K. A. P. Edman

Double-hyperbolic force-velocity relation in frog muscle fibres.

1. The relationship between force and velocity of shortening was studied at 2.10 micron sarcomere length during fused tetani (1‐3 degrees C) in single fibres isolated from the anterior tibialis muscle of Rana temporaria. The speed of shortening was recorded from the whole fibre and, in some experiments, simultaneously from a short (ca. 0.6 mm) segment, while the preparation was released to shorten isotonically at selected force levels (‘load‐clamp’ recording). The segment was defined by opaque markers of hair that were placed on the fibre surface. The distance between the markers was recorded by means of a photo‐electric detector system. 2. The force‐velocity relation had two distinct regions, each one exhibiting an upwards concave shape, that were located within the ranges 0‐78 and 78‐100% of the measured isometric force (P0), respectively. The two portions of the force‐velocity relation could be fitted well by hyperbolic functions or by single‐exponential functions. The curvature was more pronounced in the high‐force region than at low‐intermediate loads. The transition between the two portions of the force‐velocity relation (the ‘break point’ of the force‐velocity curve) occurred at 78.4 +/‐ 0.4% of P0 (mean +/‐ S.E. of mean, n = 12) corresponding to 10.9 +/‐ 0.4% of maximum velocity of shortening (Vmax). The general shape of the force‐velocity curve, and the appearance of a break point near 78% of P0, was the same when measurements were made from the whole fibre and from a short segment along the same fibre. 3. The ‘negative’ branch of the force‐velocity relation was delineated for loads ranging from P0 to 1.6‐1.8 P0 in five experiments. The negative branch formed a smooth continuation of the force‐velocity relation recorded between 0.78 P0 and P0. The force‐velocity relation was nearly flat between 0.90 P0 and 1.20 P0, the difference in speed of shortening or elongation being 1.8 +/‐ 0.3% (mean +/‐ S.E. of mean, n = 5) of Vmax over this range. 4. An increase in sarcomere length from 1.85 to 2.60 micron did not affect Vmax but caused a steady decrease in curvature of the force‐velocity relation, both at low‐intermediate loads and in the high‐force range. Similar changes in shape of the force‐velocity relation were produced by osmotic compression of the fibre in a Ringer solution made hypertonic by addition of 98 mM‐sucrose.(ABSTRACT TRUNCATED AT 400 WORDS)

Strain of passive elements during force enhancement by stretch in frog muscle fibres.

1. The force enhancement during and after stretch (0.15 micron per sarcomere) was studied during fused tetani of single fibres isolated from the anterior tibialis muscle of Rana temporaria (0.5‐3.6 degrees C; sarcomere length, 2.05‐2.65 microns). Changes in length were recorded simultaneously from the fibre as a whole (puller movement) and from marked segments (approximately 0.5 mm in length) of the same fibre. 2. The residual force enhancement after stretch (recorded at the end of a long tetanus) was found to be linearly related to the slow component of tension rise during the stretch ramp. 3. The fibres were released to shorten against a very small load at different times after stretch (load clamp). The shortening records derived after a preceding stretch exhibited a larger and steeper initial transient than that recorded in an isometric tetanus without stretch. The excess length change (LS; nanometres per half‐sarcomere) recorded during the initial transient increased with the amplitude of stretch and was linearly related to the force enhancement produced by the stretch (FE; % of maximum tetanic tension) according to the following regression: LS = 0.200 FE + 8.65 (P < 0.001). The length changes recorded from the whole fibre agreed well with measurements from individual segments. 4. Slack‐test measurements confirmed the existence of a large initial transient phase when the fibre was released to shorten after a preceding stretch. The excess length change determined from the slack tests agreed closely with the values derived from load‐clamp recordings. 5. The results support the view that stretching a muscle fibre during tetanus leads to strain of elastic elements and, presumably, to variation of filament overlap due to non‐uniform distribution of the length change within the fibre volume. Regions with greater filament overlap are likely to generate the long‐lasting extra force referred to as ‘residual force enhancement after stretch’. The elastic elements recruited during stretch can be presumed to play an essential part in this process by supporting regions in which the filament overlap has been reduced during the stretch ramp. Recoil of these elastic elements is responsible for the excess length change that is recorded during the initial transient after release as described under point 3.

Laser diffraction studies of sarcomere dynamics during ‘isometric’ relaxation in isolated muscle fibres of the frog

1. A study has been made of changes in sarcomere length and tension which occur during relaxation from isometric (‘fixed ends’) tetani in isolated muscle fibres of the frog. Sarcomere lengths were calculated from measurements of the separation of the zero‐to‐first‐order intensity maxima in diffraction patterns generated by illuminating small segments of fibre with a He—Ne laser. Diffraction spectra were recorded continuously on cine‐film using the method of ‘streak’ photography.

The Biphasic Force–Velocity Relationship in Frog Muscle Fibres and its Evaluation in Terms of Cross‐Bridge Function

1 The relationship between force and velocity of shortening was studied during fused tetani of single fibres isolated from the anterior tibialis muscle of Rana temporaria (1.5–3.3°C; sarcomere length, 2.20 mm). Stiffness was measured as the change in force that occurred in response to a 4 kHz length oscillation of the fibre. 2 The results confirmed the existence of two distinct curvatures of the force–velocity relationship located on either side of a breakpoint in the high‐force, low‐velocity range. Reduction of the isometric force (P0) to 83.4 ± 1.7% (mean ±s.e.m., n= 5) of the control value by dantrolene did not affect the relative shape of the force–velocity relationship. The breakpoint between the two curvatures was located at 75.9 ± 0.9% of P0 and 11.4 ± 0.6% of maximum velocity of shortening (Vmax) in control Ringer solution and at 75.6 ± 0.7% of P0 and 12.2 ± 0.7% of Vmax in the presence of dantrolene. These results provide evidence that the transition between the two curvatures of the forcevelcity relationship is primarily related to the speed of shortening, not to the actual force within the fibre. 3 The instantaneous stiffness varied with the speed of shortening forming a biphasic relationship with a breakpoint near 0.15 Vmax and 0.8 P0, respectively. The force/stiffness ratio (probably reflecting the average force per cross‐bridge), increased with force during shortening. The increase of the force/stiffness ratio with force was less steep at forces exceeding 0.8 P0 than below this point. 4 A four‐state cross‐bridge model (described in the Appendix) was used to evaluate the experimental results. The model reproduces with great precision the characteristic features of the force–stiffness–velocity relationships recorded in intact muscle fibres.

Force-velocity relation for frog muscle fibres: effects of moderate fatigue and of intracellular acidification.

1. Intact frog single fibres were investigated under control conditions (1 s tetanus every 2, 3 or 5 min) and during moderate fatigue (interval between tetani 15 or 30 s). 2. Fatigue reduced isometric force (P0) by 25.8 +/‐ 1.6% (S.E.M.; n = 13) and depressed the maximum velocity of shortening (Vmax) by 10.2 +/‐ 2.2% (n = 13). The force‐velocity relation became less curved, a/P0* (see Methods) being increased by 29.5 +/‐ 8.8% (n = 13). Thus, power was less affected than isometric force or Vmax. 3. The velocity of unloaded shortening (V0), from slack test measurements, was reduced proportionally more than Vmax during fatigue. Under control conditions V0 was larger than Vmax, but during fatigue their values were not significantly different. 4. Stiffness during shortening was reduced during fatigue indicating fewer attached cross‐bridges in fatigue. Force was reduced more than stiffness indicating that, on average, there is less force per attached cross‐bridge. 5. The force‐lengthening velocity relation showed that the ability to resist forces greater than isometric was well preserved in fatigue. 6. Compared with fatigue, intracellular acidification with CO2 produced a smaller reduction in isometric force. However, reduction in Vmax was not significantly different from that in fatigue. These results are consistent with both inorganic phosphate and H+ increasing in fatigue, but only H+ increasing during acidification, and isometric force being reduced by both, Vmax being sensitive only to H+.

The force‐velocity relationship in vertebrate muscle fibres at varied tonicity of the extracellular medium

1. The relationship between active force and velocity of shortening was studied during tetanic contraction of isolated semitendinosus muscle fibres of the frog (0·5‐2·0° C). Measurements were carried out with the fibre immersed in isotonic (1·00R) Ringer solution and in solutions that were made hypotonic by reduction of NaCl (osmolality 0·62 and 0·81 of normal Ringer) and hypertonic by addition of sucrose (osmolality 1·22 and 1·44 of normal Ringer).

Residual force enhancement after stretch in striated muscle. A consequence of increased myofilament overlap

Abstract  When skeletal muscle is stretched above optimal sarcomere length during tetanic activity there is an increase in force that stays above the isometric force level throughout the activity period. This long‐lasting increase in contractile force, generally referred to as ‘residual force enhancement after stretch’ (FEresid), has been studied in great detail in various muscle preparations over more than half a century. Substantial evidence has been presented to show that non‐uniform sarcomere behaviour plays a major part in the development of FEresid. However, in a great number of recent studies the role of sarcomere non‐uniformity has been challenged and alternative mechanisms have instead been proposed to explain the increase in force such as enhancement of cross‐bridge function and/or strengthening of parallel elastic elements along the muscle fibres. This article presents a short review of the salient features of FEresid and provides evidence that non‐uniform sarcomere behaviour is indeed likely to play a major role in the development of FEresid. Electron microscopical studies of fibres rapidly fixed after active stretch demonstrate that, dispersed in the preparation, there are assymetrical length changes within the two halves of myofibrillar sarcomeres resulting in greater filament overlap in one half of the sarcomere than in the opposite sarcomere half. Sarcomere halves with increased filament overlap will consequently be in a situation where they are able to produce a greater force than that recorded in the isometric control. Weaker regions in series will be able to keep the enhanced force by recruitment of elastic elements.

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°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 (Vmax) 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 Vmax during the plateau of the tetanus. Together differences in rate of activation and in Vmax 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 Vmax. 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.

The force bearing capacity of frog muscle fibres during stretch: its relation to sarcomere length and fibre width

1 Single fibres isolated from the anterior tibialis muscle of Rana temporaria were tetanized (0.9‐1.8 °C) while a marked (≈1 mm) segment was held at constant length by feedback control. Force enhancement was produced by applying a controlled stretch ramp to the fibre segment during the tetanus plateau, the steady force reached during stretch being used as a measure of the maximum force that the myosin cross‐bridges can hold before they detach. 2 The amplitude of force enhancement during stretch did not vary in proportion to the isometric force as the sarcomere length was changed, maximum force enhancement being attained near 2.4 μm sarcomere length compared with 2.0 μm for the isometric force. 3 The influence of fibre width on the force enhancement‐sarcomere length relationship was evaluated by normalizing force enhancement to the tetanic (pre‐stretch) force in this way allowing for the differences in myofilament overlap at the various lengths. The amplitude of force enhancement (normalized to the tetanic force) increased by approximately 70 % as the relative width of the myofilament lattice was reduced from a nominal value of 1.05 at a sarcomere length of 1.8 μm to 0.85 at a sarcomere length of 2.8 μm. 4 Changes in fibre width equivalent to those produced by altering the sarcomere length were produced by varying the tonicity of the extracellular medium. Force enhancement, normalized to the control isometric force at each tonicity, exhibited a width dependence that agreed well with that described in the previous point. Stretch ramps applied to frog skinned muscle fibres during calcium‐induced contracture likewise resulted in a greater force enhancement during stretch after reducing the fibre width by osmotic compression. 5 The results suggest that the strength of binding of the myosin cross‐bridges, unlike the isometric force, varies with the lateral distance between the myofilaments.

Changes in the maximum speed of shortening of frog muscle fibres early in a tetanic contraction and during relaxation

1 Isotonic shortening velocities at very light loads were examined in single fibres of the anterior tibialis muscle of the frog, Rana temporaria, using load‐clamp recording and slack tests (temperature, 1‐3 °C; initial sarcomere length, 2.25 μm). 2 Shortening velocities at very light loads (force‐clamp recording) were found to be higher early in the rise of a tetanic contraction than during the plateau of the contraction. The upper limit of the load at which there was elevated shortening velocity early in the contraction was 1.5‐5.4 % of the maximum tetanic tension (Fo) depending on the particular fibre. 3 The maximum shortening velocity determined using the slack test method (Vo) was as much as 30 % greater early in a contraction than at the tetanic plateau. Vo was elevated above the plateau level up to about 30 ms after the end of the latent period, which is equivalent to the time required for the force in an isometric contraction to rise to about 30 % of Fo. Vo is depressed below the plateau value during relaxation at the cessation of stimulation. 4 Simulation studies show that the cross‐bridge model of Huxley (1957) predicts the maximum shortening velocity to be greater early in a contraction, when new actin binding sites are becoming activated and new cross‐bridge connections are being formed rapidly, than during steady‐state contraction. The elevated shortening velocity in the model is a consequence of new cross‐bridges being formed in the pulling configuration, and there being a delay before the newly added bridges are dragged beyond their equilibrium position so they begin to retard shortening. The model also predicts that maximum shortening velocity should be depressed below the plateau level during early relaxation as cross‐bridge binding sites are rapidly removed from the active population.