The time course of the contractile force measured during a twitch under fixed sarcomere length

The activation time-course of contractile elements estimated from in vivo fascicle behaviours during twitch contractions

To better understand the cascade from neural activation up to force production within in vivo contracting muscle-tendon units, we estimated activation of contractile elements from experimentally measured human fascicle length change and force using a Hill-type muscle model. The experiment was conducted with respect to twitch contractions of the tibialis anterior muscle at three joint angles. As muscle contractile element force is a function of its length and velocity, the activation of contractile elements was calculated using a Hill-type muscle model and measured data. The results were able to reproduce the continuous rising activation of contractile elements after termination of electromyographic activity, the earlier shift of peak activation in time compared to twitch force, and the differences in time-course activation at three different joint angles. These findings are consistent with the predicted change in the activation of contractile elements from previous reports. Also, the results suggest that the time-course of the activation of contractile elements was greatly influenced by the change in force generating capacities related to both length and velocity, even in fixed end contractions, which could result from muscle-tendon interaction.

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

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.

Biomimetic model of skeletal muscle isometric contraction: I. an energetic-viscoelastic model for the skeletal muscle isometric force twitch

This paper describes a revision of the Hill-type muscle model so that it will describe the chemo-mechanical energy conversion process (energetic) and the internal-element stiffness variation (viscoelastic) during a skeletal muscle isometric force twitch contraction. The derivation of this energetic-viscoelastic model is described by a first-order linear ordinary differential equation with constant energetic and viscoelastic coefficients. The model has been implemented as part of a biomimetic model, which describes the excitation-contraction coupling necessary to drive the energetic-viscoelastic model. Finally, the energetic-viscoelastic model is validated by comparing its isometric force-time profile with that of various muscles reported in the literature.

Effect of stretch and release on equatorial X-ray diffraction during a twitch contraction of frog skeletal muscle

Time-resolved intensity measurements of the x-ray equatorial reflections were made during twitch contractions of frog skeletal muscles, to which stretches or releases were applied at various times. A ramp stretch applied at the onset of a twitch (duration, 15 ms; amplitude, approximately 3% of muscle length) caused a faster and larger development of contractile force than in an isometric twitch. The stretch accelerated the decrease of the 1.0 reflection intensity (I1,0). The magnitude of increase of the 1,1 reflection intensity (I1,1) was reduced by the stretch, but its time course was also accelerated. A release applied at the peak of a twitch or later (duration, 5 ms; amplitude, approximately 1.5%) caused only a partial redevelopment of tension. The release produced clear reciprocal changes of reflections toward their relaxed levels, i.e., the I1,0 increased and the I1,1 decreased. A release applied earlier than the twitch peak had smaller effects on the reflection intensities. The results suggest that a strength applied at the onset of a twitch causes a faster radial movement of the myosin heads toward actin, whereas a release applied at or later than the peak of a twitch accelerates their return to the thick filament backbone. The results are discussed in the context of the regulation of the myosin head attachment by calcium.

Strain sensitivity and turnover rate of low force cross-bridges in contracting skeletal muscle fibers in the presence of phosphate

Inorganic phosphate (Pi) decreases the isometric tension of skinned skeletal muscle fibers, presumably by increasing the relative fraction of a low force quaternary complex of actin, myosin, ADP, and Pi (A.M.ADP.Pi). At the same time, Pi gives rise to a fast relaxing mechanical component as detected by oscillations at 500 Hz. To characterize the dynamic properties of this A.M.ADP.Pi complex, the effect of Pi on the tension response to stretch was investigated with rabbit psoas fibers. A ramp stretch applied in the presence of 20 mM Pi increased tension more than in the control solution (0 mM Pi) but reduced the fast relaxing component to the control level. Thus, a stretch seems to convert the low force, fast relaxing A.M.ADP.Pi complex to a high force, slow relaxing form. However, the Pi-induced enhancement of the tension response was not observed until the fibers were stretched more than 0.4% of their length, suggesting that a critical cross-bridge extension of approximately 4 nm is required for this conversion. The rate constant of the attachment/detachment of this low force complex was estimated from the velocity dependence of the enhancement. It was approximately 10 s-1, in marked contrast to the A.M.ADP.Pi complex under low salt, relaxed conditions (approximately 10,000 s-1). The enhancement of the tension response was not observed when isometric tension was reduced by lowering free calcium, implying that calcium and Pi affect different steps in the actomyosin ATPase cycle during contraction.

Calcium transients in skeletal muscle fibres under isometric conditions and during and after a quick stretch

The transient change in the sarcoplasmic concentration of Ca2+ was measured in intact fibres isolated from the anterior tibial muscle of the frog Litoria moorei. The fibres had been injected with the calcium-sensitive dye arsenazo III and the change of the calcium concentration was calculated from the changes in light absorbance at 570, 600 and 720 nm wavelengths. Absorbance and force were measured under three different conditions: (1) during a normal isometric twitch, (2) when a quick ramp-and-hold stretch had been applied to the fibre during onset of the contraction, and (3) when the fibre was allowed to contract isometrically at a length corresponding to the final length of the stretch. A method was devised to neutralize most of the movement artefacts encountered in such measurements. While the quick stretch caused substantial increase in the level and the duration of the contractile force such as originally described in whole muscle by A. V. Hill, the calcium transients appeared basically unaffected. It thus seems that the mechanism behind the phenomenon of the force enhancement lies at a step in the excitation-contraction coupling subsequent to the calcium release. From the present results, however, it is not clear whether the phenomenon is caused by an increase in the level of activation of the calcium-dependent regulatory system, or whether it is to be found in the acto-myosin interaction itself. The latter alternative would be consistent with the stiffness measurements published earlier.

Changes in contractile dynamics during the course of a twitch of a frog muscle fibre

Single skeletal muscle fibres from the frog were stimulated to produce isometric twitches and released after a delay to shorten isotonically unloaded or against a finite load (P). When varying the delay, the velocity of the initial shortening (V) against a given non-zero load reached its maximum value earlier than the peak of the isometric tension. The velocity of unloaded shortening (V0, slack test, range: 3.7-5.6 nm ms-1 per half-sarcomere) was independent of the delay of the release. For any given delay, V was hyperbolically related to P, except for the high-load end of the P-V curve at which the velocity took lower values than extrapolated from the hyperbolic relation. The relation between V and the load in units of P1 (corresponding to V = 1 nm ms-1 per half-sarcomere) coincided in the hyperbolic range with the relations obtained at other delays of the release. P1 was basically proportional to the maximum power which also had its peak value during the rising phase of the twitch. The quick releases required to reach the non-hyperbolic range of the P-V curves were estimated to be less than 9 nm per half-sarcomere irrespective of the delay of the release. At load levels in the non-hyperbolic range V could be increased if the quick release was followed by a brief (2 ms) extra reduction in the load preceding the shortening at isotonic load. The results can be explained if the kinetic properties of the individual strongly bound crossbridges are unaffected by the changing level of activation during the course of the contraction. The time-dependence of the non-hyperbolic range of the P-V relation can be accounted for if crossbridges attached before the release remain attached after the release thus constituting an internal load. The difference in time course of isometric tension as compared to velocity of initial shortening against a given load, P1, and maximum power may arise as the result of a reduction in the level of activation caused by the release to the isotonic load level.