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Ising Model of Cardiac Thin Filament Activation with Nearest-Neighbor Cooperative Interactions

John Jeremy Rice^*, Gustavo Stolovitzky^*, Yuhai Tu^* and Pieter P. de Tombe

^* IBM T. J. Watson Research Center, Yorktown Heights, New York 10598 and Physiology & Biophysics, University of Illinois, Chicago, Illinois 60607

Correspondence: Address reprint requests to J. Jeremy Rice, IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598. Tel.: 914-945-3728; Fax: 914-945-4104; E-mail: johnrice{at}us.ibm.com.

We have developed a model of cardiac thin filament activation using an Ising model approach from equilibrium statistical physics. This model explicitly represents nearest-neighbor interactions between 26 troponin/tropomyosin units along a one-dimensional array that represents the cardiac thin filament. With transition rates chosen to match experimental data, the results show that the resulting force-pCa (F-pCa) relations are similar to Hill functions with asymmetries, as seen in experimental data. Specifically, Hill plots showing (log(F/(1-F)) vs. log [Ca]) reveal a steeper slope below the half activation point (Ca₅₀) compared with above. Parameter variation studies show interplay of parameters that affect the apparent cooperativity and asymmetry in the F-pCa relations. The model also predicts that Ca binding is uncooperative for low [Ca], becomes steeper near Ca₅₀, and becomes uncooperative again at higher [Ca]. The steepness near Ca₅₀ mirrors the steep F-pCa as a result of thermodynamic considerations. The model also predicts that the correlation between troponin/tropomyosin units along the one-dimensional array quickly decays at high and low [Ca], but near Ca₅₀, high correlation occurs across the whole array. This work provides a simple model that can account for the steepness and shape of F-pCa relations that other models fail to reproduce.

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