NDLI: Compositionality results for cardiac cell dynamics

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Compositionality results for cardiac cell dynamics

Content Provider	ACM Digital Library
Author	Smolka, Scott A. Girard, Antoine Islam, Md. Ariful Murthy, Abhishek Grosu, Radu
Abstract	By appealing to the small-gain theorem of one of the authors (Girard), we show that the 13-variable sodium-channel component of the 67-variable IMW cardiac-cell model (Iyer-Mazhari-Winslow) can be replaced by an approximately bi-similar, 2-variable HH-type (Hodgkin-Huxley) abstraction. We show that this substitution of (approximately) equals for equals is safe in the sense that the approximation error between sodium-channel models is not amplified by the feedback-loop context in which it is placed. To prove this feedback-compositionality result, we exhibit quadratic-polynomial, exponentially decaying bisimulation functions between the IMW and HH-type sodium channels, and also for the IMW-based context in which these sodium-channel models are placed. These functions allow us to quantify the overall error introduced by the sodium-channel abstraction and subsequent substitution in the IMW model. To automate computation of the bisimulation functions, we employ the SOSTOOLS optimization toolbox. Our experimental results validate our analytical findings. To the best of our knowledge, this is the first application of δ-bisimilar, feedback-assisting, compositional reasoning in biological systems.
Starting Page	243
Ending Page	252
Page Count	10
File Format	PDF
ISBN	9781450327329
DOI	10.1145/2562059.2562138
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-04-15
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Feedback Approximate bisimulation Compositionality
Content Type	Text
Resource Type	Article

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Compositionality results for cardiac cell dynamics.

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