Cross-bridge model of muscle contraction. Quantitative analysis

Instabilities in the transient response of muscle

We investigate the isometric transient response of muscle using a quantitative stochastic model of the actomyosin cycle based on the swinging lever-arm hypothesis. We first consider a single pair of filaments, and show that when values of parameters such as the lever-arm displacement and the cross-bridge elasticity are chosen to provide effective energy transduction, the T(2) curve (the tension recovered immediately after a step displacement) displays a region of negative slope. If filament compliance and the discrete nature of the binding sites are taken into account, the negative slope is diminished, but not eliminated. This implies that there is an instability in the dynamics of individual half sarcomeres. However, when the symmetric nature of whole sarcomeres is taken into account, filament rearrangement becomes important during the transient: as tension is recovered, some half sarcomeres lengthen whereas others shorten. This leads to a flat T(2) curve, as observed experimentally. In addition, we investigate the isotonic transient response and show that for a range of parameter values the model displays damped oscillations, as recently observed in experiments on single muscle fibers. We conclude that it is essential to consider the collective dynamics of many sarcomeres, rather than the dynamics of a single pair of filaments, when interpreting the transient response of muscle.

Creatine phosphate consumption and the actomyosin crossbridge cycle in cardiac muscles

To investigate the regulation of the actomyosin crossbridge cycle in cardiac muscles, the effects of ATP, ADP, Pi, and creatine phosphate (CP) on the rate of force redevelopment (ktr) were measured. We report that CP is a primary determinant in controlling the actomyosin crossbridge cycling kinetics of cardiac muscles, because a reduction of CP from 25 to 2.5 mmol/L decreased ktr by 51% despite the presence of 5 mmol/L MgATP. The effects of CP on ktr were not a reflection of reduced ATP or accumulated ADP, because lowering ATP to 1 mmol/L or increasing ADP to 1 mmol/L did not significantly decrease ktr. Therefore, the effect of CP on the actomyosin crossbridge cycle is proposed to occur through a functional link between ADP release from myosin and its rephosphorylation by CP-creatine kinase to regenerate ATP. In activated fibers, the functional link influenced the kinetics of activated crossbridges without affecting the aggregate number of force-generating crossbridges. This was demonstrated by the ability of CP to affect ktr in maximally and submaximally activated fibers without altering the force per cross-sectional area. The data also confirm the important contribution of strong binding crossbridges to cardiac muscle activation, likely mediated by cooperative recruitment of adjacent crossbridges to maximize force redevelopment against external load. These data provide additional insight into the role of CP during pathophysiological conditions such as ischemia, suggesting that decreased CP may serve as a primary determinant in the observed decline of dP/dt.

Effect of an ADP analog on isometric force and ATPase activity of active muscle fibers

The role played by ADP in modulating cross-bridge function has been difficult to study, because it is hard to buffer ADP concentration in skinned muscle preparations. To solve this, we used an analog of ADP, spin-labeled ADP (SL-ADP). SL-ADP binds tightly to myosin but is a very poor substrate for creatine kinase or pyruvate kinase. Thus ATP can be regenerated, allowing well-defined concentrations of both ATP and SL-ADP. We measured isometric ATPase rate and isometric tension as a function of both [SL-ADP], 0.1-2 mM, and [ATP], 0.05-0.5 mM, in skinned rabbit psoas muscle, simulating fresh or fatigued states. Saturating levels of SL-ADP increased isometric tension (by P'), the absolute value of P' being nearly constant, approximately 0.04 N/mm(2), in variable ATP levels, pH 7. Tension decreased (50-60%) at pH 6, but upon addition of SL-ADP, P' was still approximately 0.04 N/mm(2). The ATPase was inhibited competitively by SL-ADP with an inhibition constant, K(i), of approximately 240 and 280 microM at pH 7 and 6, respectively. Isometric force and ATPase activity could both be fit by a simple model of cross-bridge kinetics.

Cooperative behavior of molecular motors

Both experimental evidence and theoretical models for collective effects in the working mechanism of molecular motors are reviewed at three different levels, namely: (i) interaction between the two heads of double-headed motors, particularly in processive motors like kinesin, myosin V and myosin VI, (ii) cooperative regulation of muscle thin filaments by accessory proteins and the Ca2+ level, and (iii) collective dynamic effects stemming from the mechanical coupling of molecular motors within macroscopic structures such as muscle thick filaments or axonemes. We aim to bridge the gap between structural information at the molecular level and physiological data with accompanying specific models on the one hand, and general stochastic physical models for the action of molecular motors on the other hand. An underlying assumption is that while, ultimately, the function of molecular motors will be explainable by a quantitative description of specific intramolecular dynamics and intermolecular interactions, for some coarse grained larger scale dynamic features it will be sufficient and illuminating to construct physical models that are simplified to the bare essentials.

Activation of striated muscle: nearest-neighbor regulatory-unit and cross-bridge influence on myofilament kinetics

We have formulated a three-compartment model of muscle activation that includes both strong cross-bridge (XB) and Ca(2+)-activated regulatory-unit (RU) mediated nearest-neighbor cooperative influences. The model is based on the tight coupling premise--that XB retain activating Ca(2+) on the thin filament. Using global non-linear least-squares, the model produced excellent fits to experimental steady-state force-pCa and ATPase-pCa data from skinned rat soleus fibers. In terms of the model, nearest-neighbor influences over the range of Ca(2+) required for activation cause the Ca(2+) dissociation rate from regulatory-units (k(off)) to decrease and the cross-bridge association rate (f) to increase each more than ten-fold. Moreover, the rate variations occur in separate Ca(2+) regimes. The energy of activation governing f is strongly influenced by both neighboring RU and XB. In contrast, the energy of activation governing k(off) is less affected by neighboring XB than by neighboring RU. Nearest-neighbor cooperative influences provide both an overall sensitization to Ca(2+) and the well-known steep response of force to free Ca(2+). The apparent sensitivity for Ca(2+)-activation of force and ATPase is a function of cross-bridge kinetic rates. The model and derived parameter set produce simulated behavior in qualitative agreement with steady-state experiments reported in the literature for partial TnC replacement, increased [P(i)], increased [ADP], and MalNEt-S1 addition. The model is an initial attempt to construct a general theory of striated muscle activation-one that can be consistently used to interpret data from various types of muscle manipulation experiments.

Force kinetics and individual sarcomere dynamics in cardiac myofibrils after rapid ca(2+) changes

Kinetics of force development and relaxation after rapid application and removal of Ca(2+) were measured by atomic force cantilevers on subcellular bundles of myofibrils prepared from guinea pig left ventricles. Changes in the structure of individual sarcomeres were simultaneously recorded by video microscopy. Upon Ca(2+) application, force developed with an exponential rate constant k(ACT) almost identical to k(TR), the rate constant of force redevelopment measured during steady-state Ca(2+) activation; this indicates that k(ACT) reflects isometric cross-bridge turnover kinetics. The kinetics of force relaxation after sudden Ca(2+) removal were markedly biphasic. An initial slow linear decline (rate constant k(LIN)) lasting for a time t(LIN) was abruptly followed by an ~20 times faster exponential decay (rate constant k(REL)). k(LIN) is similar to k(TR) measured at low activating [Ca(2+)], indicating that k(LIN) reflects isometric cross-bridge turnover kinetics under relaxed-like conditions (see also. Biophys. J. 83:2142-2151). Video microscopy revealed the following: invariably at t(LIN) a single sarcomere suddenly lengthened and returned to a relaxed-type structure. Originating from this sarcomere, structural relaxation propagated from one sarcomere to the next. Propagated sarcomeric relaxation, along with effects of stretch and P(i) on relaxation kinetics, supports an intersarcomeric chemomechanical coupling mechanism for rapid striated muscle relaxation in which cross-bridges conserve chemical energy by strain-induced rebinding of P(i).

Regulatory and essential light chains of myosin rotate equally during contraction of skeletal muscle

Myosin head consists of a globular catalytic domain and a long alpha-helical regulatory domain. The catalytic domain is responsible for binding to actin and for setting the stage for the main force-generating event, which is a "swing" of the regulatory domain. The proximal end of the regulatory domain contains the essential light chain 1 (LC1). This light chain can interact through the N and C termini with actin and myosin heavy chain. The interactions may inhibit the motion of the proximal end. In consequence the motion of the distal end (containing regulatory light chain, RLC) may be different from the motion of the proximal end. To test this possibility, the angular motion of LC1 and RLC was measured simultaneously during muscle contraction. Engineered LC1 and RLC were labeled with red and green fluorescent probes, respectively, and exchanged with native light chains of striated muscle. The confocal microscope was modified to measure the anisotropy from 0.3 microm(3) volume containing approximately 600 fluorescent cross-bridges. Static measurements revealed that the magnitude of the angular change associated with transition from rigor to relaxation was less than 5 degrees for both light chains. Cross-bridges were activated by a precise delivery of ATP from a caged precursor. The time course of the angular change consisted of a fast phase followed by a slow phase and was the same for both light chains. These results suggest that the interactions of LC1 do not inhibit the angular motion of the proximal end of the regulatory domain and that the whole domain rotates as a rigid body.

Characterization of the cross-bridge force-generating step using inorganic phosphate and BDM in myofibrils from rabbit skeletal muscles

The inhibitory effects of inorganic phosphate (P(i)) on isometric force in striated muscle suggest that in the ATPase reaction P(i) release is coupled to force generation. Whether P(i) release and the power stroke are synchronous events or force is generated by an isomerization of the quaternary complex of actomyosin and ATPase products (AM.ADP.P(i)) prior to the following release of P(i) is still controversial. Examination of the dependence of isometric force on [P(i)] in rabbit fast (psoas; 5-15 degrees C) and slow (soleus; 15-20 degrees C) myofibrils was used to test the two-step hypothesis of force generation and P(i) release. Hyperbolic fits of force-[P(i)] relations obtained in fast and slow myofibrils at 15 degrees C produced an apparent asymptote as [P(i)]-->infinity of 0.07 and 0.44 maximal isometric force (i.e. force in the absence of P(i)) in psoas and soleus myofibrils, respectively, with an apparent K(d) of 4.3 mM in both. In each muscle type, the force-[P(i)] relation was independent of temperature. However, 2,3-butanedione 2-monoxime (BDM) decreased the apparent asymptote of force in both muscle types, as expected from its inhibition of the force-generating isomerization. These data lend strong support to models of cross-bridge action in which force is produced by an isomerization of the AM.ADP.P(i) complex immediately preceding the P(i) release step.

Myosin cross-bridge kinetics in airway smooth muscle: a comparative study of humans, rats, and rabbits

To analyze the kinetics and unitary force of cross bridges (CBs) in airway smooth muscle (ASM), we proposed a new formalism of Huxley's equations adapted to nonsarcomeric muscles (Huxley AF. Prog Biophys Biophys Chem 7: 255-318, 1957). These equations were applied to ASM from rabbits, rats, and humans (n = 12/group). We tested the hypothesis that species differences in whole ASM mechanics were related to differences in CB mechanics. We calculated the total CB number per square millimeter at peak isometric tension (Psi x10(9)), CB unitary force (Pi), and the rate constants for CB attachment (f(1)) and detachment (g(1) and g(2)). Total tension, Psi, and Pi were significantly higher in rabbits than in humans and rats. Values of Pi were 8.6 +/- 0.1 pN in rabbits, 7.6 +/- 0.3 pN in humans, and 7.7 +/- 0.2 pN in rats. Values of Psi were 4.0 +/- 0.5 in rabbits, 1.2 +/- 0.1 in humans, and 1.9 +/- 0.2 in rats; f(1) was lower in humans than in rabbits and rats; g(2) was higher in rabbits than in rats and in rats than in humans. In conclusion, ASM mechanical behavior of different species was characterized by specific CB kinetics and CB unitary force.

Myosin cross bridges in skeletal muscles: "rower" molecular motors

Different classes of molecular motors, "rowers" and "porters," have been proposed to describe the chemomechanical transduction of energy. Rowers work in large assemblies and spend a large percentage of time detached from their lattice substrate. Porters behave in the opposite way. We calculated the number of myosin II cross bridges (CB) and the probabilities of attached and detached states in a minimal four-state model in slow (soleus) and fast (diaphragm) mouse skeletal muscles. In both muscles, we found that the probability of CB being detached was approximately 98% and the number of working CB was higher than 10(9)/mm(2). We concluded that muscular myosin II motors were classified in the category of rowers. Moreover, attachment time was higher than time stroke and time for ADP release. The duration of the transition from detached to attached states represented the rate-limiting step of the overall attached time. Thus diaphragm and soleus myosins belong to subtype 1 rowers.

Theoretical formalism for bead movement powered by single two-headed motors in a motility assay

Kinesins and dyneins are protein motors that can use the free energy of ATP hydrolysis to carry a cargo and move uni-directionally along a microtubule filament. The purpose of this paper is to derive the formalism connecting the ATP-driven translocation reactions of these motors on microtubule filaments and the movement of the bead carried by the motor in a motility assay in which the bead is clamped at an arbitrary constant force. The formalism is thus useful in elucidating the load-dependent kinetic mechanism of the free-energy transduction of the motor using the mechanical data obtained from the motility assay. The formalism is also useful in assessing the effect on the measured motility data of various physical and hydrodynamic parameters of the assay, such as the size of the bead, the viscosity of the medium, the stiffness of the elastic element connecting the motor and the bead, etc. In a previous paper [Biophys. J. 67 (2000) 313] (hereafter referred to as paper I), we have derived the formalism for the case that the motor in the assay has only one head. In this paper we extend the derivation to the case that the motor is two-headed. The formalism is derived based on a simple two-state hand-over-hand model for the movement of the motor on microtubule, but can be easily extended to more complicated kinetic models. Effects of various hydrodynamic parameters on the velocity of the bead are studied with numerical calculations of the model. The difference between the formalism presented in this paper and the widely used "chemical" formalism, in which the movement of the kinesin and the bead is described by pure chemical reactions, is discussed.

The effect of inorganic phosphate on force generation in single myofibrils from rabbit skeletal muscle

In striated muscle, force generation and phosphate (P(i)) release are closely related. Alterations in the [P(i)] bathing skinned fibers have been used to probe key transitions of the mechanochemical coupling. Accuracy in this kind of studies is reduced, however, by diffusional barriers. A new perfusion technique is used to study the effect of [P(i)] in single or very thin bundles (1-3 microM in diameter; 5 degrees C) of rabbit psoas myofibrils. With this technique, it is possible to rapidly jump [P(i)] during contraction and observe the transient and steady-state effects on force of both an increase and a decrease in [P(i)]. Steady-state isometric force decreases linearly with an increase in log[P(i)] in the range 500 microM to 10 mM (slope -0.4/decade). Between 5 and 200 microM P(i), the slope of the relation is smaller ( approximately -0.07/decade). The rate constant of force development (k(TR)) increases with an increase in [P(i)] over the same concentration range. After rapid jumps in [P(i)], the kinetics of both the force decrease with an increase in [P(i)] (k(Pi(+))) and the force increase with a decrease in [P(i)] (k(Pi(-))) were measured. As observed in skinned fibers with caged P(i), k(Pi(+)) is about three to four times higher than k(TR), strongly dependent on final [P(i)], and scarcely modulated by the activation level. Unexpectedly, the kinetics of force increase after jumps from high to low [P(i)] is slower: k(Pi(-)) is indistinguishable from k(TR) measured at the same [P(i)] and has the same calcium sensitivity.

The two-state cross-bridge model of muscle is an asymptotic limit of multi-state models

The relationship between the two-state model of muscle contraction and multi-state models is examined from the perspective of matched asymptotic expansions, under the assumption that transition rates between attached states are fast compared to those between detached and attached states. A detailed formal analysis of a three-state model reveals that the classic Huxley (1957. Prog. Biophys. Biophys. Chem.7, 225-318) rate equation, as modified for thermodynamic self-consistency by Hill et al. (1975. Biophys. J.15, 335-372), governs the "outer" solution of the three-state equations. Thus, the two-state model remains a valid description of muscle dynamics on physiologically relevant time scales, which are slow compared to millisecond-scale transitions between attached states. But the asymptotic analysis reveals also that the cross-bridge force must be considered to be a nonlinear function of the cross-bridge strain, in contrast to the usual assumption of two-state models. This apparent, or effective, force is determined by both the intrinsic stiffness of the cross-bridge and the equilibrium distribution of cross-bridges among attached states. Further, the asymptotic analysis yields an expression for the energy liberation rate that implies a reduced rate in stretch vs. shortening. Some behaviors of multi-state models that are suggested by the three-state analysis are discussed in qualitative terms.

Cross-bridge movement and stiffness during the rise of tension in skeletal muscle--a theoretical analysis

Predictions for the time courses of cross-bridge attachment. N(t), stiffness, S(t), and force, T(t), during the tetanus rise were analysed for a special class of cross-bridge models where cross-bridges initially attach in a non-stereospecific weak-binding state, AW. This state is in rapid equilibrium (equilibrium constant K) with detached states and the force generating transition (rate constant F+) is delayed. One model (model IA) which assumed step-function rise of activation at onset of tetanus, gave a poor fit to the experimental data (judged by root mean square error, RMSe approximately 0.038) but the experimentally observed lead of N(t) over T(t) was reproduced qualitatively. An activation mechanism where K increased towards its maximum value according to an exponential function (Model IB) improved the fit considerably (RMSe approximately 0.013). However, the activation time constant (r = 30 ms) derived in the fit was too high to reflect Ca2+ binding to troponin. In a further developed model (model II) both Ca2+ -binding to troponin and cross-bridge attachment were assumed to be required for full activation. This more complex model gave a good fit to the experimental data (RMSe approximately 0.013) with a realistic time constant for Ca2+ binding to troponin (9 ms). In both model IB and model II the best fit was obtained with F+ approximately 40 s(-1). An extended version of model IB, with distributed cross-bridge attachment and a series elastic element, gave a fit of similar quality (RMSe approximately 0.009) as obtained with model IB and model II and with a similar value of F+. The results support the view that weakly bound cross-bridges (state AW) may account for the lead of cross-bridge movement over force during tension rise. It is also shown that, if the stiffness of the myofilaments is non-linear (stiffness increasing with tension) the experimentally observed lead of S(t) over T(t) may, to a significant degree, be attributed to cross-bridges in the state AW.

Cooperativity of myosin molecules through strain-dependent chemistry

There is mounting evidence that the myosin head domain contains a lever arm which amplifies small structural changes that occur at the nucleotide-binding site. The mechanical work associated with movement of the lever affects the rates at which the products of ATP hydrolysis are released. During muscle contraction, this strain-dependent chemistry leads to cooperativity of the myosin molecules within a thick filament. Two aspects of cooperative action are discussed, in the context of a simple stochastic model. (i) A modest motion of the lever arm on ADP release can serve to regulate the fraction of myosin bound to the thin filament, in order to recruit more heads at higher loads. (ii) If the lever swings through a large angle when phosphate is released, the chemical cycles of the myosin molecules can be synchronized at high loads. This leads to stepwise sliding of the filaments and suggests that the isometric condition is not a steady state.

Regulation of contraction in striated muscle

Ca(2+) regulation of contraction in vertebrate striated muscle is exerted primarily through effects on the thin filament, which regulate strong cross-bridge binding to actin. Structural and biochemical studies suggest that the position of tropomyosin (Tm) and troponin (Tn) on the thin filament determines the interaction of myosin with the binding sites on actin. These binding sites can be characterized as blocked (unable to bind to cross bridges), closed (able to weakly bind cross bridges), or open (able to bind cross bridges so that they subsequently isomerize to become strongly bound and release ATP hydrolysis products). Flexibility of the Tm may allow variability in actin (A) affinity for myosin along the thin filament other than through a single 7 actin:1 tropomyosin:1 troponin (A(7)TmTn) regulatory unit. Tm position on the actin filament is regulated by the occupancy of NH-terminal Ca(2+) binding sites on TnC, conformational changes resulting from Ca(2+) binding, and changes in the interactions among Tn, Tm, and actin and as well as by strong S1 binding to actin. Ca(2+) binding to TnC enhances TnC-TnI interaction, weakens TnI attachment to its binding sites on 1-2 actins of the regulatory unit, increases Tm movement over the actin surface, and exposes myosin-binding sites on actin previously blocked by Tm. Adjacent Tm are coupled in their overlap regions where Tm movement is also controlled by interactions with TnT. TnT also interacts with TnC-TnI in a Ca(2+)-dependent manner. All these interactions may vary with the different protein isoforms. The movement of Tm over the actin surface increases the "open" probability of myosin binding sites on actins so that some are in the open configuration available for myosin binding and cross-bridge isomerization to strong binding, force-producing states. In skeletal muscle, strong binding of cycling cross bridges promotes additional Tm movement. This movement effectively stabilizes Tm in the open position and allows cooperative activation of additional actins in that and possibly neighboring A(7)TmTn regulatory units. The structural and biochemical findings support the physiological observations of steady-state and transient mechanical behavior. Physiological studies suggest the following. 1) Ca(2+) binding to Tn/Tm exposes sites on actin to which myosin can bind. 2) Ca(2+) regulates the strong binding of M.ADP.P(i) to actin, which precedes the production of force (and/or shortening) and release of hydrolysis products. 3) The initial rate of force development depends mostly on the extent of Ca(2+) activation of the thin filament and myosin kinetic properties but depends little on the initial force level. 4) A small number of strongly attached cross bridges within an A(7)TmTn regulatory unit can activate the actins in one unit and perhaps those in neighboring units. This results in additional myosin binding and isomerization to strongly bound states and force production. 5) The rates of the product release steps per se (as indicated by the unloaded shortening velocity) early in shortening are largely independent of the extent of thin filament activation ([Ca(2+)]) beyond a given baseline level. However, with a greater extent of shortening, the rates depend on the activation level. 6) The cooperativity between neighboring regulatory units contributes to the activation by strong cross bridges of steady-state force but does not affect the rate of force development. 7) Strongly attached, cycling cross bridges can delay relaxation in skeletal muscle in a cooperative manner. 8) Strongly attached and cycling cross bridges can enhance Ca(2+) binding to cardiac TnC, but influence skeletal TnC to a lesser extent. 9) Different Tn subunit isoforms can modulate the cross-bridge detachment rate as shown by studies with mutant regulatory proteins in myotubes and in in vitro motility assays. (ABSTRACT TRUNCATED)

Cross-bridge attachment during high-speed active shortening of skinned fibers of the rabbit psoas muscle: implications for cross-bridge action during maximum velocity of filament sliding

To characterize the kinetics of cross-bridge attachment to actin during unloaded contraction (maximum velocity of filament sliding), ramp-shaped stretches with different stretch-velocities (2-40,000 nm per half-sarcomere per s) were applied to actively contracting skinned fibers of the rabbit psoas muscle. Apparent fiber stiffness observed during such stretches was plotted versus the speed of the imposed stretch (stiffness-speed relation) to derive the rate constants for cross-bridge dissociation from actin. The stiffness-speed relation obtained for unloaded shortening conditions was shifted by about two orders of magnitude to faster stretch velocities compared to isometric conditions and was almost identical to the stiffness-speed relation observed in the presence of MgATPgammaS at high Ca(2+) concentrations, i.e., under conditions where cross-bridges are weakly attached to the fully Ca(2+) activated thin filaments. These data together with several control experiments suggest that, in contrast to previous assumptions, most of the fiber stiffness observed during high-speed shortening results from weak cross-bridge attachment to actin. The fraction of strongly attached cross-bridges during unloaded shortening appears to be as low as some 1-5% of the fraction present during isometric contraction. This is about an order of magnitude less than previous estimates in which contribution of weak cross-bridge attachment to observed fiber stiffness was not considered. Our findings imply that 1) the interaction distance of strongly attached cross-bridges during high-speed shortening is well within the range consistent with conventional cross-bridge models, i.e., that no repetitive power strokes need to be assumed, and 2) that a significant part of the negative forces that limit the maximum speed of filament sliding might originate from weak cross-bridge interactions with actin.

Imaging and nano-manipulation of single actomyosin motors at work

1. Muscle contraction is achieved by the sliding movement of myosin and actin using the energy of ATPase. 2. Our research has focused on the question of how chemical energy is used to perform mechanical work. Recent developments of single molecule imaging and manipulation techniques have allowed us to study the chemical and mechanical events at a molecular level. 3. There are many lines of evidence that show that the energy liberated from ATPase is stored in the actomyosin molecules for later use. 4. The displacement produced by a single ATP molecule is made up of several steps, each of 5.3 nm. Sometimes the mechanical event is delayed after the ADP is released from myosin. 5. This storage of energy may be explained by a slow conformational transition between the metastable states of the proteins. This suggestion has been supported by results obtained using single-molecule fluorescence spectroscopy.

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

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

Theoretical formalism for kinesin motility I. Bead movement powered by single one-headed kinesins

The directional movement on a microtubule of a plastic bead connected elastically to a single one-headed kinesin motor is studied theoretically. The kinesin motor can bind and unbind to periodic binding sites on the microtubule and undergo conformational changes while catalyzing the hydrolysis of ATP. An analytic formalism relating the dynamics of the bead and the ATP hydrolysis cycle of the motor is derived so that the calculation of the average velocity of the bead can be easily carried out. The formalism was applied to a simple three-state biochemical model to investigate how the velocity of the bead movement is affected by the external load, the diffusion coefficient of the bead, and the stiffness of the elastic element connecting the bead and the motor. The bead velocity was found to be critically dependent on the diffusion coefficient of the bead and the stiffness of the elastic element. A linear force-velocity relation was found for the model no matter whether the bead velocity was modulated by the diffusion coefficient of the bead or by the externally applied load. The formalism should be useful in modeling the mechanisms of chemimechanical coupling in kinesin motors based on in vitro motility data.

Myosin molecular motor dysfunction in dystrophic mouse diaphragm

Cross-bridge properties and myosin heavy chain (MHC) composition were investigated in isolated diaphragm from 6-mo-old control (n = 12) and mdx (n = 12) mice. Compared with control, peak tetanic tension fell by 50% in mdx mice (P < 0.001). The total number of cross bridges per square millimeter (x10(9)), the elementary force per cross bridge, and the peak mechanical efficiency were lower in mdx than in control mice (each P < 0.001). The duration of the cycle and the rate constant for cross-bridge detachment were significantly lower in mdx than in control mice. In the overall population, there was a linear relationship between peak tetanic tension and either total number of cross bridges per square millimeter or elementary force per cross bridge (r = 0.996 and r = 0.667, respectively, each P < 0.001). The mdx mice presented a higher proportion of type IIA MHC (P < 0.001) than control mice and a reduction in type IIX MHC (P < 0.001) and slow myosin isoforms (P < 0.01) compared with control mice. We concluded that, in mdx mice, impaired diaphragm strength was associated with qualitative and quantitative changes in myosin molecular motors. It is proposed that reduced force generated per cross bridge contributed to diaphragm weakness in mdx mice.

Stiffness-distortion sarcomere model for muscle simulation

A relatively simple method is presented for incorporating cross-bridge mechanisms into a muscle model. The method is based on representing force in a half sarcomere as the product of the stiffness of all parallel cross bridges and their average distortion. Differential equations for sarcomeric stiffness are derived from a three-state kinetic scheme for the cross-bridge cycle. Differential equations for average distortion are derived from a distortional balance that accounts for distortion entering and leaving due to cross-bridge cycling and for distortion imposed by shearing motion between thick and thin filaments. The distortion equations are unique and enable sarcomere mechanodynamics to be described by only a few ordinary differential equations. Model predictions of small-amplitude step and sinusoidal responses agreed well with previously described experimental results and allowed unique interpretations to be made of various response components. Similarly good results were obtained for model reproductions of force-velocity and large-amplitude step and ramp responses. The model allowed reasonable predictions of contractile behavior by taking into account what is understood to be basic muscle contractile mechanisms.

A protein friction model of the actin sliding movement generated by myosin in mixtures of MgATP and MgGTP in vitro

The sliding movement of an actin filament generated by myosin heads with MgGTP bound is much slower than that by those with MgATP bound. Nonetheless, there is a report that the actin sliding velocity at low (11-21 microM) MgATP concentrations is increased by the addition of MgGTP in a range of 1-3 mM, although the actin sliding velocity at these MgATP concentrations is larger than the maximum sliding velocity attained in the presence of MgGTP alone. The convex rise in the velocity was called "mutual sensitization of MgATP and MgGTP" in the report. Here we propose a theoretical model to account for the mutual sensitization of MgATP and MgGTP. The model is an extension of a protein friction model, accommodating the presence of two different substrates and assuming the presence of motile and non-motile myosins. This new model is in accord with the characteristics of the actin/myosin sliding movement experimentally observed in mixtures of MgATP and MgGTP. Comparison of the model with the experimental results implies that the non-motile and motile myosins are those with the "converse and correct" orientations of their heads with respect to the direction of the actin sliding movement in vitro.

Energy transduction of isothermal ratchets: generic aspects and specific examples close to and far from equilibrium

We study the energetics of isothermal ratchets which are driven by a chemical reaction between two states, and operate in contact with a single heat bath of constant temperature. We discuss generic aspects of energy transduction such as Onsager relations in the linear response regime as well as the efficiency and dissipation close to and far from equilibrium. In the linear response regime where the system operates reversibly, the efficiency is in general nonzero. Studying the properties for specific examples of energy landscapes and transitions, we observe in the linear response regime that the efficiency can have a maximum as a function of temperature. Far from equilibrium in the fully irreversible regime, we find a maximum of the efficiency with values larger than in the linear regime for an optimal choice of the chemical driving force. We show that the corresponding efficiencies can be of the order of 50%. A simple analytic argument allows us to estimate the efficiency in this irreversible regime for small external forces.

Two heads of myosin are better than one for generating force and motion

Several classes of the myosin superfamily are distinguished by their "double-headed" structure, where each head is a molecular motor capable of hydrolyzing ATP and interacting with actin to generate force and motion. The functional significance of this dimeric structure, however, has eluded investigators since its discovery in the late 1960s. Using an optical-trap transducer, we have measured the unitary displacement and force produced by double-headed and single-headed smooth- and skeletal-muscle myosins. Single-headed myosin produces approximately half the displacement and force (approximately 6 nm; 0.7 pN) of double-headed myosin (approximately 10 nm; 1.4 pN) during a unitary interaction with actin. These data suggest that muscle myosins require both heads to generate maximal force and motion.

Shortening properties of two biochemically defined muscle fibre types of the Norway lobster Nephrops norvegicus L

Mechanical properties of myofibrillar bundles from single chemically skinned fibres from the superficial abdominal flexor muscle of the Norway lobster Nephrops norvegicus were measured, and the protein content of these fibres was analysed by SDS-PAGE. Two slow fibre phenotypes (S1, S2) were distinguished on the basis of their myofibrillar protein assemblages. Data from 9 S1 and 8 S2 fibres obtained at similar sarcomere length demonstrate significant differences between the fibre types in maximal tension (N cm-2, S1: 10.5 +/- 3.9; S2: 3.1 +/- 0.8), in the delay of the peak of stretch activation (ms, S1: 122 +/- 18; S2: 412 +/- 202), in fibre stiffness (N cm-2 per nm half sarcomere, S1: 0.36 +/- 0.19; S2: 0.09 +/- 0.03) and in maximal shortening velocity (fibre length s-1, S1: 0.53 +/- 0.10; S2: 0.27 +/- 0.06). Furthermore, the maximal power output of the type S1 fibres was about five times larger than that of S2 fibres. The power output was maximal at lower loads in S1 fibres (relative load = 0.37 +/- 0.04) than in S2 fibres (relative load = 0.44 +/- 0.05). This study represents a comprehensive investigation of two slow muscle fibre types which are thought to be specialized for slow movements (S1 fibres) and for the postural control of the abdomen (S2 fibres).

Molecular model of muscle contraction

A quantitative stochastic model of the mechanochemical cycle of myosin, the protein that drives muscle contraction, is proposed. It is based on three premises: (i) the myosin head incorporates a lever arm, whose equilibrium position adjusts as each of the products of ATP hydrolysis dissociates from the nucleotide pocket; (ii) the chemical reaction rates are modified according to the work done in moving the arm; and (iii) the compliance of myosin's elastic element is designed to permit many molecules to work together efficiently. The model has a minimal number of parameters and provides an explanation, at the molecular level, of many of the mechanical and thermodynamic properties of steadily shortening muscle. In particular, the inflexion in the force-velocity curve at a force approaching the isometric load is reproduced. Moreover, the model indicates that when large numbers of myosin molecules act collectively, their chemical cycles can be synchronized, and that this leads to stepwise motion of the thin filament. The oscillatory transient response of muscle to abrupt changes of load is interpreted in this light.

Amphidinolide B, a powerful activator of actomyosin ATPase enhances skeletal muscle contraction

Amphidinolide B caused a concentration-dependent increase in the contractile force of skeletal muscle skinned fibers. The concentration-contractile response curve for external Ca2+ was shifted to the left in a parallel manner, suggesting an increase in Ca2+ sensitivity. Amphidinolide B stimulated the superprecipitation of natural actomyosin. The maximum response of natural actomyosin to Ca2+ in superprecipitation was enhanced by it. Amphidinolide B increased the ATPase activity of myofibrils and natural actomyosin. The ATPase activity of actomyosin reconstituted from actin and myosin was enhanced in a concentration-dependent manner in the presence or absence of troponin-tropomyosin complex. Ca2+-, K+-EDTA- or Mg2+-ATPase of myosin was not affected by amphidinolide B. These results suggest that amphidinolide B enhances an interaction of actin and myosin directly and increases Ca2+ sensitivity of the contractile apparatus mediated through troponin-tropomyosin system, resulting in an increase in the ATPase activity of actomyosin and thus enhances the contractile response of myofilament.

A weakly coupled version of the Huxley crossbridge model can simulate energetics of amphibian and mammalian skeletal muscle

This study aimed to establish whether quantitatively accurate predictions of the rate of crossbridge-dependent energy output from shortening muscle could be made on the basis of a 2-state model of crossbridge kinetics incorporating weak coupling between mechanical cycles and ATP hydrolysis. The model was based on Huxley's (1957) model but included rapid detachment, without ATP hydrolysis, of crossbridges when their strain energy increased sufficiently that crossbridge free energy exceeded that of the unbound state (Cooke et al., 1994). An expression was derived relating force to steady-state velocity in terms of the model's rate constants. The values of the rate constants that both provided the best fit through force-velocity data and correctly predicted crossbridge-dependent rate of energy output during an isometric contraction were found and used to predict the variation in rate of energy liberation with shortening velocity. The model predictions closely matched the estimated crossbridge energetics of frog sartorius muscle, including the decline in rate of enthalpy output at high shortening velocities. Data from fast- and slow-twitch muscles of the mouse were also simulated. The velocity-dependence of rate of energy liberation from fast-twitch EDL muscle was well described by the model. The model overestimated crossbridge-dependent energy output from slow-twitch soleus at low shortening velocities but provided accurate predictions of energy output at high velocities. In terms of this model, the distinctive energetics of fast and slow muscles cannot be explained exclusively by differences in cross-bridge detachment rate; differences in the relative rates of crossbridge attachment must also be considered to explain the different relations between energy output and shortening velocity.

Phase transition in force during ramp stretches of skeletal muscle

Active glycerinated rabbit psoas fibers were stretched at constant velocity (0.1-3.0 lengths/s) under sarcomere length control. As observed by previous investigators, force rose in two phases: an initial rapid increase over a small stretch (phase I), and a slower, more modest rise over the remainder of the stretch (phase II). The transition between the two phases occurred at a critical stretch (LC) of 7.7 +/- 0.1 nm/half-sarcomere that is independent of velocity. The force at critical stretch (PC) increased with velocity up to 1 length/s, then was constant at 3.26 +/- 0.06 times isometric force. The decay of the force response to a small step stretch was much faster during stretch than in isometric fibers. The addition of 3 mM vanadate reduced isometric tension to 0.08 +/- 0.01 times control isometric tension (P0), but only reduced PC to 0.82 +/- 0.06 times P0, demonstrating that prepowerstroke states contribute to force rise during stretch. The data can be explained by a model in which actin-attached cross-bridges in a prepowerstroke state are stretched into regions of high force and detach very rapidly when stretched beyond this region. The prepowerstroke state acts as a mechanical rectifier, producing large forces during stretch but small forces during shortening.

Estimation of cross-bridge stiffness from maximum thermodynamic efficiency

In muscle, work is performed by myosin cross-bridges during interactions with actin filaments. The amount of work performed during each interaction can be related to the mechanical properties of the cross-bridge; work is the integral of the force produced with respect to the distance that the cross-bridge moves the actin filament, and force is determined by the stiffness of the attached cross-bridge. In this paper, cross-bridge stiffness in frog sartorius muscle was estimated from thermodynamic efficiency (work/free energy change) using a two-state cross-bridge model, assuming constant stiffness over the working range and tight-coupling between cross-bridge cycles and ATP use. This model accurately predicts mechanical efficiency (work/enthalpy output). A critical review of the literature indicates that a realistic value for maximum thermodynamic efficiency of frog sartorius is 0.45 under conditions commonly used in experiments on isolated muscle. Cross-bridge stiffness was estimated for a range of power stroke amplitudes. For realistic amplitudes (10-15 nm), estimated cross-bridge stiffness was between 1 and 2.2 pN nm-1. These values are similar to those estimated from quick-release experiments, taking into account compliance arising from structures other than cross-bridges, but are substantially higher than those from isolated protein studies. The effects on stiffness estimates of relaxing the tight-coupling requirement and of incorporating more force-producing cross-bridge states are also considered.

Mechanics, energetics, and crossbridge kinetics of rabbit diaphragm during congestive heart failure

Crossbridge (CB) properties were investigated in isolated diaphragm of rabbits during congestive heart failure (CHF, n=9) induced by chronic volume and pressure overload. This model induced cardiac hypertrophy and heart failure. Controls (C) were prepared (n=14). Compared to C, peak tension in CHF fell by 57% in twitch and by 40% in tetanus; Vmax declined by 47% in twitch and by 48% in tetanus. Our study provided an analytical means of calculating from A. F. Huxley's equations the rate constants for CB attachment and detachment, CB single force (II), CB number per mm3 (m'), peak mechanical efficiency (Effmax), and turnover rate of myosin ATPase (kcat); m', II, and Effmax were lower in CHF than in C in both twitch and tetanus. The marked decline in m' and II accounted for the fall in diaphragm strength. In the overall population of C and CHF, Effmax was linearly related to II. Conversely, there was no relationship between Vmax and kcat. Dissociation between Vmax and kcat might be explained by the crucial role attributed to two apparently nonconserved surface 'loops' on the motor domain of myosin head.

Myosin conformational states determined by single fluorophore polarization

Muscle contraction is powered by the interaction of the molecular motor myosin with actin. With new techniques for single molecule manipulation and fluorescence detection, it is now possible to correlate, within the same molecule and in real time, conformational states and mechanical function of myosin. A spot-confocal microscope, capable of detecting single fluorophore polarization, was developed to measure orientational states in the smooth muscle myosin light chain domain during the process of motion generation. Fluorescently labeled turkey gizzard smooth muscle myosin was prepared by removal of endogenous regulatory light chain and re-addition of the light chain labeled at cysteine-108 with the 6-isomer of iodoacetamidotetramethylrhodamine (6-IATR). Single myosin molecule fluorescence polarization data, obtained in a motility assay, provide direct evidence that the myosin light chain domain adopts at least two orientational states during the cyclic interaction of myosin with actin, a randomly disordered state, most likely associated with myosin whereas weakly bound to actin, and an ordered state in which the light chain domain adopts a finite angular orientation whereas strongly bound after the powerstroke.

Activation of skinned muscle fibres from the Norway lobster Nephrops norvegicus L. by manganese ions

Effects of Mn2+ and Ca2+ on the mechanical properties of glycerinated myofibrillar bundles originating from slow S1 type muscle fibres of superficial flexor muscles of the lobster Nephrops norvegicus were investigated. Mn2+ (5-20 microM) activated the preparations in a dose-dependent manner. The sensitivity of myofibrillar force generation for Mn2+ was around 30 times lower than that for Ca2+. The maximal tension produced under Mn2+ activation was about 75% of that under Ca2+ activation. At higher free Mn2+ concentrations (>2 mM), the steady-state force decreased; it was completely abolished at 30 mM free Mn2+. These high Mn2+ solutions were accompanied by changed in MgATP and MnATP concentrations, and in the ionic strength. Control experiments have shown that none of these parameters seemed fo account fully for the observed force depression in high Mn2+ solutions. It is likely that direct effects of Mn2+ such as a change of the myofilament surface charges are responsible. The maximal unloaded shortening velocity of the myofibrillar preparations was shown to be similar under maximal Mn2+ and Ca2+ activation. Conversely, the kinetics of stretch-induced delayed force increase were about two to three times faster under Mn2+ activation. These results suggest that certain steps of the cross-bridge cycle depend on the ion species bound to the regulatory proteins.

Myocardial contractile depression from high-frequency vibration is not due to increased cross-bridge breakage

Experiments were conducted in 10 isolated rabbit hearts at 25 degrees C to test the hypothesis that vibration-induced depression of myocardial contractile function was the result of increased cross-bridge breakage. Small-amplitude sinusoidal changes in left ventricular volume were administered at frequencies of 25, 50, and 76.9 Hz. The resulting pressure response consisted of a depressive response [delta Pd(t), a sustained decrease in pressure that was not at the perturbation frequency] and an infrequency response [delta Pf(t), that part at the perturbation frequency]. delta Pd(t) represented the effects of contractile depression. A cross-bridge model was applied to delta Pf(t) to estimate cross-bridge cycling parameters. Responses were obtained during Ca2+ activation and during Sr2+ activation when the time course of pressure development was slowed by a factor of 3. delta Pd(t) was strongly affected by whether the responses were activated by Ca2+ or by Sr2+. In the Sr(2+)-activated state, delta Pd(t) declined while pressure was rising and relaxation rate decreased. During Ca2+ and Sr2+ activation, velocity of myofilament sliding was insignificant as a predictor of delta Pd(t) or, when it was significant, participated by reducing delta Pd(t) rather than contributing to its magnitude. Furthermore, there was no difference in cross-bridge cycling rate constants when the Ca(2+)-activated state was compared with the Sr(2+)-activated state. An increase in cross-bridge detachment rate constant with volume-induced change in cross-bridge distortion could not be detected. Finally, processes responsible for delta Pd(t) occurred at slower frequencies than those of cross-bridge detachment. Collectively, these results argue against a cross-bridge detachment basis for vibration-induced myocardial depression.

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.

Simultaneous observation of individual ATPase and mechanical events by a single myosin molecule during interaction with actin

We have developed a technique that allows mechanical and ligand-binding events in a single myosin molecule to be monitored simultaneously. We describe how steps in the ATPase reaction are temporally related to mechanical events at the single molecule level. The results show that the force generation does not always coincide with the release of bound nucleotide, presumably ADP. Instead the myosin head produces force several hundreds of milliseconds after bound nucleotide is released. This finding does not support the widely accepted view that force generation is directly coupled to the release of bound ligands. It suggests that myosin has a hysteresis or memory state, which stores chemical energy from ATP hydrolysis.

Depletion of phosphate in active muscle fibers probes actomyosin states within the powerstroke

Variation in the concentration of orthophosphate (Pi) in actively contracting, chemically skinned muscle fibers has proved to be a useful probe of actomyosin interaction. Previous studies have shown that isometric tension (Po) decreases linearly in the logarithm of [Pi] for [Pi] > or = 200 microM. This result can be explained in terms of cross-bridge models in which the release of Pi is involved in the transition from a weakly bound, low-force actin x myosin x ADP x Pi state to a strongly bound, high-force, actin x myosin x ADP state. The 200 microM minimum [Pi] examined results from an inability to buffer the intrafiber, diffusive buildup of Pi resulting from the fiber ATPase. In the present study, we overcome this limitation by employing the enzyme purine nucleoside phosphorylase with substrate 7-methylguanosine to reduce the calculated internal [Pi] in contracting rabbit psoas fibers to < 5 microM. At 10 degrees C we find that Po continues to increase as the [Pi] decreases for [Pi] > or = 100 microM. Below this [Pi], Po is approximately constant. These results indicate that the free energy drop in the cross-bridge powerstroke is approximately 9 kT. This value is shown to be consistent with observations of muscle efficiency at physiological temperatures.

Molecular motors: structural adaptations to cellular functions

Molecular motors are protein machines whose directed movement along cytoskeletal filaments is driven by ATP hydrolysis. Eukaryotic cells contain motors that help to transport organelles to their correct cellular locations and to establish and alter cellular morphology during cell locomotion and division. The best-studied motors, myosin from skeletal muscle and conventional kinesin from brain, are remarkably similar in structure, yet have very different functions. These differences can be understood in terms of the 'duty ratio', the fraction of the time that a motor is attached to its filament. Differences in duty ratio can explain the diversity of structures, speeds and oligomerization states of members of the large kinesin, myosin and dynein families of motors.

Left ventricular pressure response to small-amplitude, sinusoidal volume changes in isolated rabbit heart

The objective was to determine the dynamics of contractile processes from pressure responses to small-amplitude, sinusoidal volume changes in the left ventricle of the beating heart. Hearts were isolated from 14 anesthetized rabbits and paced at 1 beats/s. Volume was perturbed sinusoidally at four frequencies (f) (25, 50, 76.9, and 100 Hz) and five amplitudes (0.50, 0.75, 1.00, 1.25, and 1.50% of baseline volume). A prominent component of the pressure response occurred at the f of perturbation [infrequency response, delta Pf(t)]. A model, based on cross-bridge mechanisms and containing both pre- and postpower stroke states, was constructed to interpret delta Pf(t). Model predictions were that delta Pf(t) consisted of two parts: a part with an amplitude rising and falling in proportion to the pressure around that which delta Pf(t) occurred [Pr(t)], and a part with an amplitude rising and falling in proportion to the derivative of Pr(t) with time. Statistical analysis revealed that both parts were significant. Additional model predictions concerning response amplitude and phase were also confirmed statistically. The model was further validated by fitting simultaneously to all delta Pf(t) over the full range of f and delta V in a given heart. Residual errors from fitting were small (R2 = 0.978) and were not systematically distributed. Elaborations of the model to include noncontractile series elastance and distortion-dependent cross-bridge detachment did not improve the ability to represent the data. We concluded that the model could be used to identify cross-bridge rate constants in the whole heart from responses to 25- to 100-Hz sinusoidal volume perturbations.

Efficiency of human skeletal muscle in vivo: comparison of isometric, concentric, and eccentric muscle action

The purpose of this study was to estimate the efficiency of ATP utilization for concentric, eccentric, and isometric muscle action in the human tibialis anterior and extensor digitorum longus in vivo. A dynamometer was used to quantitate muscle work, or tension, while simultaneous 31P-nuclear magnetic resonance data were collected to monitor ATP, phosphocreatine, inorganic phosphate, and pH. The relative efficiency of the actions was estimated in two ways: steady-state effects on high-energy phosphates and a direct comparison of ATP synthesis rates with work. In the steady state, the cytosolic free energy dropped to the lowest value with concentric activity, followed by eccentric and isometric action for comparative muscle tensions. Estimates of ATP synthesis rates revealed a mechanochemical efficiency [i.e., ATP production rate/work (both in J/s)] of 15.0 +/- 1.3% in concentric and 34.7 +/- 6.1% in eccentric activity. The estimated maximum ATP production rate was highest in concentric action, suggesting an activation of energy metabolism under these conditions. By using direct measures of metabolic strain and ATP turnover, these data demonstrate a decreasing metabolic efficiency in human muscle action from isometric, to eccentric, to concentric action.

Developmental changes in crossbridge properties and myosin isoforms in hamster diaphragm

The aim of this study was to determine the effects of maturation on crossbridge properties and myosin isoform composition in hamster diaphragm muscle. Diaphragm strips were obtained at postnatal Days 1 and 8 and in adults (10 to 12 wk). Peak isometric tension and maximum unloaded shortening velocity (Vmax) increased with age (p < 0.001). The single crossbridge force (pi), the total number of crossbridges normalized per cross-sectional area (m x 10(9)/mm2), the turnover rate of myosin ATPase (kcat), and peak mechanical efficiency (Effmax) were calculated from Huxley's equations. The value of m increased significantly from birth to adulthood (p < 0.001), with no changes in pi or Effmax; kcat increased significantly only after the first week postpartum. There was a strong linear relationship between peak isometric tension and m (p < 0.001). Conversely, changes in Vmax were not related to kcat. Myosin electrophoresis showed that neonatal bands and slow myosin isoforms (S) were present at birth. The number of fast adult myosin isoforms increased progressively from birth to adulthood, whereas S increased during the first week postpartum. In conclusion, development changes in diaphragm muscle force and myosin isoform composition were associated with changes in crossbridge number and kinetics, with no changes in the average force per crossbridge or in mechanical efficiency.

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.

Stretch activation and myosin heavy chain isoforms of rat, rabbit and human skeletal muscle fibres

The underlying mechanism of stretch-induced delayed force increase (stretch activation) of activated muscles is unknown. To assess the molecular correlate of this phenomenon, we measured stretch activation of single, Ca2+-activated skinned muscle fibres from rat, rabbit and the human and analysed their myosin heavy chain complement by SDS gradient gel electrophoresis. Stretch activation kinetics was found to be closely correlated with the myosin heavy chain isoform complement (I, IIa, IId/x and IIb). In hybrid fibres containing two myosin heavy chain isoforms (especially IId and IIb), the kinetics of stretch activation depended on the percentage distribution of the two isoforms. Muscle fibres of the same type but originating from different mammalian species exhibited similar kinetics of stretch activation. Considering the differing unloaded shortening velocities of these fibres, the time-limiting factors for stretch activation and unloaded shortening velocity appear not to be the same. The stretch activation kinetics of the fibre types IIB, IID and IIA more likely seemed to follow a Normal Gaussian distribution than that of type I fibres. Several type I fibres had extraordinarily slow kinetics. This observation corroborates biochemical data indicating the possible existence of more than one slow myosin heavy chain isoform.

Muscle contraction and fatigue. The role of adenosine 5'-diphosphate and inorganic phosphate

Though many explanations are offered for the fatigue process in contracting skeletal muscle (both central and peripheral factors), none completely explain the decline in force production capability because fatigue is specific to the activity being performed. However, one needs to look no further than the muscle contraction crossbridge cycle itself in order to explain a major contributor to the fatigue process in exercise of any duration. The byproducts of adenosine 5'-triphosphate (ATP) hydrolysis, adenosine 5'-diphosphate (ADP) and inorganic phosphate (Pi) are released during the crossbridge cycle and can be implicated in the fatigue process due to the requirement of their release for proper crossbridge activity. Pi release is coupled to the powerstroke of the crossbridge cycle. The accumulation of Pi during exercise would lead to a reversal of its release step, therefore causing a decrement in force production capability. Due to the release of Pi with both the immediate (phosphagen) energy system and the hydrolysis of ATP, Pi accumulation is probably the largest contributor to the fatigue process in exercise of any duration. ADP release occurs near the end of the crossbridge cycle and therefore controls the velocity of crossbridge detachment. Therefore, ADP accumulation, which occurs during exercise of extended duration (or in ischaemic conditions), causes a slowing of the rate constants (and therefore a decrease in the maximal velocity of shortening). in the crossbridge cycle and a reduced oscillatory power output. The combined effects of these accumulated hydrolysis byproducts accounts for a large amount of the fatigue process in exercise of any intensity or duration.

In vitro actin filament sliding velocities produced by mixtures of different types of myosin

Using in vitro motility assays, we examined the sliding velocity of actin filaments generated by pairwise mixings of six different types of actively cycling myosins. In isolation, the six myosins translocated actin filaments at differing velocities. We found that only small proportions of a more slowly translating myosin type could significantly inhibit the sliding velocity generated by a myosin type that translocated filaments rapidly. In other experiments, the addition of noncycling, unphosphorylated smooth and nonmuscle myosin to actively translating myosin also inhibited the rapid sliding velocity, but to a significantly reduced extent. The data were analyzed in terms of a model derived from the original working cross-bridge model of A.F. Huxley. We found that the inhibition of rapidly translating myosins by slowly cycling was primarily dependent upon only a single parameter, the cross-bridge detachment rate at the end of the working powerstroke. In contrast, the inhibition induced by the presence of noncycling, unphosphorylated myosins required a change in another parameter, the transition rate from the weakly attached actomyosin state to the strongly attached state at the beginning of the cross-bridge power stroke.

Strain-dependent modulation of phosphate transients in rabbit skeletal muscle fibers

When inorganic phosphate (Pi) is photogenerated from caged Pi during isometric contractions of glycerinated rabbit psoas muscle fibers, the released Pi binds to cross-bridges and reverses the working stroke of cross-bridges. The consequent force decline, the Pi-transient, is exponential and probes the kinetics of the power-stroke and Pi release. During muscle shortening, the fraction of attached cross-bridges and the average strain on them decreases (Ford, L. E., A.F. Huxley, and R.M. Simmons, 1977. Tension responses to sudden length change in stimulated frog muscle fibers near slack length. J. Physiol. (Lond.). 269:441-515; Ford, L. E., A. F. Huxley, and R.M. Simmons, 1985. Tension transients during steady state shortening of frog muscle fibers. J. Physiol. (Lond.). 361:131-150. To learn to what extent the Pi transient is strain dependent, muscle fibers were activated and shortened or lengthened at a fixed velocity during the photogeneration of Pi. The Pi transients observed during changes in muscle length showed three primary characteristics: 1) during shortening the Pi transient rate, Kpi, increased and its amplitude decreased with shortening velocity; Kpi increased linearly with velocity to > 110 s-1 at 0.3 muscle lengths per second (ML/s). 2) At a specific shortening velocity, increases in [Pi] produce increases in Kpi that are nonlinear with [Pi] and approach an asymptote. 3) During forced lengthening Kpi and the amplitude of the Pi transient are little different from the isometric contractions. These data can be approximated by a strain-dependent three-state cross-bridge model. The results show that the power stroke's rate is strain-dependent, and are consistent with biochemical studies indicating that the rate-limiting step at low strains is a transition from a weakly to a strongly bound cross-bridge state.

Rapid regeneration of power stroke in contracting muscle by attachment of second myosin head

When Lombardi and colleagues reported the phenomenon of rapid regeneration of the power stroke after a quick release of muscle fibre during a tetanus, they gave an explanation in terms of detachment of cross-bridges and re-attachment further along the thin filament. We show here that the phenomenon can also be explained on assumptions that lead to a majority of myosin molecules being attached by only one head during steady isometric contraction; the other head may then become attached after a quick release and can add its contribution to the early tension recovery after a second release.

Cross-bridge detachment and attachment following a step stretch imposed on active single frog muscle fibres

1. The time course of cross-bridge detachment-attachment following a step stretch was determined in single frog muscle fibres (at 4 degrees (1 and 2.1 microns sarcomere length) by imposing, under sarcomere length control by a striation follower, test step releases of various amplitudes (2-13 nm per half-sarcomere) at successive times (4-55 ms) after a conditioning stretch of approximately 4 nm per half-sarcomere. 2. The comparison with the control tension transients, elicited by releases not preceded by the conditioning stretch, shows that, early after the conditioning stretch, the quick tension recovery following small releases is depressed and the quick tension recovery following large releases is potentiated. Both effects are expected as a consequence of the strain produced in the cross-bridges by the conditioning stretch. 3. These effects disappear and the tension transient is reprimed, indicating substitution of freshly attached cross-bridges for strained cross-bridges, with a time constant of approximately 10 ms. 4. A novel multiple-exponential equation, based on the hypothesis of complete substitution of freshly attached cross-bridges for the cross-bridges that underwent the stretch, has been used to fit the whole tension transient following step stretches of different sizes (2-6 nm per half-sarcomere). For a stretch of 4 nm, the time constant of the exponential process responsible for cross-bridge detachment (tau d, 9.3 ms) almost coincides with the time constant of repriming as measured by the double-step experiments. The time constant of the exponential process representing the cumulative effects of attachment and force generation (tau 3) is 13.6 ms. 5. For stretches of different sizes the amount of quick tension recovery attributable to the reversal of the working stroke elicited by the stretches is estimated by subtracting, from the original tension transient, the contribution to tension recovery due to detachment-attachment of cross-bridges as estimated by the multiple-exponential analysis. Following this calculation, the structural change in the myosin heads responsible for the reversal of the working stroke can be 2 nm at maximum, suggesting that the elastic component in the cross-bridges is at least twice as rigid as previously thought.