Parametric Resonance in DNA
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We consider a simple mesoscopic model of DNA in which the binding of the RNA polymerase enzyme molecule to the promoter sequence of the DNA is included through a substrate energy term modeling the enzymatic interaction with the DNA strands. We focus on the differential system for solitary waves and derive conditions—in terms of the model parameters—for the occurrence of the parametric resonance phenomenon. We find that what truly matters for parametric resonance is not the ratio between the strength of the stacking and the inter-strand forces but the ratio between the substrate and the inter-strands. On the basis of these results, the standard objection that longitudinal motion is negligible because of the second order seems to fail, suggesting that all the studies involving the longitudinal degree of freedom in DNA should be reconsidered when the interaction of the RNA polymerase with the DNA macromolecule is not neglected.
KeywordsDNA mesoscopic models RNA polymerase Solitary waves Hill’s equation Parametric resonance
The present work has been performed under the auspices of the italian National Group for Mathematical Physics (GNFM-Indam). The research is supported by PRIN-2009 project Matematica e meccanica dei sistemi biologici e dei tessuti molli. The authors warmly thank Ivonne Sgura for her precious contribution in achieving numerical simulations provided in Sect. 6. We also thank the anonymous referees and the handling Editor for their helpful comments and remarks.
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