Kinetic and thermodynamic studies of the cross-bridge cycle in rabbit psoas muscle fibers.

The effect of temperature on elementary steps of the cross-bridge cycle was investigated with sinusoidal analysis technique in skinned rabbit psoas fibers. We studied the effect of MgATP on exponential process (C) to characterize the MgATP binding step and cross-bridge detachment step at six different temperatures in the range 5-30 degrees C. Similarly, we studied the effect of MgADP on exponential process (C) to characterize the MgADP binding step. We also studied the effect of phosphate (Pi) on exponential process (B) to characterize the force generation step and Pi-release step. From the results of these studies, we deduced the temperature dependence of the kinetic constants of the elementary steps and their thermodynamic properties. We found that the MgADP association constant (K0) and the MgATP association constant (K1) significantly decreased when the temperature was increased from 5 to 20 degrees C, implying that nucleotide binding became weaker at higher temperatures. K0 and K1 did not change much in the 20-30 degree C range. The association constant of Pi to cross-bridges (K5) did not change much with temperature. We found that Q10 for the cross-bridge detachment step (k2) was 2.6, and for its reversal step (k-2) was 3.0. We found that Q10 for the force generation step (Pi-isomerization step, k4) was 6.8, and its reversal step (k-4) was 1.6. The equilibrium constant of the detachment step (K2) was not affected much by temperature, whereas the equilibrium constant of the force generation step (K4) increased significantly with temperature increase. Thus, the force generation step consists of an endothermic reaction. The rate constant of the rate-limiting step (k6) did not change much with temperature, whereas the ATP hydrolysis rate increased significantly with temperature increase. We found that the force generation step accompanies a large entropy increase and a small free energy change; hence, this step is an entropy-driven reaction. These observations are consistent with the hypothesis that the hydrophobic interaction between residues of actin and myosin underlies the mechanism of force generation. We conclude that the force generation step is the most temperature-sensitive step among elementary steps of the cross-bridge cycle, which explains increased isometric tension at high temperatures in rabbit psoas fibers.     

The effect of the lattice spacing change on cross-bridge kinetics in chemically skinned rabbit psoas muscle fibers. II. Elementary steps affected by the spacing change.

The actin-myosin lattice spacing of rabbit psoas fibers was osmotically compressed with a dextran T-500, and its effect on the elementary steps of the cross-bridge cycle was investigated. Experiments were performed at the saturating Ca (pCa 4.5-4.9), 200 mM ionic strength, pH 7.0, and at 20 degrees C, and the results were analyzed by the following cross-bridge scheme: [formula: see text] where A = actin, M = myosin head, S = MgATP, D = MgADP, and P = Pi = phosphate. From MgATP and MgADP studies on exponential process (C) and (D), the association constants of cross-bridges to MgADP (K0), MgATP (K1a), the rate constants of the isomerization of the AM S state (k1b and k-1b), and the rate constants of the cross-bridge detachment step (k2 and k-2) were deduced. From Pi study on process (B), the rate constants of the cross-bridge attachment (power stroke) step (k4- and k-4) and the association constant of Pi ions to cross-bridges (K5) were deduced. From ATP hydrolysis measurement, the rate constant of ADP-isomerization (rate-limiting) step (k6) was deduced. These kinetic constants were studied as functions of dextran concentrations. Our results show that nucleotide binding, the ATP-isomerization, and the cross-bridge detachment steps are minimally affected by the compression. The rate constant of the reverse power stroke step (k-4) decreases with mild compression (0-6.3% dextran), presumably because of the stabilization of the attached cross-bridges in the AM*DP state. The rate constant of the power stroke step (k4) does not change with mild compression, but it decreases with higher compression (> 6.3% dextran), presumably because of an increased difficulty in performing the power stroke. These results are consistent with the observation that isometric tension increases with a low level of compression and decreases with a high level of compression. Our results also show that the association constant K5 of Pi with cross-bridge state AM*D is not changed with compression. Our result further show that the ATP hydrolysis rate decreased with compression, and that the rate constants of the ADP-isomerization step (k6) becomes progressively less with compression. The effect of compression on the power stroke step and rate-limiting step implies that a large-scale molecular rearrangement in the myosin head takes place in these two slow reaction steps.     

Cross-bridge scheme and force per cross-bridge state in skinned rabbit psoas muscle fibers.

The rate and association constants (kinetic constants) which comprise a seven state cross-bridge scheme were deduced by sinusoidal analysis in chemically skinned rabbit psoas muscle fibers at 20 degrees C, 200 mM ionic strength, and during maximal Ca2+ activation (pCa 4.54-4.82). The kinetic constants were then used to calculate the steady state probability of cross-bridges in each state as the function of MgATP, MgADP, and phosphate (Pi) concentrations. This calculation showed that 72% of available cross-bridges were (strongly) attached during our control activation (5 mM MgATP, 8 mM Pi), which agreed approximately with the stiffness ratio (active:rigor, 69 +/- 3%); active stiffness was measured during the control activation, and rigor stiffness after an induction of the rigor state. By assuming that isometric tension is a linear combination of probabilities of cross-bridges in each state, and by measuring tension as the function of MgATP, MgADP, and Pi concentrations, we deduced the force associated with each cross-bridge state. Data from the osmotic compression of muscle fibers by dextran T500 were used to deduce the force associated with one of the cross-bridge states. Our results show that force is highest in the AM*ADP.Pi state (A = actin, M = myosin). Since the state which leads into the AM*ADP.Pi state is the weakly attached AM.ADP.Pi state, we confirm that the force development occurs on Pi isomerization (AM.ADP.Pi --> AM*ADP.Pi). Our results also show that a minimal force change occurs with the release of Pi or MgADP, and that force declines gradually with ADP isomerization (AM*ADP -->AM.ADP), ATP isomerization (AM+ATP-->AM*ATP), and with cross-bridge detachment. Force of the AM state agreed well with force measured after induction of the rigor state, indicating that the AM state is a close approximation of the rigor state. The stiffness results obtained as functions of MgATP, MgADP, and Pi concentrations were generally consistent with the cross-bridge scheme.     

Modulation of cross-bridge affinity for MgGTP by Ca2+ in skinned fibers of rabbit psoas muscle.

Previously we reported that saturation of cross-bridges with MgATP gamma S in skinned muscle fibers was calcium sensitive. In the present study we investigate whether this observation can be generalized to other nucleotides by studying saturation of cross-bridges with MgGTP. In solution, myosin-subfragment 1 (S1) in the presence of 10 mM MgGTP was found to bind to actin with low affinity, similar to that in the presence of MgATP and MgATP gamma S. In EGTA buffer, the equatorial x-ray diffraction intensity ratio I11/I10 recorded in single skinned fibers decreased upon increasing MgGTP concentration from 0 to 10 mM (1 degree C and 170 mM ionic strength). The I11/I10 ratio leveled off at 10 mM MgGTP, indicating full saturation of cross-bridges with the nucleotide. Under these conditions, the value of I11/I10 is indistinguishable from that obtained in the presence of saturating [MgATP]. In CaEGTA buffer, however, the decrease in I11/I10 occurs over a wider range of concentrations, and there is no indication of I11/I10 leveling off at 10 mM MgGTP, suggesting that full saturation is not reached. The Ca2+ dependence of GTP binding appears to be a direct consequence of the differences in the affinities of the strongly bound cross-bridges to actin versus weakly bound cross-bridges to actin. A biochemical scheme that could qualitatively explain the titration behavior of ATP gamma S and GTP is presented.     

The effect of pyrophosphate on the rigor fibers of rabbit m. psoas fibers

The effect of MgPPi on the rigor force of glycerinated fibres in the range of ionic strength 75-250 mM at two temperatures 18 degrees and 5 degrees C was studied. At 18 degrees C the maximum of this effect was above the range of average ionic strength. At 5 degrees C the greatest effect of MgPPi was observed at low ionic strength.     

The effect of lattice spacing change on cross-bridge kinetics in chemically skinned rabbit psoas muscle fibers. I. Proportionality between the lattice spacing and the fiber width.

Chemically skinned rabbit psoas muscle fibers/bundles were osmotically compressed with a macromolecule dextran T-500 (0-16%, g/100 ml) at 20 degrees C, 200 mM ionic strength, and pH 7.0. The lattice spacing of psoas bundles was measured by equatorial x-ray diffraction studies during relaxation and after rigor induction, and the results were compared with the fiber width measurements by optical microscopy. The purpose of the present study is to determine whether fiber width is a reliable measure of the lattice spacing, and to determine the available spacing for myosin cross-bridges between the thick and thin filaments. We observed that both the lattice spacing and the fiber width decreased with an increase in the dextran concentration during relaxation or after rigor induction, and that the spacing and the fiber width were proportionately related. We further observed that, in the absence of dextran, the lattice spacing (and the fiber width) shrank on a relax-to-rigor transition, whereas in the presence of 16% dextran, the spacing expanded on a relax-to-rigor transition. The cross-over of these plots occurred at the 4-7% dextran concentration. During Ca activation, the fiber width shrank in the absence of dextran, and it slightly expanded in the presence of 14.4% dextran. The degree of expansion was not as large as in the relax-to-rigor transition, and the cross-over occurred at about 11% dextran concentration. We also carried out experiments with dextran T-40 and T-10 to determine the upper limit of the molecular weight that enters the lattice space. We found that the upper limit is about 20 kD.     

Ca2+-sensitive cross-bridge dissociation in the presence of magnesium pyrophosphate in skinned rabbit psoas fibers.

We find that at 6 degrees C in the presence of 4 mM MgPPi, at low or moderate ionic strength, skinned rabbit psoas fibers exhibit a stiffness and an equatorial x-ray diffraction pattern similar to that of rigor fibers. As the ionic strength is increased in the absence of Ca2+, both the stiffness and the equatorial x-ray diffraction pattern approach those of the relaxed state. This suggests that, as in solution, increasing ionic strength weakens the affinity of myosin cross-bridges for actin, which results in a decrease in the number of cross-bridges attached. The effect is Ca2+-sensitive. Assuming that stiffness is a measure of the number of cross-bridge heads attached, in the absence of Ca2+, the fraction of attached cross-bridge heads varies from approximately 75% to approximately 25% over an ionic strength range where ionic strength in solution weakens the binding constant for myosin subfragment-1 binding to unregulated actin by less than a factor of 3. Therefore, this phenomenon appears similar to the cooperative Ca2+-sensitive binding of S1 to regulated actin in solution (Greene, L. E., and E. Eisenberg, 1980, Proc. Natl. Acad. Sci. USA, 77:2616). By comparing the binding constants in solution and in the fiber under similar conditions, we find that the "effective actin concentration," that is, the concentration that gives the same fraction of S1 molecules bound to actin in solution as cross-bridge heads are bound to actin in a fiber, is in the millimolar range.(ABSTRACT TRUNCATED AT 250 WORDS)     

The effect of sarcomere length and stretching on the rate of ATP splitting in glycerinated rabbit psoas muscle fibers.

The effect of sarcomere length and stretching on the tension and the rate of ATP splitting was studied using small fiber bundles from glycerinated rabbit psoas muscle. The rate of ATP slitting was determined by measuring ADP production, while the tension development in response to a contracting solution (at pCa 5.3) was recorded in the same preparation. The isometric tension developed by the preparation decreased when the sarcomere length was increased. The decrease of tension development was accompanied by a decrease in the rate of ATP splitting. If a preparation exerting steady isometric tension was stretched by 5--10% at a velocity of 0.1 mm/s, the rate of ATP splitting was increased after stretching, while the steady isometric tension attained after stretching was also higher than the initial value. The extent of the excess ATP splitting caused by stretching decreased with increasing sarcomere length. These results suggest that the rate of the interaction cycle between actin and myosin molecules may increase as a result of stretching.     

Subsarcomeric distribution of calcium in demembranated fibers of rabbit psoas muscle.

Direct measurements were made of the Ca distribution within sarcomeres of glycerinated rabbit psoas muscle fibers in rigor using electron probe x-ray microanalysis. Both analogue raster analysis and digital x-ray imaging were used to quantitate the Ca distribution along thick and thin filaments as a function of the concentration of free Ca2+. Even when corrected for the estimated contribution of Ca bound to thick filaments, the Ca measured in the region of overlap between thick and thin filaments significantly exceeded the Ca in the I-band at subsaturating concentrations of free Ca2+. At saturating levels of free Ca2+, the excess Ca in the overlap region was diminished but still statistically significant. The data thus suggest that the formation of rigor linkages exerts multiple effects on the binding of Ca2+ to thin filaments in the overlap region by increasing the affinity of troponin C for Ca2+ and possibly by unmasking additional Ca2+ binding sites. The data also show that the cooperativity invested in the thin filaments is insufficient to permit the effects of rigor cross-bridge formation on Ca2+ binding to propagate far along the thin filaments into the I-band.     

Mechano-chemical properties of actomyosin-ADP complexes in rabbit psoas muscle fibers

The relaxing effect of vanadate on active contractile system is found to be completely absent from rigor skinned fibres with ADP even on their stretching up to the forces comparable with the active ones, though vanadate is likely to bind not very firmly with crossbridges not containing inorganic phosphate. Probable reasons of such distinction are considered. The complex actomyosin-ADP in the rigor fibres is supposed to have significantly lower free energy independently of its deformation than the one of the same composition in the active ones. Possible role of different actomyosin-ADP states in the mechanochemical cycle of crossbridge is discussed.     

Elementary steps of the cross-bridge cycle in fast-twitch fiber types from rabbit skeletal muscles

To understand the molecular mechanism underlying the diversity of mammalian skeletal muscle fibers, the elementary steps of the cross-bridge cycle were investigated in three fast-twitch fiber types from rabbit limb muscles. Skinned fibers were maximally Ca(2+)-activated at 20 degrees C and the effects of MgATP, phosphate (P, P(i)), and MgADP were studied on three exponential processes by sinusoidal analysis. The fiber types (IIA, IID, and IIB) were determined by analyzing the myosin heavy-chain isoforms after mechanical experiments using high-resolution SDS-PAGE. The results were consistent with the following cross-bridge scheme: where A is actin, M is myosin, D is MgADP, and S is MgATP. All states except for those in brackets are strongly bound states. All rate constants of elementary steps (k(2), 198-526 s(-1); k(-2), 51-328 s(-1); k(4), 13.6-143 s(-1); k(-4), 13.6-81 s(-1)) were progressively larger in the order of type IIA, type IID, and type IIB fibers. The rate constants of a transition from a weakly bound state to a strongly bound state (k(-2), k(4)) varied more among fiber types than their reversals (k(2), k(-4)). The equilibrium constants K(1) (MgATP affinity) and K(2) (=k(2)/k(-2), ATP isomerization) were progressively less in the order IIA, IID, and IIB. K(4) (=k(4)/k(-4), force generation) and K(5) (P(i) affinity) were larger in IIB than IIA and IID fibers. K(1) showed the largest variation indicating that the myosin head binds MgATP more tightly in the order IIA (8.7 mM(-1)), IID (4.9 mM(-1)), and IIB (0.84 mM(-1)). Similarly, the MgADP affinity (K(0)) was larger in type IID fibers than in type IIB fibers.     

Cardiac myosin binding protein C and its phosphorylation regulate multiple steps in the cross-bridge cycle of muscle contraction

Cardiac myosin binding protein C (c-MyBPC) is a thick filament protein that is expressed in cardiac sarcomeres and is known to interact with myosin and actin. While both structural and regulatory roles have been proposed for c-MyBPC, its true function is unclear; however, phosphorylation has been shown to be important. In this study, we investigate the effect of c-MyBPC and its phosphorylation on two key steps of the cross-bridge cycle using fast reaction kinetics. We show that unphosphorylated c-MyBPC complexed with myosin in 1:1 and 3:1 myosin:c-MyBPC stoichiometries regulates the binding of myosin to actin (K(D)) cooperatively (Hill coefficient, h) (K(D) = 16.44 ± 0.33 μM, and h = 9.24 ± 1.34; K(D) = 11.48 ± 0.75 μM, and h = 3.54 ± 0.67) and significantly decelerates the ATP-induced dissociation of myosin from actin (K(1)k(+2) values of 0.12 ± 0.01 and 0.22 ± 0.01 M(-1) s(-1), respectively, compared with a value of 0.42 ± 0.01 M(-1) s(-1) for myosin alone). Phosphorylation of c-MyBPC abolished the regulation of the association phase (K(1)k(+2) values of 0.32 ± 0.02 and 0.33 ± 0.01 M(-1) s(-1) at 1:1 and 3:1 myosin:c-MyBPC ratios, respectively) and also accelerated the dissociation of myosin from actin (K(1)k(+2) values of 0.23 ± 0.01 and 0.29 ± 0.01 M(-1) s(-1) at a 1:1 and 3:1 myosin:c-MyBPC ratios, respectively) relative to the dissociation of myosin from actin in the presence of unphosphorylated c-MyBPC. These results indicate a direct effect of c-MyBPC on cross-bridge kinetics that is independent of the thin filament that together with its phosphorylation provides a mechanism for fine-tuning cross-bridge behavior to match the contractile requirements of the heart.     

The cross-bridge cycle and skeletal muscle fatigue.

The functional correlates of fatigue observed in both animals and humans during exercise include a decline in peak force (P0), maximal velocity, and peak power. Establishing the extent to which these deleterious functional changes result from direct effects on the myofilaments is facilitated through understanding the molecular mechanisms of the cross-bridge cycle. With actin-myosin binding, the cross-bridge transitions from a weakly bound low-force state to a strongly bound high-force state. Low pH reduces the number of high-force cross bridges in fast fibers, and the force per cross bridge in both fast and slow fibers. The former is thought to involve a direct inhibition of the forward rate constant for transition to the strong cross-bridge state. In contrast, inorganic phosphate (Pi) is thought to reduce P0 by accelerating the reversal of this step. Both H+ and Pi decrease myofibrillar Ca2+ sensitivity. This effect is particularly important as the amplitude of the Ca2+ transient falls with fatigue. The inhibitory effects of low pH and high Pi on P0 are reduced as temperature increases from 10 to 30 degrees C. However, the H+-induced depression of peak power in the slow fiber type, and Pi inhibition of myofibrillar Ca2+ sensitivity in slow and fast fibers, are greater at high compared with low temperature. Thus the depressive effects of H+ and Pi at in vivo temperatures cannot easily be predicted from data collected below 25 degrees C. In vitro, reactive oxygen species reduce myofibrillar Ca2+ sensitivity; however, the importance of this mechanism during in vivo exercise is unknown.     

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.     

Role of MgATP and MgADP in the cross-bridge kinetics in chemically skinned rabbit psoas fibers. Study of a fast exponential process (C)

The role of the substrate (MgATP) and product (MgADP) molecules in cross-bridge kinetics is investigated by small amplitude length oscillations (peak to peak: 3 nm/cross-bridge) and by following amplitude change and phase shift in tension time courses. The range of discrete frequencies used for this investigation is 0.25-250 Hz, which corresponds to 0.6-600 ms in time domain. This report investigates the identity of the high frequency exponential advance (process C), which is equivalent to "phase 2" of step analysis. The experiments are performed in maximally activated (pCa 4.5-5.0) single fibers from chemically skinned rabbit psoas fibers at 20 degrees C and at the ionic strength 195 mM. The rate constant 2 pi c deduced from process (C) increases and saturates hyperbolically with an increase in MgATP concentration, whereas the same rate constant decreases monotonically with an increase in MgADP concentration. The effects of MgATP and MgADP are opposite in all respects we have studied. These observations are consistent with a cross-bridge scheme in which MgATP and MgADP are in rapid equilibria with rigorlike cross-bridges, and they compete for the substrate site on myosin heads. From our measurements, the association constants are found to be 1.4 mM-1 for MgATP and 2.8 mM-1 for MgADP. We further deduced that the composite second order rate constant of MgATP binding to cross-bridges and subsequent isomerization/dissociation reaction to be 0.57 x 10(6)M-1s-1.     

The effects of partial extraction of TnC upon the tension-pCa relationship in rabbit skinned skeletal muscle fibers

The activation of contraction in vertebrate skeletal muscle involves the binding of Ca2+ to low-affinity binding sites on the troponin C (TnC) subunit of the regulatory protein troponin. The present study is an investigation of possible cooperative interactions between adjacent functional groups, composed of seven actin monomers, one tropomyosin, and one troponin, along the same thin filament. Single skinned fibers were obtained from rabbit psoas muscles and were then placed in an experimental chamber containing relaxing solution maintained at 15 degrees C. Isometric tension was measured in solutions containing maximally and submaximally activating levels of free Ca2+ (a) in control fiber segments, (b) in the same segments after partial extraction of TnC, and finally (c) after recombination of TnC into the segments. The extraction was done at 11-13 degrees C in 20 mM Tris, 5 mM EDTA, pH 7.85 or 8.3, a procedure derived from that of Cox et al. (1981. Biochem. J. 195:205). Extraction of TnC was quantitated by sodium dodecyl sulfate-polyacrylamide gel electrophoresis of the control and experimental samples. Partial extraction of TnC resulted in reductions in tension during maximal Ca activation and in a shift of the relative tension-pCa (i.e., -log[Ca2+]) relationship to lower pCa's. The readdition of TnC to the extracted fiber segments resulted in a recovery of tension to near-control levels and in the return of the tension-pCa relation to its original position. On the basis of these findings, we conclude that the sensitivity to Ca2+ of a functional group within the thin filament may vary depending upon the state of activation of immediately adjacent groups.