TORSION DYNAMICS AND DEPOLARIZATION OF FLUORESCENCE OF LINEAR MACROMOLECULES .1. THEORY AND APPLICATION TO DNA

A model consisting of a series of N+ 1 identical rigid rods connected at their ends by torsion springs and undergoing rotational brownian motion about their fixed symmetry axes is proposed as a model for the torsion dynamics of DNA. The fluorescence anisotropy bfbnund flunrophores is expressed in terms of angular correlation functions, the subsequent calculation of which is virtually identical to that recently presented for the dynamic structure factor of tIse RouseùZimm model. Tin complete time course of the fluorescence anisotropy is divided into four zones, (i) initial exponential decay zone, (ii) iotermediate zone, (iii) longest internal mude zone, and (iv) uniform mode zone. Simple approximate expressions for the lluoresccnee anisotropy are derived for the initial exponential decay zone and for the intermediate zone. The mag- nitude of end-effects, due to enhanced amplitudes of motion near the chain ends, in the intermediate zone is investigated botls numerically and analytically, and the domain of validity of the approximate expression pertinent to that zone is de- termined to be 100-fold smaller than previously supposed. The fluorescence anisotropy decay data of Wahl, Paoletti and Le Pecq for ethidium bound to DNA is interpreted in terms of this nsodel. Although relaxations in zones (iii) and (iv) can be ruled out, it is possible to obtain equally good fits to the decay dala either in zone (i) witls parameters pertinent to a rod-length of 86 base-pairs or in zone (ii) with parameters pertinent to a rod-length of I base pair. However, other data, in- cluding the steady-state polarization anisotropy in concentrated sucrose solution, definitely favor the zone (i) fit with a rod-length of 86 base-pairs, thus providing evidence for isolated torsion joints, or inhomogeneities in the torsional rigidity, nf that particular calf-thymus DNA. A comparison of twisting energies compused from the present optimum torsion con- stants with the measured free-energies of supercoil formation is also given. © 1979.