Viscous DNA and RNA: Quantum damped dynamical random systems

From a physics perspective, DNA and RNA molecules are characterized as dynamic biological structures that exhibit vibrations across a range of time scales. To conduct a more accurate investigation of their dynamic properties, it is essential to consider the environmental conditions surrounding these molecules. A harmonic Hamiltonian that incorporates damping, along with the Green's function method, has been utilized to analyze the vibrational responses of viscous DNA and RNA strands. The DNA molecule is represented using a fishbone model alongside two distinct double-strand configurations, while a half-ladder model is applied to the RNA molecule. The interconnections between sub-sites are represented by linear springs, with the stiffness of the vertical springs and the damping coefficients of the dashpots varying randomly throughout the length of the systems. Furthermore, each model is examined under three distinct configurations: infinite, finite, and cyclic. The results reveal that the fluctuations in the density of states curves exhibit a gradual decline, leading to a broadening of the sharp peaks as the damping coefficient increases. Additionally, the vibrational modes become progressively less distinct with an increase in system damping, a finding that aligns well with the principles of wave mechanics and vibrational motion.