Elastic model of DNA supercoiling in the infinite-length limit

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Abstract
The energies of plectonemic and toroidal supercoiled DNA are calculated by treating DNA as an elastic rod with a finite radius. End effects are ignored and all extensive quantities (e.g., writhe, bend energy) are treated as linear densities (writhe per unit length, bend energy per unit length). Minimum energy configurations are found. For plectonemic DNA, the superhelical pitch angle α is in the range 45°<α≤90°. For low values of specific linking difference, most superhelicity is in writhe. As specific linking difference increases, a greater proportion of superhelicity is in twist. Under physiological conditions, roughly 88% of superhelicity is in writhe. Ionic strength effects are discussed, and it is found that variation of excluded volume with ionic strength has a large effect, resulting in significantly greater torsional stress in supercoiled DNA at low ionic strength. For biologically relevant values of specific linking difference, the plectonemic conformation is energetically favored over toroidal conformations. Results are compared with electron microscopy data. The application of the model to DNA conformational transitions is discussed.