2013
DOI: 10.1063/1.4801941
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Perspective: Stochastic algorithms for chemical kinetics

Abstract: We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discretestochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-determinis… Show more

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Cited by 299 publications
(360 citation statements)
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“…The assumption is that the events belonging to each subset (j 1 , j 2 , .., j N ) are independent and identically distributed (i.i.d.). Such an assumption does not lead to loss of generality because the constraints used in building different subsets can contain the information about the dependencies between events [13]. Then if n(j 1 , j 2 , .., j N ) → +∞, the probability P i (j 1 , j 2 , .., j N ) for the i-th outcome to occur in the set (j 1 , j 2 , .., j N ) corresponds to the limit of frequency of the i-th outcome, i.e.…”
Section: Relative Asymptotic Frequencies Of Events In Constrained Stomentioning
confidence: 99%
“…The assumption is that the events belonging to each subset (j 1 , j 2 , .., j N ) are independent and identically distributed (i.i.d.). Such an assumption does not lead to loss of generality because the constraints used in building different subsets can contain the information about the dependencies between events [13]. Then if n(j 1 , j 2 , .., j N ) → +∞, the probability P i (j 1 , j 2 , .., j N ) for the i-th outcome to occur in the set (j 1 , j 2 , .., j N ) corresponds to the limit of frequency of the i-th outcome, i.e.…”
Section: Relative Asymptotic Frequencies Of Events In Constrained Stomentioning
confidence: 99%
“…For example, reaction volume affects many propensities. 3,16,21 If the volume is affected in small steps by many actions in the system, then its impact on propensities is similar to that of hubs: frequent small changes in volume trigger frequent small updates to many propensities. Biological examples for such endogenously driven changes include active cellular nutrient import, 44 osmosis, 44 and export of molecules.…”
Section: Introductionmentioning
confidence: 99%
“…Continuous-time Markov chains [10][11][12][13][14][15] (CTMCs) have a track record of excellence in this area and provide a rigorous basis for transforming certain types of well-mixed stochastic models with infinitely large part numbers into equivalent ODE models. 3,14,15 CTMCs have no "memory," as they assume that the future state of a model only depends on its current state and not on its history. CTMCs also assume that the waiting times between actions (which lead to state transitions) are exponentially distributed, unless external noise affects the probabilities that determine how often these actions occur.…”
Section: Introductionmentioning
confidence: 99%
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