
methods for modeling and analyzing biological systems, in particular
cellular systems. It shows how to use predictive mathematical models Y
to acquire and analyze knowledge about cellular systems. The text also
explores how the models are systematically applied in biotechnology.
Features
• Presents methods for the analysis of motifs, modules, and large-
scale networks
• Explains how deterministic models and graphs can be used in the
analysis and verification of networks K
• Shows how to model the complete synthesis of macromolecules and r
e
compare measured data m
• Uses the lactose uptake system to demonstrate various modeling
l
i
and analysis tools n
• Contains many analytical and numerical examples g
Andreas Kremling
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K16367_Cover.indd 1 9/23/13 9:27 AM
SYSTEMS
BIOLOGY
Mathematical Modeling
and Model Analysis
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SYSTEMS
BIOLOGY
Mathematical Modeling
and Model Analysis
Andreas Kremling
Technische Universität München
Germany
Originally published in the German language by Vieweg + Teubner, 65189 Wiesbaden, Germany as
Kremling, Andreas: Kompendium Systembiologie, Mathematische Modellierung und Modellanalyse,
©Vieweg+Teubner-Springer Fachmedien Wiesbaden GmbH 2012, Springer Fachmedien is part of Springer
Science + Business Media.
CRC Press
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© 2014 by Taylor & Francis Group, LLC
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Version Date: 20130910
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Contents
Preface xiii
About the Author xv
I Fundamentals 1
1 Introduction 3
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Biological Basics 11
2.1 The Cell — an Introduction . . . . . . . . . . . . . . . . . . 11
2.2 Cell Division and Growth . . . . . . . . . . . . . . . . . . . . 12
2.3 Basics of Metabolism . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 Energy generation . . . . . . . . . . . . . . . . . . . . 14
2.3.2 Metabolic pathways . . . . . . . . . . . . . . . . . . . 16
2.3.3 Enzymes. . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.4 Degradation of carbohydrates . . . . . . . . . . . . . . 17
2.3.5 Respiratory chain. . . . . . . . . . . . . . . . . . . . . 19
2.3.6 Mass transport into the cell . . . . . . . . . . . . . . . 19
2.4 Replication, Transcription and Translation . . . . . . . . . . 22
2.4.1 Regulation of enzyme activity and enzyme synthesis . 24
2.4.2 Signal transduction. . . . . . . . . . . . . . . . . . . . 27
2.4.3 Cell-cell communication . . . . . . . . . . . . . . . . . 29
3 Fundamentals of Mathematical Modeling 31
3.1 Definition — Overview of Different Model Classes . . . . . . 31
3.1.1 System . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1.3 Process of modeling . . . . . . . . . . . . . . . . . . . 34
3.2 Basics of Reaction Engineering . . . . . . . . . . . . . . . . . 36
3.3 Stochastic Description . . . . . . . . . . . . . . . . . . . . . . 40
3.3.1 Stochastic simulation using the Gillespie algorithm . 45
3.4 Deterministic Modeling . . . . . . . . . . . . . . . . . . . . . 50
3.4.1 Relationship between specific growth rate µ and
rates r0 . . . . . . . . . . . . . . . . . . . . . . . . . . 54
ai
3.4.2 Intracellular reaction networks . . . . . . . . . . . . . 56
vii
viii Contents
3.5 Qualitative Modeling and Analysis . . . . . . . . . . . . . . . 59
3.5.1 Cycles, loops and elementary modes . . . . . . . . . . 62
3.6 ModelingontheLevelofSingleCells—thePopulationBalance 63
3.7 Data Driven Modeling . . . . . . . . . . . . . . . . . . . . . 67
3.8 Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . 68
3.8.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . 68
3.8.2 Relation between ∆G and flux distributions . . . . . . 72
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4 Model Calibration and Experimental Design 87
4.1 Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.1.1 Least square method & maximum likelihood estimation 87
4.1.2 Linear models . . . . . . . . . . . . . . . . . . . . . . . 89
4.2 Model and Parameter Accuracy . . . . . . . . . . . . . . . . 90
4.2.1 Nonlinear models . . . . . . . . . . . . . . . . . . . . . 96
4.2.1.1 Linearization . . . . . . . . . . . . . . . . . . 97
4.2.1.2 Bootstrapping . . . . . . . . . . . . . . . . . 97
4.2.2 Experimental design . . . . . . . . . . . . . . . . . . . 99
4.3 Dynamic Systems . . . . . . . . . . . . . . . . . . . . . . . . 101
4.4 Identifiability of Dynamic Systems . . . . . . . . . . . . . . . 103
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
II Modeling of Cellular Processes 109
5 Enzymatic Conversion 111
5.1 Fundamentals of Enzyme Kinetics . . . . . . . . . . . . . . . 111
5.2 Models for Allosteric Enzymes . . . . . . . . . . . . . . . . . 115
5.3 Influence of Effectors . . . . . . . . . . . . . . . . . . . . . . 119
5.3.1 Competitive inhibition . . . . . . . . . . . . . . . . . . 119
5.3.2 Essential activation. . . . . . . . . . . . . . . . . . . . 120
5.4 The Hill Equation . . . . . . . . . . . . . . . . . . . . . . . . 122
5.5 Multi-substrate Kinetics . . . . . . . . . . . . . . . . . . . . 124
5.6 Transport Processes . . . . . . . . . . . . . . . . . . . . . . . 127
5.7 The Wegscheider Condition . . . . . . . . . . . . . . . . . . . 128
5.8 Alternative Kinetic Approaches . . . . . . . . . . . . . . . . 130
5.9 Thermodynamic of a Single Reaction . . . . . . . . . . . . . 132
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6 Polymerization Processes 139
6.1 Macroscopic View . . . . . . . . . . . . . . . . . . . . . . . . 139
6.2 Microscopic View . . . . . . . . . . . . . . . . . . . . . . . . 140
6.2.1 Calculation of the transcription rate . . . . . . . . . . 141
6.2.2 Calculation of the translation rate . . . . . . . . . . . 143
Contents ix
6.2.3 Combination of equations . . . . . . . . . . . . . . . . 145
6.3 Influence of Regulatory Proteins (Transcription Factors,
Repressors) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.3.1 Induction model . . . . . . . . . . . . . . . . . . . . . 146
6.3.2 Repression model . . . . . . . . . . . . . . . . . . . . . 148
6.3.3 Extended induction model . . . . . . . . . . . . . . . . 148
6.4 Interaction of Several Regulators . . . . . . . . . . . . . . . . 151
6.4.1 AND – OR gates . . . . . . . . . . . . . . . . . . . . . 151
6.4.2 Hierarchal approach . . . . . . . . . . . . . . . . . . . 152
6.5 Replication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
7 Signal Transduction and Genetically Regulated Systems 163
7.1 Simple Schemes of Signal Transduction . . . . . . . . . . . . 163
7.2 Oscillating Systems . . . . . . . . . . . . . . . . . . . . . . . 171
7.3 Genetically Regulated Networks . . . . . . . . . . . . . . . . 173
7.3.1 Inputs/outputs . . . . . . . . . . . . . . . . . . . . . . 173
7.3.2 Negative and positive feedback reactions . . . . . . . . 174
7.3.3 Toggle switch . . . . . . . . . . . . . . . . . . . . . . . 177
7.4 Spatial Gradients by Signal Transduction . . . . . . . . . . 180
7.5 Analysis of Signaling Pathways by Heinrich . . . . . . . . . 183
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
III Analysis of Modules and Motifs 189
8 General Methods of Model Analysis 191
8.1 Analysis of Time Hierarchies . . . . . . . . . . . . . . . . . . 191
8.1.1 Linear systems . . . . . . . . . . . . . . . . . . . . . . 192
8.1.2 Classification of fast and slow reactions . . . . . . . . 197
8.1.3 Complete procedure for model reduction . . . . . . . . 199
8.1.4 Singular perturbation theory . . . . . . . . . . . . . . 201
8.2 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . 204
8.2.1 Definition of the parametric sensitivity w . . . . . . 205
ij
8.2.2 Sensitivity analysis using Hearne’s method . . . . . . 207
8.2.3 Sensitivity matrix . . . . . . . . . . . . . . . . . . . . 209
8.2.4 Sensitivities for dynamic systems . . . . . . . . . . . . 210
8.3 Robustness in Stoichiometric Networks . . . . . . . . . . . . 211
8.4 Metabolic Control Analysis . . . . . . . . . . . . . . . . . . . 216
8.4.1 Control coefficients . . . . . . . . . . . . . . . . . . . . 216
8.4.2 Summation and connectivity theorems for linear
pathways . . . . . . . . . . . . . . . . . . . . . . . . . 218
8.4.3 General summation and connectivity theorems . . . . 220
8.5 Biochemical Systems Theory . . . . . . . . . . . . . . . . . . 222