Free Energy Calculation In Complex Systems Based On Configurational Space Discretization

Studying the correlation of structure and function of biomolecule is critical in computational biology and computational chemistry. No matter the process of protein folding, docking or protein structure prediction, studying the biomolecular conformational changes and developing an accurate method to estimate the free energy difference are the main challenges. For the complexity of biomelocules, it’s hard to study protein configurational space. For the lacking of high-correlation analysis and effective method of free energy calculation, we demonstrated a hierarchical conformational analysis of protein and then designed a free energy calculation method based on configurational space discretizaion.Free energy landscape has been widely used to study the correlation of structure and function of native globular proteins. However, free energy landscape of native globular proteins is usually projected onto one or a few dimensions. Due to the complicated structure of biomolecules, we hope to study the detailed conformational analysis for biomolecules in a multidimensional ways. We defined different timescales by the dynamics of backbone torsional degrees of freedom by generated a 0.2 milli-second molecular dynamics(MD) simulations of hen egg white lysozyme. Our results demonstrated that crystal structures always occupying the dominant structural ensemble which is harder to transfer to other structures. By comparing the MD ensemble with experimental data, we demonstrated some mechanism of conformational change and function with some important backbone torsional change at multiple temporal resolutions.Free energy is an essential state function in studying the process of biology and chemistry. Free energy calculation is always divided into two major categories of scoring function by experimental data and physical formula. However scoring functions are limited by more experimental condition and can’t be easily extended. The method of physical formula to calculate free energy includes two categories. On the one hand,rigorous free energy calculation methods, such as thermodynamic integration, free energy perturbation, are not suitable to large number of complex systems due to prohibitive cost. On the other hand, two approximate methodologies, including MM/P(G)BSA and linear interaction energy, are gradually widely used. Due to entropy-enthalpy compensation and the lack of entropy calculation, these methods will lead to inaccurate results. In this paper, we proposed a new method based on configurational space discretization in complex molecular systems. We demonstrated that snapshots in converged trajectories set are associated with implicit conformers have invariant statistical weight distribution(ISWD). We hypothesized that explicit conformers with ISWD may be constructed for complex molecular systems through systematic increase of conformer fineness. The hypothesis was proved as an effective way to get the free energy difference of different macrostates by tested in MD simulation trajectories of lipid and proteins. Based on the explicit conformers with ISWD, we define the conformational entropy, change of which between two given macrostates was found to be equivalent to change of free energy except a mere difference of a negative temperature factor, and change of enthalpy essential cancels corresponding change of average intra-conformer entropy. By implicitly taking advantage of entropy enthalpy compensation and forgoing all dynamical information, constructing explicit conformers with ISWD and counting thermally accessible number of which for interested end macrostate is likely to be an efficient and reliable alternative end point free energy calculation strategy.At last, we found that change of minimum and corresponding maximum potential energy terms exhibit similar level of correlation with change of free energy, based on analysis of extensive molecular dynamics simulation of three native globular proteins. More importantly, we demonstrated that change of span of potential energy terms exhibit considerably stronger correlations with change of free energy than the corresponding change of minimum and maximum potential energy terms.