The close-packed triple helix as a possible new structural motif for collagen

The one-dimensional problem of selecting the triple helix with the highest volume fraction is solved and hence the condition for a helix to be close-packed is obtained. The close-packed triple helix is shown to have a pitch angle of v _CP =?43.3°. Contrary to the conventional notion, we suggest that close packing form the underlying principle behind the structure of collagen, and the implications of this suggestion are considered. Further, it is shown that the unique zero-twist structure with no strain-twist coupling is practically identical to the close-packed triple helix. Some of the difficulties for the current understanding of the structure of collagen are reviewed: The ambiguity in assigning crystal structures for collagen-like peptides, and the failure to satisfactorily calculate circular dichroism spectra. Further, the proposed new geometrical structure for collagen is better packed than both the 10/3 and the 7/2 structure. A feature of the suggested collagen structure is the existence of a central channel with negatively charged walls. We find support for this structural feature in some of the early x-ray diffraction data of collagen. The central channel of the structure suggests the possibility of a one-dimensional proton lattice. This geometry can explain the observed magic angle effect seen in NMR studies of collagen. The central channel also offers the possibility of ion transport and may cast new light on various biological and physical phenomena, including biomineralization.     

Energy calculations on helical polypeptides: Structure of polyglycine II

Single chain and packing energy calculations have been made on polyglycine (threefold and fourfold helical structures) with interchain NH…?O hydrogen bonds. In conformation A of polyglycine, in which the NH groups point away from the helix axis and the CO groups are nearer to the helix axis, the conformational energy is nearly the same for threefold and fourfold structures. However, the minimum energy conformation corresponds to a threefold structure of polyglycine with peptide configurations in conformation B in which the CO groups point away from the helix axis and NH groups are nearer to the helix axis. This structure is consistent with the polyglycine II x-ray diffraction data.     

Layer-by-layer growth of attractive binary colloidal particles

We investigate the two-dimensional (2D) colloidal structures formed by oppositely charged polystyrene monolayers grown layer-by-layer, where the electrostatic forces are recruited to assist in the packing of the layers. Our results show a transition through several 2D-superlattices to more close-packed structures with increasing ionic strength. The observed geometrical packing constraints of the 2D-superlattice structures agree well with the estimated Debye screening length of the electric double layer. By tuning interaction forces between charged colloids, electrostatic interactions could enhance the template-directed self-assembly process to achieve more complex and diverse structures.     

Aromatic Foldamer Helices as α-Helix Extended Surface Mimetics

Helically folded aromatic oligoamide foldamers have a size and geometrical parameters very distinct from those of α-helices and are not obvious candidates for α-helix mimicry. Nevertheless, they offer multiple sites for attaching side chains. It was found that some arrays of side chains at the surface of an aromatic helix make it possible to mimic extended α-helical surfaces. Synthetic methods were developed to produce quinoline monomers suitably functionalized for solid phase synthesis. A dodecamer was prepared. Its crystal structure validated the initial design and showed helix bundling involving the α-helix-like interface. These results open up new uses of aromatic helices to recognize protein surfaces and to program helix bundling in water.     

A Disulfide Switch Providing Absolute Handedness Control in Double Helices via Conversion from the Antiparallel to Parallel Helical Pattern

A strategy to reversibly switch the parallel/antiparallel helical conformation of aromatic double helices through the formation/breakage of a disulfide bond is presented. Single-crystal X-ray structures, NMR, and circular dichroism spectroscopy demonstrate that the double helices with terminal thiol groups favor an antiparallel helical arrangement both in the solid state and in solution, while the P/M bias of helicity induced by chiral segments from another extremity of the sequence is weak in this structural motif. The antiparallel helices can be rearranged to parallel helices through the disulfide connection of the sequences. This change enhances the bias of helical handedness and results in absolute chirality control of the double helices. The handedness-mediated process can be governed by the oxidation-reduction cycle, thereby switching the structural arrangement and the enhancement of chiral bias. In addition, we find that the sequences can dimerize into an intermolecular double helix with the disulfide connection. And the helical handedness is also fully controlled due to the head-to-head structural motif.     

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.     

Length-Dependent Collective Vibrational Dynamics in Alpha-Helices

Functions of protein molecules in nature are closely associated with their well-defined three-dimensional structures and dynamics in body fluid. So far, many efforts have been made to reveal the relation of protein structure, dynamics, and function, but the structural origin of protein dynamics, especially for secondary structures as building blocks of conformation transition, is still ambiguous. Here we theoretically uncover the collective vibrations of elastic poly-alanine α-helices and find vibration patterns that are distinctively different over residue numbers ranging from 20 to 80. Contrary to the decreasing vibration magnitude from ends to the middle region for short helices, the vibration magnitude for long helices takes the minimum at approximately 1/5 of helix length from ends but reaches a peak at the center. Further analysis indicates that major vibrational modes of helical structures strongly depend on their lengths, where the twist mode dominates in the vibrations of short helices while the bend mode dominates the long ones analogous to an elastic Euler beam. The helix-coil transition pathway is also affected by the alternation of the first-order mode in helices with different lengths. The dynamic properties of the helical polypeptides are promising to be harnessed for de novo design of protein-based materials and artificial biomolecules in clinical treatments.     

Conformational possibilities of double-helical nucleic acids: Theory and experiment

This survey covers the following topics: (1) Theoretical calculation of the total multitude of the energetically permitted regular DNA helices. (2) Theoretical study of flexibility of the double helix with emphasis on nucleosome structure. (3) Experimental data on the properties of the B to A transition of DNA in solution: the degree of cooperativity and influence of sequence. (4) The B -A transition and its possible role in genes activation.     

Multilayer DNA origami packed on hexagonal and hybrid lattices

"Scaffolded DNA origami" has been proven to be a powerful and efficient approach to construct two-dimensional or three-dimensional objects with great complexity. Multilayer DNA origami has been demonstrated with helices packing along either honeycomb-lattice geometry or square-lattice geometry. Here we report successful folding of multilayer DNA origami with helices arranged on a close-packed hexagonal lattice. This arrangement yields a higher density of helical packing and therefore higher resolution of spatial addressing than has been shown previously. We also demonstrate hybrid multilayer DNA origami with honeycomb-lattice, square-lattice, and hexagonal-lattice packing of helices all in one design. The availability of hexagonal close-packing of helices extends our ability to build complex structures using DNA nanotechnology.     

Solvation-Mediated Self-Assembly from Crystals to Helices of Protic Acyclic Carbene AuI-Enantiomers with Chirality Amplification

Constructing chiral supramolecular assembly and exploring the underlying mechanism are of great significance in promoting the development of circularly polarized luminescence (CPL)-active materials. Herein, we report a solvation-mediated self-assembly from single-crystals to helical nanofibers based on the first protic acyclic (methoxy)(amino)carbenes (pAMACs) Au^I-enantiomers driven by a synergetic aurophilic interactions and H-bonds. Their aggregation-dependent thermally activated delayed fluorescence properties with high quantum yields (Φ_FL) up to 95 % were proved to be attributed to packing modes of Au⋅⋅⋅Au dimers with π-stacking or one-dimensional extended Au⋅⋅⋅Au chains. Via drop-casting method, supramolecular P- or M-helices were prepared. Detailed studies on the helices demonstrate that formations of extended helical Au⋅⋅⋅Au molecular chains amplify supramolecular chirality, leading to strong CPL with high dissymmetry factor (|g_lum|=0.030, Φ_FL=67 %) and high CPL brightness (B_CPL) of 4.87×10⁻³. Our findings bring new insights into the fabrication of helical structures to improve CPL performance by modifying aurophilic interactions.     

α-Indolyl-β-nitroacrylates. Synthesis and structure

A one-pot procedure has been developed for the synthesis of α-indolyl-β-nitroacrylates by reaction of β-bromo-β-nitroacrilates with indole and substituted indoles. All indolylnitroacrilates thus obtained have Z configuration of the double bond. According to the X-ray diffraction data, ethyl 2-(1-methyl-1H-indol-3-yl)-3-nitroacrylate is characterized by s-trans conformation of the double C=C bond and indole ring; its crystal packing involves intermolecular hydrogen bonds C-H…O and C-H…π with formation of centrosymmetric dimers which give rise to bilayer supramolecular structures.     

Structural relationships in close-packed AB2O4 oxides involving spinel,olivine, and hexagonal LiFeSnO4 structures

Close-packed structures with formula AB₂O₄ were studied in terms of polyhedra arrangement. The junction between octahedral layers (kagome) and mixed (octahedral and tetrahedral) layers were analyzed; this association allows one to determine two types of double layers whose packing leads to three closely related structural types: spinel, double-hexagonal LiFeSnO₄, and a hypothetical hexagonal structure. Olivine structure shows a polyhedral arrangement closely related to those of these three structures and can be described alike in terms of mixed layers and double layers. AB₂O₄ close-packed oxides can exhibit polymorphism; from this analysis a mechanism, involving geometrical operations applied to the double layers, is proposed for the different transitions, really observed as (DH) LiFeSnO₄ spinel and olivine-spinel or theoretical as (DH) LiFeSnO₄—hypothetical hexagonal and olivine—hypothetical hexagonal.     

Chalcogen-Bond-Induced Double Helix Based on Self-Assembly of a Small Planar Building Block

As a rule, helical structures at the molecular level are formed by non-planar units. This makes the design of helices, starting from planar building blocks via self-assembly, even more fascinating. Until now, however, this has only been achieved in rare cases, where hydrogen and halogen bonds were involved. Here, we show that the carbonyl-tellurium interaction motif is suitable to assemble even small planar units into helical structures in solid phase. We found two different types of helices: both single and double helices, depending on the substitution pattern. In the double helix, the strands are connected by additional Te⋅⋅⋅Te chalcogen bonds. In the case of the single helix, a spontaneous enantiomeric resolution occurs in the crystal. This underlines the potential of the carbonyl-tellurium chalcogen bond to generate complex three-dimensional patterns.     

Predictions of compounds in the family of delafossites

This paper reports the results of our crystal-chemical analysis of structures from the delafossite family A⁺B³⁺X₂, where A and B are cations, and is oxygen. The family is represented by structures of two types, CuFeO₂ and α-NaFeO₂ (R \(\bar 3\) m, Z = 1). Predictions of new compounds are presented. About a hundred new crystals can be synthesized.     

A modular strategy for generating starting conformations and data structures of polynucleotide helices for potential energy calculations

We describe a simple and rapid algorithm for generating data structures and starting coordinates of polynucleotides for potential energy calculations. The algorithm is tailored to investigations in cartesian coordinate, rather than dihedral angle, space. First, instead of a tree structure for molecular design, we set up a helix from a simple list of bonds for the basic DNA subunits (sugar, phosphate, and bases). Second, instead of using successive transformations to obtain a set of coordinates in one reference frame, we apply a simple “matching” routine to patch DNA subunits. Third, we avoid ring closure and geometry optimization by allowing deviations from equilibrium values only for P? O3′ bond lengths and O5′? P? O3′ bond angles at the residue connection sites. A double-stranded helix is constructed from duplex building blocks (2 hydrogen-bonded nucleotides) which are in turn built from the basic structural units. Every building block is constructed from two sets of geometric variables: {α, β, γ, χ, P, τ_max}, one for each strand. The building blocks are then assembled into a helix by using the 6 rigid body transformations {Δx, Δy, Δz, Θ_ROLL , Θ_TILT , Θ_TWIST }. For cartesian space programs, generating starting coordinates by this procedure is particularly useful as an alternative to using actual crystal structure coordinates. After describing the algorithm in detail, we illustrate how it was used to generate model A, B, and Z DNA helices. We conclude by suggesting how the algorithm can be used to pursue a build-up technique and to set up a wide range of starting conformations in the goal of locating novel helical structures.     

Chiral tether-mediated stabilization and helix-sense control of complementary metallo-double helices

A series of novel Pt^II-linked double helices were prepared by inter- or intrastrand ligand-exchange reactions of the complementary duplexes composed of chiral or achiral amidine dimer and achiral carboxylic acid dimer strands joined by trans-Pt^II–acetylide complexes with PPh₃ ligands using chiral and achiral chelating diphosphines. The structure and stability of the Pt^II-linked double helices were highly dependent on the diphosphine structures. An interstrand ligand exchange took place with chiral and achiral 1,3-diphosphine-based ligands, resulting in trans-Pt^II-bridged double helices, whose helical structures were quite stable even in dimethyl sulfoxide (DMSO) due to the interstrand cross-link, whereas a 1,2-diphosphine-based ligand produced non-cross-linked cis-Pt^II-linked duplexes, resulting from an intrastrand ligand-exchange that readily dissociated into single strands in DMSO. When enantiopure 1,3-diphosphine-based ligands were used, the resulting trans-Pt^II-bridged double helices adopted a preferred-handed helical sense biased by the chirality of the bridged diphosphines. Interestingly, the interstrand ligand exchange with racemic 1,3-diphosphine toward an optically-active Pt^II-linked duplex, composed of chiral amidine and achiral carboxylic acid strands, was found to proceed in a diastereoselective manner, thus forming complete homochiral trans-Pt^II-bridged double helices via a unique chiral self-sorting.     

Enantioselective Assembly of a Ruthenium(II) Polypyridyl Complex into a Double Helix

Evolution can increase the complexity of matter by self‐organization into helical architectures, the best example being the DNA double helix. One common aspect, apparently shared by most of these architectures, is the presence of covalent bonds within the helix backbone. Here, we report the unprecedented crystal structures of a metal complex that self‐organizes into a continuous double helical structure, assembled by non‐covalent building blocks. Built up solely by weak stacking interactions, this alternating tread stairs‐like double helical assembly mimics the DNA double helix structure. Starting from a racemic mixture in aqueous solution, the ruthenium(II) polypyridyl complex forms two polymorphic structures of a left‐handed double helical assembly of only the Λ‐enantiomer. The stacking of the helices is different in both polymorphs: a crossed woodpile structure versus a parallel columnar stacking.     

HELFIT: Helix fitting by a total least squares method

The problem of fitting a helix to data arises in analysis of protein structure, in nuclear physics, and in engineering. A continuous helix is described by five parameters: helix axis, helix radius, and helix pitch. One of these helix parameters is frequently predefined in the helix fitting. Other algorithms find only the helix axis or determine separately the helix axis, the helix radius, or the helix pitch. Here we describe a total least squares method, HELFIT, for helix fitting. HELFIT enables one to calculate simultaneously all five of the helix parameters with high accuracy. The minimum number of data points required for the analysis is only four. HELFIT is very insensitive to noise even in short helices. HELFIT also calculates a parameter, p = rmsd/(N − 1)^1/2, which estimates the regularity of helical structures independent of the number of data points, where rmsd is the root mean square distance from the best-fit helix to data points and N is the number of data points. It should become a basic tool of structural bioinformatics.     

GXXXG‐Mediated Parallel and Antiparallel Dimerization of Transmembrane Helices and Its Inhibition by Cholesterol: Single‐Pair FRET and 2D IR Studies

Small‐residue‐mediated interhelical packings are ubiquitously found in helical membrane proteins, although their interaction dynamics and lipid dependence remain mostly uncharacterized. We used a single‐pair FRET technique to examine the effect of a GXXXG motif on the association of de novo designed (AALALAA)₃ helices in liposomes. Dimerization occurred with sub‐second lifetimes, which was abolished by cholesterol. Utilizing the nearly instantaneous time‐resolution of 2D IR spectroscopy, parallel and antiparallel helix associations were identified by vibrational couplings across helices at their interface. Taken together, the data illustrate that the GXXXG motif controls helix packing but still allows for a dynamic and lipid‐regulated oligomeric state.     

Evolution of Helical Mesostructures

An intriguing evolution from a simple internal helix to a hierarchical helical (HH) mesostructure with both internal and external helices or a complicated screwlike and concentric circular (CC) mesostructure is successfully observed. The complicated helical structures are determined by TEM studies and 3D electron tomography. We demonstrate a topological helix–coil transition between the internal and external helices to reveal the origin of the HH mesostructure and the relationship between the straight helical and HH rods. Moreover, the boundary condition of the helix–coil transition is clarified to explain in detail the formation of complex helical structures, such as the screwlike mesostructure. It is proposed that the final structural characteristics are determined exactly by the balance between the decrease in the surface free energy and the maintenance of the hexagonal packing in one individual rod, which explains the formation of unusual CC, HH, and screwlike morphologies in one pot. Our success has opened new opportunities in the characterization of complex porous architectures, thus paving a way to remarkable advances in the fields of synthesis, understanding, and application of novel porous materials.