Model-order reduction of ion channel dynamics using approximate bisimulation

Md. Ariful Islam, Abhishek Murthy, Ezio Bartocci, Elizabeth M. Cherry, Flavio H. Fenton, James Glimm, Scott A. Smolka, Radu Grosu
2015 Theoretical Computer Science  
We show that in the context of the Iyer et al. (IMW) 67-variable cardiac myocycte model, 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 model, while only incurring a bounded approximation error. We then extend our technique to the 10-state model of the fast recovering calcium-independent potassium channel. The basis of our results is the construction of an approximate bisimulation between
more » ... he HH-type abstraction and the corresponding detailed ion channel model, 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 Manuscript (PDF) and h gates in the HH-type models via a two-step fitting process, carried out over more than 20,000 representative observational traces of the detailed sodium and potassium ion channel models. (2) Proving that the distance between observations of the detailed models and their respective abstraction is bounded. (3) Exploring the sensitivity of the overall IMW model to the HH-type approximations. Our extensive simulation results experimentally validate our findings, for varying IMW-type input stimuli.
doi:10.1016/j.tcs.2014.03.018 fatcat:yot5xlpl7raszohwr6xthgfxky