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.     

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.     

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.     

A density matrix variational calculation for atomic Be

The ground-state energy of the beryllium atom is calculated using a variational procedure in which the elements of the two-body reduced density matrix (particle–particle matrix) are the variational parameters. It is shown that, for this problem and with the limited number of spin-orbitals used, the trace condition and the simultaneous nonnegativity conditions on the particle–particle, the particle–hole, and the hole–hole matrices form a complete solution to the N-representability problem. The energy obtained is – 14.61425 a.u., practically identical to the value given by a configuration interaction calculation which uses the same states. The effects of weakening the nonnegativity conditions on each of the matrices in turn were also explored.     

Neural network pairwise interaction fields for protein model quality assessment and ab initio protein folding

In order to use a predicted protein structure one needs to know how good it is, as the utility of a model depends on its quality. To this aim, many Model Quality Assessment Programs (MQAP) have been developed over the last decade, with MQAP also being assessed at the CASP competition. We present a new knowledge-based MQAP which evaluates single protein structure models. We use a tree representation of the Cα trace to train a novel Neural Network Pairwise Interaction Field (NN-PIF) to predict the global quality of a model. NN-PIF allows fast evaluation of multiple structure models for a single sequence. In our tests on a large set of structures, our networks outperform most other methods based on different and more complex protein structure representations in global model quality prediction. Moreover, given NN-PIF can evaluate protein conformations very fast, we train a separate version of the model to gauge its ability to fold protein structures ab initio. We show that the resulting system, which relies only on basic information about the sequence and the Cα trace of a conformation, generally improves the quality of the structures it is presented with and may yield promising predictions in the absence of structural templates, although more research is required to harness the full potential of the model.     

Optimal designs for pairwise calculation: An application to free energy perturbation in minimizing prediction variability

Pairwise-based methods such as the free energy perturbation (FEP) method have been widely deployed to compute the binding free energy differences between two similar host–guest complexes. The calculated pairwise free energy difference is either directly adopted or transformed to absolute binding free energy for molecule rank ordering. We investigated, through both analytic derivations and simulations, how the selection of pairs in the experiment could impact the overall prediction precision. Our studies showed that (1) the estimated absolute binding free energy () derived from calculated pairwise differences (ΔΔG) through weighted least squares fitting is more precise in prediction than the pairwise difference values when the number of pairs is more than the number of ligands and (2) prediction precision is influenced by both the total number of pairs and the specifically selected pairs, the latter being critically important when the number of calculated pairs is limited. Furthermore, we applied optimal experimental design in pair selection and found that the optimally selected pairs can outperform randomly selected pairs in prediction precision. In an illustrative example, we showed that, upon weighing ligand structure similarity into design optimization, the weighted optimal designs are more efficient than the literature reported designs. This work provides a new approach to assess retrospective pairwise-based prediction results, and a method to design new prospective pairwise-based experiments for molecular lead optimization. © 2019 Wiley Periodicals, Inc.     

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 hybrid approach combining energy density analysis with the interaction energy decomposition method

We propose a new analysis technique for characterizing molecular interactions that combines an energy decomposition scheme, such as the Kitaura-Morokuma decomposition method, with energy density analysis, which partitions the total energy of the system into atomic contributions. The combined scheme, termed Interaction-EDA, enables us to estimate the local contribution of interaction energy components, such as electrostatic, exchange, polarization, and charge transfer. The evaluation of the local interaction energy is rather important in large systems. For a numerical assessment, the Interaction-EDA method is applied to the process of CO adsorption on Si(100) - (2 x 1) surface.     

The interaction energy between two parallel plates with constant surface charge density

On the basis of Langmuir's suggestion we simplify the Poisson-Boltzmann equation and derive the relation of surface potential, potential midway, and the plate distance. Thus we obtain the interaction force and energy equations between two dissimilar plates in the case of constant surface charge density. Agreement with the exact numerical values of the interaction of dissimilar plates is good. This method may not only apply to the cases of high constant potential but to the case of high constant charge density.     

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.     

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.     

An all-electron calculation of an antihypertensive protein with the Gaussian-based density functional method

An all-electron calculation of the antihypertensive and antiviral protein BDS-I from the sea anemone Anemonia sulcata was carried out using the density functional method based on Gaussian-type orbitals with workstations. Our computer program ProteinDF coded by the object-oriented language C++, was originally designed for all-electron calculations of proteins and controlled in parallel with high efficiency. The numbers of residues, atoms, orbitals and auxiliary functions of the calculated protein were 43, 629, 3615 and 6545, respectively. This Letter reports timing data of the computation and some calculated electronic properties. Our program will open the door for advanced studies of larger proteins.     

Additive-multiplicative relationship for chemical interaction energy and calculation of the energy of chemical bond dissociation to neutral atoms

Samara State University. Translated from Zhurnal Strukturnoi Khimii, Vol. 33, No. 5, pp. 137–140, September–October, 1992.     

Reduced interaction matrix for doubly-excited configurations and the correlation energy by a partitioning method

Analyses of the correlation energy of an N-electron system by Nesbet and Löwdin are extended to obtain a reduced interaction matrix for doubly-excited configurations and an exact expression for correlation energy; the latter is separable in a basis diagonalizing this matrix.     

Numerical integration of atomic electron density with double exponential formula for density functional calculation

In the preceding study, we reported an application of the double exponential formula to the radial quadrature grid for numerical integration of the radial electron distribution function. Three-type new radial grids with the double exponential transformation were introduced. The performance of radial grids was compared between the double exponential grids and the grids proposed in earlier studies by applying to the electron-counting integrals of noble gas atoms and diatomic molecules including alkali metals, halogens, and transition metals. It was confirmed that the change in accuracy of the quadrature approximation depending on atomic or molecular species is not significant for the double exponential integration schemes rather than the other integration schemes. In the present study, we further investigate the accuracy of the double exponential formula for the electron-counting integrals of all the atoms from H to Kr in the periodic table to elucidate the stable performance of the double exponential radial grids. The electron densities of the atoms are calculated with the Gauss-type orbital basis functions at the B3LYP level. The quadrature accuracy and convergence behavior of numerical integration are compared among the double exponential formula and the formulas proposed by Treutler et al. and by Mura et al. The results reveal that the double exponential radial grids remarkably improve the convergence rate toward high accuracy compared with the previous radial grids, particularly for heavy elements in the 4th period, without fine tuning of the radial grids for each atom.     

Nonempirical calculation of the energy of the interaction of the methyl cation with the helium atom

Journal of Structural Chemistry -