Linear Response Theory Of Fluorescence Stokes Shift In Protein Solution

Ultrafast fluorescence technique has been widely used to study the interaction and dynamics of microcosm.In the studying of protein hydrodynamics,Stokes shift can be observed by ultrafast fluorescence technique.The linear response theory has been used to explain the relationship between Stokes shift and the equilibrium fluctuations of system.Stokes shift in solution follows the linear response theory.In most literatures,equilibrium fluctuations on the ground state energy surface are often used to evaluate the non-equilibrium processes of fluorescence spectrum.However,through molecular dynamics simulation,we found that Stokes shift depends on equilibrium statistics of the excited state surface,when the ground state and excited state energy surfaces of the system are different.In this paper,we simulated tryptophan and staphylococcus nuclease solution.The connections between the non-equilibrium solvation dynamics upon optical transitions and the system's equilibrium fluctuations are explored in aqueous liquid.Linear response theory correlates time-dependent fluorescence with the equilibrium time correlation functions.The relationship between non-equilibrium processes and equilibrium fluctuations of protein in solution was explained.The relationship between Gaussian statistics and linear response was discussed.Whether the attenuation of all order cross-time correlation function shows consistency was illuminated.The main research contents are as follows:1.Tryptophan solution was simulated using molecular dynamics simulations.Stokes shift was calculated,and the relaxation process was compared with the fluctuation of the energy and configuration of the ground state and the excited state water molecules.The correlation between Stokes shift and the excited state hydrodynamics was confirmed,and the significance of the fluorescence spectrum was clarified.The hydrodynamic process of tryptophan solution was studied under different ground state conditions.It is found that the hydrodynamic process is always consistent with the first-order normalized time correlation function of the excited state,rather than depending on the first-order normalized time correlation function of the ground state.The ground state linear correspondence theory can describe the hydrodynamic process,when the first-order normalized time correlation functions of the ground state and the excited state are equal.The Gaussian distribution under various ground state conditions is analyzed,and the failure of linear response theory is explained by the change of s(t),the width of Gaussian statistics data.The linear response theory fails when s(t)shows a large intermediate broadening over time.2.Staphylococcus nuclease solution was simulated using molecular dynamics simulations.The configurations at different stages of the hydrodynamic relaxation process were captured using molecular view software.The general probability distribution of the excited state energy was plotted,which showed a typical Gaussian distribution.The energy probability distribution curve of each subsystem is plotted,and we found that the energy of the protein molecules deviates from gaussian distribution.Through the excited linear response theory formula,we found that as long as the total energy system satisfy the gaussian statistical distribution,even if part of the composition of solution deviates from gaussian statistical distribution,Stokes shift can be solved by the excited linear response theory.For each order of time correlation function of the whole system and each subsystem,the higher order function is consistent with the linear order one.Based on the components of the system,the total Stokes shift was decomposed,and the sum of all order time correlation functions and cross-time correlation functions were constructed,which was respectively expressed by(35)E_S(t)and(35)E_S~x(t).The decomposed time correlation functions _nc~x(t)and S~x(t)could be used to describe the equilibrium and non-equilibrium dynamics of the subsystem.