article · Chinese Physics Letters
This research investigates the nonlinear dynamics of DNA molecules at physiological temperature within a viscous environment using the Peyrard Bishop model. The behaviour of the molecular chain is described mathematically through the discrete complex Ginzburg Landau equation, which simplifies to the standard nonlinear Schroedinger equation under non-viscous conditions. Mathematical conditions for modulational instability were established for both viscous and non-viscous scenarios, and numerical simulations were conducted to verify these theoretical criteria. Starting with a planar wave solution, the system demonstrates localised oscillations of DNA base pairs that result in the concentration of energy along the molecule. Furthermore, the findings reveal that the viscosity of the surrounding solvent plays a dampening role, systematically reducing the amplitude of the resulting wave patterns over time.
Understanding how energy travels and concentrates within DNA molecules is fundamental to biophysics. Because biological processes take place in fluid cellular environments, accounting for the damping effects of surrounding viscosity provides a more realistic description of how molecular structures vibrate and dissipate energy at normal body temperatures.
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We study the nonlinear dynamics of a DNA molecular system at physiological temperature in a viscous media by using the Peyrard–Bishop model. The nonlinear dynamics of the above system is shown to be governed by the discrete complex Ginzburg–Landau equation. In the non-viscous limit, the equation reduces to the nonlinear Schrödinger equation. Modulational instability criteria are derived for both the cases. On the basis of these criteria, numerical simulations are made, which confirm the analytical predictions. The planar wave solution used as the initial condition makes localized oscillations of base pairs and causes energy localization. The results also show that the viscosity of the solvent in the surrounding damps out the amplitude of wave patterns.
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DOI: 10.1088/0256-307x/26/6/068703
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