Alchemical free energy calculations via metadynamics: Application to the theophylline-RNA aptamer complex.

We propose a computational workflow for robust and accurate prediction of both binding poses and their affinities at early stage in designing drug candidates. Small, rigid ligands with few intramolecular degrees of freedom, for example, fragment-like molecules, have multiple binding poses, even at a single binding site, and their affinities are often close to each other. We explore various structures of ligand binding to a target through metadynamics using a small number of collective variables, followed by reweighting to obtain the atomic coordinates. After identifying each binding pose by cluster analysis, we perform alchemical free energy calculations on each structure to obtain the overall value. We applied this protocol in computing free energy of binding for the theophylline-RNA aptamer complex. Of the six (meta)stable structures found, the most favorable binding structure is consistent with the structure obtained by NMR. The overall free energy of binding reproduces the experimental values very well.

Graph Classification of Molecules Using Force Field Atom and Bond Types.

Classification of the biological activities of chemical substances is important for developing new medicines efficiently. Various machine learning methods are often employed to screen large libraries of compounds and predict the activities of new substances by training the molecular structure-activity relationships. One such method is graph classification, in which a molecular structure can be represented in terms of a labeled graph with nodes that correspond to atoms and edges that correspond to the bonds between these atoms. In a conventional graph definition, atomic symbols and bond orders are employed as node and edge labels, respectively. In this study, we developed new graph definitions using the assignment of atom and bond types in the force fields of molecular dynamics methods as node and edge labels, respectively. We found that these graph definitions improved the accuracies of activity classifications for chemical substances using graph kernels with support vector machines and deep neural networks. The higher accuracies obtained using our proposed definitions can enhance the development of the materials informatics using graph-based machine learning methods.

Full-Quantum chemical calculation of the absorption maximum of bacteriorhodopsin: a comprehensive analysis of the amino acid residues contributing to the opsin shift.

Herein, the absorption maximum of bacteriorhodopsin (bR) is calculated using our recently developed method in which the whole protein can be treated quantum mechanically at the level of INDO/S-CIS//ONIOM (B3LYP/6-31G(d,p): AMBER). The full quantum mechanical calculation is shown to reproduce the so-called opsin shift of bR with an error of less than 0.04 eV. We also apply the same calculation for 226 different bR mutants, each of which was constructed by replacing any one of the amino acid residues of the wild-type bR with Gly. This substitution makes it possible to elucidate the extent to which each amino acid contributes to the opsin shift and to estimate the inter-residue synergistic effect. It was found that one of the most important contributions to the opsin shift is the electron transfer from Tyr185 to the chromophore upon excitation. We also indicate that some aromatic (Trp86, Trp182) and polar (Ser141, Thr142) residues, located in the vicinity of the retinal polyene chain and the ß-ionone ring, respectively, play an important role in compensating for the large blue-shift induced by both the counterion residues (Asp85, Asp212) and an internal water molecule (W402) located near the Schiff base linkage. In particular, the effect of Trp86 is comparable to that of Tyr185. In addition, Ser141 and Thr142 were found to contribute to an increase in the dipole moment of bR in the excited state. Finally, we provide a complete energy diagram for the opsin shift together with the contribution of the chromophore-protein steric interaction.

Docking study and binding free energy calculation of poly (ADP-ribose) polymerase inhibitors.

Recently, the massively parallel computation of absolute binding free energy with a well-equilibrated system (MP-CAFEE) has been developed. The present study aimed to determine whether the MP-CAFEE method is useful for drug discovery research. In the drug discovery process, it is important for computational chemists to predict the binding affinity accurately without detailed structural information for protein/ligand complex. We investigated the absolute binding free energies for Poly (ADP-ribose) polymerase-1 (PARP-1)/inhibitor complexes, using the MP-CAFEE method. Although each docking model was used as an input structure, it was found that the absolute binding free energies calculated by MP-CAFEE are well consistent with the experimental ones. The accuracy of this method is much higher than that using molecular mechanics Poisson-Boltzmann/surface area (MM/PBSA). Although the simulation time is quite extensive, the reliable predictor of binding free energies would be a useful tool for drug discovery projects.

Massively parallel computation of absolute binding free energy with well-equilibrated states.

A force field formulator for organic molecules (FF-FOM) was developed to assign bond, angle, and dihedral parameters to arbitrary organic molecules in a unified manner including proteins and nucleic acids. With the unified force field parametrization we performed massively parallel computations of absolute binding free energies for pharmaceutical target proteins and ligands. Compared with the previous calculation with the ff99 force field in the Amber simulation package (Amber99) and the ligand charges produced by the Austin Model 1 bond charge correction (AM1-BCC), the unified parametrization gave better absolute binding energies for the FK506 binding protein (FKBP) and ligand system. Our method is based on extensive work measurement between thermodynamic states to calculate the free energy difference and it is also the same as the traditional free energy perturbation. There are important requirements for accurate calculations. The first is a well-equilibrated bound structure including the conformational change of the protein induced by the binding of the ligand. The second requirement is the convergence of the work distribution with a sufficient number of trajectories and dense spacing of the coupling constant between the ligand and the rest of the system. Finally, the most important requirement is the force field parametrization.

High-Level ab Initio Calculations To Improve Protein Backbone Dihedral Parameters.

We present new molecular mechanical dihedral parameters for the Ramachandran angles ϕ and ψ of a protein backbone based on high-level ab initio molecular orbital calculations for hydrogen-blocked or methyl-blocked glycine and alanine dipeptides. Fully relaxed 15° (ϕ, ψ) contour maps were calculated at the MP2/6-31G(d) level of theory. Finding out the lowest energy path for ϕ (or ψ) to change from -180° to 180° in the contour map, we performed a DF-LCCSD(T0)/Aug-cc-pVTZ//DF-LMP2/Aug-cc-pVTZ level calculation to get the torsional energy profiles of ϕ (or ψ). Molecular mechanical torsion profiles with AMBER force field variants significantly differed from the ab initio profiles, so we derived new molecular mechanical dihedral parameters of a protein backbone to fit the ab initio profiles.

Accurate evaluation of the absorption maxima of retinal proteins based on a hybrid QM/MM method.

Here we improved our hybrid QM/MM methodology (Houjou et al. J Phys Chem B 2001, 105, 867) for evaluating the absorption maxima of photoreceptor proteins. The renewed method was applied to evaluation of the absorption maxima of several retinal proteins and photoactive yellow protein. The calculated absorption maxima were in good agreement with the corresponding experimental data with a computational error of <10 nm. In addition, our calculations reproduced the experimental gas-phase absorption maxima of model chromophores (protonated all-trans retinal Schiff base and deprotonated thiophenyl-p-coumarate) with the same accuracy. It is expected that our methodology allows for definitive interpretation of the spectral tuning mechanism of retinal proteins.

Excited states of phosphorescent platinum(II) complexes containing N wedge C wedge N-coordinating tridentate ligands: spectroscopic investigations and time-dependent density functional theory calculations.

The absorption and emission spectra of the Pt(II) complexes containing N wedge C wedge N-coordinating tridentate ligands, platinum(II) 1,3-di(2-pyridyl)benzene chloride [Pt(dpb)Cl] and platinum(II) 3,5-di(2-pyridyl)toluene chloride [Pt(dpt)Cl], together with their corresponding free ligands, 1,3-di(2-pyridyl)benzene (dpbH) and 3,5-di(2-pyridyl)toluene (dptH), have been analyzed by density functional theory (DFT) for the ground state and time-dependent DFT (TDDFT) for the excited states. T(1)(A(1)) and S(1)(B(2)) of the complexes (in C(2)(v) symmetry) were assigned on the basis of the calculated excitation energies as well as comparison of the experimental spectroscopic properties and the calculated states' characteristics. The calculated excitation energies for T(1) and S(1) of the complexes as well as those for T(1) of the free ligands were in good agreement with their observed values within 600 cm(-1). The d-pi* characters of the excited states were evaluated from the change in electron densities between the ground and excited states by Mulliken population analysis; values of 25% for T(1) and 32% for S(1) were obtained for both complexes. The calculated values of d-pi* character were found to be consistent with the reported emission lifetimes as well as the observed emission energy shifts from the corresponding free ligands. Most spectroscopic properties of the complexes and the free ligands, which include solvatochromic shift, Stokes shifts, methyl substitution shifts, and emission spectra profiles, were well explained from the calculation results.