Aggregation of Capped Hexaglycine Strands into Hydrogen-Bonding Motifs Representative of Pleated and Rippled β-Sheets, Collagen, and Polyglycine I and II Crystal Structures. A Density Functional Theory Study

Abstract

We compare the energies and enthalpies of interaction of three and seven stranded capped polyglycine aggregates in both the pleated and rippled antiparallel and parallel β-sheet structures as well as the collagenic (3-strand) or polyglycine II-like (7-strand) forms using DFT theory at the B3LYP/D95(d,p) level. We present the overall interaction energies as broken down into pure Hbonding 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 β-sheet constrained to C s symmetry has a lower enthalpy, but higher energy, of interaction than the fully optimized structure.Polyglycine crystalizes in three forms, polyglycine I (actually a dimorph) and II. Polyglycine I includes two different crystal structures each containing a different type of β-sheet. 1 -5 The structure of polyglycine II (PII) consists of parallel β-sheets oriented 120 degrees to each other.6 , 7 Three of these sheets intersect at each polyglycine strand. Each triad of nearest neighbor strands bears a striking resemblance to collagen, the most abundant protein in the human body. In collagen, the three strands of polyglycine taken from the crystal structure are replaced with strands comprised of triads of XYG (where X and Y can be any amino acid, most often proline and 4-hydroxyproline) and G is glycine. These are connected by H-bonds from the glycines (donors) on one strand to C=O's (acceptors) of the amide couplings on another peptide strand. The 'sheets' each contain only two strands in collagen-like structures. The principal differences between collagen-like structures and PII lie in the inability of collagen to form the infinite pattern of H-bonds normal to the peptide backbone (found in PII) beyond the three strands of the collagenic triple helix, due to a) the lack of N-H donors on the proline and hydroxyproline residues and b) the steric impediments caused by the side chains of all the amino acids except for glycine. Comparison of the PII and collagen structures begs the questions: a) Does the triple helical (XYG) N structure of collagen result from an evolutionary selection against structures that jdannenberg@gc.cuny.edu. Supporting Information Available: Cartesian coordinates for optimized structures, figures illustrating the structures containing three strands and seven stranded sheets with the constrain that the strands be equivalent.. This material is available free of charge via the Internet at http://pubs.acs.org. could form additional H-bonds such as those present in polyglycine? b) How competitive are the PII structures with β-sheets of the same size? While β...

Comparison of β-Sheets of Capped Polyalanine with Those of the Tau-Amyloid Structures VQIVYK and VQIINK. A Density Functional Theory Study

“…4,9,40,41 Comparison of VQIVYK with VQIINK reveals that the interaction enthalpy for the strands at the edge of the sheet (1–2) reach a similar asymptotic value for both structures. However, the interactions nearer the center of the sheets are much stronger for VQIINK.…”

“…9 We define the H-bonding energies as the interactions between the strands in the geometries of the optimized sheet, and the distortion energies as the energy required to change the geometry of the completely relaxed extended strand to that it assumes in the optimized sheet. This procedure has the advantage of allowing different conformations of the individual strands to be considered as starting points.…”

“…Earlier DFT calculations on β-sheets have focused on antiparallel glycine-like fragments, 11–13 which tend to form an almost planar, or a rippled structure in addition to the pleated-sheet structure typical of most β-sheets. 9 In another interesting paper, Perczel has explored the relative energies of b-sheets compared to other secondary structural motifs for short polyalanines containing up to 8 residues per strand. 14 …”

Capping Amyloid β-Sheets of the Tau-Amyloid Structure VQIVYK with Hexapeptides Designed To Arrest Growth. An ONIOM and Density Functional Theory Study

“…4,35 Hence, we would expect AP interaction between the sheet and the cap to probably enhance the affinity of the cap for the sheet.…”

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

“…[ 41, 45–47 ] We have recently shown that B3LYP/D95(d,p) is among the better functional/basis set combinations for the water dimer. [ 48 ] We have used this level of calculation to calculate the differential enthalpies of adding successive alanines to a growing α‐helix, [ 49 ] the magnitudes of 13 C‐ 15 N 3 J‐trans H‐bonding scalar coupling constants, [ 50 ] the structures of polyglycine models, [ 51 ] and the H‐bonding interactions of the DNA base pairs. [ 52 ] Comparisons with experimental confirm the validity of the method in several cases.…”