Quasi-stationary evolution of cubic-quintic NLSE drop-like solitons in DNA-protein systems

TL;DR

This paper investigates the quasi-stationary evolution of cubic-quintic nonlinear Schrödinger equation solitons in DNA-protein systems, incorporating damping effects to better understand molecular excitations relevant to transcription.

Contribution

It introduces a quasi-stationary method to model damping effects on cubic-quintic NLSE solitons in DNA-protein interactions, extending previous models to include dissipative forces.

Findings

Damping influences soliton stability and propagation in DNA-protein systems.

The model captures energy dissipation effects relevant to biological processes.

Potential implications for understanding transcription mechanisms.

Abstract

Nonlinear molecular excitations in DNA have traditionally been modelled using the nonlinear Schr\"odinger equation (NLSE). An alternative approach is based on the plane-base rotator model and the SU(2)/U(1) generalized spin coherent states, which leads to a cubic quintic NLSE. Higher-order nonlinearities are particularly useful for modelling complex interactions, such as those in DNA-protein systems, where multiple competing forces play a significant role. Additionally, the surrounding viscous medium introduces dissipative forces that affect the propagation of molecular excitations, leading to energy dissipation and damping effects. These damping effects are modelled using the quasi-stationary method, which describes the system's near-equilibrium behaviour. In this work, we explore the evolution of nonlinear molecular excitations in DNA-protein systems, accounting for damping effects, and discuss potential applications to the transcription process.