On the rejection-based algorithm for simulation and analysis of large-scale reaction networks

Abstract

Stochastic simulation for in-silico studies of large biochemical networks requires a great amount of computational time. We recently proposed a new exact simulation algorithm, called the rejection-based stochastic simulation algorithm (RSSA) [J. Chem. Phys. 141(13):134116 (2014)], to improve simulation performance by postponing and collapsing as much as possible the propensity updates. In this paper, we analyze the performance of this algorithm in detail, and improve it for simulating large-scale biochemical reaction networks. We also present a new algorithm, called simultaneous RSSA (SRSSA), which generates many independent trajectories simultaneously for the analysis of the biochemical behavior. SRSSA improves simulation performance by utilizing a single data structure across simulations to select reaction firings and forming trajectories. The memory requirement for building and storing the data structure is thus independent of the number of trajectories. The updating of the data structure when needed is performed collectively in a single operation across the simulations. The trajectories generated by SRSSA are exact and independent of each other by exploiting the rejection-based mechanism. We test our new improvement on real biological systems with a wide range of reaction networks to demonstrate its applicability and efficiency.

Stochastic simulation algorithms for computational systems biology: Exact, approximate, and hybrid methods

“…The successive versions of RSSA (Thanh & Priami, ; Thanh, Zunino, & Priami, , , ) improve the simulation performance by using search techniques, such as tree‐based search or composition‐rejection search, as the one we discussed in Section 2.1. In Thanh et al (), RSSA is extended to account for the biological extrinsic noise.…”

HSimulator: Hybrid Stochastic/Deterministic Simulation of Biochemical Reaction Networks

“…The Rejection-based Stochastic Simulation Algorithm (RSSA) is a novel exact stochastic simulation algorithm introduced in [10] and further improved in [7,[24][25][26]. RSSA constitutes the state of the art of exact stochastic simulation tailored for complex biochemical reactions with time-consuming propensity functions.…”

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

“…For large reaction networks, an efficient search can be applied to improve performance of this step. 22 Then, RSSA validates the candidate R j through a rejection test with success probability a j (X(t))/a j . To do that, RSSA generates a random number r 2 ∼ U(0, 1) and checks whether r 2 ≤ a j (X(t))/a j .…”

“…A candidate R j is selected so that its index j is the smallest one satisfying  j k=1 a k > r 2 a 0 , where r 2 ∼ U(0, 1) (line 21). The candidate R j is then validated to ensure if it is accepted with success probability a j /a j (lines [22][23][24][25][26][27][28][29][30]. The validation of candidate requires a random number r 3 ∼ U(0, 1).…”

“…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.…”