Free Energy Calculation By Jarzynski Equality For Biomolecular Complex

Free energy calculation is a very important research subject in computational science, due to the close relationship between all the physical, chemical and biological processes and their free energy differences. And the free energy calculation is especially important for bio-systems, in which the energetics of bio-complex is vital in providing valuable insight into the role of structure-function relationships of bio-complexes and in providing a rational basis for the design and modeling of new molecular effectors that can act as novel substrates, inhibitors or drugs for the treatment of disease. Thus, the characterization of the energetics of bio-complex is a significant way to understand biological processes. At present, several methods have been presented to calculate free energy differences from equilibrium MD simulation trajectories, such as thermodynamic integration, free energy perturbation, and umbrella sampling with WHAM. These classic methods potentially offer accurate estimation of free energy differences. However, bio-complexes in aqueous solution are very large systems, and these classic methods are time-consuming and expensive given the requirement of sufficient sampling to achieve computational accuracy. The great expense in sampling has prevented wide adoption of these classic methods for the estimation of free energy differences in bio-complex systems.Besides these classic methods, a non-equilibrium method based on the Jarzynski Equality, the so-called "fast growth" method, has been developed for free energy calculations. The Jarzynski Equality suggests that one may be able to extract free energy profiles from repeated non-equilibrium pulling trajectories, which could be easily carried out by SMD simulations. This method has been applied to several benchmark systems to evaluate the accuracy of the free energy differences, providing favorable results. And there are two advantages of this non-equilibrium method in free energy calculations compared to classic methods:i) it is convenient to operate, which could save the manpower; ii) it’s more time-saving than the classic free energy calculation methods; iii) The method is simple to implement in many existing simulation packages. Thus, there have been a number of applications of Jarzynski’s Equality employed to calculate free energy differences for bio-molecular systems. Despite its popularity in applications to bio-complex systems, the accuracy of Jarzynski Equality has not been properly tested for free energy calculations. Recently, the importance of checking convergence of the free energy results in bio-complex systems has been stressed, and a few doubts have been raised about the applicability of Jarzynski Equality to free energy calculations in complex biomolecular processes.In this thesis, MD and SMD simulations were carried out to calculate the binding free energy of DHP and its inhibitor4-BP via Jarzynski Equality and umbrella sampling. The result calculated by Jarzynski Equality was compared with that of umbrella sampling and experiment, confirming that the Jarzynski Equality could provide relatively accurate free energy difference in DHP-4-BP systems.Then, we adopted Jarzynski Equality in free energy calculation in bio-mineralization process:the morphological control of DCPD crystal by Glu. First, the crystallographic parameters of DCPD crystal faces were demarcated by the DCDP crystal dissolution experiments. Then, the energetics of Glu adsorbed on DCPD crystal steps were further studied by Jarzynski Equality. Finally, the mechanism of Glu’s regulation effect on DCPD crystal was illustrated.However, the accuracy of the adsorption free energy of Glu on DCPD steps was doubtful. We hence investigated the application of Jarzynski Equality on the adsorption free energy calculation for water-HAp and RGD-HAp system. The umbrella sampling with WHAM was also employed to calculate the adsorption free energy profiles. The results calculated by Jarzynski Equality was carefully compared with that of umbrella sampling, and the high-density interfacial water layer was found having severely effect on the free energy profiles calculated by Jarzynski Equality. Finally, a hybrid scheme was proposed to eliminate the effect of high-density interfacial water layer.