Crossbridge viscosity in activated frog muscle fibres.

Force responses to fast ramp stretches at various velocities were recorded in single muscle fibres isolated from tibialis anterior muscle of the frog (Rana esculenta) at a sarcomere length between 2.15 and 3.25 microns at 15 degrees C. Stretches were applied at the tetanus plateau and during tetanus rise. Length changes were recorded at the sarcomere level using either a laser diffractometer or a striation follower apparatus. The immediate force response to the stretch is not simply elastic, as is usually assumed, but is composed of the sum of at least two components: (i) elastic (force proportional to the amount of stretch); and (ii) viscous (force proportional to the rate of stretch). The viscous response is associated with a short (about 10 microseconds) relaxation time. The amplitude of the viscous component increases progressively with tension during the tetanus rise and scales down with sarcomere length approximately in the same way as the tetanic tension. These results suggest that the viscosity of activated fibres may arise from crossbridge kinetics.

Mechanical properties of frog muscle fibres at rest and during twitch contraction.

Data reported in the literature suggest that crossbridges in rapid equilibrium between attached and detached states (weakly binding bridges), demonstrated in relaxed skinned fibres at low ionic strength, could be present also in intact fibres under physiological conditions. In addition, it was suggested that the well known leading of stiffness over force during the tension development in stimulated muscle fibres could be due to an increased number of weakly binding bridges induced by the stimulation. The experiments reviewed in this paper were made to investigate these possibilities. Fast ramp length changes were applied to single frog muscle fibres at rest and during the early phases of activation. The corresponding force changes were analysed, searching for the components expected from the presence of weakly binding bridges. The results showed no mechanical indication for the presence of weakly binding bridges in both skinned and intact fibres, either at rest or during activation. It was also found that a portion of the fibre stiffness increase induced by stimulation leads the formation of crossbridges.

The mechanisms of force enhancement during constant velocity lengthening in tetanized single fibres of frog muscle.

The present paper deals with the mechanism responsible for the force enhancement in response to constant velocity lengthenings imposed at the plateau of isometric tetanic contractions. Experiments were performed at 3.5-5.6 degrees C on single fibres isolated from the tibialis anterior muscle of the frog. The resting sarcomere length was about 2.15 microns. The large variation observed in the characteristics of the force responses to lengthening and therefore in the shape of the force-lengthening velocity relations is mainly determined by the degree of longitudinal dishomogenities of muscle fibres. "Homogeneous" fibres and individual "tendon-free segments" selected along them exhibited superimposable force-lengthening velocity relations with negligible shape variation. Stiffness and force increased with lengthening, reaching, approximately steady values, respectively 10-15% and 60-70% greater than at the isometric tetanus plateau, at velocities of about 0.1 micron/s per half-sarcomere (hs). At higher lengthening velocities stiffness remained practically unvaried, whereas the steady component of the force responses continued to increase, reaching asymptotically a maximum value, about 100% greater than at the isometric tetanus plateau, at velocities between about 0.5 and 1 micron/s per hs. The amount of lengthening required to attain the peak value was smaller for stiffness (10 nm per hs) than for force (12-14 nm per hs). In terms of 1957 model of A. F. Huxley, the results indicate that lengthening (i) potentiates the mechanical output of muscle by increasing the number and the degree of extension of attached cross-bridges, (ii) enhances the speed of cross-bridge attachment and detachment.

Force-velocity relation and stiffness in frog single muscle fibres during the rise of tension in an isometric tetanus.

The force-velocity (T-V) relation and the force-extension (T1) relation are determined at present times and at increasing isometric tensions during a tetanic contraction in frog single muscle fibres in which the passive compliance in series with the sarcomeres was made very small. The slope of the instantaneous T1 relation, the fibre stiffness, increases roughly in proportion to the level of the rising isometric tension at which the measurements were made. The value of V0 (the velocity of shortening under zero load) is time-independent, whereas the force T exerted during shortening at any velocity V lower than V0 increases gradually with time after the beginning of the tetanus volley and attains its steady state level before the isometric tension has attained the tetanus plateau and the fibre stiffness its final value. It is concluded that the delay of the development of the isometric tension and of the fibre stiffness with respect to the development of the T-V relation is determined by a specific factor of the contractile process. It is interesting to note that in a cross-bridge model of contraction, in which the value of the rate constant for cross-bridge formation is moderate, the recruitment of actin sites which is measured by the characteristics of the instantaneous T-V relation, is expected to lead significantly the actual cross-bridge formation, which is measured both by the instantaneous isometric tension and by the instantaneous stiffness.

Taking the first steps in contraction mechanics of single myocytes from frog heart.

Intact or skinned atrial and ventricular myocytes from frog heart were mounted horizontally between the lever arms of a force transducer and a servo-controlled electromagnetic loud-speaker "motor" in a trough filled with Ringer or relaxing solution. The myocyte length-sarcomere length relation for intact preparations at rest is linear at least in the range from l0 (sarcomere length about 2.1 microns, resting force zero) to 1.6 l0 (resting force about 100 nN). The peak force value for control twitches (21-23 degrees C, stimulus interval 10 s, [Ca2+]o 1 mM) varies from 20 to 100 nN in atrial and ventricular intact myocytes. The effects induced by isoprenaline or changes in [Ca2+]o, stimulation pattern and bath temperature on twitch characteristics are comparable to those observed in multicellular preparations. The steady force produced by maximally Ca(2+)-activated skinned myocytes is much greater than that developed in control twitches and varies from 0.5 to 3.5 microN in different cells. The saturating pCa in the activating solution is around 5.50. The force response of a resting myocyte to slow ramp stretches shows an initial velocity- and length-dependent component during the stretch itself and, after completion of the length change, a gradual recovery towards a steady level which only depends on the stretch extent. The force response of a stimulated myocyte to length steps complete in 2 ms consists of an apparently elastic change during the step itself and then of a rapid partial recovery followed by slowering of recovery. Whether or not the force recovery includes different phases as reported for skeletal muscle remains unclear.

Force response of unstimulated intact frog muscle fibres to ramp stretches.

The possibility that weakly binding bridges are attached to actin in the absence of Ca2+ under physiological conditions was investigated by studying the force response of unstimulated intact muscle fibres of the frog to fast ramp stretches. The force response during the stretching period is divided into two phases: phase 1, coincident with the acceleration period of the sarcomere length change and phase 2, synchronous with sarcomere elongation at constant speed. The phase 1 amplitude increases linearly with the stretching speed in all the range tested, while phase 2 increases with the speed but reaches a plateau level at about 50 x 10(3) nm/half sarcomere per second. The analysis of data shows that phase 1, which corresponds to the initial 5-10 nm/half sarcomere of elongation, is very likely a pure viscous response; its amplitude increases with sarcomere length and it is not affected by the electrical stimulation of the fibre. Phase 2 is a viscoelastic response with a relaxation time of the order of 1 ms; its amplitude increases with sarcomere lengths and with the stimulation. These data suggest that weakly binding bridges are not present in a significant amount in unstimulated intact fibres.

Calcium dependence of the apparent rate of force generation in single striated muscle myofibrils activated by rapid solution changes.

Single myofibrils or small groups of myofibrils were isolated from different types of striated muscle: rabbit psoas, frog tibialis anterior, frog atrial and ventricular muscle. The Ca2+ concentration of the solution perfusing the myofibrils was changed within few milliseconds by translating the interface between two flowing streams of solution across the preparations. In all types of myofibrils tested, the time course of force rise in response to maximal activation (pCa 4.75) was approximately monoexponential and nearly superimposable on that observed after a release-restretch protocol applied to the myofibril at the plateau of maximal contractions. This suggests that the kinetics of force development following rapid myofibril activation essentially reflects the kinetics of interaction between contractile proteins. The half time of force rise in response to maximal activation varied among different myofibril types; it was shortest in frog tibialis anterior myofibrils and longest in frog ventricular myofibrils. In all types of myofibril preparations tested the half time of force rise increased with decreasing Ca2+ levels in the activating solution. The finding provides support for a kinetic mechanism of force regulation by Ca2+ in all types of striated muscle. The extent of this Ca2+ effect, however, varied among the different myofibril preparations tested; at 15 degrees C for instance, it was smaller in frog tibialis anterior myofibrils than in the other preparations.

Myofilament compliance and sarcomere tension-stiffness relation during the tetanus rise in frog muscle fibres.

The sarcomere stiffness was measured in single muscle fibres during the development of tetanic tension using a method insensitive to fibre inertia and viscosity. The stiffness was calculated as the ratio between tension changes and sarcomere length changes during a period of fast sarcomere elongation at constant velocity. The results show that, unlike previous measurements with step or sinusoidal length changes, the relation between relative force and relative stiffness on the tetanus rise is linear. Consequently, the development of stiffness upon stimulation is synchronous with the development of force. Since a substantial fraction of sarcomere compliance is localized in the myofilaments, this result can be accounted for by assuming that either myofilament compliance is highly non-linear or that crossbridges stiffness during the tetanus rise is not proportional to crossbridge tension.

The mechanical characteristics of the contractile machinery at different levels of activation in intact single muscle fibres of the frog.

The relation between stiffness and tension and the characteristics of the early tension recovery in response to applied small length step were studied both during tetanus rise and redevelopment of tension following a period of shortening at Vmax. Experiments were performed on single fibres isolated from tibialis anterior and lumbricalis muscles of the frog. Development of stiffness preceded that of tension during tension redevelopment, but the leading of stiffness was reduced to about one half of that found during the tetanus rise. The relation between relative stiffness and relative tension was the same either during tetanus rise and tension redevelopment. The speed of the early tension recovery in response to a step length change applied during the tension redevelopment was unchanged with respect to that found at the same tension during the tetanus rise. These results suggest that a cross-bridge state generating no force (or low force) may be a normal intermediate of the cross-bridge cycle even when the fibre is fully activated.

Third-order phase transition in random tilings.

We consider the domino tilings of an Aztec diamond with a cut-off corner of macroscopic square shape and given size and address the bulk properties of tilings as the size is varied. We observe that the free energy exhibits a third-order phase transition when the cut-off square, increasing in size, reaches the arctic ellipse-the phase separation curve of the original (unmodified) Aztec diamond. We obtain this result by studying the thermodynamic limit of a certain nonlocal correlation function of the underlying six-vertex model with domain wall boundary conditions, the so-called emptiness formation probability (EFP). We consider EFP in two different representations: as a τ function for Toda chains and as a random matrix model integral. The latter has a discrete measure and a linear potential with hard walls; the observed phase transition shares properties with both Gross-Witten-Wadia and Douglas-Kazakov phase transitions.

Interaction between sodium and calcium ions in the process of transmitter release at the neuromuscular junction.

1. The interaction between Na and Ca ions on quantal transmitter release at the frog neuromuscular junction has been studied, using intracellular recording and averaging of responses.2. At low calcium concentrations, partial withdrawal of Na ions increases end-plate potential (e.p.p.) amplitudes and quantal content (m) and decreases the amplitude of the miniature e.p.p.s (m.e.p.p.s). Under these conditions the relation between [Ca] and m is highly non-linear. When plotted on double logarithmic co-ordinates withdrawal of [Na] causes a nearly parallel shift of this relation.3. Mutual interaction occurs between Ca, Na and Mg in transmitter release. With a constant low [Ca] in the medium, withdrawal of [Na] produces a smaller increase in m when [Mg] is high, than when [Mg] is low.4. In the presence of normal [Ca] (1.8 mM), [Na] withdrawal decreases the amplitude of the e.p.p. and produces a small decrease in m.5. The results can be explained by assuming that [Na] reduction has two mutually opposing effects on transmitter release: it makes more sites available for the action of Ca, and it lowers the amplitude of the action potential in the nerve terminals. The former effect dominates at low, the latter at high, calcium concentrations.

Force-velocity relation in deuterium oxide-treated frog single muscle fibres during the rise of tension in an isometric tetanus.

1. The force-velocity (P-V) relation from a single fibres isolated from the semitendinosus muscle of the frog was determined at pre-set times during the rise of tension and the plateau of isometric tetani. The controlled-velocity release method was used. Experiments were performed at about 2.25 micrometers sarcomere length and at 3-4 degrees C or at 19-21 degrees C. 2. Replacing H2O with D2O resulted in a rapid large reduction of the peak twitch tension and of the speed of development of twitch and tetanic tensions. The tetanic tension (P0) was usually reduced, in certain fibres to as low as 5% of the value in H2O-Ringer solution. 3. The depression of twitch and tetanus characteristics was followed by a recovery, the duration of which varied greatly in different fibres. During the recovery period previous conditioning activity potentiated the tetanus characteristics. 4. After the end of the recovery period in D2O-Ringer solution both the peak twitch tension and the speed of development of tetanic tension was still greatly depressed, whereas the value of P0 was slightly greater than in H2O-Ringer. The speed of rise of isometric tension after a quick release imposed at the tetanus plateau was reduced in D2O-Ringer, usually to about 50% of the value in H2O-Ringer. 5. D2O increased the development time of the P-V relation and produced a conspicuous increase in the degree of its curvature. The value of V0 (the velocity of shortening at zero load) was not significantly depressed by D2O and it was the same independent both of the time after the beginning of stimulation and of the isometric tension at which the measurement was made. The P-V relation attained its final characteristics before the isometric tension reached the plateau. During the recovery period in D2O-Ringer, at the plateau of isometric tetani of different size, the relative force exerted at a given velocity of shortening was constant. 6. In D2O-treated fibres, NO3- and caffeine (i) potentiated the peak twitch tension and the speed of development of tetanic tension without affecting significantly the speed of the redevelopment of tension after a quick release imposed at the tetanus plateau and (ii) reduced the development time of the P-V relation, but did not affect either the degree of its curvature or the value of V0 and P0. 7. The results are discussed by assuming that the release of Ca2+ from the sarcoplasmic reticulum is a rate-limiting process for the development of activation and in turn for the development of isometric tension. In terms of the cross-bridge model of Huxley (1957), the time or Ca2+-dependent factor of activation appears to be the recruitment of actin sites for cross-bridge formation, whereas the value of the rate constants regulating the cross-bridge kinetics appears to be time and Ca2+-independent.

Force-velocity and unloaded shortening velocity during graded potassium contractures in frog skeletal muscle fibres.

Steady-state conditions of contraction, at maximal and submaximal forces, were produced in intact single muscle fibres, from Rana esculenta, using full tetani and graded K+-contractures. The uniformity in radial direction. of spreading of activation produced in K+-contractures, was checked in relation to the fibre diameters. The absolute isometric force was similar in tetani and maximal contractures, for fibres with diameters between 40 and 60 microm, but not for fibres with diameters greater than about 70 microm in which contracture force never reached tetanic force. The force [K+]o relation was similar for fibres with diameters between 40 and 60 microm. but it was right shifted and it had a minor slope for fibres with diameters greater than 65-70 microm. This suggests that only in the small diameter fibres (40-60 microm) the activation does not fail to penetrate uniformly from the surface towards the fibre core. For fibres selected in the diameter range between 40 and 60 microm, force-velocity relations and unloaded shortening velocities were determined in tetani and maximal and submaximal contractures. Data were obtained across a force range of 0.3 to 1 P0 (tetanic plateau force). Controlled velocity method was used to obtain force-velocity relations, and slack test to determine the unloaded shortening velocity (VU). The values of the parameters characterising the force velocity relation (V0 and a/P0) and VU as determined by the slack test did not differ significantly in tetani and contractures, independent of the activation level or absolute force developed by the fibre. These results show that. at least within the range of forces tested. crossbridge kinetics is independent of the number of cycling crossbridges, in agreement with the prediction of the 'recruitment' model of myofilament activation.

Force responses to rapid length changes in single intact cells from frog heart.

1. Force transients in response to step perturbations in length were recorded in intact atrial cells from frog heart at various temperatures (6-15 degrees C). Length changes of various sizes and in either direction, complete in 0.5 ms, were applied to single myocytes near slack length (initial sarcomere length 2.1-2.2 microns) just before the peak of an isometric twitch. The frequency response of the force transducers used was 2-4 kHz in Ringer solution. 2. An early quick force recovery phase was clearly observed after the elastic force response to the length step and before the start of much slower recovery processes. The quick recovery phase became progressively faster with larger shortening steps and was almost as fast as that originally described in intact frog skeletal muscle fibres (rate constants above 1000 s-1 in large releases at 10 degrees C). 3. The force-extension relation determined at the end of the length change (T1 curve) indicates that an instantaneous shortening of 0.5-0.6% of the initial cell length (L0) brings the force to zero. The force--extension relation determined at the end of the quick recovery phase (T2 curve) showed that the early recovery leads to an almost complete restoration of the original force with small stretches and releases (up to 0.3% L0) and that it becomes negligible in shortening steps of about 1.4% L0. 4. The results suggest that the mechanical properties of attached cross-bridges and the rate of transitions between attached cross-bridge states are approximately the same in frog atrial cells and fast skeletal muscle fibres.(ABSTRACT TRUNCATED AT 250 WORDS)

A velocity-dependent shortening depression in the development of the force-velocity relation in frog muscle fibres.

During the onset of activation in isolated frog muscle fibres the development of the force-velocity (T-V) relation was determined by imposing single and double ramp releases. The experiments were performed at 3.5-6 degrees C or 19-22 degrees C and at a starting sarcomere length of about 2.25 micron. A velocity- and time-dependent shortening deactivation was shown to exist during the development of contraction. It was found that, early during the tetanus rise, at submaximal levels of activation, the values of T (the steady force exerted by the muscle fibres at any velocity of shortening V lower than V0) were significantly affected by previous conditioning shortening. Conditioning shortening at lower speeds led to potentiation of T and, at higher speeds, to depression. Both these effects were independent of the amount of shortening and, in addition, were not present at the tetanus plateau. At each given time or isometric tension throughout the tetanus rise the values of T. normalized for those determined at the same velocities at the tetanus plateau, were found to be inversely correlated with the actual velocities of shortening. The slope of this relation (a measure of the velocity-dependent shortening deactivation) decreased exponentially with time, attaining, in six fibres at low temperature, 10% of its initial value within 26-73 ms. The results may be explained in terms of a cross-bridge model of contraction by assuming that the rate of development of activation is controlled by the rate of release of the Ca2+ as well as by the velocity at which the muscle fibres are allowed to shorten and in turn by the actual number of attached cross-bridges.

Miniature synaptic potentials at frog spinal neurones in the presence of tertodotoxin.

1. Spontaneous subthreshold potentials have been recorded with an intracellular electrode from neurones of the isolated spinal cord of the frog.2. Records of both depolarizing and hyperpolarizing potentials were obtained from cells in normal Ringer solution and also when impulse conduction in the cord had been abolished by tetrodotoxin (TTX).3. Comparisons of results before and after TTX show that the majority of the spontaneous potentials are analogous to miniature end-plate potentials.

The variation of characteristics of twitch and tetanic contractions with sarcomere length in isolated muscle fibres of the frog.

The relation between sarcomere length, tension and time course of tension development in twitch and tetanic contractions at 20 degrees C was determined for isolated fibres from the semitendinosus muscle of the frog (Rana esculenta). In twenty fibres at about 2.15 micron sarcomere length, the peak twitch tension, the maximum tetanic tension and the twitch/tetanus ratio ranged, respectively, from 0.22 to 1.6 kg/cm2, from 2.13 o 3.96 kg/cm2 an from 0.07 to 0.53. The peak twitch tension was found to be: i) directly correlated with the twitch/tetanus ratio and the time to the peak of the first derivative of the twitch tension, ii) inversely correlated with the time to the peak of the first derivative of tetanic tension. No significant correlation was found between the maximal tetanic tension and the peak twitch tension or the twitch/tetanus ratio. Peak twitch tension and twitch/tetanus ratio were not correlated with the fibre cross-sectional area which ranged from 1.052 to 6,283 micron2. Sarcomere length-tension curves for twitch and tetanic isometric contractions at 20 degrees C were determined in twelve fibres. Increases in sarcomere length from about 2.15 to 2.85 micron produced, depending on the peak twitch tension or the twitch/tetanus ratio at about 2.15 micron, either decrease and no change or increase in peak twitch tension, but constantly enhanced the twitch/tetanus ratio and the degree of this potentiation was inversely correlated with the twitch/tetanus ratio at 2.15 micron. Increase in sarcomere length above 2.15 micron did not alter the course of the early development of twitch and tetanic tensions, reduced considerably the variation in peak twitch tension and twitch/tetanus ratio, without altering that of tetanic tension and swamped the correlation between the peak twitch tension and the time to peak of the differentiated twitch tension. However, the peak twitch tension at about 2.85 micron resulted to be directly correlated with the peak twitch tension at about 2.15 micron and in addition the relative length-dependent change in the time of the peak of the first derivative of the twitch tension resulted to be directly correlated with the relative length-dependent change in the peak twitch tension. It is concluded that both the duration of the active state and the rate factors of activation contribute to the determining of the large variation in peak twitch tension at about 2.15 micron, whereas the length-dependent increase in twitch/tetanus ratio appears to be mainly determined by prolongation of the active state duration.

Force-velocity relation in normal and nitrate-treated frog single muscle fibres during rise of tension in an isometric tetanus.

1. The force-velocity (P-V) relation for normal or NO-3 treated single fibres isolated from the semitendinosus muscle of the frog was determined at given times during the rise of tension and the plateau of isometric tetani. Experiments were made at about 2.25 micron sarcomere length and at constant temperatures, from 3 to 4.5 degrees C and from 19 to 21 degrees C. The controlled-velocity release method was used. 2. During the rise of tension, at any initial tension higher than about 0.2 P0, the lowest release velocity required to drop the tension to zero was the same as at the tetanic plateau, independent of the temperature and the presence of NO-3 ions in the bathing solution. 3. The degree of activation (measured by the steady force exerted at a given velocity of shortening lower than V0) increased with time, but attained its steady-state level before isometric tension. 4. At about 20 degrees C, frog muscle fibres at about 2.2 micron sarcomere length were only partially activated after a single stimulus. 5. NO-3 ions did not affect the steady-state P-V relation. At about 20 degrees C, NO-3 ions increased the rate of development of activation. Potentiation of the twitch contraction was due at least in part to this mechanism. 6. The 'relative' P-V relation appears to be independent of both the time after start of stimulation and the presence of NO-3 ions in the bathing solution. 7. The results are discussed in terms of the sliding filament model of Huxley (1957), assuming that either the number of actin sites available for cross-bridge formation, or the value of the rate constant for making of cross-bridges, is time dependent.

The development of the force-velocity relation in normal and dantrolene-treated frog single muscle fibres.

The force-velocity (P-V) relation for single fibres isolated from the semitendinosus muscle of the frog was determined at preset times during the rise of tension and the plateau of isometric tetani. The controlled-velocity release method was used. Experiments were performed at a sarcomere length of about 2.25 micrometer. Addition of dantrolene-sodium (DaNa) to Ringer's solution resulted in a large reduction of the peak twitch tension and of the speed of rise of twitch and tetanic tensions. The plateau tetanic tension was either unaffected or only slightly reduced by DaNa. In all fibres the speed of rise of isometric tension after a quick release imposed at the tetanus plateau was not affected by DaNa. DaNa did not significantly affect the observed value of V0 and the calculated values of Hill's constants V0, P0, a/P0 and b for the P-V relation determined at the tetanus plateau. In accordance with previous work, during the tetanus rise the P-V relation gradually attained its final characteristics, but there was a significant delay of the development of the isometric tension with respect to the development of the P-V relation. Treatment of the fibre with DaNa increased both the development time of the P-V relation and the level of isometric tension at which during the tetanus rise the P-V relation attained its final characteristics. It is concluded that DaNa, which inhibits the release of Ca2+ from the sarcoplasmic reticulum, also depresses the rate of development of activation.