Hybrid deterministic/stochastic simulation of complex biochemical systems

摘要

In a biological cell, cellular functions and the genetic regulatory apparatus are implemented andrncontrolled by complex networks of chemical reactions involving genes, proteins, and enzymes. Accuraterncomputational models are indispensable means for understanding the mechanisms behind the evolutionrnof a complex system, not always explored with wet lab experiments. To serve their purpose,rncomputational models, however, should be able to describe and simulate the complexity of a biologicalrnsystem in many of its aspects. Moreover, it should be implemented by efficient algorithms requiring thernshortest possible execution time, to avoid enlarging excessively the time elapsing between data analysisrnand any subsequent experiment. Besides the features of their topological structure, the complexity ofrnbiological networks also refers to their dynamics, that is often non-linear and stiff. The stiffness is due tornthe presence of molecular species whose abundance fluctuates by many orders of magnitude. A fullyrnstochastic simulation of a stiff system is computationally time-expensive. On the other hand, continuousrnmodels are less costly, but they fail to capture the stochastic behaviour of small populations ofrnmolecular species. We introduce a new efficient hybrid stochastic–deterministic computational modelrnand the software tool MoBioS (Molecular Biology Simulator) implementing it. The mathematical modelrnof MoBioS uses continuous differential equations to describe the deterministic reactions and a Gillespielikernalgorithm to describe the stochastic ones. Unlike the majority of current hybrid methods, thernMoBioS algorithm divides the reactions’ set into fast reactions, moderate reactions, and slow reactionsrnand implements a hysteresis switching between the stochastic model and the deterministic model. Fastrnreactions are approximated as continuous-deterministic processes and modelled by deterministic raternequations. Moderate reactions are those whose reaction waiting time is greater than the fast reactionrnwaiting time but smaller than the slow reaction waiting time. A moderate reaction is approximated as arnstochastic (deterministic) process if it was classified as a stochastic (deterministic) process at the time atrnwhich it crosses the threshold of low (high) waiting time. A Gillespie First Reaction Method isrnimplemented to select and execute the slow reactions. The performances of MoBios were tested on arntypical example of hybrid dynamics: that is the DNA transcription regulation. The simulated dynamicrnprofile of the reagents’ abundance and the estimate of the error introduced by the fully deterministicrnapproach were used to evaluate the consistency of the computational model and that of thernsoftware tool.