Enhancement of energy decomposition analysis in fragment molecular orbital calculations.

Energy decomposition analysis is one of the most attractive features of fragment molecular orbital (FMO) calculations from the point of view of practical applications. Here we report some enhancements for PIEDA in the ABINIT-MP program. One is a separation of the dispersion-type stabilization from the electron correlation energy, traditionally referred to as the "dispersion interaction" (DI). Another is an alternative evaluation of the electrostatic (ES) interaction using the restrained electrostatic potential (RESP) charges. The GA:CT stacked base pair and the Trp-Cage miniprotein were used as illustrative examples.

Protein-ligand binding affinity prediction of cyclin-dependent kinase-2 inhibitors by dynamically averaged fragment molecular orbital-based interaction energy.

Fragment molecular orbital (FMO) method is a powerful computational tool for structure-based drug design, in which protein-ligand interactions can be described by the inter-fragment interaction energy (IFIE) and its pair interaction energy decomposition analysis (PIEDA). Here, we introduced a dynamically averaged (DA) FMO-based approach in which molecular dynamics simulations were used to generate multiple protein-ligand complex structures for FMO calculations. To assess this approach, we examined the correlation between the experimental binding free energies and DA-IFIEs of six CDK2 inhibitors whose net charges are zero. The correlation between the experimental binding free energies and snapshot IFIEs for X-ray crystal structures was R2  = 0.75. Using the DA-IFIEs, the correlation significantly improved to 0.99. When an additional CDK2 inhibitor with net charge of -1 was added, the DA FMO-based scheme with the dispersion energies still achieved R2  = 0.99, whereas R2 decreased to 0.32 employing all the energy terms of PIEDA.

Single-Image Super-Resolution Improvement of X-ray Single-Particle Diffraction Images Using a Convolutional Neural Network.

Femtosecond X-ray pulse lasers are promising probes for the elucidation of the multiconformational states of biomolecules because they enable snapshots of single biomolecules to be observed as coherent diffraction images. Multi-image processing using an X-ray free-electron laser has proven to be a successful structural analysis method for viruses. However, the performance of single-particle analysis (SPA) for flexible biomolecules with sizes ≤100 nm remains difficult. Owing to the multiconformational states of biomolecules and noisy character of diffraction images, diffraction image improvement by multi-image processing is often ineffective for such molecules. Herein, a single-image super-resolution (SR) model was constructed using an SR convolutional neural network (SRCNN). Data preparation was performed in silico to consider the actual observation situation with unknown molecular orientations and the fluctuation of molecular structure and incident X-ray intensity. It was demonstrated that the trained SRCNN model improved the single-particle diffraction image quality, corresponding to an observed image with an incident X-ray intensity (approximately three to seven times higher than the original X-ray intensity), while retaining the individuality of the diffraction images. The feasibility of SPA for flexible biomolecules with sizes ≤100 nm was dramatically increased by introducing the SRCNN improvement at the beginning of the various structural analysis schemes.

Fragmentation at sp2 carbon atoms in fragment molecular orbital method.

In the fragment molecular orbital (FMO) method, a given molecular system is usually fragmented at sp3 carbon atoms. However, fragmentation at different sites sometimes becomes necessary. Hence, we propose fragmentation at sp2 carbon atoms in the FMO method. Projection operators are constructed using sp2 local orbitals. To maintain practical accuracy, it is essential to consider the three-body effect. In order to suppress the corresponding increase of computational cost, we propose approximate models considering local trimers. Numerical verification shows that the present models are as accurate as or better than the standard FMO2 method in total energy with fragmentation at sp3 carbon atoms.

Two-Component Relativistic Equation-of-Motion Coupled-Cluster Methods for Excitation Energies and Ionization Potentials of Atoms and Molecules.

Two-component relativistic equation-of-motion coupled-cluster methods are developed and implemented. Scalar-relativistic and spin-orbit effects are taken into account through a two-component scheme in both Hartree-Fock and correlation calculations. Excitation energies and spin-orbit splittings of atoms and diatomic molecules, and ionization potentials of OsO4 are reported. The advantage of the present two-component scheme is illustrated particularly for heavy-element systems.

A coupled cluster theory with iterative inclusion of triple excitations and associated equation of motion formulation for excitation energy and ionization potential.

A single reference coupled cluster theory that is capable of including the effect of connected triple excitations has been developed and implemented. This is achieved by regrouping the terms appearing in perturbation theory and parametrizing through two different sets of exponential operators: while one of the exponentials, involving general substitution operators, annihilates the ground state but has a non-vanishing effect when it acts on the excited determinant, the other is the regular single and double excitation operator in the sense of conventional coupled cluster theory, which acts on the Hartree-Fock ground state. The two sets of operators are solved as coupled non-linear equations in an iterative manner without significant increase in computational cost than the conventional coupled cluster theory with singles and doubles excitations. A number of physically motivated and computationally advantageous sufficiency conditions are invoked to arrive at the working equations and have been applied to determine the ground state energies of a number of small prototypical systems having weak multi-reference character. With the knowledge of the correlated ground state, we have reconstructed the triple excitation operator and have performed equation of motion with coupled cluster singles, doubles, and triples to obtain the ionization potential and excitation energies of these molecules as well. Our results suggest that this is quite a reasonable scheme to capture the effect of connected triple excitations as long as the ground state remains weakly multi-reference.

Theoretical investigation of enantioselectivity of cage-like supramolecular assembly: the insights into the shape complementarity and host-guest interaction.

Enantioselectivity in the aza-Cope rearrangement of a guest molecule encapsulated in a cage-like supramolecular assembly [Ga4 L6 ](12-) [L = 1,5-bis(2',3'-dihydroxybenzamido)naphthalene] is investigated using density functional theory and ab initio molecular orbital calculations. Reaction pathways leading to R- and S-enantiomers encapsulated in the [Ga4 L6 ](12-) are explored. The reaction barriers and the stabilities of the prochiral structures differed in the [Ga4 L6 ](12-) , resulting that the product with an R structure is favorably produced in the Δ-structure [Ga4 L6 ](12-) . The large energy difference in the prochiral structures in the [Ga4 L6 ](12-) was attributed to the deformation of the bulky substituent. The host-guest interaction energy raises the reaction barrier for the product with an S structure. The previous study suggested that the different stability of the prochiral substrates in the assembly was the origin of the enantioselectivity, and the suggestion is supported by our computational finding. In addition, our results show that the difference in the reaction barriers also importantly contributes to the enantioselectivity.

QM/MM calculation of protein magnetic shielding tensors with generalized hybrid-orbital method: a GIAO approach.

A method to compute magnetic shielding tensors with generalized hybrid-orbital (GHO) QM/MM scheme is developed at the levels of Hartree-Fock and second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals. A feature of the GHO method is utilized to ensure gauge-origin independency of GHO shielding tensors in a simple way. The benchmark calculations indicate that the GHO method reproduced full-QM shielding constants nearly quantitatively for atoms not directly coupled to the GHO linking atoms. As an application to a realistic protein, carbon chemical shifts are calculated for the retinal chromophore in visual rhodopsin.

Lattice Boltzmann simulations for proton transport in 2-D model channels of Nafion.

Proton conductance in a 2-D channel with a slab-like structure was studied to verify that the lattice Boltzmann method (LBM) can be used as a simulation tool for proton conduction in a Nafion membrane, which is a mesoscopic system with a highly disordered porous structure. Diffusion resulting from a concentration gradient and migration by an electrostatic force were considered as the origins of proton transport. The electrostatic force acting on a proton was computed by solving the Poisson equation. The proton concentration in the membrane is expressed as a continuous function and the sulfonic charge is placed discretely. The space-averaged conductance of protons in a nonequilibrium stationary state was evaluated as a function of the structural parameters: namely, channel width and distribution of the sulfonic groups. The resulting space-averaged conductance deviates from the bulk values, depending particularly on the sulfonic group distribution. Details of the simulation scheme are described and the applicability of the present scheme to real membranes is discussed.