Empirical Energy Calculations Research Articles

Why is the Omicron main protease of SARS-CoV-2 less stable than its wild-type counterpart? A crystallographic, biophysical, and theoretical study

During the continuing evolution of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the Omicron variant of concern emerged in the second half of 2021 and has been dominant since November of that year. Along with its sublineages, it has maintained a prominent role ever since. The Nsp5 main protease (Mpro) of the Omicron virus is characterized by a single dominant mutation, P132H. Here we determined the X-ray crystal structures of the P132H mutant (or O-Mpro) as a free enzyme and in complex with the Mpro inhibitor, the alpha-ketoamide 13b-K, and we conducted enzymological, biophysical, as well as theoretical studies to characterize the O-Mpro. We found that O-Mpro has a similar overall structure and binding with 13b-K; however, it displays lower enzymatic activity and lower thermal stability compared to the WT-Mpro (with “WT” referring to the prototype strain). Intriguingly, the imidazole ring of His132 and the carboxylate plane of Glu240 are in a stacked configuration in the X-ray structures determined here. Empirical folding free energy calculations suggest that the O-Mpro dimer is destabilized relative to the WT-Mpro due to less favorable van der Waals interactions and backbone conformations in the individual protomers. All-atom continuous constant-pH molecular dynamics (MD) simulations reveal that His132 and Glu240 display coupled titration. At pH 7, His132 is predominantly neutral and in a stacked configuration with respect to Glu240 which is charged. In order to examine whether the Omicron mutation eases the emergence of further Mpro mutations, we also analyzed the P132H+T169S double mutant, which is characteristic of the BA.1.1.2 lineage. However, we found little evidence of a correlation between the two mutation sites.

Integrative Approach to Dissect the Drug Resistance Mechanism of the H172Y Mutation of SARS-CoV-2 Main Protease.

Nirmatrelvir is an orally available inhibitor of SARS-CoV-2 main protease (Mpro) and the main ingredient of Paxlovid, a drug approved by the U.S. Food and Drug Administration for high-risk COVID-19 patients. Recently, a rare natural mutation, H172Y, was found to significantly reduce nirmatrelvir's inhibitory activity. As the COVID-19 cases skyrocket in China and the selective pressure of antiviral therapy builds in the US, there is an urgent need to characterize and understand how the H172Y mutation confers drug resistance. Here, we investigated the H172Y Mpro's conformational dynamics, folding stability, catalytic efficiency, and inhibitory activity using all-atom constant pH and fixed-charge molecular dynamics simulations, alchemical and empirical free energy calculations, artificial neural networks, and biochemical experiments. Our data suggest that the mutation significantly weakens the S1 pocket interactions with the N-terminus and perturbs the conformation of the oxyanion loop, leading to a decrease in the thermal stability and catalytic efficiency. Importantly, the perturbed S1 pocket dynamics weaken the nirmatrelvir binding in the P1 position, which explains the decreased inhibitory activity of nirmatrelvir. Our work demonstrates the predictive power of the combined simulation and artificial intelligence approaches, and together with biochemical experiments, they can be used to actively surveil continually emerging mutations of SARS-CoV-2 Mpro and assist the optimization of antiviral drugs. The presented approach, in general, can be applied to characterize mutation effects on any protein drug targets.

Second Order Phase Transition and Stabilizing CH···H and CH···S Interactions in Naphthyl End-Capped Bithiophene at 3.5 GPa

The semiconducting bithiophene systems are largely unexplored structurally at high-pressures. Here, we characterize the high-pressure structure and phase behavior of 5,5′-bis(naphth-2-yl)-2,2′-bithiophene (NaT2) by single crystal X-ray diffraction, photoluminescence and Raman compression measurements in the diamond anvil cell to 7.6 GPa. Experimental results are supported by empirical interaction energy calculations. NaT2 maintains its ambient pressure structure (P21/c) on compression but undergoes a subtle second-order phase transition at ca. 3.5 GPa. The newly formed phase at 4.0 GPa is characterized by the formation of a new S···H interaction between thiophene moieties in adjacent molecules, as well as by the emergence of a more favorable compression pathway in its long-chain direction. NaT2 also undergoes a band gap closure manifested as a distinct yellow to red color change on compression that is fully reversible on decompression.

Snapshots of the Fragmentation for C70@Single-Walled Carbon Nanotube: Tight-Binding Molecular Dynamics Simulations.

In previously reported experimental studies, a yield of double-walled carbon nanotubes (DWCNTs) at C70@Single-walled carbon nanotubes (SWCNTs) is higher than C60@SWCNTs due to the higher sensitivity to photolysis of the former. From the perspective of pyrolysis dynamics, we would like to understand whether C70@SWCNT is more sensitive to thermal decomposition than C60@SWCNT, and the starting point of DWCNT formation, which can be obtained through the decomposition fragmentation of the nanopeapods, which appears in the early stages. We have studied the fragmentation of C70@SWCNT nanopeapods, using molecular dynamics simulations together with the empirical tight-binding total energy calculation method. We got the snapshots of the fragmentation structure of carbon nano-peapods (CNPs) composed of SWCNT and C70 fullerene molecules and the geometric spatial positioning structure of C70 within the SWCNT as a function of dynamics time (for 2 picoseconds) at the temperatures of 4000 K, 5000 K, and 6000 K. In conclusion, the scenario in which C70@SWCNT transforms to a DWCNT would be followed by the fragmentation of C70, after C70, and the SWCNT have been chemically bonding in the early stages. The relative stability of fullerenes in CNPs could be reversed, compared to the ranking of the relative stability of the encapsulated molecules themselves.

The effects of microstructural stability on the compressive response of two cast aluminum alloys up to 300 °C

In this study, the high temperature compressive response of cast aluminum alloys 319 and RR350 are compared in light of their microstructures. The 319 alloy is widely used in thermally critical automotive applications and provides a baseline for comparison with the RR350 alloy, whose microstructural stability at high homologous temperatures was recently reported. Cylindrical compression samples from each alloy were tested at four temperatures up to 300°C at a constant true strain rate varied over four orders of magnitude. Although both alloys are strengthened by metastable θ′ precipitates (nominally Al2Cu) in the as-aged condition, their mechanical response diverges at temperatures greater than 250°C as the strengthening precipitates coarsen and evolve in the 319 alloy while they retain their as-aged morphology in the RR350 alloy. Deformation mechanisms of each alloy are examined using microstructural analysis and empirical activation energy calculations. The stability of the θ′ phase in the RR350 alloy leads to effective precipitation hardening at homologous temperatures up to 0.6 and an extensive regime of grain boundary controlled deformation.

Unzipping of carbon nanotubes is geometry-dependent

Carbon nanotube (CNT) unzipping is a facile and efficient technique to produce narrow graphene nanoribbons. The diameter and chirality of CNTs control the geometry of the unzipped nanoribbons. In this work, we analyze the energetics of oxidation- and hydrogenation-induced unzipping processes. Empirical reactive potential-based energy calculations show that there is a geometry-dependent energy barrier for oxidation-induced unzipping, which is absent in the exothermal hydrogenation process. These results are discussed by considering the unzipping process as crack nucleation and propagation processes in a pre-stressed cylindrical shell. Fitting our simulation data through the theoretical model provides a quantitative way to estimate the key parameters in CNT unzipping that can be used to optimize the experimental procedure.

Cation-pi interactions at non-redundant protein--RNA interfaces.

Cation-pi interactions have proved to be important in proteins and protein-ligand complexes. Here, cation-pi interactions are analyzed for 282 non-redundant protein-RNA interfaces. The statistical results show that this kind of interactions exists in 65% of the interfaces. The four RNA bases are ranked as Gua>Ade>Ura>Cyt according to their propensity to participate in cation-pi interactions. The corresponding ranking for the involved amino acid residues is: Arg>Lys>Asn>Gln. The same trends are obtained based on the empirical energy calculation. The Arg-Gua pairs have the greatest stability and are also most frequently observed. The number of cation-pi pairs involving unpaired bases is 2.5 times as many as those involving paired bases. Hence, cation-pi interactions show sequence and structural specificities. For the bicyclic bases, Gua and Ade, their 5-atom rings participate in cation-pi interactions somewhat more than the 6-atom rings, with percentages of 54 and 46%, respectively, which is due to the higher cation-pi participation proportion (63%) of 5-atom rings in the paired bases. These results give a general view of cation-pi interactions at protein-RNA interfaces and are helpful in understanding the specific recognition between protein and RNA.

Ab‐initio Structure Determination of the New Ion Conductor K2Al2O3F2 from Powder Diffraction Data

AbstractThe crystal structure of K2Al2O3F2, prepared at 800 °C by ceramic methods, was determined from conventional laboratory X‐ray powder diffraction data. The compound crystallizes in the monoclinic space group C2/m (No. 12) with a = 11.21675(8), b = 8.16351(6), c = 6.12301(5) Å β = 88.8108(6) ° and Z = 4. Unit cell and space group suggestions were found by using the TOPAS program. Starting positional parameters for potassium and aluminum atoms were obtained from 548 reflections by the methods implemented in the FOX program. Oxygen and fluorine atom positions were determined by structural considerations. The structure was refined using the fundamental parameter approach of TOPAS, which gave the final residuals (%) RBragg = 1.6 and Rwp = 4.6. The crystal structure consists of individual layers of oxygen connected AlO3F tetrahedral groups with the fluorine atoms separating the layers. Empirical energy calculations agree with the crystal structure refinements and suggest no or little oxygen–fluorine exchange. Between and perpendicular to the sheets, the potassium ion can move without steric hindrance. Conductivity measurements from room temperature to 300 °C show decent potassium ion conductivity.

LuxR-dependent quorum sensing: Computer aided discovery of new inhibitors structurally unrelated to N-acylhomoserine lactones

A virtual screening, involving flexible docking sequences within the LuxR, TraR and LasR binding sites, was used as a structural binding sites similarity filter to specifically target conserved residues in the proteins of the LuxR family (namely Tyr62, Trp66, Tyr70, Asp79, Trp94 for LuxR). This docking-based screening, employing a genetic algorithm, was performed on a 2344 chemical compounds library, together with empirical binding free energy (ΔGbind) calculations. Docking results were analysed, and the compounds detected with reproducible low ΔGbind values or identified as being in the top 120 for most of the docking sequences, were selected as hits candidates which interact with conserved residues. Biological evaluation with LuxR-dependent quorum sensing led to the discovery of some new inhibitors, namely tamoxifen, sertraline, pimethixene, terfenadine, fendiline and calmidazolium. Notably, calmidazolium was identified as one of the most potent AHL-structurally unrelated inhibitors of LuxR-dependent quorum sensing, with an IC50 value of 7.0±0.2μM.

Stereochemistry and Electronic structure of anticonvulsant drugs

Anticonvulsant drugs come from a range of chemical types, but most drugs show important structural features in common. It has been suggested elsewhere that molecular conformation may be an important factor in determining activity. The present work has been designed to investigate the influence of both stereochemistry and electronic structure on anticonvulsant action. Empirical potential energy calculations are first used to determine preferred conformations. It is found that anticonvulsants adopt a common preferred conformation, which is likely to be responsible for anticonvulsant activity. Molecular electrostatic potentials are also calculated for anticonvulsants, after first being evaluated in a series of model compounds. Electrostatic potentials based on MINDO/3 wave functions are found to be well suited to molecules containing carbonyl groups, and are also able to provide a quantitative estimate of reactivity. Applications to anticonvulsants shows the existence of a common electrostatic field, where similar regions of positive and negative potential are seen throughout the series studied. The structure-activity relationship outlined here applies to anticonvulsant activity against experimental electroshock seizures, and associated clinical use in the treatment of tonic-clonic (grand mal) epilepsy. It appears that both stereochemical and electronic factors play an important role in determining the activity of anticonvulsant drugs.

Differentiation of D- and L-Thyroxine by the plasma protein prealbumin

We present empirical energy calculations on the binding of thyroxine analogs to the plasma protein prealbumin. The results of the calculations suggest a stronger binding affinity for the L isomer than the D, consistent with observed binding affinities. These calculations allow us to rationalize the significantly stronger binding of des-NH3+ than des-COO− analogs of the hormone to the protein.

Polyomaviridae Assembly Polymorphism from an Energy Landscape Perspective

Polyomaviridae assemblein vitrointo different aggregates depending on experimental conditions. We use an energy landscape approach using empirical energy calculations to quantify how the formation of these different aggregates depends on pH, the presence of bound calcium ions and disulfide linkages. Computations are carried out for SV40, a member of the Polyomaviridae family and are based on the binding free energy landscape of three distinct trimers of pentamers that correspond to the different bonding configurations between the capsid proteins observed in its crystal structure. Our computational analysis shows that the energetics of one of these environments is pivotal for the polymorphic assembly behaviour of SV40, whilst the binding energy landscapes of the other two environments are broadly funnel-shaped and thus contribute little to the formation of particles other than virus-like particles (VLP). We have quantified how the existence of bound calcium ions in the absence of disulfide linkages enhances the binding free energies of all three environments and hence, favours the assembly of VLPs. Moreover, estimation of the relative binding free energies of the three environments at pH 5 and pH 8 reveals that they are destabilized at pH 5 relative to pH 8. The extent of this destabilization is dependent on the presence of disulfide linkages and bound calcium ions and accounts for the experimentally observed polymorphic behaviour of VP1 proteins at pH 5. Interestingly, concurrent existence of bound calcium ions and disulfide linkages is found to be destabilizing and thus may disrupt the assembly of VLPs at pH 8.

Empirically Augmented Density Functional Theory for Predicting Lattice Energies of Aspirin, Acetaminophen Polymorphs, and Ibuprofen Homochiral and Racemic Crystals

Lattice energies of drug crystals are closely associated with many important physicochemical properties including polymorphism of the crystals. Current quantum mechanical methods that can be applied to calculate the lattice energy of most drug crystals are not capable of fully considering the van der Waals interaction energy, a dominant component in the lattice energy. Herein, we report the results of using empirically augmented quantum mechanical methods for predicting the lattice energies of selected drug crystals. Long-range van der Waals energies were evaluated by atom-atom pairwise C ( 6 ) R (-6 ) functions that were damped at short interatomic distance where interatomic interactions could be better evaluated by density functional theory (DFT). The atomic C ( 6 ) coefficients were taken from literature, and three damping functions were tested. For the quantum mechanical calculations, different basis sets were tested with aspirin as the model system. Basis set superposition error (BSSE) was considered. In addition to aspirin, acetaminophen Form I and Form II, and s(+)- and (+/-)-ibuprofen were calculated and the results were compared to experimental values. Experimentally determined single crystal structures were optimized prior to both empirical and DFT energy calculations. Lattice energies calculated by the empirically augmented quantum mechanical methods are in very good agreement with experimental values, suggesting the approach is acceptable. The results also indicate that the long-range van der Waals or dispersion energy is a significant part of the lattice energy, which cannot be accurately estimated by the DFT methods alone. Due to the empirical nature for estimating the dispersion energy, choosing the right empirical parameters is crucial. The methods and parameters tested seem to be able to produce reliable values of lattice energies of the drug crystals.

Calculations of solute and solvent entropies from molecular dynamics simulations

The translational, rotational and conformational (vibrational) entropy contributions to ligand-receptor binding free energies are analyzed within the standard formulation of statistical thermodynamics. It is shown that the partitioning of the binding entropy into different components is to some extent arbitrary, but an appropriate method to calculate both translational and rotational entropy contributions to noncovalent association is by estimating the configurational volumes of the ligand in the bound and free states. Different approaches to calculating solute entropies using free energy perturbation calculations, configurational volumes based on root-mean-square fluctuations and covariance matrix based quasiharmonic analysis are illustrated for some simple molecular systems. Numerical examples for the different contributions demonstrate that theoretically derived results are well reproduced by the approximations. Calculation of solvent entropies, either using total potential energy averages or van't Hoff plots, are carried out for the case of ion solvation in water. Although convergence problems will persist for large and complex simulation systems, good agreement with experiment is obtained here for relative and absolute ion hydration entropies. We also outline how solvent and solute entropic contributions are taken into account in empirical binding free energy calculations using the linear interaction energy method. In particular it is shown that empirical scaling of the nonpolar intermolecular ligand interaction energy effectively takes into account size dependent contributions to the binding free energy.

Computational investigation of Al/Si and Al/Mg ordering in aluminous tremolite amphiboles

AbstractThe [4]Al/Si and [6]Al/Mg order-disorder behaviour of minerals in the tremolite-tschermakite solid solution (namely, end-member tschermakite and the 50:50 composition, magnesiohornblende) has been investigated by Monte Carlo simulation, using a model Hamiltonian in which atomic interaction parameters Ji were derived from empirical lattice energy calculations, and chemical potential terms μj (to express the preferences of cations for particular crystallographic sites) were derived from ab initio methods. The simulations performed were increasingly complex. Firstly, ordering in one tetrahedral double chain with Al:Si = 1:3 (tschermakite) was simulated. Although the low-temperature cation distribution in this system was ordered, there was no phase transition (due to the quasi-one-dimensional nature of the system). Next, interactions between tetrahedral Al:Si = 1:3 double chains were included, and a phase transition was observed, with the cation distribution in one double chain lining up with respect to that in the next. Finally, interactions between tetrahedral and octahedral sites were incorporated, to model the whole unit cell, and compositions corresponding to tschermakite and magnesiohornblende were investigated. The whole-cell simulation results compare favourably with experimental conclusions for magnesiohornblende, in that Al at T1 is preferred over Al at T2, and Al at M2 is favoured over that at M1 and M3, but the significant amount of Al at M1 is at odds with experimental observation.

The Influence of the Thymine C5 Methyl Group on Spontaneous Base Pair Breathing in DNA

Sequences of four or more AT base pairs without a 5'-TA-3' step, so-called A-tracts, influence the global properties of DNA by causing curvature of the helix axis if phased with the helical repeat and also influence nucleosome packaging. Hence it is interesting to understand this phenomenon on the molecular level, and numerous studies have been devoted to investigations of dynamical and structural features of A-tract DNA. It was early observed that anomalously slow base pair-opening kinetics were a striking physical property unique to DNA A-tracts (Leroy, J. L., Charretier, E., Kochoyan, M., and Gueron, M. (1988) Biochemistry 27, 8894-8898). Furthermore, a strong correlation between DNA curvature and anomalously slow base pair-opening dynamics was found. In the present work it is shown, using imino proton exchange measurements by NMR spectroscopy that the main contribution to the dampening of the base pair-opening fluctuations in A-tracts comes from the C5 methylation of the thymine base. Because the methyl group has been shown to have a very limited effect on the DNA curvature as well as the structure of the DNA helix, the thymine C5 methyl group stabilizes the helix directly. Empirical potential energy calculations show that methylation of the tract improves the stacking energy of a base pair with its neighbors in the tract by 3-4 kcal/mol.

Empirical free energy analysis of the engrailed Q50K homeodomain mutant-DNA complex and its mutants

Empirical free energy calculations were performed for the engrailed homeodomain mutant protein in complex with its consensus promoter. The program, CONGEN™, was used to generate the atomic coordinates, which were missing in the original crystal structure of the Q50K mutant protein. To generate the said atomic coordinates more accurately, the initial CONGEN-generated model was subjected to 300 ps of belly dynamics in AMBER™. Complex formation energies were calculated for the ‘wild-type’ complex as well as ten computer-generated mutants that parallel mutants/substitutions studied by Sauer's group for each of three models. The hydrophobic, electrostatic, and entropic contributions were calculated. The non-linearized finite difference Poisson–Boltzmann equation was solved for the complexes at the ionic strength under which dissociation constant measurements were taken by the aforementioned group. A good overall agreement existed between calculated and experimental ΔΔG estimates. Discrepancies between absolute experimental and calculated values for ΔΔG are hypothesized to be due to the missing conformational entropic contribution of the operator DNA molecule.

Thermally stable, photoactive polymerizable diazenes. Applications in polymer technology

New and useful nonpolymerizable and polymerizable diazene free radical initiators have been designed, based on molecular orbital and empirical linear free energy calculations. The design of the polymerizable diazenes has been based on four requirements: independent reactivities of azo and vinyl moieties, high thermal stability of the trans-diazene isomers, efficient convertability of the trans isomer to the cis isomer, and high thermal reactivity (to produce free radicals) of the cis-diazene isomers. The cis-diazene isomers are obtained from the trans isomers by irradiation with visible light. A new free radical initiator has been shown to be useful in preparing graft copolymers and in crosslinking polymer chains by visible light activation. Poly(styrene-co-2-(meta-styrylazo)-2-methoxypropane) (2) was prepared by the copolymerization of styrene monomer and 2-(meta-styrylazo)-2-methoxypropane (1), either thermally or via a free radical initiator. Copolymer 2 then was reacted with methyl methacrylate monomer in the presence of visible light, to produce poly (styrene-g-methyl methacrylate) (6). Poly(styrene-co-2-(meta-styrylazo)-2-methylpropane) (17), prepared by the copolymerization of styrene monomer and 2-(meta-styrylazo)-2-methylpropane (15), was successfully crosslinked at elevated temperatures. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 3203–3213, 1999

Trimerization of C 60

Seven different regioisomers of C 60 trimers with intact cages have been calculated at the empirical tight-binding total energy calculation method. We analyze the atomic structure and energetics of seven different trimers except the sterically demanding cis-1. The trimers are formed by the linkage through a [2+2] cycloaddition. The energies of the trans-3, trans-1, trans-2, trans-4, cis-3 and cis- 2 regioisomers relative to the most stable equatorial regioisomer are 13, 19, 20, 30, 207 and 673 meV, respectively.

Computational study on the ring distortions of 1,4-dicyanobenzene in the gas phase and in the crystal

A molecular mechanics software enhanced to perform empirical energy calculations on crystals (KESSHOU) was further developed to handle intermolecular electrostatic interactions as well. The packing of the molecules of 1,4-dicyanobenzene and 1,4-diisocyanobenzene in the crystal was studied. The role of the van der Waals and the electrostatic interactions in the balance of nonbonded atom-atom interactions is analyzed. The packing forces are dominated by van der Waals forces. The electrostatic interactions have higher stabilizing contribution for the dicyano isomer than for the diisocyano form. The dependence of the results on the size of the crystal, the molecular mechanics force field (MM2 vs MM3), and the dielectric constant are also assessed. Ab initio MP2/6–311G∗∗ geometries of the isolated molecules are in accordance with the observed benzene ring distortions determined by electron diffraction.