Time correlation functions and kinetic coefficients in systems with molecular or chemical exchange

Abstract

We develop a kinetic theory for systems with molecular or chemical exchange. In such systems, particles can successively reside in two different dynamical states with the inter-state transition. A prominent example of the molecular exchange (ME) is aqueous solutions of macromolecules (proteins, DNA) or metal ions, where a water molecule can move freely in a bulk of the solution or perform a constrained motion in a bound state. This may be the surface of the macromolecule or the ion's hydration shell. Another example, which refers to the chemical exchange (CE), is a molecule in a solution, that reversibly alternates its conformation — different conformations imply different rotational and translational motion. We consider the case of Poissonian exchange between states and general, non-Poissonian exchange and derive general relations for time correlation functions and kinetic coefficients. The application of the theory is illustrated by computation of time correlation functions and kinetic coefficients for translational and rotational motion of particles in systems with exchange.