Conformational change of a DNA molecule is frequently observed in multiple biological processes and has been modelled using a chain of strongly coupled oscillators with a nonlinear bistable potential. While the mechanism and properties of conformational change in the model have been investigated and several reduced order models developed, the  dynamics as a function of the length of the oscillator chain is relatively less clear. To address this, we used a modified Lindstedt-Poincare method and numerical computations. We calculate a perturbation expansion of the frequency of the nonzero modes of the model , finding that approximating these modes with their unperturbed dynamics  as in a previous reduced model may not hold when the length of the DNA model increases. We investigate the conformational change to local perturbation in models of varying lengths, finding that for chosen input and parameters, there are two regions of DNA length in the model, first where the minimum energy required to undergo the conformational change increases with DNA length  and second, where it is almost independent of the length of the DNA model. We analyzed the conformational change in these models by adding randomness to the local perturbation, finding that the robustness of the conformational states of the model to random perturbation decreases with an increase in the DNA length. These results should help to understand the role that the length of a DNA molecule plays in influencing its conformational dynamics.
Conformational change of a DNA molecule is frequently observed in multiple biological processes and has been modelled using a chain of strongly coupled oscillators with a nonlinear bistable potential. While the mechanism and properties of conformational change in the model have been investigated and several reduced order models developed, the conformational dynamics as a function of the length of the oscillator chain is relatively less clear. To address this, we used a modified Lindstedt-Poincare method and numerical computations. We calculate a perturbation expansion of the frequency of the model's nonzero modes , finding that approximating these modes with their unperturbed dynamics , as in a previous reduced order model, may not hold when the length of the DNA model increases. We investigate the conformational change to local perturbation in models of varying lengths, finding that for chosen input and parameters, there are two regions of DNA length in the model, first where the minimum energy required to undergo the conformational change increases with DNA length ; and second, where it is almost independent of the length of the DNA model. We analyze the conformational change in these models by adding randomness to the local perturbation, finding that the tendency of the system to remain in a stable conformation against random perturbation decreases with an increase in the DNA length. These results should help to understand the role of the length of a DNA molecule in influencing its conformational dynamics.
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conformational
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nonzero modes of the model
model's nonzero modes
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,
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model
order model,
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;
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analyzed
analyze
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robustness of the conformational states of the model to
tendency of the system to remain in a stable conformation against
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that
of
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plays