Empirical Correction to Molecular Interaction Energies in Density Functional Theory (DFT) for Methane Hydrate Simulation

An improved two-rotor function for conformational potential energy surfaces of 20 amino acid diamides

Predicting the three-dimensional structure of a protein from its amino acid sequence requires a complete understanding of the molecular forces that influences the protein folding process. Each possible conformation has its corresponding potential energy, which characterizes its thermodynamic stability. This is needed to identify the primary intra- and inter-molecular interactions, so that we can reduce the dimensionality of the problem, and create a relatively simple representation of the system. Investigating this problem using quantum chemical methods produces accurate results; however, this also entails large computational resources. In this study, an improved two-rotor potential energy function is proposed to represent the backbone interactions in amino acids through a linear combination of a Fourier series and a mixture of Gaussian functions. This function is applied to approximate the 20 amino acid diamide Ramachandran-type PESs, and results yielded an average RMSE of 2.36 kJ mol−1, which suggest that the mathematical model precisely captures the general topology of the conformational potential energy surface. Furthermore, this paper provides insights on the conformational preferences of amino acid diamides through local minima geometries and energy ranges, using the improved mathematical model. The proposed mathematical model presents a simpler representation that attempts to provide a framework on building polypeptide models from individual amino acid functions, and consequently, a novel method for rapid but accurate evaluation of potential energies for biomolecular simulations.

Exploring the possibility to store the mixed oxygen-hydrogen cluster in clathrate hydrate in molar ratio 1:2 (O2+2H2)

An interesting possibility is explored: storing the mixture of oxygen and hydrogen in clathrate hydrate in molar ratio 1:2. The interaction energies between oxygen, hydrogen, and clathrate hydrate are calculated using high level quantum chemical methods. The useful conclusion points from this study are summarized as follows. (1) The interaction energies of oxygen-hydrogen mixed cluster are larger than the energies of pure hydrogen molecular cluster. (2) The affinity of oxygen molecules with water molecules is larger than that of the hydrogen molecules with water molecules. (3) The dimension of O₂-2H₂ interaction structure is smaller than the dimension of CO₂-2H₂ interaction structure. (4) The escaping energy of oxygen molecules from the hydrate cell is larger than that of the hydrogen molecules. (5) The high affinity of the oxygen molecules with both the water molecules and the hydrogen molecules may promote the stability of oxygen-hydrogen mixture in the clathrate hydrate. Therefore it is possible to store the mixed (O₂+2H₂) cluster in clathrate hydrate.

Energy benchmarks for methane-water systems from quantum Monte Carlo and second-order Møller-Plesset calculations

The quantum Monte Carlo (QMC) technique is used to generate accurate energy benchmarks for methane-water clusters containing a single methane monomer and up to 20 water monomers. The benchmarks for each type of cluster are computed for a set of geometries drawn from molecular dynamics simulations. The accuracy of QMC is expected to be comparable with that of coupled-cluster calculations, and this is confirmed by comparisons for the CH4-H2O dimer. The benchmarks are used to assess the accuracy of the second-order Møller-Plesset (MP2) approximation close to the complete basis-set limit. A recently developed embedded many-body technique is shown to give an efficient procedure for computing basis-set converged MP2 energies for the large clusters. It is found that MP2 values for the methane binding energies and the cohesive energies of the water clusters without methane are in close agreement with the QMC benchmarks, but the agreement is aided by partial cancelation between 2-body and beyond-2-body errors of MP2. The embedding approach allows MP2 to be applied without loss of accuracy to the methane hydrate crystal, and it is shown that the resulting methane binding energy and the cohesive energy of the water lattice agree almost exactly with recently reported QMC values.

Exploring Strong Interactions in Proteins with Quantum Chemistry and Examples of Their Applications in Drug Design

OBJECTIVES

Three strong interactions between amino acid side chains (salt bridge, cation-π, and amide bridge) are studied that are stronger than (or comparable to) the common hydrogen bond interactions, and play important roles in protein-protein interactions.

METHODS

Quantum chemical methods MP2 and CCSD(T) are used in calculations of interaction energies and structural optimizations.

RESULTS

The energies of three types of amino acid side chain interactions in gaseous phase and in aqueous solutions are calculated using high level quantum chemical methods and basis sets. Typical examples of amino acid salt bridge, cation-π, and amide bridge interactions are analyzed, including the inhibitor design targeting neuraminidase (NA) enzyme of influenza A virus, and the ligand binding interactions in the HCV p7 ion channel. The inhibition mechanism of the M2 proton channel in the influenza A virus is analyzed based on strong amino acid interactions.

CONCLUSION

(1) The salt bridge interactions between acidic amino acids (Glu- and Asp-) and alkaline amino acids (Arg+, Lys+ and His+) are the strongest residue-residue interactions. However, this type of interaction may be weakened by solvation effects and broken by lower pH conditions. (2) The cation- interactions between protonated amino acids (Arg+, Lys+ and His+) and aromatic amino acids (Phe, Tyr, Trp and His) are 2.5 to 5-fold stronger than common hydrogen bond interactions and are less affected by the solvation environment. (3) The amide bridge interactions between the two amide-containing amino acids (Asn and Gln) are three times stronger than hydrogen bond interactions, which are less influenced by the pH of the solution. (4) Ten of the twenty natural amino acids are involved in salt bridge, or cation-, or amide bridge interactions that often play important roles in protein-protein, protein-peptide, protein-ligand, and protein-DNA interactions.

A molecular dynamics study of guest-host hydrogen bonding in alcohol clathrate hydrates

Clathrate hydrates are typically stabilized by suitably sized hydrophobic guest molecules. However, it has been experimentally reported that isomers of amyl-alcohol C5H11OH can be enclosed into the 5(12)6(4) cages in structure II (sII) clathrate hydrates, even though the effective radii of the molecules are larger than the van der Waals radii of the cages. To reveal the mechanism of the anomalous enclathration of hydrophilic molecules, we performed ab initio and classical molecular dynamics simulations (MD) and analyzed the structure and dynamics of a guest-host hydrogen bond for sII 3-methyl-1-butanol and structure H (sH) 2-methyl-2-butanol clathrate hydrates. The simulations clearly showed the formation of guest-host hydrogen bonds and the incorporation of the O-H group of 3-methyl-1-butanol guest molecules into the framework of the sII 5(12)6(4) cages, with the remaining hydrophobic part of the amyl-alcohol molecule well accommodated into the cages. The calculated vibrational spectra of alcohol O-H bonds showed large frequency shifts due to the strong guest-host hydrogen bonding. The 2-methyl-2-butanol guests form strong hydrogen bonds with the cage water molecules in the sH clathrate, but are not incorporated into the water framework. By comparing the structures of the alcohols in the hydrate phases, the effect of the location of O-H groups in the butyl chain of the guest molecules on the crystalline structure of the clathrate hydrates is indicated.

Binding of O2 and NO to heme in heme-nitric oxide/oxygen-binding (H-NOX) proteins. A theoretical study

The binding of O2 and NO to heme in heme-nitric oxide/oxygen-binding (H-NOX) proteins has been investigated with DFT as well as dispersion-corrected DFT methods. The local protein environment was accounted for by including the six nearest surrounding residues in the studied systems. Attention was also paid to the effects of the protein environment, particularly the distal Tyr140, on the proximal iron-histidine (Fe-His) binding. The Heme-AB (AB = O2, NO) and Fe-His binding energies in iron porphyrin FeP(His)(AB), myoglobin Mb(AB), H-NOX(AB), and Tyr140 → Phe mutated H-NOX[Y140F(AB)] were determined for comparison. The calculated stabilization of bound O2 is even higher in H-NOX than that in a myoglobin (Mb), consistent with the observation that the H-NOX domain of T. tengcongensis has a very high affinity for its oxygen molecule. Among the two different X-ray crystal structures for the Tt H-NOX protein, the calculated results for both AB = O2 and NO appear to support the crystal structure with the PDB code 1XBN , where the Trp9 and Asn74 residues do not form a hydrogen-bonding network with Tyr140. A hydrogen bond interaction from the polar residue does not have obvious effects on the Fe-His binding strength, but a dispersion contribution to Ebind(Fe-His) may be significant, depending on the crystal structure used. We speculate that the Fe-His binding strength in the deoxy form of a native protein could be an important factor in determining whether the bond of His to Fe is broken or maintained upon binding of NO to Fe.

Theoretical study on the polar hydrogen-π (Hp-π) interactions between protein side chains

BACKGROUND

In the study of biomolecular structures and interactions the polar hydrogen-π bonds (Hp-π) are an extensive molecular interaction type. In proteins 11 of 20 natural amino acids and in DNA (or RNA) all four nucleic acids are involved in this type interaction.

RESULTS

The Hp-π in proteins are studied using high level QM method CCSD/6-311 + G(d,p) + H-Bq (ghost hydrogen basis functions) in vacuum and in solutions (water, acetonitrile, and cyclohexane). Three quantum chemical methods (B3LYP, CCSD, and CCSD(T)) and three basis sets (6-311 + G(d,p), TZVP, and cc-pVTZ) are compared. The Hp-π donors include R2NH, RNH2, ROH, and C6H5OH; and the acceptors are aromatic amino acids, peptide bond unit, and small conjugate π-groups. The Hp-π interaction energies of four amino acid pairs (Ser-Phe, Lys-Phe, His-Phe, and Tyr-Phe) are quantitatively calculated.

CONCLUSIONS

Five conclusion points are abstracted from the calculation results. (1) The common DFT method B3LYP fails in describing the Hp-π interactions. On the other hand, CCSD/6-311 + G(d,p) plus ghost atom H-Bq can yield better results, very close to the state-of-the-art method CCSD(T)/cc-pVTZ. (2) The Hp-π interactions are point to π-plane interactions, possessing much more interaction conformations and broader energy range than other interaction types, such as common hydrogen bond and electrostatic interactions. (3) In proteins the Hp-π interaction energies are in the range 10 to 30 kJ/mol, comparable or even larger than common hydrogen bond interactions. (4) The bond length of Hp-π interactions are in the region from 2.30 to 3.00 Å at the perpendicular direction to the π-plane, much longer than the common hydrogen bonds (~1.9 Å). (5) Like common hydrogen bond interactions, the Hp-π interactions are less affected by solvation effects.

The multiple roles of histidine in protein interactions

Background

Among the 20 natural amino acids histidine is the most active and versatile member that plays the multiple roles in protein interactions, often the key residue in enzyme catalytic reactions. A theoretical and comprehensive study on the structural features and interaction properties of histidine is certainly helpful.

Results

Four interaction types of histidine are quantitatively calculated, including: (1) Cation-π interactions, in which the histidine acts as the aromatic π-motif in neutral form (His), or plays the cation role in protonated form (His⁺); (2) π-π stacking interactions between histidine and other aromatic amino acids; (3) Hydrogen-π interactions between histidine and other aromatic amino acids; (4) Coordinate interactions between histidine and metallic cations. The energies of π-π stacking interactions and hydrogen-π interactions are calculated using CCSD/6-31+G(d,p). The energies of cation-π interactions and coordinate interactions are calculated using B3LYP/6-31+G(d,p) method and adjusted by empirical method for dispersion energy.

Conclusions

The coordinate interactions between histidine and metallic cations are the strongest one acting in broad range, followed by the cation-π, hydrogen-π, and π-π stacking interactions. When the histidine is in neutral form, the cation-π interactions are attractive; when it is protonated (His⁺), the interactions turn to repulsive. The two protonation forms (and pK_a values) of histidine are reversibly switched by the attractive and repulsive cation-π interactions. In proteins the π-π stacking interaction between neutral histidine and aromatic amino acids (Phe, Tyr, Trp) are in the range from -3.0 to -4.0 kcal/mol, significantly larger than the van der Waals energies.

Factors that distort the heme structure in Heme-Nitric Oxide/OXygen-Binding (H-NOX) protein domains. A theoretical study

DFT and dispersion-corrected DFT calculations were carried out to probe the factors that distort the heme structure in Heme-Nitric oxide/OXygen-binding (H-NOX) protein domains. Various model systems that include heme, heme+surrounding residues, and heme+surrounding residues+additional protein environment were examined; the latter system was calculated with a quantum mechanics/molecular mechanics (QM/MM) method. The computations were extended to a myoglobin (Mb) protein, in which the heme structure is quite planar, in contrast to that in H-NOX. The natural tendency of the heme is to be planar. The strong structural distortion in H-NOX is mainly brought about by the intermolecular interactions between the whole heme molecule (heme ring plus its peripheral substituents) and the surrounding residues, among which the polar residues (Tyr140, Pro115, Mse98) play major roles in distorting the heme structure. The two peripheral propionate substituents that are oriented on the same side of the heme plane can also make the molecule distort, but the distortion caused by this factor is not significant. In Mb, the surrounding residues considered are all nonpolar and do not cause a structural distortion. The different structural features of the heme macrocycle in the different proteins (H-NOX and Mb) are reproduced by the calculations. The dispersion correction is necessary, since it improves the calculated structures. The effects of the distortion on the binding affinity of the axial ligand to the heme were also examined.

Further analysis and comparative study of intermolecular interactions using dimers from the S22 database

Accurate MP2 and CCSD(T) complete basis set (CBS) interaction energy curves (14 points for each curve) have been obtained for 20 of the dimers reported in the S22 set and analytical Morse curves have been fitted that can be used in developing updated density functional theory (DFT) and force field models. The magnitude and the effect of the basis set superposition error (BSSE) were carefully investigated. We found that going up to aug-cc-pVDZ and aug-cc-pVTZ basis sets is enough to obtain accurate CBS MP2 energies when BSSE corrected values are used but aug-cc-pVTZ and aug-cc-pVQZ basis sets are needed when the BSSE uncorrected total energies are used in CBS extrapolations. MP2 interaction energies with smaller basis sets such as 6-31G* are found to have very little dispersion energy and that the true source of dispersion attributed attractive interactions is almost entirely due to BSSE. MP2 and CCSD(T) CBS interaction energies are found to be very close to one another if aromatic systems are not involved. Comparative analyses have been performed with semiempirical and ab initio methods utilizing the moderate in size but affordable 6-31G* basis set both of which can be readily applied to macromolecular systems. The new M06-2X and M06-L DFT functionals were found to be more accurate than all methods tested herein. Interaction energy curves using the SG1 grid showed discontinuities for several of the dimer systems but this problem disappeared when finer DFT numerical grids were used.

Molecular potential energies in dodecahedron cell of methane hydrate and dispersion correction for DFT

The interaction potential energies of water-water and water-methane in structure-I unit cell of methane hydrate are calculated from 2.1 to 8.0A using density functional theory (DFT) B3LYP/TZVP. The curves of potential energies are corrected for basis set superposition error (BSSE) and dispersion interaction using a 4-term L-J (4,6-8,12) correction equation, which is derived from CCSD(T)/cc-pVTZ calculations of water-water and water-methane molecular pairs, using least squares curve-fitting. The methane hydrate unit cell is a regular water dodecahedron cell consisting of 20 water molecules with a methane molecule in the center. The geometries of water and methane are optimized at CCSD(T)/cc-pVTZ level. The BSSE-corrections are calculated for water-water and water-methane interaction energies as functions of the side length, l, of the dodecahedron cell at B3LYP/TZVP level in the range from 2.1 to 8.0A. The BSSE CP-corrected and dispersion-corrected potential energy surfaces (PES) of water-water and water-methane are useful for molecular dynamics simulation of gas clathrate-hydrates.