Tension and stiffness of frog muscle fibres at full filament overlap

Myofilament dysfunction in diastolic heart failure

Diastolic heart failure (DHF), in which impaired ventricular filling leads to typical heart failure symptoms, represents over 50% of all heart failure cases and is linked with risk factors, including metabolic syndrome, hypertension, diabetes, and aging. A substantial proportion of patients with this disorder maintain normal left ventricular systolic function, as assessed by ejection fraction. Despite the high prevalence of DHF, no effective therapeutic agents are available to treat this condition, partially because the molecular mechanisms of diastolic dysfunction remain poorly understood. As such, by focusing on the underlying molecular and cellular processes contributing to DHF can yield new insights that can represent an exciting new avenue and propose a novel therapeutic approach for DHF treatment. This review discusses new developments from basic and clinical/translational research to highlight current knowledge gaps, help define molecular determinants of diastolic dysfunction, and clarify new targets for treatment.

Crossbridge and filament compliance in muscle: implications for tension generation and lever arm swing

The stiffness of myosin heads attached to actin is a crucial parameter in determining the kinetics and mechanics of the crossbridge cycle. It has been claimed that the stiffness of myosin heads in the anterior tibialis muscle of the common frog (Rana temporaria) is as high as 3.3 pN/nm, substantially higher than its value in rabbit muscle (~1.7 pN/nm). However, the crossbridge stiffness measurement has a large error since the contribution of crossbridges to half-sarcomere compliance is obtained by subtracting from the half-sarcomere compliance the contributions of the thick and thin filaments, each with a substantial error. Calculation of its value for isometric contraction also depends on the fraction of heads that are attached, for which there is no consensus. Surprisingly, the stiffness of the myosin head from the edible frog, Rana esculenta, determined in the same manner, is only 60% of that in Rana temporaria. In our view it is unlikely that the value of such a crucial parameter could differ so substantially between two frog species. Since the means of the myosin head stiffness in these two species are not significantly different, we suggest that the best estimate of the stiffness of the myosin heads for frog muscle is the average of these data, a value similar to that for rabbit muscle. This would allow both frog and rabbit muscles to operate the same low-cooperativity mechanism for the crossbridge cycle with only one or two tension-generating steps. We review evidence that much of the compliance of the myosin head is located in the pliant region where the lever arm emerges from the converter and propose that tension generation ("tensing") caused by the rotation and movement of the converter is a separate event from the passive swinging of the lever arm in its working stroke in which the strain energy stored in the pliant region is used to do work.

Is the cross-bridge stiffness proportional to tension during muscle fiber activation?

The cross-bridge stiffness can be used to estimate the number of S1 that are bound to actin during contraction, which is a critical parameter for elucidating the fundamental mechanism of the myosin motor. At present, the development of active tension and the increase in muscle stiffness due to S1 binding to actin are thought to be linearly related to the number of cross-bridges formed upon activation. The nonlinearity of total stiffness with respect to active force is thought to arise from the contribution of actin and myosin filament stiffness to total sarcomere elasticity. In this work, we reexamined the relation of total stiffness to tension during activation and during exposure to N-benzyl-p-toluene sulphonamide, an inhibitor of cross-bridge formation. In addition to filament and cross-bridge elasticity, our findings are best accounted for by the inclusion of an extra elasticity in parallel with the cross-bridges, which is formed upon activation but is insensitive to the subsequent level of cross-bridge formation. By analyzing the rupture tension of the muscle (an independent measure of cross-bridge formation) at different levels of activation, we found that this additional elasticity could be explained as the stiffness of a population of no-force-generating cross-bridges. These findings call into question the assumption that active force development can be taken as directly proportional to the cross-bridge number.

Non-linear myofilament elasticity in frog intact muscle fibres

The aim of the present investigation was to elucidate the elastic properties of the myofilaments during tetanic activity in striated muscle. The study was carried out on intact single muscle fibres from the anterior tibialis muscle of Rana temporaria (2.0-2.5 degrees C). The instantaneous stiffness was measured as the change in force that occurred in response to a high-frequency (2-4 kHz) length oscillation while the fibre was released to shorten against a pre-set constant load that ranged between 40 and 70% of maximum tetanic force in different experiments. Measurements of fibre stiffness were carried out, at a given load, both at 2.20 microm sarcomere length (S(2.20)), i.e. at full overlap between the thick and thin filaments, and at 2.60 microm sarcomere length (S(2.60)). The fact that the load on the fibre was constant during the stiffness measurements at the two sarcomere lengths implies that the stiffness of elastic elements, acting in series with the myofilaments, was constant at the two sarcomere lengths. The fibre stiffness was consistently lower at the extended sarcomere length, the S(2.60)/S(2.20) ratio ranging from 0.83 to 0.97 at the different loads investigated. Based on the S(2.60)/S(2.20) ratio, the compliance of the free portions of the thick and thin filaments could be calculated. The myofilament stiffness was found to increase progressively as the load was raised from 40 to 70% of maximum tetanic force. At 2.20 microm sarcomere length and at 40% of maximum load on the fibre, the calculated myofilament stiffness was approximately 2.5 times the maximum cross-bridge stiffness.

Force transients and minimum cross-bridge models in muscular contraction

Two- and three-state cross-bridge models are considered and examined with respect to their ability to predict three distinct phases of the force transients that occur in response to step change in muscle fiber length. Particular attention is paid to satisfying the Le Châtelier-Brown Principle. This analysis shows that the two-state model can account for phases 1 and 2 of a force transient, but is barely adequate to account for phase 3 (delayed force) unless a stretch results in a sudden increase in the number of cross-bridges in the detached state. The three-state model (A-->B-->C-->A) makes it possible to account for all three phases if we assume that the A-->B transition is fast (corresponding to phase 2), the B-->A transition is of intermediate speed (corresponding to phase 3), and the C-->A transition is slow; in such a scenario, states A and C can support or generate force (high force states) but state B cannot (detached, or low-force state). This model involves at least one ratchet mechanism. In this model, force can be generated by either of two transitions: B-->A or B-->C. To determine which of these is the major force-generating step that consumes ATP and transduces energy, we examine the effects of ATP, ADP, and phosphate (Pi) on force transients. In doing so, we demonstrate that the fast transition (phase 2) is associated with the nucleotide-binding step, and that the intermediate-speed transition (phase 3) is associated with the Pi-release step. To account for all the effects of ligands, it is necessary to expand the three-state model into a six-state model that includes three ligand-bound states. The slowest phase of a force transient (phase 4) cannot be explained by any of the models described unless an additional mechanism is introduced. Here we suggest a role of series compliance to account for this phase, and propose a model that correlates the slowest step of the cross-bridge cycle (transition C-->A) to: phase 4 of step analysis, the rate constant k(tr) of the quick-release and restretch experiment, and the rate constant k(act) for force development time course following Ca(2+) activation.

Single Skeletal Muscle Fiber Elastic and Contractile Characteristics in Young and Older Men

The current investigation was designed to: (a) assess the impact of aging on elastic characteristics of single skeletal muscle fibers from young (N = 6) and older men (N = 6); and (b) correlate the potential changes, with the fiber contractile properties. Chemically skinned single muscle fibers (n = 235) from vastus lateralis muscle were maximally activated. Maximal force and cross-sectional area were measured, and specific force calculated. The slack test was used to measure maximal unloaded shortening velocity. A quick release of 0.15% of fiber length was applied to determine instantaneous stiffness. The myosin heavy chain isoform composition of each single fiber was determined by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE). Aging induces changes in both fiber elasticity (i.e., increased instantaneous stiffness) and contractility (i.e., reduced specific force and unloaded shortening velocity) in type I and IIa fibers. However, the changes in fiber stiffness may not directly influence contractile characteristics alterations.

Temperature-dependence of isometric tension and cross-bridge kinetics of cardiac muscle fibers reconstituted with a tropomyosin internal deletion mutant

The effect of temperature on isometric tension and cross-bridge kinetics was studied with a tropomyosin (Tm) internal deletion mutant AS-Delta23Tm (Ala-Ser-Tm Delta(47-123)) in bovine cardiac muscle fibers by using the thin filament extraction and reconstitution technique. The results are compared with those from actin reconstituted alone, cardiac muscle-derived control acetyl-Tm, and recombinant control AS-Tm. In all four reconstituted muscle groups, isometric tension and stiffness increased linearly with temperature in the range 5-40 degrees C for fibers activated in the presence of saturating ATP and Ca(2+). The slopes of the temperature-tension plots of the two controls were very similar, whereas the slope derived from fibers with actin alone had approximately 40% the control value, and the slope from mutant Tm had approximately 36% the control value. Sinusoidal analysis was performed to study the temperature dependence of cross-bridge kinetics. All three exponential processes A, B, and C were identified in the high temperature range (30-40 degrees C); only processes B and C were identified in the mid-temperature range (15-25 degrees C), and only process C was identified in the low temperature range (5-10 degrees C). At a given temperature, similar apparent rate constants (2pia, 2pib, 2pic) were observed in all four muscle groups, whereas their magnitudes were markedly less in the order of AS-Delta23Tm < Actin < AS-Tm approximately Acetyl-Tm groups. Our observations are consistent with the hypothesis that Tm enhances hydrophobic and stereospecific interactions (positive allosteric effect) between actin and myosin, but Delta23Tm decreases these interactions (negative allosteric effect). Our observations further indicate that tension/cross-bridge is increased by Tm, but is diminished by Delta23Tm. We conclude that Tm affects the conformation of actin so as to increase the area of hydrophobic interaction between actin and myosin molecules.

Single skeletal muscle fiber behavior after a quick stretch in young and older men: a possible explanation of the relative preservation of eccentric force in old age

The origins of the smaller age-related decrease in eccentric force compared to isometric and concentric conditions in vivo remain unclear. Could this originate from contractile elements of muscle cells? The main intent of the current investigation was to assess the force behavior of muscle cells with aging, during lengthening. Chemically skinned single muscle fibers (n=235) from m. vastus lateralis of six young (mean age 31.6 years) and six older men (mean age 66.1 years) were maximally activated with pCa 4.5 at 15 degrees C. Maximal isometric force and cross-sectional area were measured allowing the calculation of the tension (T (0)). A quick stretch (2 nm per half-sarcomere length) was applied and caused an immediate increase in tension followed by a decrease and a secondary delayed and transient rise in tension (phase 3); finally, the tension recovered a steady state value (phase 4). The tension enhancements during phase 3 (DeltaT (3)) and phase 4 (DeltaT (4)) were evaluated. The myosin heavy-chain isoform composition of each single fiber was determined by sodium dodecyl sulfate-polyacrylamide gel electrophoresis. DeltaT (3) and DeltaT (4) were preserved in older men for both type I and IIa fibers despite a reduction in T (0). Therefore, the age-related preservation of the tension increments after a quick stretch in single muscle fibers could explain in part the smaller decrease in force during eccentric contractions compared to isometric and concentric conditions in vivo with aging usually observed.

Force recovery after activated shortening in whole skeletal muscle: transient and steady-state aspects of force depression

The depression of isometric force after active shortening is a well-accepted characteristic of skeletal muscle, yet its mechanisms remain unknown. Although traditionally analyzed at steady state, transient phenomena caused, at least in part, by cross-bridge kinetics may provide novel insight into the mechanisms associated with force depression (FD). To identify the transient aspects of FD and its relation to shortening speed, shortening amplitude, and muscle mechanical work, in situ experiments were conducted in soleus muscle-tendon units of anesthetized cats. The period immediately after shortening, in which force recovers toward steady state, was fit by using an exponential recovery function (R2 > 0.99). Statistical analyses revealed that steady-state FD (FD(ss)) increased with shortening amplitude and mechanical work. This FD(ss) increase was always accompanied by a significant decrease in force recovery rate. Furthermore, a significant reduction in stiffness was observed after all activated shortenings, presumably because of a reduced proportion of attached cross bridges. These results were interpreted with respect to the two most prominent proposed mechanisms of force depression: sarcomere length nonuniformity theory (7, 32) and a stress-induced inhibition of cross-bridge binding in the newly formed actin-myosin overlap zone (14, 28). We hypothesized that the latter could describe both steady-state and transient aspects of FD using a single scalar variable, the mechanical work done during shortening. As either excursion (overlap) or force (stress) is increased, mechanical work increases, and cross-bridge attachment would become more inhibited, as supported by this study in which an increase in mechanical work resulted in a slower recovery to a more depressed steady-state force.

Strong binding of myosin heads stretches and twists the actin helix

Calculation of the size of the power stroke of the myosin motor in contracting muscle requires knowledge of the compliance of the myofilaments. Current estimates of actin compliance vary significantly introducing uncertainty in the mechanical parameters of the motor. Using x-ray diffraction on small bundles of permeabilized fibers from rabbit muscle we show that strong binding of myosin heads changes directly the actin helix. The spacing of the 2.73-nm meridional x-ray reflection increased by 0.22% when relaxed fibers were put into low-tension rigor (<10 kN/m(2)) demonstrating that strongly bound myosin heads elongate the actin filaments even in the absence of external tension. The pitch of the 5.9-nm actin layer line increased by approximately 0.62% and that of the 5.1-nm layer line decreased by approximately 0.26%, suggesting that the elongation is accompanied by a decrease in its helical angle (approximately 166 degrees) by approximately 0.8 degrees. This effect explains the difference between actin compliance revealed from mechanical experiments with single fibers and from x-ray diffraction on whole muscles. Our measurement of actin compliance obtained by applying tension to fibers in rigor is consistent with the results of mechanical measurements.

What do we learn by studying the temperature effect on isometric tension and tension transients in mammalian striated muscle fibres?

The significance of transient analysis of isometric tension and its temperature dependence on the molecular mechanisms of contraction is reviewed. The kinetic analysis of tension transient is essential to establish the elementary steps of the cross-bridge cycle. The temperature study is essential to deduce thermodynamic parameters of the force generation step, from which surface area changes associated with hydrophobic interaction and ionic interaction can be calculated. Experimental evidence suggests that a large scale hydrophobic and stereospecific interaction takes place at the time of force generation. This interaction is promoted by regulatory proteins troponin and tropomyosin, which is the basis for endothermic force generation. The six state cross-bridge model with two apparent rate constants is capable of explaining the temperature dependence of isometric tension and tension transients induced by temperature jump experiments. This model was previously proposed to account for the tension transients induced by sinusoidal length changes [Kawai and Halvorson (1991) Biophys J 59: 329-342]. The series compliance model is suitable for explaining the temperature effect on the stiffness data as the function of temperature, leading to the conclusion that the series compliance accounts for 40 +/- 5% of the total compliance in activated psoas fibres at 20 degrees C. These results are consistent with the hypothesis that tension per cross-bridge remains the same at different temperatures, and that it is the population shift that gives rise to the characteristic temperature effect on isometric tension.

A simple model with myofilament compliance predicts activation-dependent crossbridge kinetics in skinned skeletal fibers

The contribution of thick and thin filaments to skeletal muscle fiber compliance has been shown to be significant. If similar to the compliance of cycling cross-bridges, myofilament compliance could explain the difference in time course of stiffness and force during the rise of tension in a tetanus as well as the difference in Ca(2+) sensitivity of force and stiffness and more rapid phase 2 tension recovery (r) at low Ca(2+) activation. To characterize the contribution of myofilament compliance to sarcomere compliance and isometric force kinetics, the Ca(2+)-activation dependence of sarcomere compliance in single glycerinated rabbit psoas fibers, in the presence of ATP (5.0 mM), was measured using rapid length steps. At steady sarcomere length, the dependence of sarcomere compliance on the level of Ca(2+)-activated force was similar in form to that observed for fibers in rigor where force was varied by changing length. Additionally, the ratio of stiffness/force was elevated at lower force (low [Ca(2+)]) and r was faster, compared with maximum activation. A simple series mechanical model of myofilament and cross-bridge compliance in which only strong cross-bridge binding was activation dependent was used to describe the data. The model fit the data and predicted that the observed activation dependence of r can be explained if myofilament compliance contributes 60-70% of the total fiber compliance, with no requirement that actomyosin kinetics be [Ca(2+)] dependent or that cooperative interactions contribute to strong cross-bridge binding.

Effects of substituting uridine triphosphate for ATP on the crossbridge cycle of rabbit muscle

1. Substituting uridine triphosphate (UTP) for ATP as a substrate for rabbit skeletal myosin and actin at 4 degrees C slowed the dissociation of myosin-S1 from actin by threefold, and hydrolysis of the nucleotide by sevenfold, without a decrease in the rates of phosphate or uridine diphosphate dissociation from actomyosin. 2. The same substitution in skinned rabbit psoas fibres at 2-3 degrees C reduced the maximum shortening velocity by 56 % and increased the force asymptote of the force-velocity curve relative to force (alpha/P(o)) by 112 % without altering the velocity asymptote, beta. It also decreased isometric force by 35 % and isometric stiffness by 20 %, so that the stiffness/force ratio was increased by 23 %. 3. Tension transient experiments showed that the stiffness/force increase was associated with a 10 % reduction in the amplitude of the rapid, partial (phase 2) recovery relative to the isometric force, and the addition of two new components, one that recovered at a step-size-independent rate of 100 s(-1) and another that did not recover following the length change. 4. The increased alpha/P(o) with constant beta suggests an internal load, as expected of attached crossbridges detained in their movement. An increased stiffness/force ratio suggests a greater fraction of attached bridges in low-force states, as expected of bridges with unhydrolyzed UTP detained in low-force states. Decreased phase 2 recovery suggests the detention of high-force bridges, as expected of slowed actomyosin dissociation by nucleotide. 5. These results suggest that the separation of hydrolysed phosphates from nucleotides occurs early in the attached phase of the crossbridge cycle, near and possibly identical to a transition to a firmly attached, low-force state from an initial state where bridges with hydrolysed nucleotides are easily detached by shortening.

Series-to-parallel transition in the filament lattice of airway smooth muscle

Force-velocity curves measured at different times during tetani of sheep trachealis muscle were analyzed to assess whether velocity slowing could be explained by thick-filament lengthening. Such lengthening increases force by placing more cross bridges in parallel on longer filaments and decreases velocity by reducing the number of filaments spanning muscle length. From 2 s after the onset of stimulation, when force had achieved 42% of it final value, to 28 s, when force had been at its tetanic plateau for approximately 15 s, velocity decreases were exactly matched by force increases when force was adjusted for changes in activation, as assessed from the maximum power value in the force-velocity curves. A twofold change in velocity could be quantitatively explained by a series-to-parallel change in the filament lattice without any need to postulate a change in cross-bridge cycling rate.

Sarcomere tension-stiffness relation during the tetanus rise in single 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 by measuring the ratio between tension and sarcomere length during a period of fast sarcomere elongation at constant velocity. Tension changes were corrected for force truncation by the quick recovery mechanism. The results show that the relation between force and stiffness deviates from the direct proportionality less than previously reported. If the deviation is due to the presence of a linear myofilament compliance in series with the cross-bridges, our data suggest that myofilament compliance accounts for about 30% of the sarcomere compliance. This value is significantly smaller than 50-70% determined by X-ray diffraction measurements. These two different findings, however, may be reconciled by assuming that the myofilament compliance is non-linear increasing appropriately at low tension.

Ca2+ and cross-bridge-induced changes in troponin C in skinned skeletal muscle fibers: effects of force inhibition

Changes in skeletal troponin C (sTnC) structure during thin filament activation by Ca2+ and strongly bound cross-bridge states were monitored by measuring the linear dichroism of the 5' isomer of iodoacetamidotetramethylrhodamine (5'IATR), attached to Cys98 (sTnC-5'ATR), in sTnC-5'ATR reconstituted single skinned fibers from rabbit psoas muscle. To isolate the effects of Ca2+ and cross-bridge binding on sTnC structure, maximum Ca2+-activated force was inhibited with 0.5 mM AlF4- or with 30 mM 2,3 butanedione-monoxime (BDM) during measurements of the Ca2+ dependence of force and dichroism. Dichroism was 0.08 +/- 0.01 (+/- SEM, n = 9) in relaxing solution (pCa 9.2) and decreased to 0.004 +/- 0.002 (+/- SEM, n = 9) at pCa 4.0. Force and dichroism had similar Ca2+ sensitivities. Force inhibition with BDM caused no change in the amplitude and Ca2+ sensitivity of dichroism. Similarly, inhibition of force at pCa 4.0 with 0.5 mM AlF4- decreased force to 0.04 +/- 0.01 of maximum (+/- SEM, n = 3), and dichroism was 0.04 +/- 0.03 (+/- SEM, n = 3) of the value at pCa 9.2 and unchanged relative to the corresponding normalized value at pCa 4.0 (0.11 +/- 0.05, +/- SEM; n = 3). Inhibition of force with AlF4- also had no effect when sTnC structure was monitored by labeling with either 5-dimethylamino-1-napthalenylsulfonylaziridine (DANZ) or 4-(N-(iodoacetoxy)ethyl-N-methyl)amino-7-nitrobenz-2-oxa-1,3-diazole (NBD). Increasing sarcomere length from 2.5 to 3.6 microm caused force (pCa 4.0) to decrease, but had no effect on dichroism. In contrast, rigor cross-bridge attachment caused dichroism at pCa 9.2 to decrease to 0.56 +/- 0.03 (+/- SEM, n = 5) of the value at pCa 9. 2, and force was 0.51 +/- 0.04 (+/- SEM, n = 6) of pCa 4.0 control. At pCa 4.0 in rigor, dichroism decreased further to 0.19 +/- 0.03 (+/- SEM, n = 6), slightly above the pCa 4.0 control level; force was 0.66 +/- 0.04 of pCa 4.0 control. These results indicate that cross-bridge binding in the rigor state alters sTnC structure, whereas cycling cross-bridges have little influence at either submaximum or maximum activating [Ca2+].

Does thin filament compliance diminish the cross-bridge kinetics? A study in rabbit psoas fibers

The effect of thin filament compliance on our ability to detect the cross-bridge kinetics was examined. Our experiment is based on the facts that in rabbit psoas the thin filament (1.12 micrometer) is longer than half the thick filament length (0.82 micrometer) and that the thick filament has a central bare zone (0.16 micrometer). Consequently, when sarcomere length is increased from 2.1 to 2.4 micrometer, the same number of cross-bridges is involved in force generation but extra series compliance is introduced in the I-band. Three apparent rate constants (2pia, 2pib, and 2pic) were characterized by sinusoidal analysis at pCa 4.66. Our results demonstrate that 2pia and 2pib increased 13-16% when sarcomere length was increased from 2.0 to 2.5 micrometer, and 2pic decreased slightly (9%). This slight decrease can be explained by compression of the lattice spacing. These observations are at variance with the expectation based on increased series compliance, which predicts that the rate constants will decrease. We also determined compliance of the I-band during rigor. I-band compliance during rigor induction was 35% of sarcomere compliance at sarcomere length 2.4 micrometer, and 24% at sarcomere length 2.1 micrometer. We conclude that the presence of thin filament compliance does not seriously interfere with our ability to detect cross-bridge kinetics using sinusoidal analysis.

The stiffness of skeletal muscle in isometric contraction and rigor: the fraction of myosin heads bound to actin

Step changes in length (between -3 and +5 nm per half-sarcomere) were imposed on isolated muscle fibers at the plateau of an isometric tetanus (tension T0) and on the same fibers in rigor after permeabilization of the sarcolemma, to determine stiffness of the half-sarcomere in the two conditions. To identify the contribution of actin filaments to the total half-sarcomere compliance (C), measurements were made at sarcomere lengths between 2.00 and 2.15 microm, where the number of myosin cross-bridges in the region of overlap between the myosin filament and the actin filament remains constant, and only the length of the nonoverlapped region of the actin filament changes with sarcomere length. At 2.1 microm sarcomere length, C was 3.9 nm T0(-1) in active isometric contraction and 2.6 nm T0(-1) in rigor. The actin filament compliance, estimated from the slope of the relation between C and sarcomere length, was 2.3 nm microm(-1) T0(-1). Recent x-ray diffraction experiments suggest that the myosin filament compliance is 1.3 nm microm(-1) T0(-1). With these values for filament compliance, the difference in half-sarcomere compliance between isometric contraction and rigor indicates that the fraction of myosin cross-bridges attached to actin in isometric contraction is not larger than 0.43, assuming that cross-bridge elasticity is the same in isometric contraction and rigor.

Milrinone inhibits contractility in skinned skeletal muscle fibers

Direct action of the cardiotonic bipyridine milrinone on the cross bridges of single fibers of skinned rabbit skeletal muscle was investigated. At 10 degrees C and pH 7.0, milrinone reduced isometric tension in a logarithmically concentration-dependent manner, with a 55% reduction in force at 0.6 mM. Milrinone also reduced Ca2+ sensitivity of skinned fibers in terms of force production; the shift in the force-pCa curve indicated a change in the pCa value at 50% maximal force from 6.10 to 5.94. The unloaded velocity of shortening was reduced by 18% in the presence of 0.6 mM milrinone. Parts of the transient tension response to step change in length were altered by milrinone, so that the test and control transients could not be superimposed. The results indicate that milrinone interferes with the cross-bridge cycle and possibly detains cross bridges in low-force states. The results also suggest that the positive inotropic effect of milrinone on cardiac muscle is probably not due to the drug's direct action on the muscle cross bridges. The specific and reversible action of the bipyridine on muscle cross bridges makes it a potentially useful tool for probing the chemomechanical cross-bridge cycle.

Compliant realignment of binding sites in muscle: transient behavior and mechanical tuning

The presence of compliance in the lattice of filaments in muscle raises a number of concerns about how one accounts for force generation in the context of the cross-bridge cycle--binding site motions and coupling between cross-bridges confound more traditional analyses. To explore these issues, we developed a spatially explicit, mechanochemical model of skeletal muscle contraction. With a simple three-state model of the cross-bridge cycle, we used a Monte Carlo simulation to compute the instantaneous balance of forces throughout the filament lattice, accounting for both thin and thick filament distortions in response to cross-bridge forces. This approach is compared to more traditional mass action kinetic models (in the form of coupled partial differential equations) that assume filament inextensibility. We also monitored instantaneous force generation, ATP utilization, and the dynamics of the cross-bridge cycle in simulations of step changes in length and variations in shortening velocity. Three critical results emerge from our analyses: 1) there is a significant realignment of actin-binding sites in response to cross-bridge forces, 2) this realignment recruits additional cross-bridge binding, and 3) we predict mechanical behaviors that are consistent with experimental results for velocity and length transients. Binding site realignment depends on the relative compliance of the filament lattice and cross-bridges, and within the measured range of these parameters, gives rise to a sharply tuned peak for force generation. Such mechanical tuning at the molecular level is the result of mechanical coupling between individual cross-bridges, mediated by thick filament deformations, and the resultant realignment of binding sites on the thin filament.

A strain-dependent ratchet model for [phosphate]- and [ATP]-dependent muscle contraction

A minimal strain-dependent ratchet model of muscle cross-bridge action is proposed which is broadly compatible with structural and kinetic constraints. Its essential features are: (1) dynamic binding of the S1-products complex to actin through a disorder-order transition coupled to the release of inorganic phosphate; (2) the absence of a force-generating rotation of the myosin head between the two force-holding states A.M.ADP and A.M; (3) strain-control of ADP release and ATP binding, giving net isometric tension and directed motility by the selective dissociation of negatively strained bound states. With a disordered pre-force state, the binding rate to state A.M.ADP need not be symmetric in x, the actin site displacement. With faster binding at positive x, the model predicts many steady-state and transient properties of striated muscle observed experimentally, including phases 2-4 of tension recovery from length changes and their dependence on excess phosphate (which enhances and accelerates phase 3) and reduced ATP (which gives a bimodal phase 2 and slows one mode). The response to large perturbations is often sensitive to the number of actin sites used, and to the inclusion of a 1 nm displacement of the neck region on release of ADP. The latter stabilizes the periodic tension behaviour produced by repeated releases.

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 degrees C; sarcomere length, 2.20 microns). 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 force-velocity 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 generation and phosphate release steps in skinned rabbit soleus slow-twitch muscle fibers

The force-generation and phosphate-release steps of the cross-bridge cycle in rabbit soleus slow-twitch muscle fibers (STF) were investigated using sinusoidal analysis, and the results were compared with those of rabbit psoas fast-twitch fibers (FTF). Single fiber preparations were activated at pCa 4.40 and ionic strength 180 mM at 20 degrees C. The effects of inorganic phosphate (Pi) concentrations on three exponential processes, B, C, and D, were studied. Results are consistent with the following cross-bridge scheme: [formula: see text] where A is actin, M is myosin, D is MgADP, and P is inorganic phosphate. The values determined are k4 = 5.7 +/- 0.5 s-1 (rate constant of isomerization step, N = 9, mean +/- SE), k-4 = 4.5 +/- 0.5 s-1 (rate constant of reverse isomerization), K4 = 1.37 +/- 0.13 (equilibrium constant of the isomerization), and K5 = 0.18 +/- 0.01 mM-1 (Pi association constant). The isomerization step (k4) in soleus STF is 20 times slower, and its reversal (k-4) is 20 times slower than psoas fibers. Consequently, the equilibrium constant of the isomerization step (K4) is the same in these two types of fibers. The Pi association constant (K5) is slightly higher in STF than in FTF, indicating that Pi binds to cross-bridges slightly more tightly in STF than FTF. By correlating the cross-bridge distribution with isometric tension, it was confirmed that force is generated during the isomerization (step 4) of the AMDP state and before Pi release in soleus STF.

Exchange of ATP for ADP on high-force cross-bridges of skinned rabbit muscle fibers

The contractile properties of rabbit skinned muscle fibers were studied at 1-2 degrees C in different concentrations of MgATP and MgADP. Double-reciprocal plots of maximum velocity against MgATP concentration at different MgADP concentrations all extrapolated to the same value. This finding suggests that MgATP and MgADP compete for the same site on the cross-bridge, and that the exchange of MgATP for MgADP occurs without a detectable step intervening. The K(m) for ATP was 0.32 mM. The K(i) for MgADP was 0.33 mM. Control experiments suggested that the tortuosity of diffusion paths within the fibers reduced the radial diffusion coefficients for reactants about sixfold. Increasing MgADP from 0.18 to 2 mM at 5 mM ATP or lowering MgATP from 10 to 2 mM at 0.18 mM MgADP, respectively, increased isometric force by 25% and 23%, increased stiffness by 10% and 20%, and decreased maximum velocity by 35% and 31%. Two mechanisms appeared to be responsible. One detained bridges in high-force states, where they recovered from a length step with a slower time course. The other increased the fraction of attached bridges without altering the kinetics of their responses, possibly by an increased activation resulting from cooperative effects of the detained, high-force bridges. The rigor bridge was more effective than the ADP-bound bridge in increasing the number of attached bridges with unaltered kinetics.

On the theory of muscle contraction: filament extensibility and the development of isometric force and stiffness

The newly discovered extensibility of actin and myosin filaments challenges the foundation of the theory of muscle mechanics. We have reformulated A. F. Huxley's sliding filament theory to explicitly take into account filament extensibility. During isometric force development, growing cross-bridge tractions transfer loads locally between filaments, causing them to extend and, therefore, to slide locally relative to one another. Even slight filament extensibility implies that 1) relative displacement between the two must be nonuniform along the region of filament overlap, 2) cross-bridge strain must vary systematically along the overlap region, and importantly, 3) the local shortening velocities, even at constant overall sarcomere length, reduce force below the level that would have developed if the filaments had been inextensible. The analysis shows that an extensible filament system with only two states (attached and detached) displays three important characteristics: 1) muscle stiffness leads force during force development; 2) cross-bridge stiffness is significantly higher than previously assessed by inextensible filament models; and 3) stiffness is prominently dissociated from the number of attached cross-bridges during force development. The analysis also implies that the local behavior of one myosin head must depend on the state of neighboring attachment sites. This coupling occurs exclusively through local sliding velocities, which can be significant, even during isometric force development. The resulting mechanical cooperativity is grounded in fiber mechanics and follows inevitably from filament extensibility.

Compliance of thin filaments in skinned fibers of rabbit skeletal muscle

The mechanical compliance (reciprocal of stiffness) of thin filaments was estimated from the relative compliance of single, skinned muscle fibers in rigor at sarcomere lengths between 1.8 and 2.4 micron. The compliance of the fibers was calculated as the ratio of sarcomere length change to tension change during imposition of repetitive cycles of small stretches and releases. Fiber compliance decreased as the sarcomere length was decreased below 2.4 micron. The compliance of the thin filaments could be estimated from this decrement because in this range of lengths overlap between the thick and thin filaments is complete and all of the myosin heads bind to the thin filament in rigor. Thus, the compliance of the overlap region of the sarcomere is constant as length is changed and the decrease in fiber compliance is due to decrease of the nonoverlap length of the thin filaments (the I band). The compliance value obtained for the thin filaments implies that at 2.4-microns sarcomere length, the thin filaments contribute approximately 55% of the total sarcomere compliance. Considering that the sarcomeres are approximately 1.25-fold more compliant in active isometric contractions than in rigor, the thin filaments contribute approximately 44% to sarcomere compliance during isometric contraction.

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.

Direct measurement of stiffness of single actin filaments with and without tropomyosin by in vitro nanomanipulation

In order to explain the molecular mechanism of muscle contraction, it is crucial to know the distribution of the sarcomere compliance of active muscle. Here, we directly measure the stiffness of single actin filaments with and without tropomyosin, using a recently developed technique for nanomanipulation of single actin filaments with microneedles. The results show that the stiffness for 1-micron-long actin filaments with and without tropomyosin is 65.3 +/- 6.3 and 43.7 +/- 4.6 pN/nm, respectively. When the distribution of crossbridge forces along the actin filament is taken into account, the elongation of a 1-micron-long thin filament during development of isometric contraction is calculated to be approximately 0.23%. The time constant of force in response to a sudden length change is < 0.2 ms, indicating that the viscoelasticity is negligible in the millisecond time range. These results suggest that approximately 50% of the sarcomere compliance of active muscle is due to extensibility of the thin filaments.

Effect of series elasticity on delay in development of tension relative to stiffness during muscle activation

Experimental data have indicated that during activation, the attachment of myosin to actin, measured by mechanical stiffness, precedes tension generation by 10-30 ms. Using computer simulation, we have investigated the effect of a series elastic element on the lag between stiffness and tension development during muscle activation. Two versions of the two-state cross-bridge model originally proposed by Huxley and a three-state model were considered. After simulated activation, stiffness and tension increased with rates that were strongly dependent on the series elastic strain. In the absence of a series elastic element, the rise in stiffness preceded, lagged, or was coincident with the increase in tension, depending on the model. For large elastic strains, tension lagged stiffness for all models. Lags of 10-30 ms could be obtained with elastic strains of 0.3-1% of the muscle length. This is a realistic value in experiments without sarcomere length servocontrol, suggesting that series elasticity may be an important contributor to the experimentally observed lag between tension and stiffness.

X-ray diffraction evidence for the extensibility of actin and myosin filaments during muscle contraction

To clarify the extensibility of thin actin and thick myosin filaments in muscle, we examined the spacings of actin and myosin filament-based reflections in x-ray diffraction patterns at high resolution during isometric contraction of frog skeletal muscles and steady lengthening of the active muscles using synchrotron radiation as an intense x-ray source and a storage phosphor plate as a high sensitivity, high resolution area detector. Spacing of the actin meridional reflection at approximately 1/2.7 nm-1, which corresponds to the axial rise per actin subunit in the thin filament, increased about 0.25% during isometric contraction of muscles at full overlap length of thick and thin filaments. The changes in muscles stretched to approximately half overlap of the filaments, when they were scaled linearly up to the full isometric tension, gave an increase of approximately 0.3%. Conversely, the spacing decreased by approximately 0.1% upon activation of muscles at nonoverlap length. Slow stretching of a contracting muscle increased tension and increased this spacing over the isometric contraction value. Scaled up to a 100% tension increase, this corresponds to a approximately 0.26% additional change, consistent with that of the initial isometric contraction. Taken together, the extensibility of the actin filament amounts to 3-4 nm of elongation when a muscle switches from relaxation to maximum isometric contraction. Axial spacings of the layer-line reflections at approximately 1/5.1 nm-1 and approximately 1/5.9 nm-1 corresponding to the pitches of the right- and left-handed genetic helices of the actin filament, showed similar changes to that of the meridional reflection during isometric contraction of muscles at full overlap. The spacing changes of these reflections, which also depend on the mechanical load on the muscle, indicate that elongation is accompanied by slight changes of the actin helical structure possibly because of the axial force exerted by the actomyosin cross-bridges. Additional small spacing changes of the myosin meridional reflections during length changes applied to contracting muscles represented an increase of approximately 0.26% (scaled up to a 100% tension increase) in the myosin periodicity, suggesting that such spacing changes correspond to a tension-related extension of the myosin filaments. Elongation of the myosin filament backbone amounts to approximately 2.1 nm per half sarcomere. The results indicate that a large part (approximately 70%) of the sarcomere compliance of an active muscle is caused by the extensibility of the actin and myosin filaments; 42% of the compliance resides in the actin filaments, and 27% of it is in the myosin filaments.

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.

Effects of 2,3-butanedione monoxime on the crossbridge kinetics in frog single muscle fibres

The effects of 2,3-butanedione monoxime (BDM) on contraction characteristics were studied at 5 degrees C in single intact fibres isolated from the tibialis anterior muscle of the frog. The force-velocity relation was determined using the controlled-velocity method in either whole fibres or short fibre segments in which sarcomere shortening was measured by a laser light diffraction method. It is shown that 3 mM BDM decreases the speed of rise and the amount of tetanus tension, reduces the maximum velocity of shortening and increases the curvature of the force-velocity relation, as well as the value for the stiffness to tension ratio. BDM also slowed down the redevelopment of tetanus tension after a period of unloaded shortening both in fixed-end and in length-clamp conditions. In normal and in BDM-treated fibres length-clamping increased the speed of the initial rise of tetanus tension but not that of the recovery after shortening. The observed force-velocity data points were fitted by the Huxley (1957) equation. It was found that BDM produces a conspicuous decrease of the rate constant for crossbridge attachment. This effect, and also a reduction of the force per crossbridge, are responsible for the depression of the contractile characteristics produced by BDM.