Approximate bisimulations for sodium channel dynamics

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

10 Scopus citations


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. The construction of the appropriate approximate bisimulation, as well as the overall result regarding the behavior of this modified IMW model, involves: (1) Identification of the voltage-dependent parameters of the m and h gates in the HH-type channel via a two-step fitting process, carried out over more than 22,000 representative observational traces of the IMW channel. (2) Proving that the distance between observations of the two channels is bounded. (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.

Original languageEnglish
Title of host publicationComputational Methods in Systems Biology - 10th International Conference, CMSB 2012, Proceedings
Number of pages21
StatePublished - 2012
Event10th International Conference on Computational Methods in Systems Biology, CMSB 2012 - London, United Kingdom
Duration: Oct 3 2012Oct 5 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7605 LNBI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference10th International Conference on Computational Methods in Systems Biology, CMSB 2012
Country/TerritoryUnited Kingdom


Dive into the research topics of 'Approximate bisimulations for sodium channel dynamics'. Together they form a unique fingerprint.

Cite this