title: Probability-based model of protein-protein interactions on biological timescales.
abstract: BACKGROUND
  Simulation methods can assist in describing and understanding complex networks of interacting proteins, providing fresh insights into the function and regulation of biological systems. Recent studies have investigated such processes by explicitly modelling the diffusion and interactions of individual molecules. In these approaches, two entities are considered to have interacted if they come within a set cutoff distance of each other.
  
  
  RESULTS
  In this study, a new model of bimolecular interactions is presented that uses a simple, probability-based description of the reaction process. This description is well-suited to simulations on timescales relevant to biological systems (from seconds to hours), and provides an alternative to the previous description given by Smoluchowski. In the present approach (TFB) the diffusion process is explicitly taken into account in generating the probability that two freely diffusing chemical entities will interact within a given time interval. It is compared to the Smoluchowski method, as modified by Andrews and Bray (AB).
  
  
  CONCLUSIONS
  When implemented, the AB & TFB methods give equivalent results in a variety of situations relevant to biology. Overall, the Smoluchowski method as modified by Andrews and Bray emerges as the most simple, robust and efficient method for simulating biological diffusion-reaction processes currently available.
authors.affiliation: Biomolecular Modelling Laboratory, Cancer Research UK London Research Institute, 44 Lincoln's Inn Fields, London WC2A 3PX, UK. Alexander.tournier@cancer.org.uk
authors.forename: Alexander L
authors.initials: AL
authors.lastname: Tournier
authors.forename: Paul W
authors.initials: PW
authors.lastname: Fitzjohn
authors.forename: Paul A
authors.initials: PA
authors.lastname: Bates