Inhomogeneities and nonlinear dynamics of a helical DNA interacting with a RNA-polymerase

Abstract

We have numerically investigated the effects of helicity and inhomogeneities on DNA base pairs opening. The inhomogeneities are due to the site-dependent stacking and hydrogen bonding energies in DNA and protein molecules. We have considered a situation in which the active site of the RNA-polymerase molecule binds onto the promoter site of the spin-like model of the DNA molecule at the physiological temperature and creates a bubble. During the study, we have found that the helical coupling has to be very weak compared to intra-strand coupling in the real DNA molecule. Results show that inhomogeneities do not affect the general pattern of base pair opening, even as the periodic inhomogeneity introduces a train of periodic oscillations on the tail of the bubble; while the height of the bubble is an increasing function of the helical coupling parameter. The basic properties of breather-like modes, obtained here by taking into account helical structure and inhomogeneities, are essential for DNA functioning since such breathing-like modes are considered to be much better candidates for the nonlinear modes responsible for a locally open state where biological functioning takes place.

Nonlinear dynamics of DNA systems with inhomogeneity effects

“…Also we found in Ref. [35] that, using the numerical methods, the authors demonstrate that neither the opening of base pairs in DNA molecule nor the topological character of the breatherlike soliton are affected by the localized inhomogeneity in the form of hyperbolic secant function introduced in stacking and hydrogen bonding energies of DNA.…”