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Conformational change of a DNA molecule is frequently observed in multiplebiological processes and has been modelled using a chain of strongly coupledoscillators with a nonlinear bistable potential. While the mechanism andproperties of conformational change in the model have been investigated andseveral reduced order models developed, the conformational dynamics as afunction of the length of the oscillator chain is relatively less clear. Toaddress this, we used a modified Lindstedt-Poincare method and numericalcomputations. We calculate a perturbation expansion of the frequency of themodel's nonzero modes, finding that approximating these modes with theirunperturbed dynamics, as in a previous reduced order model, may not hold whenthe length of the DNA model increases. We investigate the conformational changeto local perturbation in models of varying lengths, finding that for choseninput and parameters, there are two regions of DNA length in the model, firstwhere the minimum energy required to undergo the conformational changeincreases with DNA length; and second, where it is almost independent of thelength of the DNA model. We analyze the conformational change in these modelsby adding randomness to the local perturbation, finding that the tendency ofthe system to remain in a stable conformation against random perturbationdecreases with an increase in the DNA length. These results should help tounderstand the role of the length of a DNA molecule in influencing itsconformational dynamics.

On the length scale dependence of DNA conformational change under local perturbation