Equations for Stochastic Macromolecular Mechanics of Single Proteins: Equilibrium Fluctuations, Transient Kinetics and Nonequilibrium Steady-State

Abstract

A modeling framework for the internal conformational dynamics and external mechanical movement of single biological macromolecules in aqueous solution at constant temperature is developed. Both the internal dynamics and external movement are stochastic; the former is represented by a master equation for a set of discrete states, and the latter is described by a continuous Smoluchowski equation. Combining these two equations into one, a comprehensive theory for the Brownian dynamics and statistical thermodynamics of single macromolecules arises. This approach is shown to have wide applications. It is applied to protein-ligand dissociation under external force, unfolding of polyglobular proteins under extension, movement along linear tracks of motor proteins against load, and enzyme catalysis by single fluctuating proteins. As a generalization of the classic polymer theory, the dynamic equation is capable of characterizing a single macromolecule in aqueous solution, in probabilistic terms, (1) its thermodynamic equilibrium with fluctuations, (2) transient relaxation kinetics, and most importantly and novel (3) nonequilibrium steady-state with heat dissipation. A reversibility condition which guarantees an equilibrium solution and its thermodynamic stability is established, an H-theorem like inequality for irreversibility is obtained, and a rule for thermodynamic consistency in chemically pumped nonequilibrium steady-state is given.

23 pages, 4 figures

References in corpus (4)

• The Force Exerted by a Molecular Motor
• Relative Entropy: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations
• The Mathematical Theory of Molecular Motor Movement and Chemomechanical Energy Transduction
• Mathematical Formalism for Isothermal Linear Irreversibility

Cited by in corpus (9)

• Generalized Haldane Equation and Fluctuation Theorem in the Steady State Cycle Kinetics of Single Enzymes
• Entropy production for mechanically or chemically driven biomolecules
• Entropy Production in Mesoscopic Stochastic Thermodynamics: Nonequilibrium Kinetic Cycles Driven by Chemical Potentials, Temperatures, and Mechanical Forces
• Statistical Thermodynamics of General Minimal Diffusion Processes: Constuction, Invariant Density, Reversibility and Entropy Production
• The Zeroth Law of Thermodynamics and Volume-Preserving Conservative Dynamics with Equilibrium Stochastic Damping
• The Goldbeter-Koshland switch in the first-order region and its response to dynamic disorder
• Temporal Behavior of the Conditional and Gibbs' Entropies
• Non-equilibrium Lyapunov function and a fluctuation relation for stochastic systems: Poisson representation approach
• Stochastic Dynamics of Electrical Membrane with Voltage-Dependent Ion Channel Fluctuations