Approximate Bisimulations for Sodium Channel Dynamics

Abhishek Murthy, Md. Ariful Islam, Ezio Bartocci, Elizabeth Cherry, Flavio H. Fenton, James Glimm, Scott A. Smolka, Radu Grosu

Abstract: We show that in the context of the Iyer et al. 67-variable cardiac myocycte model (IMW), it is possible to replace the detailed 13-state probabilistic 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 sodium channel models, both of which are input-controlled (voltage in this case) CTMCs.