Theoretical formalism for bead movement powered by single two-headed motors in a motility assay

A numerical algorithm for investigating the role of the motor-cargo linkage in molecular motor-driven transport

We extend the numerical algorithm developed by Wang et al. (2003. J. Theor. Biol. 221, 491-511) for studying biomolecular transport processes to include the linkage that connects molecular motors to their cargo. The new algorithm is used to investigate how the stiffness of the linkage affects the average velocity, effective diffusion coefficient, and randomness parameter. Three different models for molecular motors are considered: (1) a discrete stepping motor (2) a motor moving in a tilted-periodic potential and (3) a motor driven by a flashing potential. We demonstrate that a flexible motor-cargo linkage can make inferences on motor behavior based on measurements of the cargo's position difficult. We also show that even for the case of a tilted-periodic potential there exists an optimal stiffness of the linkage at which transport is maximized. The MATLAB code used in this paper is available at: http://www.unc.edu/approximatelytelston/code/.

Motor proteins transporting cargos

Processive motor proteins such as kinesin and myosin-V are enzymes that use the energy of ATP hydrolysis to travel along polar cytoskeletal filaments. One of the functions of these proteins is the transport of vesicles and protein complexes that are linked to the light chains of the motors. Modeling the light chain by a linear elastic spring, and using the two-state model for one- and two-headed molecular motors, we study the influence of thermal fluctuations of the cargo on the motion of the motor-cargo complex. We solve numerically the Fokker-Planck equations of motor motion, and find that the mean velocity of the motor-cargo complex decreases monotonously as the spring becomes softer. This effect is due to the random force of thermal fluctuations of the cargo disrupting the operation of the motor. Increasing the size (thus, the friction coefficient) of the cargo also decreases the velocity. Surprisingly, we find that for a given size of the cargo, the velocity has a maximum for a certain friction of the motor. We explain this effect by the interplay between the characteristic length of thermal fluctuations of the cargo on a spring, the motor diffusion length, and the filament period. Our results may be relevant for the interpretation of single-molecule experiments with molecular motors (bead assays), where the motor motion is observed by tracking of a bead attached to the motor.

Entropy and information in flagellar axoneme cybernetics: a radial spokes integrative function

Radial spokes and the consequences of their relationships with the central apparatus seem to play a very important role in the regulation of axonemal activity. We modeled their behavior and observed that it appears to differ in the cilium and the flagellum with respect to the development of bending as a function of time. Specifically, our calculation raises the question of the real function of the radial spokes in the regulation of the axoneme, because a given curvature of the flagellar axoneme may correspond to two opposite of their tilts. The stable nil/low amplitude shear points that we had characterized along the flagellum allowed us to describe their axoneme as a series of modules [Cibert, 2002: Cell Motil. Cytoskeleton 51:89-111]. We observed that a nil/low shearing point moves along each module during beating when a new bend is created at the base of the flagellum [Cibert, 2001: Cell Motil. Cytoskeleton 49:161-175]. We propose that the structural gradients of isoforms of tubulin could be basic verniers that act as structural references for the axonemal machinery during the beating. This allowed us to interpret the axonemal organization as a segmented structure, that could be analyzed according to the complexion(1) theory and Shannon's information theory, which associate entropy and probability in the creation of information. The important consequence of this interpretation is that regulation of the axonemal machinery appears to be due to the upstream and downstream cross-talk between the axonemal segments that do not involve any dedicated integrative structure but depend on the energy level of the entire length of each module.

Fluctuations and randomness of movement of the bead powered by a single kinesin molecule in a force-clamped motility assay: Monte Carlo simulations

The motility assay of K. Visscher, M. J. Schnitzer, and S. M. Block (Nature, 400:184-189, 1999) in which the movement of a bead powered by a single kinesin motor can be measured is a very useful tool in characterizing the force-dependent steps of the mechanochemical cycle of kinesin motors, because in this assay the external force applied to the bead can be controlled (clamped) arbitrarily. However, because the bead is elastically attached to the motor and the response of the clamp is not fast enough to compensate the Brownian motion of the bead, interpretation or analysis of the data obtained from the assay is not trivial. In a recent paper (Y. Chen and B. Yan, Biophys. Chem. 91:79-91, 2001), we showed how to evaluate the mean velocity of the bead and the motor in the motility assay for a given mechanochemical cycle. In this paper we extend the study to the evaluation of the fluctuation or the randomness of the velocity using a Monte Carlo simulation method. Similar to the mean, we found that the randomness of the velocity of the motor is also influenced by the parameters that affect the dynamic behavior of the bead, such as the viscosity of the medium, the size of the bead, the stiffness of the elastic element connecting the bead and the motor, etc. The method presented in this paper should be useful in modeling the kinetic mechanism of any processive motor (such as conventional kinesin and myosin V) based on measured force-clamp motility data.