Substrate and product dependence of force and shortening in fast and slow smooth muscle

To explore the molecular mechanisms responsible for the variation in smooth muscle contractile kinetics, the influence of MgATP, MgADP, and inorganic phosphate (P(i)) on force and shortening velocity in thiophosphorylated "fast" (taenia coli: maximal shortening velocity Vmax = 0.11 ML/s) and "slow" (aorta: Vmax = 0.015 ML/s) smooth muscle from the guinea pig were compared. P(i) inhibited active force with minor effects on the V(max). In the taenia coli, 20 mM P(i) inhibited force by 25%. In the aorta, the effect was markedly less (< 10%), suggesting differences between fast and slow smooth muscles in the binding of P(i) or in the relative population of P(i) binding states during cycling. Lowering of MgATP reduced force and V(max). The aorta was less sensitive to reduction in MgATP (Km for Vmax: 80 microM) than the taenia coli (Km for Vmax: 350 microM). Thus, velocity is controlled by steps preceding the ATP binding and cross-bridge dissociation, and a weaker binding of ATP is not responsible for the lower V(max) in the slow muscle. MgADP inhibited force and V(max). Saturating concentrations of ADP did not completely inhibit maximal shortening velocity. The effect of ADP on Vmax was observed at lower concentrations in the aorta compared with the taenia coli, suggesting that the ADP binding to phosphorylated and cycling cross-bridges is stronger in slow compared with fast smooth muscle.     

The force-velocity relationship for microtubule sliding in demembranated sperm flagella of the sea urchin

We studied the relationship between the force and velocity of microtubule sliding in demembranated sperm flagella of the sea urchin, Hemicentrotus pulcherrimus, under auxotonic conditions following a quick release of the tension between sliding microtubules. The shape of the force-velocity curve was independent of the concentration of Mg-ATP over the range of 3.7 to 350 microM and appeared either linear or was the reverse of the hyperbolic curve seen for muscle. The power, calculated as the product of velocity and force, passed through a peak at c. 0.7 Fmax (the maximal isometric force). Thus, the maximal power is attained at a larger relative load than in muscle. The sliding velocity at 0.1 Fmax showed a hyperbolic dependence on Mg-ATP concentration, with a Km of 210 microM and a Vmax of 19 micron.sec-1. The maximal force did not significantly change over the Mg-ATP concentration range of 3.7 to 350 microM. These results are discussed in terms of a crossbridge model similar to the one originally proposed by Huxley. It is suggested that the dynein crossbridge cycle is characterized by a relatively rapid rate of attachment and a relatively slow rate of detachment.     

Mutation of a conserved glycine in the SH1-SH2 helix affects the load-dependent kinetics of myosin

The ATP hydrolysis rate and shortening velocity of muscle are load-dependent. At the molecular level, myosin generates force and motion by coupling ATP hydrolysis to lever arm rotation. When a laser trap was used to apply load to single heads of expressed smooth muscle myosin (S1), the ADP release kinetics accelerated with an assistive load and slowed with a resistive load; however, ATP binding was mostly unaffected. To investigate how load is communicated within the motor, a glycine located at the putative fulcrum of the lever arm was mutated to valine (G709V). In the absence of load, stopped-flow and laser trap studies showed that the mutation significantly slowed the rates of ADP release and ATP binding, accounting for the ~270-fold decrease in actin sliding velocity. The load dependence of the mutant's ADP release rate was the same as that of wild-type S1 (WT) despite the slower rate. In contrast, load accelerated ATP binding by ~20-fold, irrespective of loading direction. Imparting mechanical energy to the mutant motor partially reversed the slowed ATP binding by overcoming the elevated activation energy barrier. These results imply that conformational changes near the conserved G709 are critical for the transmission of mechanochemical information between myosin's active site and lever arm.     

Force-velocity shifts with repetitive isometric and isotonic contractions of canine gastrocnemius in situ.

The force-velocity (F-V) relationships of canine gastrocnemius-plantaris muscles at optimal muscle length in situ were studied before and after 10 min of repetitive isometric or isotonic tetanic contractions induced by electrical stimulation of the sciatic nerve (200-ms trains, 50 impulses/s, 1 contraction/s). F-V relationships and maximal velocity of shortening (Vmax) were determined by curve fitting with the Hill equation. Mean Vmax before fatigue was 3.8 +/- 0.2 (SE) average fiber lengths/s; mean maximal isometric tension (Po) was 508 +/- 15 g/g. With a significant decrease of force development during isometric contractions (-27 +/- 4%, P < 0.01, n = 5), Vmax was unchanged. However, with repetitive isotonic contractions at a low load (P/Po = 0.25, n = 5), a significant decrease in Vmax was observed (-21 +/- 2%, P < 0.01), whereas Po was unchanged. Isotonic contractions at an intermediate load (P/Po = 0.5, n = 4) resulted in significant decreases in both Vmax (-26 +/- 6%, P < 0.05) and Po (-12 +/- 2%, P < 0.01). These results show that repeated contractions of canine skeletal muscle produce specific changes in the F-V relationship that are dependent on the type of contractions being performed and indicate that decreases in other contractile properties, such as velocity development and shortening, can occur independently of changes in isometric tension.     

The interrelation between mechanical characteristics of contracting muscle, cross-bridge internal structure, and the mechanism of chemomechanical energy transduction

The cross-bridge working stroke is regarded as a continuous (without jumps) change of myosin head internal state under the action of a force exerted within the nucleotide-binding site. Involvement of a concept of continuous cross-bridge conformation enables discussion of the nature of the force propelling muscle, and the Coulomb repulsion of like-charged adenosine triphosphate (ATP) fragments ADP(2-) and P (i) (2-) can quite naturally be considered as the source of this force. Two entirely different types of working stroke termination are considered. Along with the fluctuation mechanism, which controls the working stroke duration t (w) at isometric contraction, another interrupt mechanism is initially taken into account. It is triggered when the lever arm shift amounts to the maximal value S?≈?11?nm, the back door opens, and P(i) crashes out. As a result, t (w) becomes inversely proportional to the velocity v of sliding filaments t (w)?≈?S/v for a wide range of values of v. Principal features of the experimentally observed dependences of force, efficiency, and rate of heat production on velocity and ATP concentration can then be reproduced by fitting a single parameter: the velocity-independent time span t (r) between the termination of the last and beginning of the next working stroke. v becomes the principal variable of the model, and the muscle force changes under external load are determined by variations in v rather than in the tension of filaments. The Boltzmann equation for an ensemble of cross-bridges is obtained, and some collective effects are discussed.     

A simple theoretical model explains dynein's response to load

Recent experiment showed that cytoplasmic dynein 1, a molecular motor responsible for cargo transport in cells, functions as a gear in response to external load. In the presence of vanishing or small external load, dynein walks with 24- or 32-nm steps, whereas at high external load, its step size is reduced to 8 nm. A simple model is proposed to account for this property of dynein. The model assumes that the chemical energy of ATP hydrolysis is used through a loose coupling between the chemical reaction and the translocation of dynein along microtubule. This loose chemomechanical coupling is represented by the loosely coupled motions of dynein along two different reaction coordinates. The first reaction coordinate is tightly coupled to the chemical reaction and describes the protein conformational changes that control the chemical processes, including ATP binding and hydrolysis, and ADP-Pi release. The second coordinate describes the translocation of dynein along microtubule, which is directly subject to the influence of the external load. The model is used to explain the experimental data on the external force dependence of the dynein step size as well as the ATP concentration dependence of the stall force. A number of predictions, such as the external force dependence of speed of translocation, ATP hydrolysis rate, and dynein step sizes, are made based on this theoretical model. This model provides a simple understanding on how a variable chemomechanical coupling ratio can be achieved and used to optimize the biological function of dynein.     

肌球蛋白Ⅵ定向运动的蒙特卡罗模拟

根据myosin Ⅵ分子马达头部核苷的变化建立一个四态循环,然后利用蒙特卡罗方法模拟分子马达的动力学性质,讨论了myosin Ⅵ速度、滞留时间与溶液中ATP浓度、ADP浓度和负载力F的关系。模拟得到：myosin Ⅵ会在轨道微丝上进行梯跳运动并且每次在微丝上的滞留时间并不相同;另外,myosin Ⅵ的速度会随着ATP浓度的增加而增大,随着ADP浓度和负载力的增加而减小;负载力对myosin Ⅵ在胞内执行输运还是连接功能起一定的调节作用。     

Entropic elasticity in the generation of muscle force--a theoretical model

A novel simplified structural model of sarcomeric force production in striate muscle is presented. Using some simple assumptions regarding the distribution of myosin spring lengths at different sliding velocities it is possible to derive a very simple expression showing the main components of the experimentally observed force-velocity relationship of muscle: nonlinearity during contraction (Hill, 1938), maximal force production during stretching equal to two times the isometric force (Katz, 1939), yielding at high stretching velocity, slightly concave force-extension relationship during sudden length changes (Ford et al., 1977; Lombardi & Piazzesi, 1990), accurate reproduction of the rate of ATP consumption (Shirakawa et al., 2000; He et al., 2000) and of the extra energy liberation rate (Hill, 1964a). Different assumptions regarding the force-length relationship of individual cross-bridges are explored [linear, power function and worm-like chain (WLC) model based], and it is shown that the best results are obtained if the individual myosin-spring forces are modelled using a WLC model, thus hinting that entropic elasticity could be the main source of force in myosin undergoing the conformational changes associated with the power stroke.     

Structural changes in the neck linker of kinesin explain the load dependence of the motor's mechanical cycle.

The two-headed motor protein kinesin hydrolyzes ATP and moves on microtubule tracks towards the plus end. The motor develops speeds and forces of the order of hundreds of nanometers per second and piconewtons, respectively. Recently, the dependence of the velocity, the dissociation rate and the displacement variance on the load and the ATP concentration were measured in vitro for individual kinesin molecules (Coppin et al., 1997; Visscher et al., 1999) over a wide range of forces. The structural changes in the kinesin motor that drive motility were discovered by Rice et al. (1999). Here we present a phenomenological model for force generation in kinesin based on the bi-stable, nucleotide-dependent behavior of the neck linker. We demonstrate that the model explains the mechanical, kinetic and statistical (experimental) data of Coppin et al. (1997). We also discuss the relationship between the model results and experimental data of Visscher et al. (1999).     

Phenomenological analysis of ATP dependence of motor proteins

In this study, through phenomenological comparison of the velocity-force data of processive motor proteins, including conventional kinesin, cytoplasmic dynein and myosin V, I found that, the ratio between motor velocities of two different ATP concentrations is almost invariant for any substall, superstall or negative external loads. Therefore, the velocity of motors can be well approximated by a Michaelis-Menten like formula V = [ATP]k(F)L([ATP] + K(M)), with L the step size, and k(F) the external load F dependent rate of one mechanochemical cycle of motor motion in saturated ATP solution. The difference of Michaelis-Menten constant K(M) for substall, superstall and negative external load indicates, the configurations at which ATP molecule can bind to motor heads for these three cases might be different, though the expression of k(F) as a function of F might be unchanged for any external load F. Verifications of this Michaelis-Menten like formula has also been done by fitting to the recent experimental data.     

Dynamic performance of a load-moving skeletal muscle

The dynamic response of the tibialis anterior muscle of the cat was determined while it was subjected to sinusoidally varying orderly stimulation of motor units and to different isotonic loads in the range of 14-85% of the maximal isometric force. The dynamic response consisted of three major components: the displacement gain, the displacement attenuation, and a pure time delay. The displacement gain was dependent on the passive load applied to the muscle and the active force generated during contraction, which could be determined from the length-tension relationships and the corresponding shortening velocity. In general, the load displacement decreased as the load mass increased from 25 to 85% of the maximal isometric force. For loads less than 25% of the maximal isometric force, slight decrease in displacement was consistently observed. The displacement attenuation was dependent on the contraction frequency but uniform for all the load masses applied to the muscle. A pure time delay of 5 ms was present and accounted for various physiological processes such as conduction time in nerve and muscle, neuromuscular junction transmission, and excitation-contraction coupling. A quantitative equation was developed to describe the muscle's dynamic response under isotonic conditions and for a wide range of loads for use in various applications.     

Relationship between intracellular pH and energy metabolism in dog brain as measured by 31P-NMR

The relationships between pHi (intracellular pH) and phosphate compounds were evaluated by nuclear magnetic resonance (NMR) in normo-, hypo-, and hypercapnia, obtained by changing fractional inspired concentration of CO2 in dogs anesthetized with 0.75% isoflurane and 66% N2O. Phosphocreatine (PCr) fell by 2.02 mM and Pi (inorganic phosphate) rose by 1.92 mM due to pHi shift from 7.10 to 6.83 during hypercapnia. The stoichiometric coefficient was 1.05 (r2 = 0.78) on log PCr/Cr against pHi, showing minimum change of ADP/ATP and equilibrium of creatine kinase in the pH range of 6.7 to 7.25. [ADP] varied from 21.6 +/- 4.1 microM in control (pHi = 7.10) to 26.8 +/- 6.3 microM in hypercapnia (pHi = 6.83) and 24.0 +/- 6.8 microM in hypocapnia (pHi = 7.17). ATP/ADP X Pi decreased from 66.4 +/- 17.1 mM-1 during normocapnia to 25.8 +/- 6.3 mM-1 in hypercapnia. The ADP values are near the in vitro Km; thus ADP is the main controller. The velocity of oxidative metabolism (V) in relation to its maximum (Vmax) as calculated by a steady-state Michaelis-Menten formulation is approximately 50% in normocapnia. In acidosis (pH 6.7) and alkalosis (pH 7.25), V/Vmax is 10% higher than the normocapnic brain. This increase of V/Vmax is required to maintain cellular homeostasis of energy metabolism in the face of either inhibition at extremes of pH or higher ATPase activity.     

A kinetic model that explains the effect of inorganic phosphate on the mechanics and energetics of isometric contraction of fast skeletal muscle

A conventional five-step chemo-mechanical cycle of the myosin–actin ATPase reaction, which implies myosin detachment from actin upon release of hydrolysis products (ADP and phosphate, Pi) and binding of a new ATP molecule, is able to fit the [Pi] dependence of the force and number of myosin motors during isometric contraction of skeletal muscle. However, this scheme is not able to explain why the isometric ATPase rate of fast skeletal muscle is decreased by an increase in [Pi] much less than the number of motors. The question can be solved assuming the presence of a branch in the cycle: in isometric contraction, when the force generation process by the myosin motor is biased at the start of the working stroke, the motor can detach at an early stage of the ATPase cycle, with Pi still bound to its catalytic site, and then rapidly release the hydrolysis products and bind another ATP. In this way, the model predicts that in fast skeletal muscle the energetic cost of isometric contraction increases with [Pi]. The large dissociation constant of the product release in the branched pathway allows the isometric myosin–actin reaction to fit the equilibrium constant of the ATPase.     

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

The role played by ADP in modulatingcross-bridge function has been difficult to study, because it is hardto buffer ADP concentration in skinned muscle preparations. To solvethis, we used an analog of ADP, spin-labeled ADP (SL-ADP). SL-ADP bindstightly to myosin but is a very poor substrate for creatine kinase orpyruvate kinase. Thus ATP can be regenerated, allowing well-definedconcentrations of both ATP and SL-ADP. We measured isometric ATPaserate and isometric tension as a function of both [SL-ADP], 0.1-2mM, and [ATP], 0.05-0.5 mM, in skinned rabbit psoas muscle,simulating fresh or fatigued states. Saturating levels of SL-ADPincreased isometric tension (by P'), the absolute value of P' beingnearly constant, ~0.04 N/mm², in variable ATP levels, pH7. Tension decreased (50-60%) at pH 6, but upon addition ofSL-ADP, P' was still ~0.04 N/mm². The ATPase wasinhibited competitively by SL-ADP with an inhibition constant,K_i, of ~240 and 280 µM at pH 7 and 6, respectively. Isometric force and ATPase activity could both be fit bya simple model of cross-bridge kinetics.

     

A kinetic model of coordinated myosin V

We present a kinetic model for the walking of myosin V on actin under conditions of zero external force. The model includes three pathways and the termination of the processivity. Experimentally measured kinetic parameters are used in the model to obtain quantitative results. Using the model and associated parameters, we compute the proportion of the pathway containing an intermediate state, as well as the walking velocities and run lengths at various concentrations of ATP and ADP. The resulting trends agree with experimental data. The model explains the surprising experimental finding that myosin walks at a faster speed but for a shorter distance as the ATP concentration increases in the absence of ADP. It also suggests that under physiological condition ([ADP] approximately 12-50 microM), myosin walks with a higher speed and for longer distances when ATP is more abundant.     

Force and Premature Binding of ADP Can Regulate the Processivity of Individual Eg5 Dimers

Using a high-resolution optical trapping instrument, we directly observed the processive motions of individual Eg5 dimers over a range of external loads and ATP, ADP, and phosphate concentrations. To constrain possible models for dissociation from the microtubule, we measured Eg5 run lengths and also compared the duration of the last step of a processive run to all previous step durations. We found that the application of large longitudinal forces in either hindering or assisting directions could induce Eg5-microtubule dissociation. At a constant moderate force, maintained with a force clamp, the premature binding of ADP strongly promoted microtubule release by Eg5, whereas the addition of ATP or phosphate had little effect on dissociation. These results imply that run length is determined not only by the load, but also by the concentration and type of nucleotides present, and therefore that the biochemical cycles of the two motor domains of the Eg5 dimer are coordinated to promote processive stepping.     

A modified active Brownian dynamics model using asymmetric energy conversion and its application to the molecular motor system

We consider a modified energy depot model in the overdamped limit using an asymmetric energy conversion rate, which consists of linear and quadratic terms in an active particle’s velocity. In order to analyze our model, we adopt a system of molecular motors on a microtubule and employ a flashing ratchet potential synchronized to a stochastic energy supply. By performing an active Brownian dynamics simulation, we investigate effects of the active force, thermal noise, external load, and energy-supply rate. Our model yields the stepping and stalling behaviors of the conventional molecular motor. The active force is found to facilitate the forwardly processive stepping motion, while the thermal noise reduces the stall force by enhancing relatively the backward stepping motion under external loads. The stall force in our model decreases as the energy-supply rate is decreased. Hence, assuming the Michaelis–Menten relation between the energy-supply rate and the an ATP concentration, our model describes ATP-dependent stall force in contrast to kinesin-1.     

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

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

Force generation in single conventional actomyosin complexes under high dynamic load

The mechanical load borne by a molecular motor affects its force, sliding distance, and its rate of energy transduction. The control of ATPase activity by the mechanical load on a muscle tunes its efficiency to the immediate task, increasing ATP hydrolysis as the power output increases at forces less than isometric (the Fenn effect) and suppressing ATP hydrolysis when the force is greater than isometric. In this work, we used a novel 'isometric' optical clamp to study the mechanics of myosin II molecules to detect the reaction steps that depend on the dynamic properties of the load. An actin filament suspended between two beads and held in separate optical traps is brought close to a surface that is sparsely coated with motor proteins on pedestals of silica beads. A feedback system increases the effective stiffness of the actin by clamping the force on one of the beads and moving the other bead electrooptically. Forces measured during actomyosin interactions are increased at higher effective stiffness. The results indicate that single myosin molecules transduce energy nearly as efficiently as whole muscle and that the mechanical control of the ATP hydrolysis rate is in part exerted by reversal of the force-generating actomyosin transition under high load without net utilization of ATP.     

A rheological motor model for vertebrate skeletal muscle in due consideration of non-linearity

A rheological motor model that satisfies the major mechanical properties of the skeletal muscle is proposed. The model consists of two Maxwell elements and a Voigt element connected in parallel with each other and has a force generator in it. The model well explains the mechanical behavior in quick and slow recovery phases in the isometric contraction of the muscle and achieves a sufficient isotonic shortening speed. The energy liberation of the motor in isotonic contraction is calculated and a mechanism of control is proposed, which operates so as to decrease the dissipated energy by altering the weights of the elastic and viscous constants in Maxwell elements. And thereby it becomes possible for the motor to possess non-linearity in energy liberation and load-velocity relation alike in muscle. The model would be a base model to be utilized for analyzing the kinetics of human macrosystems and/or for modeling the human neuromuscular system of motion control.