Hybrid Chernoff Tau-Leap

Moraes, Alvaro; Tempone, Raúl; Vilanova, Pedro

doi:10.1137/130925657

Cited by 21 publications

(61 citation statements)

References 19 publications

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“…The main difficulty in designing such a multilevel Monte Carlo approach for the estimation of the sensitivity indices will be the enforcement of consistent realizations for the channels' Poisson processes in tau-leaping approximations. 23,[42][43][44] Indeed, one would need to sample the same realization of a Poisson process for different time step and parameter values and not just to generate highly correlated but distinct realizations of the Poisson process. This can be achieved via a conditional sampling of the Poisson process increments.…”

Section: Discussionmentioning

confidence: 99%

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

Jimenez

Maître

Knio

2016

The Journal of Chemical Physics

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Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol’s decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.

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Section: Discussionmentioning

confidence: 99%

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

Jimenez

Maître

Knio

2016

The Journal of Chemical Physics

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“…In particular, complex systems involving large numbers of channels and species would benefit from the incorporation of more elaborate time-integrators; for instance, if an unaffordable number of elementary reactions fires before reaching the final time, tau-leap methods [4][5][6]28,29 should be considered to accelerate the simulations. Extending our methodology to tau-leap methods will require consistent time-approximations for the individual realizations of the Poisson processes associated with each channel.…”

Section: Discussionmentioning

confidence: 99%

Variance decomposition in stochastic simulators

2015

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Articles you may be interested inThis work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models. C 2015 AIP Publishing LLC. [http://dx

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“…The τ ‐leaping method may provide a significant speed gain, since many single reaction events can be leaped over, but there are several problems for its practical implementation. First, the efficiency and accuracy of the τ ‐leaping method strongly depends on the selection of τ that satisfies the leap condition (Anderson, ; Cao, Gillespie, & Petzold, ; Gillespie & Petzold, ; Moraes, Tempone, & Vilanova, ). Second, given a τ that satisfies the leap condition, the procedure must ensure that only few reactions fire together, thereby, avoiding reaching a negative population of reactant species (Cao, Gillespie, & Petzold, ).…”

Section: Stochastic Simulation Algorithmmentioning

confidence: 99%

Stochastic simulation algorithms for computational systems biology: Exact, approximate, and hybrid methods

Simoni

Reali

Priami

et al. 2019

WIREs Mechanisms of Disease

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Nowadays, mathematical modeling is playing a key role in many different research fields. In the context of system biology, mathematical models and their associated computer simulations constitute essential tools of investigation. Among the others, they provide a way to systematically analyze systems perturbations, develop hypotheses to guide the design of new experimental tests, and ultimately assess the suitability of specific molecules as novel therapeutic targets. To these purposes, stochastic simulation algorithms (SSAs) have been introduced for numerically simulating the time evolution of a well‐stirred chemically reacting system by taking proper account of the randomness inherent in such a system. In this work, we review the main SSAs that have been introduced in the context of exact, approximate, and hybrid stochastic simulation. Specifically, we will introduce the direct method (DM), the first reaction method (FRM), the next reaction method (NRM) and the rejection‐based SSA (RSSA) in the area of exact stochastic simulation. We will then present the τ‐leaping method and the chemical Langevin method in the area of approximate stochastic simulation and an implementation of the hybrid RSSA (HRSSA) in the context of hybrid stochastic‐deterministic simulation. Finally, we will consider the model of the sphingolipid metabolism to provide an example of application of SSA to computational system biology by exemplifying how different simulation strategies may unveil different insights into the investigated biological phenomenon. This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Analytical and Computational Methods > Computational Methods

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Hybrid Chernoff Tau-Leap

Cited by 21 publications

References 19 publications

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

Variance decomposition in stochastic simulators

Stochastic simulation algorithms for computational systems biology: Exact, approximate, and hybrid methods

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