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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  
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

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

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.  ...  Semi-quantitative extend semi-qualitative with absolute time values by referring to to the predefined system variable time.  ... 
doi:10.1007/978-3-642-21834-7_2 fatcat:jhckua5qhvc3xohjwrrfqswxpq

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

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 formulate an algorithm for approximate computation of time-bounded reachability probabilities on the resulting DTMC and show how to extend it to more complex temporal properties.  ...  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

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.  ...  In [13] the authors explore how discrete qualitative models can be extended to quantitative models using a stochastic or continuous approach and how the three paradigms complement each other.  ... 
doi:10.1007/978-3-642-02481-8_161 fatcat:a4jah5qo5vekpcol3c6fqyn2ua

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.  ...  There are techniques to abstract (or approximate) continuous-value models by discrete-value models.  ... 
doi:10.1007/978-3-642-38874-3_3 fatcat:gko33i5f6fe33jl4zi2cdte6ha

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

Decisiveness of Stochastic Systems and its Application to Hybrid Models (Full Version) [article]

Patricia Bouyer, Thomas Brihaye, Mickael Randour, Cédric Rivière, Pierre Vandenhove
2022 arXiv   pre-print
Later, this concept was extended to more general stochastic transition systems (STSs), allowing the design of various verification algorithms for large classes of (infinite) STSs.  ...  We establish the decisiveness of a large class of SHSs and, under a few classical hypotheses from mathematical logic, we show how to decide reachability problems in this class, even though they are undecidable  ...  Approximate Quantitative Reachability Analysis In this section, we show under strengthened numerical hypotheses that we can solve the quantitative reachability problem in cycle-reset SHSs.  ... 
arXiv:2009.13152v2 fatcat:rujzjx5wkjf23pcokpwepas6de

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  
models will need to be further enhanced by various abstraction techniques to interpret phenomenological models of cancer progression.  ...  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.  ...  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

Semi-Quantitative Abstraction and Analysis of Chemical Reaction Networks [article]

Milan Češka, Jan Křetínský
2019 arXiv   pre-print
In this work we focus on population models arising from chemical reaction networks (CRNs), which play a fundamental role in analysis and design of biochemical systems.  ...  It focuses on qualitative description of the behaviour and aims at quantitative precision only in orders of magnitude.  ...  The common idea of these models is as follows: the dynamics of low population species is described by the discrete stochastic process and the dynamics of large population species is approximated by a continuous  ... 
arXiv:1905.09914v1 fatcat:tmwsps2u2rfjtjyufuop2hghqi

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

Paolo Ballarini, Maria Luisa Guerriero
2010 Theoretical Computer Science  
We illustrate the proposed querybased classification on a number of simple abstract models of biochemical systems.  ...  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  ...  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

Decisiveness of Stochastic Systems and its Application to Hybrid Models [article]

Patricia Bouyer, Thomas Brihaye, Mickael Randour, Cédric Rivière, Pierre Vandenhove
2020 arXiv   pre-print
Later, this concept was extended to more general stochastic transition systems (STSs), allowing the design of various verification algorithms for large classes of (infinite) STSs.  ...  We establish the decisiveness of a large class of SHSs and, under a few classical hypotheses from mathematical logic, we show how to decide reachability problems in this class, even though they are undecidable  ...  Approximate Quantitative Reachability Analysis In this section, we show under strenghtened numerical hypotheses that we can solve the quantitative reachability problem in cycle-reset SHSs.  ... 
arXiv:2001.04347v1 fatcat:6qq46rzlpzbv7d62dbdnap4ytm

Formal Quantitative Analysis of Reaction Networks Using Chemical Organisation Theory [chapter]

Chunyan Mu, Peter Dittrich, David Parker, Jonathan E. Rowe
2016 Lecture Notes in Computer Science  
In this paper, we build on these ideas to develop novel techniques for formal quantitative analysis of chemical reaction networks, using discrete stochastic models represented as continuous-time Markov  ...  be used to approximate and predict the behaviour of the original reaction network.  ...  Kreyssig et. al [14] studied the effects of small particle numbers on long-term behaviours in discrete biochemical systems.  ... 
doi:10.1007/978-3-319-45177-0_15 fatcat:cn4nivol4zdbnk2n6hczzlngmy
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