Automated Symbolic Reachability Analysis; with Application to Delta-Notch Signaling Automata

Ghosh, Ronojoy; Tiwari, Ashish; Tomlin, Claire J.

doi:10.1007/3-540-36580-x_19

Cited by 64 publications

(57 citation statements)

References 15 publications

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“…Methods similar in spirit have been proposed in the hybrid systems community [22,23]. QR methods have been applied to the regulation of tryptophan synthesis [33] and phage growth [32] in E. coli, and to the regulation of the transcription factor families AP-1 and NF-B in different classes of animals [68].…”

Section: Discussionmentioning

confidence: 99%

“…On a formal level, the PL models are related to a class of asynchronous logical models proposed by Thomas and colleagues [66,67]. PL models and their logical relatives have been used for the study of a number of prokaryotic and eukaryotic regulatory networks [1,22,23,46,50,55,58,65]. In addition, they have been used for modeling food webs [53], neural networks [42], and biological computers [6].…”

Section: Introductionmentioning

confidence: 99%

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Qualitative simulation of genetic regulatory networks using piecewise-linear models

Jong

Gouzé

Hernandez

et al. 2004

Bulletin of Mathematical Biology

319

305

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In order to cope with the large amounts of data that have become available in genomics, mathematical tools for the analysis of networks of interactions between genes, proteins, and other molecules are indispensable. We present a method for the qualitative simulation of genetic regulatory networks, based on a class of piecewise-linear (PL) differential equations that has been well-studied in mathematical biology. The simulation method is well-adapted to state-of-the-art measurement techniques in genomics, which often provide qualitative and coarsegrained descriptions of genetic regulatory networks. Given a qualitative model of a genetic regulatory network, consisting of a system of PL differential equations and inequality constraints on the parameter values, the method produces a graph of qualitative states and transitions between qualitative states, summarizing the qualitative dynamics of the system. The qualitative simulation method has been implemented in Java in the computer tool Genetic Network Analyzer.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Qualitative simulation of genetic regulatory networks using piecewise-linear models

Jong

Gouzé

Hernandez

et al. 2004

Bulletin of Mathematical Biology

319

305

View full text Add to dashboard Cite

show abstract

“…These methods translate hybrid systems into an underlying verification framework, such as STeP [15], PVS [1], SAL [9], Fluctuat [5], and Event-B [2,21]. However, neither the translation nor the verification is fully automated, because some invariants must be added manually, and the theorem provers require some interactions.…”

Section: Related Workmentioning

confidence: 99%

Inductive Verification of Hybrid Automata with Strongest Postcondition Calculus

Ishii

Melquiond

Nakajima

2013

Lecture Notes in Computer Science

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Abstract. Safety verification of hybrid systems is a key technique in developing embedded systems that have a strong coupling with the physical environment. We propose an automated logical analytic method for verifying a class of hybrid automata. The problems are more general than those solved by the existing model checkers: our method can verify models with symbolic parameters and nonlinear equations as well. First, we encode the execution trace of a hybrid automaton as an imperative program. Its safety property is then translated into proof obligations by strongest postcondition calculus. Finally, these logic formulas are discharged by state-of-the-art arithmetic solvers (e.g., Mathematica). Our proposed algorithm efficiently performs inductive reasoning by unrolling the execution for some steps and generating loop invariants from verification failures. Our experimental results along with examples taken from the literature show that the proposed approach is feasible.

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“…The algorithm was implemented using MATLAB and QEPCAD, to compute reachable sets for the biologically observed equilibria of the multiple cell Delta Notch protein signaling automaton with symbolic parameters. The results were analyzed to show that novel, non-intuitive, and biologically interesting properties can be deduced from the reachability computation, thus demonstrating the utility of the algorithm [3,7,9].…”

Section: (I) Hybrid Systems Models For Parameter Identification In Bimentioning

confidence: 99%

Hybrid Control Models and Tools for Biological Regulatory Networks

Tomlin¹,

Axelrod²,

Sastry³

2003

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Public Reporting Burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. The research performed under this agreement produced: (i) a procedure, based on deterministic and stochastic hybrid system reachability tools, for identifying parameters of different biological systems; (ii) a technique for identifying parameters for continuous state models of protein regulatory networks; (iii) new insights, provided by these tools, into the operation of the mechanisms behind Planar Cell Polarity in Drosophila wings, and into the survival analysis of Bacillus subtilis.

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Automated Symbolic Reachability Analysis; with Application to Delta-Notch Signaling Automata

Cited by 64 publications

References 15 publications

Qualitative simulation of genetic regulatory networks using piecewise-linear models

Qualitative simulation of genetic regulatory networks using piecewise-linear models

Inductive Verification of Hybrid Automata with Strongest Postcondition Calculus

Hybrid Control Models and Tools for Biological Regulatory Networks

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