1. Introduction ................................................ 1
The increasing role of computational analysis in biology .... 1
What this book tries to achieve ............................. 3
Who should read this book ................................... 4
How this book is organized .................................. 6
Acknowledgments ............................................. 7
Feedback .................................................... 7
2. What Is a System, and Why Should We Care? ................... 9
Linearity versus nonlinearity ............................... 9
Nonlinear systems .......................................... 13
Nonlinear systems are the norm, not the exception,
in biology ................................................. 14
3. What Models Can and Cannot Predict ......................... 17
Interpolation versus extrapolation ......................... 17
Iterative model refinement by experimental falsification
of model extrapolations .................................... 21
The importance of remembering the limitations of data ...... 22
Cross-validation ........................................... 23
Function approximation versus classification ............... 25
Appendix: A model of biphasic kinetics ..................... 26
4. Why Make Computational Models of Gene Regulatory
Networks? .................................................. 29
What is a model? ........................................... 29
What is the goal of GRN modeling? .......................... 31
Why make computational models of GRNs? ..................... 32
Serendipitous benefits of computational GRN modeling ....... 33
Some pitfalls of modeling .................................. 34
Good practice guidelines ................................... 35
Appendix: Working definitions of 'genes' and
'Gene Regulatory Networks' ................................. 36
5. Graphical Representations of Gene Regulatory Networks ...... 39
Desirable features of computational GRN representations .... 39
Graphical representation of GRN activity in multiple
compartments ............................................... 43
Computational network building, editing, and topological
analysis ................................................... 46
6. Implicit Modeling via Interaction Network Maps ............. 49
Data interpretation through implicit modeling .............. 49
Global molecular interaction maps — Guilt by association ... 50
Why do we need global molecular interaction maps? .......... 53
Example uses of interaction maps as predictive models ...... 54
7. The Biochemical Basis of Gene Regulation ................... 61
The probability of a chemical reaction ..................... 61
A simple method for modeling stochastic molecular
reaction events ............................................ 63
Chemical kinetics in cells are different from in vitro
kinetics ................................................... 65
Compared to transcription, most signaling events are
instantaneous .............................................. 66
How transcription factors find their targets on DNA ........ 67
DNA bending and looping by transcription factors ........... 70
Spatial localization: multi-compartment modeling ........... 71
Morphogen gradients ........................................ 72
Appendix: Stochastic simulation using Gillespie's
algorithm .................................................. 73
8. A Single-Cell Model of Transcriptional Regulation .......... 77
Modeling strategy .......................................... 77
Modeling framework and notation ............................ 78
A single-cell stochastic model of transcriptional
regulation ................................................. 79
Recruitment of RNA polymerase II complex and
transcription initiation ................................... 82
Appendix: Simulation of the distribution of gene
expression levels in a population of genetically
identical cells ............................................ 89
9. Simplified Models: Mass-Action Kinetics .................... 99
Why model with mass-action kinetics? ....................... 99
The fundamentals of Ordinary Differential Equations
(ODEs) .................................................... 100
Steady states ............................................. 103
Average promoter occupancy by a single transcription
factor .................................................... 104
Promoter occupancy by two or more factors ................. 105
A two-step kinetic model of mRNA and protein
concentration ............................................. 107
mRNA and protein levels at steady state ................... 109
Promoter occupancy as a function of regulator
concentration ............................................. 109
Analytical solution of mRNA and protein time-course
kinetics for genes regulated by posttranscriptionally
activated factors ......................................... 110
The time-course behavior of genes regulated by other
genes ..................................................... 112
The Boolean approximation to transcription kinetics ....... 114
In the absence of feedback, transcription factors
in animals do not reach steady state ...................... 115
Positive and negative feedback loops can drive
gene expression to fixed steady-state levels .............. 117
Gene expression as a function of DNA-bound regulator
activity .................................................. 117
Appendix A: ODE modeling with Berkeley Madonna ............ 119
Appendix B: Derivation of mathematical expressions
for mRNA and protein levels as a function of changing
occupancy levels .......................................... 120
Appendix C: Time to steady state for genes not
regulated by feedback ..................................... 122
10. Simplified Models: Boolean and Multi-valued Logic ......... 123
Background ................................................ 123
Discrete-variable piecewise linear ODEs ................... 125
Multi-valued logic networks ............................... 129
Implicit-time logic networks (a.k.a. kinetic logic) ....... 132
Learning discrete logic models directly from data ......... 135
Linear ODE models of transcriptional regulation ........... 136
Process algebras .......................................... 139
Appendix: Logic simulation model files .................... 140
11. Simplified Models: Bayesian Networks ...................... 143
A preview ................................................. 145
Probabilities: A brief review ............................. 146
Continuous and discrete probability distributions ......... 148
The theoretical foundation of BNs: Conditional
probabilities ............................................. 149
Making predictions with a given BN ........................ 151
Modeling networks with feedback as Dynamic Bayesian
Networks .................................................. 154
Constructing BNs directly from data ....................... 156
Causality in BNs .......................................... 161
Computational efficiency in BNs ........................... 162
Current limitations of Bayesian Networks .................. 163
Resources for BNs ......................................... 164
Appendix: Exploring BNs with Hugin ........................ 165
12. The Relationship between Logic and Bayesian Networks ...... 167
Noisy logic networks ...................................... 167
Probabilistic Boolean Networks ............................ 169
Learning PBNs from data ................................... 171
Some useful properties of PBNs ............................ 172
13. Network Inference in Practice ............................. 175
A summary of the general approach to network
reconstruction ............................................ 175
Learning logic models from gene expression data alone ..... 178
Learning continuous-valued network models from
expression data ........................................... 182
Network structure building by data integration ............ 184
14. Searching DNA Sequences for Transcription Factor
Binding Sites ............................................. 189
Consensus sequences ....................................... 189
Position Weight Matrices .................................. 191
Visualizing PWMs with sequence logos ...................... 194
A taxonomy of TFBS prediction algorithms .................. 196
Resources for TFBS prediction ............................. 201
Some good practice guidelines ............................. 202
Measuring the performance of binding site prediction
algorithms ................................................ 204
Extracting predicted TFBSs from ChIP-chip data ............ 206
Appendix: DNA sequence processing ......................... 211
15. Model Selection Theory .................................... 213
Fitting error versus generalization error ................. 213
Model misspecification .................................... 214
Model invalidation ........................................ 215
Computational Modeling of Gene RegulatoryNetworks —
A Primer Model selection criteria ......................... 216
How to calculate the log-likelihood value for a
regression model .......................................... 219
Parameter counts of common modeling frameworks ............ 221
The effect of function complexity ......................... 222
Multi-model averaging ..................................... 223
Other approaches to model refinement ...................... 224
16. Simplified Models — GRN State Signatures in Data .......... 225
Principal Component Analysis .............................. 226
Nonlinear PCA ............................................. 232
Multi-dimensional Scaling (MDS) ........................... 235
Partial Least Squares (PLS) ............................... 237
The implicit approach to pattern detection in complex
data ...................................................... 237
Appendix: Step-by-step example PCA transformations ........ 239
17. System Dynamics ........................................... 243
Transients and steady states .............................. 243
Phase portraits ........................................... 245
Parameter analysis ........................................ 249
Parameter optimization and the evolution of
optimal dynamics .......................................... 252
Bistability through mutual inhibition ..................... 254
Negative auto-regulation .................................. 255
Mixed positive and negative feedback ...................... 258
Appendix: Analyzing feedback dynamics ..................... 260
18. Robustness Analysis ....................................... 265
Robustness and sensitivity ................................ 265
Perturbations in system state variables versus
perturbations in system parameters ........................ 266
Failure tolerance versus graceful degradation ............. 266
Global and local perspectives ............................. 268
Local sensitivity analysis ................................ 268
Global sensitivity analysis ............................... 270
The role of network topology in robustness ................ 273
Evolution of robustness ................................... 275
Robustness to transcriptional noise ....................... 277
Context and completeness of models ........................ 277
19. GRN Modules and Building Blocks ........................... 279
Hierarchical modularity in engineered systems ............. 279
Organizational principles in GRNs ......................... 281
Network motifs in GRNs .................................... 283
Functional building blocks ................................ 288
Using network motifs and functional building blocks
to decode GRNs ............................................ 290
20. Notes on Data Processing for GRN Modeling ................. 293
What type of data is best for modeling? ................... 293
Beware of the side-effects of the methods used to
collect data .............................................. 294
How many time points are sufficient for modeling
dynamics? ................................................. 295
In vivo versus ex vivo and in vitro data .................. 296
Using meaningful units to quantify data ................... 297
Misinterpreting data ...................................... 297
21. Applications of Computational GRN Modeling ................ 299
Overview .................................................. 299
GRN modeling challenges in medical systems biology ........ 301
Modeling hierarchical, distributed processing in the
immune system ............................................. 305
22. Quo Vadis ................................................ 311
The US$ 1000 genome and its challenges .................... 311
Single-cell biology ....................................... 313
Multi-scale modeling ...................................... 315
Software engineering challenges ........................... 316
Becoming bilingual ........................................ 318
Molecular biology is still in the discovery phase ......... 319
Index ......................................................... 321
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