Dependence of energy transduction in intact skeletal muscles on the time in tension

Biomechanical evaluation of flash-frozen and cryo-sectioned papillary muscle samples by using sinusoidal analysis: cross-bridge kinetics and the effect of partial Ca2+ activation

We examined the integrity of flash-frozen and cryo-sectioned cardiac muscle preparations (introduced by Feng and Jin, 2020) by assessing tension transients in response to sinusoidal length changes at varying frequencies (1-100 Hz) at 25 °C. Using 70-μm-thick sections, we isolated fiber preparations to study cross-bridge (CB) kinetics: preparations were activated by saturating Ca2+ as well as varying concentrations of ATP and phosphate (Pi). Our results showed that, compared to ordinary skinned fibers, in-series stiffness decreased to 1/2, which resulted in a decrease of isometric tension to 62%, but CB kinetics and Ca2+ sensitivity were little affected. The pCa study demonstrated that the rate constant of the force generation step (2πb) is proportionate to [Ca2+] at < 5 μM, suggesting that the activation mechanism can be described by a simple second order reaction. We also found that tension, stiffness, and magnitude parameters are related to [Ca2+] by the Hill equation, with a cooperativity coefficient of 4-5, which is consistent with the fact that Ca2+ activation mechanisms involve cooperative multimolecular interactions. Our results support the long-held hypothesis that Process C (Phase 2) represents the CB detachment step, and Process B (Phase 3) represents the force generation step. Moreover, we discovered that constant H may represent the work-performing step in cardiac preparations. Our experiments demonstrate excellent CB kinetics with two well-defined exponentials that can be more distinguished than those found using ordinary skinned fibers. Flash-frozen and cryo-sectioned preparations are especially suitable for multi-institutional collaborations nationally and internationally because of their ease of transportation.

Mechanical Evaluation of Frozen and Cryo-Sectioned Papillary Muscle Samples by Using Sinusoidal Analysis: Cross-bridge Kinetics and the Effect of Partial Ca2+ activation

The use of frozen and cryo-sectioned cardiac muscle preparations, introduced recently by (Feng & Jin, 2020), offers promising advantages of easy transport and exchange of muscle samples among collaborating laboratories. In this report, we examined integrity of such preparation by studying tension transients in response to sinusoidal length changes and following concomitant amplitude and phase shift in tension time courses at varying frequencies. We used sections with 70 μm thickness, isolated fiber preparations, and studied cross-bridge (CB) kinetics: we activated the preparations with saturating Ca2+, and varying concentrations of ATP and phosphate (Pi). Our experiments have demonstrated that this preparation has the normal active tension and elementary steps of the CB cycle. Furthermore, we investigated the effect of Ca2+ on the rate constants and found that the rate constant r 4 of the force generation step is proportionate to [Ca2+] when it is <5 μM. This observation suggests that the activation mechanism can be described by a simple second order reaction. As expected, we found that magnitude parameters including tension and stiffness are related to [Ca2+] by the Hill equation with cooperativity of 4-5, consistent to the fact that Ca2+ activation mechanisms involve cooperative multimolecular interactions. Our results are consistent with a long-held hypothesis that process C (phase 2 of step analysis) represents the CB detachment step, and process B (phase 3) represents the force generation step. In this report, we further found that constant H may also represent work performance step. Our experiments have demonstrated excellent CB kinetics with reduced noise and well-defined two exponentials, which are better than skinned fibers, and easier to handle and study than single myofibrils.

Mechanisms of Frank-Starling law of the heart and stretch activation in striated muscles may have a common molecular origin

Vertebrate cardiac muscle generates progressively larger systolic force when the end diastolic chamber volume is increased, a property called the "Frank-Starling Law", or "length dependent activation (LDA)". In this mechanism a larger force develops when the sarcomere length (SL) increased, and the overlap between thick and thin filament decreases, indicating increased production of force per unit length of the overlap. To account for this phenomenon at the molecular level, we examined several hypotheses: as the muscle length is increased, (1) lattice spacing decreases, (2) Ca2+ sensitivity increases, (3) titin mediated rearrangement of myosin heads to facilitate actomyosin interaction, (4) increased SL activates cross-bridges (CBs) in the super relaxed state, (5) increased series stiffness at longer SL promotes larger elementary force/CB to account for LDA, and (6) stretch activation (SA) observed in insect muscles and LDA in vertebrate muscles may have similar mechanisms. SA is also known as delayed tension or oscillatory work, and universally observed among insect flight muscles, as well as in vertebrate skeletal and cardiac muscles. The sarcomere stiffness observed in relaxed muscles may significantly contributes to the mechanisms of LDA. In vertebrate striated muscles, the sarcomere stiffness is mainly caused by titin, a single filamentary protein spanning from Z-line to M-line and tightly associated with the myosin thick filament. In insect flight muscles, kettin connects Z-line and the thick filament to stabilize the sarcomere structure. In vertebrate cardiac muscles, titin plays a similar role, and may account for LDA and may constitute a molecular mechanism of Frank-Starling response.

Phosphate has dual roles in cross-bridge kinetics in rabbit psoas single myofibrils

In this study, we aimed to study the role of inorganic phosphate (P_i) in the production of oscillatory work and cross-bridge (CB) kinetics of striated muscle. We applied small-amplitude sinusoidal length oscillations to rabbit psoas single myofibrils and muscle fibers, and the resulting force responses were analyzed during maximal Ca²⁺ activation (pCa 4.65) at 15°C. Three exponential processes, A, B, and C, were identified from the tension transients, which were studied as functions of P_i concentration ([P_i]). In myofibrils, we found that process C, corresponding to phase 2 of step analysis during isometric contraction, is almost a perfect single exponential function compared with skinned fibers, which exhibit distributed rate constants, as described previously. The [P_i] dependence of the apparent rate constants 2πb and 2πc, and that of isometric tension, was studied to characterize the force generation and P_i release steps in the CB cycle, as well as the inhibitory effect of P_i. In contrast to skinned fibers, P_i does not accumulate in the core of myofibrils, allowing sinusoidal analysis to be performed nearly at [P_i] = 0. Process B disappeared as [P_i] approached 0 mM in myofibrils, indicating the significance of the role of P_i rebinding to CBs in the production of oscillatory work (process B). Our results also suggest that P_i competitively inhibits ATP binding to CBs, with an inhibitory dissociation constant of ∼2.6 mM. Finally, we found that the sinusoidal waveform of tension is mostly distorted by second harmonics and that this distortion is closely correlated with production of oscillatory work, indicating that the mechanism of generating force is intrinsically nonlinear. A nonlinear force generation mechanism suggests that the length-dependent intrinsic rate constant is asymmetric upon stretch and release and that there may be a ratchet mechanism involved in the CB cycle.

Phosphorylation of cMyBP-C affects contractile mechanisms in a site-specific manner

Cardiac myosin binding protein-C (cMyBP-C) is a cardiac-specific, thick-filament regulatory protein that is differentially phosphorylated at Ser(273), Ser(282), and Ser(302) by various kinases and modulates contraction. In this study, phosphorylation-site-specific effects of cMyBP-C on myocardial contractility and cross-bridge kinetics were studied by sinusoidal analysis in papillary and trabecular muscle fibers isolated from t/t (cMyBP-C-null) mice and in their counterparts in which cMyBP-C contains the ADA (Ala(273)-Asp(282)-Ala(302)), DAD (Asp(273)-Ala(282)-Asp(302)), and SAS (Ser(273)-Ala(282)-Ser(302)) mutations; the results were compared to those from mice expressing the wild-type (WT) transgene on the t/t background. Under standard activating conditions, DAD fibers showed significant decreases in tension (~50%), stiffness, the fast apparent rate constant 2πc, and its magnitude C, as well as its magnitude H, but an increase in the medium rate constant 2πb, with respect to WT. The t/t fibers showed a smaller drop in stiffness and a significant decrease in 2πc that can be explained by isoform shift of myosin heavy chain. In the pCa-tension study using the 8 mM phosphate (Pi) solution, there was hardly any difference in Ca(2+) sensitivity (pCa50) and cooperativity (nH) between the mutant and WT samples. However, in the solutions without Pi, DAD showed increased nH and slightly decreased pCa50. We infer from these observations that the nonphosphorylatable residue 282 combined with phosphomimetic residues Asp(273) and/or Asp(302) (in DAD) is detrimental to cardiomyocytes by lowering isometric tension and altering cross-bridge kinetics with decreased 2πc and increased 2πb. In contrast, a single change of residue 282 to nonphosphorylatable Ala (SAS), or to phosphomimetic Asps together with the changes of residues 273 and 302 to nonphosphorylatable Ala (ADA) causes minute changes in fiber mechanics.

Invertebrate muscles: thin and thick filament structure; molecular basis of contraction and its regulation, catch and asynchronous muscle

This is the second in a series of canonical reviews on invertebrate muscle. We cover here thin and thick filament structure, the molecular basis of force generation and its regulation, and two special properties of some invertebrate muscle, catch and asynchronous muscle. Invertebrate thin filaments resemble vertebrate thin filaments, although helix structure and tropomyosin arrangement show small differences. Invertebrate thick filaments, alternatively, are very different from vertebrate striated thick filaments and show great variation within invertebrates. Part of this diversity stems from variation in paramyosin content, which is greatly increased in very large diameter invertebrate thick filaments. Other of it arises from relatively small changes in filament backbone structure, which results in filaments with grossly similar myosin head placements (rotating crowns of heads every 14.5 nm) but large changes in detail (distances between heads in azimuthal registration varying from three to thousands of crowns). The lever arm basis of force generation is common to both vertebrates and invertebrates, and in some invertebrates this process is understood on the near atomic level. Invertebrate actomyosin is both thin (tropomyosin:troponin) and thick (primarily via direct Ca(++) binding to myosin) filament regulated, and most invertebrate muscles are dually regulated. These mechanisms are well understood on the molecular level, but the behavioral utility of dual regulation is less so. The phosphorylation state of the thick filament associated giant protein, twitchin, has been recently shown to be the molecular basis of catch. The molecular basis of the stretch activation underlying asynchronous muscle activity, however, remains unresolved.

The stiffness and phase frequency response of taenia coli smooth muscle: Comparison of the step and sinusoidal perturbation analysis

The present study aimed to show that the stiffness and phase frequency responses obtained from sinusoidal and step length changes have similar form in guinea pig taenia coli smooth muscles. Sinusoidal length changes at 20 discrete frequencies in the range of 0.0007-1Hz or step length changes with a rise time of 60ms were applied during plateau level of the tetanic contraction (60mM KCl) and the force responses were recorded. Similar experiments were performed on the passive muscle with 0.1mg/mL verapamil. The stiffness and phase responses for tetanic contraction and passive muscle were obtained by using Fourier transformed results of force and length. Then the frequency response of the passive muscle was subtracted from that obtained for tetanic contraction. The general profiles of the stiffness and phase responses were similar for the two types of perturbations. The minimum stiffness occurred at 0.0012+/-0.0005Hz for sinusoidal perturbation and at 0.0022+/-0.0009Hz for step length perturbation. The minimum stiffness value was 3.79+/-0.59mN/mm (n=10) for sinusoidal perturbation and 4.02+/-1.18mN/mm (n=10) for step perturbation. The minimum phase angle was -30.2+/-5.5 degrees for sinusoidal perturbation and -28.2+/-11.6 degrees for step perturbation. In conclusion, results showed that step length perturbations instead of sinusoidal length perturbations could be used to find the frequency characteristics of smooth muscles. The results also indicate that 0.001-0.002Hz corresponds to the cycling rate of overall processes for the stretch-induced contraction mechanism in taenia coli smooth muscle contracted with high K, including the depolarization of the plasma membrane, calcium influx, phosphorylation of light chain, and cross-bridge action.

Faster force transient kinetics at submaximal Ca2+ activation of skinned psoas fibers from rabbit

The early, rapid phase of tension recovery (phase 2) after a step change in sarcomere length is thought to reflect the force-generating transition of myosin bound to actin. We have measured the relation between the rate of tension redevelopment during phase 2 (r), estimated from the half-time of tension recovery during phase 2 (r = t0.5(-1)), and steady-state force at varying [Ca2+] in single fibers from rabbit psoas. Sarcomere length was monitored continuously by laser diffraction of fiber segments (length approximately 1.6 mm), and sarcomere homogeneity was maintained using periodic length release/restretch cycles at 13-15 degrees C. At lower [Ca2+] and forces, r was elevated relative to that at pCa 4.0 for both releases and stretches (between +/- 8 nm). For releases of -3.4 +/- 0.7 nm.hs-1 at pCa 6.6 (where force was 10-20% of maximum force at pCa 4.0), r was 3.3 +/- 1.0 ms-1 (mean +/- SD; N = 5), whereas the corresponding value of r at pCa 4.0 was 1.0 +/- 0.2 ms-1 for releases of -3.5 +/- 0.5 nm.hs-1 (mean +/- SD; N = 5). For stretches of 1.9 +/- 0.7 nm.hs-1, r was 1.0 +/- 0.3 ms-1 (mean +/- SD; N = 9) at pCa 6.6, whereas r was 0.4 +/- 0.1 ms-1 at pCa 4.0 for stretches of 1.9 +/- 0.5 (mean +/- SD; N = 14). Faster phase 2 transients at submaximal Ca(2+)-activation were not caused by changes in myofilament lattice spacing because 4% Dextran T-500, which minimizes lattice spacing changes, was present in all solutions. The inverse relationship between phase 2 kinetics and force obtained during steady-state activation of skinned fibers appears to be qualitatively similar to observations on intact frog skeletal fibers during the development of tetanic force. The data are consistent with models that incorporate a direct effect of [Ca2+] on phase 2 kinetics of individual cross-bridges or, alternatively, in which phase 2 kinetics depend on cooperative interactions between cross-bridges.

Barnacle muscle: Ca2+, activation and mechanics

In this review, aspects of the ways in which Ca2+ is transported and regulated within muscle cells have been considered, with particular reference to crustacean muscle fibres. The large size of these fibres permits easy access to the internal environment of the cell, allowing it to be altered by microinjection or microperfusion. At rest, Ca2+ is not in equilibrium across the cell membrane, it enters the cell down a steep electrochemical gradient. The free [Ca2+] at rest is maintained at a value close to 200 nM by a combination of internal buffering systems, mainly the SR, mitochondria, and the fixed and diffusible Ca(2+)-binding proteins, as well as by an energy-dependent extrusion system operating across the external cell membrane. This system relies upon the inward movement of Na+ down its own electrochemical gradient to provide the energy for the extrusion of Ca2+ ions. As a result of electrical excitation, voltage-sensitive channels for Ca2+ are activated and permit Ca2+ to enter the cell more rapidly than at rest. It has been possible to determine both the amount of Ca2+ entering by this step, and what part this externally derived Ca2+ plays in the development of force as well as in the free Ca2+ change. The latter can be determined directly by Ca(2+)-sensitive indicators introduced into the cell sarcoplasm. A combination of techniques, allowing both the total and free Ca2+ changes to be assessed during electrical excitation, has provided valuable information as to how muscle cells buffer their Ca2+ in order to regulate the extent of the change in the free Ca2+ concentration. The data indicate that the entering Ca2+ can only make a small direct contribution to the force developed by the cell. The implication here is that the major source of Ca2+ for contraction must be derived from the internal Ca2+ storage sites within the SR system, a view reinforced by caged Ca2+ methods. The ability to measure the free Ca2+ concentration changes within a single cell during activation has also provided the opportunity to analyse, in detail, the likely relations between free Ca2+ and the process of force development in muscle. The fact that the free Ca2+ change precedes the development of force implies that there are delays in the mechanism, either at the site of Ca2+ attachment on the myofibril, or at some later stage in the process of force development that were not previously anticipated.(ABSTRACT TRUNCATED AT 400 WORDS)

The theory of sliding filament models for muscle contraction. II. Biochemically-based models of the contraction cycle

A seven-state sliding filament model is proposed which differs from the model of Eisenberg & Greene. It is based on a simplified version of the in-vitro contraction cycle of Stein et al., and also has some desirable dynamical features of the empirical three-state model of Nishiyama & Murase. Appropriate x-dependences for all reaction rates are derived from the transition-state theory. The seventh-state is assumed to be a high-tension intermediate of A.M.ATP, from which direct but x-dependent dissociation can occur. If the final A.M.ATP state has a sufficiently lower tension than that of A.M.ADP.Pi, then the dominant escape path from the intermediate state is shown to be direct dissociation of the actin-myosin bond. This leads to an approximate five-state model for active and relaxed muscle in which A.M and the final A.M.ATP state are omitted.

Mechanical characteristics of skinned and intact muscle fibres from the giant barnacle, Balanus nubilus

Intact muscle fibres from Balanus nubilus develop tensions of up to 600 kN.m-2 during electrical stimulation. The rise of tension occurs with a half-time (177 ms at 12 degrees C) about fivefold longer than that of tetanised frog muscle at the same temperature. The response of myofibrillar bundles to a rapid stretch resembles that of frog muscle but has a yo value (i.e. the size of an instantaneous release necessary to just discharge tension) which is ca. 2.5 times smaller, and phase 2 of the tension transient (the "quick phase") occurs at a rate comparable to that of frog muscle. In contrast, the ATPase activity (0.018 mmoles.kg wet weight-1.s-1) of this preparation and its maximum shortening velocity (0.15-0.16 muscle lengths.s-1) are both at least fivefold slower than frog muscle. These findings can be accounted for by a cross-bridge cycle in barnacle muscle in which events prior and subsequent to the tension generating step(s) occur at a rate at least fivefold slower than comparable steps in frog muscle, but the step(s) associated with tension development occur at similar rates in the two preparations. Since the rate of mechanical relaxation in barnacle muscle is modified in the presence of intracellular calcium buffers and by depolarisation-induced elevation of the free calcium during the relaxation phase, it is proposed that the time course of relaxation is not determined exclusively by the kinetics of the cross-bridge cycle, but is also dependent on the free calcium concentration during relaxation.

Measurement of rate constants for the contractile cycle of intact mammalian muscle fibers

Small, random length changes were applied to bundles of intact fibers from rat and mouse extensor digitorum longus (EDL) and soleus muscles, while they were being tetanically stimulated. With increasing frequency of length changes, EDL muscle stiffness (tension change per unit change in length) increased, then decreased and increased again. The decrease was not seen in the soleus muscles. The EDL frequency-response could be well fitted by three exponential components with apparent rate constants of approximately 25, 150, and 500 s-1 at 20 degrees C. All rate constants increased steadily with temperature and for each 10 degrees C increase in temperature, the rates in the mouse EDL increased by a factor (Q10) between 1.8 and 2.4. With tetanic stimulation, force increased nearly exponentially to a steady level with a rate constant of 24 s-1 at 20 degrees C in mouse EDL muscles, and a Q10 of 2.4. These values correspond closely to the lowest frequency rate constant measured with length perturbations, which suggests that this process may limit the rate of rise of force in intact muscle fibers. During fatigue the high frequency and intermediate frequency rate constants declined, but the low frequency rate constant remained unchanged. These results are discussed in relation to current biochemical models for cross-bridge cycling.

The role of orthophosphate in crossbridge kinetics in chemically skinned rabbit psoas fibres as detected with sinusoidal and step length alterations

The role of orthophosphate (Pi) ions in crossbridge kinetics was investigated in chemically skinned rabbit psoas fibres in the presence of saturating Ca2+. The muscle length was altered sinusoidally, and the resulting tension time courses were analysed in terms of three exponential processes (A), (B) and (C). Experiments were also performed with step length changes, and the resulting tension transients were correlated with the results of sinusoidal analysis. It was shown that addition of a low millimolar concentration of Pi increased both the rate constant and magnitude of process (B), which resulted in a dramatic increase in the oscillatory power output. The Pi effect was greater at higher oscillation amplitude and at higher MgATP concentration. At 5 mM MgATP, the amplitude effect became saturated at a 6 nm length change per crossbridge, whereas the Pi effect did not become saturated in the concentration range tested (0-16 mM). An introduction of MgADP to the activating saline resulted in a decrease of all rate constants, and these effects were opposite to MgATP. The effect of Pi resembled neither MgADP nor MgATP. Based on these observations, all the crossbridge reactions except for one (ADP desorption reaction) were eliminated as the possible site of action of Pi ions, supposing that Pi affects only one specific site in the crossbridge cycle. Other mechanisms, which might account for the Pi effects, are the presence of parallel hydrolysis pathways and the presence of multiple sites of action of the Pi ions.

A kinetic model of muscle contraction and its oscillatory characteristics

A set of five differential equations has been found which gives a satisfactory account of the isotonic and isometric properties of striated muscle. Four of these differential equations give an equally satisfactory account of the results of length-drive experiments with sinusoidal variation of length. In this case, the fifth equation (of motion) is redundant. These sets of equations predict a number of results not yet measured relating to the superposition of oscillatory length changes on isotonic contraction. The equations predict correctly the variation of tension with time when the amplitude of the driven oscillation increases beyond the region where it can be treated as a perturbation, and the deviation of the mean tension per cycle from the steady-state tension for isotonic contraction with superimposed oscillations in length or velocity. The equations can be derived rigorously from a more complex set of eight equations which themselves are formulated from the basic principles of chemical physics, the theory of molecular force fields and radiationless transitions. The reduced model may be consistent with many other molecular theories and its predictive success does not prove the correctness or otherwise of the level 1 assumptions of the seven-state theory. By the same token, macroscopic mechanical experiments of the type presently carried out cannot give information on level 1 questions such as the existence or otherwise of 'binding' of crossbridges to the thin filament. The experimental kinetic results can be described with or without this assumption. The theory needs considerable development in so far as it does not consider elastic elements at all at present, nor have detailed conclusions yet been extracted from the equations for the case of stretching, except for isotonic steady states where agreement is encouraging.

Differences in the transient response of fast and slow skeletal muscle fibers. Correlations between complex modulus and myosin light chains

Sinusoidal analysis of the mechanochemical properties of skinned muscle fibers under conditions of maximal activation was applied to fibers from several rabbit skeletal muscles (psoas, tibialis anterior, extensor digitorum longus, diaphragm, soleus, semitendinosus). This investigation distinguished between two general classes of fibers, which on the basis of their myosin light chain complements could be classified as fast and slow. In fast fibers (e.g., psoas) we identified the presence of at least three exponential processes (A), (B), (C) of comparable magnitudes. In slow fibers (e.g., soleus) we identified the presence of at least four exponential processes (A)-(D) of very different magnitudes; magnitudes of processes (A) and (B) are very small compared with those of (C) and (D). The apparent rate constants are 8-29-fold slower in slow fibers. Because our sinusoidal characterization takes less than or equal to 22 s and does not involve chemical denaturation or other means of disruption of the myofilament lattice, it allows the different physiological classes of fibers to be characterized and then studied further by other techniques. The perfect correlation between physiological and molecular properties as assayed by gel electrophoresis after sinusoidal analysis demonstrates this and justifies its use in distinguishing between fiber types.

Stiffness, force, and sarcomere shortening during a twitch in frog semitendinosus muscle bundles

The time course of force and stiffness during a twitch was determined at 6 and 26 degrees C in frog semitendinosus muscle bundles using the transmission time technique of Schoenberg, M., J.B. Wells, and R.J. Podolsky, 1974, J. Gen. Physiol. 64:623-642. Sarcomere shortening due to series compliance was also measured using a laser light diffraction technique. Following stimulation, stiffness developed more rapidly than force, but had a slower time course than published Ca2+ transients determined from light signals using Ca2+ sensitive dyes (Baylor, S.M., W.K. Chandler, and M.W. Marshall, 1982, J. Physiol. (Lond.). 331:139-177). Stiffness (S) did not reach its tetanic value during a twitch at 6 or 26 degrees C, although at 6 degrees C, it approached close to this value with S-twitch/S-tetanus = 0.82 +/- 0.07 (+/- SEM). During relaxation, force fell more rapidly than stiffness both for a twitch and also a tetanus. Also in this paper, several of the assumptions inherent in using the transmission time technique for the measurement of stiffness are considered in detail.

Muscle tension response to sinusoidal length perturbation: a theoretical study

The set of kinetic equations that defines a deterministic model of muscle contraction, based on the sliding filament hypothesis in which the relative sliding velocity is an independent variable, is numerically integrated under the simulated conditions of sinusoidal length perturbation. The frequency response curve of phase angle and dynamic stiffness are in agreement with experimental curves. The resultant mean tension per cycle is lower than the unperturbed steady-state tension. The magnitude of the negative tension deviation is greater when either the amplitude or the frequency of the oscillation is increased. The tension-time curve differs from a simple sine when the perturbing frequency is in the vicinity of the stiffness minimum. These consequences are in agreement with the few experimental results that are available.

Effect of Ca ion concentration on cross-bridge kinetics in rabbit psoas fibers. Evidence for the presence of two Ca-activated states of thin filament

The effect of Ca ion concentration on cross-bridge kinetics in a small bundle (one to three fibers) of chemically skinned rabbit psoas muscle is studied. The length of the muscle is oscillated in small amplitude sine waves (0.2% L0 peak-to-peak) at varying frequencies (0.125 -- 167 Hz), and the resulting amplitude and phase shift in tension are measured. The frequency response function (complex stiffness) thus obtained can be divided into three parts, which we name process (A) (centered at 1 Hz), process (B) (3--17 Hz), and process (C) (50 Hz). Process (B), which represents oscillatory work, further splits into two processes (B' and B) at partial Ca activation (less than 50% P0), where the phase-frequency plot appears W-shaped. The slower of the two processes (B') disappears by full activation, at which time the plot appears V-shaped. The characteristic frequencies associated with the minima of the plot do not shift in a graded way with Ca concentration, indicating that there is no change in apparent rate constants. Apparent rate constants of processes (A) and (C) are minimally affected by Ca. The above results are not altered when ionic strength is changed between 128 and 265 mM. We propose that activated thin filaments can have two "on" states and that Ca concentration controls the distribution of these two states. This mechanism generally supports the "switch" hypothesis of Ca regulation.

Alternate energy transduction routes in chemically skinned rabbit psoas muscle fibres: a further study of the effect of MgATP over a wide concentration range

Complex stiffness data were studied over an extended range of MgATP concentrations (3 muM-5 nM) in single fibres of Ca2+-activated, chemically skinned adult rabbit psoas. The data were analysed in terms of a model involving three exponential processes, the presence of which was previously observed in fully activated muscles. As fibres were transferred from a rigor solution into solutions of gradually increasing MgATP concentration, the three processes appeared sequentially, each with a unique Km. The order of appearance as MgATP increase is (1) the slowest of three processes [designated process (A)], (2) the fastest of the three processes [designated (C)], and (3) process (B), which occupies the middle range of frequencies; the KmS are approximately 10 muM, 0.2 mM, and 0.8 mM, respectively. The single phase advance [process (A)] remaining at very low substrate concentrations was found to be better described by a distribution of rate constants than by a single rate constant. The influence of substrate concentration on these processes is examined and two parallel hydrolysis routes are suggested as a possible mechanism.

Sinusoidal analysis: a high resolution method for correlating biochemical reactions with physiological processes in activated skeletal muscles of rabbit, frog and crayfish

A high resolution method for determining the complex stiffness of single muscle fibres is described. In this method the length of the fibre is oscillated sinusoidally, and the resulting force amplitude and phase shift are observed and interpreted in terms of chemo-mechanical energy transduction. In activated, fast skeletal muscles of rabbit (psoas), frog (semitendinosus) and crayfish (walking leg flexor), we resolved at least three exponential rate processes. We named these (A), (B), (C) in order of slow to fast. These processes should reflect ATP hydrolysis and concomitant energy transduction since they are absent in muscles that the relaxed, in rigor or fixed. The great similarities in the complex stiffness data from different muscles suggests that there is a common mechanism of chemo-mechanical energy transduction across a broad phylogenetic range.

Frequency-domain study of the mechanical response of living striated muscle

Small-amplitude sinusoidal displacements, in the frequency range 4-100 Hz, were applied to intact whole frog sartorius muscle whilst in a state of tetanus. At low frequencies the muscle was observed to do oscillatory work, while at higher frequencies it tended towards elastic behaviour. Frequency-response plots obtained were compared with those from other muscle preparations. Results were interpreted in terms of mechano-chemical transduction properties of muscle.

Filament interaction in intact muscle fibers monitored by light scattering

Measurement of changes in optical properties of intact muscle fibers during contraction has proven to be difficult or, in some cases, impossible due to movement of the muscle relative to the incident beam. In this paper we describe a technique for immobilizing single fibers in clear gelatin, which permits measurement of light scattering signals undistorted by movement artifacts. We also describe the phase and amplitude relationship between changes in intensity of light scattering (at 90 degrees to incident beam) and tensions induced by electrically activating single fibers. With tensions that range up to 50% Po (Po = maximal tension measured by exposure of fibers to 200 mM K+), the maximal increase in light scattering is about 25% of that for resting fibers. The scattering increase precedes tension, and at low temperatures the interval between the two peaks can be 50--100 msec. We interpret these data on intact fibers, as we did our earlier data from studied on skinned fibers, as indicating that increases in light scattering power of muscle are primarily due to attachment of myosin cross-bridges to actin filaments.

The force-velocity relation of isolated twitch and slow muscle fibres of Xenopus laevis

1. A study has been made of the relation between force and speed of shortening, or lengthening, in isolated twitch and slow muscle fibres, dissected from the iliofibularis muscle of Xenopus laevis. Both after-loaded and quick-release contractions were studied. Twitch fibres were stimulated electrically to give tetanic contractions (5-20 degrees C); slow fibres were activated by a rapid change to solutions with high K concentration (30-75 mM; experiments at 21-24 degrees C).2. The velocity of slow fibres was constant during shortening over 10% length change in after-loaded contractions, except at forces exceeding about 0.8 of isometric tension, P(0). In quick-release experiments, shortening velocity was found to depend not only on the relative load, P/P(0), but also on the instant when the release was made. With increasing time after onset of contraction the initial rate of shortening decreased; also, a progressive fall in speed during shortening became more marked.3. The fall in initial shortening speed with time of release from the onset of a contracture was more pronounced at high [K](o) than at low.4. The relation between the relative force, P/P(0), and shortening velocity, V, in after-loaded contractions (75 mM-K) and quick-release contractions (45 mM-K, early releases) in slow fibres could be represented by a hyperbola with the constants a = 0.10P(0), b = 0.11 lengths/sec; extrapolated V(max.) was 1.10 lengths/sec.5. Isometric tension and maximum shortening velocity in slow fibres were very nearly constant between 32 and 75 mM-K. a/P(0), however, was clearly reduced at 32 mM-K, representing a more curved P-V relation.6. Force-velocity data for twitch fibres (quick-release contractions, 20 degrees C) were reasonably well fitted by a hyperbola (a = 0.38P(0), b = 1.97 lengths/sec, V(max.) = 5.20 lengths/sec), but a systematic deviation was observed for forces exceeding 0.6P(0).7. a/P(0) for twitch fibres was found to be independent of temperature in the range 5-20 degrees C. Q(10) for b was 2.24 (10-20 degrees C), and 2.86 (5-10 degrees C).8. V(max.) for twitch fibres was calculated to be 6.34 lengths/sec at 22.5 degrees C, the average temperature in the slow fibre experiments. The maximum shortening velocity in twitch fibres is thus 6 times higher than in slow fibres.9. When loads in the range 1.1-1.4P(0) were quickly applied to an actively contracting slow fibre, lengthening of the fibre occurred in two phases, an initial rapid phase, followed by a phase of extremely slow lengthening. In corresponding experiments on twitch fibres lengthening was rapid at first and then gradually became slower.10. Factors affecting the shape of the force-velocity curve are discussed. Calculations based on A. F. Huxley's (1957) model for muscle contraction indicated that cross-bridge turnover rate is about 15 times lower in slow than in twitch fibres.

Head rotation or dissociation? A study of exponential rate processes in chemically skinned rabbit muscle fibers when MgATP concentration is changed

The mechanical response of fully activated muscle bundles (one to five fibers) to sinusoidal length perturbation ( approximately 0.4% L(0)) was studied as a function of MgATP concentration. The frequency response (0.25-167 Hz; corresponding to 1 ms time resolution) of chemically skinned rabbit muscle fibers was resolved into three exponential rate processes, (A), (B), and (C). At 20 degrees C, the apparent rate constants associated with the fast exponential lead (2pic = 388-588 s(-1)) and the oscillatory work (2pib = 59-116 s(-1)) both increase with increment of the MgATP concentration from 1 to 5 mM, and they both saturate for further increase. Over the whole range of MgATP concentrations the slow exponential lead (2pia = 9-7 s(-1)) remains constant. The effect of MgATP on processes (B) and (C) can be interpreted in the context of the biochemical evidence, in which MgATP enters the cross-bridge cycle after the desorption of the product, and the binding of MgATP to rigorlike cross-bridges promotes a rapid dissociation of actomyosin (Lymn and Taylor, 1971. Biochemistry.10:4617-4624.). The effect is not predicted by a model for force generation in which head rotation dominates the fast component ("stage 2" of Huxley and Simmons, 1971. Nature (Lond.).233:533-538. and 1973. Cold Spring Harbor Symp. Quant. Biol.37:669-680.), and head dissociation dominates the slow component ("phase 4" of Huxley, 1974. J. Physiol. (Lond.).243:1-43; Julian et al., 1974. Biophys. J.14: 546-562.).

Effectof MgATP on stiffness measured at two frequencies in Ca2+-activated muscle fibers

The stiffness of skinned crayfish single muscle fibers was continuously monitored at two frequencies. The length of the fibers was oscillated by the sum of two sine waves (5 Hz and 100 Hz) of small amplitudes. In saline containing saturating amounts of Ca2+, the stiffness ratio (5 Hz:100Hz) was constant as the MgATP (substrate) concentration was raised from 0 to 2 mu M, then it decreased with a further increment in MgATP. The systematic decrease in the stiffness ratio in MgATP above 2 mu M indicates the presence of faster transitions in the cross-bridge cycle. This dependence of the stiffness ratio on MgATP is predictable if we use the two-state model of A. F. Huxley (1957) with a modification, in which MgATP promotes the dissociation of the attached cross-bridges.