Efficient rejection-based simulation of biochemical reactions with stochastic noise and delays

Abstract

We propose a new exact stochastic rejection-based simulation algorithm for biochemical reactions and extend it to systems with delays. Our algorithm accelerates the simulation by pre-computing reaction propensity bounds to select the next reaction to perform. Exploiting such bounds, we are able to avoid recomputing propensities every time a (delayed) reaction is initiated or finished, as is typically necessary in standard approaches. Propensity updates in our approach are still performed, but only infrequently and limited for a small number of reactions, saving computation time and without sacrificing exactness. We evaluate the performance improvement of our algorithm by experimenting with concrete biological models.

Optimization Algorithms for Computational Systems Biology

“…This is often the case in the simulation of chemical reaction networks. In such cases, the stochastic simulation of fast reactions may require more time than the deterministic approach [47,48]. On the other hand, when the model includes particularly low abundances of certain species, e.g., few individuals, considering average behaviors may not accurately describe the phenomena, and hence deterministic simulation cannot be applied [3,49].…”

Simulation of biochemical reactions with time-dependent rates by the rejection-based algorithm

“…(4). In other words, RSSA selects reaction R j to fire with probability a j /a 0 and its firing time τ is drawn from an exponential distribution Exp(a 0 ) (see the work of Thanh et al 21 for a formal proof of the exactness of RSSA).…”

“…The update of propensity bounds can be performed locally by applying a Species-Reaction (SR) dependency graph. 21 The SR dependency graph is a directed bipartite graph which shows the dependency of reactions on species. A directed edge from a species S i to a reaction R j is in the graph if a change in the population of species S i requires reaction R j to recompute its propensity.…”

“…We present a novel formulation by extending the RSSA. 21 Our time-dependent RSSA (tRSSA) exploits the rejection-based mechanism to select next reaction firings. tRSSA uses propensity bounds of reactions to select a candidate reaction and then validates the candidate with a rejection-based test by its exact propensity value.…”

“…FRM generates the putative waiting time to the firing of each reaction and selects the reaction having the smallest waiting time to be the next reaction firing. Many improvements have been introduced to accelerate both of these algorithms including the next reaction method (NRM), 10 the optimized direct method (ODM), 11 the sorting direct method (SDM), 12 the composition-rejection SSA (CR-SSA), 13,14 the tree-based search SSA, [15][16][17][18] the partial-propensity SSA, 19,20 a) Electronic mail: vo@cosbi.eu b) Electronic mail: priami@cosbi.eu the rejection-based SSA (RSSA), [21][22][23] and other improvements including approximate and parallel algorithms. [24][25][26][27][28][29][30] SSA assumes reaction rates to be constant.…”