MOTIVATION: We compare stochastic computational methods accounting for space and discrete nature of reactants in biochemical systems. Implementations based on Brownian dynamics (BD) and the reaction-diffusion master equation are applied to a simplified gene expression model and to a signal transduction pathway in Escherichia coli. RESULTS: In the regime where the number of molecules is small and reactions are diffusion-limited predicted fluctuations in the product number vary between the methods, while the average is the same. Computational approaches at the level of the reaction-diffusion master equation compute the same fluctuations as the reference result obtained from the particle-based method if the size of the sub-volumes is comparable to the diameter of reactants. Using numerical simulations of reversible binding of a pair of molecules we argue that the disagreement in predicted fluctuations is due to different modeling of inter-arrival times between reaction events. Simulations for a more complex biological study show that the different approaches lead to different results due to modeling issues. Finally, we present the physical assumptions behind the mesoscopic models for the reaction-diffusion systems. AVAILABILITY: Input files for the simulations and the source code of GMP can be found under the following address: http://www.cwi.nl/projects/sic/bioinformatics2007/

MOTIVATION: Many biochemical networks involve reactions localized on the cell membrane. This can give rise to spatial gradients of the concentration of cytosolic species. Moreover, the number of membrane molecules can be small and stochastic effects can become relevant. Pathways usually consist of a complex interaction network and are characterized by a large set of parameters. The inclusion of spatial and stochastic effects is a major challenge in developing quantitative and dynamic models of pathways. RESULTS: We have developed a particle-based spatial stochastic method (GMP) to simulate biochemical networks in space, including fluctuations from the diffusion of particles and reactions. Gradients emerging from membrane reactions can be resolved. As case studies for the GMP method we used a simple gene expression system and the phosphoenolpyruvate:glucose phosphotransferase system pathway. AVAILABILITY: The source code for the GMP method is available at http://www.science.uva.nl/research/scs/CellMath/GMP.