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Hybrid deterministic/stochastic simulation of complex biochemical systems


In a biological cell, cellular functions and the genetic regulatory apparatus are implemented and controlled by complex networks of chemical reactions involving genes, proteins, and enzymes. Accurate computational models are indispensable means for understanding the mechanisms behind the evolution of a complex system, not always explored with wet lab experiments. To serve their purpose computational models, however, should be able to describe and simulate the complexity of a biological system in many of its aspects. Moreover, it should be implemented by efficient algorithms requiring the shortest possible execution time, to avoid enlarging excessively the times elapsing between the data analysis and any subsequent experiment. Besides the features of their topological structure, the complexity of biological networks is also referred to their dynamics, that is often non-linear and stiff. The stiffness is due the presence of molecular species whose abundance fluctuates by many orders of magnitude. A fully stochastic simulation of stiff system is computationally time-expensive. On the other hand, continuous models are less costly, but they fail to capture the stochastic behaviour of small populations of molecular species. We propose a new efficient hybrid stochastic-deterministic computational model and the software tool MoBioS (MOlecular Biology Simulator) implementing it. The mathematical model of MoBioS uses continuous differential equations to describe the deterministic reactions and a Gillespie-like algorithm to describe stochastic ones. Unlike the majority of current hybrid methods, MoBioS algorithm divides the reactions' set into fast reactions, moderate reactions, and slow reactions and implements a hysteresis switching between stochastic mode and deterministic model. Fast reactions are approximated as continuous-deterministic processes and modelled by deterministic rate equations. Moderate reactions are those whose reaction waiting time is greater than the fast reaction waiting time but smaller than the slow reaction waiting time. A moderate reaction is approximated as stochastic (deterministic) process if it was classified as stochastic (deterministic) process at the time at which it crosses the threshold of low (high) waiting time. A Gillespie First Reaction Method is implemented to select and execute the slow reactions. The performances of MoBios were tested on a typical example of hybrid dynamics: that is the DNA transcription regulation. The simulated dynamic profile of the reagent abundance and the estimate of the error introduced by the fully deterministic approach were used to evaluate the consistency of the computational model and of the software tool.

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Publication details

The article was received on 14 Jul 2017, accepted on 29 Sep 2017 and first published on 29 Sep 2017

Article type: Paper
DOI: 10.1039/C7MB00426E
Citation: Mol. BioSyst., 2017, Accepted Manuscript
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    Hybrid deterministic/stochastic simulation of complex biochemical systems

    P. Lecca, F. Bagagiolo and M. Scarpa, Mol. BioSyst., 2017, Accepted Manuscript , DOI: 10.1039/C7MB00426E

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