Binomial distribution based τ-leap accelerated stochastic simulation

Abstract

Recently, Gillespie introduced the tau-leap approximate, accelerated stochastic Monte Carlo method for well-mixed reacting systems [J. Chem. Phys. 115, 1716 (2001)]. In each time increment of that method, one executes a number of reaction events, selected randomly from a Poisson distribution, to enable simulation of long times. Here we introduce a binomial distribution tau-leap algorithm (abbreviated as BD-tau method). This method combines the bounded nature of the binomial distribution variable with the limiting reactant and constrained firing concepts to avoid negative populations encountered in the original tau-leap method of Gillespie for large time increments, and thus conserve mass. Simulations using prototype reaction networks show that the BD-tau method is more accurate than the original method for comparable coarse-graining in time.

Exact results for noise power spectra in linear biochemical reaction networks

“…There is a growing literature on the adiabatic elimination of fast reactions for stochastic chemical kinetics [16,17,18,19,20,21,22,23,24,25]. For example Kepler and Elston [16], and Shibata [18,19], have a formalism that permits a systematic approach to the problem, involving the identification of the fast and slow variables in the system.…”

Incorporating postleap checks in tau-leaping

“…15,16 As negative population values are physically unreasonable, this constitutes a problem, and a number of solutions have been proposed. Tian et al 16 and Chatterjee et al 17 independently developed a method in which binomial random variables, as opposed to Poisson random variables, are used to perform the leap. Because binomial random variables have bounded support, the parameters of the binomial random variable can be chosen in a way that guarantees no molecular species will become negative in the course of a leap.…”

Stochastic hybrid modeling of intracellular calcium dynamics

“…Algorithmic consistency requires that, in addition to satisfying the leap condition, be selected in a way that prevents number of any species from becoming negative. The binomial tau-leap algorithm 9,57 imposes this constraint by introducing a new control parameter n c ͑typically a small positive integer͒, which defines "critical reactions" as those having at least one species with the number of molecules less than n c . If there are one or more critical reactions then is chosen so that no critical reaction fires more than once.…”

“…Some of the more recent contributions in this area include ͑1͒ speed-up of computation through a binomial tauleaping approach 9 and k-skip method, 10 ͑2͒ time-scale/ reaction partitioning based on the propensity values, 11 a hybrid approach, 12 and quasi-steady-state approximation, 13 ͑3͒ partial-propensity-based approach, 14 and ͑4͒ alternative formulations of CLE. 15 Besides, Cai 16 has developed an approach to perform stochastic simulation of reaction systems with time-delays.…”