Simulation methods with extended stability for stiff biochemical Kinetics |
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Authors: | Pau Rué Jordi Villà-Freixa Kevin Burrage |
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Institution: | 1.Computational Biochemistry and Biophysics Group, Research Unit on Biomedical Informatics, IMIM/Universitat Pompeu Fabra,Barcelona, Catalonia,Spain;2.Departament de Física i Enginyeria Nuclear,Universitat Politècnica de Catalunya, Edifici GAIA,Terrassa, Barcelona,Spain;3.Institute for Molecular Bioscience, The University of Queensland, Brisbane, QLD,Australia;4.COMLAB and OCISB, University of Oxford,Oxford,UK |
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Abstract: | Background With increasing computer power, simulating the dynamics of complex systems in chemistry and biology is becoming increasingly
routine. The modelling of individual reactions in (bio)chemical systems involves a large number of random events that can
be simulated by the stochastic simulation algorithm (SSA). The key quantity is the step size, or waiting time, τ, whose value inversely depends on the size of the propensities of the different channel reactions and which needs to be re-evaluated
after every firing event. Such a discrete event simulation may be extremely expensive, in particular for stiff systems where
τ can be very short due to the fast kinetics of some of the channel reactions. Several alternative methods have been put forward
to increase the integration step size. The so-called τ-leap approach takes a larger step size by allowing all the reactions to fire, from a Poisson or Binomial distribution, within
that step. Although the expected value for the different species in the reactive system is maintained with respect to more
precise methods, the variance at steady state can suffer from large errors as τ grows. |
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