CATASTROPHIC VARIATION OF TWIST AND WRITHING OF CIRCULAR DNAS WITH CONSTRAINT

The number of constraint turns is defined as the number of bound unwinding ligands converted in turns necessary to relax the energy stored in a supercoiled DNA. It is equal to the sum of the twist and of the writhing and is interpreted geometrically. The twist is shown to be related to the derivative of the energy of superhelix formation with respect to the constraint turns. This leads to a semiempirical evaluation of the variation of the conformational energy with the writhing and of the writhing number. The bending contribution to the conformational energy is estimated independently using first‐order elasticity. The variation of the twist and of the writhing with the constraint is, in this model, catastrophic. In particular, the writhing number jumps between intervals of allowed values. Copyright © 1979 John Wiley & Sons, Inc.