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.Comment: 23 pages, 4 figure