The Development And Application Of Fragment Quantum Chemical Approach For Computation And Dynamic Simulation Of Biomolecules

Currently, standard ab initio calculations of macromolecular properties are computationally inhibitive. As a result, such calculations are almost exclusively carried out using empirical force fields. However, the defect of empirical force fields for describing biomolecular properties is a long standing issue and a subject of debate. To extend the applicability of rigorous quantum mechanical (QM) method to large systems, considerable effort has been made to the development of various linear-sealing and/or fragmentation methods over the past decades for property calculations of macromolecules. Among the various methodologies, the fragment approach has become very popular in developing a linear-scaling QM method for large systems.The molecular fractionation with conjugate caps (MFCC) method was initially developed in our group to calculate protein-ligand interaction energy by a quantum method and was later extended to compute the total energy of proteins at diverse ab initio levels. Then, an efficient generalized molecular fractionation with conjugate caps/molecular mechanics (GMFCC/MM) scheme, in which molecular force field interactions were introduced to represent the long-range interaction between distant non-neighboring fragments whereas the short-range non-neighboring fragment interactions were calculated by QM, was proposed. In this work, we developed an electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method for accurately describing the electronic structure of protein systems, and the protein-ligand binding affinities. Then, the first and second derivatives of the EE-GMFCC energy were derived and employed in protein geometry optimization and vibrational spectra (infrared and Raman spectra) calculation. And, the ab initio molecular dynamics (AIMD) simulation for proteins in explicit solvent was also performed.In the EE-GMFCC scheme, fragment-based energies of neighboring residues and interaction energies of non-neighboring residues that are spatially in close contact are computed by QM, whereas the interaction energies between distant non-neighboring residues are treated by charge-charge Coulomb interactions. The quantum calculation of each fragment is embedded in the field of point charges of all other fragments to mimic the electrostatic environment of the remaining system. Numerical tests for various benchmark systems have demonstrated the efficacy of the EE-GMFCC method. For 18 real three-dimensional proteins of up to 1142 atoms, the EE-GMFCC calculated protein energies were found to be in good agreement with those obtained from the full system ab initio calculations at the HF/6-31G* level, and the overall mean unsigned error was only 2.39 kcal/mol. The EE-GMFCC approach was also applied for proteins at the levels of the density functional theory (DFT) and second-order many-body perturbation theory (MP2), also showing only a few kcal/mol deviation from the corresponding full system result. The binding affinities of 14 avidin-biotin analogues were calculated using EE-GMFCC combined with a conductor-like polarizable continuum model (CPCM). The correlation coefficient (R) between the calculated binding energies and experimental values is 0.75 at the HF/6-31G*-D level based on single complex structure calculations, as compared to 0.73 of the force field result. On the other hand, the correlation coefficient between the calculated binding energies and the experimental values is 0.85 at the B3LYP/6-31G*-D level based on single complex structure calculations, and this correlation can be further improved to 0.88 when multiple snapshots are considered. The EE-GMFCC method is linear-scaling with a low prefactor, trivially parallel, and can be readily applied to routinely perform structural optimization of proteins and molecular dynamics (MD) simulation with high level ab initio electronic structure theories. Comparison of the optimized protein structures and vibrational spectra with those obtained from full system QM calculations shows that the EE-GMFCC approach can give accurate molecular geometries, vibrational frequencies and vibrational intensities. The EE-GMFCC method is also employed to simulate the amide I vibration of proteins, which has been widely used for the analysis of peptide and protein structures, and the results are in good agreement with the experimental observations. EE-GMFCC based ab initio molecular dynamics approach is also presented for practical application in protein dynamics in explicit solvent. Comparison to the simulation result using the AMBER force field shows that the AIMD gives a more stable protein structure in the simulation, indicating that quantum chemical energy is more reliable. Importantly, the present fragment-based AIMD simulation captures quantum effects including electrostatic polarization and charge transfer that are missing in standard classical MD simulations.