Stochastic Modelling驱动的系统生物学：新发展与方法整合指南

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"《随机建模在系统生物学中的应用》第二版是CRC出版社Mathematical and Computational Biology Series的一部分，该系列旨在聚焦生物医学领域内数学与计算方法的最新进展，并全面总结这一学科的知识体系。该书的目标是促进生物科学、统计学、计算机科学的融合，通过发布各类教科书、参考文献和手册，满足学生、研究人员以及在基础生物学、生物工程、数学、统计学和计算机科学专业领域的专业人士的需求。同时，该系列特别强调实践性和实用性，鼓励书中包含具体案例分析、应用实例和编程技术的介绍。系列编委会由四位专家组成，分别是来自巴斯大学数学科学系的N.F. Britton，哈佛大学生物统计系的Xihong Lin，特拉维夫大学计算机科学学校的Hershel M. Safer，以及欧洲生物信息研究所的Maria Victoria Schneider。Mona Sin可能是另一位贡献者或顾问，但具体职责未在提供的信息中明确。本书涵盖了随机建模在系统生物学中的应用，这涉及到对生物系统的随机性、不确定性以及复杂动态过程的数学描述。它可能包括马尔可夫链、布朗运动、随机微分方程、概率论等统计模型的理论介绍，以及如何将这些模型应用于基因表达调控、细胞信号转导、疾病建模、生态学等多个生物学领域。此外，书中可能还会讨论如何利用现代软件工具和编程语言（如R、Python等）进行随机模拟和数据分析，帮助读者理解和解决实际生物问题。《随机建模在系统生物学中的应用》不仅提供了深入的理论知识，还提供了实用的工具和技术，使读者能够在这个快速发展的交叉学科中保持竞争力，并推动科学研究和实践的创新。"

xvi LIST OF FIGURES

7.13 Left: Close-up showing the time-evolution of the number of

molecules of P over a 10-second period. Right: Empirical PMF

for the number o f molecules of P at time t = 10 seconds, based on

10,000 ru ns. 215

7.14 Left: Empirical PMF for the number of molecule s of P at time

t = 10 seconds when k

is changed from 0.01 to 0.02, based

on 10,000 runs. Right: Empiric al PMF for the prior predictive

uncertainty regarding the observed value of P at tim e t = 10 based

on the prior distribution k

∼ U(0.005, 0 .03). 216

7.15 SBML-shorthand for the lac-operon model ( discrete stochastic

version). 218

7.16 A simulated realisation of the discrete stochastic dyn amics of the

lac-operon model for a perio d of 50 ,000 seconds. 219

8.1 An R function to implement the ﬁrst reaction method for a stochastic

Petri net representation of a coupled chemical reaction system. 223

8.2 An R function to implement the Poisson timestep method for a

stochastic Petri net repre sentation of a coupled chemical reaction

system. 228

8.3 An R function to integrate the CLE using an Euler method for a

stochastic Petri net repre sentation of a coupled chemical reaction

system. 232

8.4 An R function to integrate a multivariate diffusion process using a

simple Euler–Maruyama method. 235

8.5 Example showing how to use the fu nction StepSDE for the SDE

given in (8.4). 236

8.6 Figure showing realisation s of the SDE models fo r the immigration-

death proc ess discussed in Section 8.3 .4 incorporating different

combinations of intrinsic and extrinsic noise. 237

9.1 Plot showing the prio r and posterior for the Poisson rate example. 252

9.2 An R function to implement a Gibbs sampler for the simple normal

random sample model. 259

9.3 Example R c ode illustrating the use of the function normgibbs

from Figur e 9.2. 260

9.4 Figure showing the Gibbs sampler output resulting from running the

example code in Figure 9.3. 261

9.5 An R function to implement a Metropolis sam pler for a standa rd

normal rando m quantity based o n U (−α, α) in novations. 268

9.6 Output from the Metropolis sam pler given in Figure 9.5. 269

10.1 An R function to c reate a function closure for margin al likelihood

estimation using a bootstrap particle ﬁlter. 296

10.2 An R session showing how to use the function pfMLLik from

Figure 10.1. 297

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