Conformational Energy Research Articles

Enthalpy Differences of the n-Pentane Conformers.

The energy and enthalpy differences of alkane conformers in various temperature ranges have been the subject for both experimental and theoretical studies over the last few decades. It was shown previously for the conformers of butane [G. Tasi et al., J. Chem. Theory Comput. 2012, 8, 479-486] that quantum chemical results can compete with spectroscopic techniques and results obtained even from the most carefully performed experiments could be biased due to the improper statistical model utilized to evaluate the raw experimental data. In the current study, on one hand, the experimental values and their uncertainties for the enthalpy differences for pentane conformers are re-evaluated using the appropriate statistical model. On the other hand, a coupled-cluster-based focal-point analysis has been performed to calculate energy and enthalpy differences for the conformers of pentane. The model chemistry defined in this study includes contributions up to the perturbative quadruple excitations augmented with further small correction terms beyond the Born-Oppenheimer and nonrelativistic approximations. Benchmark quality energy and enthalpy differences for the pentane conformers are given at temperatures 0 and 298.15 K as well as for the various temperature ranges used in the gas-phase experimental measurements. Furthermore, a slight positive shift for the experimental enthalpy differences is also predicted due to an additional Raman active band belonging to the gauche-gauche conformer.

Accurate Structure Prediction and Conformational Analysis of Cyclic Peptides with Residue-Specific Force Fields.

Cyclic peptides (CPs) are promising candidates for drugs, chemical biology tools, and self-assembling nanomaterials. However, the development of reliable and accurate computational methods for their structure prediction has been challenging. Here, 20 all-trans CPs of 5-12 residues selected from Cambridge Structure Database have been simulated using replica-exchange molecular dynamics with four different force fields. Our recently developed residue-specific force fields RSFF1 and RSFF2 can correctly identify the crystal-like conformations of more than half CPs as the most populated conformation. The RSFF2 performs the best, which consistently predicts the crystal structures of 17 out of 20 CPs with rmsd < 1.1 Å. We also compared the backbone (ϕ, ψ) sampling of residues in CPs with those in short linear peptides and in globular proteins. In general, unlike linear peptides, CPs have local conformational free energies and entropies quite similar to globular proteins.

Towards an understanding of crystallization from solution. DFT studies of multi-component serotonin crystals

A potential energy surface (PES) has been calculated for the protonated serotonin (5-HT) molecule in aqueous media. Three pairs of symmetrically equivalent minima were located using fully relaxed optimization at B3LYP/6-31G(d,p) level of theory. Insensitivity to basis set was verified over a range of different functionals and levels of theory. All 9 transition structures were found using the QST3 method with ansatz structures taken directly from the result of the calculated PES. Energies associated with conformational changes of protonated 5-HT in aqueous media were calculated and found to vary between 6 and 23kJmol−1. Lattice energies of serotonin picrate monohydrate and serotonin adipate were calculated as −741.7 and −716.9kJmol−1, respectively, and compared to conformational energies to consider the relative importance of each interaction type. The study contributes to achieving better insight into the importance of molecular conformations in solution as a precursor for the formation of the final crystal structure.

The Hydrogen Bonded Structures of Two 5-Bromobarbituric Acids and Analysis of Unequal C5-X and C5-X' Bond Lengths (X = X' = F, Cl, Br or Me) in 5,5-Disubstituted Barbituric Acids.

The crystal structure of the methanol hemisolvate of 5,5-dibromobarbituric acid (1MH) displays an H-bonded layer structure which is based on N–H⋯O=C, N–H⋯O(MeOH) and (MeOH)O–H⋯O interactions. The barbiturate molecules form an H-bonded substructure which has the fes topology. 5,5′-Methanediylbis(5-bromobarbituric acid) 2, obtained from a solution of 5,5-dibromobarbituric acid in nitromethane, displays a N–H⋯O=C bonded framework of the sxd type. The conformation of the pyridmidine ring and the lengths of the ring substituent bonds C5–X and C5–X′ in crystal forms of 5,5-dibromobarbituric acid and three closely related analogues (X = X′ = Br, Cl, F, Me) have been investigated. In each case, a conformation close to a C5-endo envelope is correlated with a significant lengthening of the axial C5–X′ in comparison to the equatorial C5–X bond. Isolated molecule geometry optimizations at different levels of theory confirm that the C5-endo envelope is the global conformational energy minimum of 5,5-dihalogenbarbituric acids. The relative lengthening of the axial bond is therefore interpreted as an inherent feature of the preferred envelope conformation of the pyrimidine ring, which minimizes repulsive interactions between the axial substituent and pyrimidine ring atoms.

Elastic model for dinucleosome structure and energy.

The equilibrium structure of a dinucleosome is studied using an elastic model that takes into account the force and torque balance conditions. Using the proper boundary conditions, it is found that the conformational energy of the problem does not depend on the length of the linker DNA. In addition it is shown that the two histone octamers are almost perpendicular to each other, and the linker DNA in short lengths is almost straight. These findings could shed some light on the role of DNA elasticity in the chromatin structure.

Assessing the performance of popular QM methods for calculation of conformational energies of trialanine

Accurate description of the conformational energies of the amino acids is essential for molecular dynamics simulation of protein structures. In this study, we compute the relative energies at 51 conformations for a trialanine tetrapeptide at different levels of theory. The computed energies at various theoretical levels, including the semiempirical DFTB method, HF, DFT, MP2 and CCSD(T), are compared with each other. The calculated energies from density-fitting local CCSD(T)/CBS (complete basis set) calculations are taken as the benchmark. The accuracy of the theoretical methods is highly dependent on the electronic correlation and dispersion corrections as well as the size of the basis sets. The involvement of the empirical dispersion energies in HF and DFT methods consistently improves their performance. Considering both the accuracy and computational efficiency, the Minnesota density functional M06-L-D and M06-2X-D are efficient and accurate for modeling of trialanine structures.

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.

Insights into How Cyclic Peptides Switch Conformations.

Cyclic peptides have recently emerged as promising modulators of protein-protein interactions. However, it is currently highly difficult to predict the structures of cyclic peptides owing to their rugged conformational free energy landscape, which prevents sampling of all thermodynamically relevant conformations. In this article, we first investigate how a relatively flexible cyclic hexapeptide switches conformations. It is found that, although the circular geometry of small cyclic peptides of size 6-8 may require rare, coherent dihedral changes to sample a new conformation, the changes are rather local, involving simultaneous changes of ϕi and ψi or ψi and ϕi+1. The understanding of how these cyclic peptides switch conformations enables the use of metadynamics simulations with reaction coordinates specifically targeting such coupled two-dihedral changes to effectively sample cyclic peptide conformational space.

Direct observation of transition paths during the folding of proteins and nucleic acids.

Transition paths, the fleeting trajectories through the transition states that dominate the dynamics of biomolecular folding reactions, encapsulate the critical information about how structure forms. Owing to their brief duration, however, they have not previously been observed directly. We measured transition paths for both nucleic acid and protein folding, using optical tweezers to observe the microscopic diffusive motion of single molecules traversing energy barriers. The average transit times and the shapes of the transit-time distributions agreed well with theoretical expectations for motion over the one-dimensional energy landscapes reconstructed for the same molecules, validating the physical theory of folding reactions. These measurements provide a first look at the critical microscopic events that occur during folding, opening exciting new avenues for investigating folding phenomena.

How biomolecules fold

Biophysics In order to fold, biomolecules must search a conformational energy landscape to find low-energy states. There are peaks in the landscape where the molecules must occupy unstable conformations for a short time. Neupane et al. used optical tweezers to observe these transition paths directly for single nucleic acid and protein molecules (see the Perspective by Wolynes). They measured a distribution of times taken to cross the transition path and found that the shape of the distribution agrees well with theory that assumes one-dimensional diffusion over the landscape. Science , this issue p. [239][1]; see also p. [150][2] [1]: /lookup/doi/10.1126/science.aad0637 [2]: /lookup/doi/10.1126/science.aaf6626

Long-Range Communication between Different Functional Sites in the Picornaviral 3C Protein

The 3C protein is a master regulator of the picornaviral infection cycle, responsible for both cleaving viral and host proteins, and interacting with genomic RNA replication elements. Here we use nuclear magnetic resonance spectroscopy and molecular dynamics simulations to show that 3C is conformationally dynamic across multiple timescales. Binding of peptide and RNA lead to structural dynamics changes at both the protease active site and the RNA-binding site, consistent with these sites being dynamically coupled. Indeed, binding of RNA influences protease activity, and likewise, interactions at the active site affect RNA binding. We propose that RNA and peptide binding re-shapes the conformational energy landscape of 3C to regulate subsequent functions, including formation of complexes with other viral proteins. The observed channeling of the 3C energy landscape may be important for regulation of the viral infection cycle.

Conformational free energy surfaces of non-ionized glycine in aqueous solution

Ab initio calculations on glycine and quantum mechanical/molecular mechanical molecular dynamics simulations (QM/MM-MD) on solvated non-ionized glycine were performed to explore the free energy landscapes of non-ionic glycine conformers in aqueous solution. Among nine different conformers of glycine, QM/MM-MD simulations found ttc and gtc conformers stable in addition to ttt, ccc, gtt, tct and gct which were well known as stable isomers in pure QM calculation. The stabilities of ttc and gtc come from a strong solvation at their carboxylic group side (–COOH) in solution. The preferred rotation along C–C (φ) as compared to C–O (θ) in both pure QM calculations and QM/MM-MD indicates the importance of intramolecular effects in determining relative free energies. On the other hand, the existence of stable ttc and gtc conformers only in solution phase clearly shows the importance of intermolecular interaction by explicit solvents. The same intermolecular interactions have a mixed effect on the free energy barriers. They reduced the barriers of A (ccc) → B (gtc) and A (ccc) → C (gct) isomerizations as compared to the ab initio or PCM results. At the same time, they also increased the barriers of B (ttc, gtc) → D (ttt, gtt). In short, the conformational free energy surfaces of non-ionized glycine in solution are largely different from the corresponding potential energy surfaces of gas phase. The fact that the initial conformer for tautomerization ccc is stable makes the N → Z tautomerization facile. However, concurrently, diverse conformational isomerizations to ccc make the tautomerization dependent on the isomerizations.

Molecular Plasticity of the Human Voltage-Dependent Anion Channel Embedded Into a Membrane

The voltage-dependent anion channel (VDAC) regulates the flux of metabolites and ions across the outer mitochondrial membrane. Regulation of ion flow involves conformational transitions in VDAC, but the nature of these changes has not been resolved to date. By combining single-molecule force spectroscopy with nuclear magnetic resonance spectroscopy we show that the β barrel of human VDAC embedded into a membrane is highly flexible. Its mechanical flexibility exceeds by up to one order of magnitude that determined for β strands of other membrane proteins and is largest in the N-terminal part of the β barrel. Interaction with Ca(2+), a key regulator of metabolism and apoptosis, considerably decreases the barrel's conformational variability and kinetic free energy in the membrane. The combined data suggest that physiological VDAC function depends on the molecular plasticity of its channel.

Molecular modeling of zinc paddlewheel molecular complexes and the pores of a flexible metal organic framework.

A new all-atom first-principles force field (FF) is constructed for the bimetallic, four-bladed zinc paddlewheel (ZPW) motif. Zinc-ligand interactions are described via Morse functions and the angular geometry at the metal centers is modeled with a pure ligand-ligand repulsion term. The ZPW-FF is principally based on 15 DFT-optimized model systems of general formula ZnPR.nL, where ZnP is the base Zn2(O2CR)4 unit, R = H, CH3 or CF3, L = NH3 or pyridine, and n = 0, 1 or 2. It correctly generates the distorted tetrahedral coordination of the uncapped [Zn2(O2CR)4] species in their ground states as well as giving reasonable structures and energies for the higher symmetry D4h transition state conformations. The zinc-ligand Morse function reference distance, r0, is further refined against 30 complexes located in the Cambridge Structural Database and this FF is applied to pore models of the flexible metal-organic framework (MOF) [Zn(bdc)2(dabco)]n (bdc = 1,4-benzendicarboxylate; dabco = 1,4-diazabicyclo(2.2.2)octane). A single pore model reproduces the unit cell of the evacuated MOF system while a 3×3 grid model is necessary to provide good agreement with the observed pronounced structural changes upon adsorption of either dimethylformamide or benzene.Graphical Structural simulations of a zinc paddlewheel metal organic framework reproduce the observed breathing behaviourElectronic supplementary materialThe online version of this article (doi:10.1007/s00894-016-2949-5) contains supplementary material, which is available to authorized users.

Towards understanding the unbound state of drug compounds: Implications for the intramolecular reorganization energy upon binding

There has been an explosion of structural information for pharmaceutical compounds bound to biological targets, but the conformations and dynamics of compounds free in solution are poorly characterized, if at all. Yet, knowledge of the unbound state is essential to understand the fundamentals of molecular recognition, including the much debated conformational intramolecular reorganization energy of a compound upon binding (ΔEReorg). Also, dependable observation of the unbound compounds is important for ligand-based drug discovery, e.g. with pharmacophore modelling. Here, these questions are addressed with long (⩾0.5μs) state-of-the-art molecular dynamics (MD) simulations of 26 compounds (including 7 approved drugs) unbound in explicit solvent. These compounds were selected to be chemically diverse, with a range of flexibility, and good quality bioactive X-ray structures. The MD-simulated free compounds are compared to their bioactive structure and conformers generated with ad hoc sampling in vacuo or with implicit generalized Born (GB) aqueous solvation models. The GB conformational models clearly depart from those obtained in explicit solvent, and suffer from conformational collapse almost as severe as in vacuo. Thus, the global energy minima in vacuo or with GB are not suitable representations of the unbound state, which can instead be extensively sampled by MD simulations. Many, but not all, MD-simulated compounds displayed some structural similarity to their bioactive structure, supporting the notion of conformational pre-organization for binding. The ligand–protein complexes were also simulated in explicit solvent, to estimate ΔEReorg as an enthalpic difference ΔHReorg between the intramolecular energies in the bound and unbound states. This fresh approach yielded ΔHReorg values⩽6kcal/mol for 18 out of 26 compounds. For three particularly polar compounds 15⩽ΔHReorg⩽20kcal/mol, supporting the notion that ΔHReorg can be substantial. Those large ΔHReorg values correspond to a redistribution of electrostatic interactions upon binding. Overall, the study illustrates how MD simulations offer a promising avenue to characterize the unbound state of medicinal compounds.

How Does Hyperphopsphorylation Promote Tau Aggregation and Modulate Filament Structure and Stability?

Tau proteins are hyperphosphorylated at common sites in their N- and C-terminal domains in at least three neurodegenerative diseases, Parkinson, dementia with Lewy bodies, and Alzheimer's, suggesting specific pathology but general mechanism. Full-length human tau filament comprises a rigid core and a two-layered fuzzy coat. Tau is categorized into two groups of isoforms, with either four repeats (R1-R4) or three repeats (R1, R3, and R4); their truncated constructs are respectively called K18 and K19. Using multiscale molecular dynamics simulations, we explored the conformational consequences of hyperhposphorylation on tau's repeats. Our lower conformational energy filament models suggest a rigid filament core with a radius of ∼30 to 40 Å and an outer layer with a thickness of ∼140 Å consisting of a double-layered polyelectrolyte. The presence of the phosphorylated terminal domains alters the relative stabilities in the K18 ensemble, thus shifting the populations of the full-length filaments. However, the structure with the straight repeats in the core region is still the most stable, similar to the truncated K18 peptide species without the N- and C-terminus. Our simulations across different scales of resolution consistently reveal that hyperphosphorylation of the two terminal domains decreases the attractive interactions among the N- and C-terminus and repeat domain. To date, the relationship on the conformational level between phosphorylation and aggregation has not been understood. Our results suggest that the exposure of the repeat domain upon hyperphosphorylation could enhance tau filament aggregation. Thus, we discovered that even though these neurodegenerative diseases vary and their associated tau filaments are phosphorylated to different extents, remarkably, the three pathologies appear to share a common tau aggregation mechanism.

Molecular energies from an incremental fragmentation method

The systematic molecular fragmentation method by Collins and Deev [J. Chem. Phys. 125, 104104 (2006)] has been used to calculate total energies and relative conformational energies for a number of small and extended molecular systems. In contrast to the original approach by Collins, we have tested the accuracy of the fragmentation method by utilising an incremental scheme in which the energies at the lowest level of the fragmentation are calculated on an accurate quantum chemistry level while lower-cost methods are used to correct the low-level energies through a high-level fragmentation. In this work, the fragment energies at the lowest level of fragmentation were calculated using the random-phase approximation (RPA) and two recently developed extensions to the RPA while the incremental corrections at higher levels of the fragmentation were calculated using standard density functional theory (DFT) methods. The complete incremental fragmentation method has been shown to reproduce the supermolecule results with a very good accuracy, almost independent on the molecular type, size, or type of decomposition. The fragmentation method has also been used in conjunction with the DFT-SAPT (symmetry-adapted perturbation theory) method which enables a breakdown of the total nonbonding energy contributions into individual interaction energy terms. Finally, the potential problems of the method connected with the use of capping hydrogen atoms are analysed and two possible solutions are supplied.

Specific energy contributions from competing hydrogen-bonded structures in six polymorphs of phenobarbital.

BackgroundIn solid state structures of organic molecules, identical sets of H-bond donor and acceptor functions can result in a range of distinct H-bond connectivity modes. Specifically, competing H-bond structures (HBSs) may differ in the quantitative proportion between one-point and multiple-point H-bond connections. For an assessment of such HBSs, the effects of their internal as well as external (packing) interactions need to be taken into consideration. The semi-classical density sums (SCDS-PIXEL) method, which enables the calculation of interaction energies for molecule–molecule pairs, was used to investigate six polymorphs of phenobarbital (Pbtl) with different quantitative proportions of one-point and two-point H-bond connections.ResultsThe structures of polymorphs V and VI of Pbtl were determined from single crystal data. Two-point H-bond connections are inherently inflexible in their geometry and lie within a small PIXEL energy range (−45.7 to −49.7 kJ mol−1). One-point H-bond connections are geometrically less restricted and subsequently show large variations in their dispersion terms and total energies (−23.1 to −40.5 kJ mol−1). The comparison of sums of interaction energies in small clusters containing only the strongest intermolecular interactions showed an advantage for compact HBSs with multiple-point connections, whereas alternative HBSs based on one-point connections may enable more favourable overall packing interactions (i.e. V vs. III). Energy penalties associated with experimental intramolecular geometries relative to the global conformational energy minimum were calculated and used to correct total PIXEL energies. The estimated order of stabilities (based on PIXEL energies) is III > I > II > VI > X > V, with a difference of just 1.7 kJ mol−1 between the three most stable forms.ConclusionsFor an analysis of competing HBSs, one has to consider the contributions from internal H-bond and non-H-bond interactions, from the packing of multiple HBS instances and intramolecular energy penalties. A compact HBS based on multiple-point H-bond connections should typically lead to more packing alternatives and ultimately to a larger number of viable low-energy structures than a competing one-point HBS (i.e. dimer vs. catemer). Coulombic interaction energies associated with typical short intermolecular C–H···O contact geometries are small in comparison with dispersion effects associated with the packing complementary molecular shapes.Graphical abstractCompeting H-bond motifs can differ markedly in their energy contributionsElectronic supplementary materialThe online version of this article (doi:10.1186/s13065-016-0152-5) contains supplementary material, which is available to authorized users.

Structural diversity of manganese(II) complexes containing 2,2′-dipyridylamine and benzenedicarboxylates. Conformational analysis of tere-, iso- and phthalate ions: An experimental and quantum chemical approach

Four novel manganese(II) complexes with 2,2′-dipyridylamine (dipya) and various benzenedicarboxylate, BDC, ligands as anions of phthalic (pht), isophthalic (ipht) and terephthalic (tpht) acids were hydrothermally synthesized, namely, [Mn(dipya)(pht)(H2O)]2 (1), [Mn(dipya)(ipht)]n (2), [Mn(dipya)2(tpht)]n (3), and [Mn(dipya)(H2O)4](tpht) (4). All complexes were characterized by single-crystal X-ray diffraction, TG/DSC analysis and IR spectroscopy. The obtained complexes display a plenty of different structural features, including geometry of central metal atoms, BDC coordination modes and crystal packing. The coordination numbers of Mn(II) are different: 5 (in 2), 6 (in 3 and 4) and 7 (in 1). 3D networks in 1–4 are determined by strong non-covalent interactions. A survey of the Cambridge Structural Database for BDC complexes was performed in order to analyze orientation of COO groups. The energies of various BDC conformers were calculated by the second order Møller–Plesset perturbation theory and three hybrid HF/DFT methods with 6-311G∗∗ basis set. To explain different behavior, BDC ions were also examined by Localized Molecular Orbital Energy Decomposition and Natural Bond Orbital analyses. Experimental and calculated geometries are in agreement, showing that tpht and ipht anions prefer the planar conformation, while in pht anions COO groups are inclined and make complementary angles relative to the aromatic rings.

Structure and conformational dynamics of formamide molecule in the ground and lowest excited electronic states

Electronic state calculations, such as equilibrium geometry parameters, harmonic vibrational frequencies and potential barriers to conformational transitions (as well as conformer energy differences in excited states), using ab initio methods, such as MP2, CCSD(T), CASSCF, CASPT2 and MRCI, were carried out on the formamide molecule in the ground (S0) and the lowest excited singlet (S1) and triplet (T1) states. One-, two- and three-dimensional PES sections corresponding to different large amplitude motions (LAMs) were calculated using the MP2/aug-cc-pVTZ (S0) and CASPT2/cc-pVTZ (S1, T1) methods. In each excited electronic state, six minima with comparatively small potential barriers to internal rotation (less than 15kJ/mol) between them were discovered. Using PES sections, the anharmonic vibrational problem was solved, and the frequencies of the LAMs were determined.