The Mathematical Theory of Molecular Motor Movement and Chemomechanical Energy Transduction

Abstract

The mathematical formulation of the model for molecular movement of single motor proteins driven by cyclic biochemical reactions in an aqueous environment leads to a drifted Brownian motion characterized by coupled diffusion equations. In this article, we introduce the basic notion for the continuous model and review some asymptotic solutions for the problem. Stochastic, nonequilibrium thermodynamic interpretations of the mathematical equations and their solutions are presented. Some relevant mathematics, mainly in the field of stochastic processes, are discussed.

arXiv comment20 pages

References in corpus (4)

• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Asymptotic Exit Location Distributions in the Stochastic Exit Problem
• Mathematical Formalism for Isothermal Linear Irreversibility

Cited by in corpus (20)

• Theory of nonequilibrium free energy transduction by molecular machines
• Mesoscopic Nonequilibrium Thermodynamics of Single Macromolecules and Dynamic Entropy-Energy Compensation
• Entropy Production in Mesoscopic Stochastic Thermodynamics: Nonequilibrium Kinetic Cycles Driven by Chemical Potentials, Temperatures, and Mechanical Forces
• Coupling of Two Motor Proteins: a New Motor Can Move Faster
• Statistical Thermodynamics of General Minimal Diffusion Processes: Constuction, Invariant Density, Reversibility and Entropy Production
• Mathematical Formalism for Isothermal Linear Irreversibility
• Allocating dissipation across a molecular machine cycle to maximize flux
• Equations for Stochastic Macromolecular Mechanics of Single Proteins: Equilibrium Fluctuations, Transient Kinetics and Nonequilibrium Steady-State
• Irreversible Thermodynamics in Multiscale Stochastic Dynamical Systems
• Effective rates from thermodynamically consistent coarse-graining of models for molecular motors with probe particles
• Dichotomous noise models of gene switches
• Overshoot in biological systems modeled by Markov chains: a nonequilibrium dynamic phenomenon
• The efficiency of the molecular motors
• Properties of tug-of-war model for cargo transport by molecular motors
• An allosteric model of the inositol trisphosphate receptor with nonequilibrium binding
• Numerical Methods for Computing Effective Transport Properties of Flashing Brownian Motors
• Stochastic Dynamics of Electrical Membrane with Voltage-Dependent Ion Channel Fluctuations
• Minimum Power to Maintain a Nonequilibrium Distribution of a Markov Chain
• Resource Letter: Bio-molecular Nano-machines: where Physics, Chemistry, Biology and Technology meet
• Simulation of Gene Regulatory Networks