Theory of friction‐limited DNA unwinding

The theory of friction‐limited DNA unwinding is developed explicitly for moderate tind large perturbations. This extension of the earlier theory of the relaxation kinetics is necessary because of the complex nature of the rate limitation for small perturbations. The assumption of the theory that is violated under relaxation conditions is that base pairing reactions occurring at a constant local degree of twist of the strands are fast compared to the net unwinding of the molecule. However, these reactions that are slow for small perturbations have a large activation energy, and become faster than friction‐limited un winding for large enough temperature jumps and sufficiently large DXA molecules. Thus only the rate for moderate and large perturbations is clearly limited by frictional resistance to turning the molecule in solution. The model used is a diffusional unwinding of the two strands, driven by the accompanying decrease in free energy. For large perturbations a numerical solution of the diffusion equation is required, since the diffusion coefficient is not constant. Two new parameters must be introduced into the equilibrium statistical theory to describe friction‐limited unwinding kinetics. These are the force constant b, for winding up coil regions and the frictional coefficient per base pair βcfor rotating coil regions in solution. We find by fitting the theory to experiment that b = 1.8 × 10−13 ergs/ rad2‐ and βc = 3.5 × 10−21 erg see/base pair, both for DNA melted in alkali at 0.4.M Na + and ∼30 °C. The latter value is in agreement with predictions based on the viscosity of single stranded DNA in alkali. The quoted value of bcan be interpreted to mean that the number of conformational states of a nucleolide is reduced by an average factor of 1.55 when it is wound around another strand to the degree of twist in a double helix, but without forming a base pair.