Conformational Potential Energy Research Articles

Comparing ANI-2x, ANI-1ccx neural networks, force field, and DFT methods for predicting conformational potential energy of organic molecules

In this study, the conformational potential energy surfaces of Amylmetacresol, Benzocaine, Dopamine, Betazole, and Betahistine molecules were scanned and analyzed using the neural network architecture ANI-2 × and ANI-1ccx, the force field method OPLS, and density functional theory with the exchange-correlation functional B3LYP and the basis set 6-31G(d). The ANI-1ccx and ANI-2 × methods demonstrated the highest accuracy in predicting torsional energy profiles, effectively capturing the minimum and maximum values of these profiles. Conformational potential energy values calculated by B3LYP and the OPLS force field method differ from those calculated by ANI-1ccx and ANI-2x, which account for non-bonded intramolecular interactions, since the B3LYP functional and OPLS force field weakly consider van der Waals and other intramolecular forces in torsional energy profiles. For a more comprehensive analysis, electronic parameters such as dipole moment, HOMO, and LUMO energies for different torsional angles were calculated at two levels of theory, B3LYP/6-31G(d) and ωB97X/6-31G(d). These calculations confirmed that ANI predictions are more accurate than density functional theory calculations with B3LYP functional and OPLS force field for determining potential energy surfaces. This research successfully addressed the challenges in determining conformational potential energy levels and shows how machine learning and deep neural networks offer a more accurate, cost-effective, and rapid alternative for predicting torsional energy profiles.

Exploration of the Conformational Scenario for α-, β-, and γ-Cyclodextrins in Dry and Wet Conditions, from Monomers to Crystal Structures: A Quantum-Mechanical Study

Cyclodextrins (CDs) constitute a class of cyclic oligosaccharides that are well recognized and largely applied in the drug delivery field, thanks to their biocompatibility, low cost, and the possibility to be derivatized in order to tune and optimize the complexation/release of the specific drug. The conformational flexibility of these systems is one of their key properties and requires a cost-effective methodology to be studied by combining the accuracy of results with the possibility of exploring a large set of conformations. In the present paper, we have explored the conformational potential energy surface of the monomers and dimers of α-, β-, and γ-cyclodextrins (i.e., 6, 7, and 8 monomeric units, respectively) by means of fast but accurate semiempirical methods, which are then refined by state-of-the-art DFT functionals. Moreover, the crystal structure is considered for a more suitable comparison with the IR spectrum experimentally recorded. Calculations are carried out in the gas phase and in water environments, applying both implicit and explicit treatments. We show that the conformation of the studied molecules changes from the gas phase to the water, even if treated implicitly, thus modifying their complexation capability.

Additive energy functions have predictable landscape topologies.

Recent work [Mirth et al., J. Chem. Phys. 154, 114114 (2021)] has demonstrated that sublevelset persistent homology provides a compact representation of the complex features of an energy landscape in 3 N-dimensions. This includes information about all transition paths between local minima (connected by critical points of index ≥1) and allows for differentiation of energy landscapes that may appear similar when considering only the lowest energy pathways (as tracked by other representations, such as disconnectivity graphs, using index 1 critical points). Using the additive nature of the conformational potential energy landscape of n-alkanes, it became apparent that some topological features-such as the number of sublevelset persistence bars-could be proven. This work expands the notion of predictable energy landscape topology to any additive intramolecular energy function on a product space, including the number of sublevelset persistent bars as well as the birth and death times of these topological features. This amounts to a rigorous methodology to predict the relative energies of all topological features of the conformational energy landscape in 3N dimensions (without the need for dimensionality reduction). This approach is demonstrated for branched alkanes of varying complexity and connectivity patterns. More generally, this result explains how the sublevelset persistent homology of an additive energy landscape can be computed from the individual terms comprising that landscape.

Conformer-Specific Spectroscopy and IR-Induced Isomerization of a Model γ-Peptide: Ac-γ4-Phe-NHMe.

Single-conformation IR and UV spectroscopy of the prototypical capped γ-peptide Ac-γ4-Phe-NHMe (γ4F) was carried out under jet-cooled conditions in the gas phase in order to understand its innate conformational preferences in the absence of a solvent. We obtained conformer-specific IR and UV spectra and compared the results with calculations to make assignments and explore the differences between the γ2- and γ4-substituted molecules. We found four conformers of γ4F in our experiment. Three conformers form nine-membered hydrogen-bonded rings (C9) enclosed by an NH···O═C H-bond but differing in their phenyl ring positions (a, g+, and g-). The fourth conformer forms a strained seven-membered hydrogen-bonded ring in which the amide groups lie in a nominally anti-parallel arrangement stacked on top of one another (labeled S7). This conformer is a close analogue of the amide-stacked conformer (S) found previously in γ2F, in which the Phe side chain is substituted at the γ2 position, Ac-γ2-Phe-NHMe (J. Am. Chem. Soc. 2009, 131, 14243-14245). IR population transfer spectroscopy was used to determine the fractional abundances of the γ4F conformers in the expansion. A combination of force field and density functional theory calculations is used to map out the conformational potential energy surfaces for γ4F and compare it with its γ2F counterpart. Based on this analysis, the phenyl ring prefers to take up structures that facilitate NH···π interactions in γ4F or avoid phenyl interactions with the C═O group in γ2F. The disconnectivity graph for γ4F reveals separate basins associated with the C9 and amide-stacked conformational families, which are separated by a barrier of about 42 kJ/mol. The overall shape of the potential energy surface bears a resemblance to peptides and proteins that have a misfolding pathway that competes with the formation of the native structure.

Conformational and electronic study of dopamine interacting with the D2 dopamine receptor.

We report an exhaustive conformational and electronic study on dopamine (DA) interacting with the D2 dopamine receptor (D2 DR). For the first time, the complete surface of the conformational potential energy of the complex DA/D2 DR is reported. Such a surface was obtained through the use of QM/MM calculations. A detailed study of the molecular interactions that stabilize and destabilize the different molecular complexes was carried out using two techniques: Quantum Theory of Atoms in Molecules computations and nuclear magnetic shielding constants calculations. A comparative study of the behavior of DA in the gas phase, aqueous solution, and in the active site of D2 DR has allowed us to evaluate the degree of deformation suffered by the ligand and, therefore, analyze how rustic are the lock-key model and the induced fit theory in this case. Our results allow us to propose one of the conformations obtained as the "biologically relevant" conformation of DA when it is interacting with the D2 DR.

Conformational potential energy surfaces and cationic structure of 3,4-dihydro-2H-pyran by VUV-MATI spectroscopy and Franck-Condon fitting.

Ring conformations of 3,4-dihydro-2H-pyran (34DHP) have attracted considerable interest owing to their structural similarity to cyclohexene, an important molecule in stereochemistry. In this study, we investigated the conformational interconversion of 34DHP in both the neutral (S0) and the cationic (D0) ground states. High-resolution vacuum ultraviolet mass-analyzed threshold ionization (VUV-MATI) spectroscopy was utilized to obtain information regarding the adiabatic ionic transition between the S0 and the D0 states. Based on the 0-0 band in the VUV-MATI spectrum supported by the VUV-photoionization efficiency curve, the adiabatic ionization energy of 34DHP was accurately determined to be 8.3355 ± 0.0005 eV (67 230 ± 4 cm-1). To identify the conformer corresponding to this measured value, two-dimensional potential energy surfaces (2D PESs) associated with conformational interconversion in the S0 and the D0 states were constructed at the B3LYP/aug-cc-pVTZ level. It was revealed that in the S0 state, the twisted conformers undergo interconversion through the asymmetric bent conformation on the pseudorotational pathway, whereas in the D0 state, the half-bent conformers directly undergo interconversion via the planar conformation at the saddle point of 2D PES. The change in the conformational interconversion pathway upon ionization is attributed to electron removal from the highest occupied molecular orbital, which consists of a π orbital in the 2C-3C double bond interacting with a nonbonding orbital in the oxygen atom of 34DHP. Then, vibrational assignment of the observed spectrum could be achieved through Franck-Condon fitting for ionic transitions between the neutral twisted and the cationic half-bent conformers. The strong promotion of the ring bending and the 1O-2C-3C asymmetric stretching modes in the adiabatic ionic transitions confirmed the determined cationic structure of 34DHP.

A prelude to building mathematical models for polypeptide folding: analysis on the conformational potential energy hypersurface cross-sections of N-acetyl-glycyl-glycine-N′-methylamide

Finding a relationship on how a three-dimensional protein folds from its linear amino acid chain gets more complex with increasing chain length, so working on a smaller peptide conformational problem can provide initial ideas on what are the main molecular forces and how these influence the folding process. Following the study of conformations of amino acid units entering the proteins to understand the secondary structure of small peptides, this paper proposes mathematical models for the several two-rotor cross-sections of the five-dimensional N-acetyl-glycyl-glycine-N′-methylamide potential energy hypersurface (PEHS). These cross-sections are extracted along the first glycine subunit, with its coordinates fixed at the five energy minima of the glycine diamide. The resulting mathematical models yield an average RMSE of 1.36 kJ mol−1 and an average R2 of 0.9923 with respect to energy values obtained from DFT calculations. The minima geometries obtained from these models are also in good agreement with DFT-optimized energy minima conformers. An important aspect of this study also tackles the relationship between the PEHS of the glycyl-glycine diamide and its glycine subunits. It has been observed that there are deviations up to 28.35 kJ mol−1 and 29.52 kJ mol−1 between the PEHS cross-sections along γL and γD conformations, respectively, in the first glycine subunit. This may suggest that there are significant backbone–backbone intermolecular forces acting on the dipeptide. The abovementioned findings can help in developing more complex mathematical models for polypeptide folding from amino acid subunits.

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.

Amber-Compatible Parametrization Procedure for Peptide-like Compounds: Application to 1,4- and 1,5-Substituted Triazole-Based Peptidomimetics.

Peptidomimetics are molecules of particular interest in the context of drug design and development. They are proteolytically and metabolically more stable than their natural peptide counterparts but still offer high specificity toward their biological targets. In recent years, 1,4- and 1,5-disubstituted 1,2,3-triazole-based peptidomimetics have emerged as promising lead compounds for the design of various inhibitory and tumor-targeting molecules as well as for the synthesis of peptide analogues. The growing popularity of triazole-based peptidomimetics and a constantly broadening range of their application generated a demand for elaborate theoretical investigations by classical molecular dynamics simulations and molecular docking. Despite this rising interest, accurate and coherent force field parameters for triazole-based peptidomimetics are still lacking. Here, we report the first complete set of parameters dedicated to this group of compounds, named TZLff. This parametrization is compatible with the latest version of the AMBER force field (ff14SB) and can be readily applied for the modeling of pure triazole-based peptidomimetics as well as natural peptide sequences containing one or more triazole-based modifications in their backbone. The parameters were optimized to reproduce HF/6-31G* electrostatic potentials as well as MP2/cc-pVTZ equilibrium Hessian matrices and conformational potential energy surfaces through the use of a genetic algorithm-based search and least-squares fitting. Following the standards of AMBER, we introduce residue building units, thus allowing the user to define any given sequence of triazole-based peptidomimetics. Validation of the parameter set against ab initio- and NMR-based reference systems shows that we obtain fairly accurate results, which properly capture the conformational features of triazole-based peptidomimetics. The successful and efficient parametrization strategy developed in this work is general enough to be applied in a straightforward manner for parametrization of other peptidomimetics and, potentially, any polymeric assemblies.

Dimension reduction in conformational analysis: a two-rotor mathematical model of amino acid diamide conformational potential energy surface

The conformational potential energy surface (PES) of a molecule provides insights into the relative stability of the possible foldamers. However, the time and space complexity of electronic structure calculations, commonly used to generate PES, increases exponentially with an increasing number of atoms. The use of mathematical functions to model the topology of conformational PES is an alternative to more computer-intensive quantum chemical calculations, but the choice and complexity of functions used are crucial in achieving more accurate results. This paper presents a method to illustrate the topology of amino acid diamide PESs through a linear combination of a Fourier series and a mixture of Gaussian functions. Results yield a significantly small error, with an average RMSE of 4.9946 kJ mol−1 for all fits, which suggest that these functions may be used to represent the topology of the PESs, with around twofold order of magnitude decrease in computational time, with respect to DFT electronic structure calculations. This study ultimately aims to provide a foundation for a framework on building polypeptide PES from individual amino acid PESs.

Method Dependence of Proline Ring Flexibility in the Poly-l-Proline Type II Polymer.

We studied the sensitivity of the energetic and geometrical features of the proline ring (pyrrolidine) to the quantum mechanical computational approach by adopting the proline monomer, trimer, and polymer, as simplified collagen protein models. Within the Density Functional Theory (DFT) approach, we tested the ability of different functionals (GGA PBE and the hybrid B3LYP), added with a posteriori empirical dispersion corrections (D), to predict the conformational potential energy surface of the five-membered heterocycle pyrrolidine ring for the above models, dictating the collagen main features. We also compared the DFT-D results with those from the recently proposed cost-effective HF-3c method and our variant HF-3c-027, both based on Hartree-Fock Hamiltonian and Gaussian minimal basis set properly corrected for basis set superposition error, structure deficiencies, and dispersion interactions. We found that dispersion interactions are essential to destabilize specific conformers. While the HF-3c and its HF-3c-027 variant are unreliable to predict accurately the energy of the ring conformers, structures are accurate. Indeed, the cost-effective DFT-D//HF-3c-027 approach in which the energetic is from the accurate DFT-D method on HF-3c-027 structures provides energetic in line with that derived by the costly DFT-D//DFT-D approach, paving the way to simulate more realistic collagen models of much larger size. The adoption of either PBE or B3LYP functional for the electronic part of the DFT-D method gives very similar results, recommending the first as the most cost-effective method for simulating large collagen models. The predicted most stable conformation computed for the periodic poly proline (type II) model allows for a higher flexibility, in agreement with experimental studies on collagen protein. The present results open the way to large-scale calculations of the collagen/hydroxyapatite system, crucial for understanding the atomistic details in bones and teeth.

Conformational Equilibrium and Potential Energy Functions of the O-H Internal Rotation in the Axial and Equatorial Species of 1-Methylcyclohexanol.

The rotational spectra of four conformers (At, Ag, Et, Eg) of the tertiary alcohol 1-methylcyclohexanol were assigned by pulsed jet Fourier transform microwave spectroscopy. The transitions of two gauche conformers were split in two separated component lines, but it was not possible-from the available measured transitions-to accurately determine their vibrational ΔE0+0- ground-state splittings, respectively. In addition, the rotational spectra of the four OD deuterated isotopologues were measured and assigned. For the gauche species of this isotopologue we were able to determine the tunneling splittings, ΔE0+0-(Ag, OD) = 15.581(5) GHz and ΔE0+0-(Eg, OD) = 18.17(3) GHz, respectively. From these splittings the inversion barriers for Ag and Eg were determined, by using a flexible model, to be B2(Ag) = 356(10) and B2(Eg) = 320(10) cm(-1), respectively.

Elucidating Hyperconjugation from Electronegativity to Predict Drug Conformational Energy in a High Throughput Manner.

Computational chemists use structure-based drug design and molecular dynamics of drug/protein complexes which require an accurate description of the conformational space of drugs. Organic chemists use qualitative chemical principles such as the effect of electronegativity on hyperconjugation, the impact of steric clashes on stereochemical outcome of reactions, and the consequence of resonance on the shape of molecules to rationalize experimental observations. While computational chemists speak about electron densities and molecular orbitals, organic chemists speak about partial charges and localized molecular orbitals. Attempts to reconcile these two parallel approaches such as programs for natural bond orbitals and intrinsic atomic orbitals computing Lewis structures-like orbitals and reaction mechanism have appeared. In the past, we have shown that encoding and quantifying chemistry knowledge and qualitative principles can lead to predictive methods. In the same vein, we thought to understand the conformational behaviors of molecules and to encode this knowledge back into a molecular mechanics tool computing conformational potential energy and to develop an alternative to atom types and training of force fields on large sets of molecules. Herein, we describe a conceptually new approach to model torsion energies based on fundamental chemistry principles. To demonstrate our approach, torsional energy parameters were derived on-the-fly from atomic properties. When the torsional energy terms implemented in GAFF, Parm@Frosst, and MMFF94 were substituted by our method, the accuracy of these force fields to reproduce MP2-derived torsional energy profiles and their transferability to a variety of functional groups and drug fragments were overall improved. In addition, our method did not rely on atom types and consequently did not suffer from poor automated atom type assignments.

Low energy conformations and gas-phase acidity and basicity of pyrrolysine.

The gas-phase conformational potential energy surfaces (PES) of the last, 22nd amino acid pyrrolysine and related derivatives (neutral, deprotonated, and protonated) were extensively searched for the first time. By considering all possible combinations of the single-bond rotational degrees of freedom with a semiempirical and ab initio combined computational approach, a large set of unique low-energy conformers was identified for each pyrrolysine species, and essential properties such as vibrational frequencies, dipole moments, rotational constants, and intramolecular hydrogen bonding configurations were presented and characterized. The conformational electronic energies and thermochemical properties of proton affinity/dissociation energy (PA/PDE) and gas-phase acidity/basicity (GA/GB) were determined by the density functional BHandHLYP, B3LYP, and M062X, and Møller-Plesset MP2 methods. The MP2 and DFT methods are found to predict disparate PES for neutral and protonated conformations and sufficiently different thermochemical data. The measurements of dipole moments and characteristic IR modes at low temperature as well as GA/GB are demonstrated to be feasible approaches to verify the theoretical predictions.

Global Optimization of Protein–peptide Docking by a Filling Function Method

Molecular docking programs play a crucial role in drug design and development. In recent years, much attention has been devoted to the protein---peptide docking problem in which docking of a flexible peptide with a given protein is sought. In this work, we present a docking algorithm which is based on the use of a filling function method for continuous global optimization. In particular, the protein---peptide docking position is found by minimizing the conformational potential free energy function based on a new approximate mathematical model. The resulting global optimization problem presents some difficulties, since it is a large-scale one and the objective function is non-convex, so that it has many local minima. To solve the problem, we adopt a global optimization method based on the use of a filling function to escape from local solutions. Moreover, in order to obtain more accurate results, we search the correct docking position by performing a two-phase optimization process. In particular, in a first step, only the carbon $$\mathrm{C}_\alpha $$ C ? atoms of the protein and peptide are considered, thus obtaining an approximate docking solution. Then, the energy function is completed by considering all the peptide and protein atoms so that, starting from the solution of the first phase, the new minimization process gives a more accurate result. We present numerical results on a set of benchmark docking pairs and their comparison with those obtained by the known software package PacthDock for molecular docking.

Broad band free jet absorption mm-wave spectrum of 3-phenyl-1-propanol

The rotational broad band spectra of the OH and OD isotopologues of 3-phenyl-1-propanol have been investigated by broad band free-jet absorption millimeter-wave spectroscopy in the 60.0–78.3GHz frequency range. The spectra of the GGt and of the TGt conformers, where the three labels refer to the torsions of the benzyl, phenylethyl and hydroxyl groups, respectively, have been assigned. Ab initio calculations, performed at the MP2/6-311++G** level, were used to characterize the minima of the conformational potential energy surface.

An improved torsional force field for cis-enol malonaldehyde

An improved torsional force field for cis-enol malonaldehyde is presented. First, the conformational potential energy has been calculated by ab initio method at MP2/6-31G** level as a function of two torsional angles around C–C and C–O single bonds. Then, the calculated 2D potential energy surface has been fitted to a potential function, where cross terms of the two dihedrals are added to the ordinary single cosine terms of the optimised potentials for liquid simulations all atom (OPLS-aa) type. The optimised function excellently reproduces the energies with the standard deviation as small as 1.9 kJ/mol. The function may be used easily in the molecular dynamics calculation.

Global optimization of protein-peptide docking by a filling function method

Molecular docking programs play a crucial role in drug design and development. In recent years, much attention has been devoted to the protein-peptide docking problem in which docking of a flexible peptide with a known protein is sought. In this work we present a new docking algorithm which is based on the use of a filling function method for continuos constrained global optimization. Indeed, the protein-peptide docking position is sought by minimizing the conformational potential energy subject to constraints necessary to maintain the primary sequence of the given peptide. The resulting global optimization problem is difficult mainly for two reasons. First, the problem is large scale in constrained global optimization; second, the energy function is multivariate non-convex so that it has many local minima. The method is based on the device of modifying the original objective function once a local minimum has been attained by adding to it a filling term. This allows the overall algorithm to escape from local minima thus, ultimately, giving the algorithm ability to explore large regions in the peptide conformational space. We present numerical results on a set of benchmark docking pairs and comparison with the well-known software package for molecular docking PacthDock.

Searching the “Biologically Relevant”Conformation of Dopamine: A Computational Approach

We report here an exhaustive and complete conformational study on the conformational potential energy hypersurface (PEHS) of dopamine (DA) interacting with the dopamine D2 receptor (D2-DR). A reduced 3D model for the binding pocket of the human D2-DR was constructed on the basis of the theoretical model structure of bacteriorhodopsin. In our reduced model system, only 13 amino acids were included to perform the quantum mechanics calculations. To obtain the different complexes of DA/D2-DR, we combined semiempirical (PM6), DFT (B3LYP/6-31G(d)), and QTAIM calculations. The molecular flexibility of DA interacting with the D2-DR was evaluated from potential energy surfaces and potential energy curves. A comparative study between the molecular flexibility of DA in the gas phase and at D2-DR was carried out. In addition, several molecular dynamics simulations were carried out to evaluate the molecular flexibility of the different complexes obtained. Our results allow us to postulate the complexes of type A as the "biologically relevant conformations" of DA. In addition, the theoretical calculations reported here suggested that a mechanistic stepwise process takes place for DA in which the protonated nitrogen group (in any conformation) acts as the anchoring portion, and this process is followed by a rapid rearrangement of the conformation allowing the interaction of the catecholic OH groups.

Theoretical study of the conformational energy hypersurface of cyclotrisarcosyl

Abstract The multidimensional Conformational Potential Energy Hypersurface (PEHS) of cyclotrisarcosyl was comprehensively investigated at the DFT (B3LYP/6-31G(d), B3LYP/6-31G(d,p) and B3LYP/6-311++G(d,p)), levels of theory. The equilibrium structures, their relative stability, and the Transition State (TS) structures involved in the conformational interconversion pathways were analyzed. Aug-cc-pVTZ//B3LYP/6-311++G(d,p) and MP2/6-31G(d)//B3LYP/6-311++G(d,p) single point calculations predict a symmetric cis-cis-cis crown conformation as the energetically preferred form for this compound, which is in agreement with the experimental data. The conformational interconversion between the global minimum and the twist form requires 20.88 kcal mol-1 at the MP2/6-31G(d)//B3LYP/6-311++G(d,p) level of theory. Our results allow us to form a concise idea about the internal intricacies of the PEHSs of this cyclic tripeptide, describing the conformations as well as the conformational interconversion processes in this hypersurface. In addition, a comparative analysis between the conformational behaviors of cyclotrisarcosyl with that previously reported for cyclotriglycine was carried out