Path reconstruction as a tool for actin filament speed determination in the in vitro motility assay.

The in vitro motility assay is used to measure speed of actin filaments moving over a glass surface coated with heavy meromyosin. In this paper a new method, the path reconstruction method, is presented to evaluate observed speeds. The method is compared with the commonly used centroid method, in which the centroids of the filaments are followed from frame to frame. Instead, in the path reconstruction method speed is evaluated from determination of perimeters of the filaments in each frame and by reconstruction of the traversed paths of the filaments over a number of frames. Biases in the determination of speed occurring in the centroid method due to curvature of paths and to video noise and Brownian motion are eliminated in the path reconstruction method, allowing measurement over a range of frame rates from 5 to 25 per second. The path reconstruction method leads to a clear separation of motile and nonmotile filaments provided that filaments are analyzed over at least 10 successive frames and allows easier separation of uniform and nonuniform sliding behavior.

The effect of actin filament compliance on the interpretation of the elastic properties of skeletal muscle fibres.

Recently, X-ray diffraction studies provided direct evidence for an appreciable length change in the actin filament upon activation. This finding has profound implications on the interpretation of the elastic properties of skeletal muscle fibre. In this study we determined the compliance of the actin filament during activation, using the data obtained previously from quick stretch and release experiments on skeletal muscle fibres of the frog. The effects of filament compliance are demonstrated clearly in the elastic properties of partially activated fibres. The low-frequency elasticity increases linearly with tension, reflecting an increase in the number of force-producing cross-bridges. At higher frequencies, this linearity is lost. In this study we describe the data consistently in terms of a cross-bridge stiffness increasing linearly with tension and a constant Young's modulus for the actin filament of 44 MN m-2. This corresponds to a compliance of 23 pm microns-1 per kN m-2 tension developed. Using this value for the actin filament Young's modulus, its contribution to the elastic properties of skeletal muscle fibre of the frog is considered in rigor and relaxation. The filament compliance hardly affects the overall elasticity of the muscle fibre in relaxation. In contrast, it contributes to a large extent to the overall elasticity in rigor. Taking account of the filament compliance, we find that the Young's modulus in rigor exhibits an increase from 14 MN m-2 at frequencies below 500 Hz to 55 MN m-2 above 40 kHz.

Strain dependence of the elastic properties of force-producing cross-bridges in rigor skeletal muscle.

Stretch and release experiments carried out on skinned single fibers of frog skeletal muscle under rigor conditions indicate that the elastic properties of the fiber depend on strain. For modulation frequencies below 1000 Hz, the results show an increase in Young's modulus of 20% upon a stretch of 1 nm/half-sarcomere. Remarkably, the strain dependence of Young's modulus decreases at higher frequencies to about 10% upon a 1-nm/half-sarcomere stretch at a modulation frequency of 10 kHz. This suggests that the cause of the effect is less straightforward than originally believed: a simple slackening of the filaments would result in an equally large strain dependence at all frequencies, whereas strain-dependent properties of the actin filaments should show up most clearly at higher frequencies. We believe that the reduction of the strain dependence points to transitions of the cross-bridges between distinct force-producing states. This is consistent with the earlier observation that Young's modulus in rigor increases toward higher frequencies.

Viscoelastic properties of cross bridges in cardiac muscle.

Tension responses of rat right ventricular trabeculae to fast length changes are measured with microsecond resolution to obtain information about elastic properties of ventricular myocardium. Responses of these isometrically mounted trabeculae at 22 degrees C to fast length changes completed within 30 microseconds at 22 degrees C to fast length changes completed within 30 microseconds were similar in shape to those of skeletal muscle fibers. Results of quantitative evaluation of responses are interpreted in terms of cross-bridge properties. An upper bound for the elastic range of cross bridges in trabeculae, derived from the maximal developed force during Ca2+ activation and from stiffness in rigor, has been estimated as 8.4 +/- 2.2 nm. Their working stroke, estimated from the tension loss in the rigor state due to a shortening and from tension remaining after (partial) recovery, was 20 +/- 4 nm. The estimated working stroke of cross bridges is about three times larger in trabeculae than in freeze-dried skeletal muscle fibers of the frog at 4 degrees C, which points to important differences between cross-bridge mechanisms of contraction in cardiac and skeletal muscle.

High frequency characteristics of elasticity of skeletal muscle fibres kept in relaxed and rigor state.

The viscoelastic properties of crossbridges in rigor state are studied by means of application of small length changes, completed within 30 microseconds, to isometric skinned fibre segments of the iliofibularis muscle of the frog in relaxed and rigor state and measurement of the tension response. Results are expressed as a complex Young's modulus, the real part of which denotes normalized stiffness, while the imaginary part denotes normalized viscous mechanical impedance. Young's modulus was examined over a wide frequency range varying from 5 Hz up to 50 kHz. Young's modulus can be interpreted in terms of stiffness and viscous friction of the half-sarcomere or in terms of elastic changes in tension and recovery upon a step length change. The viscoelastic properties of half-sarcomeres of muscle fibre segments in rigor state showed strong resemblance to those of activated fibres in that shortening a muscle fibre in rigor state resulted in an immediate drop in tension, after which half of the drop in tension was recovered. The following slower phases of tension recovery--a subsequent drop in tension and slow completion of tension recovery--as seen in the activated state, do not occur in rigor state. The magnitude of Young's moduli of fibres in rigor state generally decreased from a value of 3.12 x 10(7) N m-2 at 40 kHz to 1.61 x 10(7) N m-2 at about 100 Hz. Effects of increased viscosity of the incubation medium, decreased interfilament distance in the relaxed state and variation of rigor tension upon frequency dependence of complex Young's modulus have been investigated. Variation of tension of crossbridges in rigor state influenced to some extent the frequency dependence of the Young's modulus. Recovery in relaxed state is not dependent on the viscosity of the medium. Recovery in rigor is slowed down at raised viscosity of the incubation medium, but less than half the amount expected if viscosity of the medium would be the cause of internal friction of the half-sarcomere. Internal friction of the half-sarcomere in the relaxed fibre at the same interfilament distance as in rigor is different from internal friction in rigor. It will be concluded that time necessary for recovery in rigor cannot be explained by friction due to the incubation medium. Instead, recovery in rigor expressed by the frequency dependence of the Young's modulus has to be due to intrinsic properties of crossbridges. These intrinsic properties can be explained by the occurrence of state transitions of crossbridges in rigor.(ABSTRACT TRUNCATED AT 400 WORDS)

The complex Young's modulus of skeletal muscle fibre segments in the high frequency range determined from tension transients.

Stiffness measurements of muscle fibres are often based on application of a length change at one end of the muscle fibre and recording of the following tension change at the other end. In this study a method is developed to determine in the high frequency range (up to 40 kHz) the complex Young's modulus of skeletal muscle fibre as a function of frequency from the tension transient, following a rapid stepwise length change completed within 40 microseconds. For this purpose both a new mechanical moving part of the displacement generating system and a force transducer with a high natural frequency (70 kHz) had to be developed. In addition to stiffness measurements of a silk fibre to test the displacement generating system and the method of analysis, stiffness of skeletal muscle fibres in relaxed and rigor state have been measured. The complex Young's moduli of relaxed muscle fibres as well as muscle fibres in rigor state are frequency dependent. In both cases the complex Young's modulus increases smoothly with increasing frequency over a range of 250 Hz up to 40 kHz. The phase angles of the responses remained almost constant at a value of 0.3 radians for a fibre in rigor and 0.6 radians for a relaxed fibre. This leads to the conclusion that for muscle fibres in rigor state the recovery in the tension response to a step length change shows a continuous distribution of relaxation times rather than a few discrete ones. Results of our stiffness measurements are compared with results obtained from current viscoelastic models used to describe stiffness of muscle fibre in this frequency range.(ABSTRACT TRUNCATED AT 250 WORDS)

Cross-bridge stiffness in Ca(2+)-activated skinned single muscle fibres.

Tension transients, in response to small and rapid length changes (completed within 40 microseconds), were obtained from skinned single frog muscle fibres incubated in activating solutions with varying concentrations of Ca2+. The first 2 ms of these transients were described by a linear model in which the fibre is regarded as a rod composed of infinitesimally small, identical segments containing a mass, one undamped elastic element and in the case of relaxed fibres two damped elastic elements in series, or in the case of activated fibres three such elastic elements in series. The stiffness of activated fibres, expressed in elastic constants or apparent elastic constants, increased with increasing concentrations of Ca2+. All the damped elastic constants that were necessary to describe the tension responses of activated fibres were proportional to isometric tension. However, the undamped elastic constant did not increase linearly with increasing isometric tension. Equatorial X-ray diffraction patterns were obtained from single frog muscle fibres under similar conditions as under which the tension transients were obtained. The filament spacing (d10) of Ca(2+)-activated single frog muscle fibres decreased with increasing isometric force, whereas the intensity ratio (I11/I10) increased linearly with increasing isometric force. From experiments in which dextran (MW 200,000 Da) was added, it followed that such a change in filament spacing would modify passive stiffness. The d10 value of relaxed fibres decreased and stiffness increased with increasing concentrations of the polymer dextran, whereas I11/I10 remained constant. The relation of stiffness and filament spacing with concentration of dextran was used to eliminate the effect of decreased filament spacing on stiffness of activated fibres. After correction for changes in filament spacing the undamped complicance C1, normalized to tension, was not constant, but increased with increasing isometric tension. If we assume that isometric tension is proportional to the number of force generating cross-bridges, this means that only part of the undamped compliance of activated fibres is located in the cross-bridges.

Weakly attached cross-bridges in relaxed frog muscle fibers.

Tension responses due to small, rapid length changes (completed within 40 microseconds) were obtained from skinned single frog muscle fiber segments (4-10 mm length) incubated in relaxing and rigor solutions at various ionic strengths. The first 2 ms of these responses can be described with a linear model in which the fiber is regarded as a rod, composed of infinitesimally small, identical segments, containing one undamped elastic element and two or three damped elastic elements and a mass in series. Rigor stiffness changed less than 10% in a limited range, 40-160 mM, of ionic strength conditions. Equatorial x-ray diffraction patterns show a similar finding for the filament spacing and intensity ratio I(11)/I(10). Relaxed fibers became stiffer under low ionic strength conditions. This stiffness increment can be correlated with a decreasing filament spacing and (an increased number of) weakly attached cross-bridges. Under low ionic strength conditions an additional recovery (1 ms time constant) became noticeable which might reflect characteristics of weakly attached cross-bridges.

Elastic properties of relaxed, activated, and rigor muscle fibers measured with microsecond resolution.

Tension responses due to small and rapid length changes (completed within 40 microseconds) were obtained from skinned single-fiber segments (4- to 7-mm length) of the iliofibularis muscle of the frog incubated in relaxing, rigor, and activating solution. The fibers were skinned by freeze-drying. The first 500 microseconds of the responses for all three conditions could be described with a linear model, in which the fiber is regarded as a rod composed of infinitesimally small identical segments, containing an undamped elastic element, two damped elastic elements and a mass in series. An additional damped elastic element was needed to describe tension responses of activated fibers up to the first 5 ms. Consequently phase 1 and phase 2 of activated fibers can be described with four apparent elastic constants and three time constants. The results indicate that fully activated fibers and fibers in rigor have similar elastic properties within the first 500 microseconds of tension responses. This points either to an equal number of attached cross-bridges in rigor and activated fibers or to a different number of attached cross-bridges in rigor and activated fibers and nonlinear characteristics in rigor cross-bridges. Mass-shift measurements obtained from equatorial x-ray diffraction patterns support the latter possibility.

Tension development and calcium sensitivity in skinned muscle fibres of the frog.

Calcium activated isometric tension development was measured in single skinned muscle fibres of the ileofibularis muscle of the frog. The experiments were carried out at 5 degrees C, pH = 6.9, 1 mM free Mg2+ and an ionic strength of 160 mM. A Hill curve was fitted to the isometrically developed tension at different Ca2+ concentrations by means of a non-linear least mean square approximation. At a sarcomere length of 2.15 micron, the Ca2+ concentration for half maximum tension (K) was 1.6 microM. This Ca2+ concentration decreased with increasing sarcomere length; at 2.7 micron, K was 1.1 microM and at 3.1 micron, K was 0.9 microM. Therefore, Ca sensitivity is increased at larger sarcomere lengths. Consequently, the optimal sarcomere length for tension development shifted to larger values when the Ca2+ concentration was lowered. Osmotic compression of the fibre at 2.15 micron by means of 5% Dextran also caused an increase in Ca sensitivity (K was 1.0 microM). At 2.7 micron, addition of 5% Dextran hardly affected the Ca sensitivity. The possible role of the interfilament spacing in the explanation of these results discussed.

Electrophysiological effects of alinidine on nodal and atrial fibers in the guinea-pig heart.

The effect of alinidine on transmembrane electrical activity of nodal and atrial fibers was studied in the isolated right auricle of the guinea-pig. Alinidine was applied in concentrations between 0.72 and 28.5 X 10(-5) M. In nodal fibers the main effect was a dose-dependent decrease in rate of diastolic depolarization and a delayed repolarization of especially the terminal part of the action potential. In both fiber types alinidine causes a marked delay of the terminal part of repolarization; the increase of the duration of the action potential was related to the alinidine concentration over the whole concentration range used. In addition the amplitude of the action potential and the maximal diastolic potential are increased dose dependently up to a concentration of 2.8 x 10(-5) M. Application of higher concentrations does not increase these parameters. In nodal fibers diastolic depolarization is already depressed considerably at a relatively low concentration. This is particularly so in fibers that normally have a high rate of diastolic depolarization, i.e., the dominant pacemaker fibers. A shifting of the pacemaker seems only to occur at high concentrations (11.4 X 10(-5) M or higher). The strong negative chronotropic effect of alinidine can be attributed to both the depression of diastolic depolarization and the increase in duration of the action potential. At low concentrations the increase of the maximum diastolic potential can also contribute to the slowing of the heart rate.