Showing papers by "Michael E. Fisher published in 2007"

Molecular Motors: A Theorist's Perspective

Abstract: Individual molecular motors, or motor proteins, are enzymatic molecules that convert chemical energy, typically obtained from the hydrolysis of ATP (adenosine triphosphate), into mechanical work and motion. Processive motor proteins, such as kinesin, dynein, and certain myosins, step unidirectionally along linear tracks, specifically microtubules and actin filaments, and play a crucial role in cellular transport processes, organization, and function. In this review some theoretical aspects of motor-protein dynamics are presented in the light of current experimental methods that enable the measurement of the biochemical and biomechanical properties on a single-molecule basis. After a brief discussion of continuum ratchet concepts, we focus on discrete kinetic and stochastic models that yield predictions for the mean velocity, V(F, [ATP], ...), and other observables as a function of an imposed load force F, the ATP concentration, and other variables. The combination of appropriate theory with single-molecule observations should help uncover the mechanisms underlying motor-protein function.

Back-stepping, hidden substeps, and conditional dwell times in molecular motors.

Abstract: Processive molecular motors take more-or-less uniformly sized steps, along spatially periodic tracks, mostly forwards but increasingly backwards under loads. Experimentally, the major steps can be ...

Mechanoenzymes under superstall and large assisting loads reveal structural features

Abstract: Single-molecule experiments on the motor protein kinesin have observed runs of backsteps and thus a negative, that is, reverse mean velocity, V, under superstall loads, F; but, counterintuitively, beyond stall, V(F) displays a shallow minimum and then decreases in magnitude. Conversely, under assisting loads V(F) rises to a maximum before decreasing monotonically. By contrast, while the velocity of myosin V also saturates under assisting loads, the motor moves backward increasingly rapidly under superstall loads. For both kinesin and myosin V this behavior is implied remarkably well by simple two-state kinetic models when extrapolated to large loads. To understand the origins of such results in general mechanoenzymes, biochemical kinetic descriptions are discussed on the basis of a free-energy landscape picture. It transpires that the large-load performance is determined by the geometrical placement of the intermediate mechanochemical states of the enzymatic cycles relative to the associated transition states. Explicit criteria are presented for N-state sequential kinetics, including side-reaction chains, etc., and for parallel-pathway models. Physical colocalization of biochemically distinct states generally implies large-load velocity saturation.

Simulating critical dynamics in liquid mixtures: short-range and long-range contributions.

Abstract: Recently, Das et al. [J. Chem. Phys. 125, 024506 (2006)] established that computer simulations of critical dynamics in a binary Lennard-Jones mixture are consistent with the predicted Stokes-Einstein behavior of the asymptotic decay rate of the order-parameter fluctuations near criticality. Here, we show that the noncritical or “background” contributions to the computed diffusion coefficient are also in agreement with both theory and experiment, thus further validating the feasibility of molecular dynamics simulations for studying dynamic critical behavior.

Interdiffusion in Critical Binary Mixtures by Molecular Dynamics Simulation

Abstract: A simulation study of the static and dynamic critical behavior of a symmetric binary Lennard-Jones mixture is briefly reviewed. Using a combination of semi-grand-canonical Monte Carlo (SGMC) and molecular dynamics (MD) methods near the critical temperature of liquid-liquid unmixing, the correlation length and “susceptibility” related to the critical concentration fluctuations are estimated, as well as the self- and interdiffusion coefficients. While the self-diffusion coefficient does not show a detectable critical anomaly, the interdiffusion coefficient is found to vanish when one approaches the critical temperature at fixed critical concentration. It is shown that in the corresponding Onsager coefficient both a divergent singular part and a nonsingular background term need to be taken into account. With appropriate finite-size scaling analysis (the particle numbers studied for the dynamics lie only in the range from N = 400 to 6400), the critical behavior of the interdiffusion coefficient is found to be compatible both with the theoretically predicted behavior and with corresponding experimental evidence.