Modelling non-Markovian dynamics in biochemical reactions

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.

An Assertion Language for Slicing Constraint Logic Languages

“…The translation to CCP is similar to the example we gave in Section 2.1. An excerpt of a possible trace for the execution of the goal length( [10,20], Ans). is In this trace, we can see how the calls to the process definition length are unfolded and, in each state, new constraints are added.…”

“…CCP is intended for reasoning, modeling and programming concurrent agents (or processes) that interact with each other and their environment by posting and asking information in a medium, a so-called store. CCP is a very flexible model and has been applied to an increasing number of different fields such as probabilistic and stochastic, timed and mobile systems [26,9], and more recently to social networks with spatial and epistemic behaviors [25], as well as modeling of biological systems [11,10,24,6].…”

General Galilei Covariant Gaussian Maps

“…Although the assumption of Markovianity is often well justified, recent technological advances have lead to investigating several phenomena exhibiting memory effects [27], e.g., ultrafast chemical reactions [28][29][30][31][32][33], side band cooling [34] and light harvesting in photosynthesis [35][36][37][38][39][40]. This is of little surprise, as the time resolution of experimental apparatuses has increased severalfold in the last decades.…”

“…To be more concrete we suggest the exponential correlation function D(t, s) = 1 2τ c e −|t−s|/τc (33) and the Gaussian operators…”

“…[42], and a more general definition is needed, as the one we propose, based on Eqs. (17), (33), and (34).…”