Quantum Mechanical Studies In Biological Systems And Protein Folding

Due to a large number of atoms in protein, force field method which is built with relatively simple atomic pairwise functions is the main method for studying the macromoleculars like proteins. Current standard force fields include AMBER, CHARMM, OPLS, GROMOS and et at. According to force field methods, the complicated interaction is simplified to be the combinations of bond stretch, angle bending, dihedral terms, the Coulomb electrostatic and VDW interactions. Parameters for these potential energy terms are fitted to quantum mechanical calculations or some experimental date. The simple format of the force fields enable the straightforward and rapid evaluation of interaction forces of the complex systems, and they have been used to all kinds of molecular systems successfully in the past several decades. While, they still have significant limitations. Since the biomolecular is usually in a solution environment and the polarization effect is very obvious in water. In force field, the electronic movement is ignored and the energy of system is a function of nuclear location, so it cannot deal with the system with strong electronic effect. For example, the standard force field does not describe chemical bond breaking and bond formation process, and more notably, does not include polarization effect.Only quantum mechanical theory and computation can truly overcome these deficiencies of the empirical force field. However, straightforward application of the existing quantum chemistry methods to complex systems is beyond the computational limit. In order to apply quantum methods to study properties of proteins or other biomolecules, some linear scaling methods have been proposed in the past several decades, including divide-and-conquer method, adjustable density matrix assembler method, fragment molecular orbital method, and the molecular fragmentation with conjugate caps method (MFCC).MFCC method is one of the molecular tailoring methods, based on the locality of electronic structure. In this approach, molecular is cut into fragments along the backbone and each position of cut, a pair of conjugate caps is added to saturate the covalent bonds and represent the neighboring environment. Therefore, calculation of a large molecule can be divided into several calculations of small molecules, and return the properties of the large molecule by simple plus and minus. The electronic properties of protein systems can be computed through an efficient linear scaling scheme using a variety of methods. The MFCC method scales linearly with the size of the molecular and, in particular, its numerical computation can be easily parallelized for even greater computational efficiency. This approach has been successfully applied to study the electron density of protein, protein total energy, ligand optimization in binding pocket of protein, protein/ligand interaction, protein salvation and drug design.This thesis contains mainly six parts: Part I: MFCC study of HIV-1 protease-bridge water interaction. Part II: MFCC-CPCM calculation of the contribution of W301 water for the protein-ligand binding free energy for HIV-1 protease/ligand complex. Part III: The quantum calculation of protein is made possible by developing MFCC in combination with the implicit continuum model to fit the atomic charge (PPC). Our PPC makes each atom into specific protein environment. MD simulations are preformed for a number of benchmark proteins and the computational result shows that the protein structure are more stable using PPC than AMBER. Part IV: Protein's native structure is dynamically stabilized by PPC. Part V: Thermodynamics of folding and unfolding of TC5B by replica exchange molecular dynamics simulations. Part VI: Ultrafast protein folding accelerated by PPC fitted on-the-fly. The main results obtained in this thesis are as follows.I. MFCC study of HIV-1 protease-bridge water interactionAccording to the MFCC approach, we decompose the protease into 198 amino acid fragments and 196 concaps by cutting all backbone peptide bonds, then every position that is cut is sealed with proper conjugate caps (CH3CO- and CH3NH-). Ab initio methods at HF, B3LYP and MP2 levels with a fixed basis set 6-31+G* have been employed in the present calculation. Our result shows the following features: (1) W301 hydrogen bonds more strongly to ILE50 (B) than ILE50 (A). (2) In additions to strong hydrogen bonding by W301 to ILE50's, W301 also interacts strongly with the deprotonated ASP25 (A) through relatively long range ion-dipole interaction. But no such long range ion-dipole interaction exits between W301 and the protonated ASP25 (B). (3) W301 hydrogen bonds more strongly to the ligand ABT-538 than to the ILE50's of protease. (4) However, the total interaction energy between the bridge water W301 and either chain of protease is very close. II. MFCC-CPCM calculation of the contribution of W301 water for the protein-ligand binding free energy for HIV-1 protease/ligand complexWe developed a novel method that combines the linear scaling quantum mechanical method, termed the molecular fragmentation with conjugate caps (MFCC), with conductor-like polarizable continuum model (CPCM) to study protein salvation. In this work, we apply this MFCC-CPCM approach to study the contribution to the binding free energy from a conserved water molecular in HIV-1 protease/ABT538 complex. The MFCC method is applied to calculate the interaction energy in gas phase at MP2/6-31+G* level and the MFCC-CPCM method is applied to calculate the electrostatic solvation energies at HF/6-31G* level. The non-electrostatic salvation free energy is calculated using surface area (SA) approach and the entropy loss from normal mode analysis. As an advantage over the frequently used MM/PBSA method, this approach includes polarization effect explicitly. The results, which are in good agreement with FEP/TI method, show that the conserved W301 contributes significantly to the binding free energy of HIV-1PR/ABT538 complex.III. Intra-protein hydrogen bonding is dynamically stabilized by polarized protein-specific charge (PPC)In current standard force fields, the partical charge of each atom is fixed and therefore they fail to give accurate representation of the electrostatic of the specific protein environment which is highly inhomogeneous and protein-specific. We employ linearized Poisson-Boltzmann method to solve the self-consistent reaction-field equation coupled with quantum chemistry calculation of the solute using the MFCC scheme to fit the polarized protein-specific charge (PPC). The PPC correctly represent the electronically polarized state of the protein and therefore provide accurate electrostatic interaction near the native structure. When MD simulation is preformed, the AMEBR charges are simply by the PPC while the rest of the force field parameters are intact. The computational result of six proteins shows that occupancy percentage of hydrogen bonds averaged over simulation time, as well as the number of hydrogen bonds as a function of simulation time, are consistently higher under PPC than AMBER charge. In particular, some intra-protein hydrogen bonds are found broken during MD simulation using AMBER charge but they are stable using PPC. The breaking of some intra-protein hydrogen bonds in AMBER simulation is responsible for deformation or denaturing of some local structures of proteins during MD simulation. In PPC simulation, the hydrogen bonds and secondary structure are kept intact, and the protein structure is stable.IV. Protein's native structure is dynamically stabilized by PPCPrevious study finds that those native energy are the lowest energy using PPC, while using AMBER none of native structures have the lowest energy among decoys. So MD simulation is performed for those proteins using AMBER and PPC. Our results shows that MD simulation can drive the protein away from its native state when standard AMBER force field is used, while PPC can still reflect protein's real structure after long time simulation. The primary cause of the difference is some intra-protein hydrogen bonds are broken using AMBER charge, and the breaking of intra-protein hydrogen bonds cause the deformation or denaturing of structure, thereby away from their correct structures. In contrast, those intra-protein hydrogen bonds which are significant to stabilize protein structure remain intact using PPC.V. Thermodynamics of folding and unfolding of TC5B by replica exchange molecular dynamics simulationsMolecular dynamics simulations based on AMBER force fields (ff96 and ff03) and generalized Born models (igb1 and igb5) have been carried out to study folding/unfolding of mini-protein Trp-cage. The thermodynamic properties of Trp-cage are found to be sensitive to the specific version of the solvation model and force field employed. When ff96/igb5 combination is used, the predicted melting temperature from unfolding simulation is in good agreement with the experimental value of 315K, but the folding simulation does not converge. The most stable thermodynamic profile in both folding and unfolding simulations is obtained when ff03/igb5 combination is employed, and the predicted melting temperature is about 345K, showing over-stabilization of the protein. And the free energy landscapes of TC5B have also been explored and the contour maps from unfolding and folding simulations using ff03/igb5 show similar characteristics. Simulations using the igb1 version in combination with ff96 or ff03 are difficult to converge within our simulation time limit (50 ns). VI. Ultrafast protein folding accelerated by PPC fitted on-the-fly Since PPC is fitted from a static structure, more precisely the native structure, it can only well reflect the charge distribution in a very small portion of phace space, and may not be suitable for the study of large conformation change such as protein folding. In this work, we incorporate PPC into molecular dynamics and propose a on-the-fly charge fitting scheme for folding simulation of a short peptide (PDB entry 2I9M). We carry out two direct folding simulations with AMBER force field and polarized protein-specific charge for 30ns. Starting from a fully extended structure, protein successfully folds to the native conformation in an ultrafast time (6.3ns) in PPC simulation. In AMBER simulation not a single folded structure has been seen during the 30ns MD simulation.With successive development of MFCC theory, we believe our MFCC method, together with other linear scaling quantum mechanical methods, can play a more and more important role in studying biological systems. We extend the linear scaling quantum mechanical methods to the study about dynamic structure, and it has been successfully used toα-helix folding.