The ADP release step of the smooth muscle cross-bridge cycle is not directly associated with force generation.

When smooth muscle myosin subfragment 1 (S1) is bound to actin filaments in vitro, the light chain domain tilts upon release of MgADP, producing a approximately 3.5-nm axial motion of the head-rod junction (Whittaker et al., 1995. Nature. 378:748-751). If this motion contributes significantly to the power stroke, rigor tension of smooth muscle should decrease substantially in response to cross-bridge binding of MgADP. To test this prediction, we monitored mechanical properties of permeabilized strips of chicken gizzard muscle in rigor and in the presence of MgADP. For comparison, we also tested psoas and soleus muscle fibers. Any residual bound ADP was minimized by incubation in Mg2+-free rigor solution containing 15 mM EDTA. The addition of 2 mM MgADP, while keeping ionic strength and free Mg2+ concentration constant, resulted in a slight increase in rigor tension in both gizzard and soleus muscles, but a decrease in psoas muscle. In-phase stiffness monitored during small (<0.1%) 500-Hz sinusoidal length oscillations decreased in all three muscle types when MgADP was added. The changes in force and stiffness with the addition of MgADP were similar at ionic strengths from 50 to 200 mM and were reversible. The results with gizzard muscle were similar after thiophosphorylation of the regulatory light chain of myosin. These results suggest that the axial motion of smooth muscle S1 bound to actin, upon dissociation of MgADP, is not associated with force generation. The difference between the present mechanical data and previous structural studies of smooth S1 may be explained if geometrical constraints of the intact contractile filament array alter the motions of the myosin heads.     

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.     

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.     

Muscle force depends on the amount of transversal muscle loading

Skeletal muscles are embedded in an environment of other muscles, connective tissue, and bones, which may transfer transversal forces to the muscle tissue, thereby compressing it. In a recent study we demonstrated that transversal loading of a muscle with 1.3 N cm⁻² reduces maximum isometric force (F_im) and rate of force development by approximately 5% and 25%, respectively. The aim of the present study was to examine the influence of increasing transversal muscle loading on contraction dynamics.     

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.     

Dynamics of actomyosin interactions in relation to the cross-bridge cycle

Transient kinetic measurements of the actomyosin ATPase provided the basis of the Lymn-Taylor model for the cross-bridge cycle, which underpins current models of contraction. Following the determination of the structure of the myosin motor domain, it has been possible to introduce probes at defined sites and resolve the steps in more detail. Probes have been introduced in the Dicytostelium myosin II motor domain via three routes: (i) single tryptophan residues at strategic locations throughout the motor domain; (ii) green fluorescent protein fusions at the N and C termini; and (iii) labelled cysteine residues engineered across the actin-binding cleft. These studies are interpreted with reference to motor domain crystal structures and suggest that the tryptophan (W501) in the relay loop senses the lever arm position, which is controlled by the switch 2 open-to-closed transition at the active site. Actin has little effect on this process per se. A mechanism of product release is proposed in which actin has an indirect effect on the switch 2 and lever arm position to achieve mechanochemical coupling. Switch 1 closing appears to be a key step in the nucleotide-induced actin dissociation, while its opening is required for the subsequent activation of product release. This process has been probed with F239W and F242W substitutions in the switch 1 loop. The E706K mutation in skeletal myosin IIa is associated with a human myopathy. To simulate this disease we investigated the homologous mutation, E683K, in the Dictyostelium myosin motor domain.     

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.     

Energetics of the actomyosin bond in the filament array of muscle fibers.

The interaction between actin and myosin in the filament array of glycerinated muscle fibers has been monitored using paramagnetic probes and mechanical measurements. Both fiber stiffness and the spectra of probes bound to a reactive sulfydral on the myosin head were measured as the actomyosin bond was weakened by addition of magnesium pyrophosphate (MgPPi) and glycerol. In the absence of MgPPi, all myosin heads are attached to actin with oriented probes. When fibers were incubated in buffers containing MgPPi, a fraction of the probes became disordered, and this effect was greater in the presence of glycerol. To determine whether the heads with disordered probes were detached from actin, spin-labeled myosin subfragment-1 (MSL-S1) was diffused into unlabeled fibers, and the fractions bound to actin and free in the medium were correlated with the oriented and disordered spectral components. These experiments showed that the label was oriented when MSL-S1 was attached to actin in a ternary complex with the ligand and that all heads with disordered probes were detached from actin. Thus the fraction of oriented labels could be used to determine the fraction of heads attached to actin in a fiber in the presence of ligand. The fraction of myosin heads attached to actin decreased with increasing [MgPPi], and in the absence of glycerol approximately 50% of the myosin heads were dissociated at 3.3 mM ligand with little change in fiber stiffness. In the presence of 37% glycerol plus ligand, up to 80% of the heads could be detached with a 50% decrease in fiber stiffness. The data indicate that there are two populations of myosin heads in the fiber. All the data could be fit with a model in which one population of myosin heads (comprising approximately 50% of the total) sees an apparent actin concentration of 0.1 mM and can be released from actin with little change in fiber stiffness. A second population of myosin heads (approximately 50%) sees a higher actin concentration (5 mM) and is only released in the presence of both glycerol and ligand.     

Influence of ionic strength on the actomyosin reaction steps in contracting skeletal muscle fibers

Muscle contraction occurs as the result of actin-myosin interaction, which is mediated by the intermolecular forces exerted at the actin-myosin interface. To obtain information about the nature of these intermolecular forces, we tested the sensitivity of various contractile parameters of skinned skeletal muscle fibers to ionic strength (IS) at 3-5 degrees C; IS variation is a useful technique for distinguishing between ionic and nonionic (primarily hydrophobic) types of intermolecular forces. The most striking effect of elevated IS was the strong suppression of isometric tension. However, none of the measured parameters suggested a corresponding decrease in the number of force-generating myosin heads on actin. The rate of actin-myosin association seemed to be only modestly IS-sensitive. The following force-generating isomerization was apparently IS-insensitive. The dissociation of the force-generating actomyosin complex was decelerated by elevated IS, contrary to the expectation from the suppressed isometric tension. These results led us to conclude that an IS-sensitive step, responsible for the large suppression of tension, occurs after force-generating isomerization but before dissociation. The present study suggests that the actomyosin interaction is generally nonionic in nature, but there are at least two ionic processes, one at the beginning and the other close to the end of the actomyosin interaction.     

The role of membrane stiffness and actin turnover on the force exerted by DRG lamellipodia

We used optical tweezers to analyze the effect of jasplakinolide and cyclodextrin on the force exerted by lamellipodia from developing growth cones (GCs) of isolated dorsal root ganglia (DRG) neurons. We found that 25 nM of jasplakinolide, which is known to inhibit actin filament turnover, reduced both the maximal exerted force and maximal velocity during lamellipodia leading-edge protrusion. By using atomic force microscopy, we verified that cyclodextrin, which is known to remove cholesterol from membranes, decreased the membrane stiffness of DRG neurons. Lamellipodia treated with 2.5 mM of cyclodextrin exerted a larger force, and their leading edge could advance with a higher velocity. Neither jasplakinolide nor cyclodextrin affected force or velocity during lamellipodia retraction. The amplitude and frequency of elementary jumps underlying force generation were reduced by jasplakinolide but not by cyclodextrin. The action of both drugs at the used concentration was fully reversible. These results support the notion that membrane stiffness provides a selective pressure that shapes force generation, and confirm the pivotal role of actin turnover during protrusion.     

The force exerted by the membrane potential during protein import into the mitochondrial matrix

The force exerted on a targeting sequence by the electrical potential across the inner mitochondrial membrane is calculated on the basis of continuum electrostatics. The force is found to vary from 3.0 pN to 2.2 pN (per unit elementary charge) as the radius of the inner membrane pore (assumed aqueous) is varied from 6.5 to 12 A, its measured range. In the present model, the decrease in force with increasing pore width arises from the shielding effect of water. Since the pore is not very much wider than the distance between water molecules, the full shielding effect of water may not be present; the extreme case of a purely membranous pore without water gives a force of 3.2 pN per unit charge, which should represent an upper limit. When applied to mitochondrial import experiments on the protein barnase, these results imply that forces between 11 +/- 2 pN and 13.5 +/- 2.5 pN catalyze the unfolding of barnase in those experiments. A comparison of these results with unfolding forces measured using atomic force microscopy is made.     

Amplitude of the tension developed by glycerinated muscle fibers during rigidity depends on the nature of the structural reorganizations in F-actin induced by formation of the actomyosin complex

Dependence between the amplitude of tension, developed by glycerinated muscle fibers during rigidity, and the character of structural changes in F-actin, induced by the formation of actomyosin complex, was studied by polarized microfluorimetry and tensiometry. It is shown that during rigidity the anisotropy of intrinsic tryptophan residues as well as of rhodamine phalloidin bound to F-actin, and amplitude of tension depend on pH (6-8) and ionic strength (mu = 0.07 M-0.14 M) of solution. Greater changes in polarized fluorescence and in amplitude of tension were registered during rigidity in solutions with low ionic strength (mu = 0.07 M) and pH 8. It suggested that the amplitude of muscle fibre tension depends on the relative quantity of actin monomers, being in the "switched on" state.     

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.     

In vivo 3-dimensional measurement of the force exerted on a tooth during clenching

We have developed a three-dimensional (3D) force-measuring device for teeth and used it to measure functional forces in vivo. It comprises an inner part forming a metal core (abutment), a 3D piezoelectric force transducer, and an outer part forming a metal crown, all joined together with a steel screw. The force transducer can measure +/- 500 N along the z-axis and +/- 150 N along the x- and y-axes. We evaluated the relationship between output and load and the effects of hysteresis and temperature on the output. The transducer had high linearity (r>0.9999), low hysteresis (1.7% at maximum), and high thermal stability (0.05% per degree) along each axis. The measuring device was mounted on the maxillary left second molar of a healthy male subject; the tooth had been endodontically treated (neurovascular bundle removed) and prepared for metal abutment and a crown. The 3D load calculated from the outputs of the transducer was expressed as a vector of the coordinates based on the Frankfort horizontal (x-y) and sagittal (y-z) planes. The force measured during maximum voluntary clenching was about 170 N; the force vector was directed from the crown to the root medially at an angle of about 10 degrees from the y-z plane and posteriorly at an angle of about 3 degrees from the x-z plane. This transducer will enable measurement of forces applied to different types of prosthetic appliances and has the potential to provide important basic in vivo data for analysis using computer simulation.     

Mechanism of inhibition of skeletal muscle actomyosin by N-benzyl-p-toluenesulfonamide

N-Benzyl-p-toluenesulfonamide (BTS) is a small organic molecule that specifically inhibits the contraction of fast skeletal muscle fibers. To determine the mechanism of inhibition by BTS, we performed a kinetic analysis of its effects on the elementary steps of the actomyosin subfragment-1 ATPase cycle. BTS decreases the steady-state acto-S1 ATPase rate approximately 10-fold and increases the actin concentration for half-maximal activation. BTS primarily affects three of the elementary steps of the reaction pathway. It decreases the rate of P(i) release >20-fold in the absence of actin and >100-fold in the presence of actin. It decreases the rate of S1.ADP dissociation from 3.9 to 0.8 s(-)(1) while decreasing the S1.ADP dissociation constant from 2.3 to 0.8 microM. BTS weakens the apparent affinity of S1.ADP for actin, increasing the K(d) from 7.0 to 29.5 microM. ATP binding to S1, hydrolysis, and the affinity of nucleotide-free S1 for actin are unaffected by BTS. Kinetic modeling indicates that the binding of BTS to myosin depends on actin association/dissociation and on nucleotide state. Our results suggest that the reduction of the acto-S1 ATPase rate is due to the inhibition of P(i) release, and the suppression of tension is due to inhibition of P(i) release in conjunction with the decreased apparent affinity of S1.ADP.P(i) and S1.ADP for actin.     

The myosin cross-bridge cycle and its control by twitchin phosphorylation in catch muscle

The anterior byssus retractor muscle of Mytilus edulis was used to characterize the myosin cross-bridge during catch, a state of tonic force maintenance with a very low rate of energy utilization. Addition of MgATP to permeabilized muscles in high force rigor at pCa > 8 results in a rapid loss of some force followed by a very slow rate of relaxation that is characteristic of catch. The fast component is slowed 3-4-fold in the presence of 1 mM MgADP, but the distribution between the fast and slow (catch) components is not dependent on [MgADP]. Phosphorylation of twitchin results in loss of the catch component. Fewer than 4% of the myosin heads have ADP bound in rigor, and the time course (0.2-10 s) of ADP formation following release of ATP from caged ATP is similar whether or not twitchin is phosphorylated. This suggests that MgATP binding to the cross-bridge and subsequent splitting are independent of twitchin phosphorylation, but detachment occurs only if twitchin is phosphorylated. A similar dependence of detachment on twitchin phosphorylation is seen with AMP-PNP and ATPgammaS. Single turnover experiments on bound ADP suggest an increase in the rate of release of ADP from the cross-bridge when catch is released by phosphorylation of twitchin. Low [Ca(2+)] and unphosphorylated twitchin appear to cause catch by 1) markedly slowing ADP release from attached cross-bridges and 2) preventing detachment following ATP binding to the rigor cross-bridge.