Daniel Gillespie

Daniel Thomas Gillespie (15 August 1938 – 19 April 2017) was a physicist who is best known for his derivation in 1976 of the stochastic simulation algorithm (SSA), also called the Gillespie algorithm. The SSA is a procedure for numerically simulating the time evolution of the molecular populations in a chemically reacting system in a way that takes account of the fact that molecules react in whole numbers and in a largely random way. Since the late 1990s, the SSA has been widely used to simulate chemical reactions inside living cells, where the small molecular populations of some reactant species often invalidate the differential equations of traditional deterministic chemical kinetics. Gillespie's original derivation of the SSA began by considering how chemical reactions actually occur in a well-stirred dilute gas. Reasoning from physics (and not by heuristically extrapolating deterministic reaction rates to a stochastic context), he showed that the probability that a specific reaction will occur in the next very small time dt could be written as an explicit function of the current species populations multiplied by dt. From that result he deduced, using only the laws of probability, an exact formula for the joint probability density function p(τ,j) of the {time τ to the next reaction event} and the {index j of that reaction}. The SSA consists of first generating random values for τ and j according to p(τ,j), and then actualizing the next reaction accordingly. The generating step of the SSA can be accomplished using any of several different methods, and Gillespie's original paper presented two: the "direct method", which follows from a straightforward application of the well known Monte Carlo inversion method for generating random numbers; and the "first-reaction method", which is less straightforward but mathematically equivalent. Later workers derived additional methods for generating random numbers according to Gillespie's function p(τ,j) which offer computationa