Alternative chelator for 89Zr radiopharmaceuticals: radiolabeling and evaluation of 3,4,3-(LI-1,2-HOPO).

Zirconium-89 is an effective radionuclide for antibody-based positron emission tomography (PET) imaging because its physical half-life (78.41 h) matches the biological half-life of IgG antibodies. Desferrioxamine (DFO) is currently the preferred chelator for (89)Zr(4+); however, accumulation of (89)Zr in the bones of mice suggests that (89)Zr(4+) is released from DFO in vivo. An improved chelator for (89)Zr(4+) could eliminate the release of osteophilic (89)Zr(4+) and lead to a safer PET tracer with reduced background radiation dose. Herein, we present an octadentate chelator 3,4,3-(LI-1,2-HOPO) (or HOPO) as a potentially superior alternative to DFO. The HOPO ligand formed a 1:1 Zr-HOPO complex that was evaluated experimentally and theoretically. The stability of (89)Zr-HOPO matched or surpassed that of (89)Zr-DFO in every experiment. In healthy mice, (89)Zr-HOPO cleared the body rapidly with no signs of demetalation. Ultimately, HOPO has the potential to replace DFO as the chelator of choice for (89)Zr-based PET imaging agents.

Capping amyloid ß-sheets of the tau-amyloid structure VQIVYK with hexapeptides designed to arrest growth. An ONIOM and density functional theory study.

We present ONIOM calculations using density functional theory (DFT) as the high and AM1 as the medium level that explore the abilities of different hexapeptide sequences to terminate the growth of a model for the tau-amyloid implicated in Alzheimer's disease. We delineate and explore several design principles (H-bonding in the side chains, using antiparallel interactions on the growing edge of a parallel sheet, using all-d residues to form rippled interactions at the edge of the sheet, and replacing the H-bond donor N-H's that inhibit further growth) that can be used individually and in combination to design such peptides that will have a greater affinity for binding to the parallel ß-sheet of acetyl-VQIVYK-NHCH3 than the natural sequence and will prevent another strand from binding to the sheet, thus providing a cap to the growing sheet that arrests further growth. We found peptides in which the Q is replaced by an acetyllysine (aK) residue to be particularly promising candidates, particularly if the reverse sequence (KYVIaKV) is used to form an antiparallel interaction with the sheet.

Capping parallel ß-sheets of acetyl(Ala)6NH2 with an acetyl(Ala)5ProNH2 can arrest the growth of the sheet, suggesting a potential for curtailing amyloid growth. An ONIOM and density functional theory study.

We present ONIOM calculations using B3LYP/d95(d,p) as the high level and AM1 as the medium level on parallel ß-sheets containing four strands of Ac-AAAAAA-NH2 capped with either Ac-AAPAAA-NH2 or Ac-AAAPAA-NH2. Because Pro can form H-bonds from only one side of the peptide linkage (that containing the C═O H-bond acceptor), only one of the two Pro-containing strands can favorably add to the sheet on each side. Surprisingly, when the sheet is capped with AAPAAA-NH2 at one edge, the interaction between the cap and sheet is slightly more stabilizing than that of another all Ala strand. Breaking down the interaction enthalpies into H-bonding and distortion energies shows the favorable interaction to be due to lower distortion energies in both the strand and the four-stranded sheet. Because another strand would be inhibited for attachment to the other side of the capping (Pro-containing) strand, we suggest the possible use of Pro residues in peptides designed to arrest the growth of many amyloids.

The interactions of phenylalanines in ß-sheet-like structures from molecular orbital calculations using density functional theory (DFT), MP2, and CCSD(T) methods.

We present density functional theory calculations designed to evaluate the importance of π-stacking interactions to the stability of in-register Phe residues within parallel ß-sheets, such as amyloids. We have used a model of a parallel H-bonded tetramer of acetylPheNH2 as a model and both functionals that were specifically designed to incorporate dispersion effects (DFs), as well as, several traditional functionals which have not been so designed. None of the functionals finds a global minimum for the π-stacked conformation, although two of the DFs find this to be a local minimum. The stacked phenyls taken from the optimized geometries calculated for each functional have been evaluated using MP2 and CCSD(T) calculations for comparison. The results suggest that π-stacking does not make an important contribution to the stability of this system and (by implication) to amyloid formation.

The folding of acetyl(Ala)28NH2 and acetyl(Ala)40NH2 extended strand peptides into antiparallel ß-sheets. A density functional theory study of ß-sheets with ß-turns.

We report ONIOM calculations using B3LYP/D95** and AM1 on ß-sheet formation from acetyl(Ala)(N)NH(2) (N = 28 or 40). The sheets contain from one to four ß-turns for N = 28 and up to six for N = 40. We have obtained four types of geometrically optimized structures. All contain only ß-turns. They differ from each other in the types of ß-turns formed. The unsolvated sheets containing two turns are most stable. Aqueous solvation (using the SM5.2 and CPCM methods) reduces the stabilities of the folded structures compared to the extended strands.

Comparison of some dispersion-corrected and traditional functionals with CCSD(T) and MP2 ab initio methods: dispersion, induction, and basis set superposition error.

We compare dispersion and induction interactions for noble gas dimers and for Ne, methane, and 2-butyne with HF and LiF using a variety of functionals (including some specifically parameterized to evaluate dispersion interactions) with ab initio methods including CCSD(T) and MP2. We see that inductive interactions tend to enhance dispersion and may be accompanied by charge-transfer. We show that the functionals do not generally follow the expected trends in interaction energies, basis set superposition errors (BSSE), and interaction distances as a function of basis set size. The functionals parameterized to treat dispersion interactions often overestimate these interactions, sometimes by quite a lot, when compared to higher level calculations. Which functionals work best depends upon the examples chosen. The B3LYP and X3LYP functionals, which do not describe pure dispersion interactions, appear to describe dispersion mixed with induction about as accurately as those parametrized to treat dispersion. We observed significant differences in high-level wavefunction calculations in a basis set larger than those used to generate the structures in many of the databases. We discuss the implications for highly parameterized functionals based on these databases, as well as the use of simple potential energy for fitting the parameters rather than experimentally determinable thermodynamic state functions that involve consideration of vibrational states.

Comparison of some dispersion-corrected and traditional functionals as applied to peptides and conformations of cyclohexane derivatives.

We compare the energetic and structural properties of fully optimized α-helical and antiparallel ß-sheet polyalanines and the energetic differences between axial and equatorial conformations of three cyclohexane derivatives (methyl, fluoro, and chloro) as calculated using several functionals designed to treat dispersion (B97-D, ωB97x-D, M06, M06L, and M06-2X) with other traditional functionals not specifically parametrized to treat dispersion (B3LYP, X3LYP, and PBE1PBE) and with experimental results. Those functionals developed to treat dispersion significantly overestimate interaction enthalpies of folding for the α-helix and predict unreasonable structures that contain Ramachandran φ and ψ and C = O...N H-bonding angles that are out of the bounds of databases compiled the ß-sheets. These structures are consistent with overestimation of the interaction energies. For the cyclohexanes, these functionals overestimate the stabilities of the axial conformation, especially when used with smaller basis sets. Their performance improves when the basis set is improved from D95∗∗ to aug-cc-pVTZ (which would not be possible with systems as large as the peptides).

A reinvestigation of the dimer of para-benzoquinone and pyrimidine with MP2, CCSD(T), and DFT using functionals including those designed to describe dispersion.

We reevaluate the interaction of pyridine and p-benzoquinone using functionals designed to treat dispersion. We compare the relative energies of four different structures: stacked, T-shaped (identified for the first time), and two planar H-bonded geometries using these functionals (B97-D, ωB97x-D, M05, M05-2X, M06, M06L, and M06-2X), other functionals (PBE1PBE, B3LYP, X3LYP), MP2, and CCSD(T) using basis sets as large as cc-pVTZ. The functionals designed to treat dispersion behave erratically as the predictions of the most stable structure vary considerably. MP2 predicts the experimentally observed structure (H-bonded) to be the least stable, while single-point CCSD(T) at the MP2 optimized geometry correctly predicts the observed structure to be the most stable. We have confirmed the assignment of the experimental structure using new calculations of the vibrational frequency shifts previously used to identify the structure. The MP2/cc-pVTZ vibrational calculations are in excellent agreement with the observations. All methods used to calculate the energies provide vibrational shifts that agree with the observed structure even though most do not predict this structure to be most stable. The implications for evaluating possible π-stacking in biologically important systems are discussed.

Density functional theory study of ß-hairpins in antiparallel ß-sheets, a new classification based upon H-bond topology.

We present a new classification of ß-turns specific to antiparallel ß-sheets based upon the topology of H-bond formation. This classification results from ONIOM calculations using B3LYP/D95** density functional theory and AM1 semiempirical calculations as the high and low levels, respectively. We chose acetyl(Ala)(6)NH(2) as a model system as it is the simplest all-alanine system that can form all the H-bonds required for a ß-turn in a sheet. Of the 10 different conformations we have found, the most stable structures have C(7) cyclic H-bonds in place of the C(10) interactions specified in the classic definition. Also, the chiralities specified for residues i + 1 and i + 2 in the classic definition disappear when the structures are optimized using our techniques, as the energetic differences among the four diastereomers of each structure are not substantial for 8 of the 10 conformations.

A Density Functional Theory Evaluation of Hydrophobic Solvation: Ne, Ar and Kr in a 50-Water Cluster. Implications for the Hydrophobic Effect.

The physical explanation for the hydrophobic effect has been the subject of disagreement. Physical organic chemists tend to use a explanation related to pressure, while many biochemists prefer an explanation that involves decreased entropy of the aqueous solvent. We present DFT calculations at the B3LYP/6-31G(d,p) and X3LYP/6-31G(d,p) levels on the solvation of three noble gases (Ne, Ar, and Kr) in clusters of 50 waters. Vibrational analyses show no substantial decreases in the vibrational entropies of the waters in any of the three clusters. The observed positive free energies of transfer from the gas phase or from nonpolar solvents to water appear to be due to the work needed to make a suitable hole in the aqueous solvent. We distinguish between hydrophobic solvations (explicitly studied here) and the hydrophobic effect that occurs when a solute (or transition state) can decrease its volume through conformational change (which is not possible for the noble gases).

Aqueous solvation of polyalanine α-helices with specific water molecules and with the CPCM and SM5.2 aqueous continuum models using density functional theory.

We present density functional theory (DFT) calculations at the X3LYP/D95(d,p) level on the solvation of polyalanine α-helices in water. The study includes the effects of discrete water molecules and the CPCM and AMSOL SM5.2 solvent continuum model both separately and in combination. We find that individual water molecules cooperatively hydrogen-bond to both the C- and N-termini of the helix, which results in increases in the dipole moment of the helix/water complex to more than the vector sum of their individual dipole moments. These waters are found to be more stable than in bulk solvent. On the other hand, individual water molecules that interact with the backbone lower the dipole moment of the helix/water complex to below that of the helix itself. Small clusters of waters at the termini increase the dipole moments of the helix/water aggregates, but the effect diminishes as more waters are added. We discuss the somewhat complex behavior of the helix with the discrete waters in the continuum models.

The Effects of Regularly Spaced Glutamine Substitutions on Alpha-Helical Peptide Structures. A DFT/ONIOM Study.

The side-chains of the residues of glutamine (Q) and asparagine (N) contain amide groups. These can H-bond to each other in patterns similar to those of the backbone amides in α-helices. We show that mutating multiple Q's for alanines (A's) in a polyalanine helix stabilizes the helical structure, while similar mutations with multiple N's do not. We suggest that modification of peptides by incorporating Q's in such positions can make more robust helices that can be used to test the effects of secondary structures in biochemical experiments linked to proteins with variable structures such as tau and α-synuclein.

J-coupling constants for a trialanine peptide as a function of dihedral angles calculated by density functional theory over the full Ramachandran space.

We present 13 (3)J, seven (2)J and four (1)J coupling constants (24 in all) calculated using B3LYP/D95** as a function of the φ and ψ Ramachandran dihedral angles of the acetyl(Ala)(3)NH(2) capped trialanine peptide over the entire Ramachandran space. With the exception of three of these J couplings, all show significant dependence upon both dihedral angles. For each J coupling considered, a two dimensional grid with respect to φ and ψ angles can be used to interpolate the values for any pair of φ and ψ values. Such simple interpolation is shown to be very accurate. Most of these calculated J couplings should prove useful for improving the accuracy of the determination of peptide and protein structures from NMR measurements in solution over that provided by the common procedure of treating the J couplings as functions of a single dihedral angle by means of Karplus-type fittings.

Comparison of ß-sheets of capped polyalanine with those of the tau-amyloid structures VQIVYK and VQIINK. A density functional theory study.

We present ONIOM calculations using B3LYP/d95(d,p) as the high and AM1 as the low level on parallel ß-sheets containing from two to ten strands of Ac-VQIVYK-NHMe and Ac-VQIINK-NHMe, as well as both parallel and antiparallel Ac-AAAAAA-NHMe. We find that the first two sequences form more stable sheets due to the additional H-bonding between the Q's in the side chains of both and the N's in the side chain of Ac-VQIINK-NHMe. However, the H-bonds in the amyloid chains are significantly weakened by attractive strain, which prevents all the interstrand H-bonds from achieving their optimal geometries simultaneously and requires high distortion energies for the individual strands in the sheets. The antiparallel Ac-AAAAAA-NHMe's are generally more stable and more cooperative than the parallel sheets, principally due to the higher distortion energies of the latter.

The effect of polarization on multiple hydrogen-bond formation in models of self-assembling materials.

We report density functional theory calculations at the B3LYP/D95(d,p) level on several different cyclic H-bonding dimers, where the monomers of each are connected by a pair of N-H···O=C H-bonding interactions, and the H-bonding donors and acceptors on each monomer are separated by polarizable spacers. Depending on the structures, the individual H-bonds vary in strength (enthalpy) by over a factor of four, from 2.41 to 10.99 kcal/mol. We attribute most of the variation in interaction energies to differences in the extent of polarization due to each of the H-bonds, which can either combine constructively or destructively. The dipole-dipole interactions between the pair of H-bonds also contribute somewhat to the relative stabilities. The relevance of these results to the design of self-assembling materials is discussed.

A comparison of the behavior of functional/basis set combinations for hydrogen-bonding in the water dimer with emphasis on basis set superposition error.

We evaluate the performance of ten functionals (B3LYP, M05, M05-2X, M06, M06-2X, B2PLYP, B2PLYPD, X3LYP, B97D, and MPWB1K) in combination with 16 basis sets ranging in complexity from 6-31G(d) to aug-cc-pV5Z for the calculation of the H-bonded water dimer with the goal of defining which combinations of functionals and basis sets provide a combination of economy and accuracy for H-bonded systems. We have compared the results to the best non-density functional theory (non-DFT) molecular orbital (MO) calculations and to experimental results. Several of the smaller basis sets lead to qualitatively incorrect geometries when optimized on a normal potential energy surface (PES). This problem disappears when the optimization is performed on a counterpoise (CP) corrected PES. The calculated interaction energies (ΔEs) with the largest basis sets vary from -4.42 (B97D) to -5.19 (B2PLYPD) kcal/mol for the different functionals. Small basis sets generally predict stronger interactions than the large ones. We found that, because of error compensation, the smaller basis sets gave the best results (in comparison to experimental and high-level non-DFT MO calculations) when combined with a functional that predicts a weak interaction with the largest basis set. As many applications are complex systems and require economical calculations, we suggest the following functional/basis set combinations in order of increasing complexity and cost: (1) D95(d,p) with B3LYP, B97D, M06, or MPWB1k; (2) 6-311G(d,p) with B3LYP; (3) D95++(d,p) with B3LYP, B97D, or MPWB1K; (4) 6-311++G(d,p) with B3LYP or B97D; and (5) aug-cc-pVDZ with M05-2X, M06-2X, or X3LYP.

Aggregation of capped hexaglycine strands into hydrogen-bonding motifs representative of pleated and rippled ß-sheets, collagen, and polyglycine I and II crystal structures. A density functional theory study.

We compare the energies and enthalpies of inter-action of three- and seven-stranded capped polyglycine aggregates in both the pleated and rippled antiparallel and parallel ß-sheet structures as well as the collagenic (three-strand) or polyglycine II-like (seven-strand) forms using density functional theory at the B3LYP/D95(d,p) level. We present the overall interaction energies as broken down into pure H-bonding between the strands at the geometries they assume in the aggregates and the distortion energies required to achieve those geometries starting from the fully relaxed single strands. While the antiparallel sheets represent the most stable structures for both the three- and seven-strand structures, the pure H-bonding interactions are the smallest for these structures. The overall interaction energies are dominated by the energy required to distort the relaxed polyglycine strands rather than the H-bonding energies. The antiparallel ß-sheet constrained to C(s) symmetry has a lower enthalpy, but higher energy, of interaction than the fully optimized structure.

The importance of hydrogen bonding between the glutamine side chains to the formation of amyloid VQIVYK parallel beta-sheets: an ONIOM DFT/AM1 study.

We report DFT calculations indicating that beta-sheet formation involving the capped amino acid sequence VQIVYK is due (at least in part) to cooperative H-bonding between the glutamine side chains. The sequence VQIVYK has been reported to be essential for the aggregation of the tau protein into the amyloids associated with Alzheimer's disease and has been crystallized. Sheets containing only capped Q's form cooperative H-bonds between the side chains that enhance stabilization while keeping the backbones of the individual strands close to the quasi-planarity expected for a beta-sheet. Sheets containing only capped A's cannot form H-bonds between the side chains, do not interact cooperatively, and form helical structures that deviate considerably from the quasi-planarity expected for beta-sheets. Comparisons between the sheets made from capped VQIVYK's, Q's, and A's illustrate the importance of the cooperative H-bonds between the Q's to the stability of tau amyloids.

Ramachandran revisited. DFT energy surfaces of diastereomeric trialanine peptides in the gas phase and aqueous solution.

We report DFT calculations at the B3LYP/D95(d,p) level on the gas phase, aqueous solvation and solvated energies as functions of the central psi and phi dihedral angles (in steps of 5 degrees each) of acetyl-(L)Ala-(L)Ala-(L)Ala-NH(2) (3AL) and its diastereomer, acetyl-(L)Ala-(D)Ala-(L)Ala-NH(2) (3AD). In addition to structures without internal H-bonds (C(5) interactions are neglected), many (95) structures containing internal H-bonds were completely optimized. The only minima for non-H-bonding structures in the gas phase correspond to extended beta-strands for both diastereomers. Some (but not all) structures with internal H-bonds are more stable than those without them. The energy landscapes for the solvated species show multiple minima for the non-H-bonding species and a single minimum for the H-bonding species (3(10)-helix), suggesting that the equilibrium conformational mixture in water be composed of the extended beta-strand, polyproline II, 3(10)-helix, and alpha-helix-like (with no H-bonds) conformations which are all within about 1 kcal/mol of each other. Most H-bonding structures are destabilized relative to the non-H-bonding structures in aqueous solution, but some with large dipole moments are not. The large dipole moment of the alpha-helix-like conformation leads to its increased stability in water (vs the gas phase). Significant qualitative and quantitative differences are reported for the energy landscapes of the two diastereomers when one is compared with the mirror image of the other landscape (particularly in the beta-turn region), suggesting that the differences in the energies of the unfolded peptides need to be considered when considering the stabilities of folded peptides and proteins with single amino acid mutations.

A density functional theory study of vibrational coupling in the amide I band of beta-sheet models.

We report the first molecular orbital/density functional theory (DFT) calculations on the vibrational frequencies involved in the amide I band of completely geometrically optimized models for beta-sheet peptides based upon (up to 16) glycine residues. These calculations use the B3LYP/D95** level of DFT. The primary means of vibrational coupling occurs through H bond, rather than through space, interactions, which is consistent with a previous report on alpha-helical polyalanines and H-bonding chains of both formamides and 4-pyridones. We decoupled the C=O stretching vibrations using selected 14C substitutions to probe the coupling mechanism and to determine "natural" frequencies for individual 14C=Os. The intermolecular H-bonding interactions affect the geometries of the amide groups. Those near the center of H-bonding chains have long C=O bonds. The C=O bond lengths correlate with these "natural" frequencies, The frequencies obtained from the DFT calculations are generally more coupled, and the most intense are more red shifted than those calculated by transition dipole coupling (TDC). TDC inverts the order of the shifted frequencies compared to DFT in several cases.