Power Stroke Model Research Articles

Dynamics of the Bacterial Flagellar Motor: The Effects of Stator Compliance, Back Steps, Temperature, and Rotational Asymmetry

The rotation of a bacterial flagellar motor (BFM) is driven by multiple stators tethered to the cell wall. Here, we extend a recently proposed power-stroke model to study the BFM dynamics under different biophysical conditions. Our model explains several key experimental observations and reveals their underlying mechanisms. 1), The observed independence of the speed at low load on the number of stators is explained by a force-dependent stepping mechanism that is independent of the strength of the stator tethering spring. Conversely, without force-dependent stepping, an unrealistically weak stator spring is required. 2), Our model with back-stepping naturally explains the observed absence of a barrier to backward rotation. Using the same set of parameters, it also explains BFM behaviors in the high-speed negative-torque regime. 3), From the measured temperature dependence of the maximum speed, our model shows that stator-stepping is a thermally activated process with an energy barrier. 4), The recently observed asymmetry in the torque-speed curve between counterclockwise- and clockwise-rotating BFMs can be quantitatively explained by the asymmetry in the stator-rotor interaction potentials, i.e., a quasilinear form for the counterclockwise motor and a quadratic form for the clockwise motor.

Single-Molecule Protein Unfolding and Translocation by an ATP-Fueled Proteolytic Machine

All cells employ ATP-powered proteases for protein-quality control and regulation. In the ClpXP protease, ClpX is a AAA+ machine that recognizes specific protein substrates, unfolds these molecules, and then translocates the denatured polypeptide through a central pore and into ClpP for degradation. Here, we use optical-trapping nanometry to probe the mechanics of enzymatic unfolding and translocation of single molecules of a multidomain substrate. Our experiments demonstrate the capacity of ClpXP and ClpX to perform mechanical work under load, reveal very fast and highly cooperative unfolding of individual substrate domains, suggest a translocation step size of 5-8 amino acids, and support a power-stroke model of denaturation in which successful enzyme-mediated unfolding of stable domains requires coincidence between mechanical pulling by the enzyme and a transient stochastic reduction in protein stability. We anticipate that single-molecule studies of the mechanical properties of other AAA+ proteolytic machines will reveal many shared features with ClpXP.

Remarks on Muscle Contraction Mechanism II. Isometric Tension Transient and Isotonic Velocity Transient

Mitsui and Ohshima (2008) criticized the power-stroke model for muscle contraction and proposed a new model. In the new model, about 41% of the myosin heads are bound to actin filaments, and each bound head forms a complex MA3 with three actin molecules A1, A2 and A3 forming the crossbridge. The complex translates along the actin filament cooperating with each other. The new model well explained the experimental data on the steady filament sliding. As an extension of the study, the isometric tension transient and isotonic velocity transient are investigated. Statistical ensemble of crossbridges is introduced, and variation of the binding probability of myosin head to A1 is considered. When the binding probability to A1 is zero, the Hill-type force-velocity relation is resulted in. When the binding probability to A1 becomes finite, the deviation from the Hill-type force-velocity relation takes place, as observed by Edman (1988). The characteristics of the isometric tension transient observed by Ford, Huxley and Simmons (1977) and of the isotonic velocity transient observed by Civan and Podolsky (1966) are theoretically reproduced. Ratios of the extensibility are estimated as 0.22 for the crossbridge, 0.26 for the myosin filament and 0.52 for the actin filament, in consistency with the values determined by X-ray diffraction by Wakabayashi et al. (1994).

Prometaphase spindle maintenance by an antagonistic motor-dependent force balance made robust by a disassembling lamin-B envelope

We tested the classical hypothesis that astral, prometaphase bipolar mitotic spindles are maintained by balanced outward and inward forces exerted on spindle poles by kinesin-5 and -14 using modeling of in vitro and in vivo data from Drosophila melanogaster embryos. Throughout prometaphase, puncta of both motors aligned on interpolar microtubules (MTs [ipMTs]), and motor perturbation changed spindle length, as predicted. Competitive motility of purified kinesin-5 and -14 was well described by a stochastic, opposing power stroke model incorporating motor kinetics and load-dependent detachment. Motor parameters from this model were applied to a new stochastic force-balance model for prometaphase spindles, providing a good fit to data from embryos. Maintenance of virtual spindles required dynamic ipMTs and a narrow range of kinesin-5 to kinesin-14 ratios matching that found in embryos. Functional perturbation and modeling suggest that this range can be extended significantly by a disassembling lamin-B envelope that surrounds the prometaphase spindle and augments the finely tuned, antagonistic kinesin force balance to maintain robust prometaphase spindles as MTs assemble and chromosomes are pushed to the equator.

Step-size Analyses of the Mitochondrial Hsp70 Import Motor Reveal the Brownian Ratchet in Operation

Newly synthesized mitochondrial precursor proteins have to become unfolded by the mitochondrial Hsp70 (mtHsp70) import motor to cross the mitochondrial membranes. To assess the mechanism of unfolding of precursor proteins by mtHsp70, we designed a system to measure step sizes of the mtHsp70 import motor, which are distances at which the motor system moves along polypeptide chains during a single turnover of ATP. We made a series of fusion proteins consisting of a mitochondrial presequence containing the first mtHsp70 binding site, a spacer sequence containing an Hsp70 avoidance segment followed by the second mtHsp70 binding site, and different folded mature domains. Analyses of the dependence of the import rates of those fusion proteins on the lengths of Hsp70 avoidance segments allowed us to estimate the step sizes, which differ for different mature domains and different lengths of the spacers. These results suggest that the mtHsp70 import motor functions at least as a molecular Brownian ratchet to unfold mitochondrial precursor proteins.

Remarks on muscle contraction mechanism.

Muscle contraction mechanism is discussed by reforming the model described in an article by Mitsui (Adv. Biophys. 1999, 36, 107–158). A simple thermodynamic relationship is presented, which indicates that there is an inconsistency in the power stroke model or the swinging lever model. To avoid this difficulty, a new model is proposed. It is assumed that a myosin head forms a polaron-like complex with about three actin molecules when it attaches to an actin filament and the complex translates along the actin filament producing force. Various experimental data on the muscle contraction are well explained based upon the model.

Centipede and inchworm models to explain Mycoplasma gliding

The twelve Mycoplasma species known to glide on solid surfaces all lack surface flagella or pili, and no genes homologous to known motility systems have been found in the five genomes sequenced to date. Recent studies on the fastest of these species, M. mobile, examined novel proteins involved in the gliding mechanism, binding targets on the solid surfaces, energy sources and mechanical characteristics of the movements. Accordingly, I propose a working model for the gliding mechanism, called the centipede (power stroke) model, in which the 'leg' proteins repeat a cycle of binding to and release from the solid surface, using energy from ATP. Another 'inchworm model' suggested from the structural studies of a human pathogen, M. pneumoniae, is also discussed.

Kinetic Characterization of Tail Swing Steps in the ATPase Cycle of Dictyostelium Cytoplasmic Dynein

According to the power stroke model of dynein deduced from electron microscopic and fluorescence resonance energy transfer studies, the power stroke and the recovery stroke are expected to take place at the two isomerization steps of the ATPase cycle at the primary ATPase site. Here, we have conducted presteady-state kinetic analyses of these two isomerization steps with the single-headed motor domain of Dictyostelium cytoplasmic dynein by employing fluorescence resonance energy transfer to probe ATPase steps at the primary site and tail positions. Our results show that the recovery stroke at the first isomerization step proceeds quickly ( approximately 180 s(-1)), whereas the power stroke at the second isomerization step is very slow ( approximately 0.2 s(-1)) in the absence of microtubules, and that the presence of microtubules accelerates the second but not the first step. Moreover, a comparison of the microtubule-induced acceleration of the power stroke step and that of steady-state ATP hydrolysis implies the intriguing possibility that microtubules simultaneously accelerate the ATPase activity not only at the primary site but also at other site(s) in the motor domain.

Pushing, pulling and trapping – Modes of motor protein supported protein translocation

Protein translocation across the cellular membranes is an ubiquitous and crucial activity of cells. This process is mediated by translocases that consist of a protein conducting channel and an associated motor protein. Motor proteins interact with protein substrates and utilize the free energy of ATP binding and hydrolysis for protein unfolding, translocation and unbinding. Since motor proteins are found either at the cis- or trans-side of the membrane, different mechanisms for translocation have been proposed. In the Power stroke model, cis-acting motors are thought to push, while trans-motors pull on the substrate protein during translocation. In the Brownian ratchet model, translocation occurs by diffusion of the unfolded polypeptide through the translocation pore while directionality is achieved by trapping and refolding. Recent insights in the structure and function of the molecular motors suggest that different mechanisms can be employed simultaneously.

Kinesin’s Biased Stepping Mechanism: Amplification of Neck Linker Zippering

A physically motivated model of kinesin’s motor function is developed within the framework of rectified Brownian motion. The model explains how the amplification of neck linker zippering arises naturally through well-known formulae for overdamped dynamics, thereby providing a means to understand how weakly-favorable zippering leads to strongly favorable plus-directed binding of a free kinesin head to microtubule. Additional aspects of kinesin’s motion, such as head coordination and rate-limiting steps, are directly related to the force-dependent inhibition of ATP binding to a microtubule bound head. The model of rectified Brownian motion is presented as an alternative to power stroke models and provides an alternative interpretation for the significance of ATP hydrolysis in the kinesin stepping cycle.

The physics of chaperones

A simple physical property based on entropy gives Hsp70 a pulling force, say Paolo De Los Rios (EPFL, Lausanne, Switzerland), Pierre Goloubinoff (University of Lausanne, Switzerland), and colleagues. The new theory resolves two deadlocked models. Figure 1 Adding Hsp70 reduces mobility and drives motion away from the membrane. Hsp70s have two major activities: they help unfold stable protein aggregates, and they pull proteins through membrane channels. In the Brownian ratchet model for protein import, Hsp70 grabs part of a protein once it is spontaneously unfolded by random thermal fluctuations, and passively prevents it from sliding backward. By contrast, the power stroke model has the Hsp70 using a channel protein as the fulcrum for a lever arm movement that yanks the protein inwards. The Lausanne group suggested that an emerging protein with a bulky Hsp70 attached would keep bumping against the nearby membrane. But if the whole complex moved further away from the membrane, this bumping no longer happened. The resulting increase in mobility and thus entropy meant a favorable change in free energy—a change that powers Hsp70's pulling force away from the membrane. Similar physics would draw Hsp70-bound protein segments away from the bulk of an aggregate and thus tease apart the tangles. “We made a chimeric theory,” says Goloubinoff. “Yes, there is active pulling, but there is no lever.” The Brownian ratchet remains partly intact also, as the unfavorable change of free energy forbids Hsp70 from being pushed back toward the membrane. “The physics behind it is very simple,” says statistical physicist De Los Rios. “It's been known that you can generate forces on polymers when you manipulate the number of conformations that the polymer can exist in.” With the Hsp70 case, he worked out how much work this change could do and found it was compatible with the forces required for protein unfolding and accelerated import. In theory, this leap in thinking could have been made at any time in the last 20 years. In fact, says De Los Rios, “the first thing I said is, this is a nice application, but I asked who must I cite. But I couldn't find anything.” Goloubinoff suggests a precedent. “When I was doing my Ph.D. we had all the tools of molecular biology,” he says. “But there was only one person who thought of PCR.” Reference: De Los Rios, P., et al. 2006. Proc. Natl. Acad. Sci. USA. doi:.10.1073/pnas.0510496103 [PubMed] [Cross Ref]

Considerations on muscle contraction

The independent force generator and the power-stroke cross-bridge model have dominated the thinking on mechanisms of muscular contraction for nearly the past five decades. Here, we review the evolution of the cross-bridge theory from its origins as a two-state model to the current thinking of a multi-state mechanical model that is tightly coupled with the hydrolysis of ATP. Finally, we emphasize the role of skeletal muscle myosin II as a molecular motor whose actions are greatly influenced by Brownian motion. We briefly consider the conceptual idea of myosin II working as a ratchet rather than a power stroke model, an idea that is explored in detail in the companion paper.

The Brownian Ratchet and Power Stroke Models for Posttranslational Protein Translocation into the Endoplasmic Reticulum

A quantitative analysis of experimental data for posttranslational translocation into the endoplasmic reticulum is performed. This analysis reveals that translocation involves a single rate-limiting step, which is postulated to be the release of the signal sequence from the translocation channel. Next, the Brownian ratchet and power stroke models of translocation are compared against the data. The data sets are simultaneously fit using a least-squares criterion, and both models are found to accurately reproduce the experimental results. A likelihood-ratio test reveals that the optimal fit of the Brownian ratchet model, which contains one fewer free parameter, does not differ significantly from that of the power stroke model. Therefore, the data considered here cannot be used to reject this import mechanism. The models are further analyzed using the estimated parameters to make experimentally testable predictions.

Models of Post-Translational Protein Translocation

Organellar Hsp-70 is required for post-translational translocation into the endoplasmic reticulum and mitochondria. The functional role played by Hsp-70 is unknown. However, two operating principles have been suggested. The power stroke model proposes that Hsp-70 undergoes a conformational change, which pulls the precursor protein through the translocation pore, whereas, in the Brownian ratchet model, the role of Hsp-70 is simply to block backsliding through the pore. A mathematical analysis of both mechanisms is presented and reveals that qualitative differences between the models occur in the behavior of the mean velocity and effective diffusion coefficient as a function of Hsp-70 concentration. An experimental method is proposed for measuring these two quantities that only relies on current experimental techniques.

A Chemically Reversible Brownian Motor: Application to Kinesin and Ncd

Kinesin and nonclaret disjunctional protein (ncd) are two microtubule-based molecular motors that use energy from ATP hydrolysis to drive motion in opposite directions. They are structurally very similar and bind with similar orientations on microtubule. What is the origin of the different directionality? Is it some subtle feature of the structure of the motor domains, not apparent in x-ray diffraction studies, or possibly some difference near the neck regions far from the microtubule binding site? Perhaps because the motors function as dimers, the explanation involves differences in the strength of the interaction between the two motor monomers themselves. Here we present another possibility, based on a Brownian ratchet, in which the direction of motion of the motor is controlled by the chemical mechanism of ATP hydrolysis and is an inherent property of a single head. In contrast to conventional power stroke models, dissociation of the individual heads is not obligatory in the chemomechanical cycle, and the steps during which motion and force generation occurs are best described as one-dimensional thermally activated transitions that take place while both heads are attached to the microtubule. We show that our model is consistent with experiments on kinesin in which the velocity is measured as a function of external force and with the observed stiochiometry of one ATP/8-nm step at low load. Further, the model provides a way of understanding recent experiments on the ATP dependence of the variance (randomness) of the distance moved in a given time.

Kinesin Takes One 8-nm Step for Each ATP That It Hydrolyzes

Conventional kinesin is a motor protein that moves stepwise along microtubules carrying membrane-bound organelles toward the periphery of cells. The steps are of amplitude 8.1 nm, the distance between adjacent tubulin binding sites, and are powered by the hydrolysis of ATP. We have asked: how many steps does kinesin take for each molecule of ATP that it hydrolyzes? To answer this question, the motility and ATP hydrolysis of recombinant, heterotetrameric and homodimeric conventional Drosophila kinesins adsorbed to 200-nm-diameter casein-coated silica beads were assayed under identical, single-molecule conditions. Division of the speed by the maximum microtubule-activated ATPase rate gave a stoichiometry of 1. 08 +/- 0.09 steps for each ATP hydrolyzed at 1 mM ATP. Therefore, under low loads in which the drag force << 1 pN, coupling between the chemical and mechanical cycles of kinesin is tight, consistent with conventional power stroke models. Our results rule out models that require two or more ATPs/step, such as some thermal ratchet models, or that propose multiple steps powered by single ATPs.