Landscape-Based View on the Stepping Movement of Myosin VI

Myosin VI dimer walks toward the minus end of the actin filament with a large and variable step size of 25–36 nm. Two competing models have been put forward to explain this large step size. The Spudich model assumes that the myosin VI dimer associates at a distal tail near the cargo-binding domain, which makes two full-length single α-helix (SAH) domains serve as long legs. In contrast, the Houdusse–Sweeney model assumes that the association occurs in the middle (between residues 913 and 940) of the SAH domain and that the three-helix bundles unfold to ensure the large step size. Their consistency with the observation of stepping motion with a large and variable step size has not been examined in detail. To compare the two proposed models of myosin VI, we computationally characterized the free energy landscape experienced by the leading head during the stepping movement along the actin filament using the elastic network model of two heads and an implicit model of the SAH domains. Our results showed that the Spudich model is more consistent with the 25–36 nm step size than the Houdusse–Sweeney model. The unfolding of the three-helix bundles gives rise to the free energy bias toward a shorter distance between two heads. Besides, the stiffness of the SAH domain is a key factor for giving strong energetic bias toward the longer distance of stepping. Free energy analysis of the stepping motion complements the visual inspection of static structures and enables a deeper understanding of underlying mechanisms of molecular motors.

Mechanochemical Model of the Power Stroke of the Single-Headed Motor Protein KIF1A

During the process of ATP binding to an apo-kinesin microtubule (MT), the kinesin core rotates on the MT, and the neck linker (NL) of the kinesin undergoes an undocked to docked transition. This has been suggested to be a power stroke of kinesin, on the basis of the structural analysis. Here, we developed a mesoscopic structure-based model and studied the power stroke of KIF1A. We quantified the underlying free energy landscape and showed the emergence of several states for the power stroke of KIF1A: UB-UR-UD (unbound, unrotating, undock), B-IR-UD (bound, initial rotating, undock), B-PR-UD (bound, partial rotating, undock), and B-R-D (bound, rotating, dock). We found that ATP binding triggered conformational fluctuations of key elements. We also explored the conformational change of key structural elements during the rotation of KIF1A and docking of the NL. In addition, we semiquantitatively and qualitatively estimated the free energy released by the ATP binding, and how much of this remains for the docking of the NL during the power stroke process at different temperatures. Finally, based on results from the thermodynamics landscape and conformational change of structural key elements, we proposed a mechanochemical model of the power stroke of KIF1A.

Including Thermal Fluctuations in Actomyosin Stable States Increases the Predicted Force per Motor and Macroscopic Efficiency in Muscle Modelling

Muscle contractions are generated by cyclical interactions of myosin heads with actin filaments to form the actomyosin complex. To simulate actomyosin complex stable states, mathematical models usually define an energy landscape with a corresponding number of wells. The jumps between these wells are defined through rate constants. Almost all previous models assign these wells an infinite sharpness by imposing a relatively simple expression for the detailed balance, i.e., the ratio of the rate constants depends exponentially on the sole myosin elastic energy. Physically, this assumption corresponds to neglecting thermal fluctuations in the actomyosin complex stable states. By comparing three mathematical models, we examine the extent to which this hypothesis affects muscle model predictions at the single cross-bridge, single fiber, and organ levels in a ceteris paribus analysis. We show that including fluctuations in stable states allows the lever arm of the myosin to easily and dynamically explore all possible minima in the energy landscape, generating several backward and forward jumps between states during the lifetime of the actomyosin complex, whereas the infinitely sharp minima case is characterized by fewer jumps between states. Moreover, the analysis predicts that thermal fluctuations enable a more efficient contraction mechanism, in which a higher force is sustained by fewer attached cross-bridges.

Mathematical models are of fundamental importance in the quantitative verification of biological hypotheses. Muscle contraction models assume the existence of several stable states for the myosin head, whereas the transition rates between states are defined to fit experimental data. The ratio of the forward and backward rates is linked to the ratio of the probabilities of being in one or other stable state at equilibrium through a detailed balance condition. A commonly used assumption leads to a relatively simple expression for this balance condition that depends only on the values of the energy at the minima and not on the minima shape. Mathematically, this hypothesis corresponds to infinite sharpness at these minima; physically, it neglects the small thermal fluctuations within actomyosin stable states. In this work, we compare this classical approach with a model that includes thermal fluctuations within wide minima, and quantitatively assess how much this hypothesis affects the model outcomes at the single molecule, single fiber, and whole heart levels. It is shown that, using parameters compatible with known behavior in muscle mechanics, relaxing the infinitely sharp minima hypothesis improves the predicted force generation and efficiency at the macroscopic level.

Protein Ensembles: How Does Nature Harness Thermodynamic Fluctuations for Life? The Diverse Functional Roles of Conformational Ensembles in the Cell

All soluble proteins populate conformational ensembles that together constitute the native state. Their fluctuations in water are intrinsic thermodynamic phenomena, and the distributions of the states on the energy landscape are determined by statistical thermodynamics; however, they are optimized to perform their biological functions. In this review we briefly describe advances in free energy landscape studies of protein conformational ensembles. Experimental (nuclear magnetic resonance, small-angle X-ray scattering, single-molecule spectroscopy, and cryo-electron microscopy) and computational (replica-exchange molecular dynamics, metadynamics, and Markov state models) approaches have made great progress in recent years. These address the challenging characterization of the highly flexible and heterogeneous protein ensembles. We focus on structural aspects of protein conformational distributions, from collective motions of single- and multi-domain proteins, intrinsically disordered proteins, to multiprotein complexes. Importantly, we highlight recent studies that illustrate functional adjustment of protein conformational ensembles in the crowded cellular environment. We center on the role of the ensemble in recognition of small- and macro-molecules (protein and RNA/DNA) and emphasize emerging concepts of protein dynamics in enzyme catalysis. Overall, protein ensembles link fundamental physicochemical principles and protein behavior and the cellular network and its regulation.

Difference in the hydration water mobility around F-actin and myosin subfragment-1 studied by quasielastic neutron scattering

Hydration water is essential for a protein to perform its biological function properly. In this study, the dynamics of hydration water around F-actin and myosin subfragment-1 (S1), which are the partner proteins playing a major role in various cellular functions related to cell motility including muscle contraction, was characterized by incoherent quasielastic neutron scattering (QENS). The QENS measurements on the D₂O- and H₂O-solution samples of F-actin and S1 provided the spectra of hydration water, from which the translational diffusion coefficient (D_T), the residence time (τ_T), and the rotational correlation time (τ_R) were evaluated. The D_T value of the hydration water of S1 was found to be much smaller than that of the hydration water of F-actin while the τ_T values were similar between S1 and F-actin. On the other hand, the τ_R values of the hydration water of S1 was found to be larger than that of the hydration water of F-actin. It was also found that the D_T and τ_R values of the hydration water of F-actin are similar to those of bulk water. These results suggest a significant difference in mobility of the hydration water between S1 and F-actin: S1 has the typical hydration water, the mobility of which is reduced compared with that of bulk water, while F-actin has the unique hydration water, the mobility of which is close to that of bulk water rather than the typical hydration water around proteins.

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Hydration water dynamics of F-actin and myosin S1 was studied by neutron scattering.

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Both translational and rotational motions are higher for F-actin hydration water.

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Mobility of F-actin hydration water is close to that of bulk water.

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High mobility of F-actin hydration water would promote the actomyosin interaction.

Internal dynamics of F-actin and myosin subfragment-1 studied by quasielastic neutron scattering

Various biological functions related to cell motility are driven by the interaction between the partner proteins, actin and myosin. To obtain insights into how this interaction occurs, the internal dynamics of F-actin and myosin subfragment-1 (S1) were characterized by the quasielastic neutron scattering measurements on the solution samples of F-actin and S1. Contributions of the internal motions of the proteins to the scattering spectra were separated from those of the global macromolecular diffusion. Analysis of the spectra arising from the internal dynamics showed that the correlation times of the atomic motions were about two times shorter for F-actin than for S1, suggesting that F-actin fluctuates more rapidly than S1. It was also shown that the fraction of the immobile atoms is larger for S1 than for F-actin. These results suggest that F-actin actively facilitates the binding of myosin by utilizing the more frequent conformational fluctuations than those of S1.

Nucleotide-dependent structural fluctuations and regulation of microtubule-binding affinity of KIF1A

Molecular motors such as kinesin regulate affinity to a rail protein during the ATP hydrolysis cycle. The regulation mechanism, however, is yet to be determined. To understand this mechanism, we investigated the structural fluctuations of the motor head of the single-headed kinesin called KIF1A in different nucleotide states using molecular dynamics simulations of a Gō-like model. We found that the helix α4 at the microtubule (MT) binding site intermittently exhibits a large structural fluctuation when MT is absent. Frequency of this fluctuation changes systematically according to the nucleotide states and correlates strongly with the experimentally observed binding affinity to MT. We also showed that thermal fluctuation enhances the correlation and the interaction with the nucleotide suppresses the fluctuation of the helix α4. These results suggest that KIF1A regulates affinity to MT by changing the flexibility of the helix α4 during the ATP hydrolysis process: the binding site becomes more flexible in the strong binding state than in the weak binding state.