Power Stroke Model Research Articles

The Problem with Inventing Molecular Mechanisms to Fit Thermodynamic Equations of Muscle.

Almost every model of muscle contraction in the literature to date is a molecular power stroke model, even though this corpuscular mechanism is opposed by centuries of science, by 85 years of unrefuted evidence that muscle is a thermodynamic system, and by a quarter century of direct observations that the molecular mechanism of muscle contraction is a molecular switch, not a molecular power stroke. An ensemble of molecular switches is a binary mechanical thermodynamic system from which A.V. Hill's muscle force-velocity relationship is directly derived, where Hill's parameter a is the internal force against which unloaded muscle shortens, and Hill's parameter b is the product of the switch displacement, d, and the actin-myosin ATPase rate. Ignoring this model and the centuries of thermodynamics that preceded it, corpuscularians continue to develop molecular power stroke models, adding to their 65-year jumble of "new", "innovative", and "unconventional" molecular mechanisms for Hill's a and b parameters, none of which resemble the underlying physical chemistry. Remarkably, the corpuscularian community holds the thermodynamicist to account for these discrepancies, which, as outlined here, I have done for 25 years. It is long past time for corpuscularians to be held accountable for their mechanisms, which by all accounts have no foundation in science. The stakes are high. Molecular power stroke models are widely used in research and in clinical decision-making and have, for over half a century, muddied our understanding of the inner workings of one of the most efficient and clean-burning machines on the planet. It is problematic that corpuscularians present these models to stakeholders as science when in fact corpuscularians have been actively defending these models against science for decades. The path forward for scientists is to stop baseless rejections of muscle thermodynamics and to begin testing corpuscular and thermodynamic mechanisms with the goal of disproving one or the other of these hypotheses.

Structural snapshots of V/A-ATPase reveal the rotary catalytic mechanism of rotary ATPases

V/A-ATPase is a motor protein that shares a common rotary catalytic mechanism with FoF1 ATP synthase. When powered by ATP hydrolysis, the V1 domain rotates the central rotor against the A3B3 hexamer, composed of three catalytic AB dimers adopting different conformations (ABopen, ABsemi, and ABclosed). Here, we report the atomic models of 18 catalytic intermediates of the V1 domain of V/A-ATPase under different reaction conditions, determined by single particle cryo-EM. The models reveal that the rotor does not rotate immediately after binding of ATP to the V1. Instead, three events proceed simultaneously with the 120˚ rotation of the shaft: hydrolysis of ATP in ABsemi, zipper movement in ABopen by the binding ATP, and unzipper movement in ABclosed with release of both ADP and Pi. This indicates the unidirectional rotation of V/A-ATPase by a ratchet-like mechanism owing to ATP hydrolysis in ABsemi, rather than the power stroke model proposed previously for F1-ATPase.

A chemical thermodynamic model of motor enzymes unifies chemical-Fx and powerstroke models

Molecular motors play a central role in many biological processes, ranging from pumping blood and breathing to growth and wound healing. Through motor-catalyzed chemical reactions, these nanomachines convert the chemical free energy from ATP hydrolysis into two different forms of mechanical work. Motor enzymes perform reversible work, wrev, through an intermediate step in their catalyzed reaction cycle referred to as a working step, and they perform Fx work when they move a distance, x, against a force, F. In a powerstroke model, wrev is performed when the working step stretches a spring within a given motor enzyme. In a chemical-Fx model, wrev is performed in generating a conserved Fx potential defined external to the motor enzyme. It is difficult to find any common ground between these models even though both have been shown to account for mechanochemical measurements of motor enzymes with reasonable accuracy. Here, I show that, by changing one simple assumption in each model, the powerstroke and chemical-Fx model can be reconciled through a chemical thermodynamic model. The formal and experimental justifications for changing these assumptions are presented. The result is a unifying model for mechanochemical coupling in motor enzymes first presented by A.V. Hill in 1938 that is consistent with single-molecule structural and mechanical data.

Conformational dynamics during high-fidelity DNA replication and translocation defined using a DNA polymerase with a fluorescent artificial amino acid

We address the role of enzyme conformational dynamics in specificity for a high-fidelity DNA polymerase responsible for genome replication. We present the complete characterization of the conformational dynamics during the correct nucleotide incorporation forward and reverse reactions using stopped-flow and rapid-quench methods with a T7 DNA polymerase variant containing a fluorescent unnatural amino acid, (7-hydroxy-4-coumarin-yl) ethylglycine, which provides a signal for enzyme conformational changes. We show that the forward conformational change (>6000 s−1) is much faster than chemistry (300 s−1) while the enzyme opening to allow release of bound nucleotide (1.7 s−1) is much slower than chemistry. These parameters show that the conformational change selects a correct nucleotide for incorporation through an induced-fit mechanism. We also measured conformational changes occurring after chemistry and during pyrophosphorolysis, providing new insights into processive polymerization. Pyrophosphorolysis occurs via a conformational selection mechanism as the pyrophosphate binds to a rare pretranslocation state of the enzyme–DNA complex. Global data fitting was achieved by including experiments in the forward and reverse directions to correlate conformational changes with chemical reaction steps. This analysis provided well-constrained values for nine rate constants to establish a complete free-energy profile including the rates of DNA translocation during processive synthesis. Translocation does not follow Brownian ratchet or power stroke models invoking nucleotide binding as the driving force. Rather, translocation is rapid and thermodynamically favorable after enzyme opening and pyrophosphate release, and it appears to limit the rate of processive synthesis at 4 °C.

Protease protection assays show polypeptide movement into the SecY channel by power strokes of the SecA ATPase.

Bacterial secretory proteins are translocated post-translationally by the SecA ATPase through the protein-conducting SecY channel in the plasma membrane. During the ATP hydrolysis cycle, SecA undergoes large conformational changes of its two-helix finger and clamp domains, but how these changes result in polypeptide movement is unclear. Here, we use a reconstituted purified system and protease protection assays to show that ATP binding to SecA results in a segment of the translocation substrate being pushed into the channel. This motion is prevented by mutation of conserved residues at the finger's tip. Mutation of SecA's clamp causes backsliding of the substrate in the ATP-bound state. Together, these data support a power stroke model of translocation in which, upon ATP binding, the two-helix finger pushes the substrate into the channel, where it is held by the clamp until nucleotide hydrolysis has occurred.

Driving Forces of Translocation Through Bacterial Translocon SecYEG

This review focusses on the energetics of protein translocation via the Sec translocation machinery. First we complement structural data about SecYEG’s conformational rearrangements by insight obtained from functional assays. These include measurements of SecYEG permeability that allow assessment of channel gating by ligand binding and membrane voltage. Second we will discuss the power stroke and Brownian ratcheting models of substrate translocation and the role that the two models assign to the putative driving forces: (i) ATP (SecA) and GTP (ribosome) hydrolysis, (ii) interaction with accessory proteins, (iii) membrane partitioning and folding, (iv) proton motive force (PMF), and (v) entropic contributions. Our analysis underlines how important energized membranes are for unravelling the translocation mechanism in future experiments.

Analysis of spontaneous oscillations for a three-state power-stroke model.

Our study considers the mechanism of the spontaneous oscillations of molecular motors that are driven by the power stroke principle by applying linear stability analysis around the stationary solution. By representing the coupling equation of microscopic molecular motor dynamics and mesoscopic sarcomeric dynamics by a rank-1 updated matrix system, we derived the analytical representations of the eigenmodes of the Jacobian matrix that cause the oscillation. Based on these analytical representations, we successfully derived the essential conditions for the oscillation in terms of the rate constants of the power stroke and the reversal stroke transitions of the molecular motor. Unlike the two-state model, in which the dependence of the detachment rates on the motor coordinates or the applied forces on the motors plays a key role for the oscillation, our three-state power stroke model demonstrates that the dependence of the rate constants of the power and reversal strokes on the strains in the elastic elements in the motor molecules plays a key role, where these rate constants are rationally determined from the free energy available for the power stroke, the stiffness of the elastic element in the molecular motor, and the working stroke size. By applying the experimentally confirmed values to the free energy, the stiffness, and the working stroke size, our numerical model reproduces well the experimentally observed oscillatory behavior. Furthermore, our analysis shows that two eigenmodes with real positive eigenvalues characterize the oscillatory behavior, where the eigenmode with the larger eigenvalue indicates the transient of the system of the quick sarcomeric lengthening induced by the collective reversal strokes, and the smaller eigenvalue correlates with the speed of sarcomeric shortening, which is much slower than lengthening. Applying the perturbation analyses with primal physical parameters, we find that these two real eigenvalues occur on two branches derived from a merge point of a pair of complex-conjugate eigenvalues generated by Hopf bifurcation.

Clathrin-coat disassembly illuminates the mechanisms of Hsp70 force generation.

Hsp70s use ATP hydrolysis to disrupt protein:protein associations or move macromolecules. One example is Hsc70-mediated disassembly of clathrin coats that form on vesicles during endocytosis. We exploit the exceptional features of these coats to test three models—Brownian ratchet, power-stroke and entropic pulling—proposed to explain how Hsp70s transform their substrates. Our data rule out the ratchet and power-stroke models, and instead support a collision pressure mechanism whereby collisions between clathrin coat walls and Hsc70s drive coats apart. Collision pressure is the complement to the pulling force described in the entropic pulling model. We also find that self-association can augment collision pressure to allow disassembly of clathrin lattices predicted to resist disassembly. These results illuminate how Hsp70s generate the forces that transform their substrates.

The Physics and Physical Chemistry of Molecular Machines.

The concept of a "power stroke"-a free-energy releasing conformational change-appears in almost every textbook that deals with the molecular details of muscle, the flagellar rotor, and many other biomolecular machines. Here, it is shown by using the constraints of microscopic reversibility that the power stroke model is incorrect as an explanation of how chemical energy is used by a molecular machine to do mechanical work. Instead, chemically driven molecular machines operating under thermodynamic constraints imposed by the reactant and product concentrations in the bulk function as information ratchets in which the directionality and stopping torque or stopping force are controlled entirely by the gating of the chemical reaction that provides the fuel for the machine. The gating of the chemical free energy occurs through chemical state dependent conformational changes of the molecular machine that, in turn, are capable of generating directional mechanical motions. In strong contrast to this general conclusion for molecular machines driven by catalysis of a chemical reaction, a power stroke may be (and often is) an essential component for a molecular machine driven by external modulation of pH or redox potential or by light. This difference between optical and chemical driving properties arises from the fundamental symmetry difference between the physics of optical processes, governed by the Bose-Einstein relations, and the constraints of microscopic reversibility for thermally activated processes.

Beam finite-element model of a molecular motor for the simulation of active fibre networks.

Molecular motors are proteins that excessively increase the efficiency of subcellular transport processes. They allow for cell division, nutrient transport and even macroscopic muscle movement. In order to understand the effect of motors in large biopolymer networks, e.g. the cytoskeleton, we require a suitable model of a molecular motor. In this contribution, we present such a model based on a geometrically exact beam finite-element formulation. We discuss the numerical model of a non-processive motor such as myosin II, which interacts with actin filaments. Based on experimental data and inspired by the theoretical understanding offered by the power-stroke model and the swinging-cross-bridge model, we parametrize our numerical model in order to achieve the effect that a physiological motor has on its cargo. To this end, we introduce the mechanical and mathematical foundations of the model, then discuss its calibration, prove its usefulness by conducting finite-element simulations of actin-myosin motility assays and assess the influence of motors on the rheology of semi-flexible biopolymer networks.

Optical vs. chemical driving for molecular machines.

Molecular machines use external energy to drive transport, to do mechanical, osmotic, or electrical work on the environment, and to form structure. In this paper the fundamental difference between the design principles necessary for a molecular machine to use light or external modulation of thermodynamic parameters as an energy source vs. the design principle for using an exergonic chemical reaction as a fuel will be explored. The key difference is that for catalytically-driven motors microscopic reversibility must hold arbitrarily far from equilibrium. Applying the constraints of microscopic reversibility assures that a coarse grained model is consistent with an underlying model for motion on a single time-independent potential energy surface. In contrast, light-driven processes, and processes driven by external modulation of the thermodynamic parameters of a system cannot in general be described in terms of motion on a single time-independent potential energy surface, and the rate constants are not constrained by microscopic reversibility. The results presented here call into question the value of the so-called power stroke model as an explanation of the function of autonomous chemically-driven molecular machines such as are commonly found in biology.

Drosophila Ncd reveals an evolutionarily conserved powerstroke mechanism for homodimeric and heterodimeric kinesin-14s

Drosophila melanogaster kinesin-14 Ncd cross-links parallel microtubules at the spindle poles and antiparallel microtubules within the spindle midzone to play roles in bipolar spindle assembly and proper chromosome distribution. As observed for Saccharomyces cerevisiae kinesin-14 Kar3Vik1 and Kar3Cik1, Ncd binds adjacent microtubule protofilaments in a novel microtubule binding configuration and uses an ATP-promoted powerstroke mechanism. The hypothesis tested here is that Kar3Vik1 and Kar3Cik1, as well as Ncd, use a common ATPase mechanism for force generation even though the microtubule interactions for both Ncd heads are modulated by nucleotide state. The presteady-state kinetics and computational modeling establish an ATPase mechanism for a powerstroke model of Ncd that is very similar to those determined for Kar3Vik1 and Kar3Cik1, although these heterodimers have one Kar3 catalytic motor domain and a Vik1/Cik1 partner motor homology domain whose interactions with microtubules are not modulated by nucleotide state but by strain. The results indicate that both Ncd motor heads bind the microtubule lattice; two ATP binding and hydrolysis events are required for each powerstroke; and a slow step occurs after microtubule collision and before the ATP-promoted powerstroke. Note that unlike conventional myosin-II or other processive molecular motors, Ncd requires two ATP turnovers rather than one for a single powerstroke-driven displacement or step. These results are significant because all metazoan kinesin-14s are homodimers, and the results presented show that despite their structural and functional differences, the heterodimeric and homodimeric kinesin-14s share a common evolutionary structural and mechanochemical mechanism for force generation.

Mechano-chemical kinetics of DNA replication: identification of the translocation step of a replicative DNA polymerase.

During DNA replication replicative polymerases move in discrete mechanical steps along the DNA template. To address how the chemical cycle is coupled to mechanical motion of the enzyme, here we use optical tweezers to study the translocation mechanism of individual bacteriophage Phi29 DNA polymerases during processive DNA replication. We determine the main kinetic parameters of the nucleotide incorporation cycle and their dependence on external load and nucleotide (dNTP) concentration. The data is inconsistent with power stroke models for translocation, instead supports a loose-coupling mechanism between chemical catalysis and mechanical translocation during DNA replication. According to this mechanism the DNA polymerase works by alternating between a dNTP/PPi-free state, which diffuses thermally between pre- and post-translocated states, and a dNTP/PPi-bound state where dNTP binding stabilizes the post-translocated state. We show how this thermal ratchet mechanism is used by the polymerase to generate work against large opposing loads (∼50 pN).

Intermolecular Cooperativity of Skeletal Myosins Enhances Force Output in Myofilaments

Muscle contraction is powered by the cyclic interaction of skeletal myosin molecules with actin filaments. Recent experiments suggest cooperative actions between myosin molecules, when part of an ensemble. In order to gain more insight into the mechanism of intermolecular cooperativity between myosins in a myofilament, displacements of actin generated by ∼17 interacting myosins embedded in myosin-rod cofilament were measured by optical tweezers. Results showed stepwise displacements of actin (3-6 nm) under high loads of ∼30 pN at every 1-2 ms. Dwell times gradually increased with increasing loads, which is distinctively different from highly load-dependent characteristics of dwell time observed in single myosins, implying that the number of force generating myosins increases with increasing loads. These results suggest that stepwise displacements may be generated by synchronous force generations of myosin molecules. In order to elucidate potential mechanisms of synchronous actions between myosins, we developed the simulation model, consisting of 17 myosins arranged in series with six transition states defined during actomyosin mechanochemical cycles. We have two types of model, implemented with either one or two power strokes. Interestingly, two power stroke model generates stepwise movements of actin at loads up to 30 pN, but one power stroke model generates forces up to 20 pN. These differences in force output are attributed to modulation of number of synchronous power stroke motors. The numbers of synchronous power stroke motors increase with increasing loads from 1.5 to 3 molecules in two power stroke model on average, while they are virtually the same in one power stroke model. Combined with results from both in-vitro and in-silico experiments, multiple power stroke states associated with strain-dependent kinetics are essential for synchronous force generations between myosins, that is a key feature for force enhancement of myosin ensembles.

Master equation approach for a cross-bridge power-stroke model with a finite number of motors

The cross-bridge power-stroke model has been widely used to describe the motion of large motor assemblies connected to a common rigid filament. In this paper, we go beyond the original velocity-ensemble approach and propose a master equation approach to account for the cooperative motion of a finite number of motors based on the cross-bridge model. By studying the force-velocity relationship for motors with strain-independent detachment rate, we show the convergence of our approach to the velocity-ensemble approach in the limit of large motor numbers. In the case that the detachment rate of motors is strain dependent, based on two assumptions for the strain distribution among motors, we show the occurrence of the bimodal distribution of the number of motors bound to the filament. This provides a new perspective to look at the instability of a multimotor system, which is essential for all the experimentally observed complex motions displayed by a group of motors, such as hysteresis, bidirectional motion, and spontaneous oscillation. By comparing the velocities calculated using the two assumptions with the stochastic simulation, it suggests that the coupling between motors via the common connection to the filament might facilitate the fast movement of filaments at small loading forces.

Theory of muscle contraction mechanism with -cooperative interaction among crossbridges

The power stroke model was criticized and a model was proposed for muscle contraction mechanism (Mitsui, 1999). The proposed model was further developed and calculations based on the model well reproduced major experimental data on the steady filament sliding (Mitsui and Ohshima, 2008) and on the transient phenomena (Mitsui, Takai and Ohshima, 2011). In this review more weight is put on explanation of the basic ideas of the model, especially logical necessity of the model, leaving mathematical details to the above-mentioned papers. A thermodynamic relationship that any models based upon the sliding filament theory should fulfill is derived. The model which fulfills the thermodynamic relationship is constructed on the assumption that a myosin head bound to an actin filament forms a complex with three actin molecules. In shortening muscles, the complex moves along the actin filament changing the partner actin molecules with steps of about 5.5 nm. This process is made possible through cooperative interaction among cross-bridges. The ATP hydrolysis energy is liberated by fraction at each step through chemical reactions between myosin and actin molecules. The cooperativity among crossbridges disappears in length-clamped muscles, in agreement with experimental observations that the cross-bridge produces force independently in the isometric tetanus state. The distance of the head movement per ATP hydrolysis cycle is expected to be about 5.5 nm or a few times of it under the condition of the in vitro single head experiments. Calculation results are surveyed illustrating that they are in good agreement with major experimental observations.

1A1510 キネシン様モータータンパク質NcdのPower-strokeモデルの検証(分子モーターI,口頭発表,日本生物物理学会第50回年会(2012年度))

1A1510 キネシン様モータータンパク質NcdのPower-strokeモデルの検証(分子モーターI,口頭発表,日本生物物理学会第50回年会(2012年度))

Single-Molecule Protein Unfolding and Translocation by the AAA+ Protease, ClpXP

All cells employ ATP-fueled AAA+ proteases for protein-quality control and regulation. In the ClpXP protease, the ring-shaped AAA+ molecular motor ClpX first recognizes and mechanically unfolds specific protein substrates, then translocates the denatured polypeptide through a central axial pore into the barrel-shaped peptidase ClpP for degradation. Although the mechanisms of ATP utilization and substrate degradation have been extensively studied in solution and recently at the single-molecule level[1, 2], the molecular details underlying mechanical substrate unfolding and stepping along the polypeptide track remain unexamined.Using a dual-laser optical trap, we probed how ClpXP unfolds and translocates a multi-domain protein substrate at the single-molecule level. In our assay, a ClpXP-substrate complex is tethered between two trapped polystyrene beads held in a dumbbell configuration [2]. Motility records of ClpXP along the polypeptide track show unique, fingerprint-like, substrate unfolding and translocation events. Following rapid and cooperative unfolding of individual domains, we find that ClpX translocates the polypeptide into ClpP, taking small steps of 5-8 amino acids. The nature of the polypeptide track affects ClpXP mechanochemical activity. ClpX step size does not depend on ClpP, though we observe substantial substrate refolding and slippage events when only ClpX is examined. Our results support a power-stroke model of denaturation in which successful unfolding requires mechanical pulling by the enzyme to coincide with transient stochastic protein destabilization.[1] Shin, Y., Davis, J.H., Brau, R.R., Martin, A., Kenniston, J.A., Baker T.A., Sauer, R.T., Lang, M.J. Single-molecule denaturation and degradation of proteins by the AAA+ ClpXP protease. PNAS, 106, 19340 (2009)[2] Aubin-Tam, M. E., Olivares, A. O., Sauer, R. T., Baker, T. A., Lang, M. J. Single-molecule protein unfolding and translocation by an ATP-fueled proteolytic machine. Cell, 145, 257-67 (2011)

Force Generation: ATP-Powered Proteasomes Pull the Rope

Recently, single-molecule force spectroscopy techniques have provided unprecedented opportunities to apply and to quantify forces that guide protein (un-)folding. A new study provides fascinating insights into the sophisticated mechanism by which an ATP-fueled proteolytic machine generates mechanical forces to unfold and translocate multidomain substrates.

The different muscle-energetics during shortening and stretch.

The helical shape of the thin filaments causes their passive counterclockwise rotation during muscle stretch that increases tensile stress and torque at first by unwinding and then by winding up the four anchoring Z-filaments. This means storage of energy in the series elastic Z-filaments and a considerable decrease of the liberated energy of heat and work to (h—wap), where h is the heat energy and wap the stretch energy induced from outside by an apparatus. The steep thin filament helix with an inclination angle of 70° promotes the passive rotation during stretch, but impedes the smooth sliding of shortening by increased friction and production of frictional heat. The frictional heat may be produced by the contact with the myosin cross-bridges: (1) when they passively snap on drilling thin filaments from cleft to cleft over a distance 2 × 2.7 nm = 5.4 nm between the globular actin monomers in one groove, causing stepwise motion; or (2) when they passively cycle from one helical groove to the next (distance 36 nm). The latter causes more heat and may take place on rotating thin filaments without an effective forward drilling (“idle rotation”), e.g., when they produce “unexplained heat” at the beginning of an isometric tetanus. In an Appendix to this paper the different states of muscle are defined. The function of its most important components is described and rotation model and power-stroke model of muscular contraction is compared.