Striated muscle regulation of isometric tension by multiple equilibria

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 approximately 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.

Figure 1. Novel myosin-based cooperative mechanism for vertebrate striated muscle.

The diagram depicts positions of tropomyosin (Tm) generated by interactions of troponin (Tn) and myosin with actin. An interaction between Tn and actin (not depicted) is energetically coupled to the stability of Tm in Position B (open rectangle), which blocks the association of myosin (open myosin head) with actin (filled monomers). An interaction of myosin with actin and Tm (closed myosin head) is coupled to a conformational change in Tm and the stability of Tm in Position M (closed rectangle). The conformational change stiffens one or more Tm subunits into a functional unit, referred to as a segment (S), which requires one coupled myosin and excludes all other myosin bound within S from being coupled. The stiffening of Tm requires multiple myosin to be coupled, but, since S can have only one coupled myosin, myosin from multiple S must cooperate to form a larger functional unit of Tm, referred to as a super segment (SS). Only one bound myosin per Tm subunit has the potential to be coupled within a segment, referred to as free myosin (open head attached to actin). Free myosin stabilizes the coupled state of myosin by being available to be coupled, as coupling within the segment is dynamic. The number of Tm subunits per S depends on the probability that myosin can be coupled (P_M). The maximum number of Tm per S and the number of myosin that must be coupled to form SS are intrinsic properties of Tm arbitrarily chosen to be 4 and 3 respectively for this diagram.

Figure 2. Annotated equilibrium model.

B₁, B₂, B₃, C, and M represent mole fractions of binding states coupled to the positions of Tm denoted by the letters (blocking, central, and myosin dependent, respectively). B₁, B₂, and B₃ are represented by Tm (open rectangle) held in a blocking position on actin by interactions between actin and Tn in each of three possible calcium bound states, namely, zero sites filled (open circle), one site filled (one dot), and two sites filled (two dots). Tn held by Tm in Positions C and M is uncoupled. T₁, T₂, and T₃, represent the mole fractions of uncoupled Tn with zero, one, and two calcium bound respectively (single symbol with open circle, one dot, and two dots). T₁, T₂, and T₃ must be carried by thermal motions of Tm to the vicinity of actin binding sites in Position B for coupling to occur. The mole fraction of Tm in Position B, {C/K _B} (brackets denote non-equilibrium state), determines the mole fraction of actin binding sites available for interaction with T₁, T₂, and T₃ (circle, one dot, and two dots dissociated from actin in Position B). The segment conformation of Tm (filled rectangle) requires the formation of a coupled myosin state (closed myosin head). The coupled myosin state is stabilized by the mole fraction of free myosin present in segments (open myosin head attached to actin) and the mole fraction of C transiently present in Position M (given by {C/K _A}). Each segment is composed of a variable number of Tm subunits (1+αP_M; P_M is the probability of the M state) and a super segment is composed of n segments. The mole fractions of segments (S) and super segments (S_s) each equal M. Tm in Positions C and M supports cycling myosin intermediates (pair of myosin heads) for sliding filaments and isometric tension respectively. Omitted from the diagram for clarity are the redundant reactions for calcium binding to Tn in Positions C and M and the explicit reaction with actin that forms free myosin.

Figure 3. Factors that determine cooperative activation by calcium.

Activation is calculated as the sum of the dependent variables C and M (Table 1) by solving Eqs. 9, 18, 21, and 22 given arbitrary calcium. Inset. Non-cooperative fractional activation in the absence of myosin. Myosin is excluded by setting the parameter K ₀ (Table 2) to zero. Fractional Activation is the dependent variable C (Table 1) as a function of calcium. Inset adjustable parameters: (Curve A); (Curve B); (Curve C); (Curve D); (Curve E). Outset. Myosin induces cooperative fractional activation. All curves except Curve 1 include myosin contribution by setting the parameter, K ₀, to one; for visual comparison to a non-cooperative activation, Curve 1 is reproduced (Curve E; inset). Curves 2, 3, 5, 7, and 8 illustrate the effects of parameters that control cooperativity: Curves 2 and 3 compare the effects of varying α and n given fixed and Curves 5, 7, and 8 compare the effects of varying n given fixed α and . For constant n and α (Curves 4–6), increasing shifts the curves toward greater calcium sensitivity while the steepness remains nearly the same. Curve 0 shows the mole fraction of Tm in Position C as a function of calcium. Outset adjustable parameters: , (Curve 1); , , , (Curve 2); , , , (Curve 3); , , , (Curve 4); , , , (Curve 5); , , , (Curve 6); , , , (Curve 7); , , , (Curve 8). Outset constants: , .

Figure 4. Fit of isometric tension data.

Tension data are taken from . The symbols represent the fractional change in isometric tension of skeletal muscle fibers reconstituted with a mixture of wild-type Tn and mutant Tn unable to bind calcium; the mole fraction of wild-type Tn is indicated as, filled diamond (100%), square (80%), trianlge (60%), circle (20%), cross (15%). Theoretical curves represent the mole fraction of Tm in Positions C and M, which is a measure of fractional activation. C and M are determined for arbitrary calcium by solving Eqs. 9, 18, 21, and 22. We normalized the raw simulations by subtracting the baseline (value at lowest calcium) and setting the maximum value (100% wild-type Tn at saturating calcium) equal to 1. The raw simulation with 100% wild-type Tn appears in Fig. 3 (Curve 7). Curves from left to right were generated with the following percentages of wild-type Tn: (left to right) 100% (), 83% (), 70% (), 33% (), 15% (). Adjustable parameters: p. Constants: , , , , , .

Figure 5. Relationship of IANBD fluorescence data and total myosin binding.

All data are replotted from Trybus and Taylor . Fluorescence data (circles) are fit by eye with Eq. 24, given and ; the curve through the data is generated by Eq. 23 using . Total myosin binding data (squares) are fit with a curve representing the sum of coupled and free myosin binding using Eq. 25. As inputs to Eq. 25, coupled myosin binding is given by the change in fluorescence generated by Eq. 23 () and the free myosin binding is generated by simple mass action ( ; Eq. 26). Inset. Simulated calcium binding to Tn is non-cooperative. The sum of B₂, B₃, T₂, and T₃ (Table 1), which represents the total calcium bound to Tn, is plotted on the Y-axis. Values for these dependent variables were determined by solving Eqs. 9, 18, 21, 22 for arbitrary calcium. Total calcium binding with zero myosin (−M) and saturating myosin (+M) was simulated using K ₀ = 0 and , respectively. Fixed inset parameters: , , , , .