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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
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7605)

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.

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.

Keywords

Sodium Channel Invariant Manifold Sodium Current Label Transition System Transmembrane Voltage 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Abhishek Murthy
    • 1
  • Md. Ariful Islam
    • 1
  • Ezio Bartocci
    • 2
  • Elizabeth M. Cherry
    • 5
  • Flavio H. Fenton
    • 3
  • James Glimm
    • 4
  • Scott A. Smolka
    • 1
  • Radu Grosu
    • 2
  1. 1.Department of Computer ScienceStony Brook UniversityUSA
  2. 2.Department of Computer EngineeringVienna University of TechnologyAustria
  3. 3.Department of Biomedical SciencesCornell UniversityUSA
  4. 4.Department of Applied Mathematics and StatisticsStony Brook UniversityUSA
  5. 5.School of Mathematical SciencesRochester Institute of TechnologyUSA

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