Quantum mechanical map for protein-ligand binding with application to beta-trypsin/benzamidine complex

We report full ab initio Hartree-Fock calculation to compute quantum mechanical interaction energies for beta-trypsin/benzamidine binding complex. In this study, the full quantum mechanical ab initio energy calculation for the entire protein complex with 3238 atoms is made possible by using a recently developed MFCC (molecular fractionation with conjugate caps) approach in which the protein molecule is decomposed into amino acid-based fragments that are properly capped. The present MFCC ab initio calculation enables us to obtain an "interaction spectrum" that provides detailed quantitative information on protein-ligand binding at the amino acid levels. These detailed information on individual residue-ligand interaction gives a quantitative molecular insight into our understanding of protein-ligand binding and provides a guidance to rational design of potential inhibitors of protein targets.     

Fully quantum mechanical energy optimization for protein-ligand structure

We present a quantum mechanical approach to study protein-ligand binding structure with application to a Adipocyte lipid-binding protein complexed with Propanoic Acid. The present approach employs a recently develop molecular fractionation with a conjugate caps (MFCC) method to compute protein-ligand interaction energy and performs energy optimization using the quasi-Newton method. The MFCC method enables us to compute fully quantum mechanical ab initio protein-ligand interaction energy and its gradients that are used in energy minimization. This quantum optimization approach is applied to study the Adipocyte lipid-binding protein complexed with Propanoic Acid system, a complex system consisting of a 2057-atom protein and a 10-atom ligand. The MFCC calculation is carried out at the Hartree-Fock level with a 3-21G basis set. The quantum optimized structure of this complex is in good agreement with the experimental crystal structure. The quantum energy calculation is implemented in a parallel program that dramatically speeds up the MFCC calculation for the protein-ligand system. Similarly good agreement between MFCC optimized structure and the experimental structure is also obtained for the streptavidin-biotin complex. Due to heavy computational cost, the quantum energy minimization is carried out in a six-dimensional space that corresponds to the rigid-body protein-ligand interaction.     

Fractionation of peptide with disulfide bond for quantum mechanical calculation of interaction energy with molecules

We present a computational study of a recently developed molecular fractionation with conjugated caps (MFCC) method for application to peptide/protein that has disulfide bonds. Specifically, we employ the MFCC approach to generate peptide fragments in which a disulfide bond is cut and a pair of conjugated caps are inserted. The method is tested on two peptides interacting with a water molecule. The first is a dipeptide consisting of two cysteines (Cys-Cys) connected by a disulfide bond and the second is a seven amino acid peptide consisting of Gly-Cys-Gly-Gly-Gly-Cys-Gly with a disulfide cross link. One-dimensional peptide-water potential curves are computed using the MFCC method at various ab initio levels for a number of interaction geometries. The calculated interaction energies are found to be in excellent agreement with the results obtained from the corresponding full system ab initio calculations for both peptide/water systems. The current study provides further numerical support for the accuracy of the MFCC method in full quantum mechanical calculation of protein/peptide that contains disulfide bonds.     

A new quantum method for electrostatic solvation energy of protein

A new method that incorporates the conductorlike polarizable continuum model (CPCM) with the recently developed molecular fractionation with conjugate caps (MFCC) approach is developed for ab initio calculation of electrostatic solvation energy of protein. The application of the MFCC method makes it practical to apply CPCM to calculate electrostatic solvation energy of protein or other macromolecules in solution. In this MFCC-CPCM method, calculation of protein solvation is divided into calculations of individual solvation energies of fragments (residues) embedded in a common cavity defined with respect to the entire protein. Besides computational efficiency, the current approach also provides additional information about contribution to protein solvation from specific fragments. Numerical studies are carried out to calculate solvation energies for a variety of peptides including alpha helices and beta sheets. Excellent agreement between the MFCC-CPCM result and those from the standard full system CPCM calculation is obtained. Finally, the MFCC-CPCM calculation is applied to several real proteins and the results are compared to classical molecular mechanics Poisson-Boltzmann (MM/PB) and quantum Divid-and-Conque Poisson-Boltzmann (D&C-PB) calculations. Large wave function distortion energy (solute polarization energy) is obtained from the quantum calculation which is missing in the classical calculation. The present study demonstrates that the MFCC-CPCM method is readily applicable to studying solvation of proteins.     

Theoretical method for full ab initio calculation of DNA/RNA-ligand interaction energy

In this paper, we further develop the molecular fractionation with conjugate caps (MFCC) scheme for quantum mechanical computation of DNA-ligand interaction energy. We study three oligonuclear acid interaction systems: dinucleotide dCG/water, trinucleotide dCGT/water, and a Watson-Crick paired DNA segment, dCGT/dGCA. Using the basic MFCC approach, the nucleotide chains are cut at each phosphate group and a pair of conjugate caps (concaps) are inserted. Five cap molecules have been tested among which the dimethyl phosphate anion is proposed to be the standard concap for application. For each system, one-dimensional interaction potential curves are computed using the MFCC method and the calculated interaction energies are found to be in excellent agreement with corresponding results obtained from the full system ab initio calculations. The current study extends the application of the MFCC method to ab initio calculations for DNA- or RNA-ligand interaction energies.     

A new method for direct calculation of total energy of protein

A new scheme is developed for efficient quantum mechanical calculation of total energy of protein based on a recently developed MFCC (molecular fractionation with conjugate caps) approach. In this scheme, the linear-scaling MFCC method is first applied to calculate total electron density of protein. The computed electron density is then employed for direct numerical integration in density functional theory (DFT) to yield total energy of protein, with the kinetic energy obtained by a proposed ansatz. Numerical studies are carried out to calculate torsional energies of two polypeptides using this approach and the energies are shown to be in good agreement with the corresponding full system DFT calculation.     

New method for direct linear-scaling calculation of electron density of proteins

A new scheme for direct linear-scaling quantum mechanical calculation of electron density of protein systems is developed. The new scheme gives much improved accuracy of electron density for proteins than the original MFCC (molecular fractionation with conjugate caps) approach in efficient linear-scaling calculation for protein systems. In this new approach, the error associated with each cut in the MFCC approach is estimated by computing the two neighboring amino acids in both cut and uncut calculations and is corrected. Numerical tests are performed on six oligopeptide taken from PDB (protein data bank), and the results show that the new scheme is efficient and accurate.     

The generalized molecular fractionation with conjugate caps/molecular mechanics method for direct calculation of protein energy

A generalized molecular fractionation with conjugate caps/molecular mechanics (GMFCC/MM) scheme is developed for efficient linear-scaling quantum mechanical calculation of protein energy. In this GMFCC/MM scheme, the interaction energy between neighboring residues as well as between non-neighboring residues that are spatially in close contact are computed by quantum mechanics while the rest of the interaction energy is computed by molecular mechanics. Numerical studies are carried out to calculate torsional energies of six polypeptides using the GMFCC/MM approach and the energies are shown to be in general good agreement with the full system quantum calculation. Among those we tested is a polypeptide containing 396 atoms whose energies are computed at the MP26-31G* level. Our study shows that using GMFCC/MM, it is possible to perform high level ab initio calculation such as MP2 for applications such as structural optimization of protein complex and molecular dynamics simulation.     

An efficient fragment-based approach for predicting the ground-state energies and structures of large molecules

An efficient fragment-based approach for predicting the ground-state energies and structures of large molecules at the Hartree-Fock (HF) and post-HF levels is described. The physical foundation of this approach is attributed to the "quantum locality" of the electron correlation energy and the HF total energy, which is revealed by a new energy decomposition analysis of the HF total energy proposed in this work. This approach is based on the molecular fractionation with conjugated caps (MFCC) scheme (Zhang, D. W.; Zhang, J. Z. H. J. Chem. Phys. 2003, 119, 3599), by which a macromolecule is partitioned into various capped fragments and conjugated caps formed by two adjacent caps. We find that the MFCC scheme, if corrected by the interaction between non-neighboring fragments, can be used to predict the total energy of large molecules only from energy calculations on a series of small subsystems. The approach, named as energy-corrected MFCC (EC-MFCC), computationally achieves linear scaling with the molecular size. Our test calculations on a broad range of medium- and large molecules demonstrate that this approach is able to reproduce the conventional HF and second-order Moller-Plesset perturbation theory (MP2) energies within a few millihartree in most cases. With the EC-MFCC optimization algorithm described in this work, we have obtained the optimized structures of long oligomers of trans-polyacetylene and BN nanotubes with up to about 400 atoms, which are beyond the reach of traditional computational methods. In addition, the EC-MFCC approach is also applied to estimate the heats of formation for a series of organic compounds. This approach provides an appealing approach alternative to the traditional additivity rules based on either bond or group contributions for the estimation of thermochemical properties.     

Molecular caps for full quantum mechanical computation of peptide-water interaction energy

We present a systematic study of numerical accuracy of various forms of molecular caps that are employed in a recently developed molecular fractionation scheme for full quantum mechanical computation of protein-molecule interaction energy. A previously studied pentapeptide (Gly-Ser-Ala-Asp-Val) or P5 interacting with a water molecule is used as a benchmark system for numerical testing. One-dimensional potential energy curves are generated for a number of peptide-water interaction pathways. Our study shows that various forms of caps all give consistently accurate energies compared to the corresponding full system calculation with only small deviations. We also tested the accuracy of cutting peptide backbone at different positions and comparisons of results are presented.     

Molecular fractionation with conjugated caps density matrix with pairwise interaction correction for protein energy calculation

Pairwise interaction correction (PIC) is introduced to account for electron density polarization due to short-range interactions such as hydrogen bonding and close contact between molecular fragments in the molecular fractionation with conjugated caps density matrix (MFCC-DM) approach for energy calculation of protein and other polymers [Chen et al., J. Chem. Phys. 122, 184105 (2005)]. With this PIC, the accuracy of the calculated protein energy and other electronic properties are improved, and the MFCC approach can be applied to study real proteins with short-range structural complexity. In the present MFCC-DM-PIC approach, the short-range interresidual interactions are represented by a pair of small molecules (interacting units) which are made from the two residues that fall within a certain distance criterion. The density matrices of fragments, concaps, interacting units and pairs are calculated by conventional Hartree-Fock or density functional theory methods and are combined to construct the full density matrix which is finally employed to calculate the total energy, electron density, electrostatic potential, dipole moment, etc., of the protein. Numerical tests on seven conformationally varied peptides are presented to demonstrate the accuracy of the MFCC-DM-PIC method.     

An efficient approach for ab initio energy calculation of biopolymers

We present a new method for efficient total-energy calculation of biopolymers using the density-matrix (DM) scheme based on the molecular fractionation with conjugate caps (MFCC) approach. In this MFCC-DM method, a biopolymer such as a protein is partitioned into properly capped fragments whose density matrices are calculated by conventional ab initio methods which are then assembled to construct the full system density matrix. The assembled full density matrix is then employed to calculate the total energy and dipole moment of the protein using Hartree-Fock or density-functional theory methods. Using this MFCC-DM method, the self-consistent-field procedure for solving the full Hamiltonian problem is avoided and an efficient approach for ab initio energy calculation of biopolymers is achieved. Two implementations of the approach are presented in this paper. Systematic numerical studies are carried out on a series of extended polyglycines CH3CO-(GLY)n-NHCH3(n = 3-25) and excellent results are obtained.     

Fully ab initio protein‐ligand interaction energies with dispersion corrected density functional theory

Dispersion corrected density functional theory (DFT‐D3) is used for fully ab initio protein‐ligand (PL) interaction energy calculation via molecular fractionation with conjugated caps (MFCC) and applied to PL complexes from the PDB comprising 3680, 1798, and 1060 atoms. Molecular fragments with n amino acids instead of one in the original MFCC approach are considered, thereby allowing for estimating the three‐body and higher many‐body terms. n > 1 is recommended both in terms of accuracy and efficiency of MFCC. For neutral protein side‐chains, the computed PL interaction energy is visibly independent of the fragment length n. The MFCC fractionation error is determined by comparison to a full‐system calculation for the 1060 atoms containing PL complex. For charged amino acid side‐chains, the variation of the MFCC result with n is increased. For these systems, using a continuum solvation model with a dielectricity constant typical for protein environments (? = 4) reduces both the variation with n and improves the stability of the DFT calculations considerably. The PL interaction energies for two typical complexes obtained ab initio for the first time are found to be rather large (?30 and ?54 kcal/mol). © 2012 Wiley Periodicals, Inc.     

Fragment‐based quantum mechanical calculation of protein–protein binding affinities

The electrostatically embedded generalized molecular fractionation with conjugate caps (EE‐GMFCC) method has been successfully utilized for efficient linear‐scaling quantum mechanical (QM) calculation of protein energies. In this work, we applied the EE‐GMFCC method for calculation of binding affinity of Endonuclease colicin–immunity protein complex. The binding free energy changes between the wild‐type and mutants of the complex calculated by EE‐GMFCC are in good agreement with experimental results. The correlation coefficient (R) between the predicted binding energy changes and experimental values is 0.906 at the B3LYP/6‐31G*‐D level, based on the snapshot whose binding affinity is closest to the average result from the molecular mechanics/Poisson–Boltzmann surface area (MM/PBSA) calculation. The inclusion of the QM effects is important for accurate prediction of protein–protein binding affinities. Moreover, the self‐consistent calculation of PB solvation energy is required for accurate calculations of protein–protein binding free energies. This study demonstrates that the EE‐GMFCC method is capable of providing reliable prediction of relative binding affinities for protein–protein complexes. © 2018 Wiley Periodicals, Inc.     

Binding free energy contributions of interfacial waters in HIV-1 protease/inhibitor complexes

Water molecules are commonly observed in crystal structures of protein-ligand complexes where they mediate protein-ligand binding. It is of considerable theoretical and practical importance to determine quantitatively the individual free energy contributions of these interfacial water molecules to protein-ligand binding and to elucidate factors that influence them. The double-decoupling free energy molecular dynamics simulation method has been used to calculate the binding free energy contribution for each of the four interfacial water molecules observed in the crystal structure of HIV-1 protease complexed with KNI-272, a potent inhibitor. While two of these water molecules contribute significantly to the binding free energy, the other two have close to zero contribution. It was further observed that the protonation states of two catalytic aspartate residues, Asp25 and Asp125, strongly influence the free energy contribution of a conserved water molecule Wat301 and that different inhibitors significantly influence the free energy contribution of Wat301. Our results have important implications on our understanding of the role of interfacial water molecules in protein-ligand binding and to structure-based drug design aimed at incorporating these interfacial water molecules into ligands.     

Formal Estimation of Errors in Computed Absolute Interaction Energies of Protein-ligand Complexes

A largely unsolved problem in computational biochemistry is the accurate prediction of binding affinities of small ligands to protein receptors. We present a detailed analysis of the systematic and random errors present in computational methods through the use of error probability density functions, specifically for computed interaction energies between chemical fragments comprising a protein-ligand complex. An HIV-II protease crystal structure with a bound ligand (indinavir) was chosen as a model protein-ligand complex. The complex was decomposed into twenty-one (21) interacting fragment pairs, which were studied using a number of computational methods. The chemically accurate complete basis set coupled cluster theory (CCSD(T)/CBS) interaction energies were used as reference values to generate our error estimates. In our analysis we observed significant systematic and random errors in most methods, which was surprising especially for parameterized classical and semiempirical quantum mechanical calculations. After propagating these fragment-based error estimates over the entire protein-ligand complex, our total error estimates for many methods are large compared to the experimentally determined free energy of binding. Thus, we conclude that statistical error analysis is a necessary addition to any scoring function attempting to produce reliable binding affinity predictions.     

Interpretation of protein/ligand crystal structure using QM/MM calculations: case of HIV-1 protease/metallacarborane complex

Deltahedral metallacarborane compounds have recently been discovered as potent, specific, stable, and nontoxic inhibitors of HIV-1 protease (PR), the major target for AIDS therapy. The 2.15 A-resolution X-ray structure has exhibited a nonsymmetrical binding of the parental compound [Co(3+)-(C2B9H11)2](-) (GB-18) into PR dimer and a symmetrical arrangement in the crystal of two PR dimer complexes into a tetramer. In order to explore structural and energetic details of the inhibitor binding, quantum mechanics coupled with molecular mechanics approach was utilized. Realizing the close positioning of anionic inhibitors in the active site cavity, the possibility of an exchange of structural water molecules Wat50 and Wat128 by Na+ counterions was studied. The energy profiles for the rotation of the GB-18 molecules along their longitudinal axes in complex with PR were calculated. The results show that two Na+ counterions are present in the active site cavity and provide energetically favorable and unfavorable positions for carbon atoms within the carborane cages. Eighty-one rotamer combinations of four molecules of GB-18 bound to PR out of 4 x 10(5) are predicted to be highly populated. These results lay ground for further calculations of interaction energies between GB-18 and amino acids of PR active site and will make it possible to interpret computationally the binding of similar metallacarborane molecules to PR as well as to resistant PR variants. Moreover, this computational tool will allow the design of new, more potent metallacarborane-based HIV-1 protease inhibitors.     

Electrostatic field-adapted molecular fractionation with conjugated caps for energy calculations of charged biomolecules

An electrostatic field-adapted molecular fractionation with conjugated caps (EFA-MFCC) approach is implemented for treating macromolecules with several charge centers. The molecular fragmentation is performed in an "electrostatic field," which is described by putting point charges on charge centers, directly affecting the Hamiltonians of both fragments and conjugated caps. So the present method does not need truncation during the calculation of electrostatic interactions. Our test calculations on a series of charged model systems and biological macromolecules using the HF and B3LYP methods have demonstrated that this approach is capable of describing the electronic structure with accuracy comparable to other fragment-based methods. The EFA-MFCC approach is an alternative way for predicting the total energies of charged macromolecules with acyclic, loop, and intersectional loop structures and interaction energies between two molecules.     

Role of structural water molecule in HIV protease-inhibitor complexes: a QM/MM study

Structural water molecule 301 found at the interface of HIV protease-inhibitor complexes function as a hydrogen bond (H-bond) donor to carbonyl groups of the inhibitor as well as H-bond acceptor to amide/amine groups of the flap region of the protease. In this study, six systems of HIV protease-inhibitor complexes were analyzed, which have the presence of this "conserved" structural water molecule using a two-layer QM/MM ONIOM method. The combination of QM/MM and QM method enabled the calculation of strain energies of the bound ligands as well as the determination of their binding energies in the ligand-water and ligand-water-protease complexes. Although the ligand experiences considerable strain in the protein bound structure, the H-bond interactions through the structural water overcomes this strain effect to give a net stability in the range of 16-24 kcal/mol. For instance, in 1HIV system, the strain energy of the ligand was 12.2 kcal/mol, whereas the binding energy associated with the structural water molecule was 20.8 kcal/mol. In most of the cases, the calculated binding energy of structural water molecule showed the same trend as that of the experimental binding free energy values. Further, the classical MD simulations carried out on 1HVL system with and without structural water 301 showed that this conserved water molecule enhances the H-bond dynamics occurring at the Asp-bound active site region of the protease-inhibitor system, and therefore it will have a direct influence on the mechanism of drug action.