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Reachability in Biochemical Dynamical Systems by Quantitative Discrete Approximation (extended abstract)

L. Brim, J. Fabriková, S. Dražan, D. Šafránek
2011 Electronic Proceedings in Theoretical Computer Science  
In this paper, a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced.  ...  By employing this approximation technique, we present algorithms solving the reachability problem for biochemical dynamical systems.  ...  Biochemical dynamical system According to [19] , by a biochemical dynamical system we understand a collection of n biochemical species interacting in biochemical reactions.  ... 
doi:10.4204/eptcs.67.9 fatcat:lhrizlshanao3c4l4qw6hje2iy

Reachability analysis of a biodiesel production system using stochastic hybrid systems

Derek Riley, Xenofon Koutsoukos, Kasandra Riley
2007 2007 Mediterranean Conference on Control & Automation  
In this paper we model a biodiesel production system as a stochastic hybrid system, and we present a probabilistic verification method for reachability analysis.  ...  The verification method employs dynamic programming based on a discretization of the state space and therefore suffers from the curse of dimensionality.  ...  This paper adopts a SHS model that is a special case of the general model presented in [6] and employs a reachability analysis method based on discrete approximations.  ... 
doi:10.1109/med.2007.4433779 fatcat:kfypa2seabgpxacleuep5pt3zm

Reachability in Biochemical Dynamical Systems by Quantitative Discrete Approximation [article]

Lubos Brim and Jana Fabrikova and Sven Drazan and David Safranek
2011 arXiv   pre-print
By employing this approximation technique, we present algorithms solving the reachability problem for biochemical dynamical systems.  ...  In this paper a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced.  ...  Biochemical dynamical system According to [18] , by a biochemical dynamical system we understand a collection of n biochemical species interacting in biochemical reactions.  ... 
arXiv:1107.5924v1 fatcat:hrxrx4w36zhfboilt35jkn4zfa

Modelling and analysis of the sugar cataract development process using stochastic hybrid systems

D. Riley, K. Riley, X. Koutsoukos
2009 IET Systems Biology  
A novel feature of the framework is that it allows modelling the effect of drug treatment on the system dynamics.  ...  Modelling and analysis of biochemical systems such as sugar cataract development (SCD) are critical because they can provide new insights into systems, which cannot be easily tested with experiments; however  ...  We would like to thank Howard Salis and Yiannis Kaznessis from the University of Minnesota for their help with this project.  ... 
doi:10.1049/iet-syb.2008.0101 pmid:19449975 fatcat:c34eseql7rb2lagt7ijwr7ovjq

Control mechanisms for stochastic biochemical systems via computation of reachable sets

Eszter Lakatos, Michael P. H. Stumpf
2017 Royal Society Open Science  
We show that our reachability analysis formalism can describe the potential behaviour of biological (naturally evolved as well as engineered) systems, and provides a set of bounds on their dynamics at  ...  We present an approach to studying the impact of control measures on motifs of molecular interactions, that addresses the problems faced in biological systems: stochasticity, parameter uncertainty, and  ...  The first system presents the use of reachability analysis for the study of noisy biochemical reactions and evaluating a control on the levels of cell heterogeneity; the second example considers the task  ... 
doi:10.1098/rsos.160790 pmid:28878957 pmcid:PMC5579072 fatcat:wwdkzpekvvdfrijkaq4d3h26cm

High-performance analysis of biological systems dynamics with the DiVinE model checker

J. Barnat, L. Brim, D. Safranek
2010 Briefings in Bioinformatics  
In this review, we provide a brief description of the tool DiVinE adapted for automatized analysis of biological systems dynamics.  ...  The current interest in systems biology is to gain a better understanding of how the complex dynamic behaviour of the cell emerges from mutual interactions of molecular species.  ...  The technique of model checking can provide a powerful scalable tool for analysis of biological systems dynamics.  ... 
doi:10.1093/bib/bbp074 pmid:20478855 fatcat:ufnwwxw3pfffvjjbv3koejbjrm

Control mechanisms for stochastic biochemical systems via computation of reachable sets [article]

Eszter Lakatos, Michael Stumpf
2016 biorxiv/medrxiv   pre-print
We show that our reachability analysis formalism can describe the potential behaviour of biological (naturally evolved as well as engineered) systems, and provides a set of bounds on their dynamics at  ...  We present an approach to studying the impact of control measures on motifs of molecular interactions, that addresses the problems faced in biological systems: stochasticity, parameter uncertainty, and  ...  The first system presents the use of reachability analysis for the study of noisy biochemical reactions and evaluating a control on the levels of cell heterogeneity; the second example considers the task  ... 
doi:10.1101/079723 fatcat:xuiropcfhzbkrl2cdn5xicinuy

Reachability Analysis of Stochastic Hybrid Systems: A Biodiesel Production System

Derek Riley, Kasandra Riley, Xenofon Koutsoukos
2010 European Journal of Control  
Reachability analysis of stochastic hybrid systems (SHS) is an important problem because it provides a formal framework to analyze complex systems.  ...  We also present an exhaustive verification technique based on dynamic programming, and we use the method to analyze the likelihood of quality biodiesel production.  ...  SHS extend hybrid systems by considering stochastic dynamics and providing a probabilistic framework for modeling and analysis of biochemical systems.  ... 
doi:10.3166/ejc.16.609-623 fatcat:h3gcnij2enh7xht7pgum5kgezm

Verification of Biochemical Processes Using Stochastic Hybrid Systems

Derek Riley, Xenofon Koutsoukos, Kasandra Riley
2007 2007 IEEE 22nd International Symposium on Intelligent Control  
Modeling and analysis of biochemical systems are critical problems because they can provide new insights into systems which can not be easily tested with real experiments.  ...  Our analysis can potentially provide useful insights into the complicated dynamics of the process and assist in focusing experiments on specific regions of concentrations.  ...  This paper employs a reachability analysis method based on discrete approximations. Discrete approximation methods based on finite differences have been studied extensively in [16] .  ... 
doi:10.1109/isic.2007.4450868 dblp:conf/IEEEisic/RileyKR07 fatcat:r65cpasls5azdemhqsohb6ixti

Analysis of lactose metabolism in E.coli using reachability analysis of hybrid systems

Á. Halász, V. Kumar, M. Imieliński, S. Pathak, O. Sokolsky, C. Belta, H. Rubin
2007 IET Systems Biology  
We propose an abstraction method for medium scale biomolecular networks, based on hybrid dynamical systems with continuous multi-affine dynamics.  ...  We use reachability analysis together with the knowledge of the steady state structure to identify ranges of parameter values for which the system maintains the bistable switching property.  ...  There has been recent progress on reachability analysis of linear systems, including piecewise linear switched systems.  ... 
doi:10.1049/iet-syb:20060035 pmid:17441554 fatcat:a6tpgy2tb5gzzge7jso6tz5aqi

Supplementary Derivations and Results from Control mechanisms for stochastic biochemical systems via computation of reachable sets

Eszter Lakatos, Michael P. H. Stumpf
2017 Figshare  
We show that our reachability analysis formalism can describe the potential behaviour of biological (naturally evolved as well as engineered) systems, and provides a set of bounds on their dynamics at  ...  We present an approach to studying the impact of control measures on motifs of molecular interactions, that addresses the problems faced in many biological systems: stochasticity, parameter uncertainty  ...  Analysis of the controlled gene expression system with uncertainty in all parameters We also studied the set of states reachable in the controlled gene expression system, in case both degradation rates  ... 
doi:10.6084/m9.figshare.5306884.v1 fatcat:w7fhzgjaarhmdgsw6jb2pzfqvy

BioDiVinE: A Framework for Parallel Analysis of Biological Models

Jiří Barnat, Luboš Brim, Ivana Černá, Sven Dražan, Jana Fabriková, Jan Láník, David Šafránek, Hongwu Ma
2009 Electronic Proceedings in Theoretical Computer Science  
At that level, parallel analysis algorithms based on model checking are provided. In the paper, the key tool features are described and their application is demonstrated by means of a case study.  ...  In this paper a novel tool BioDiVinEfor parallel analysis of biological models is presented. The tool allows analysis of biological models specified in terms of a set of chemical reactions.  ...  Since the analysed systems are typically non-affine, we can still employ the liveness checking on their linearised approximations.  ... 
doi:10.4204/eptcs.6.3 fatcat:dxboa3v4anbybi4ehzaa4opcci

Computing reachable states for nonlinear biological models

Thao Dang, Colas Le Guernic, Oded Maler
2011 Theoretical Computer Science  
We believe these results constitute a promising contribution to the analysis of complex models of biological systems.  ...  We summarize the state-of-the-art for linear systems and then develop a novel algorithm for computing reachable states for nonlinear systems.  ...  The analysis techniques that we use and extend originate from the study of hybrid dynamical systems, a domain situated in the intersection of control theory and computer science and are based on reachability  ... 
doi:10.1016/j.tcs.2011.01.014 fatcat:p2pyk4aulbcghlzerijychsmla

Computing Reachable States for Nonlinear Biological Models [chapter]

Thao Dang, Colas Le Guernic, Oded Maler
2009 Lecture Notes in Computer Science  
We believe these results constitute a promising contribution to the analysis of complex models of biological systems.  ...  We summarize the state-of-the-art for linear systems and then develop a novel algorithm for computing reachable states for nonlinear systems.  ...  The analysis techniques that we use and extend originate from the study of hybrid dynamical systems, a domain situated in the intersection of control theory and computer science and are based on reachability  ... 
doi:10.1007/978-3-642-03845-7_9 fatcat:ac54vmltbncjdgwuymzeb4l6zm

Computing the projected reachable set of switched affine systems: an application to systems biology [article]

Francesca Parise, Maria Elena Valcher, John Lygeros
2017 arXiv   pre-print
Motivated by this application, we propose a new method to approximate the reachable set of switched affine systems.  ...  A remarkable feature of our approach is that it allows one to easily compute projections of the reachable set for pairs of moments of interest, without requiring the computation of the full reachable set  ...  We thus start our analysis by proposing a new method to approximate the reachable set of a switched affine system.  ... 
arXiv:1705.00400v1 fatcat:gyx3kchhprayri3aeeja54qjga
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