Jump-Diffusion Approximation of Stochastic Reaction Dynamics: Error Bounds and Algorithms

Ganguly, Arnab; Altintan, Derya; Koeppl, Heinz

doi:10.1137/140983471

Cited by 41 publications

(46 citation statements)

References 42 publications

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“…Moreover, the proposed method can be extended to a hybrid framework (e.g. [45][46][47]) where a diffusion approximation can be performed for some states and reactions. This is especially interesting for multi-scale cellular processes, for instance in signal transduction coupled to gene expression where different abundance scales of molecules are involved.…”

Section: Resultsmentioning

confidence: 99%

Reconstructing dynamic molecular states from single-cell time series

Huang

Paulevé

Zechner

et al. 2016

J. R. Soc. Interface.

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The notion of state for a system is prevalent in the quantitative sciences and refers to the minimal system summary sufficient to describe the time evolution of the system in a self-consistent manner. This is a prerequisite for a principled understanding of the inner workings of a system. Owing to the complexity of intracellular processes, experimental techniques that can retrieve a sufficient summary are beyond our reach. For the case of stochastic biomolecular reaction networks, we show how to convert the partial state information accessible by experimental techniques into a full system state using mathematical analysis together with a computational model. This is intimately related to the notion of conditional Markov processes and we introduce the posterior master equation and derive novel approximations to the corresponding infinite-dimensional posterior moment dynamics. We exemplify this state reconstruction approach using both in silico data and single-cell data from two gene expression systems in Saccharomyces cerevisiae, where we reconstruct the dynamic promoter and mRNA states from noisy protein abundance measurements.

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Section: Resultsmentioning

confidence: 99%

Reconstructing dynamic molecular states from single-cell time series

Huang

Paulevé

Zechner

et al. 2016

J. R. Soc. Interface.

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“…The algorithm can be used to convert differential equations representing the dynamics of biochemical reaction networks into differential algebraic forms. In [18], the algorithm is used to convert SDEs to SDAEs and involved in computer based simulation algorithm of jump diffusion approximation. In this paper, we used proposed algorithm to improve DM, FRM, NRM such that these new versions of algorithms can obtain independent variables, conservation constants and original state vectors whose definitions can be found in Section III.…”

Section: Discussionmentioning

confidence: 99%

“…If we use ODEs to model a system with conserved cycles [4], [10], [12], using conservation relations transforms ODEs into Differential Algebraic Equa-tions (DAEs). Similarly, in case of using SDEs to model such systems, involving conservation relations transform SDEs into Stochastic Differential Algebraic Equations (SDAE) [17], [18].…”

Section: Introductionmentioning

confidence: 99%

Using Conserved Cycles in Exact Stochastic Simulation Algorithms

Altintan¹

2016

SAUFenBilDer

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Biochemical reaction systems involve many different species interacting via many different reaction channels. When the number of species and the abundance of species are so high, pure modeling approaches based on differential equations suffer from curse of dimensionality. If a system involves conserved cycles, abundances of some species can be obtained via algebraic relations which in turn will reduce the dimension of differential equations representing the dynamics of the system. In the present paper, we propose a numerical algorithm that uses Gauss-Jordan method to obtain conserved cycles in biochemical systems. We give this algorithm in Direct Method (DM), First Reaction Method (FRM) and Next Reaction Method (NRM) which obtain exact realizations of the state vector in stochastic modeling approach. We apply these three algorithms with/without using conservation relations to biochemical systems in different sizes and compare the computational costs of two different versions of each exact algorithm.

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“…Stochastic simulations. We use a hybrid scheme that simulates reactions either using the next-reaction method or ODEs as described in 57 . To account for non-exponential reaction-time distributions 58 , we update propensities every 0.05 minutes.…”

Section: Methodsmentioning

confidence: 99%

Stochasticity of cellular growth: sources, propagation and consequences

Thomas

Terradot

Danos

et al. 2018

Preprint

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Cellular growth impacts a range of phenotypic responses. Identifying the sources of fluctuations in growth and how they propagate across the cellular machinery can unravel mechanisms that underpin cell decisions. We present a stochastic cell model linking gene expression, metabolism and replication to predict growth dynamics in single bacterial cells. In addition to several population-averaged data, the model quantitatively recovers how growth fluctuations in single cells change across nutrient conditions. We develop a framework to analyse stochastic chemical reactions coupled with cell divisions and use it to identify sources of growth heterogeneity. By visualising cross-correlations we then determine how such initial fluctuations propagate to growth rate and affect other cell processes. We further study antibiotic responses and find that complex drugnutrient interactions can both enhance and suppress heterogeneity. Our results provide a predictive framework to integrate single-cell and bulk data and draw testable predictions with implications for antibiotic tolerance, evolutionary biology and synthetic biology.

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Jump-Diffusion Approximation of Stochastic Reaction Dynamics: Error Bounds and Algorithms

Cited by 41 publications

References 42 publications

Reconstructing dynamic molecular states from single-cell time series

Reconstructing dynamic molecular states from single-cell time series

Using Conserved Cycles in Exact Stochastic Simulation Algorithms

Stochasticity of cellular growth: sources, propagation and consequences

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