Stochastic processes in cell biology. Volume I

Preface to 2nd edition
Preface to 1st edition
Organization of volumes I and II
	Volume I: Molecular processes
	Volume II: Cellular processes
Contents
Boxes
1 Introduction
	1.1 Stochastic processes in living cells
	1.2 A brief introduction to probability theory
		1.2.1 Random variables
		1.2.2 Conditional expectations
		1.2.3 Adding and transforming random variables
		1.2.4 Moments and cumulants
	1.3 Equilibrium systems
		1.3.1 Boltzmann–Gibbs distribution
		1.3.2 Free energy and entropy
		1.3.3 Chemical potential.
		1.3.4 Law of mass action and chemical kinetics
		1.3.5 Michaelis–Menten kinetics
	1.4 Exercises
2 Random walks and Brownian motion
	2.1 Random walks and diffusion
		2.1.1 Discrete-time random walks
		2.1.2 Diffusion as the continuum limit of a random walk
	2.2 Stochastic differential equations and Ito calculus
		2.2.1 Wiener process
		2.2.2 Continuous Markov processes
		2.2.3 Stochastic integrals and Ito calculus
		2.2.4 Ornstein–Uhlenbeck process (OU)
	2.3 The Fokker–Planck equation
		2.3.1 1D Fokker–Planck equation
		2.3.2 Higher dimensions
		2.3.3 Boundary value problems
		2.3.4 FP equation and symmetrization
		2.3.5 Multiplicative noise: Ito versus Stratonovich
	2.4 First passage time problems
		2.4.1 Mean first passage time on an interval
		2.4.2 Noise-induced transitions in bistable systems
		2.4.3 Multiplicative noise and the quasi-potential
	2.5 Simulation of stochastic differential equations
	2.6 Exercises
3 Protein receptors and ion channels
	3.1 Types of receptors
	3.2 Cooperative binding
		3.2.1 Monod-Wyman-Changeux (MWC) model
		3.2.2 Ising model of cooperative binding
	3.3 Markov chain models of ion channel kinetics
		3.3.1 Single ion channel models
		3.3.2 Birth–death master equation for an ensemble of ion channels
		3.3.3 First passage times for a birth-death process
	3.4 Voltage-gated ion channels
		3.4.1 Conductance-based model of a neuron
		3.4.2 Stochastic Morris–Lecar model
	3.5 Stochastic models of Ca2+ release
		3.5.1 Stochastic model of Ca2+ puffs in a cluster of IP3Rs
		3.5.2 Stochastic model of Ca2+ sparks in cardiac myocytes
	3.6 Markov chains
		3.6.1 Master equation of a continuous-time Markov chain
		3.6.2 Poisson processes
	3.7 Exercises
4 Molecular motors
	4.1 Simple model of actin polymerization
	4.2 Microtubule catastrophes
		4.2.1 Dogterom–Leibler model
		4.2.2 First passage times
		4.2.3 Model of hydrolysis and caps
	4.3 Brownian motion in a periodic potential
		4.3.1 Polymerization ratchet
		4.3.2 Translocation ratchet
	4.4 Brownian ratchet model of a processive molecular motor
	4.5 Collective effects of multiple molecular motors
		4.5.1 Cooperative cargo transport by multiple motors
		4.5.2 Tug-of-war model
		4.5.3 Rigidly linked molecular motors
	4.6 Exercises
5 Stochastic gene expression and regulatory networks
	5.1 Gene regulatory networks
		5.1.1 Autoregulatory gene network
		5.1.2 Mutual repressor model (toggle switch)
		5.1.3 Repressilator and degrade-and-fire models of a genetic oscillator
		5.1.4 Activator-repressor relaxation oscillator
	5.2 Molecular noise and the chemical master equation
		5.2.1 Master equation for chemical reaction networks
		5.2.2 System-size expansion of chemical master equation
		5.2.3 The stochastic simulation algorithm (SSA)
		5.2.4 Translational protein bursting
		5.2.5 Noise-induced switching
		5.2.6 Noise-induced oscillations
	5.3 Promoter noise and stochastic hybrid systems
		5.3.1 Two-state gene network with promoter and protein noise
		5.3.2 Two-state gene network as a stochastic hybrid system
		5.3.3 Noisy mutual repressor model
	5.4 Transcriptional bursting and queuing theory
	5.5 Time-limiting steps in gene regulation
		5.5.1 Kinetic proofreading in protein synthesis
		5.5.2 Fluctuations in DNA elongation times
	5.6 Epigenetics
		5.6.1 Regulatory network of λ phage lysogeny
		5.6.2 Two-state epigenetic model of nucleosome modification
	5.7 Morphogen gradients and gene expression
	5.8 Exercises
6 Diffusive transport
	6.1 Anomalous diffusion
		6.1.1 Molecular crowding, diffusion–trapping, and long-time correlations
		6.1.2 Continuous-time random walks
		6.1.3 Molecular crowding and homogenization theory
		6.1.4 Diffusion in the plasma membrane
	6.2 Diffusion–trapping model of protein receptor trafficking in dendrites
		6.2.1 One-dimensional cable model
		6.2.2 Steady-state solution
		6.2.3 Accumulation time.
	6.3 Diffusion-limited reactions
		6.3.1 Smoluchowski reaction rate theory
		6.3.2 Facilitated diffusion and protein search for DNA binding sites
		6.3.3 Stochastically gated diffusion-limited reactions
		6.3.4 Enzymatic reactions with multiple binding sites
	6.4 Narrow capture and escape problems, small traps, and singular perturbation methods
		6.4.1 Diffusion in a bounded domain with small interior traps
		6.4.2 Diffusion-limited reaction for a small target
		6.4.3 Narrow escape problem
	6.5 Extreme statistics and the fastest escape time.
	6.6 Diffusion in randomly switching environments
		6.6.1 Stochastic gating model of confinement
		6.6.2 1D diffusion with a switching boundary
		6.6.3 Stochastically gated Brownian motion
		6.6.4 Brownian motion with dichotomous fluctuating diffusivity
		6.6.5 Diffusion over a fluctuating barrier
	6.7 Stochastically gated gap junctions
		6.7.1 Effective diffusion coefficient for a deterministic 1D model
		6.7.2 Effective permeability for cells coupled by stochastically gated gap junctions
		6.7.3 Splitting probabilities and MFPT
	6.8 Diffusive transport through nanopores and channels
		6.8.1 Confined diffusion and the Fick–Jacobs equation
		6.8.2 Single-file diffusion
		6.8.3 Nuclear transport
	6.9 Diffusive transport on a Cayley tree
	6.10 Exercises
7 Active transport
	7.1 Vesicular transport in axons and dendrites
		7.1.1 Slow axonal transport
		7.1.2 Reversible vesicular transport and synaptic democracy
	7.2 Intracellular motor transport as a velocity-jump process
		7.2.1 Active transport along a 1D track
		7.2.2 Quasi-steady-state reduction
		7.2.3 Active transport on microtubular networks
		7.2.4 Virus trafficking
	7.3 Intracellular transport as a random search-and-capture process
		7.3.1 Optimal unbiased transport
		7.3.2 Biased cargo transport
		7.3.3 Effects of local chemical signaling
		7.3.4 Directed search along an array of synaptic targets
	7.4 Multiple search-and-capture events and queuing theory
		7.4.1 Analysis in terms of a G/M/infty queue
		7.4.2 Multiple packets and searchers
	7.5 Search processes with stochastic resetting
		7.5.1 Brownian particle with Poissonian resetting
		7.5.2 Single search-and-capture event and renewal theory
		7.5.3 Finite return times and refractory periods
		7.5.4 Splitting probabilities and conditional MFPTs for multiple targets
	7.6 Exclusion processes
		7.6.1 Asymmetric exclusion process and the hydrodynamic limit
		7.6.2 Steady-state analysis
		7.6.3 Method of characteristics and shocks
	7.7 Exercises
8 The WKB method, path integrals,  and large deviations
	8.1 Metastability analysis of SDEs with weak noise
		8.1.1 The WKB method for one-dimensional SDEs
		8.1.2 Higher-dimensional SDEs.
		8.1.3 Path integral representation of an SDE
	8.2 Metastability analysis of birth–death processes
		8.2.1 The WKB method for a birth–death process
		8.2.2 Path integral representation of a birth–death process
	8.3 Metastability analysis of stochastic hybrid systems
		8.3.1 The WKB method for a stochastic hybrid system
		8.3.2 Path integral representation of a stochastic hybrid system
		8.3.3 Finite discrete systems and the Perron-Frobenius theorem
	8.4 Noise-induced transitions in an autoregulatory gene network
	8.5 Noise-induced transitions in the stochastic Morris-Lecar model
		8.5.1 Bistability in a reduced Morris-Lecar model
		8.5.2 Excitability in the full stochastic Morris-Lecar model
	8.6 Brownian functionals
	8.7 Large deviation theory
		8.7.1 Sums of random variables and generalized central limit theorems
		8.7.2 Large deviation principle
		8.7.3 Large deviation principle for Brownian functionals
	8.8 Exercises
9 Probability theory and martingales
	9.1 Probability spaces, random variables and conditional expectations
	9.2 Discrete-time stochastic processes and martingales
		9.2.1 Filtrations and martingales
		9.2.2 Stopping times
	9.3 The Galton–Watson branching process
		9.3.1 Generating functions and basic properties
		9.3.2 Extinction and criticality
		9.3.3 Asymptotic properties
		9.3.4 Application to gene amplification
	9.4 Modeling chemical reaction networks as counting processes
		9.4.1 Poisson processes and counting processes
		9.4.2 Chemical reactions and counting processes
References
Index