Energetics of DNA twisting: II. Topoisomer analysis*

A gel electrophoresis method has been developed for resolving small (≊250 bp) DNA topoisomers. In this size range only one major topoisomer band is observed, except for ligase closure conditions in which the probabilities are nearly equal for circularization by untwisting and overtwisting the corresponding linear DNA. The two probabilities are nearly equal when ΔTw is close to 0·5, if the mean helical twist of the linear DNA is n + ΔTw, where n is an integer and ΔTw is the fractional twist. We determine ΔTw of the linear DNA in standard conditions (20°C, no ethidium) by titration experiments in which ΔTw is varied at the time of ligase closure, either by changing temperature or ethidium concentration. The endpoint (ΔTw = 0·5) is found when the two topoisomers formed by untwisting and overtwisting are present at equal concentrations. This analysis assumes that the net writhe is zero and the DNA helix is isotropically bendable. The results confirm the analysis of cyclization probabilities given in the preceding paper: ΔTw = 0 at the two maxima in the curve of j-factor versus DNA length and ΔTw = 0·5 at the minimum. Consequently, we can determine the DNA lengths at which Tw takes on integral values and use them to measure precisely the average helix repeat. From the difference between the ΔTw values of DNAs with 237 and 247 bp, we obtain an approximate value for the helix repeat of h = 10·4±0·1 bp/turn, in good agreement with earlier values found by the band-shift and nuclease-cutting methods. The twist is integral at 250·8±0·4 bp and from h = 10·4±0·1 we find n = 24; then 250·8/24 gives h = 10·45±0·02 bp/turn. The mean linking number (Lk) changes in a stepwise manner as ΔTw is varied for 250 bp DNAs. This result is expected when the free energy of twisting half a turn becomes large compared to thermal fluctuations. In these experiments, it is possible to obtain the mean Tw value from the mean Lk value only when ΔTw = 0·5, and consequently the mean Lk value is not simply related to DNA length for 250 bp DNAs except when ΔTw = 0·5. The relative concentrations of two adjacent topoisomers have been measured as a function of DNA twist for DNAs between 245 and 1361 bp, and the results have been used to analyze the contributions of twisting and writhing in determining the distribution of topoisomers. These experiments are analogous to those for much larger DNAs, which use the breadth of the topoisomer distribution to determine the free energy of supercoiling, as in the work of Depew & Wang (1975) and of Pulleyblank et al. (1975) . For the small DNAs, the topoisomer titration data yield an apparent twisting coefficient Kapp that equals KTw when fluctuations in writhe do not contribute to the topoisomer ratio. Le Bret's (1979) theory for the onset of writhing predicts that about two turns of torsional stress are taken up in twisting before writhing begins. Because the free energy of twisting depends on an inverse function of DNA length, Le Bret's theory can be used to predict that only twisting fluctuations will contribute to Kapp below a critical DNA length. We find that Kapp/2RT is proportional to N between 245 and 880 bp, as expected if only twisting fluctuations contribute to Kapp in this size range. At about 1000 bp, the plot curves upwards, indicating that fluctuations in writhe begin to contribute to Kapp near 1 kb. These results are relevant to the problem of analyzing the contributions of twisting and writhing to the free energy of DNA supercoiling.