Muscle cross-bridge kinetics in rigor and in the presence of ATP analogues.

Recently we reported preliminary mechanical experiments on freshly skinned rabbit psoas fibers that suggested that while almost all of the cross-bridges are attached to actin in the presence of 4 mM adenyl-5'-yl-imidodiphosphate (AMP-PNP) (ionic strength, 0.13 M), there is an equilibrium between the attached and detached states, so that, in the presence of 4 mM AMP-PNP, fibers should not be able to maintain tension (Schoenberg, et al., 1984, in Contractile Mechanisms in Muscle, Pollack and Sugi, editors., Plenum Publishing Corp., NY). Since this suggestion was at variance with published results of Clarke and Tregear (1982, FEBS [Fed. Eur. Biochem. Soc.] Lett, 143:217), we reinvestigated the ability of rabbit psoas fibers to support tension following a 2-nm stretch in rigor and in the presence of the nucleotide analogues, PPi and AMP-PNP, for analogue concentrations ranging from 0.25 to 4 mM. We find that, whereas in rigor there is very little tension decay following a stretch, in 4 mM nucleotide analogue solution, the force generated by stretch quickly decays to zero. The force decay is not exponential; rather, it can be described by rate constants that range from approximately 0.1 to 100 s-1 in 4 mM PPi, and 0.01 to 10 s-1 in 4 mM AMP-PNP. This large range of decay rate constants may be partially related to the dependence of either analogue binding or cross-bridge dissociation upon strain, since we find that the rate constants for force decay decrease with decreasing size of stretch or with decrease of analogue concentration below the maximum studied (4 mM).(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

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.     

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 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.     

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.     

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.     

Muscle contraction: a mechanism of energy transduction

A mechanism of muscle contraction is presented in which energy from the hydrolysis of MgATP is transferred directly to conformational strain in a flexible segment of the myosin head. That segment is proximal to both the active site and the subfragment 1—subfragment 2 hinge (the portion of the myosin molecule that connects each of its two enzymatically active globular heads to the long thin helical body). This proximity allows configurational changes at the active site, which are an intrinsic part of the enzymatic mechanism, to impose a localized strain, or distortion, near the hinge. The energy, trapped in the protein this way, is subsequently used for mechanical work when other enzymatically-induced conformational changes free the strained segment of the myosin head to unbend. As this happens, the head rotates and the distal end (opposite the hinge) attaches to the actin filament and pulls on it. In this mechanism, actin interacts with myosin in two different ways: (1) at the active site where it activates a step in the hydrolysis of MgATP that frees the head to rotate; (2) at the distal end of myosin, where it forms the grip through which the rotating head pulls on the actin filament. The first interaction allows actin to initiate primary movement of the myosin head; the second directs the force and allows the movement of the head to be used for the sliding motion of the actin and myosin filaments during contraction. In this model, there are also two different energy transfers: one occurs in the transduction process itself when energy from hydrolysis is trapped as conformational distortion in the hinge region; the other occurs, reversibly, when actin and myosin form and then break the distal grip; in this second transfer there is no net energy change in the course of a cycle. A chemical mechanism is suggested to explain actin-activation of hydrolysis at the active site-hinge region.     

Muscle contraction: viscous-like frictional forces and the impulsive model

The thermal denaturation of yeast enolase 1 was studied by differential scanning calorimetry (DSC) under conditions of subunit association/dissociation, enzymatic activity or substrate binding without turnover and substrate analogue binding. Subunit association stabilizes the enzyme, that is, the enzyme dissociates before denaturing. The conformational change produced by conformational metal ion binding increases thermal stability by reducing subunit dissociation. 'Substrate' or analogue binding additionally stabilizes the enzyme, irrespective of whether turnover is occurring, perhaps in part by the same mechanism. More strongly bound metal ions also stabilize the enzyme more, which we interpret as consistent with metal ion loss before denaturation, though possibly the denaturation pathway is different in the absence of metal ion. We suggest that some of the stabilization by 'substrate' and analogue binding is owing to the closure of moveable polypeptide loops about the active site, producing a more 'closed' and hence thermostable conformation.     

Muscle contraction: viscous-like frictional forces and the impulsive model

Apart from a few experimental studies muscle viscosity has not received much recent analytical attention as a determinant of the contractile process. This is surprising, since any muscle cell is 80% water, and may undergo large shape changes during its working cycle. Intuitively one might expect the viscosity of the solvent to be an important determinant of the physiological activity of muscle tissue. This was apparent to pioneers of the study of muscle contraction such as Hill and his contemporaries, whose putative theoretical formulations contained terms related to muscle viscosity. More recently, though, a hydrodynamic calculation by Huxley, using a solvent viscosity close to that of water, has been held to demonstrate that viscous forces are negligible in muscle contraction. We have re-examined the role of viscosity in contraction, postulating impulsive acto-myosin forces that are opposed by a viscous resistance between the filaments. The viscous force required, 10⁴ times the hydrodynamic estimate, is close to recent experimental measurements, themselves 10²–10³ times the hydrodynamic estimate. This also agrees with contemporary measurements of cytoplasmic viscosity in other biological cells using magnetic bead micro-rheometry. These are several orders of magnitude greater than the viscosity of water. In the course of the analysis we have derived the force-velocity equation for an isolated half-sarcomere containing a single actin filament for the first time, and from first principles. We conclude that muscle viscosity is indeed important for the contractile process, and that it has been too readily discounted.     

The force exerted by a muscle cross-bridge depends directly on the strength of the actomyosin bond

Myosin produces force in a cyclic interaction, which involves alternate tight binding to actin and to ATP. We have investigated the energetics associated with force production by measuring the force generated by skinned muscle fibers as the strength of the actomyosin bond is changed. We varied the strength of the actomyosin bond by addition of a polymer that promotes protein-protein association or by changing temperature or ionic strength. We estimated the free energy available to generate force by measuring isometric tension, as the free energy of the states that precede the working stroke are lowered with increasing phosphate. We found that the free energy available to generate force and the force per attached cross-bridge at low [Pi] were both proportional to the free energy available from the formation of the actomyosin bond. We conclude that the formation of the actomyosin bond is involved in providing the free energy driving the production of isometric tension and mechanical work. Because the binding of myosin to actin is an endothermic, entropically driven reaction, work must be performed by a "thermal ratchet" in which a thermal fluctuation in Brownian motion is captured by formation of the actomyosin bond.     

Wnt pathway activation: new relations and locations

Recent advances in the Wnt signaling field reveal new components, such as a G protein and an atypical receptor tyrosine kinase, and novel connections between known components. In addition, different subcellular localization of receptors may help to explain distinctions between canonical and noncanonical Wnt pathway activity.     

Cardiac length dependence of force and force redevelopment kinetics with altered cross-bridge cycling

We examined the influence of cross-bridge cycling kinetics on the length dependence of steady-state force and the rate of force redevelopment (k(tr)) during Ca(2+)-activation at sarcomere lengths (SL) of 2.0 and 2.3 microm in skinned rat cardiac trabeculae. Cross-bridge kinetics were altered by either replacing ATP with 2-deoxy-ATP (dATP) or by reducing [ATP]. At each SL dATP increased maximal force (F(max)) and Ca(2+)-sensitivity of force (pCa(50)) and reduced the cooperativity (n(H)) of force-pCa relations, whereas reducing [ATP] to 0.5 mM (low ATP) increased pCa(50) and n(H) without changing F(max). The difference in pCa(50) between SL 2.0 and 2.3 microm (Delta pCa(50)) was comparable between ATP and dATP, but reduced with low ATP. Maximal k(tr) was elevated by dATP and reduced by low ATP. Ca(2+)-sensitivity of k(tr) increased with both dATP and low ATP and was unaffected by altered SL under all conditions. Significantly, at equivalent levels of submaximal force k(tr) was faster at short SL or increased lattice spacing. These data demonstrate that the SL dependence of force depends on cross-bridge kinetics and that the increase of force upon SL extension occurs without increasing the rate of transitions between nonforce and force-generating cross-bridge states, suggesting SL or lattice spacing may modulate preforce cross-bridge transitions.     

Force enhancement without changes in cross-bridge turnover kinetics: the effect of EMD 57033.

The thiadiazinon derivative EMD 57033 has been found previously in cardiac muscle to increase isometric force generation without a proportional increase in fiber ATPase, thus causing a reduction in tension cost. To analyze the mechanism by which EMD 57033 affects the contractile system, we studied its effects on isometric force, isometric fiber ATPase, the rate constant of force redevelopment (k(redev)), active fiber stiffness, and its effect on Fo, which is the force contribution of a cross-bridge in the force-generating states. We used chemically skinned fibers of the rabbit psoas muscle. It was found that with 50 microM EMD 57033, isometric force increases by more than 50%, whereas Kredev, active stiffness, and isometric fiber ATPase increase by at most 10%. The results show that EMD 57033 causes no changes in cross-bridge turnover kinetics and no changes in active fiber stiffness that would result in a large enough increase in occupancy of the force-generating states to account for the increase in active force. However, plots of force versus length change recorded during stretches and releases (T plots) indicate that in the presence of EMD 57033 the y(o) value (x axis intercept) for the cross-bridges becomes more negative while its absolute value increases. This might suggest a larger cross-bridge strain as the basis for increased active force. Analysis of T plots with and without EMD 57033 shows that the increase in cross-bridge strain is not due to a redistribution of cross-bridges among different force-generating states favoring states of larger strain. Instead, it reflects an increased cross-bridge strain in the main force-generating state. The direct effect of EMD 57033 on the force contribution of cross-bridges in the force-generating states represents an alternative mechanism for a positive inotropic intervention.     

Effects of MgATP and MgADP on the cross-bridge kinetics of rabbit soleus slow-twitch muscle fibers.

The elementary steps surrounding the nucleotide binding step in the cross-bridge cycle were investigated with sinusoidal analysis in rabbit soleus slow-twitch muscle fibers. The single-fiber preparations were activated at pCa 4.40, ionic strength 180 mM, 20 degrees C, and the effects of MgATP (S) and MgADP (D) concentrations on three exponential processes B, C, and D were studied. Our results demonstrate that all apparent (measured) rate constants increased and saturated hyperbolically as the MgATP concentration was increased. These results are consistent with the following cross-bridge scheme: [cross-bridge scheme: see text] where A = actin, M = myosin, S = MgATP, and D = MgADP. AM+S is a collision complex, and AM*S is its isomerized form. From our studies, we obtained K0 = 18 +/- 4 mM-1 (MgADP association constant, N = 7, average +/- sem), K1a = 1.2 +/- 0.3 mM-1 (MgATP association constant, N = 8 hereafter), k1b = 90 +/- 20 s-1 (rate constant of ATP isomerization), k-1b = 100 +/- 9 s-1 (rate constant of reverse isomerization), K1b = 1.0 +/- 0.2 (equilibrium constant of isomerization), k2 = 21 +/- 3 s-1 (rate constant of cross-bridge detachment), k-2 = 14.1 +/- 1.0 s-1 (rate constant of reversal of detachment), and K2 = 1.6 +/- 0.3 (equilibrium constant of detachment). K0 is 8 times and K1a is 2.2 times those in rabbit psoas, indicating that nucleotides bind to cross-bridges more tightly in soleus slow-twitch muscle fibers than in psoas fast-twitch muscle fibers. These results indicate that cross-bridges of slow-twitch fibers are more resistant to ATP depletion than those of fast-twitch fibers. The rate constants of ATP isomerization and cross-bridge detachment steps are, in general, one-tenth to one-thirtieth of those in psoas.