Research Article: Striated Muscle Regulation of Isometric Tension by Multiple Equilibria

Date Published: December 8, 2009

Publisher: Public Library of Science

Author(s): Henry G. Zot, Javier E. Hasbun, Nguyen Van Minh, Joel M. Schnur.

Abstract: Cooperative activation of striated muscle by calcium is based on the movement of tropomyosin described by the steric blocking theory of muscle contraction. Presently, the Hill model stands alone in reproducing both myosin binding data and a sigmoidal-shaped curve characteristic of calcium activation (Hill TL (1983) Two elementary models for the regulation of skeletal muscle contraction by calcium. Biophys J 44: 383–396.). However, the free myosin is assumed to be fixed by the muscle lattice and the cooperative mechanism is based on calcium-dependent interactions between nearest neighbor tropomyosin subunits, which has yet to be validated. As a result, no comprehensive model has been shown capable of fitting actual tension data from striated muscle. We show how variable free myosin is a selective advantage for activating the muscle and describe a mechanism by which a conformational change in tropomyosin propagates free myosin given constant total myosin. This mechanism requires actin, tropomyosin, and filamentous myosin but is independent of troponin. Hence, it will work equally well with striated, smooth and non-muscle contractile systems. Results of simulations with and without data are consistent with a strand of tropomyosin composed of ∼20 subunits being moved by the concerted action of 3–5 myosin heads, which compares favorably with the predicted length of tropomyosin in the overlap region of thick and thin filaments. We demonstrate that our model fits both equilibrium myosin binding data and steady-state calcium-dependent tension data and show how both the steepness of the response and the sensitivity to calcium can be regulated by the actin-troponin interaction. The model simulates non-cooperative calcium binding both in the presence and absence of strong binding myosin as has been observed. Thus, a comprehensive model based on three well-described interactions with actin, namely, actin-troponin, actin-tropomyosin, and actin-myosin can explain the cooperative calcium activation of striated muscle.

Partial Text: For vertebrate striated muscle, modeling steady-state isometric tension data with the known properties of calcium binding has proven difficult to achieve. The tension response to varying calcium is distinctly sigmoidal, suggesting an underlying cooperative mechanism. A potential basis for cooperative activation is the association of myosin with thin filaments [1], [2]. All present models of striated muscle regulation were derived originally from fitting myosin binding to thin filaments at fixed calcium [2]–[9]. An allosteric mechanism based on seven myosin binding sites has been proposed [1], [10], but a strictly allosteric model must be reconciled with the muscle lattice, which allows only 1–2 myosin bound per structural repeat [11], [12]. In addition, calcium rather than myosin varies in the muscle. Given these restrictions, cooperative calcium binding has been proposed as a mechanism for activating muscle contraction [8], [9]. However, direct measurements of calcium binding have been consistently documented to be non-cooperative both in the presence and the absence of myosin [13], [14].

Experimental observations and energy conservation place constraints on the equilibrium constants, K0, K1, K3, K5, K′2, and K′4, which serve as parameters of the system. To establish values for K′2 and K′4 from published transient calcium binding measurements [14], we paired the fastest measured on-rate with the two measured off rates. Thus, based on the ratio of measured rates (association/dissociation), and (Table 2). From the ratio, and conservation at equilibrium (Fig. 2), values for and can be established (Table 2). This leaves K1 as the only adjustable parameter in the absence of myosin (Fig. 2).

We demonstrated that a model based on well-described biochemical reactions and the known positions of Tm can fit disparate data related to muscle regulation. The requirement for a super segment follows from our simulations of cooperative calcium activation and experimental observation. Although a sigmoidal dependence on calcium can be achieved for a single segment (Curve 3; Fig. 3), experiments show that a single myosin cannot move the entire Tm strand of a thin filament and, instead, demonstrate that the likely length of a single segment is represented by 3–7 Tm subunits [22]. To be consistent with this segment size and with the steepness of experimental activation curves, our simulations requires simultaneous coupling by 3–5 myosin. The length of a super segment is determined by the number of coupled myosin (separate segments) multiplied by the number of Tm subunits of a component segment. The best fit of experimental data is consistent with a super segment length equal to the overlap region of the thin filament (∼20 Tm subunits).



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