Thermodynamic properties of superhelical DNAs.

Binding isotherms of ethidium to the superhelical DNA from phage PM2, and to PM2 DNA containing -1 single-chain scission per molecule, have been determined at six temperatures from 2.5 to 50 degrees, in 3M CsCl-0.01 M Na3EDTA. Spectrophotometric measurements in both the visible and ultraviolet (uv) regions were used to obtain the binding isotherms. The isotherm at 20 degrees was also obtained by determining the free ethidium concentrations in equilibrium with DNA-ethidium complexes in boundary sedimentation experiments. A simple thermodynamic analysis shows that for a superhelical DNA with v bound ethidium per nucleotide, the change in free energy per unit change in the number of superhelical turns T, dGT/dT, is directly related the ratio of the free ethidium concentrations, cf,v and cf,v, in equilibrium with the ethidium complexes of the superhelical and the nicked DNA, respectively, at the same values of v. The relationship is dGT/dT = (360/E)RTln (cf,v/cf,v), where e is the unwinding angle of the DNA helix per bound ethidium molecule. Experimentally, it was found that ln (cf,v/cf,v) = a1(v - vc), where a1 is a constant at a given temperature and vc is the value of v at which the originally superhelical DNA is completely relaxed, i.e., containing no superhelical turns. The equation relating dGT/dT and v, upon transformation and integration, gives finite difference GT,v=o = -a1NRTvc2/2, where finite difference GT,v=0 is the free energy of superhelix formation of the superhelical DNA in the absence of ethidium and N is the number of nucleotides per DNA molecule. This equation is independent of the unwinding angle e. The values of a1 are 11.2 plus or minus 0.9, 11.2 plus or minus 0.7, 11.2 plus or minus 0.6, 10.7 plus or minus 0.8, 10.0 pl.us or minus 1.0, and 9.8 plus or minus 1.4 at 2.5, 10, 20, 30, 40, and 50 degrees, respectively. Measurements with lambda b2b5c DNA, and monomeric and trimeric lambda dv DNA, indicate that the constant a1 is insensitive to the molecular length of DNA. The present results are compared with the previous results of Bauer and Vinograd (Bauer, W., and Vinograd, M. (1970), J. Mol. Biol. 47, 419), obtained by a statistical mechanical analysis of the ethidium binding isotherms (determined by density gradient centrifugation measurements) to two forms of simian virus 40 DNA at 25 degrees. The effects of superhelical turns on a number of processes, such as the binding of a ligand which unwinds or winds the DNA helix, the denaturation of a DNA segment, and the formation of hair-pinned structures from base sequences with a twofold rotational symmetry, are discussed from the thermodynamic point of view, based on the present results.