Mitsunori Takano

Unidirectional Brownian motion observed in an in silico single molecule experiment of an actomyosin motor

The actomyosin molecular motor, the motor composed of myosin II and actin filament, is responsible for muscle contraction, converting chemical energy into mechanical work. Although recent single molecule and structural studies have shed new light on the energy-converting mechanism, the physical basis of the molecular-level mechanism remains unclear because of the experimental limitations. To provide a clue to resolve the controversy between the lever-arm mechanism and the Brownian ratchet-like mechanism, we here report an in silico single molecule experiment of an actomyosin motor. When we placed myosin on an actin filament and allowed myosin to move along the filament, we found that myosin exhibits a unidirectional Brownian motion along the filament. This unidirectionality was found to arise from the combination of a nonequilibrium condition realized by coupling to the ATP hydrolysis and a ratchet-like energy landscape inherent in the actin-myosin interaction along the filament, indicating that a Brownian ratchet-like mechanism contributes substantially to the energy conversion of this molecular motor.

Temperature-Enhanced Association of Proteins Due to Electrostatic Interaction: A Coarse-Grained Simulation of Actin–Myosin Binding

Association of protein molecules constitutes the basis for the interaction network in a cell. Despite its fundamental importance, the thermodynamic aspect of protein-protein binding, particularly the issues relating to the entropy change upon binding, remains elusive. The binding of actin and myosin, which are vital proteins in motility, is a typical example, in which two different binding mechanisms have been argued: the binding affinity increases with increasing temperature and with decreasing salt-concentration, indicating the entropy-driven binding and the enthalpy-driven binding, respectively. How can these thermodynamically different binding mechanisms coexist? To address this question, which is of general importance in understanding protein-protein bindings, we conducted an in silico titration of the actin-myosin system by molecular dynamics simulation using a residue-level coarse-grained model, with particular focus on the role of the electrostatic interaction. We found a good agreement between in silico and in vitro experiments on the salt-concentration dependence and the temperature dependence of the binding affinity. We then figured out how the two binding mechanisms can coexist: the enthalpy (due to electrostatic interaction between actin and myosin) provides the basal binding affinity, and the entropy (due to the orientational disorder of water molecules) enhances it at higher temperatures. In addition, we analyzed the actin-myosin complex structures observed during the simulation and obtained a variety of weak-binding complex structures, among which were found an unusual binding mode suggested by an earlier experiment and precursor structures of the strong-binding complex proposed by electron microscopy. These results collectively indicate the potential capability of a residue-level coarse-grained model to simulate the association-dissociation dynamics (particularly for transient weak-bindings) exhibited by larger and more complicated systems, as in a cell.

Investigating a link between all-atom model simulation and the Ising-based theory on the helix–coil transition: Equilibrium statistical mechanics

To describe the polypeptide helix–coil transition, while the Ising-based theory has been playing the principal role for 40 years, we can now make use of computer simulation using the so-called “all-atom model” that is far more precise than the Ising-based model. In this study, by conducting molecular dynamics (MD) simulations of helix–coil transition exhibited by a short polyalanine chain, we investigated how the MD simulation results and the Ising-based theoretical values coincide with each other, placing a focus on their equilibrium statistical mechanical properties. Several important physical properties, such as temperature-dependent helix ratio, distribution of the helix-residue number, position-dependent helix ratio, and pair-correlation between residue states were taken up as the proving grounds on which we made a comparison between the all-atom model simulation and the Ising-based theory. As an overall trend, we realized that the Ising-based theoretical results agreed with the all-atom simulation r...

Residue network in protein native structure belongs to the universality class of a three-dimensional critical percolation cluster

Single protein molecules are regarded as contact networks of amino-acid residues. Relationships between the shortest path lengths and the numbers of residues within single molecules in the native structures are examined for various sized proteins. A universal scaling among proteins is obtained, which shows that the residue networks are fractal networks. This universal fractal network is characterized with three kinds of dimensions: the network topological dimension D{c} approximately 1.9 , the fractal dimension D{f} approximately 2.5 , and the spectral dimension D{s} approximately 1.3 . These values are in surprisingly good coincidence with those of the three-dimensional critical percolation cluster. Hence the residue contact networks in the protein native structures belong to the universality class of the three-dimensional percolation cluster. The criticality is relevant to the ambivalence in the protein native structures, the coexistence of stability and instability, both of which are necessary for protein functions.

Violation of the Fluctuation-Dissipation Theorem in a Protein System

We report the results of molecular dynamics simulations of the protein myosin carried out with an elastic network model. Quenching the system, we observe glassy behavior of a density correlation function and a density response function that are often investigated in structure glasses and spin glasses. In the equilibrium, the fluctuation-response relation, a representative relation of the fluctuation-dissipation theorem, holds that the ratio of the density correlation function to the density response function is equal to the temperature of the environment. We show that, in the quenched system that we study, this relation can be violated. In the case that this relation does not hold, this ratio can be regarded as an effective temperature. We find that this effective temperature of myosin is higher than the temperature of the environment. We discuss the relation between this effective temperature and energy transduction that occurs after ATP hydrolysis in the myosin molecule.

Intrinsic disorder accelerates dissociation rather than association.

The intrinsically disordered protein (IDP) has distinct properties both physically and biologically: it often becomes folded when binding to the target and is frequently involved in signal transduction. The physical property seems to be compatible with the biological property where fast association and dissociation between IDP and the target are required. While fast association has been well studied, fueled by the fly‐casting mechanism, the dissociation kinetics has received less attention. We here study how the intrinsic disorder affects the dissociation kinetics, as well as the association kinetics, paying attention to the interaction strength at the binding site (i.e., the quality of the “fly lure”). Coarse‐grained molecular dynamics simulation of the pKID‐KIX system, a well‐studied IDP system, shows that the association rate becomes larger as the disorder‐inducing flexibility that was imparted to the model is increased, but the acceleration is marginal and turns into deceleration as the quality of the fly lure is worsened. In contrast, the dissociation rate is greatly enhanced as the disorder is increased, indicating that intrinsic disorder serves for rapid signal switching more effectively through dissociation than association. Proteins 2016; 84:1124–1133.

Conformational Ensembles of an Intrinsically Disordered Protein pKID with and without a KIX Domain in Explicit Solvent Investigated by All-Atom Multicanonical Molecular Dynamics

The phosphorylated kinase-inducible activation domain (pKID) adopts a helix–loop–helix structure upon binding to its partner KIX, although it is unstructured in the unbound state. The N-terminal and C-terminal regions of pKID, which adopt helices in the complex, are called, respectively, αA and αB. We performed all-atom multicanonical molecular dynamics simulations of pKID with and without KIX in explicit solvents to generate conformational ensembles. Although the unbound pKID was disordered overall, αA and αB exhibited a nascent helix propensity; the propensity of αA was stronger than that of αB, which agrees with experimental results. In the bound state, the free-energy landscape of αB involved two low free-energy fractions: native-like and non-native fractions. This result suggests that αB folds according to the induced-fit mechanism. The αB-helix direction was well aligned as in the NMR complex structure, although the αA helix exhibited high flexibility. These results also agree quantitatively with experimental observations. We have detected that the αB helix can bind to another site of KIX, to which another protein MLL also binds with the adopting helix. Consequently, MLL can facilitate pKID binding to the pKID-binding site by blocking the MLL-binding site. This also supports experimentally obtained results.

Systematic single base-pair substitution analysis of DNA binding by the cAMP receptor protein in cyanobacterium Synechocystis sp. PCC 6803.

The cAMP receptor protein SYCRP1 in cyanobacterium Synechocystis sp. PCC 6803 is a regulatory protein that binds to the consensus DNA sequence (5′‐AAATGTGATCTAGATCACATTT‐3′) for the cAMP receptor protein CRP in Escherichia coli. Here we examined the effects of systematic single base‐pair substitutions at positions 4–8 (TGTGA) of the consensus sequence on the specific binding of SYCRP1. The consensus sequence exhibited the highest affinity, and the effects of base‐pair substitutions at positions 5 and 7 were the most deleterious. The result is similar to that previously reported for CRP, whereas there were differences between SYCRP1 and CRP in the rank order of affinity for each substitution.

A DNA Computing-based Genetic Program for In Vitro Protein Evolution via Constrained Pseudomodule Shuffling

An in vitro domainal shuffling strategy for protein evolution was proposed in (J. Kolkman and W. Stemmer, Nat. Biotech.19 (423) 2001). Due to backhybridization, however this method appears unlikely to be an efficient means of iteratively generating massive libraries of combinatorially shuffled genes. Recombination at the domain level (30–300 residues) also appears too coarse to support the evolution of proteins with substantially new folds. In this work, the module (10–25 residues long) and pseudomodule are adopted as the fundamental units of protein structure. Each protein is modelled as an N to C-terminal tour of a digraph composed of pseudomodules. An in vitro method based on PNA-mediated Whiplash PCR (PWPCR), RNA-protein fusion, and restriction-based recombination, XWPCR is then presented for evolving proteins with a high affinity for a given motif, subject to the constraint that each corresponds to a walk on the pseudomodule digraph of interest. Simulations predict that PWPCR is an efficient method of producing massive, shuffled gene libraries encoding for proteins as long as roughly 600 residues.

Coupling of Lever Arm Swing and Biased Brownian Motion in Actomyosin

An important unresolved problem associated with actomyosin motors is the role of Brownian motion in the process of force generation. On the basis of structural observations of myosins and actins, the widely held lever-arm hypothesis has been proposed, in which proteins are assumed to show sequential structural changes among observed and hypothesized structures to exert mechanical force. An alternative hypothesis, the Brownian motion hypothesis, has been supported by single-molecule experiments and emphasizes more on the roles of fluctuating protein movement. In this study, we address the long-standing controversy between the lever-arm hypothesis and the Brownian motion hypothesis through in silico observations of an actomyosin system. We study a system composed of myosin II and actin filament by calculating free-energy landscapes of actin-myosin interactions using the molecular dynamics method and by simulating transitions among dynamically changing free-energy landscapes using the Monte Carlo method. The results obtained by this combined multi-scale calculation show that myosin with inorganic phosphate (Pi) and ADP weakly binds to actin and that after releasing Pi and ADP, myosin moves along the actin filament toward the strong-binding site by exhibiting the biased Brownian motion, a behavior consistent with the observed single-molecular behavior of myosin. Conformational flexibility of loops at the actin-interface of myosin and the N-terminus of actin subunit is necessary for the distinct bias in the Brownian motion. Both the 5.5–11 nm displacement due to the biased Brownian motion and the 3–5 nm displacement due to lever-arm swing contribute to the net displacement of myosin. The calculated results further suggest that the recovery stroke of the lever arm plays an important role in enhancing the displacement of myosin through multiple cycles of ATP hydrolysis, suggesting a unified movement mechanism for various members of the myosin family.