title: Computational methods for diffusion-influenced biochemical reactions.
abstract: BACKGROUND
  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.
  
  
  BACKGROUND
  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/
authors.affiliation: CWI (Center for Mathematics and Computer Science), Kruislaan 413 and Section Computational Science, Faculty of Science, University of Amsterdam, Kruislaan 403, Amsterdam, The Netherlands. m.dobrzynski@cwi.nl
authors.forename: Maciej
authors.initials: M
authors.lastname: Dobrzynski
authors.forename: Jordi Vidal
authors.initials: JV
authors.lastname: Rodríguez
authors.forename: Jaap A
authors.initials: JA
authors.lastname: Kaandorp
authors.forename: Joke G
authors.initials: JG
authors.lastname: Blom
mesh_terms: D000465:Algorithms; D001671:Biochemistry / Q000379:methods*; D001704:Biopolymers / Q000737:chemistry* / Q000378:metabolism*; D003198:Computer Simulation; D004058:Diffusion; D008954:Models, Biological; D008956:Models, Chemical; D015398:Signal Transduction / Q000502:physiology*
chemical_list: D001704:Biopolymers