title: Modelling non-Markovian dynamics in biochemical reactions.
abstract: BACKGROUND
  Biochemical reactions are often modelled as discrete-state continuous-time stochastic processes evolving as memoryless Markov processes. However, in some cases, biochemical systems exhibit non-Markovian dynamics. We propose here a methodology for building stochastic simulation algorithms which model more precisely non-Markovian processes in some specific situations. Our methodology is based on Constraint Programming and is implemented by using Gecode, a state-of-the-art framework for constraint solving.
  
  
  RESULTS
  Our technique allows us to randomly sample waiting times from probability density functions that not necessarily are distributed according to a negative exponential function. In this context, we discuss an important case-study in which the probability density function is inferred from single-molecule experiments that describe the distribution of the time intervals between two consecutive enzymatically catalysed reactions. Noticeably, this feature allows some types of enzyme reactions to be modelled as non-Markovian processes.
  
  
  CONCLUSIONS
  We show that our methodology makes it possible to obtain accurate models of enzymatic reactions that, in specific cases, fit experimental data better than the corresponding Markovian models.
authors.forename: Davide
authors.initials: D
authors.lastname: Chiarugi
authors.forename: Moreno
authors.initials: M
authors.lastname: Falaschi
authors.forename: Diana
authors.initials: D
authors.lastname: Hermith
authors.forename: Carlos
authors.initials: C
authors.lastname: Olarte
authors.forename: Luca
authors.initials: L
authors.lastname: Torella
mesh_terms: D002468:Cell Physiological Phenomena; D003198:Computer Simulation; D004798:Enzymes / Q000378:metabolism*; D008954:Models, Biological; D009010:Monte Carlo Method
chemical_list: D004798:Enzymes