Model Checking Tap Withdrawal in C. Elegans

  • Md. Ariful IslamEmail author
  • Richard De Francisco
  • Chuchu Fan
  • Radu Grosu
  • Sayan Mitra
  • Scott A. Smolka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9271)


We present what we believe to be the first formal verification of a biologically realistic (nonlinear ODE) model of a neural circuit in a multicellular organism: Tap Withdrawal (TW) in C. Elegans, the common roundworm. TW is a reflexive behavior exhibited by C. Elegans in response to vibrating the surface on which it is moving; the neural circuit underlying this response is the subject of this investigation. Specially, we perform reach-tube-based reachability analysis on the TW circuit model of Wicks et al. (1996) to estimate key model parameters. Underlying our approach is the use of Fan and Mitra’s recently developed technique for automatically computing local discrepancy (convergence and divergence rates) of general nonlinear systems.

The results we obtain are a significant extension of those of Wicks et al. (1996), who equip their model with fixed parameter values that reproduce the predominant TW response they observed experimentally in a population of 590 worms. In contrast, our techniques allow us to much more fully explore the model’s parameter space, identifying in the process the parameter ranges responsible for the predominant behavior as well as the non-dominant ones. The verification framework we developed to conduct this analysis is model-agnostic, and can thus be re-used on other complex nonlinear systems.


Model Check Neural Circuit Central Pattern Generator Reachability Analysis Synaptic Conductance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We would like to thank Junxing Yang, Heraldo Memelli, Farhan Ali, and Elizabeth Cherry for their numerous contributions to this project. Our research is supported in part by the following grants: NSF IIS 1447549, NSF CAR 1054247, AFOSR FA9550-14-1-0261, AFOSR YIP FA9550-12-1-0336, CCF-0926190, and NASA NNX12AN15H.


  1. 1.
    Donzé, A., Maler, O.: Systematic simulation using sensitivity analysis. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 174–189. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Duggirala, P.S., Mitra, S., Viswanathan, M.: Verification of annotated models from executions. In: Proceedings of the International Conference on Embedded Software, EMSOFT 2013, Montreal, Canada. IEEE, September–October 2013Google Scholar
  3. 3.
    Duggirala, P.S., Mitra, S., Viswanathan, M., Potok, M.: C2E2: a verification tool for stateflow models. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 68–82. Springer, Heidelberg (2015)Google Scholar
  4. 4.
    Duggirala, P.S., Wang, L., Mitra, S., Viswanathan, M., Muñoz, C.: Temporal precedence checking for switched models and its application to a parallel landing protocol. In: Jones, C., Pihlajasaari, P., Sun, J. (eds.) FM 2014. LNCS, vol. 8442, pp. 215–229. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  5. 5.
    Fan, C., Mitra, S.: Bounded verification using on-the-fly discrepancy computation. Technical report UILU-ENG-15-2201, Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, February 2015Google Scholar
  6. 6.
    Grosu, R., Batt, G., Fenton, F.H., Glimm, J., Le Guernic, C., Smolka, S.A., Bartocci, E.: From cardiac cells to genetic regulatory networks. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 396–411. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physio. 117, 500–544 (1952)CrossRefGoogle Scholar
  8. 8.
    Huang, Z., Fan, C., Mereacre, A., Mitra, S., Kwiatkowska, M.: Invariant verification of nonlinear hybrid automata networks of cardiac cells. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 373–390. Springer, Heidelberg (2014)Google Scholar
  9. 9.
    Islam, M.A., Murthy, A., Girard, A., Smolka, S.A., Grosu, R.: Compositionality results for cardiac cell dynamics. In: Proceedings of the 17th International Conference on Hybrid Systems: Computation and Control. ACM (2014)Google Scholar
  10. 10.
    Iyengar, S.M., Talcott, C., Mozzachiodi, R., Cataldo, E., Baxter, D.A.:Executable symbolic models of neural processes. Netw. tools appl. biol. NETTAB07 (2007)Google Scholar
  11. 11.
    Lohmiller, W., Slotine, J.J.E.: On contraction analysis for non-linear systems. Automatica 34, 683–696 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Murthy, A., Islam, M.A., Grosu, R. Smolka, S.A.: Computing bisimulation functions using SOS optimization and delta-decidability over the reals. In: Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control. ACM (2015)Google Scholar
  13. 13.
    Tiwari, A., Talcott, C.: Analyzing a discrete model of aplysia central pattern. In: Heiner, M., Uhrmacher, A.M. (eds.) CMSB 2008. LNCS (LNBI), vol. 5307, pp. 347–366. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  14. 14.
    Varshney, L.R.: Individual differences (2015).
  15. 15.
    Wicks, S.R., Rankin, C.H.: Integration of mechanosensory stimuli in caenorhabditis elegans. J. Neurosci. 15(3), 2434–2444 (1995)Google Scholar
  16. 16.
    Wicks, S.R., Roehrig, C.J., Rankin, C.H.: A dynamic network simulation of the nematode tap withdrawal circuit: predictions concerning synaptic function using behavioral criteria. J. Neurosci. 16(12), 4017–4031 (1996)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Md. Ariful Islam
    • 1
    Email author
  • Richard De Francisco
    • 1
  • Chuchu Fan
    • 3
  • Radu Grosu
    • 1
    • 2
  • Sayan Mitra
    • 3
  • Scott A. Smolka
    • 1
  1. 1.Department of Computer ScienceStony Brook UniversityNew YorkUSA
  2. 2.Department of Computer EngineeringVienna University of TechnologyViennaAustria
  3. 3.Department of Electrical and Computer EngineeringUniversity of Illinois Urbana ChampaignChampaignUSA

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