Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Introduction to Algorithms
Journal of Computational Physics
COPASI---a COmplex PAthway SImulator
Bioinformatics
Computational Biology and Chemistry
A compositional approach for modeling and simulation of bio-molecular systems
Proceedings of the Winter Simulation Conference
Splitting for rare event simulation in biochemical systems
Proceedings of the 6th International ICST Conference on Simulation Tools and Techniques
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One can generate trajectories to simulate a system of chemical reactions using either Gillespie's direct method or Gibson and Bruck's next reaction method. Because one usually needs many trajectories to understand the dynamics of a system, performance is important. In this paper, we present new formulations of these methods that improve the computational complexity of the algorithms. We present optimized implementations, available from http://cain.sourceforge.net/, that offer better performance than previous work. There is no single method that is best for all problems. Simple formulations often work best for systems with a small number of reactions, while some sophisticated methods offer the best performance for large problems and scale well asymptotically. We investigate the performance of each formulation on simple biological systems using a wide range of problem sizes. We also consider the numerical accuracy of the direct and the next reaction method. We have found that special precautions must be taken in order to ensure that randomness is not discarded during the course of a simulation.