Stochastic modelling for systems biology:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press, Taylor & Francis
2012
|
| Edition: | 2. ed. |
| Series: | Chapman & Hall, CRC mathematical and computational biology series
A Chapman & Hall book |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XXVII, 335 S. graph. Darst. |
| ISBN: | 9781439837726 1439837724 |
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MARC
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| 250 | |a 2. ed. | ||
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| 650 | 4 | |a Models, Statistical | |
| 650 | 4 | |a Stochastic Processes | |
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Record in the Search Index
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| adam_text | Contents
List of tables
xi
List of figures
xiii
Author biography
xix
Acknowledgements
xxi
Preface to the second edition
xxiii
Preface to the first edition
xxv
I Modelling and networks
1
1
Introduction to biological modelling
3
1.1
What is modelling?
3
1.2
Aims of modelling
4
1.3
Why is stochastic modelling necessary?
4
1.4
Chemical reactions
9
1.5
Modelling genetic and biochemical networks
10
1.6
Modelling higher-level systems
18
1.7
Exercises
20
1.8
Further reading
20
2
Representation of biochemical networks
21
2.1
Coupled chemical reactions
21
2.2
Graphical representations
21
2.3
Petri
nets
24
2.4
Stochastic process algebras
34
2.5
Systems Biology Markup Language (SBML)
36
2.6
SBML-shorthand
41
2.7
Exercises
47
2.8
Further reading
48
viii CONTENTS
II
Stochastic
processes
and simulation
49
3
Probability models
51
3.1
Probability
51
3.2
Discrete probability models
62
3.3
The discrete uniform distribution
70
3.4
The binomial distribution
71
3.5
The geometric distribution
72
3.6
The
Poisson
distribution
74
3.7
Continuous probability models
77
3.8
The uniform distribution
82
3.9
The exponential distribution
85
3.10
The normal/Gaussian distribution
89
3.11
The gamma distribution
93
3.12
Quantifying noise
96
3.13
Exercises
97
3.14
Further reading
98
4
Stochastic simulation
99
4.1
Introduction
99
4.2
Monte Carlo integration
99
4.3
Uniform random number generation
100
4.4
Transformation methods
101
4.5
Lookup methods
106
4.6
Rejection samplers
107
4.7
Importance resampling
110
4.8
The
Poisson
process 111
4.9
Using the statistical programming language,
R
112
4.10
Analysis of simulation output
118
4.11
Exercises
120
4.12
Further reading
122
5
Markov processes
123
5.1
Introduction
123
5.2
Finite discrete time Markov chains
123
5.3
Markov chains with continuous state-space
130
5.4
Markov chains in continuous time
137
5.5
Diffusion processes
152
5.6
Exercises
166
5.7
Further reading
168
HI Stochastic chemical kinetics
169
6
Chemical and biochemical kinetics
171
6.1
Classical continuous deterministic chemical kinetics
171
CONTENTS ix
6.2
Molecular
approach to kinetics
178
6.3
Mass-action stochastic kinetics
180
6.4
The Gillespie algorithm
182
6.5
Stochastic Petri nets (SPNs)
183
6.6
Structuring stochastic simulation codes
186
6.7
Rate constant conversion
189
6.8
Kolmogorov s equations and other analytic representations
194
6.9
Software for simulating stochastic kinetic networks
199
6.10
Exercises
200
6.11
Further reading
200
7
Case studies
203
7.1
Introduction
203
7.2
Dimerisation kinetics
203
7.3
Michaelis-Menten enzyme kinetics
208
7.4
An auto-regulatory genetic network
212
7.5
The lac
operan
217
7.6
Exercises
219
7.7
Further reading
220
8
Beyond the Gillespie algorithm
221
8.1
Introduction
221
8.2
Exact simulation methods
221
8.3
Approximate simulation strategies
226
8.4
Hybrid simulation strategies
239
8.5
Exercises
245
8.6
Further reading
245
IV
Bayesian inference
247
9
Bayesian inference and MCMC
249
9.1
Likelihood and Bayesian inference
249
9.2
The Gibbs sampler
254
9.3
The Metropolis-Hastings algorithm
264
9.4
Hybrid MCMC schemes
268
9.5
Metropolis-Hastings algorithms for Bayesian inference
269
9.6
Bayesian inference for latent variable models
270
9.7
Alternatives to MCMC
274
9.8
Exercises
275
9.9
Further reading
275
10
Inference for stochastic kinetic models
277
10.1
Introduction
277
10.2
Inference given complete data
278
10.3
Discrete-time observations of the system state
281
10.4 Diffusion
approximations
for inference
288
10.5
Likelihood-free methods
292
10.6
Network inference and model comparison
308
10.7
Exercises
309
10.8
Further reading
310
11
Conclusions
311
Appendix A SBML Models
315
A.I Auto-regulatory network
315
A.2
Lotka-
Volterra reaction system
318
A.3 Dimerisation-kinetics model
319
References
323
Index
331
Praise for the First Edition
...well suited as an in-depth introduction into stochastic chemical simulation,
both for self-study or as a course text...
—Biomedicai Engineering
Online, December
2006
Since the first edition of Stochastic Modelling for Systems Biology, there have
been many interesting developments in the use of likelihood-free methods
of Bayesian inference for complex stochastic models. Re-written to reflect this
modern perspective, this second edition covers everything necessary for a good
appreciation of stochastic kinetic modelling of biological networks in the systems
biology context.
Keeping with the spirit of the first edition, all of the new theory is presented in a
very informal and intuitive manner, keeping the text as accessible as possible to
the widest possible readership.
New in the Second Edition
•
All examples have been updated to Systems Biology Markup Language
Level
3
•
All code relating to simulation, analysis, and inference for stochastic kinetic
■
models has been rewritten and restructured in a more modular way
•
An ancillary website provides links, resources, errata, and up-to-date
information on installation and use of the associated
R
package
•
More background material on the theory of Markov processes and
stochastic differential equations, providing more substance for
mathematically inclined readers
•
Discussion of some of the more advanced concepts relating to stochastic
kinetic models, such as random time change representations, Kolmogorov
equations, Fokker-Planck equations and the linear noise approximation
•
Simple modelling of extrinsic and intrinsic noise
An effective introduction to the area of stochastic modelling in computational
systems biology, this new edition adds additional mathematical detail and
computational methods which will provide a stronger foundation for the
development of more advanced courses in stochastic biological modelling.
|
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| spelling | Wilkinson, Darren James Verfasser (DE-588)171711181 aut Stochastic modelling for systems biology Darren J. Wilkinson 2. ed. Boca Raton, Fla. [u.a.] CRC Press, Taylor & Francis 2012 XXVII, 335 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall, CRC mathematical and computational biology series A Chapman & Hall book Mathematisches Modell Biological systems Mathematical models Kinetics Models, Biological Models, Statistical Stochastic Processes Systems Biology methods Systems biology Systembiologie (DE-588)4809615-5 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 s Systembiologie (DE-588)4809615-5 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024440031&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024440031&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Wilkinson, Darren James Stochastic modelling for systems biology Mathematisches Modell Biological systems Mathematical models Kinetics Models, Biological Models, Statistical Stochastic Processes Systems Biology methods Systems biology Systembiologie (DE-588)4809615-5 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| subject_GND | (DE-588)4809615-5 (DE-588)4057633-4 |
| title | Stochastic modelling for systems biology |
| title_auth | Stochastic modelling for systems biology |
| title_exact_search | Stochastic modelling for systems biology |
| title_full | Stochastic modelling for systems biology Darren J. Wilkinson |
| title_fullStr | Stochastic modelling for systems biology Darren J. Wilkinson |
| title_full_unstemmed | Stochastic modelling for systems biology Darren J. Wilkinson |
| title_short | Stochastic modelling for systems biology |
| title_sort | stochastic modelling for systems biology |
| topic | Mathematisches Modell Biological systems Mathematical models Kinetics Models, Biological Models, Statistical Stochastic Processes Systems Biology methods Systems biology Systembiologie (DE-588)4809615-5 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| topic_facet | Mathematisches Modell Biological systems Mathematical models Kinetics Models, Biological Models, Statistical Stochastic Processes Systems Biology methods Systems biology Systembiologie Stochastisches Modell |
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