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The thermodynamics of superhelix formation was determined by combining superhelix density data with enthalpy values obtained from microcalorimetric measurements of the relaxation of supercoiled ColE1 amp plasmid DNA in the presence of topoisomerase I from Escherichia coli (omega protein). The thermodynamic quantities for superhelix formation at 37 degrees C in 10 mM Tris/2 mM MgCl2/1 mM EDTA pH 8, are: delta G = 921 kJ X (mol of plasmid)-1; delta H 2260 kJ X (mol of plasmid)-1; deltaS = 4.3 kJ X (mol of plasmid X K)-1. These data clearly demonstrate that the unfavorable Gibbs free energy associated with supercoiling of DNA results exclusively from the positive enthalpy involved in formation of superhelical turns. A positive overall entropy change accompanies superhelix formation, which overcompensates the expected decrease of configurational entropy. By neglecting contributions from bending, an estimate of the torsional rigidity C = 1.79 X 10(-19) erg X cm (1 erg = 0.1 microJ) of the supercoiled ColE1 amp plasmid DNA was made on the basis of the enthalpy value. This value is in excellent agreement with values of C derived from subnanosecond time-resolved fluorescence depolarization measurements for pBR322 DNA [Millar, D. P., Robbins, R. J. &amp; Zewai, A.H. (1982) J. Chem. Phys. 76, 2080-2094]. The magnitude of C is larger than for linear DNAs, indicating that supercoiled DNA is more rigid than linear DNA.

The free energy of DNA supercoiling is enthalpy-determined.