The Transient Mechanics of Muscle Require Only a Single Force-Producing Cross-Bridge State and a 100 Å Working Stroke

Figures

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  Figure 1. Illustration of transient experiments on muscle starting from the plateau of an isometric tetanus. Upper panel: length-step experiments showing the length trace (top) and the resulting tension transient (bottom). Lower panel: force step experiments where the load was suddenly reduced (bottom trace) and there was a length transient (top). Phase 1 is the change during the step, phase 2 is the rapid recovery in (a) or rapid shortening in (b), phase 3 is a slowing stage, and phase 4 is the gradual return to plateau tension in (a) or steady shortening in (b). Based on Huxley and Simmons (1971).

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  Figure 2. (a) The myosin head, showing the motor domain, lever arm and light chains in the putative pre-powerstroke state (left; Dominguez et al. [23]) and post-powerstroke state (middle; Rayment et al. [8]) assuming a horizontal actin (Z-band to the right). (a) Right: our approximation of a myosin head as a motor domain and lever arm, with a spring between the two that can pull back when stretched. (b) The simple mechanical cross-bridge cycle used in the simulations. For details, see text.

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  Figure 3. Illustration of the model with (A) the centre of attached state 1 (AS1) 12.5 Å in the positive x direction (away from the M-band) from the head origin on the myosin filament and (B) the motor position at the AS2#1-to-AS2#2 switch site at −10 Å.

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  Figure 4. Experimental observations (grey traces) in length-step experiments of Ford et al. [2] and our simulations (black traces) of the same experiments using the cycle in Figure 2b and starting from the initial stimulus at zero time. The agreement over the whole set of experiments is reasonably good.

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  Figure 5. Results of modelling the isotonic transient studies of Reconditi et al. [6]. (a) The observed length changes as a function of load (black traces) and the modelled simulations in other colours (see key). (b) The computed X-ray diffraction intensities (IM3) for the traces in (a) against the observed values (dots). (c) Modelled RM3 values relative to the observed values (dots). For details, see text.

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  Figure 6. Variation of populations in the modelling of data in Figure 4. Detached state 2 population—continuous line; attached state 1 population—segmented line; attached state 2 force-producing population—dotted line; detached state 1 population—alternating segmented–dotted line. For details, see main text.

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  Figure 7. Populations of the various states in Figure 2b throughout the isotonic experiment modelling in Figure 5. Top panel, populations against time. Lower panel, populations against distance. Detached state 2 population—continuous line; attached state 1 population—segmented line; attached state 2 force-producing population—dotted line; detached state 1 population—alternating segmented-dotted line. For details, see main text.

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  Figure 8. Illustration of the possible positions of heads attaching in AS1 (x = +12.5 Å) with a Gaussian spread (solid bell-shaped curve) as listed in Table 1, the probability change across the AS2#1-to-AS2#2 switch position (solid blue line), and the effect of a step-length change (red arrow) in bringing heads to the AS2#2 position (dashed bell-shaped curve) where the AS1-to-AS2 transition is more likely. (The heights of the bell-shaped curves are not to scale.)

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  Figure 9. Variations in transition probability (boxes, vertical axis) around the cycle in Figure 2b as a function of load in the isotonic experiments in Figure 5 (horizontal axis). The biggest changes are in the DS2-to-AS1 transition, which increases almost linearly as the load reduces. For details, see text.

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  Figure 10. (a) The time courses of the population changes in strong-force-producing (AS2) heads and weak/pre-powerstroke heads (AS1) in the present modelling of an isometric tetanus in frog m. tib. ant. Muscle, and (b) the same parameters determined by fitting of time-resolved X-ray diffraction patterns from bony fish muscle [28].