A series of covalently closed bacteriophage PM2 DNA samples with varying degrees of superhelicity were prepared in vitro. The amount of bound ethidium per DNA nueleotide needed for the removal of all superhelical turns, vc0, was determined for each sample by a number of methods. In order to evaluate the unwinding angle for the binding of one ethidium molecule to a DNA double helix, the pH dependence of the buoyant densities in CsCI of these samples was examined. A new calibration relating the change in buoyant density of a DNA to the fraction of bases titrated has been obtained, by measuring the buoyant densities of a number of catenanes (interlocked rings) containing both single-stranded and double-stranded λ DNA rings, at a pH such that the single-stranded DNA is fully titrated while the double-stranded DNA is not titrated. This calibration was used to obtain the pH dependence of the fraction of DNA bases titrated for the phage PM2 DNAs with differing extents of supercoiling. A simple theoretical analysis shows that in a restricted pH range close to pHm, the melting pH of the DNA in the absence of the topological constraint associated with covalently closed double-stranded DNAs, the difference in the fraction of bases titrated at a certain pH between two covalently closed DNAs with different degrees of superhelicity is directly proportional to the difference in the vc0 values of the DNAs. The unwinding angle per bound ethidium molecule can be obtained from the proportionality constant. In this way, it is not necessary to know precisely the actual pH value for either DNA, pHe, at which the DNA is titrated to the extent that it contains no superhelical turns. The conclusion of the theoretical analysis and the experimental results is that the binding of an ethidium molecule to a double-stranded DNA unwinds the DNA helix by an angle φe = 26 °. The uncertainty in this value is estimated to be less than 10%. The new value for φe is approximately a factor of two larger than the value 12 °, which has been in use in the past decade. In the earlier alkaline titration results for polyoma DNA (Vinograd et al., 1968), which had been interpreted as supporting the 12 ° value, the calculation of φe was critically dependent on knowing pHe. It is believed that pHe was underestimated in the earlier work, resulting in a low φe value. Since the previous value φe = 12 ° has been widely used in the determination of the number of superhelical turns for many DNAs, and in measurements on the angular alterations of the DNA helix by the binding of a variety of small and large molecules and by solvent and temperature changes, the new value φe = 26 ° requires proportional adjustments of many previous results.
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