Approximate accelerated stochastic simulation of chemically reacting systems

By Daniel T. Gillespie. 2001

2,020 citations recorded by the source corpus.

The stochastic simulation algorithm (SSA) is an essentially exact procedure for numerically simulating the time evolution of a well-stirred chemically reacting system. Despite recent major improvements in the efficiency of the SSA, its drawback remains the great amount of computer time that is often required to simulate a desired amount of system time. Presented here is the “τ-leap” method, an approximate procedure that in some circumstances can produce significant gains in simulation speed with acceptable losses in accuracy. Some primitive strategies for control parameter selection and error mitigation for the τ-leap method are described, and simulation results for two simple model systems are exhibited. With further refinement, the τ-leap method should provide a viable way of segueing from the exact SSA to the approximate chemical Langevin equation, and thence to the conventional deterministic reaction rate equation, as the system size becomes larger.

Subfields: Biomedical Engineering, Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cfa3cb6b21410352a9aacb991cb0bd7e7d6a4ec0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

In Molecular Biology

In Statistical and Nonlinear Physics

Citations in the corpus

Stochastic delay differential equations for genetic regulatory networks (2007, methodology): “Although the stochastic simulation method (SSA) is a statistically exact method for simulating the dynamics of GRNs based on detailed biochemical reactions [10], the large computational time of the SSA is a barrier in the applications of this method to large biological systems.”
Networks and the Epidemiology of Infectious Disease (2010, methodology): “The τleap method [111], where multiple events are allowed to occur during a time period τ, is clearly related to the discretetime formulation discussed above.”
A Dynamical Low-Rank Approach to the Chemical Master Equation (2008, methodology): “that many reaction events will occur without significantly changing the reaction propensities, allowing to locally approximate the inhomogenous Poisson process by a simpler distribution [17, 36, 7, 5].”
Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decoding (2025, positive): “A common strategy to accelerate this is to employ a 𝜏 -leaping [6] approximation for the reverse process.”
Continuous Time Markov Chain Models for Chemical Reaction Networks (2011, positive): “we obtain Gillespie’s [23] τ -leap method.”
A Continuous Time Framework for Discrete Denoising Models (2022, methodology): “Instead, we use tau-leaping [20, 23], a very popular approximate simulation method developed in chemical physics.”
An overview of spatial microscopic and accelerated kinetic Monte Carlo methods (2007, methodology): “The following year, Gillespie introduced two different rejection-free algorithms for well-mixed systems, namely, the direct and the first reaction method [66,124].”
Tensor-product approach to global time-space-parametric discretization of chemical master equation (2012, methodology): “Several improvements include the advanced sampling techniques [6], τ-leaping methods [7], system-partitioning hybrid methods [8, 9].”
Construction of Equivalent Stochastic Differential Equation Models (2008, background): “2) are referred to as chemical Langevin systems [15].”
Stochastic approaches for modelling in vivo reactions (2004, methodology): “We discuss some further streamlining of the algorithm by Gibson and Bruck (2000), Gillespie (2001), Burrage and Tian (2003), Rathinam et al. (2003) and Tian and Burrage (2004a) leading to greater computational efficiency.”
Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution (2023, methodology): “Instead, a natural alternative has been to use τ -leaping (Gillespie, 2001), which performs an Euler step at each position simultaneously.”
Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains (2014, background): “A second broad class of methods are the kinetic Monte Carlo approaches which instead seek to produce either exact or approximate realizations of the underlying Markov process [3,9,10].”