Possible Origin of the Increased Torsion Elastic Constant of Small Circular DNAs: Bending-Induced Axial Tension

Abstract

Deforming an intrinsically straight elastic rod into a circle is shown to introduce an axial tension that acts to extend the rod, much like an externally applied force. The response of a circular DNA to such axial tension was reckoned using a previously suggested model of a force-dependent cooperative transition between a shorter torsionally softer a conformation and a longer torsionally stiffer b conformation. Each of three earlier reported optimal sets of parameters, that well-fitted both relative extension vs force and torsion elastic constant vs force data on single DNAs under tension, was applied here to predict torsion elastic constants of the effective springs between base pairs for both linear and circular 181 bp and ∼210.8 bp DNAs under their respective conditions. Predicted values for both linear and circular species agreed well with their corresponding experimental values, which strongly suggests that the observed 1.4- to 1.5-fold enhancement of the torsion elastic constants upon circularization arises from such axial tension. Experimental torsion elastic constants lie in the range (6.4-6.6) × 10-19 J for these linear DNAs and in the range (9.1-9.9) × 10-19 J for the corresponding circles, significantly below the limiting value ∼12 × 10-19 J at tensions exceeding 4 pN.