A Critical Comparison of Rejection-Based Algorithms for Simulation of Large Biochemical Reaction Networks

Abstract

The rejection-based simulation technique has been applying to improve the computational efficiency of the stochastic simulation algorithm (SSA) in simulating large reaction networks, which are required for a thorough understanding of biological systems. We compare two recently proposed simulation methods, namely the composition-rejection algorithm (SSA-CR) and the rejection-based SSA (RSSA), aiming for this purpose. We discuss the right interpretation of the rejection-based technique used in these algorithms in order to make an informed choice when dealing with different aspects of biochemical networks. We provide the theoretical analysis as well as the detailed runtime comparison of these algorithms on concrete biological models. We highlight important factors that are omitted in previous analysis of these algorithms. The numerical comparison shows that for reaction networks where the search cost is expensive then SSA-CR is more efficient, and for reaction networks where the update cost is dominant, often the case in practice, then RSSA should be the choice.

Beyond Deterministic Models in Drug Discovery and Development

“…Some stochastic simulation software tools exist for easier computation of these processes, including StochSS [ 16 ], GillesPy [ 17 ], or COPASI [ 18 ], but numerous published studies of stochastic process simulation in biomedicine are still accomplished using self-coded algorithms in programming languages such as C++ due to the fast computing time needed. Recent advances in this field have greatly reduced the computational complexity; the sorting direct method [ 19 ], composition-rejection SSA [ 20 ], and rejection-based SSA (RSSA) [ 21 ] tend to be orders of magnitude faster than the traditional Gillespie SSA [ 22 ]. These more efficient methodologies, along with the first adaptive methods for stiff stochastic differential equations, are implemented in newer Julia-based stochastic simulation software tools, such as DifferentialEquations.jl [ 23 ].…”

Efficient anticorrelated variance reduction for stochastic simulation of biochemical reactions

“…For each iteration, three random numbers r 1 , r 2 , and r 3 ∼ U(0, 1) are generated. The random number r 1 is used to generate the waiting time (line 13) while r 2 and r 3 are used to select the candidate reaction and validate it through an acceptancerejection test (lines [15][16][17][18][19][20][21][22][23][24]. The random numbers are then transformed to produce the anticorrelated realisation.…”

“…SSA is an exact simulation procedure in the sense that it does not introduce approximation error in the sampling of reaction firings. Many methods have been introduced for implementing the Monte Carlo sampling step including the well known direct method [9,10], the next reaction method [11], and their improvements [12][13][14][15][16][17][18][19][20] as well as others [21][22][23][24][25][26][27][28]. The rejection-based SSA (RSSA), introduced recently by Thanh [29] and Thanh et al [30], provides an alternative approach for an exact realisation of the next reaction firings.…”

Efficient finite-difference method for computing sensitivities of biochemical reactions

“…Two first implementations of the Monte Carlo step are the direct method (DM) and first reaction method (FRM) [10]. Since then, many efficient implementations of the Monte Carlo step have been introduced including DM with improved search [12][13][14], with tree-based search [15][16][17], with composition-rejection search [18] and with partial-propensity approach [19], the next reaction method (NRM) [20,21], the rejection-based SSA (RSSA) [22][23][24][25][26] and other improvements [27][28][29][30][31][32][33][34]. Extensions of SSA have been introduced to cope with different aspects of biochemical reactions like time delays [14,21,[35][36][37] and time-dependent reaction rates [21,[38][39][40].…”