Approximate Bisimulations for Sodium-Channel Dynamics.*

A. Murthy, A. Islam, E. Bartocci, E. Cherry, F.H. Fenton, J. Glimm, S.A. Smolka, and R. Grosu.

This paper shows that, in the context of the Iyer et al. 67-variable cardiac myocycte model (IMW), it is possible to replace the detailed 13-state continuous-time MDP model of the sodium-channel dynamics, with a much simpler Hodgkin-Huxley (HH)-like two-state sodium-channel model, while only incurring a bounded approximation error. The technical basis for this result is the construction of an approximate bisimulation between the HH and IMW channel models, both of which are input-controlled (voltage in this case) continuous-time Markov chains. The construction of the appropriate approximate bisimulation, as well as the overall result regarding the behavior of this modified IMW model, involves: (1) The identification of the voltage-dependent parameters of the m and h gates in the HH-type channel, based on the observations of the IMW channel. (2) Proving that the distance between observations of the two channels never exceeds a given error. (3) Exploring the sensitivity of the overall IMW model to the HH-type sodium-channel approximation. Our extensive simulation results experimentally validate our findings, for varying IMW-type input stimuli.

In Proc. of CMSB'12, the 10th International Conference on Computational Methods in Systems Biology, London, UK, October, 2012, Springer LNCS/LNBI.

*This work was partially supported by the NSF Expeditions Award CNS-09-26190, the and the AFOSR FA-0550-09-1-0481 Award.