Quantum Transport in Disordered and Noisy Harmonic Networks to Simulate Protein Dynamics Structures

Energy or charge transfer is one of the most important phenomena in physical and biological systems. Life-enabling transport phenomena in the molecular mechanism of biological systems take place at scales size from large macro molecule biology dawn to atom. Charge transfer through DNA or charge and energy transfer processes in photosynthetic structures are good examples. Due to discovery biological processes, researchers have been recently focusing on how quantum mechanics related to biology and quantum mechanics might have positive effect on the efficiency of energy or charge transfer in living systems. Recently, researchers works in theoretical and experimental quantum methods to describe biological possesses. Natural systems, definitely, suffer from various types of noise with internal and external sources. In biological systems, exchange of energy can be happened inside the system as well as between the system and environment which can be simulated by open quantum systems. For theoretical, It is well known that many quantum master equation apply to well-describe biological system such as cell growth, enzyme reaction, gene expression and so on. One of the method in quantum mechanics is applying Markovian approximation by employing the Lindblad formulation that this super master equation is very powerful method to explain excited energy transport (EET). In this thesis, we investigate the effect of noise of excitation energy transfer (EET) in a linear chain made of N= 5 sites with dynamical dipole-dipole couplings and also describe a disordered dynamical chain that can be a model for one P-loop strand of the selectivity filter backbone in ion channels. Firstly, investigate of excitation energy transfer (EET) in a linear chain made of N=5 sites with dynamical dipole-dipole couplings (static structure) in ion channel (5 sites and sink) and then, the sites are allowed to move a little in their places. The potential between the sites are estimated with a spring-mass model and the normal modes are obtained(dynamic structure). The Lindblad equation is then solved considering these assumptions. Adding noise to the Lindblad equation will result in different answers, thus, local noise is added to the Lindblad equation at first and then the noises which coefficients have a temporal dependency in the Lindblad equation are added. Since finding a configuration and a mechanism that could save the most energy in the sink of particular importance, more attention is paid to sink population. Our analysis may help for better understanding of fast and efficient functioning of the selectivity filters in ion channels.