The Force Exerted by a Molecular Motor

The stochastic driving force exerted by a single molecular motor (e.g., a kinesin, or myosin) moving on a periodic molecular track (microtubule, actin filament, etc.) is discussed from a general viewpoint open to experimental test. An elementary "barometric" relation for the driving force is introduced that (i) applies to a range of kinetic and stochastic models, (ii) is consistent with more elaborate expressions entailing explicit representations of externally applied loads and, (iii) sufficiently close to thermal equilibrium, satisfies an Einstein-type relation in terms of the velocity and diffusion coefficient of the (load-free) motor. Even in the simplest two-state models, the velocity-vs.-load plots exhibit a variety of contrasting shapes (including nonmonotonic behavior). Previously suggested bounds on the driving force are shown to be inapplicable in general by analyzing discrete jump models with waiting time distributions.Comment: submitted to PNA

Extended Kinetic Models with Waiting-Time Distributions: Exact Results

Inspired by the need for effective stochastic models to describe the complex behavior of biological motor proteins that move on linear tracks exact results are derived for the velocity and dispersion of simple linear sequential models (or one-dimensional random walks) with general waiting-time distributions. The concept of ``mechanicity'' is introduced in order to conveniently quantify departures from simple ``chemical,'' kinetic rate processes, and its significance is briefly indicated. The results are extended to more elaborate models that have finite side-branches and include death processes (to represent the detachment of a motor from the track).Comment: 17 pages, 2 figure

Theoretical Investigation of Totally Asymmetric Exclusion Processes on Lattices with Junctions

Totally asymmetric simple exclusion processes on lattices with junctions, where particles interact with hard-core exclusion and move on parallel lattice branches that at the junction combine into a single lattice segment, are investigated. A simple approximate theory, that treats the correlations around the junction position in a mean-field fashion, is developed in order to calculate stationary particle currents, density profiles and a phase diagram. It is shown that there are three possible stationary phases depending on the state of each of the lattice branch. At first-order phase boundaries, where the density correlations are important, a modified phenomenological domain-wall theory, that accounts for correlations, is introduced. Extensive Monte Carlo computer simulations are performed to investigate the system, and it is found that they are in excellent agreement with theoretical predictions.Comment: 16 pages, 7 figure

Understanding Mechanochemical Coupling in Kinesins Using First-Passage Time Processes

Kinesins are processive motor proteins that move along microtubules in a stepwise manner, and their motion is powered by the hydrolysis of ATP. Recent experiments have investigated the coupling between the individual steps of single kinesin molecules and ATP hydrolysis, taking explicitly into account forward steps, backward steps and detachments. A theoretical study of mechanochemical coupling in kinesins, which extends the approach used successfully to describe the dynamics of conventional motor proteins, is presented. The possibility of irreversible detachments of kinesins from the microtubules is also explicitly taken into account. Using the method of first- passage times, experimental data on the mechanochemical coupling in kinesins are fully described using the simplest two-state model. It is shown that the dwell times for the kinesin to move one step forward or backward, or to dissociate irreversibly are the same, although the probabilities of these events are different. It is concluded that the current theoretical view, that only the forward motion of the motor protein molecule is coupled to ATP hydrolysis, is consistent with all available experimental observations for kinesins.Comment: Submitted to Biophysical Journa

Inhomogeneous Coupling in Two-Channel Asymmetric Simple Exclusion Processes

Asymmetric exclusion processes for particles moving on parallel channels with inhomogeneous coupling are investigated theoretically. Particles interact with hard-core exclusion and move in the same direction on both lattices, while transitions between the channels is allowed at one specific location in the bulk of the system. An approximate theoretical approach that describes the dynamics in the vertical link and horizontal lattice segments exactly but neglects the correlation between the horizontal and vertical transport is developed. It allows us to calculate stationary phase diagrams, particle currents and densities for symmetric and asymmetric transitions between the channels. It is shown that in the case of the symmetric coupling there are three stationary phases, similarly to the case of single-channel totally asymmetric exclusion processes with local inhomogeneity. However, the asymmetric coupling between the lattices lead to a very complex phase diagram with ten stationary-state regimes. Extensive Monte Carlo computer simulations generally support theoretical predictions, although simulated stationary-state properties slightly deviate from calculated in the mean-field approximation, suggesting the importance of correlations in the system. Dynamic properties and phase diagrams are discussed by analyzing constraints on the particle currents across the channels

Current reversal and exclusion processes with history-dependent random walks

A class of exclusion processes in which particles perform history-dependent random walks is introduced, stimulated by dynamic phenomena in some biological and artificial systems. The particles locally interact with the underlying substrate by breaking and reforming lattice bonds. We determine the steady-state current on a ring, and find current-reversal as a function of particle density. This phenomenon is attributed to the non-local interaction between the walkers through their trails, which originates from strong correlations between the dynamics of the particles and the lattice. We rationalize our findings within an effective description in terms of quasi-particles which we call front barriers. Our analytical results are complemented by stochastic simulations.Comment: 5 pages, 6 figure

A Simple Kinetic Model Describes the Processivity of Myosin-V

Myosin-V is a motor protein responsible for organelle and vesicle transport in cells. Recent single-molecule experiments have shown that it is an efficient processive motor that walks along actin filaments taking steps of mean size close to 36 nm. A theoretical study of myosin-V motility is presented following an approach used successfully to analyze the dynamics of conventional kinesin but also taking some account of step-size variations. Much of the present experimental data for myosin-V can be well described by a two-state chemical kinetic model with three load-dependent rates. In addition, the analysis predicts the variation of the mean velocity and of the randomness -- a quantitative measure of the stochastic deviations from uniform, constant-speed motion -- with ATP concentration under both resisting and assisting loads, and indicates a {\it sub}step of size $d_{0} \simeq$ 13-14 nm (from the ATP-binding site) that appears to accord with independent observations.Comment: 20 pages, 7 figures, to be published in Biophys. J. in 200

Two-Channel Totally Asymmetric Simple Exclusion Processes

Totally asymmetric simple exclusion processes, consisting of two coupled parallel lattice chains with particles interacting with hard-core exclusion and moving along the channels and between them, are considered. In the limit of strong coupling between the channels, the particle currents, density profiles and a phase diagram are calculated exactly by mapping the system into an effective one-channel totally asymmetric exclusion model. For intermediate couplings, a simple approximate theory, that describes the particle dynamics in vertical clusters of two corresponding parallel sites exactly and neglects the correlations between different vertical clusters, is developed. It is found that, similarly to the case of one-channel totally asymmetric simple exclusion processes, there are three stationary state phases, although the phase boundaries and stationary properties strongly depend on inter-channel coupling. An extensive computer Monte Carlo simulations fully support the theoretical predictions.Comment: 13 pages, 10 figure

Spontaneous Symmetry Breaking in Two-Channel Asymmetric Exclusion Processes with Narrow Entrances

Multi-particle non-equilibrium dynamics in two-channel asymmetric exclusion processes with narrow entrances is investigated theoretically. Particles move on two parallel lattices in opposite directions without changing them, while the channels are coupled only at the boundaries. A particle cannot enter the corresponding lane if the exit site of the other lane is occupied. Stationary phase diagrams, particle currents and densities are calculated in a mean-field approximation. It is shown that there are four stationary phases in the system, with two of them exhibiting spontaneous symmetry breaking phenomena. Extensive Monte Carlo computer simulations confirm qualitatively our predictions, although the phase boundaries and stationary properties deviate from the mean-field results. Computer simulations indicate that several dynamic and phase properties of the system have a strong size dependency, and one of the stationary phases predicted by the mean-field theory disappears in the thermodynamic limit.Comment: 13 page

Lattice Models of Ionic Systems

A theoretical analysis of Coulomb systems on lattices in general dimensions is presented. The thermodynamics is developed using Debye-Huckel theory with ion-pairing and dipole-ion solvation, specific calculations being performed for 3D lattices. As for continuum electrolytes, low-density results for sc, bcc and fcc lattices indicate the existence of gas-liquid phase separation. The predicted critical densities have values comparable to those of continuum ionic systems, while the critical temperatures are 60-70% higher. However, when the possibility of sublattice ordering as well as Debye screening is taken into account systematically, order-disorder transitions and a tricritical point are found on sc and bcc lattices, and gas-liquid coexistence is suppressed. Our results agree with recent Monte Carlo simulations of lattice electrolytes.Comment: 25 pages, 3 figures, ReVTeX 4, Submitted to J. Chem. Phy