Diffusion assisted end–to–end relaxation of a flexible Rouse polymer chain: Fluorescence quenching through a model energy transfer

Abstract

The diffusion-influenced end–to–end conformational relaxation of a flexible polymer chain molecule (within the Rouse model) is investigated theoretically in the Markovian limit utilizing a generalized diffusion equation for the probability distribution of the end–to–end distance of a chain molecule, which has its origin in the Zwanzig’s treatment of Onsager’s theory of irreversible processes. The end–to–end diffusion dynamics of the chain molecule is considered to be probed by fluorescence resonance energy transfer between two chromophores, attached to the chain ends. The resulting diffusion equation with a sink term representing this energy transfer through a suitably modified Förster rate expression is solved numerically for equilibrium close/open conformations, and end–to–end irreversible ring opening or closure of the chain. Illustrative calculations and comparisons between the kinetics arising out of these conformations are presented to demonstrate the competitive interplay between the transfer sink strength, diffusion, and chain relaxation. From the numerical results for a variety of transfer parameters and end–to–end diffusion coefficients, it is found that a nonmonotonic distribution of reaction times is a confirmative signature for a cyclization transition, whereas a monotonic decay of distribution of the reaction times, as is always the case with the chain opening transition or with the equilibrium configuration (either closed or opened) of the chain, cannot also be ruled out for the cyclization transition. The knowledge of the distribution of energy-transfer distances is utilized to help delineate the features associated with the reaction time distribution during the end–to–end relaxation.