Stochastic Modelling of Reaction–Diffusion Processes by Radek Erban and S. Jonathan Chapman

Stochastic simulation has become an indispensable tool in the scientific toolkit. We were all told as students that molecules jostle one another incessantly because of thermal motion and that chemical reactions rely on the resulting chance encounters between molecules. However, most of us took chemistry and physics classes in which attention quickly shifted to vast collections of molecules, for which the inherent randomness washed out when viewing overall concentrations; we then formulated and solved deterministic rate equations. However, some key actors in cells appear in only a small number of copies (perhaps just one, for some genes). Moreover, experimental technique now allows routine study of single cells and even single molecules, so corresponding analytical tools that go beyond ensemble averaging are needed, just to extract the lessons that are latent in our datasets. Most of us also took classes in which chemical reactions were studied in imagined ‘‘well-stirred’’ conditions, and diffusion was studied separately in contexts where chemical reactions were not important. However, a vesicle of neurotransmitter must travel across a synapse while being degraded; a morphogen must bind and activate receptors while establishing a spatial gradient; and so on. This book’s title expresses the authors’ aim to establish a framework capable of handling biophysically relevant situations like these. Student interest in this topic is strong. My own students are at least implicitly aware that results from even the simplest stochastic simulation seem more ‘‘lifelike’’ than deterministic results, and they are always excited to see the gradual emergence of deterministic behavior as copy numbers get large. I realized some time ago that stochastic simulation belongs in any biophysics curriculum, starting from the very first introductory course and reappearing as appropriate at later stages. However, it was not so easy to find appropriate course materials. Erban and Chapman now give us a concise, elegant, and practical survey of numerical methods that are useful for such analyses, although at a level somewhat higher than first-year courses. An advanced undergraduate who is comfortable with ordinary differential equations and conditional probability and the associated mathemat-