Refining Molecular Mechanical Force Field For Protein Simulation

Proteins carry out biological functions. The function of protein is dependent on its three-dimensional structure and dynamics. Most proteins exist in unique conformations exquisitely suited to their function. Experimentally, the three-dimensional protein structure can be analyzed by x-ray diffraction of protein crystals or nuclear magnetic resonance spectroscopy. Currently, the miscorscopic distributions of protein conformations in time and space are not accessible by experiments. Experiments also can not provide detailed dynamics of proteins when they carry out their functions. Molecular dynamic (MD) simulation can provide such complementary information. Under further developments, simulation may also become an important tool for ab initio structure prediction. In MD simulations, the evolution of molecular structures in space and time are traced by solving Newton's equations of motion. MD is based on representing the energy of the protein as a function of its atomic coordinates by an empirical function, which is also known as molecular mechanics "force field". The quality of molecular dynamic simulations for protein depends greatly on the accuracy of empirical force fields. There are two well-known difficulties in molecular simulations, one is the limited accuracy of the energy functions modeling intra- and inter-molecular interactions and another is limited sampling in the higher dimensional conformational space, many efforts have been made to solve these questions.Traditional force field refinements are based on the structural and energy properties of small molecule systems. In GROMOS force field, parameters for non-bonded interaction are obtained by fitting thermodynamic quantities such as density, heats of vaporization, excess free energy and free energy of solvation to experimental data for small molecule systems. The torsional angle terms which affect the peptide conformational equilibriums arc usually not fully refined in force field. In addition, because of the high dimensionality of the force field parameters, we cannot confirm the best parameters just relying on the reference data used in force field developments.The precision of the description of the conformational equilibriums of force field is very important for molecular simulation. The emphases of this paper are how to refine the force field and ensure that it not only reproduces the condensed phase thermodynamics data, but also describes the conformational equilibriums accurately.There are mainly two works described in this paper, one is refining the description of peptide backbone conformations improves protein simulations using the GROMOS 53A6 force field, the other is using free energy perturbation to predict effects of changing force field parameters on computed conformational equilibriums of peptides.In chapter 2, we show that refining the descriptions of peptide backbone conformations can improve protein simulations using the GROMOS 53A6 force field. Many research indicated that there existed systematic biases in the description of protein local conformations involving the backbone Ramachandran dihedral angles by widely-used molecular mechanics force fields. Comparisons of molecular mechanics free energy surfaces of dipeptide system with quantum mechanical ones and conformation distributions in protein crystal structures indicated that refined treatments of backbone torsional angle terms are necessary. The high accuracy of the computed free energy surfaces allowed us to consider two types of corrections, one numerically and exactly reproducing the quantum mechanical results, and the other using small analytical terms to correct major deficiencies for the dipeptide systems. In addition, aiming at improving the directionality of backbone-backbone hydrogen bonds, we optimized and tested an off-center charge model for the peptide backbone carbonyl oxygen. Extensive molecular dynamics simulations of five proteins and two peptides in solution indicated that refined treatments of backbone dihedral angles lead to substantial improvements of the simulations. Being much simpler, the analytical terms perform as good as or even slightly better than the exact numerical corrections. While using off-center charges brought some improvements, the directionality of hydrogen bonds have not been significantly improved.In chapter 3, we have proposed an approach combines free energy perturbation with improved sampling techniques which may allow data about the conformational equilibriums of peptides to enter the parameter calibration phase in force field developments. To demonstrate the method, we consider a previously parameterized generalized born/solvent accessible surface area model for the GROMOS 43a1 force field. The model is applied to four peptides, including twoα-helices and twoβ-hairpins. Based on conformations sampled using temperature replica exchange molecular dynamics simulations, we predict how perturbations of various force field parameters would shift the computed equilibriums between the native conformational states and other conformational states of different systems. We considered two different approaches to define conformational states of four peptides. One is based on reaction coordinates and two-dimensional free energy surfaces. The other is based on clustering analysis of sampled conformations. Effects of perturbing various model parameters on the equilibriums between native-like states with other conformational states were considered. For one type of perturbation predicted to have consistent effects on different peptides, the predictions have been verified by actual simulations using a perturbed model.