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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.  ...  This makes the method sufficient for approximating reachability in complex biochemical dynamical systems. In general, the following main contributions are brought by this paper.  ... 
arXiv:1107.5924v1 fatcat:hrxrx4w36zhfboilt35jkn4zfa

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  
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.  ...  This makes the method sufficient for approximating reachability in complex biochemical dynamical systems. In general, the following main contributions are brought by this paper.  ... 
doi:10.4204/eptcs.67.9 fatcat:lhrizlshanao3c4l4qw6hje2iy

Analysing Biochemical Oscillation through Probabilistic Model Checking

Paolo Ballarini, Radu Mardare, Ivan Mura
2009 Electronical Notes in Theoretical Computer Science  
In the second one a stochastic (discrete-state) model is obtained and analysed through (stochastic) simulation techniques, yielding statistical estimates of the system behaviour.  ...  In the first one a system of ordinary differential equations (ODEs) is developed and solved through numerical integration techniques yielding a deterministic solution of the model.  ...  Introduction The quantitative analysis of the dynamics of biological systems is a fundamental task in systems biology, a new research field that focuses on the systematic study of complex interactions  ... 
doi:10.1016/j.entcs.2009.02.002 fatcat:xvikdggc35etvclo4jld4t3nnu

From Petri Nets to Differential Equations – An Integrative Approach for Biochemical Network Analysis [chapter]

David Gilbert, Monika Heiner
2006 Lecture Notes in Computer Science  
We show that analysis based on a discrete Petri net model of the system can be used to derive the sets of initial concentrations required by the corresponding continuous ordinary differential equation  ...  Altogether, this paper represents a tutorial in step-wise modelling and analysis of larger models as well as in structured design of ODEs.  ...  This work has been supported by the DTI Bioscience Beacons Projects programme.  ... 
doi:10.1007/11767589_11 fatcat:2b7qkeayhvhjbky5gp55fmcdri

Query-based verification of qualitative trends and oscillations in biochemical systems

Paolo Ballarini, Maria Luisa Guerriero
2010 Theoretical Computer Science  
Qualitative/quantitative analysis of biochemical systems a b s t r a c t We investigate the application of query-based verification to the analysis of behavioural trends of stochastic models of biochemical  ...  We illustrate the proposed querybased classification on a number of simple abstract models of biochemical systems.  ...  The Centre for Systems Biology at Edinburgh is a Centre for Integrative Systems Biology (CISB) funded by the BBSRC and EPSRC in 2006.  ... 
doi:10.1016/j.tcs.2010.02.010 fatcat:5erppsuuanaz5bwy5qywep3zma

Computing reachable states for nonlinear biological models

Thao Dang, Colas Le Guernic, Oded Maler
2011 Theoretical Computer Science  
In this paper, we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models.  ...  We summarize the state-of-the-art for linear systems and then develop a novel algorithm for computing reachable states for nonlinear systems.  ...  Comments made by anonymous referees improved the presentation.  ... 
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  
In this paper, we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models.  ...  We summarize the state-of-the-art for linear systems and then develop a novel algorithm for computing reachable states for nonlinear systems.  ...  Comments made by anonymous referees improved the presentation.  ... 
doi:10.1007/978-3-642-03845-7_9 fatcat:ac54vmltbncjdgwuymzeb4l6zm

Qualitative analysis of biochemical reaction systems

Venkatramana N. Reddy, Michael N. Liebman, Michael L. Mavrovouniotis
1996 Computers in Biology and Medicine  
The qualitative analysis of biochemical reaction systems is presented. A discrete event systems approach is used to represent and analyze bioreaction pathways.  ...  Petri nets Biochemical pathways Qualitative analysis Modeling Discrete event  ...  Acknowledgements-This work was supported in part by the National Library of Medicine, Bethesda, MD (LM05278) and the Institute for Systems Research.  ... 
doi:10.1016/0010-4825(95)00042-9 pmid:8654057 fatcat:ohin5ltvgncc5oawns76hamwfm

How Might Petri Nets Enhance Your Systems Biology Toolkit [chapter]

Monika Heiner, David Gilbert
2011 Lecture Notes in Computer Science  
This includes the facilitation of an active and productive interaction between biomodellers and bioscientists during the construction and analysis of dynamic models of biological systems.  ...  How might Petri nets enhance my Systems Biology toolkit?" -this is one of the questions that we get on a regular basis, which motivated us to write an answer in the form of this paper.  ...  In addition, Snoopy files are directly read by ADAM -a tool applying computational algebra to analyse the dynamics of discrete models [65] , and simulation traces generated with Snoopy are read by MC2  ... 
doi:10.1007/978-3-642-21834-7_2 fatcat:jhckua5qhvc3xohjwrrfqswxpq

Approximation of Probabilistic Reachability for Chemical Reaction Networks Using the Linear Noise Approximation [chapter]

Luca Bortolussi, Luca Cardelli, Marta Kwiatkowska, Luca Laurenti
2016 Lecture Notes in Computer Science  
The LNA approximates the discrete stochastic semantics of a CRN in terms of a continuous space Gaussian process.  ...  We study time-bounded probabilistic reachability for Chemical Reaction Networks (CRNs) using the Linear Noise Approximation (LNA).  ...  A promising approach is to instead approximate the CTMC induced by a biochemical system as a continuous state space stochastic process by means of the Linear Noise Approximation (LNA), a Gaussian process  ... 
doi:10.1007/978-3-319-43425-4_5 fatcat:yhv7u2ab3fb3tj2ldpl73woqky

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  
Our approach is useful in helping correctly identify such properties and in connecting them to the underlying molecular dynamical details.  ...  An efficient reachability algorithm is possible for the resulting class of hybrid systems.  ...  Acknowledgments This work was supported in part by the DARPA BioComp grant F30602-01-2-0562. AMH was supported by NIH Individual Biomedical Informatics Fellowship award 1-F37-LM-  ... 
doi:10.1049/iet-syb:20060035 pmid:17441554 fatcat:a6tpgy2tb5gzzge7jso6tz5aqi

A Model Checking-based Analysis Framework for Systems Biology Models [article]

Bing Liu
2020 arXiv   pre-print
Such systems are naturally modeled as hybrid automata, which possess multiple operational modes with specific nonlinear dynamics in each mode.  ...  However, cell signaling events or pharmacological interventions may alter the cellular state and induce multi-mode dynamics of the system.  ...  ACKNOWLEDGMENT This work is supported by National Institutes of Health grants P01DK096990, U19AI068021, and P41GM103712.  ... 
arXiv:2004.12472v1 fatcat:myvmpc4pnfenjbu4zfri7adsfy

Model Checking of Biological Systems [chapter]

Luboš Brim, Milan Češka, David Šafránek
2013 Lecture Notes in Computer Science  
We present a selection of approaches used for modeling biological systems and formalizing their interesting properties in temporal logics.  ...  We also give a brief account of high performance model checking techniques and add a few case studies that demonstrate the use of model checking in computational systems biology.  ...  of systems dynamics based on qualitative and quantitative model checking.  ... 
doi:10.1007/978-3-642-38874-3_3 fatcat:gko33i5f6fe33jl4zi2cdte6ha

Systems Biology of Cancer: A Challenging Expedition for Clinical and Quantitative Biologists

Ilya Korsunsky, Kathleen McGovern, Tom LaGatta, Loes Olde Loohuis, Terri Grosso-Applewhite, Nancy Griffeth, Bud Mishra
2014 Frontiers in Bioengineering and Biotechnology  
In this paper, we summarize and classify models of systems biology and model checking tools, which have been used to great success in computational biology and related fields.  ...  We demonstrate how these models and tools have been used to study some of the twelve biochemical pathways implicated in but not unique to pancreatic cancer, and conclude that the resulting mechanistic  ...  ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under Grant No. 0926200.  ... 
doi:10.3389/fbioe.2014.00027 pmid:25191654 pmcid:PMC4137540 fatcat:xrtry6d4ffdmrp3ggnma523e74

A Critical Review on Modelling Formalisms and Simulation Tools in Computational Biosystems [chapter]

Daniel Machado, Rafael S. Costa, Miguel Rocha, Isabel Rocha, Bruce Tidor, Eugénio C. Ferreira
2009 Lecture Notes in Computer Science  
We briefly review modelling formalisms that have been used in Systems Biology and identify the criteria that must be addressed by an integrating framework capable of modelling, analysing and simulating  ...  Hybrid automata are dynamic systems with continuous variables ruled by differential equations and discrete state transitions. They are used in [12] to model the Delta-Notch signalling pathway.  ...  We tested Snoopy by importing an SBML model of the dynamic central carbon metabolism of E. coli described in [5] .  ... 
doi:10.1007/978-3-642-02481-8_161 fatcat:a4jah5qo5vekpcol3c6fqyn2ua
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