Before revision:  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.
After revision:  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.