Detecting synchronisation of biological oscillators by model checking

Theoretical Computer Science

Volumn 411, Issue 20, 2010, Pages 1999-2018

  Bartocci, Ezio ^a   Corradini, Flavio ^a   Merelli, Emanuela ^a   Tesei, Luca ^a  

^a UNIVERSITY OF CAMERINO   (Italy)

Author keywords

Biological oscillators; Computational systems biology; Kuramoto model; Model checking; Pacemaker cells; Peskin model; Simulation; Spontaneous synchronisation; Timed automata

Indexed keywords

BIOLOGICAL OSCILLATORS; COMPUTATIONAL SYSTEMS BIOLOGY; KURAMOTO MODEL; KURAMOTO MODELS; MODEL SIMULATION; SYNCHRONISATION; TIMED AUTOMATA;

AUTOMATA THEORY; BIOLOGY; OSCILLATORS (MECHANICAL); PACEMAKERS; PARAMETRIC OSCILLATORS; ROBOTS; SYNCHRONIZATION; TRANSLATION (LANGUAGES);

MODEL CHECKING;

EID: 77950369439     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2009.12.019     Document Type: Article

References (37)

1. Buck J. Synchronous rhythmic flashing of fireflies II. The Quarterly Review of Biology 63 3 (1988) 265-289
2. C.S. Peskin, Mathematical aspects of heart physiology, Courant Institute of Mathematical Sciences, New York University, New York, 1975
3. Dye J. Ionic and synaptic mechanisms underlying a brainstem oscillator: An in vitro study of the pacemaker nucleus of apteronotus. Journal of Comparative Physiology 168 5 (1991) 521-532
4. Strogatz S.H. Sync, The Emerging Science of Spontaneous Order (2004), Hyperion
5. Kitano H. Foundations of Systems Biology (2002), MIT Press
6. Kuramoto Y. Phase dynamics of weakly unstable periodic structures: Condensed matter and statistical physics. Progress of Theoretical Physics 71 6 (1984) 1182-1196
7. Winfree A.T. Biological rhythms and the behavior of populations of coupled oscillators. Journal of Theoretical Biology 16 1 (1967) 15-42 10.1016/0022-5193(67)90051-3
8. Wang R., Chen L., and Aihara K. Synchronizing a multicellular system by external input: an artificial control strategy. Bioinformatics 22 14 (2006) 1775-1781
9. Acebron J., Bonilla L., Pérez Vicente C., Ritort F., and Spigler R. The Kuramoto model: A simple paradigm for synchronization phenomena. Reviews of Modern Physics 77 1 (2005) 137-185
10. C.S. Peskin, Mathematical Aspects of Heart Physiology, Courant Institute of Mathematical Sciences, 1975
11. Bartocci E., Corradini F., Merelli E., and Tesei L. Model checking biological oscillators. Proceedings of the Second Workshop From Biology to Concurrency and Back (FBTC 2008). Electronic Notes in Theoretical Computer Science 229 1 (2009) 41-58 10.1016/j.entcs.2009.02.004
12. Kuramoto Y. Collective synchronization of pulse-coupled oscillators and excitable units. Physica D 50 1 (1991) 15-30
13. Mirollo R.E., and Strogatz S.H. Synchronization of pulse-coupled biological oscillators. SIAM Journal of Applied Mathematics 50 6 (1990) 1645-1662
14. Kuramoto Y. Chemical Oscillations, Waves, and Turbulence (2003), Springer-Verlag
15. Mirollo R.E., and Strogatz S.H. Synchronization of pulse-coupled biological oscillators. SIAM Journal of Applied Mathematics 50 6 (1990) 1645-1662
16. Abbott L.F., and van Vreeswijk C. Asynchronous states in networks of pulse-coupled oscillators. Physical Review E 48 2 (1993) 1483-1490
17. Bressloff P.C. Mean-field theory of globally coupled integrate-and-fire neural oscillators with dynamic synapses. Physical Review E 60 2 (1999) 2160-2170
18. Golomb D., and Hansel D. The number of synaptic inputs and the synchrony of large, sparse neuronal networks. Neural Computation 12 (2000) 1095-1139
19. Alur R., and Dill D.L. A theory of timed automata. Theoretical Computer Science 126 (1994) 183-235
20. Henzinger T.A., Nicollin X., Sifakis J., and Yovine S. Symbolic model checking for real-time systems. Information and Computation 111 (1994) 193-244
21. Gupta V., Henzinger T.A., and Jagadeesan R. Robust timed automata. HART '97: Proceedings of the International Workshop on Hybrid and Real-Time Systems (1997), Springer-Verlag, London, UK 331-345
22. Jansen D.N., and Wieringa R.J. Extending CTL with actions and real time. Journal of Logic and Computation 12 4 (2002) 607-621
23. Daws C., Olivero A., Tripakis S., and Yovine S. The tool kronos. Proceedings of the DIMACS/SYCON Workshop on Hybrid Systems III: Verification and control (1996), Springer-Verlag New York, Inc., Secaucus, NJ, USA 208-219
24. Larsen K.G., Pettersson P., and Yi W. Model-checking for real-time systems. Proc. of Fundamentals of Computation Theory. LNCS vol. 965 (1995) 62-88
25. Behrmann G., David A., and Larsen K.G. A tutorial on uppaal. Formal Methods for the Design of Real-Time Systems, SFM-RT 2004. LNCS vol. 3185 (2004), Springer-Verlag 200-236
26. Maler O., and Batt G. Approximating continuous systems by timed automata. FMSB. LNCS vol. 5054 (2008) 77-89
27. Stursberg O., Kowalewski S., and Engell S. On the generation of timed discrete approximations for continuous systems. Mathematical and Computer Modelling of Dynamical Systems 6 1 (2000) 51-70
28. A. Olivero, J. Sifakis, S. Yovine, Using abstractions for the verification of linear hybrid systems, in: CAV, 1994, pp. 81-94
29. T.A. Henzinger, The theory of hybrid automata, in: LICS, 1996, pp. 278-292
30. A. Pnueli, The temporal logic of programs, in: FOCS, 1977, pp. 46-57
31. Koymans R. Specifying real-time properties with metric temporal logic. Real-Time Systems 2 4 (1990) 255-299
32. Alur R., and Henzinger T.A. A really temporal logic. Journal of the ACM 41 1 (2004) 181-203
33. E. Bartocci, F. Corradini, E. Merelli, L. Tesei, BOSL model checker prototype, URL http://cosy.cs.unicam.it/bosl/
34. Butcher J.C. Numerical Methods for Ordinary Differential Equations (2003), John Wiley and Sons
35. M. Bozga, S. Graf, L. Mounier, If-2.0: A validation environment for component-based real-time systems, CAV, 2002, pp. 343-348
36. Bleeker W.K., Mackaay A.J., Masson-Pvet M., Bouman L.N., and Becker A.E. Functional and morphological organization of the rabbit sinus node. Circulation Research 46 (1980) 11-22
37. Bartocci E., Corradini F., Grosu R., Merelli E., Riganelli O., and Smolka S.A. Stonycam: A formal framework for modeling, analyzing and regulating cardiac myocytes. Concurrency, Graphs and Models: Essays Dedicated to Ugo Montanari on the Occasion of His 65th Birthday. LNCS vol. 5065 (2008), Springer-Verlag, Berlin, Heidelberg 493-502