1,721,149 research outputs found
Force dependent transition rates in chemical kinetics models for motor proteins
No full textWe analyze the role of external forces both chemical and mechanical in the kinetics of motor proteins. Based on a generalized detailed balance condition, simple exponential force dependent transition rates are widely used to interpret the available data. Yet, the use of Fokker–Planck equations in continuous models allows for a direct insertion of the force. We describe an analytical approach, based on a renormalization group scheme, to calculate the force dependence of transition rates in a generic model. Our analysis shows that the simple exponential is a good approximation to the correct force dependence only at low values of forces and provided that the step sizes are very small. The law for the force dependent transition rates is tested on a set of data on kinesin, obtaining a good agreement with existing results and predictions for future experiments
Coarse grained models: the kinetics of motor proteins
No full textMotor proteins are able to transform the chemical energy of ATP hydrolysis into mechanical work that is essential for a variety of tasks in living cells. Major advances in single molecule nanomanipulation have made it possible to measure the displacements of these proteins along linear tracks, and therefore to obtain an approximate description of their kinetics. Discrete and continuous stochastic models are particularly suited to the interpretation of experimental data in this field, since both allow a complicated mechano-chemical process to be coarse grained in relatively few parameters. However both of them present advantages and shortcomings, though usually one model succeeds where the other fails. We have recently developed a coarse graining procedure, based on a renormalization group approach, that accounts for the force dependence of transition rates in discrete models, bridging a gap between the two stochastic approaches. We discuss the main results obtained with this procedure and possible future directions of investigation
Master equation approach to molecular motors
No full textA master equation approach to molecular motors allows us to describe a mechanochemical cyclic system where chemical and translational degrees of freedom are treated on an equal footing. A generalized detailed balance condition in the out-of-equilibrium regime is shown to be compatible with the Fokker-Planck equation in the continuum limit. The Onsager reciprocity relations hold for stationary states close to equilibrium, provided the generalized detailed balance condition is satisfied. Semiphenomenological considerations in the case of motor proteins lead to a discrete kinetics model, for which interesting observable quantities may be directly calculated and compared with experimental data
Force dependence of the Michaelis constant in a two-state ratchet model for molecular motors
No full textWe present a quantitative analysis of recent data on the kinetics of ATP hydrolysis, which has presented a puzzle regarding the load dependence of the Michaelis constant. Within the framework of coarse grained two-state ratchet models, our analysis not only explains the puzzling data, but provides a modified Michaelis law, which could be useful as a guide for future experiments
Entropy production in master equations and Fokker-Planck equations: facing the coarse-graining and recovering the information loss
No full textSystems operating out of equilibrium exchange energy and matter with the environment, thus producing entropy in their surroundings. Since the entropy production depends on the current flowing throughout the system, its quantification is affected by the level of coarse-graining we adopt. In particular, it has been shown that the description of a system via a Fokker?Planck equation (FPE) lead to an underestimation of the entropy production with respect to the corresponding one in terms of microscopic transition rates. Moreover, such a correction can be derived exactly. Here we review this derivation, generalizing it when different prescriptions to derive the FPE from a Langevin equation are adopted. Then, some open problems about Gaussian transition rates and underdamped limit are discussed. In the second part of the manuscript we present a new approach to dealing with the discrepancy in entropy production due to the coarse graining by introducing enough microscopic variables to correctly estimate the entropy production within the FPE description. We show that any discrete state system can be described by making explicit the contribution of each microscopic current.LB
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