Abstract
Many chemical reactions, such as gene transcription and translation in living cells, need a certain time to finish once they are initiated. Simulating stochastic models of reaction-diffusion systems with delay can be computationally expensive. In the present paper, a novel hybrid algorithm is proposed to accelerate the stochastic simulation of delayed reaction-diffusion systems. The delayed reactions may be of consuming or non-consuming delay type. The algorithm is designed for moderately stiff systems in which the events can be partitioned into slow and fast subsets according to their propensities. The proposed algorithm is applied to three benchmark problems and the results are compared with those of the delayed Inhomogeneous Stochastic Simulation Algorithm. The numerical results show that the new hybrid algorithm achieves considerable speed-up in the run time and very good accuracy.
Highlights
The Chemical Master Equation (CME)[1] is a widely used stochastic discrete model for simulating well-stirred biochemical systems
We propose below the Delayed Hybrid Lumped Simulation Algorithm (DHLSA) for solving numerically models of delayed reaction-diffusion systems with slow and fast dynamics
The hybrid lumped algorithm with delay is applied to three biochemical models: annihilation, Schnakenberg and Glycolysis models and the accuracy and computational cost are compared with those of the Delayed Inhomogeneous Stochastic Simulation Algorithm (DISSA)
Summary
The Chemical Master Equation (CME)[1] is a widely used stochastic discrete model for simulating well-stirred biochemical systems. The SSA was generalized to inhomogeneous systems resulting in the exact Inhomogeneous Stochastic Simulation Algorithm (ISSA) for the Reaction-Diffusion Master Equation.[23,24,25] In the RDME, the system is divided into subvolumes each of which is assumed to be homogeneous. This makes the ISSA even more computationally expensive than the SSA. The paper is organized as follows: Section II presents a brief overview of the Reaction Diffusion Master Equation and the two simulation methods that will be used in the new hybrid algorithm: ISSA and spatial tau-leaping.
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