Dynamic bending rigidity of a 200-bp DNA in 4 mM ionic strength: a transient polarization grating study

DNA may exhibit three different kinds of bends: 1) permanent bends; 2) slowly relaxing bends due to fluctuations in a prevailing equilibrium between differently curved secondary conformations; and 3) rapidly relaxing dynamic bends within a single potential-of-mean-force basin. The dynamic bending rigidity (kappa(d)), or equivalently the dynamic persistence length, P(d) = kappa(d)/k(B)T, governs the rapidly relaxing bends, which are responsible for the flexural dynamics of DNA on a short time scale, t < or = 10(-5) s. However, all three kinds of bends contribute to the total equilibrium persistence length, P(tot), according to 1/P(tot) congruent with 1/P(pb) + 1/P(sr) + 1/P(d), where P(pb) is the contribution of the permanent bends and P(sr) is the contribution of the slowly relaxing bends. Both P(d) and P(tot) are determined for the same 200-bp DNA in 4 mM ionic strength by measuring its optical anisotropy, r(t), from 0 to 10 micros. Time-resolved fluorescence polarization anisotropy (FPA) measurements yield r(t) for DNA/ethidium complexes (1 dye/200 bp) from 0 to 120 ns. A new transient polarization grating (TPG) experiment provides r(t) for DNA/methylene blue complexes (1 dye/100 bp) over a much longer time span, from 20 ns to 10 micros. Accurate data in the very tail of the decay enable a model-independent determination of the relaxation time (tau(R)) of the end-over-end tumbling motion, from which P(tot) = 500 A is estimated. The FPA data are used to obtain the best-fit pairs of P(d) and torsion elastic constant (alpha) values that fit those data equally well, and which are used to eliminate alpha as an independent variable. When the relevant theory is fitted to the entire TPG signal (S(t)), the end-over-end rotational diffusion coefficient is fixed at its measured value and alpha is eliminated in favor of P(d). Neither a true minimum in chi-squared nor a satisfactory fit could be obtained for P(d) anywhere in the range 500-5000 A, unless an adjustable amplitude of azimuthal wobble of the methylene blue was admitted. In that case, a well-defined global minimum and a reasonably good fit emerged at P(d) = 2000 A and (1/2) = 25 degrees. The discrimination against P(d) values <1600 A is very great. By combining the values, P(tot) = 500 A and P(d) = 2000 A with a literature estimate, P(pb) = 1370 A, a value P(sr) = 1300 A is estimated for the contribution of slowly relaxing bends. This value is analyzed in terms of a simple model in which the DNA is divided up into domains containing m bp, each of which experiences an all-or-none equilibrium between a straight and a uniformly curved conformation. With an appropriate estimate of the average bend angle per basepair of the curved conformation, a lower bound estimate, m = 55 bp, is obtained for the domain size of the coherently bent state. Previous measurements suggest that this coherent bend is not directional, or phase-locked, to the azimuthal orientation of the filament.