Empirical corrections and pair interaction energies in the fragment molecular orbital method

Use of caps in the auxiliary basis set formulation of the fragment molecular orbital method

An auxiliary polarization formulation of the fragment molecular orbital (FMO) method is developed, combining a basis set correction computed for capped isolated fragments with a polarization obtained from uncapped fragments. For a set of organic and inorganic test systems, it is shown that the total energy and atomic charges are accurately reproduced with respect to full unfragmented calculations. It is demonstrated that the method is accurate for computing electronic excited states. The developed approach is applied to rank the isomers of chignolin from experimental NMR data (PDB: 1UAO) according to their relative energy. Contributions of polarization and basis set effects to pair interactions between fragments are elucidated.

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.

Development and testing of an algorithm for efficient MP2/CCSD(T) energy estimation of molecular clusters with the 2-body approach

This work reports the development and testing of an automated algorithm for estimating the energies of weakly bound molecular clusters employing correlated theory. Firstly, the monomers and dimers of (homo/hetero) clusters are identified, and the sum of one-body and two-body contributions to correlation energy is calculated. The addition of this contribution to the Hartree-Fock full calculation (FC) energies provides a good estimate of the total energies at Møller-Plesset second-order perturbation theory (MP2)/coupled-cluster method with singles and doubles (CCSD) (T)-level theory using augmented Dunning basis sets. The estimated energies for several test clusters show an excellent agreement with their FC counterparts, with a substantial wall-clock time saving employing off-the-shelf hardware. Furthermore, the complete basis set (CBS) limit for MP2 energy computed using the two-body approach also agrees with its CBS energy with its FC counterpart.

Parametrized quantum-mechanical approaches combined with the fragment molecular orbital method

Fast parameterized methods such as density-functional tight-binding (DFTB) facilitate realistic calculations of large molecular systems, which can be accelerated by the fragment molecular orbital (FMO) method. Fragmentation facilitates interaction analyses between functional parts of molecular systems. In addition to DFTB, other parameterized methods combined with FMO are also described. Applications of FMO methods to biochemical and inorganic systems are reviewed.

Partitioning of the Vibrational Free Energy

Vibrational energies are partitioned into the contributions of molecular parts called segments, for instance, residues in proteins. The fragment molecular orbital method is used to facilitate vibrational calculations of large systems at the DFTB and HF-3c levels. The vibrational analysis is combined with the partitioning of the electronic energy, yielding free-energy contributions of segments to the binding energy, pinpointing hot spots for drug discovery and other studies. The analysis is illustrated on two protein-ligand complexes in solution.

Partition Analysis for Density-Functional Tight-Binding

High-order charge transfer is incorporated into the fragment molecular orbital (FMO) method using a charge transfer state with fractional charges. This state is used for a partition analysis of properties based on segments that may be different from fragments in FMO. The partition analysis is also formulated for calculations without fragmentation. All development in this work is limited to density-functional tight-binding. The analysis is applied to a water cluster, crambin (PDB: 1CBN), and two complexes of Trp-cage (1L2Y) with ligands. The contributions of functional groups in ligands are obtained, providing useful information for drug discovery.

How accurate are approximate quantum chemical methods at modelling solute-solvent interactions in solvated clusters?

In this paper, the performance of a wide range of DFT methods is assessed for the calculation of interaction energies of thermal clusters of a solute in water. Three different charge states (neutral, proton transfer transition state and zwitterion) of glycine were solvated by 1 to 40 water molecules as sampled from molecular dynamics simulations. While some ab initio composite methods that employ insufficiently large basis sets incurred significant errors even for a cluster containing only 5 water molecules relative to the W1X-2 benchmark, the DLPNO-CCSD(T)/CBS and DSD-PBEP86 (triple zeta basis set) levels of theory predicted very accurate interaction energies. These levels of theory were used to benchmark the performance of 16 density functionals from different rungs of Jacob's Ladder. Of the Rung 4 functionals examined, the ωB97M-V and ωB97X-V functionals stood out for predicting absolute interaction energies in 40-water clusters with mean absolute deviations (MAD) ∼4 kJ mol-1. The B3LYP-D3(BJ) functional performed exceptionally well with a MAD ∼1.7 kJ mol-1 and is the overall best performing method. Calculations of relative interaction energies allow for cancellation of systematic errors, including basis set truncation and superposition errors, and the ωB97M-V and B3LYP-D3(BJ) double zeta basis set calculations yielded relative interaction energies that are within ∼3 kJ mol-1 of the benchmark. The ONIOM approximation provides another strategy for accelerating the calculation of accurate absolute interaction energies provided that the calculations have converged with respect to the size of the "high-level-layer".

Geometry Optimization, Transition State Search, and Reaction Path Mapping Accomplished with the Fragment Molecular Orbital Method

Recent development of the fragment molecular orbital (FMO) method related to energy gradients, geometry optimization, transition state search, and chemical reaction mapping is summarized. The frozen domain formulation of FMO is introduced in detail, and the structure of related GAMESS input files for FMO is described.

Solvent Screening in Zwitterions Analyzed with the Fragment Molecular Orbital Method

Based on induced solvent charges, a new model of solvent screening is developed in the framework of the fragment molecular orbital combined with the polarizable continuum model. The developed model is applied to analyze interactions in a prototypical zwitterionic system, sodium chloride in water, and it is shown that the large underestimation of the interaction in the original solvent screening based on local charges is successfully corrected. The model is also applied to a complex of the Trp-cage (PDB: 1L2Y ) miniprotein with an anionic ligand, and the physical factors determined protein-ligand binding in solution are unraveled.

Computational prediction of GPCR oligomerization

There has been a recent and prolific expansion in the number of GPCR crystal structures being solved: in both active and inactive forms and in complex with ligand, with G protein and with each other. Despite this, there is relatively little experimental information about the precise configuration of GPCR oligomers during these different biologically relevant states. While it may be possible to identify the experimental conditions necessary to crystallize a GPCR preferentially in a specific structural conformation, computational approaches afford a potentially more tractable means of describing the probability of formation of receptor dimers and higher order oligomers. Ensemble-based computational methods based on structurally determined dimers, coupled with a computational workflow that uses quantum mechanical methods to analyze the chemical nature of the molecular interactions at a GPCR dimer interface, will generate the reproducible and accurate predictions needed to predict previously unidentified GPCR dimers and to inform future advances in our ability to understand and begin to precisely manipulate GPCR oligomers in biological systems. It may also provide information needed to achieve an increase in the number of experimentally determined oligomeric GPCR structures.

Characterising GPCR-ligand interactions using a fragment molecular orbital-based approach

There has been fantastic progress in solving GPCR crystal structures. However, the ability of X-ray crystallography to guide the drug discovery process for GPCR targets is limited by the availability of accurate tools to explore receptor-ligand interactions. Visual inspection and molecular mechanics approaches cannot explain the full complexity of molecular interactions. Quantum mechanical approaches (QM) are often too computationally expensive, but the fragment molecular orbital (FMO) method offers an excellent solution that combines accuracy, speed and the ability to reveal key interactions that would otherwise be hard to detect. Integration of GPCR crystallography or homology modelling with FMO reveals atomistic details of the individual contributions of each residue and water molecule towards ligand binding, including an analysis of their chemical nature.

Ab Initio Fragment Method for Calculating Molecular X-ray Diffraction

A fragment-based approach for the prediction of elastic X-ray scattering is presented. The total diffraction pattern is assembled from anisotropic form factors calculated for individual molecular fragments, optionally including corrections for pairwise interactions between fragments. The approach is evaluated against full ab initio scattering calculations in the peptide diphenylalanine, and the optimal selection of fragments is examined in the ethanol molecule. The approach is found to improve significantly on the independent atom model while remaining conceptually simple and computationally efficient. It is expected to be particularly useful for macromolecules with repeated subunits, such as peptides, proteins, DNA, or RNA and other polymers, where it is straightforward to define appropriate fragments.