Coupled Schr\"odinger equations as a model of interchain excitation transport in the DNA

TL;DR

This paper models interchain energy transport in DNA using coupled Schrödinger equations, analyzing non-stationary dynamics and predicting periodic excitation transitions between DNA strands.

Contribution

It introduces a novel analytical approach to study non-stationary interchain excitation dynamics in DNA using coupled Schrödinger equations.

Findings

Demonstrates existence of invariants reducing system complexity

Predicts periodic interchain excitation transitions

Accounts for excitation spreading over time

Abstract

In our report we consider two weakly coupled Schr\"odinger equations as a model of the interchain energy transport in the DNA double-helix. We use the reduction of the Yakushevich-type model considering the torsional dynamics of the DNA. In the previous works only small amplitude excitations and stationary dynamics were investigated, while we focus on the non-stationary dynamics of the double-helix. We consider the system as a model of two weakly interacting DNA strands. Supposing that initially only one of the chains is excited in form of breather we demonstrate the existence of invariant which allows to reduce the order of the problem and consider the system of the phase plane. The analysis provided demonstrates analytical tool for prediction of the periodic interchain excitation transitions of its localization on one of the chains. The technique also takes into account the spreading of the excitations with time.