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Averaging Methods for Stochastic Dynamics of Complex Reaction Networks: Description of Multiscale Couplings

Sergey Plyasunov, Adam P. Arkin
2006 Multiscale Modeling & simulation  
This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation.  ...  The method suggested in this work is more general than other approaches presented previously: it is not limited to a particular type of stochastic processes and can be applied to different types of processes  ...  First, we present the formulation of stochastic reaction dynamics of reaction network consisting of two subnetworks.  ... 
doi:10.1137/050633822 fatcat:rj5ub35dhrclphekd6ghidd4v4

Robust simplifications of multiscale biochemical networks

Ovidiu Radulescu, Alexander N Gorban, Andrei Zinovyev, Alain Lilienbaum
2008 BMC Systems Biology  
First, we consider linear kinetic models, which appear as "pseudo-monomolecular" subsystems of multiscale nonlinear reaction networks.  ...  ., can be modeled as large networks of biochemical reactions.  ...  AZ is member of the team "Systems Biology of Cancer "équipe labellisée par la Ligue Nationale Contre le Cancer. We thank Upinder Bhalla, Dennis Bray and John Reinitz for inspiring discussions.  ... 
doi:10.1186/1752-0509-2-86 pmid:18854041 pmcid:PMC2654786 fatcat:4iymlaglvzbpbhzhktfmg6h73i

A new class of highly efficient exact stochastic simulation algorithms for chemical reaction networks

Rajesh Ramaswamy, Nélido González-Segredo, Ivo F. Sbalzarini
2009 Journal of Chemical Physics  
of the degree of coupling of the reaction network.  ...  We introduce an alternative formulation of the exact stochastic simulation algorithm (SSA) for sampling trajectories of the chemical master equation for a well-stirred system of coupled chemical reactions  ...  SPDM uses concepts from SDM ͑Ref. 12͒ to dynamically rearrange reactions, which reduces the average search depth for sampling the next reaction in a multiscale network.  ... 
doi:10.1063/1.3154624 pmid:19566139 fatcat:qtvite3x6nbxzprmcgzpbgnkja

Reduction of multiscale stochastic biochemical reaction networks using exact moment derivation

Jae Kyoung Kim, Eduardo D. Sontag, Lingchong You
2017 PLoS Computational Biology  
Reduction of multiscale stochastic biochemical reaction networks using exact moment derivation PLOS Computational Biology | https://doi.Reduction of multiscale stochastic biochemical reaction networks  ...  The stochastic simulations of such multiscale BRNs are prohibitively slow due to high computational cost for the simulations of fast reactions.  ...  Interestingly, a feedforward network is also observed in the networks of neuronal cells where stochastic multiscale dynamics of ion channels exist [75] [76] [77] [78] .  ... 
doi:10.1371/journal.pcbi.1005571 pmid:28582397 pmcid:PMC5481150 fatcat:2j7i7gzf5jdfzbqnpl75rtoxx4

Epidemic fronts in complex networks with metapopulation structure

Jason Hindes, Sarabjeet Singh, Christopher R. Myers, David J. Schneider
2013 Physical Review E  
In this paper we expand on the use of multitype networks for combining these paradigms, such that simple contagion models can include complexity in the agent interactions and multiscale structure.  ...  Infection dynamics have been studied extensively on complex networks, yielding insight into the effects of heterogeneity in contact patterns on disease spread.  ...  We thank Drew Dolgert for his assistance with our implementation of stochastic simulations.  ... 
doi:10.1103/physreve.88.012809 pmid:23944520 fatcat:cs25fhsq7vbgva6emy7dgu7efu

Hybrid stochastic simplifications for multiscale gene networks

Alina Crudu, Arnaud Debussche, Ovidiu Radulescu
2009 BMC Systems Biology  
These general results are difficult to obtain for exact models. Results: We propose a unified framework for hybrid simplifications of Markov models of multiscale stochastic gene networks dynamics.  ...  Sets of discrete and continuous variables are treated with different methods and are coupled together in a physically justified approach.  ...  Gorban for valuable discussions, the cycle averaging algorithm is inspired by previous joint works with him [36, 52, 59, 71] .  ... 
doi:10.1186/1752-0509-3-89 pmid:19735554 pmcid:PMC2761401 fatcat:r5hocluw6vc5pkzuwpmdt36ypi

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems

Stefanie Winkelmann, Christof Schütte
2017 Journal of Chemical Physics  
We derive a novel general description of such hybrid models that allows to express various forms by one type of equation.  ...  If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded.  ...  We presented several hybrid approaches for modelling multiscale reaction dynamics based on rescaling methods.  ... 
doi:10.1063/1.4986560 pmid:28938803 fatcat:4ai7gclcsbbsjdrhix4pj3aoee

ISAP-MATLAB Package for Sensitivity Analysis of High-Dimensional Stochastic Chemical Networks

Weilong Hu, Yannis Pantazis, Markos A. Katsoulakis
2018 Journal of Statistical Software  
As a result of the gradientfree and the sparse nature of the PFIM, it is highly suitable for the sensitivity analysis of stochastic reaction networks with a very large number of model parameters, which  ...  approach to quantify the parameter sensitivities of stochastic chemical reaction network dynamics using the pathwise Fisher information matrix (PFIM; Pantazis, Katsoulakis, and Vlachos 2013).  ...  Acknowledgment We would like to thank Georgios Arampatzis for his assistance in developing an early version of the SSA code and Jie Wang for testing the software and providing feedback.  ... 
doi:10.18637/jss.v085.i03 fatcat:hpeve3mlafbhlczaq6u3pnw4yu

Introduction: Multiscale Analysis - Modeling, Data, Networks, and Nonlinear Dynamics [chapter]

Misha Meyer Z. Pesenson
2013 Multiscale Analysis and Nonlinear Dynamics  
Multiscale Analysis -Modeling, Data, Networks, and Nonlinear Dynamics Misha (Meyer) Z. Pesenson " . . . the twin difficulties of scale and complexity." P. Anderson [1] " . . .  ...  We need a conception of tiers of networks with the highest tier as complex as the lower ones." F.  ...  Diffusion maps have also been applied to stochastic chemical reaction network simulations to recover the dynamically meaningful slowly varying coordinates [65] .  ... 
doi:10.1002/9783527671632.ch01 fatcat:yqwacdtquzfl5c55rsjgb3tbcq

A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks

Asawari Samant, Babatunde A Ogunnaike, Dionisios G Vlachos
2007 BMC Bioinformatics  
Bistable models serve as stringent tests for the success of multiscale MC methods and illustrate limitations of some literature methods.  ...  In addition, we introduce the computational singular perturbation (CSP) method as a means of systematically partitioning fast and slow networks and computing relaxation times for convergence.  ...  However, any opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of the DOE.  ... 
doi:10.1186/1471-2105-8-175 pmid:17524148 pmcid:PMC1894989 fatcat:t4ob3k5wljf2dcdsjjmk4hvw7i

Quantifying stochastic effects in biochemical reaction networks using partitioned leaping

Leonard A. Harris, Aaron M. Piccirilli, Emily R. Majusiak, Paulette Clancy
2009 Physical Review E  
"Leaping" methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks.  ...  Phys. 125, 144107 (2006)], a recently-introduced multiscale leaping approach. We use the PLA to investigate stochastic effects in two model biochemical reaction networks.  ...  description of reaction dynamics to the more familiar continuous-deterministic representation [41] .  ... 
doi:10.1103/physreve.79.051906 pmid:19518479 fatcat:rlaeqwb4qndj3pzzcbk5gr75ii

Multiscale analysis of reaction networks

Luca Sbano, Markus Kirkilionis
2008 Theory in biosciences  
In this paper we demonstrate the necessity to study reaction networks in a stochastic formulation for which we can construct a coherent approximation in terms of specific space-time scales and the number  ...  We apply the asymptotic theory to derive the effective, i.e. macroscopic dynamics of the biochemical reaction system.  ...  Acknowledgements The authors would like to thank Mirela Domijan for thorough reading the paper and for her comments.  ... 
doi:10.1007/s12064-008-0036-x pmid:18446398 fatcat:52aywlvl2fbyjmyhg6l2bkafne

Multiscale Analysis of Reaction Networks [article]

L. Sbano, M. Kirkilionis
2008 arXiv   pre-print
In this paper we demonstrate the necessity to study reaction networks in a stochastic formulation for which we can construct a coherent approximation in terms of specific space-time scales and the number  ...  We apply the asymptotic theory to derive the effective, i.e. macroscopic dynamics of the biochemical reaction system.  ...  Acknowledgements The authors would like to thank Mirela Domijan for thorough reading the paper and for her comments.  ... 
arXiv:0802.4361v1 fatcat:wr4r6q7fivdrhowcdazudkosmu

A hybrid multiscale coarse-grained method for dynamics on complex networks [article]

Chuansheng Shen, Hanshuang Chen, Zhonghuai Hou, Jürgen Kurths
2016 arXiv   pre-print
Brute-force simulations for dynamics on very large networks are quite expensive.  ...  Here, we propose a hybrid multiscale coarse-grained(HMCG) method which combines a fine Monte Carlo(MC) simulation on the part of nodes of interest with a more coarse Langevin dynamics on the rest part.  ...  Simulation methods such as MC dynamics, kinetic MC dynamics, molecular dynamics, Figure 6 . Schematic illustration of the hybrid multiscale coarse-grained method.  ... 
arXiv:1605.04511v1 fatcat:ifayk2jz2jfqvagr6barke45km

Stochastic modelling of gene regulatory networks

Hana El Samad, Mustafa Khammash, Linda Petzold, Dan Gillespie
2005 International Journal of Robust and Nonlinear Control  
Modelling of such networks poses new challenges due, in part, to the small number of molecules involved and the stochastic nature of their interactions.  ...  Gene regulatory networks are dynamic and stochastic in nature, and exhibit exquisite feedback and feedforward control loops that regulate their biological function at different levels.  ...  Air Force Office of Scientific Research and the California Institute of  ... 
doi:10.1002/rnc.1018 fatcat:tutyvcbuijelpc3tzdbe6sol6q
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