Non-processive Molecular Motors Research Articles

Cooperativity of myosin II motors in the non-regulated and regulated thin filaments investigated with high-speed AFM.

Skeletal myosins II are non-processive molecular motors that work in ensembles to produce muscle contraction while binding to the actin filament. Although the molecular properties of myosin II are well known, there is still debate about the collective work of the motors: is there cooperativity between myosin motors while binding to the actin filaments? In this study, we use high-speed AFM to evaluate this issue. We observed that the initial binding of small arrays of myosin heads to the non-regulated actin filaments did not affect the cooperative probability of subsequent bindings and did not lead to an increase in the fractional occupancy of the actin binding sites. These results suggest that myosin motors are independent force generators when connected in small arrays, and that the binding of one myosin does not alter the kinetics of other myosins. In contrast, the probability of binding of myosin heads to regulated thin filaments under activating conditions (at high Ca2+ concentration in the presence of 2 μM ATP) was increased with the initial binding of one myosin, leading to a larger occupancy of available binding sites at the next half-helical pitch of the filament. The result suggests that myosin cooperativity is observed over five pseudo-repeats and defined by the activation status of the thin filaments.

Differences in cooperativity of myosin II motors in actin and regulated thin filaments

Skeletal myosins II are non-processive molecular motors that work in ensembles to produce muscle contraction while binding to the actin filament. At the sarcomere level, myosin-actin interactions are regulated by the thin filaments. There is still debate about the collective work of the myosin motors: is there a cooperativity between different myosin motors while binding to the actin filament, or the regulated thin filament? In this study, we used high-speed atomic HS-AFM and an experimental approach that allows several double headed myosins to attach to parallel actin or thin filaments to evaluate a potential cooperativity among motors.

High-Speed Optical Traps Address Dynamics of Processive and Non-Processive Molecular Motors.

Interactions between biological molecules occur on very different time scales, from the minutes of strong protein-protein bonds, down to below the millisecond duration of rapid biomolecular interactions. Conformational changes occurring on sub-ms time scales and their mechanical force dependence underlie the functioning of enzymes (e.g., motor proteins) that are fundamental for life. However, such rapid interactions are beyond the temporal resolution of most single-molecule methods. We developed ultrafast force-clamp spectroscopy (UFFCS), a single-molecule technique based on laser tweezers that allows us to investigate early and very fast dynamics of a variety of enzymes and their regulation by mechanical load. The technique was developed to investigate the rapid interactions between skeletal muscle myosin and actin, and then applied to the study of different biological systems, from cardiac myosin to processive myosin V, microtubule-binding proteins, transcription factors, and mechanotransducer proteins. Here, we describe two different implementations of UFFCS instrumentation and protocols using either acousto- or electro-optic laser beam deflectors, and their application to the study of processive and non-processive motor proteins.

Millisecond Conformational Dynamics of Skeletal Myosin II Power Stroke Studied by High-Speed Atomic Force Microscopy.

Myosin-based molecular motors are responsible for a variety of functions in the cells. Myosin II is ultimately responsible for muscle contraction and can be affected by multiple mutations, that may lead to myopathies. Therefore, it is essential to understand the nanomechanical properties of myosin II. Due to the lack of technical capabilities to visualize rapid changes in nonprocessive molecular motors, there are several mechanistic details in the force-generating steps produced by myosin II that are poorly understood. In this study, high-speed atomic force microscopy was used to visualize the actin-myosin complex at high temporal and spatial resolutions, providing further details about the myosin mechanism of force generation. A two-step motion of the double-headed heavy meromyosin (HMM) lever arm, coupled to an 8.4 nm working stroke was observed in the presence of ATP. HMM heads attached to an actin filament worked independently, exhibiting different lever arm configurations in given time during experiments. A lever arm rotation was associated with several non-stereospecific long-lived and stereospecific short-lived (∼1 ms) HMM conformations. The presence of free Pi increased the short-lived stereospecific binding events in which the power stroke occurred, followed by release of Pi after the power stroke.

Modelling cytoskeletal transport by clusters of non-processive molecular motors with limited binding sites.

Molecular motors are responsible for intracellular transport of a variety of biological cargo. We consider the collective behaviour of a finite number of motors attached on a cargo. We extend previous analytical work on processive motors to the case of non-processive motors, which stochastically bind on and off cytoskeletal filaments with a limited number of binding sites available. Physically, motors attached to a cargo cannot bind anywhere along the filaments, so the number of accessible binding sites on the filament should be limited. Thus, we analytically study the distribution and the velocity of a cluster of non-processive motors with limited number of binding sites. To validate our analytical results and to go beyond the level of detail possible analytically, we perform Monte Carlo latticed based stochastic simulations. In particular, in our simulations, we include sequence preservation of motors performing stepping and binding obeying a simple exclusion process. We find that limiting the number of binding sites reduces the probability of non-processive motors binding but has a relatively small effect on force–velocity relations. Our analytical and stochastic simulation results compare well to published data from in vitro and in vivo experiments.

Analysis of Nonprocessive Molecular Motor Transport Using Renewal Reward Theory

We propose and analyze a mathematical model of cargo transport by non-processive molecular motors. In our model, the motors change states by random discrete events (corresponding to stepping and binding/unbinding), while the cargo position follows a stochastic differential equation (SDE) that depends on the discrete states of the motors. The resulting system for the cargo position is consequently an SDE that randomly switches according to a Markov jump process governing motor dynamics. To study this system we (1) cast the cargo position in a renewal theory framework and generalize the renewal reward theorem and (2) decompose the continuous and discrete sources of stochasticity and exploit a resulting pair of disparate timescales. With these mathematical tools, we obtain explicit formulas for experimentally measurable quantities, such as cargo velocity and run length. Analyzing these formulas then yields some predictions regarding so-called non-processive clustering, the phenomenon that a single motor cannot transport cargo, but that two or more motors can. We find that having motor stepping, binding, and unbinding rates depend on the number of bound motors, due to geometric effects, is necessary and sufficient to explain recent experimental data on non-processive motors.

Theme Issue in memory of Tom Duke

This Theme Issue is dedicated to the memory of Tom Duke, who passed away in 2012 at the age of 48. Tom made lasting contributions to a broad range of topics and was highly regarded for his very elegant approaches that unravel key physical principles underlying the function of biological systems.

Ensemble velocity of non-processive molecular motors with multiple chemical states.

We study the ensemble velocity of non-processive motor proteins, described with multiple chemical states. In particular, we discuss the velocity as a function of ATP concentration. Even a simple model which neglects the strain dependence of transition rates, reverse transition rates and nonlinearities in the elasticity can show interesting functional dependencies, which deviate significantly from the frequently assumed Michaelis-Menten form. We discuss how the order of events in the duty cycle can be inferred from the measured dependence. The model also predicts the possibility of velocity reversal at a certain ATP concentration if the duty cycle contains several conformational changes of opposite directionalities.

Power-stroke-driven actomyosin contractility

In ratchet-based models describing actomyosin contraction the activity is usually associated with actin binding potential while the power-stroke mechanism, residing inside myosin heads, is viewed as passive. To show that contraction can be propelled directly through a conformational change, we propose an alternative model where the power stroke is the only active mechanism. The asymmetry, ensuring directional motion, resides in steric interaction between the externally driven power-stroke element and the passive nonpolar actin filament. The proposed model can reproduce all four discrete states of the minimal actomyosin catalytic cycle even though it is formulated in terms of continuous Langevin dynamics. We build a conceptual bridge between processive and nonprocessive molecular motors by demonstrating that not only the former but also the latter can use structural transformation as the main driving force.

Stochastic dynamics of small ensembles of non-processive molecular motors: The parallel cluster model

Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes, or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of the fraction of bound motors under load and thus to firm attachment even for small ensembles. This adaptation to load results in a concave force-velocity relation described by a Hill relation. For external load provided by a linear spring, myosin II ensembles dynamically adjust themselves towards an isometric state with constant average position and load. The dynamics of the ensembles is now determined mainly by the distribution of motors over the different kinds of bound states. For increasing stiffness of the external spring, there is a sharp transition beyond which myosin II can no longer perform the power stroke. Slow unbinding from the pre-power-stroke state protects the ensembles against detachment.

Ultrafast Force-Clamp Spectroscopy of Single Molecular Motors and DNA Binding Proteins

Force plays a fundamental role in a wide array of biological processes, regulating, for example, enzymatic activity, kinetics of molecular bonds, and molecular motors mechanics. Single molecule force spectroscopy techniques have enabled the investigation of such processes, but they are inadequate to probe short-lived (millisecond and sub-millisecond) molecular complexes. Here, we present a novel force-clamp laser trap that is capable of applying constant loads to molecular complexes with lifetimes above ∼10 μs [Capitanio et al., Nature Methods 9, 1013-1019 (2012)]. Such capability is enhanced by a detection strategy allowing the investigation of very short interactions (∼100μs). Moreover, the high temporal and spatial resolution of the method enables us to probe sub-nanometer conformational changes with a time resolution of few tens of microseconds. We tested our method on molecular motors and DNA-binding proteins. We could apply constant loads to a single motor domain of myosin before its working stroke was initiated (0.2–1 ms), thus directly measuring its load dependence. We found that, depending on the applied load, myosin weakly interacted (<1 ms) with actin without production of movement, fully developed its working stroke or prematurely detached (<5 ms), thus reducing the working stroke size with load. These results resolve the molecular mechanism underlying regulation of muscle contraction by force. Our technique could be straightforwardly applied to a wide variety of non-processive molecular motors, single domains of processive motors, protein-DNA and protein-RNA interactions, and conceivably to any short-lived protein-protein interaction, opening new avenues for investigating the effects of forces on biological processes.