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.     

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.     

A Non-derivative MFCC Optimization Study of Cyclohexapeptide Monohydrate

The MFCC-downhill simplex method is presented to study the binding structure of small ligands in large molecular complex systems. This method employs the Molecular Fractionation with Conjugated Caps (MFCC) approach to compute the interaction energy-structure relation of the system and implements the downhill simplex algorithm for structural optimization. The method is tested on a molecular system of cyclo-AAGAGG￠H2O to optimize the binding position of water molecule to the ˉxed cyclohexapeptide. The MFCC-downhill simplex optimization results are in good agreement with the crystal structure. An MFCC-Powell optimization method which uses the Powell's minimization algorithm is also described and tested on the same system. The MFCC-downhill simplex optimization is more e±cient than the MFCC-Powell method.     

GREEN: A program package for docking studies in rational drug design

Summary A program package, GREEN, has been developed that enables docking studies between ligand molecules and a protein molecule. Based on the structure of the protein molecule, the physical and chemical environment of the ligand-binding site is expressed as three-dimensional grid-point data. The grid-point data are used for the real-time evaluation of the protein-ligand interaction energy, as well as for the graphical representation of the binding-site environment. The interactive docking operation is facilitated by various built-in functions, such as energy minimization, energy contribution analysis and logging of the manipulation trajectory. Interactive modeling functions are incorporated for designing new ligand molecules while considering the binding-site environment and the protein-ligand interaction. As an example of the application of GREEN, a docking study is presented on the complex between trypsin and a synthetic trypsin inhibitor. The program package will be useful for rational drug design, based on the 3D structure of the target protein.     

SOS-NMR: a saturation transfer NMR-based method for determining the structures of protein-ligand complexes

An NMR-based alternative to traditional X-ray crystallography and NMR methods for structure-based drug design is described that enables the structure determination of ligands complexed to virtually any biomolecular target regardless of size, composition, or oligomeric state. The method utilizes saturation transfer difference (STD) NMR spectroscopy performed on a ligand complexed to a series of target samples that have been deuterated everywhere except for specific amino acid types. In this way, the amino acid composition of the ligand-binding site can be defined, and, given the three-dimensional structure of the protein target, the three-dimensional structure of the protein-ligand complex can be determined. Unlike earlier NMR methods for solving the structures of protein-ligand complexes, no protein resonance assignments are necessary. Thus, the approach has broad potential applications--especially in cases where X-ray crystallography and traditional NMR methods have failed to produce structural data. The method is called SOS-NMR for structural information using Overhauser effects and selective labeling and is validated on two protein-ligand complexes: FKBP complexed to 2-(3'-pyridyl)-benzimidazole and MurA complexed to uridine diphosphate N-acetylglucosamine.     

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.     

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.     

Quantum study of HIV-1 protease-bridge water interaction

We present a fully quantum mechanical calculation for binding interaction between HIV-1 protease (PR) and the water molecule W301 which bridges the flaps of the protease with the inhibitors of PR. The quantum calculation is made possible by applying a recently developed molecular fractionation with conjugate caps (MFCC) method which divides a protein molecule into capped amino acid-based fragments and their conjugate caps. These individual fragments are properly treated to preserve the chemical property of bonds that are cut. Ab initio methods at HF, B3LYP, and MP2 levels with a fixed basis set 6-31+G* have been employed in the present calculation. The MFCC calculation produces a quantum mechanical interaction "map" representing interactions between individual residues of PR and W301. This enables a detailed quantitative analysis on binding of W301 to specific residues of PR at quantum mechanical level.     

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.     

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.     

Topological analysis of electron density maps of chiral cyclodextrin-guest complexes: a steric interaction evaluation

This paper reports interaction energy values for the systems heptakis (2,3,6-tri-O-methyl)-β-cyclodextrin complexed with R- and S-flurbiprofen. An intermolecular steric interaction potential calculation method is applied from the topological analysis of electron density maps and is assessed by comparison with values obtained from the application of conventional molecular mechanics energy minimization procedures. Both topology-based and standard energy minimization methods predict that the crystalline form of the R-flurbiprofen is the most stable one.     

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.     

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.     

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.     

Theoretical study on aquation reaction of cis-platin complex: RISM-SCF-SEDD, a hybrid approach of accurate quantum chemical method and statistical mechanics

The ligand exchange process of cis-platin in aqueous solution was studied using RISM-SCF-SEDD (reference interaction site model-self-consistent field with spatial electron density distribution) method, a hybrid approach of quantum chemistry and statistical mechanics. The analytical nature of RISM theory enables us to compute accurate reaction free energy in aqueous solution based on CCSD(T), together with the microscopic solvation structure around the complex. We found that the solvation effect is indispensable to promote the dissociation of the chloride anion from the complex.     

Stationary phase evaluations of quantum rate constants

We compute the quantum rate constant based on two extended stationary phase approximations to the imaginary-time formulation of the quantum rate theory. The optimized stationary phase approximation to the imaginary-time flux-flux correlation function employs the optimized quadratic reference system to overcome the inaccuracy of the quadratic expansion in the standard stationary phase approximation, and yields favorable agreements with instanton results for both adiabatic and nonadiabatic processes in dissipative and nondissipative systems. The integrated stationary phase approximation to the two-dimensional barrier free energy is particularly useful for adiabatic processes and demonstrates consistent results with the imaginary-time flux-flux correlation function approach. Our stationary phase methods do not require calculation of tunneling paths or stability matrices, and work equally well in the high-temperature and the low-temperature regimes. The numerical results suggest their general applicability for calibration of imaginary-time methods and for the calculation of quantum rate constants in systems with a large number of degrees of freedom.     

PROLIX: rapid mining of protein-ligand interactions in large crystal structure databases

A central problem in structure-based drug design is understanding protein-ligand interactions quantitatively and qualitatively. Several recent studies have highlighted from a qualitative perspective the nature of these interactions and their utility in drug discovery. However, a common limitation is a lack of adequate tools to mine these interactions comprehensively, since exhaustive searches of the protein data bank are time-consuming and difficult to perform. Consequently, fundamental questions remain unanswered: How unique or how common are the protein-ligand interactions observed in a given drug design project when compared to all complexed structures in the protein data bank? Which interaction patterns might explain the affinity of a tool compound toward unwanted targets? To answer these questions and to enable the systematic and comprehensive study of protein-ligand interactions, we introduce PROLIX (Protein Ligand Interaction Explorer), a tool that uses sophisticated fingerprint representations of protein-ligand interaction patterns for rapid data mining in large crystal structure databases. Our implementation strategy pursues a branch-and-bound technique that enables mining against thousands of complexes within a few seconds. Key elements of PROLIX include (i) an intuitive interface that enables users to formulate complex queries easily, (ii) exceptional speed for results retrieval, and (iii) a sophisticated results summarization. Herein we describe the algorithms developed to enable complex queries and fast retrieval of search results, as well as the intuitive aspects of the user interface and summarization viewer.