Wave propagation of nonlinear modes and formation of bubble in a two-component helicoidal lattice

Bubble Formation in Helicoidal DNA Molecules

“…Of course, the reader should notice that from the beginning we did not include any noise to the model, rather these fluctuations in the breather solution are due to wave collision, i.e., at the point where the two counter-propagating waves mix. However, the features of that solution are expected to change for different values of the helicoidal coupling parameters S. This may be evident as the unwinding of the double helix implies a decrease of S. It was in fact shown that the resonant mode, the one supporting highly localized bubbles, is possible only when the helicoidal effects are weak [12,25]. Therefore, in the rest of the present work, the effect of small helicoidal coupling on the mixed solution is discussed.…”

“…In both cases, trains of soliton-like structures, with breathing features, are observed. Their importance in collecting the energy necessary for the initiation of the key precesses of replication and transcription has been discussed in many DNA nonlinear models, with suitable biological implications [7,10,12]. Indeed, the breaking of the hydrogen bonds starts with slight oscillations of the bases and then grow progressively in amplitude under the action of RNA-polymerase till the breaking of the hydrogen bond, condition for the genetic information to be collected by the messenger-RNA.…”

“…The same class of solution has already been obtained numerically in the previous section, and are found to be robust in DNA nonlinear models. Two classes of such waves have been discussed already, the ones describing the so-called DNA respiration and those related to the eye-like configuration usually observed in thermal denaturation experiments [12,25].…”

“…For example, modifications brought to the PB model have shown new features in the way the base pairs oscillate and its modulational instability has been extensively studied as well [5]. Analytical solutions of the helicoidal PB model have been studied [12], but no relationship has been established, to our knowledge, between fluctuating bubbles and soliton emergence in DNA nonlinear models. The main objective of the present work is therefore to show that wave mixing can has some features of fluctuating bubbles and can be used to explain the opening of the DNA double helix.…”

Helicoidal Peyrard–Bishop Model of DNA Dynamics*

“…• −1 [51] without any arguments. It was suggested that the corresponding wave length covers an integer number of the periods l [40], i.e.…”