Characterization of cross-bridge elasticity and kinetics of cross-bridge cycling during force development in single smooth muscle cells

Force development in smooth muscle, as in skeletal muscle, is believed to reflect recruitment of force-generating myosin cross-bridges. However, little is known about the events underlying cross-bridge recruitment as the muscle cell approaches peak isometric force and then enters a period of tension maintenance. In the present studies on single smooth muscle cells isolated from the toad (Bufo marinus) stomach muscularis, active muscle stiffness, calculated from the force response to small sinusoidal length changes (0.5% cell length, 250 Hz), was utilized to estimate the relative number of attached cross-bridges. By comparing stiffness during initial force development to stiffness during force redevelopment immediately after a quick release imposed at peak force, we propose that the instantaneous active stiffness of the cell reflects both a linearly elastic cross-bridge element having 1.5 times the compliance of the cross-bridge in frog skeletal muscle and a series elastic component having an exponential length-force relationship. At the onset of force development, the ratio of stiffness to force was 2.5 times greater than at peak isometric force. These data suggest that, upon activation, cross-bridges attach in at least two states (i.e., low-force-producing and high-force-producing) and redistribute to a steady state distribution at peak isometric force. The possibility that the cross-bridge cycling rate was modulated with time was also investigated by analyzing the time course of tension recovery to small, rapid step length changes (0.5% cell length in 2.5 ms) imposed during initial force development, at peak force, and after 15 s of tension maintenance. The rate of tension recovery slowed continuously throughout force development following activation and slowed further as force was maintained. Our results suggest that the kinetics of force production in smooth muscle may involve a redistribution of cross-bridge populations between two attached states and that the average cycling rate of these cross-bridges becomes slower with time during contraction.     

Rate constant of muscle force redevelopment reflects cooperative activation as well as cross-bridge kinetics.

The rate of muscle force redevelopment after release-restretch protocols has previously been interpreted using a simple two-state cross-bridge cycling model with rate constants for transitions between non-force-bearing and force-bearing states, f, and between force-bearing and non-force-bearing states, g. Changes in the rate constant of force redevelopment, as with varying levels of Ca2+ activation, have traditionally been attributed to Ca(2+)-dependent f. The current work adds to this original model a state of unactivated, noncycling cross-bridges. The resulting differential equation for activated, force-bearing cross-bridges, Ncf, was Ncf = -[g+f(K/(K + 1))] Ncf+f(K/(K + 1))NT, where K is an equilibrium constant defining the distribution between cycling and noncycling cross-bridges and NT is the total number of cross-bridges. Cooperativity by which force-bearing cross-bridges participate in their own activation was introduced by making K depend on Ncf. Model results demonstrated that such cooperativity, which tends to enhance force generation at low levels of Ca2+ activation, has a counter-intuitive effect of slowing force redevelopment. These dynamic effects of cooperativity are most pronounced at low Ca2+ activation. As Ca2+ activation increases, the cooperative effects become less important to the dynamics of force redevelopment and, at the highest levels of Ca2+ activation, the dynamics of force redevelopment reflect factors other than cooperative mechanisms. These results expand on earlier interpretations of Ca2+ dependence of force redevelopment; rather than Ca(2+)-dependent f, Ca(2+)-dependent force redevelopment arises from changing expressions of cooperativity between force-bearing cross-bridges and activation.     

Effect of length oscillations on airway smooth muscle reactivity and cross-bridge cycling

Excessive airway narrowing due to airway smooth muscle (ASM) hyperconstriction is a major symptom in many respiratory diseases. In vitro imposition of length oscillations similar to those produced by tidal breathing on contracted ASM have shown to reduce muscle active forces, which is usually attributed to unconfirmed disruption of actomyosin cross-bridges. This research focuses on an in vitro investigation of the effect of mechanical oscillations on ASM reactivity and actomyosin cross-bridges. A computerized organ bath system was used to test maximally precontracted bovine ASM subjected to length oscillations at frequencies in the range of 10-100 Hz superimposed on tidal breathing oscillation. Using an immunofluorescence technique, two specific antibodies against the phospho-serine19 myosin light chain and the α-smooth muscle actin were used to analyze the colocalization between these two filaments. Data were processed using the plug-in "colocalization threshold" of ImageJ 1.43m software. The results demonstrate that both tidal and superimposed length oscillations reduce the active force in contracted ASM for a relatively long term and that the latter enhances the force reduction of the former. This reduction was also found to be frequency and time dependent. Additionally colocalization analysis indicates that length oscillations cause the detachment of the actomyosin connections and that this condition is sustained even after the cessation of the length oscillations.     

Impact of beta-myosin heavy chain isoform expression on cross-bridge cycling kinetics

Myosin heavy chain (MHC) isoforms alpha and beta have intrinsically different ATP hydrolysis activities (ATPase) and therefore cross-bridge cycling rates in solution. There is considerable evidence of altered MHC expression in rodent cardiac disease models; however, the effect of incremental beta-MHC expression over a wide range on the rate of high-strain, isometric cross-bridge cycling is yet to be ascertained. We treated male rats with 6-propyl-2-thiouracil (PTU; 0.8 g/l in drinking water) for short intervals (6, 11, 16, and 21 days) to generate cardiac MHC patterns in transition from predominantly alpha-MHC to predominantly beta-MHC. Steady-state calcium-dependent tension development and tension-dependent ATP consumption (tension cost; proportional to cross-bridge cycling) were measured in chemically permeabilized (skinned) right ventricular muscles at 20 degrees C. To assess dynamic cross-bridge cycling kinetics, the rate of force redevelopment (ktr) was determined after rapid release-restretch of fully activated muscles. MHC isoform content in each experimental muscle was measured by SDS-PAGE and densitometry. alpha-MHC content decreased significantly and progressively with length of PTU treatment [68 +/- 5%, 58 +/- 4%, 37 +/- 4%, and 27 +/- 6% for 6, 11, 16, and 21 days, respectively; P < 0.001 (ANOVA)]. Tension cost decreased, linearly, with decreased alpha-MHC content [6.7 +/- 0.4, 5.6 +/- 0.5, 4.0 +/- 0.4, and 3.9 +/- 0.3 ATPase/tension for 6, 11, 16, and 21 days, respectively; P < 0.001 (ANOVA)]. Likewise, ktr was significantly and progressively depressed with length of PTU treatment [11.1 +/- 0.6, 9.1 +/- 0.5, 8.2 +/- 0.7, and 6.2 +/- 0.3 s(-1) for 6, 11, 16, and 21 days, respectively; P < 0.05 (ANOVA)] Thus cross-bridge cycling, under high strain, for alpha-MHC is three times higher than for beta-MHC. Furthermore, under isometric conditions, alpha-MHC and beta-MHC cross bridges hydrolyze ATP independently of one another.     

The effects of force inhibition by sodium vanadate on cross-bridge binding, force redevelopment, and Ca2+ activation in cardiac muscle

Strongly bound, force-generating myosin cross-bridges play an important role as allosteric activators of cardiac thin filaments. Sodium vanadate (Vi) is a phosphate analog that inhibits force by preventing cross-bridge transition into force-producing states. This study characterizes the mechanical state of cross-bridges with bound Vi as a tool to examine the contribution of cross-bridges to cardiac contractile activation. The K(i) of force inhibition by Vi was approximately 40 microM. Sinusoidal stiffness was inhibited with Vi, although to a lesser extent than force. We used chord stiffness measurements to monitor Vi-induced changes in cross-bridge attachment/detachment kinetics at saturating [Ca(2+)]. Vi decreased chord stiffness at the fastest rates of stretch, whereas at slow rates chord stiffness actually increased. This suggests a shift in cross-bridge population toward low force states with very slow attachment/detachment kinetics. Low angle x-ray diffraction measurements indicate that with Vi cross-bridge mass shifted away from thin filaments, implying decreased cross-bridge/thin filament interaction. The combined x-ray and mechanical data suggest at least two cross-bridge populations with Vi; one characteristic of normal cycling cross-bridges, and a population of weak-binding cross-bridges with bound Vi and slow attachment/detachment kinetics. The Ca(2+) sensitivity of force (pCa(50)) and force redevelopment kinetics (k(TR)) were measured to study the effects of Vi on contractile activation. When maximal force was inhibited by 40% with Vi pCa(50) decreased, but greater force inhibition at higher [Vi] did not further alter pCa(50). In contrast, the Ca(2+) sensitivity of k(TR) was unaffected by Vi. Interestingly, when force was inhibited by Vi k(TR) increased at submaximal levels of Ca(2+)-activated force. Additionally, k(TR) is faster at saturating Ca(2+) at [Vi] that inhibit force by > approximately 70%. The effects of Vi on k(TR) imply that k(TR) is determined not only by the intrinsic properties of the cross-bridge cycle, but also by cross-bridge contribution to thin filament activation.     

Increased cross-bridge cycling kinetics after exchange of C-terminal truncated troponin I in skinned rat cardiac muscle

The precise mechanism of cardiac troponin I (cTnI) proteolysis in myocardial stunning is not fully understood. Accordingly, we determined the effect of cTnI C terminus truncation on chemo-mechanical transduction in isolated skinned rat trabeculae. Recombinant troponin complex (cTn), containing either mouse cTnI-(1-193) or human cTnI-(1-192) was exchanged into skinned cardiac trabeculae; Western blot analysis confirmed that 60-70% of the endogenous cTn was replaced by recombinant Tn. Incorporation of truncated cTnI induced significant reductions ( approximately 50%) in maximum force and cooperative activation as well as increases ( approximately 50%) in myofilament Ca(2+) sensitivity and tension cost. Similar results were obtained with either mouse or human truncated cTn. Presence of truncated cTnI increased maximum actin-activated S1 ATPase activity as well as its Ca(2+) sensitivity in vitro. Partial exchange (50%) for truncated cTnI resulted in similar reductions in maximum force and cooperativity; tension cost was increased in proportion to truncated cTnI content. In vitro, to determine the molecular mechanism responsible for the enhanced myofilament Ca(2+) sensitivity, we measured Ca(2+) binding to cTn as reported using a fluorescent probe. Incorporation of truncated cTnI did not affect Ca(2+) binding affinity to cTn alone. However, when cTn was incorporated into thin filaments, cTnI truncation induced a significant increase in Ca(2+) binding affinity to cTn. We conclude that cTnI truncation induces depressed myofilament function. Decreased cardiac function after ischemia/reperfusion injury may directly result, in part, from proteolytic degradation of cTnI, resulting in alterations in cross-bridge cycling kinetics.     

Influence of Ca2+ on force redevelopment kinetics in skinned rat myocardium.

The influence of Ca2+ on isometric force kinetics was studied in skinned rat ventricular trabeculae by measuring the kinetics of force redevelopment after a transient decrease in force. Two protocols were employed to rapidly detach cycling myosin cross-bridges: a large-amplitude muscle length ramp followed by a restretch back to the original length or a 4% segment length step. During the recovery of force, the length of the central region of the muscle was controlled by using a segment marker technique and software feedback control. Tension redevelopment was fit by a rising exponential governed by the rate constant ktr for the ramp/restretch protocol and kstep for the step protocol. ktr and kstep averaged 7.06 s-1 and 15.7 s-1, respectively, at 15 degrees C; neither ktr nor kstep increased with the level of Ca2+ activation. Similar results were found at submaximum Ca2+ levels when sarcomere length control by laser diffraction was used. The lack of activation dependence of ktr contrasts with results from fast skeletal fibers, in which ktr varies 10-fold from low to high activation levels, and suggests that Ca2+ does not modulate the kinetics of cross-bridge attachment or detachment in mammalian cardiac muscle.     

Modeling residual force enhancement with generic cross-bridge models

The interaction of actin and myosin through cross-bridges explains much of muscle behavior. However, some properties of muscle, such as residual force enhancement, cannot be explained by current cross-bridge models. There is ongoing debate whether conceptual cross-bridge models, as pioneered by Huxley (A.F. Huxley, Muscle structure and theories of contraction, Prog. Biophys. Biophys. Chem. 7 (1957) 255) could, if suitably modified, fit experimental data showing residual force enhancement. Here we prove that there are only two ways to explain residual force enhancement with these ‘traditional’ cross-bridge models: the first requires cross-bridges to become stuck on actin (the stuck cross-bridge model) while the second requires that cross-bridges that are pulled off beyond a critical strain enter a ‘new’ unbound state that leads to a new force-producing cycle (the multi-cycle model). Stuck cross-bridge models cannot fit the velocity and stretch amplitude dependence of residual force enhancement, while the multi-cycle models can. The results of this theoretical analysis demonstrate that current kinetic models of cross-bridge action cannot explain the experimentally observed residual force enhancement. Either cross-bridges in the force-enhanced state follow a different kinetic cycle than cross-bridges in a ‘normal’ force state, or the assumptions underlying traditional cross-bridge models must be violated during experiments that show residual force enhancement.     

Estimating the length of actomyosin cross-bridge contraction

In the work by Yanagida et al. (1985) the distance was measured by which the myosin cross-bridge moved along the actin filament during one cycle of ATP hydrolysis. This distance, in the opinion of the authors, must be equal to the length of the cross-bridge power stroke. However the measured distance (60 divided by 68 nm) was considerably greater than the cross-bridge power stroke measured earlier by other methods. In the present paper it is shown on the basis of the kinetic theory of muscle contraction of V. I. Deshcherevsky that the distance, the cross-bridge passed during one cycle of ATP hydrolysis must be nearly 5 times greater than the cross-bridge power stroke. The estimation of the length of the cross-bridge power stroke from the Yanagida's et al. data on the basis of the kinetic model gives 12 divided by 14 nm which is in a good accordance with the results obtained earlier.     

Myosin cross-bridge kinetics and the mechanism of catch

Catch force in molluscan smooth muscle requires little, if any, energy input and is controlled by the phosphorylation state of the thick filament-associated mini-titin, twitchin. The kinetic parameters of myosin cross-bridge turnover in permeabilized catch muscle, and how they are potentially modified by the catch mechanism, were determined by single turnover measurements on myosin-bound ADP. Under isometric conditions, there are fast and slow components of cross-bridge turnover that probably result from kinetic separation of calcium-bound and calcium-free cross-bridge pools. The structure responsible for catch force maintenance at intermediate [Ca+2] does not alter the processes responsible for the fast and slow components under isometric conditions. Also, there is no measurable turnover of myosin-bound ADP during relaxation of catch force by phosphorylation of twitchin at pCa > 8. The only effects of the catch link on myosin-bound ADP turnover are 1), a small, very slow extra turnover when catch force is maintained at very low [Ca+2] (pCa > 8); and 2), attenuation of the shortening-induced increase in turnover at subsaturating [Ca(+2)]. These limited interactions between the catch link and myosin cross-bridge turnover are consistent with the idea that catch force is maintained by a thick and thin filament linkage other than the myosin cross-bridge.     

Cardioprotection with kappa-opioid receptor stimulation is associated with a slowing of cross-bridge cycling

Opioid and alpha-adrenergic receptor activation protect the heart from ischemic damage. One possible intracellular mechanism to explain this is that an improvement in ATP availability contributes to cardioprotection. We tested this hypothesis by correlating postischemic left ventricular developed pressure (LVDP) and myofibrillar Ca(2+)-dependent actomyosin Mg(2+)-ATPase from isolated rat hearts treated with the kappa-opioid receptor agonist U-50488H (1 microM) or the alpha-adrenergic receptor agonist phenylephrine (10 microM) + propranolol (3 microM). Preischemic treatment with U-50488H or phenylephrine + propranolol improved postischemic LVDP recovery by 25-30% over control hearts. Ca(2+)-dependent actomyosin Mg(2+)-ATPase was found to be 20% lower in both U-50488H- and phenylephrine + propranolol-treated hearts compared with control hearts. The kappa-opioid receptor antagonist nor-binaltorphimine (1 microM) abolished the effects of U-50488H on postischemic LVDP and actomyosin Mg(2+)-ATPase activity. Reduced actomyosin ATP utilization was also suggested in single ventricular myocytes treated with either U-50488H or the protein kinase C activator, phorbol 12-myristate 13-acetate (PMA), because U-50488H and PMA lowered maximum velocity of unloaded shortening by 15-25% in myocytes. U-50488H and phenylephrine + propranolol treatment both resulted in increased phosphorylation of troponin I and C protein. These findings are consistent with the hypothesis that kappa-opioid and alpha-adrenergic receptors decrease actin-myosin cycling rate, leading to a conservation of ATP and cardioprotection during ischemia.     

A multisegmental cross-bridge kinetics model of the myofibril

Striated muscle is a mechanical system that develops force and generates power in serving vital activities in the body. Striated muscle is a complex biological system; a single mammalian muscle fibre contains up to hundred or even more myofibrils in parallel connected via an inter-myofibril filament network. In one single myofibril thousands of sarcomeres are lined up as a series of linear motors. We recently demonstrated that half-sarcomeres (hS) in a single myofibril operate non-uniformly. We outline a mathematical framework based on cross-bridge kinetics for the simulation of the force response and length change of individual hS in a myofibril. The model describes the muscle myofibril in contraction experiments under various conditions. The myofibril is modeled as a multisegmental mechanical system of hS models, which have active and viscoelastic properties. In the first approach, a two-state cross-bridge formalism relates the hS force to the chemical kinetics of ATP hydrolysis, as first described by Huxley [1957. Muscle structure and theories of contraction. Prog. Biophys. Mol. Biol. 7, 255-318]. Two possible types of biological variability are introduced and modeled. Numerical simulations of a myofibril composed of four to eight hS show a non-uniform hS length distribution and complex internal dynamics upon activation. We demonstrate that the steady-state approximation holds only in restricted time zones during activation. Simulations of myofibril contraction experiments that reproduce the classic steady-state force-length and force-velocity relationships, strictly constrained or “clamped” in either end-held isometric or isotonic contraction conditions, reveal a small but conspicuous effect of hS dynamics on force.     

Evidence for increased low force cross-bridge population in shortening skinned skeletal muscle fibers: implications for actomyosin kinetics.

The dynamic characteristics of the low force myosin cross-bridges were determined in fully calcium-activated skinned rabbit psoas muscle fibers shortening under constant loads (0.04-0.7 x full isometric tension Po). The shortening was interrupted at various times by a ramp stretch (duration, 10 ms; amplitude, up to 1.8% fiber length) and the resulting tension response was recorded. Except for the earlier period of velocity transients, the tension response showed nonlinear dependence on stretch amplitude; i.e., the magnitude of the tension response started to rise disproportionately as the stretch exceeded a critical amplitude, as in the presence of inorganic phosphate (Pi). This result, as well as the result of stiffness measurement, suggests that the low force cross-bridges similar to those observed in the presence of Pi (presumably A.M.ADP.Pi) are significantly populated during shortening. The critical amplitude of the shortening fibers was greater than that of isometrically contracting fibers, suggesting that the low force cross-bridges are more negatively strained during shortening. As the load was reduced from 0.3 to 0.04 P0, the shortening velocity increased more than twofold, but the amount of the negative strain stayed remarkably constant (approximately 3 nm). This This insensitiveness of the negative strain to velocity is best explained if the dissociation of the low force cross-bridges is accelerated approximately in proportion to velocity. Along with previous reports, the results suggest that the actomyosin ATPase cycle in muscle fibers has at least two key reaction steps in which rate constants are sensitively regulated by shortening velocity and that one of them is the dissociation of the low force A.M.ADP.Pi cross-bridges. This step may virtually limit the rate of actomyosin ATPase turnover and help increase efficiency in fibers shortening at high velocities.     

Concentration dependence of alpha-synuclein fibril length assessed by quantitative atomic force microscopy and statistical-mechanical theory

The initial concentration of monomeric amyloidogenic proteins is a crucial factor in the in vitro formation of amyloid fibrils. We use quantitative atomic force microscopy to study the effect of the initial concentration of human α-synuclein on the mean length of mature α-synuclein fibrils, which are associated with Parkinson's disease. We determine that the critical initial concentration, below which low-molecular-weight species dominate and above which fibrils are the dominant species, lies at ∼15 μM, in good agreement with earlier measurements using biochemical methods. In the concentration regime where fibrils dominate, we find that their mean length increases with initial concentration. These results correspond well to the qualitative predictions of a recent statistical-mechanical model of amyloid fibril formation. In addition, good quantitative agreement of the statistical-mechanical model with the measured mean fibril length as a function of initial protein concentration, as well as with the fibril length distributions for several protein concentrations, is found for reasonable values of the relevant model parameters. The comparison between theory and experiment yields, for the first time to our knowledge, an estimate of the magnitude of the free energies associated with the intermolecular interactions that govern α-synuclein fibril formation.     

Troponin T isoforms modulate calcium dependence of the kinetics of the cross-bridge cycle: studies using a transgenic mouse line

Alternative splicing of troponin T (TnT) in striated muscle during development results in expression of different isoforms, with the splicing of a 5(') exon of TnT resulting in the expression of low-molecular-weight basic adult TnT isoforms and high-molecular-weight acidic embryonic TnT isoforms. Although other differences exist, the main differences between cardiac TnT (cTnT) and fast skeletal muscle TnT (fTnT) are in the NH(2) terminus, with fTnT being less acidic than cTnT. A transgenic mouse line expressing chicken fTnT in the heart was used to investigate the functional significance of TnT NH(2)-terminal charge differences on cardiac muscle contractility. The rates of force redevelopment (k(tr)) at four levels of Ca(2+) activation were recorded for skinned left ventricular trabeculae from control and transgenic mice. The k(tr) vs Ca(2+) relationship was different in control mice and transgenic mice, suggesting that the structure of TnT, and possibly the NH(2)-terminal region, is involved in determining the kinetics of cross-bridge cycle. These results suggest that isoform shifts in TnT may be an important molecular mechanism for determining the Ca(2+) dependence of cardiac muscle contractility.     

The length dependence of muscle active force: considerations for parallel elastic properties.

The purpose of this study was to choose between two popular models of skeletal muscle: one with the parallel elastic component in parallel with both the contractile element and the series elastic component (model A), and the other in which it is in parallel with only the contractile element (model B). Passive and total forces were obtained at a variety of muscle lengths for the medial gastrocnemius muscle in anesthetized rats. Passive force was measured before the contraction (passive A) or was estimated for the fascicle length at which peak total force occurred (passive B). Fascicle length was measured with sonomicrometry. Active force was calculated by subtracting passive (A or B) force from peak total force at each fascicle or muscle length. Optimal length, that fascicle length at which active force is maximized, was 13.1 +/- 1.2 mm when passive A was subtracted and 14.0 +/- 1.1 mm with passive B (P < 0.01). Furthermore, the relationship between double-pulse contraction force and length was broader when calculated with passive B than with passive A. When the muscle was held at a long length, passive force decreased due to stress relaxation. This was accompanied by no change in fascicle length at the peak of the contraction and only a small corresponding decrease in peak total force. There is no explanation for the apparent increase in active force that would be obtained when subtracting passive A from the peak total force. Therefore, to calculate active force, it is appropriate to subtract passive force measured at the fascicle length corresponding to the length at which peak total force occurs, rather than passive force measured at the length at which the contraction begins.     

Rapid transient analysis of myosin cross-bridge kinetics in hypertrophied hearts

Essential hypertension, with pressure overload leading to left ventricular hypertrophy, often results in coronary artery disease and congestive heart failure. The spontaneously hypertensive rat (SHR) is an attractive model for studying the effects of long-term antihypertensive therapy on the contractile properties of the myocardium. In this study we investigated differences in mechanical and biochemical characteristics of papillary muscles from SHR and normal (Wistar-Kyoto [WKY]) rats as a function of age and treatment. We found that the rate of delayed force redevelopment after rapid stretch was less in SHR than in WKY in every age group studied, even at 2 wk of age, before hypertension was evident in the SHR. In the treated SHR, blood pressure was lower, hypertrophy was reduced and the rate of delayed force redevelopment was increased compared with the untreated SHR. Finally, the pattern of myosin isoenzymes was different in treated than in untreated SHR, being shifted to more of the fast V1 and less of the slow V3 isomyosin. We conclude that long-term antihypertensive therapy not only prevents the development of left ventricular hypertrophy, but may do so by preventing the shift in myosin isoenzyme pattern normally found in hearts subjected to a long-term pressure overload.     

Effect of cross-bridge kinetics on apparent Ca2+ sensitivity

Three different ways of shifting the pCa/tension curve on the pCa axis have been studied and related to changes in the rate constants of the cross-bridge cycle. The curve midpoint shifts to higher pCa's when the substrate (Mg-ATP) is reduced from 5 to 0.25 mM, when the phosphate concentration is reduced from 7.5 mM to 0, and when the ionic strength is reduced from 0.200 to 0.120. The Hill coefficients of the pCa/tension curve in our standard saline (5 mM substrate, 5 mM free ATP, 7.5 mM phosphate, ionic strength 0.200, 15 degree C) are between 5.1 and 5.6 and fall to 3.0 with the left shift of the curve brought about by reducing both substrate and phosphate. Left shifts of the curve produced by reduction in the ionic strength do not result ina lower Hill coefficient. Reducing eigher substrate or phosphate is associated with a reduction in the optimal frequency for oscillatory work, but reduction in ionic strength is not so associated. Maximum tension increases with the left shift of the curve brought about by reducing phosphate concentration or ionic strength, but tension decreases with the left shift of the curve accompanying substrate concentration reduction in phosphate-free saline. We argue that one mechanism for the observed shift of the curve along the pCa axis is the relationship between the time a cross-bridge takes to complete a cycle and the time Ca2+ stays bound to troponin C (TnC). If the cycle rate is decreased, a smaller fraction to TnC sites must be occupied to keep a given fraction of cross-bridges active. To illustrate this concept, we present a simplified model of the cross-bridge cycle incorporating the kinetics of Ca binding to TnC.     

Isometric force redevelopment of skinned muscle fibers from rabbit activated with and without Ca2+.

Fiber isometric tension redevelopment rate (kTR) was measured during submaximal and maximal activations in glycerinated fibers from rabbit psoas muscle. In fibers either containing endogenous skeletal troponin C (sTnC) or reconstituted with either purified cardiac troponin C (cTnC) or sTnC, graded activation was achieved by varying [Ca2+]. Some fibers were first partially, then fully, reconstituted with a modified form of cTnC (aTnC) that enables active force generation and shortening in the absence of Ca2+. kTR was derived from the half-time of tension redevelopment. In control fibers with endogenous sTnC, kTR increased nonlinearly with [Ca2+], and maximal kTR was 15.3 +/- 3.6 s-1 (mean +/- SD; n = 26 determinations on 25 fibers) at pCa 4.0. During submaximal activations by Ca2+, kTR in cTnC reconstituted fibers was approximately threefold faster than control, despite the lower (60%) maximum Ca(2+)-activated force after reconstitution. To obtain submaximal force with aTnC, eight fibers were treated to fully extract endogenous sTnC, then reconstituted with a mixture of a TnC and cTnC (aTnC:cTnC molar ratio 1:8.5). A second extraction selectively removed cTnC. In such fibers containing aTnC only, neither force nor kTR was affected by changes in [Ca2+]. Force was 22 +/- 7% of maximum control (mean +/- SD; n = 15) at pCa 9.2 vs. 24 +/- 8% (mean +/- SD; n = 8) at pCa 4.0, whereas kTR was 98 +/- 14% of maximum control (mean +/- SD; n = 15) at pCa 9.2 vs. 96 +/- 15% (mean +/- SD; n = 8) at pCa 4.0.(ABSTRACT TRUNCATED AT 250 WORDS)