Accurate stochastic simulation via the step anticipation tau-leaping (SAL) algorithm

J Comput Biol. 2009 Sep;16(9):1195-208. doi: 10.1089/cmb.2008.0249.


Stochastic simulation methods are important in modeling chemical reactions, and biological and physical stochastic processes describable as continuous-time discrete-state Markov chains with a finite number of reactant species and reactions. The current algorithm of choice, tau-leaping, achieves fast and accurate stochastic simulation by taking large time steps that leap over individual reactions. During a leap interval (t, t + tau) in tau-leaping, each reaction channel operates as a Poisson process with a constant intensity. We modify tau-leaping to allow linear and quadratic changes in reaction intensities. Because our version of tau-leaping accurately anticipates how intensities change over time, we propose calling it the step anticipation tau-leaping (SAL) algorithm. We apply SAL to four examples: Kendall's process, a two-type branching process, Ehrenfest's model of diffusion, and Michaelis-Menten enzyme kinetics. In each case, SAL is more accurate than ordinary tau-leaping. The degree of improvement varies with the situation. Near stochastic equilibrium, reaction intensities are roughly constant, and SAL and ordinary tau-leaping perform about equally well.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Algorithms*
  • Computer Simulation*
  • Models, Biological
  • Models, Chemical
  • Stochastic Processes*