Determinants of force rise time during isometric contraction of frog muscle fibres

Abstract

Force-velocity (F-V) relationships were determined for single frog muscle fibres during the rise of tetanic contraction. F-V curves obtained using isotonic shortening early in a tetanic contraction were different from those obtained at equivalent times with isovelocity shortening, apparently because changing activation early in the contraction leads, in isovelocity experiments, to changing force and changing series elastic extension. F-V curves obtained with isotonic and with isovelocity shortening are similar if the shortening velocity in the isovelocity trials is corrected for series elastic extension. There is a progressive shift in the scaling of force-velocity curves along the force axis during the course of the tetanic rise, reflecting increasing fibre activation. The time taken for F-V curves to reach the steady-state position was quite variable, ranging from about 50 ms after the onset of contraction (1-3 degrees C) to well over 100 ms in different fibres. The muscle force at a fixed, moderately high shortening velocity relative to the force at this velocity during the tetanic plateau was taken as a measure of muscle activation. The reference velocity used was 60% of the maximum shortening velocity (V(max)) at the tetanic plateau. The estimated value of the fractional activation at 40 ms after the onset of contraction was used as a measure of the rate of activation. The rate of rise of isometric tension in different fibres was correlated with the rate of fibre activation and with V(max) during the plateau of the tetanus. Together differences in rate of activation and in V(max) accounted for 60-80% of the fibre-to-fibre variability in the rate of rise of isometric tension, depending on the measure of the force rise time used. There was not a significant correlation between the rate of fibre activation and V(max). The steady-state F-V characteristics and the rate at which these characteristics are achieved early in contraction are seemingly independent. A simulation study based on F-V properties and series compliance in frog muscle fibres indicates that if muscle activation were instantaneous, the time taken for force to rise to 50% of the plateau value would be about 60% shorter than that actually measured from living fibres. Thus about 60% of the force rise time is a consequence of the time course of activation processes and about 40% represents time taken to stretch series compliance by activated contractile material.

Figure 1. Force–velocity relationships during trials with force clamp and velocity clamp and the method used to measure muscle stiffness

A, force–velocity (F–V) relationships during trials with force clamp (open symbols) and velocity clamp (filled symbols). The release to force clamp or velocity clamp occurred 32 ms after force onset for the force clamp values, 33 ms after force onset for the velocity clamp values. The force at release was approximately 0.25F_max for both force clamp and velocity clamp trials. Measurements of force and velocity were made 15 ms after the release. The continuous curve is the F–V relationship during the plateau of the contraction measured with force clamp (see Fig. 4). B, the method used to measure muscle stiffness. A small release (0.04 mm = 0.47% fibre length) was imposed on the muscle at different times during the rising tension of an isometric contraction. L₁ and L₂ are muscle length, F₁ and F₂ muscle force. The figure shows one trial on a slow (L₁, F₁) and on a faster (L₂, F₂) time base. The change in force, ΔF, was measured as the difference between the force at the onset of release and the minimum force reached at the end of release. The ratio of change in force to change in length (ΔF/ΔL) was taken as a measure of muscle stiffness. C, stiffness as a function of muscle force. The force of the abscissa is the average of the force at the onset and at the end of the length change. D, F–V relationships as in A, but with the values from velocity clamp trials corrected for changing length of series elastic elements resulting from changing force levels (see text).

Figure 4. Force–velocity relationships for force clamp measurements made early in tetanic contractions and during the plateau of contractions

Data are from the same fibre as in Figs 1 and 3. B is an expanded version of the upper left portion of A. The release at 0.25F_max occurred 32 ms after force onset; that at 0.13F_max was 20 ms after force onset. Velocity was measured 15 ms after release except for the highest force points of the plateau curve, which were measured 20–50 ms after release. The horizontal, dashed line in B is the reference velocity, 0.6V_max, at which force was measured to quantify the changing level of fibre activation.

Figure 3. Examples of load clamp recordings at different force levels during tetanus of a single muscle fibre

Arrows indicate the time of release from isometric contraction. A, force clamps began 32 ms after force onset when force had reached 25% F_max. B, release to force clamp during the plateau of contraction. a is the time interval surrounding the release; b is the force for the complete contraction at the middle force level in a. The thickened portion of the base line in b marks the duration of the tetanic stimulation. Vertical dotted lines mark the time, 15 ms after the onset of load clamp, at which force and muscle shortening velocity were measured to construct F–V curves.

Figure 2. Force and fibre length during force clamp (A) and velocity clamp (B) contraction

The release to force clamp or velocity clamp contraction occurred when the force reached 0.16F_max. Note the increasing force during the isovelocity shortening in B.

Figure 5. Force at a selected shortening velocity (0.6V_max) calculated from force–velocity curves obtained at different times after force onset in tetanic contractions

Time on the abscissa is the delay between force onset and the release to isotonic contraction plus the delay (15 ms) between release and the measurement of shortening velocity. Lines join points from the same fibre. Different symbols code the amplitude of the force at the release to isotonic contraction. The vertical line at 40 ms indicates the time at which the distribution of force at 0.6V_max (designated F_(0.6Vmax)) was evaluated for the fibres of the population. Estimates of F_(0.6Vmax) at 40 ms were obtained by linear interpolation between values obtained before and after this time (effectively the intersection of the vertical dashed line with the line joining points from an individual fibre).

Figure 6. Variability in the extent of fibre activation at a common time after force onset (left) or at a common isometric force level at release to isotonic shortening (right)

The left histogram was obtained as described in the legend of Fig. 5. The right histogram includes all fibres for which the force at release to isotonic contraction was in the range 23–29% F_max.

Figure 7. Relationships between tetanic rise time, V_max and activation rate index

Relationships between (1) tetanic rise time, measured from onset to 50% F_max; (2) V_max, the maximum shortening velocity during the tetanic plateau; and (3) activation rate index (ARI), a measure of the rate of development of the fibre's force–velocity properties (= expected force, as percentage F_max, if it were to be measured 40 ms after the tetanic onset and at V = 0.6V_max). The correlations in A and B are both statistically significant (P < 0.01). There is no correlation between the ARI and the value of V_max at the plateau (plot C, r² = 0.005).

Figure 8. Predicted time course of isometric force following instantaneous fibre activation

The Hill parameter values (F_max = 277 kN m⁻², a/F_max = 0.36) were chosen to be the average for the fibres of Figure 7. The thicker line shows the predicted force rise for the average value of V_max of the fibres in Fig. 7 (1.9 s⁻¹).