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Modelling and Verifying Dynamic Properties of Biological Neural Networks in Coq

Published: 10 December 2018 Publication History

Abstract

Formal verification has become increasingly important because of the kinds of guarantees that it can provide for software systems. Verification of models of biological and medical systems is a promising application of formal verification. Human neural networks have recently been emulated and studied as a biological system. Some recent research has been done on modelling some crucial neuronal circuits and using model checking techniques to verify their temporal properties. In large case studies, model checkers often cannot prove the given property at the desired level of generality. In this paper, we provide a model using the Coq Proof Assistant and prove properties concerning the dynamic behavior of some basic neuronal structures. Understanding the behavior of these modules is crucial because they constitute the elementary building blocks of bigger neuronal circuits. By using a proof assistant, we guarantee that the properties are true for any input values, any length of input, and any amount of time. With such a model, there is the potential to detect inactive regions of the human brain and to treat mental disorders. Furthermore, our approach can be generalized to the verification of other kinds of networks, such as regulatory, metabolic, or environmental networks.

References

[1]
E.M. Clarke, O. Grumberg, and D. Peled. 1999. Model Checking. MIT Press, Cambridge, MA, USA.
[2]
D.R. Gilbert and M. Heiner. 2015. Advances in computational methods in systems biology. Theoretical Computer Science, 599, 2--3.
[3]
F. Fages, S. Soliman, and N. Chabrier-Rivier. (2004). Modelling and querying interaction networks in the biochemical abstract machine BIOCHAM. Journal of Biological Physics and Chemistry, 4(2), 64--73.
[4]
A. Richard, J.P. Comet, and G. Bernot. 2004. Graph-based modeling of biological regulatory networks: Introduction of singular states. In International Conference on Computational Methods in Systems Biology (CMSB '04), pp. 58--72.
[5]
E. De Maria, F. Fages, A. Rizk, and S. Soliman. 2011. Design, optimization and predictions of a coupled model of the cell cycle, circadian clock, DNA repair system, irinotecan metabolism and exposure control under temporal logic constraints. Theoretical Computer Science 412(21), 2108--2127.
[6]
C.L Talcott, and M. Knapp. 2017. Explaining response to drugs using pathway logic. In International Conference on Computational Methods in Systems Biology (CMSB '17), pp. 249--264.
[7]
R. Thomas, D. Thieffry, and M. Kaufman. 1995. Dynamical behaviour of biological regulatory networks-i. Biological role of feedback loops and practical use of the concept of the loop-characteristic state. Bulletin of Mathematical Biology 57(2), 247--276.
[8]
V.N Reddy, M.L. Mavrovouniotis, and M.N. Liebman. 1993. Petri net representations in metabolic pathways. In Proceedings of the 1st International Conference on Intelligent Systems for Molecular Biology (ISMB '93). pp. 328--336. AAAI Press.
[9]
A. Regev, W. Silverman, and E.Y. Shapiro. 2001. Representation and simulation of biochemical processes using the pi-calculus process algebra. In Proceedings of the sixth Pacific Symposium of Biocomputing (PSB '01), pp. 459--470.
[10]
A. Regev, E.M. Panina, W. Silverman, L. Cardelli, and E. Shapiro. (2004). Bioambients: An abstraction for biological compartments. Theoretical Computer Science 325(1), 141--167.
[11]
N. Chabrier-Rivier, M. Chiaverini, V. Danos, F. Fages, and V. Schächter. (2004). Modeling and querying biochemical interaction networks. Theoretical Computer Science 325(1), 25--44.
[12]
R. Hofestädt and S. Thelen. 1998. Quantitative modeling of biochemical networks. In Silico Biology, vol. 1, pp. 39--53. IOS Press.
[13]
R. Alur, C. Belta, F. Ivanicic, V. Kumar, M. Mintz, G.J. Pappas, H. Rubin, and J. Schug. 2001. Hybrid modeling and simulation of biomolecular networks. In Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control (HSCC'01), Springer LNCS, vol. 2034.
[14]
A. Phillips and L. Cardelli, L. 2004. A correct abstract machine for the stochastic pi-calculus. In Proceedings of BioConcur, Electronic Notes in Computer Science.
[15]
V. Danos and C. Laneve. 2004. Formal molecular biology, Theoretical Computer Science 325(1), 69--110.
[16]
A. Cimatti, E.M. Clarke, F. Giunchiglia, and M. Roveri. 1999. NUSMV: A new symbolic model verifier. In Proceedings of the 11th Intl. Conference on Computer Aided Verification. pp. 495--499. CAV '99, Springer-Verlag, London, UK.
[17]
M. Kwiatkowska, G. Norman, and D. Parker. 2011. PRISM 4.0 2001 Verification of probabilistic real-time systems. In Proceedings of the 23rd International Conference on Computer Aided Verification (CAV'11), volume 6806 of Springer LNCS, pp. 585--591.
[18]
E. De Maria, J. Despeyroux, and A.P. Felty. 2014. A Logical Framework for Systems Biology, In 1st International Conference on Formal Methods in Macro-Biology (FMMB '14), Springer LNCS 8738, pp. 136--155.
[19]
A. Rashid, O. Hasan, U. Siddique, and S. Tahar. 2017. Formal reasoning about systems biology using theorem proving. PLoS ONE 12(7): e0180179.
[20]
O. Andrei, M. Fernández, H. Kirchner, and B. Pinaud. 2016. Strategy-Driven Exploration for Rule-Based Models of Biochemical Systems with Porgy. Research Report: Université de Bordeaux, Inria; King's College London, University of Glasgow.
[21]
E. De Maria, A. Muzy, D. Gaffé, A. Ressouche, and F. Grammont. 2016. Verification of Temporal Properties of Neuronal Archetypes Modeled as Synchronous Reactive Systems. In Hybrid Systems Biology - 5th International Workshop, (HSB '16), Grenoble, France, October 20-21, 2016, pp. 97--112.
[22]
E. De Maria, T. L'Yvonnet, D. Gaffé, A. Ressouche, and F. Grammont. 2017. Modelling and Formal Verification of Neuronal Archetypes Coupling. In 8th International Conference on Computational Systems-Biology and Bioinformatics (CSBio 2017), pp. 3--10.
[23]
H. Markram. 2006. The blue brain project. Nat Rev Neurosci 7(2), 153--160.
[24]
G. Hagen and C. Tinelli. 2008. Scaling up the formal verification of Lustre programs with SMT-based techniques. In Proceedings of the 2008 International Conference on Formal Methods in Computer-Aided Design (FMCAD '08), pp. 1--9.
[25]
Y. Bertot and P. Castéran. 2004. Interactive Theorem Proving and Program Development. Coq'Art: The Calculus of Inductive Constructions. Springer.
[26]
D. Purves, G.J. Augustine, D. Fitzpatrick, W.C. Hall, A.S. LaMantia, J.O. McNamara, and S.M. Williams. (Eds.) 2006. Neuroscience (3rd ed.). Sinauer Associates, Inc.
[27]
H. Paugam-Moisy and S.M. Bohte. 2012. Computing with spiking neuron networks. In Handbook of Natural Computing, pp. 335--376.
[28]
L. Lapicque. 1907. Recherches quantitatives sur l'excitation electrique des nerfs traitee comme une polarization. J Physiol Pathol Gen 9, 620--635.
[29]
E.M. Izhikevich. 2004. Which model to use for cortical spiking neurons? IEEE Transactions on Neural Networks 15(5), 1063--1070.
[30]
B. Aman and G. Ciobanu. 2016. Modelling and verification of weighted spiking neural systems. Theoretical Computer Science 623, 92--102.
[31]
E. De Maria and C. Di Giusto. 2018. Parameter Learning for Spiking Neural Networks Modelled as Timed Automata. In 9th International Conference on Bioinformatics Models, Methods and Algorithms (BIOINFORMATICS '18), pp. 17--28.
[32]
E. De Maria, D. Gaffé, C. Girard Riboulleau, and A. Ressouche. 2018. A Model-checking Approach to Reduce Spiking Neural Networks. In 9th International Conference on Bioinformatics Models, Methods and Algorithms (BIOINFORMATICS '18), pp. 89--96.
[33]
W. Maass. 1997. Networks of spiking neurons: The third generation of neural network models. Neural Networks, 10(9):1659--1671.
[34]
Coq reference manual. Retrieved from https://coq.inria.fr/distrib/current/-refman/index.html.
[35]
T. Coquand and G. Huet. 1988. The calculus of constructions. Information and Computation, 76, 95--120.

Cited By

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  • (2023)Computational Logic for Biomedicine and NeurosciencesSymbolic Approaches to Modeling and Analysis of Biological Systems10.1002/9781394229086.ch6(187-234)Online publication date: 4-Aug-2023
  • (2020)Towards Automated Comprehension and Alignment of Cardiac Models at the System Invariant LevelCSBio '20: Proceedings of the Eleventh International Conference on Computational Systems-Biology and Bioinformatics10.1145/3429210.3429225(18-28)Online publication date: 19-Nov-2020

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  1. Modelling and Verifying Dynamic Properties of Biological Neural Networks in Coq

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      cover image ACM Other conferences
      CSBio 2018: Proceedings of the 9th International Conference on Computational Systems-Biology and Bioinformatics
      December 2018
      73 pages
      ISBN:9781450365604
      DOI:10.1145/3291757
      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

      In-Cooperation

      • KMUTT: King Mongkut's University of Technology Thonburi
      • KU: Kasetsart University

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      Association for Computing Machinery

      New York, NY, United States

      Publication History

      Published: 10 December 2018

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      Author Tags

      1. Archetypes
      2. Biological network reconstruction and analysis
      3. Coq Proof Assistant
      4. Dynamic Properties
      5. Formal Verification
      6. Human Neural Networks
      7. Leaky Integrate and Fire Model
      8. Modelling and simulation of biological processes and pathways
      9. Neuronal Modules
      10. Theorem Proving

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      CSBio 2018

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      CSBio 2018 Paper Acceptance Rate 12 of 19 submissions, 63%;
      Overall Acceptance Rate 23 of 37 submissions, 62%

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      Cited By

      View all
      • (2023)Computational Logic for Biomedicine and NeurosciencesSymbolic Approaches to Modeling and Analysis of Biological Systems10.1002/9781394229086.ch6(187-234)Online publication date: 4-Aug-2023
      • (2020)Towards Automated Comprehension and Alignment of Cardiac Models at the System Invariant LevelCSBio '20: Proceedings of the Eleventh International Conference on Computational Systems-Biology and Bioinformatics10.1145/3429210.3429225(18-28)Online publication date: 19-Nov-2020

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