Abstract
BackgroundBiochemical 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.ResultsOur 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.ConclusionsWe 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.
Highlights
Biochemical reactions are often modelled as discrete-state continuous-time stochastic processes evolving as memoryless Markov processes
We propose a Constraint Programming approach that is suited for being embedded in Monte Carlo algorithms for discrete-state continuous-time stochastic simulation of biochemical reactions
Our aim is to verify whether our method, which satisfies the relation expressed in Equation (3), can be used to perform simulations using data coming from ensemble experiments which are the most frequently present in the literature
Summary
Biochemical reactions are often modelled as discrete-state continuous-time stochastic processes evolving as memoryless Markov processes. Biochemical reactions, in particular, are often modelled as discrete-state, continuous-time Markov Processes (CTMP) This method represents an alternative to the traditional continuous deterministic modelling (CDM) approach when random fluctuations must be properly taken into account. This is the case, for instance, of systems composed of a small number of elements like molecular subsystems in living cells (e.g., metabolic networks, signalling pathways, or gene regulatory networks). Since the CME can rarely be solved either numerically or analytically especially for large systems, GSSA provides a computational method to generate statistically correct trajectories (possible solutions) of the CME These trajectories are obtained by drawing random samples from the so-called Reaction Probability Density Function (RPDF) [6,7] through the ITS
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