Theory of twisting and bending of chain macromolecules; analysis of the fluorescence depolarization of DNA

Abstract

An elastic model of semiflexible chain macromolecules is developed in order to treat internal rotatory Brownian motion in the DNA helix. Dynamical equations for torsion and bending of the chain are generated, using results from classical elasticity and hydrodynamic theories. The rotational diffusion equation in normal coordinates is derived, and the initial-boundary value problem solved for the conditions of a nanosecond fluorescence depolarization experiment. The resulting time distribution function of the angular orientation of a fluorescent probe, embedded in a chain at thermal equilibrium, is used to compute the emission anisotropy. The predicted decay law is unusual, with exponentials in ∼t due to twisting and in ∼t1/4 due to bending. Comparison with published data for ethidium–DNA complex reveals that the decay of the anisotropy arises primarily from twisting of the DNA helix, with a small contribution from bending. By fitting theory and experiment, the torsional rigidity C of DNA may be obtained.