A new class of highly efficient exact stochastic simulation algorithms for chemical reaction networks

Abstract

We introduce an alternative formulation of the exact stochastic simulation algorithm (SSA) for sampling trajectories of the chemical master equation for a well-stirred system of coupled chemical reactions. Our formulation is based on factored-out, partial reaction propensities. This novel exact SSA, called the partial-propensity direct method (PDM), is highly efficient and has a computational cost that scales at most linearly with the number of chemical species, irrespective of the degree of coupling of the reaction network. In addition, we propose a sorting variant, SPDM, which is especially efficient for multiscale reaction networks.

Discreteness-induced concentration inversion in mesoscopic chemical systems

“…The colour key is: blue for f 1,2 , orange for f 1,3 , and red for f 2,3 . The data points show the results from exact stochastic simulations 33 whereas the solid lines show the predictions of the present theory.…”

“…We start by calculating the critical volumes of this system using the present theoretical framework, and then validate these predictions against exact stochastic simulations 33 . From the Jacobian of the deterministic REs of this system and equation (2), we find: …”

“…The theoretical predictions of the critical volumes, at which the trimerization system undergoes inversion, are validated using the partialpropensity direct method 33 , an exact SSA that produces sample trajectories from the CME at a fraction of the computational cost incurred by traditional SSA formulations. The volume dependence enters the stochastic simulation through the propensity functions of the input and bimolecular reactions, which scale as Ω and 1/Ω, respectively, in accordance with the CME 1 .…”

A partial-propensity variant of the composition-rejection stochastic simulation algorithm for chemical reaction networks

“…For strongly coupled networks, however, the computational cost of these SSA formulations remains O(M ), as for Gillespie's original direct method. 6 We have recently introduced novel exact SSA formulations that are based on partial propensities. 6 These formulations, called PDM and SPDM, have a computational cost of O(N ), irrespective of the coupling class of the network.…”

“…6 We have recently introduced novel exact SSA formulations that are based on partial propensities. 6 These formulations, called PDM and SPDM, have a computational cost of O(N ), irrespective of the coupling class of the network. 6 This makes them particularly interesting for strongly coupled networks.…”