Optimization Methods For Some Non-equilibrium Molecular Dynamics Simulations

Molecular dynamics is one of the most popular simulation methods in simulating dynamic properties of proteins. In the past two decades, both methodology and application of molecular dynamics have been greatly developed in macromolecules. With the development of simulation and accumulation of experience, there is a growing emphasis on the simulation technology research of biological macromolecules, such as Steered molecular dynamics (SMD) Targeted molecular dynamics(TMD), Essential dynamics (ED), Conformational flooding (CF), Random expulsion molecular dynamics (REMD), Force probe molecular dynamics (FPMD) , Interactive molecular dynamics (IMD) and so on. By introducting techniques of external force, simple harmonic potential and the reduction of protein conformational freedom and so on, simulated time scale is more than conventional dynamic methods, and thus can simulate the ligand and receptor binding, heterogeneous effects of protein and other biological phenomena. For examples, since the late 1990's SMD and TMD have been become the favorable tools in the research of different conformations changing process. There are three main workings presented in this dissertation which is summarized as follows:In Chapter I, the basic formulation of MD and free energy methods are briefly recalled, and the main working and finding are outlined in the dissertation.In Chapter II, a brief history and basic theory of MD are reviewed and the principles of Newton's equation of motion and the finite difference method for MD are referred. As the technical basis of this work, the details of both special MD simulation methods including SMD and TMD are then introduced. In the last section of this chapter, five methods of computing free energy are illuminated; theory and application are given, respectively.In SMD simulations, the pulling direction of the spring in SMD is chosen randomly or by guesswork on the basis of structural information. A disadvantage arises from the fact that the force applied to the ligand in the chosen direction may not move along a favorable pathway, and some SMD simulations may suffer from inefficiency. In Chapter III, a new steered molecular dynamics (SMD) method with adjusting pulling direction is proposed to search an optimum trajectory of ligand dissociation. A multi-objective model and a searching technique based on information entropy with multi-population are developed to optimize the pulling direction. The improved method has been used to dissociate the substrate-bound complex structure of cytochrome P450 3A4-metyrapone. A more favorable dissociation pathway can be gained. The results show that the new pathway obtained by the proposed method has less dissociation time, smaller rapture force and lower energy barrier than that by the conventional SMD.Predicting the unbinding free energy is an important problem in biomolecular simulation. Such prediction would be great benefit in understanding protein functions and predicting ligand-unbinding strengths, and may be useful for discovering pharmaceutical drags. In Chapter FV, a non-equilibrium free energy (NE) method with a path optimization is developed to predict the dissociation free energy of protein-ligand complexes. A multi-objective model of dissociation pathway optimization is mathematically constructed and solved by using an adaptive genetic algorithm with multi-population based on information entropy. A better dissociation pathway can be gained, and the potentials of mean force can be calculated by means of SMD trajectories along this unbinding pathway. Jarzynski's equality is used to derive the free energy. The results show that the method not only has good accuracy and efficiency but also can simulate whole unbinding proceeding and give some important structural information about development of new drags.In Chapter V, as the finial chapter, we study conformational transition pathway of CaM. CaM is an important signaling protein in organism. The effects of antagonist on the conformational transition and global conformational transition pathway of CaM are investigated by means of two different conformations of open and closed states. The molecular dynamics method is firstly used to simulate conformational transitions of the calmodulins with and without an antagonist bound. The results show that CaM without antagonist tends to open from its closed state and cause allosteric interaction. And CaM with antagonist tends to keep in closed state, which is conducive to control the activities of some kinases and phosp hatases. Using TMD method simulates a global conformational transition between open and closed states, and a conformational transition pathway and four possible intermediate states are obtained.We gratefully acknowledge financial support for this work from the National Natural Science Foundation (grant 10772042) and Major State Basic Research Project (grant 2009CB918501) of China.