Fast adaptive uniformisation of the chemical master equation

Mateescu, Maria; Wolf, Verena; Didier, Frédéric; Henzinger, Thomas A.

doi:10.1049/iet-syb.2010.0005

Cited by 46 publications

(48 citation statements)

References 17 publications

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“…Other techniques can also be integrated to speed up the synthesis process, including fast adaptive uniformisation [16,34], state aggregation [1,44], and abstraction [33]. Finally, we plan to include the synthesis algorithms in the param module of the PRISM model checker [14,32], and to extend the method to general non-linear rate functions.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Precise parameter synthesis for stochastic biochemical systems

et al. 2016

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We consider the problem of synthesising rate parameters for stochastic biochemical networks so that a given time-bounded CSL property is guaranteed to hold, or, in the case of quantitative properties, the probability of satisfying the property is maximised or minimised. Our method is based on extending CSL model checking and standard uniformisation to parametric models, in order to compute safe bounds on the satisfaction probability of the property. We develop synthesis algorithms that yield answers that are precise to within an arbitrarily small tolerance value. The algorithms combine the computation of probability bounds with the refinement and sampling of the parameter space. Our methods are precise and efficient, and improve on existing approximate techniques that employ discretisation and refinement. We evaluate the usefulness of the methods by synthesising rates for three biologically motivated case studies: infection control for a SIR epidemic model; reliability

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Section: Conclusion and Discussionmentioning

confidence: 99%

Precise parameter synthesis for stochastic biochemical systems

et al. 2016

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“…The solution of CME thus gives the distribution of the state X(t) at any time t; however, an analytic solution of CME is hard to find in general due to the high dimensional state space. Recent work [36][37][38] numerically solves CME by constraining the state space exploration with a small tolerant error.…”

Section: Stochastic Reaction Kineticsmentioning

confidence: 99%

Simulation of biochemical reactions with time-dependent rates by the rejection-based algorithm

Thanh

Priami

2015

The Journal of Chemical Physics

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Articles you may be interested inWe address the problem of simulating biochemical reaction networks with time-dependent rates and propose a new algorithm based on our rejection-based stochastic simulation algorithm (RSSA) [Thanh et al., J. Chem. Phys. 141(13), 134116 (2014)]. The computation for selecting next reaction firings by our time-dependent RSSA (tRSSA) is computationally efficient. Furthermore, the generated trajectory is exact by exploiting the rejection-based mechanism. We benchmark tRSSA on different biological systems with varying forms of reaction rates to demonstrate its applicability and efficiency. We reveal that for nontrivial cases, the selection of reaction firings in existing algorithms introduces approximations because the integration of reaction rates is very computationally demanding and simplifying assumptions are introduced. The selection of the next reaction firing by our approach is easier while preserving the exactness. C 2015 AIP Publishing LLC. [http://dx

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“…In [9] the authors propose a method that dynamically limits the state space to those states that are of non-negligible probability. Since the number of states can be huge even if not all states are considered, in [10,11] approximate randomization methods have been proposed. Another natural approach is aggregation of states which can be done either by aggregating nearby states [12,13] or by exploiting the idea of flow equivalence [14].…”

Section: Introductionmentioning

confidence: 99%

Approximate analysis of biological systems by hybrid switching jump diffusion

Angius

Balbo

Beccuti

et al. 2015

Theoretical Computer Science

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In this paper we consider large state space continuous time Markov chains arising in the field of systems biology. For a class of such models, namely, for density dependent families of Markov chains that represent the interaction of large groups of identical objects, Kurtz has proposed two kinds of approximations. One is based on ordinary differential equations and provides a deterministic approximation, while the other uses a diffusion process with which the resulting approximation is stochastic. The computational cost of the deterministic approximation is significantly lower, but the diffusion approximation retains stochasticity and is able to reproduce relevant random features like variance, bimodality, and tail behavior that cannot be captured by a single deterministic quantity. In a recent paper, for particular stochastic Petri net models, we proposed a jump diffusion approximation that aims at being applicable beyond the limits of Kurtz's diffusion approximation in order to cover the case when the process reaches the boundary with non-negligible probability. In this paper we generalize the method so that it can be applied to any density dependent Markov chains. Other limitations of the diffusion approximation in its original form are that it can provide inaccurate results when the number of objects in some groups is often or constantly low and that it can be applied only to pure density dependent Markov chains. In order to overcome these drawbacks, in this paper we propose to apply the jump-diffusion approximation only to those components of the model that are in density dependent form and are associated with high population levels. The remaining components are treated as discrete quantities. The resulting process is a hybrid switching jump diffusion, i.e., a diffusion with hybrid state space and jumps where the discrete state changes can be seen as switches that take the diffusion from one condition to another. We show that the stochastic differential equations that characterize this process can be derived automatically both from the description of the original Markov chains or starting from a higher level description language, like stochastic Petri nets. The proposed approach is illustrated on three models: one modeling the so-called crazy clock reaction, one describing viral infection kinetics and the last considering transcription regulation.

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Fast adaptive uniformisation of the chemical master equation

Cited by 46 publications

References 17 publications

Precise parameter synthesis for stochastic biochemical systems

Precise parameter synthesis for stochastic biochemical systems

Simulation of biochemical reactions with time-dependent rates by the rejection-based algorithm

Approximate analysis of biological systems by hybrid switching jump diffusion

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