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Two-State Model of Acto-Myosin Attachment-Detachment Predicts C-Process of Sinusoidal Analysis

Department of Molecular Physiology and Biophysics, University of Vermont, Burlington, Vermont

Correspondence: Address reprint requests to Bradley M. Palmer, PhD, Tel.: 802-656-2650; E-mail: palmer{at}physiology.med.uvm.edu.

The force response of activated striated muscle to length perturbations includes the so-called C-process, which has been considered the frequency domain representation of the fast single-exponential force decay after a length step (phases 1 and 2). The underlying molecular mechanisms of this phenomenon, however, are still the subject of various hypotheses. In this study, we derived analytical expressions and created a corresponding computer model to describe the consequences of independent acto-myosin cross-bridges characterized solely by 1), intermittent periods of attachment (t_att) and detachment (t_det), whose values are stochastically governed by independent probability density functions; and 2), a finite Hookian stiffness (k_stiff) effective only during periods of attachment. The computer-simulated force response of 20,000 (N) cross-bridges making up a half-sarcomere (F_hs(t)) to sinusoidal length perturbations (L_hs(t)) was predicted by the analytical expression in the frequency domain, where = mean value of t_att, = mean value of t_att + t_det, = mean stiffness, and = 2 x frequency of perturbation. The simulated force response due to a length step (L_hs) was furthermore predicted by the analytical expression in the time domain, The forms of these analytically derived expressions are consistent with expressions historically used to describe these specific characteristics of a force response and suggest that the cycling of acto-myosin cross-bridges and their associated stiffnesses are responsible for the C-process and for phases 1 and 2. The rate constant 2c, i.e., the frequency parameter of the historically defined C-process, is shown here to be equal to Experimental results from activated cardiac muscle examined at different temperatures and containing predominately - or ß-myosin heavy chain isoforms were found to be consistent with the above interpretation.

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