## Stochastic Processes in Cell BiologyThis book develops the theory of continuous and discrete stochastic processes within the context of cell biology. A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods. This text is primarily aimed at graduate students and researchers working in mathematical biology and applied mathematicians interested in stochastic modeling. Applied probabilists and theoretical physicists should also find it of interest. It assumes no prior background in statistical physics and introduces concepts in stochastic processes via motivating biological applications. The book is highly illustrated and contains a large number of examples and exercises that further develop the models and ideas in the body of the text. It is based on a course that the author has taught at the University of Utah for many years. |

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actin action active analysis approximation assumed bifurcation binding Biol boundary conditions Brownian Ca2+ cell biology cell polarization complex concentration consider constant corresponding cytoplasm cytoskeleton denote determine deterministic diffusion discrete distribution domain dynamics eigenvalue equilibrium evolves according example filaments fixed point fluctuations flux follows force FP equation function Gaussian gene given gradient Hence Hopf bifurcation integral intracellular intrinsic noise ion channels kinesin kinetic equations kinetochore Langevin equation lattice length limit linear Markov process martingale master equation mechanism membrane MFPT microtubule molecular motors molecules monomer mRNA neuron oscillations parameter particle Phys polymer polymerization potential probability density problem protein random variable random walk ratchet reaction receptor resulting Sect signaling ſº spatial stationary stochastic process Suppose target theorem tion trajectories transition rates transport velocity vesicle Wiener process