Davydov Soliton in Alpha-Helix Proteins

Abstract

We derive the equations of motion of the Davydov solitons which are perfect carriers of the energy of hydrolysis of the molecules ATP(Adenosine Triphosphate) along ?-helical protein molecules without significant energy loss when T = 0K We first illustrate how the solitons are produced and the mechanism or the function of solitons Since the solitons are formed by excitons and phonons we derive the Hamiltonian and define the trial wave functions for excitons and phonons Since the phonons are coherent we first discuss the minimum uncertainty state and the coherent state Next we start by deriving the equations of motion in discrete form for the system and then we rewrite the equations of motion in continuous form Then we guess a form of function to substitute into the equations of motion and we get a non-linear Schrodinger equation which has a soliton solution We substitute the solution into the non-linear Schrodinger equation and the Hamiltonian expectation value of the coherent phonons Finally we derive the energy of the soliton as a function of the velocity of the soliton Our results agree with the literature on Davydov solitons Finally we will briefly introduce the condition of T ≠ 0K In this situation there exists a Hamiltonian term of real phonons that describes the stationary nonlocalized states which can be superimposed to form the nonstationary states causing the soliton to have a finite lifetime

Date of Award	2014 Jul 25
Original language	English
Supervisor	Su-Long Nyeo (Supervisor)