The difference in the delay to force redevelopment between a short and a long release, each of which brings the force to zero, is a measure of maximum shortening velocity uncomplicated by the recoil of stretched elastic elements. In both Fig. 3A and B increasing the release distance from R1 to R2 led to a smaller increase in slack time for the release early in contraction (ER1 to ER2) than for that later in the contraction (LR1 to LR2), clearly demonstrating that the shortening velocity under no load was greater early in the contraction. This is further illustrated in Fig. 4A which shows that the slope of the relation between release amplitude and slack time is steeper ( = higher velocity) when measurements are made during the early rising phase than during the plateau of a tetanus.
Although the maximum shortening velocity is greater early in a tetanus than later, the rate of force increase after the end of the slack period is slower early in the contraction (Fig. 3). Muscle activation is incomplete early in a contraction and shortening velocities at other than very light loads are slower early in the contraction than they are during the plateau (Fig. 1; see also Cecchi, Colomo & Lombardi, 1978, 1981; Cecchi, Colomo, Lombardi & Piazzesi, 1979). The slower rise of force following early than following later releases is presumably largely a reflection of this incomplete activation. Still another factor that probably contributes to the slower tension rise after early releases is shortening induced deactivation. This depressant effect of shortening (see overview article, Edman, 1996), is insignificant when the movement occurs at full activation, such as during the tetanus plateau, but is pronounced after shortening at submaximal activation.
The Maximum Velocity
Slack tests were done at different times during the rise of tetanic contractions in order to chart the decline in Vo following the onset of stimulation. There was considerable variation from fibre to fibre in the time course of the decline in Vo (Fig. 5). In general the maximum shortening velocity was substantially greater than the plateau value only during the first 20 ms or so after force onset, which is equivalent to the time which the force would have taken to reach about 30 %Fo had the contraction been isometric. The average shortening velocity during the tetanic rise for the data of Fig. 5, considering only the earliest set of slack tests in preparations in which two or more sets of slack tests were obtained during the rise, was 16 % greater then the velocity during the tetanic plateau (s.d. = 6.2 %, n = 12; mean time of measurement was 16 ms after force onset).
Muscle force was evaluated with the model during simulated constant velocity shortening (velocity clamp) or during isometric contraction, by determining the proportion of actin sites bound to cross-bridges as a function of x, and summing the force contributions of the attached cross-bridges over the total range of x for which there were attached bridges. Distance along the x-axis was divided into a series of length bins, each usually of width 0.1 %h. The changing proportion of sites bound to cross-bridges in the interval represented by each length bin was calculated for a series of time steps, typically of 0.1 ms, using eqns (1)-(9) above. A fourth-order Runge-Kutta evaluation was used to lessen the dependence of the performance of the model on the duration of the time step. The model behaviour was found to be relatively independent of the size of the length bin. Muscle shortening or lengthening was simulated by shifting the value for the proportion of actin sites bound to bridges in each length bin an appropriate number of bin widths toward smaller values of x for shortening or toward larger values of x for lengthening. The simulated shortening or lengthening was done at the end of each evaluation at a new time step. The following values, based on those proposed by Huxley (1957, pp. 288 and 295), were used in simulations:
Muscle force was determined as a function of time for a number of isovelocity contractions at different shortening velocities. These data were used to construct F-V curves for varied times following the onset of activity using the procedure of Wohlfart & Edman (1994). The fitted curves were used to determine the shortening velocity at zero load.
It seems reasonable to expect there to be a limit in the extent to which an attached cross-bridge can be dragged beyond its equilibrium position before the strain becomes so great that the bridge is pulled free or breaks. We have arbitrarily taken the maximum strain distance to be 3h. Any bridge which is dragged this far from its equilibrium position is detached. Even at shortening velocities approaching the maximal velocity only a very small fraction of the total bridge population still remained attached at a strain distance of 3h, and imposing this distance as a maximum strain had very little effect on the calculated force.
There are two factors leading to the variation in force during isovelocity shortening. One is a shift in the distribution of already attached cross-bridges engendered by a change in shortening velocity. This factor is particularly important during releases from high force levels; and it is responsible for the large, transient, negative-going force changes at the onset of shortening in the releases during the tetanic plateau and during early relaxation of Fig. 7. The change in velocity here is from zero velocity during the isometric part of the contraction to the constant velocity of the release phase. The rising force during the isometric phase of the contraction is a consequence of the formation of a large population of cross-bridges attached on the pulling side, i.e. on the Z-line side, of their equilibrium position. The release to isovelocity shortening results in a shift of these attached cross-bridges through their equilibrium position to the retarding side where they produce negative force. The negative force wanes as the retarding cross-bridges dissociate and some of them reattach in the pulling position. A new steady-state distribution of cross-bridges, and a constant force level, develops within a few tens of milliseconds following a release during the tetanic plateau. With releases during relaxation, forces tend to decline following recovery from the initial negative transient, as cross-bridges are removed from the active population. In real muscles the presence of a series elastic element would modify, and perhaps totally obscure, initial force transients resulting from cross-bridge movement such as those in Fig. 7. The decline in force resulting from a shift in attached cross-bridges would allow stretched series elastic elements to shorten. Thus part of the shortening imposed on the muscle would be taken up by shortening series elastic elements, lessening the shortening velocity of the contractile components themselves and in this way increasing the force generated by the contractile elements. The series elastic elements in real muscles act as a buffer which reduces the amplitude of rapid, transient force change produced by the contractile portion of the muscle.
The second factor leading to a change in force during the course of isovelocity shortening is a change in the distribution of attached cross-bridges resulting from changes in the size of the pool of activated cross-bridge binding sites. Such changes are associated with the addition of newly activated binding sites during the onset of contraction, and to the removal of active sites during relaxation. It was change in force due to changing populations of activated binding sites which was of particular interest in this study. Therefore measurements of force-velocity properties were made under conditions chosen to minimize force transients due to changing velocity. F-V properties early in contraction were quantified using shortening ramps which began at the same time as stimulation; thus there were no initial transients caused by displacement of already attached cross-bridges at the onset of shortening (Fig. 8C). F-V properties during the plateau were measured using either isovelocity shortening continued from the onset of stimulation into the plateau, or with releases from isometric to isovelocity shortening during the plateau. In the latter case measurements were made after the initial force transients had subsided (Fig. 8A and B). Measurements during relaxation were obtained by continuing isovelocity shortening, begun during the plateau, into relaxation (Fig. 8A and B).
If the activation time constant is set at 0, so that all actin binding sites become instantaneously activated, the muscle force during an isometric contraction rises abruptly with an approximately hyperbolic trajectory (Fig. 7A, dotted line). The time to half-maximum force is about 20 ms. Increasing the activation time constant to 20 ms results in a sigmoidal force trajectory with a time to half-maximum tension of about 42 ms (Fig. 7A, 2; top continuous line).
B is an expanded version of the upper left portion of A. These results were obtained with isovelocity shortening which began at the onset of stimulation. τon = 20 ms. The calculated values are shown as points; the continuous lines are Hill curves fitted to these points. This figure shows that (1) a Hill curve provides a reasonable fit to calculated values even when activation time is made part of the model, and (2) the Huxley model predicts elevated shortening velocity at low force early in a contraction.
The values for maximum velocity were determined from Hill curves fitted to sets of calculated F-V points. Values are plotted as a function of time after force onset (A) and as a function of the isometric force which would have been measured at the time at which the F-V data were collected (B).
B is an expanded version of the upper, left portion of A. Measurements during the plateau were made 40 ms after the release to isovelocity shortening, by which time the initial force transients were largely over, especially for the releases to higher velocities and lower steady-state force. Measurements during relaxation were taken 40 ms after the end of stimulation. 2ff7e9595c
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