K -leap method for accelerating stochastic simulation of coupled chemical reactions

Leap methods are very promising for accelerating stochastic simulation of a well stirred chemically reacting system, while providing acceptable simulation accuracy. In Gillespie's tau-leap method [D. Gillespie, J. Phys. Chem. 115, 1716 (2001)], the number of firings of each reaction channel during a leap is a Poisson random variable, whose sample values are unbounded. This may cause large changes in the populations of certain molecular species during a leap, thereby violating the leap condition. In this paper, we develop an alternative leap method called the K-leap method, in which we constrain the total number of reactions occurring during a leap to be a number K calculated from the leap condition. As the number of firings of each reaction channel during a leap is upper bounded by a properly chosen number, our K-leap method can better satisfy the leap condition, thereby improving simulation accuracy. Since the exact stochastic simulation algorithm (SSA) is a special case of our K-leap method when K=1, our K-leap method can naturally change from the exact SSA to an approximate leap method during simulation, whenever the leap condition allows to do so.