Formation of fibrillar aggregates in concentrated solutions of rigid-chain amphiphilic macromolecules with fixed torsion and bend angles

The molecular-dynamics method is used to study solutions of amphiphilic macromolecules with a local helical structure. A deterioration in the solvent quality in concentrated solutions of these macromolecules leads to the formation of intermolecular fibrillar helix bundles with approximately the same lengths and aggregation numbers. The number of chains in a bundle is determined by parameters that characterize the local structure and is weakly dependent on the length of the macromolecule and the volume fraction of the polymer in the solution. In racemic mixtures of these macromolecules, a deterioration in the solvent quality leads to effective demixing; that is, the resultant fibrillar bundles generally contain macromolecules of exclusively the same chirality.     

Mechanism of shear deformation of a coiled myosin coil: Computer simulation

Polymer coiled coils are composed of entangled linear chains in a helical conformation. Their mechanical characteristics are interesting because these structures are involved in the composition of natural fibrillar structures. The method of molecular dynamics is used for the simulation of stretching at a constant rate for a superhelical fragment of myosin protein composed of two identical α helices containing 126 amino acid residues in each helix. The case of shear deformation of a molecule is considered (the load is applied to the N terminus of one chain and to the C terminus of another chain). In this case of loading, slippage of chains with respect to each other can occur. Deformation of a molecule proceeds in several stages. At the initial stage, the superhelix is unfolded and there is a gradual unfolding of end fragments of individual α helices; this process is accompanied by their displacement with respect to the helical fragment of the neighboring chain. In this case, the reaction force increases. At the second stage of stretching, the process passes to the mechanism of deformation when, in the central part of the molecule, α-helical fragments of both chains unfold. In this region, the reaction-force-extension curve shows a plateau region. Between unfolded fragments, new hydrophobic contacts and hydrogen bonds are formed, and fragments of the β structure emerge. Once all turns of α helices in the central parts of the molecule are unfolded, the mechanism of deformation changes and further extension of a molecule proceeds via straightening of previously unfolded central fragments, a process that is accompanied by an increase in the reaction force. When chains achieve their limiting extension, slippage commences with an accompanying decrease in the reaction force.     

Self-organization of amphiphilic macromolecules with local helix structure in concentrated solutions

Concentrated solutions of amphiphilic macromolecules with local helical structure were studied by means of molecular dynamic simulations. It is shown that in poor solvent the macromolecules are assembled into wire-like aggregates having complex core-shell structure. The core consists of a hydrophobic backbone of the chains which intertwine around each other. It is protected by the shell of hydrophilic side groups. In racemic mixture of right-hand and left-hand helix macromolecules the wire-like complex is a chain of braid bundles of macromolecules with the same chirality stacking at their ends. The average number of macromolecules in the wire cross-section is close to that of separate bundles observed in dilute solutions of such macromolecules. The effects described here could serve as a simple model of self-organization in solutions of macromolecules with local helical structure.     

Engineering a β‐Helical d,l‐Peptide for Folding in Polar Media

β Helices—helices formed by alternating d,l ‐peptides and stabilized by β‐sheet hydrogen bonding—are found naturally in only a handful of highly hydrophobic peptides. This paper explores the scope of β‐helical structure by presenting the first design and biophysical characterization of a hydrophilic d,l ‐peptide, 1 , that forms a β helix in methanol. The design of 1 is based on the β‐hairpin/β helix—a new supersecondary that had been characterized previously only for hydrophobic peptides in nonpolar solvents. Incorporating polar residues in 1 provided solubility in methanol, in which the peptide adopts the expected β‐hairpin/β‐helical structure, as evidenced by CD, analytical ultracentrifugation (AUC), NMR spectroscopy, and NMR‐based structure calculations. Upon titration with water (at constant peptide concentration), the structure in methanol ( 1 m ) transitions cooperatively to an extended conformation ( 1 w ) resembling a cyclic β‐hairpin; observation of an isodichroic point in the solvent‐dependent CD spectra indicates that this transition is a two‐state process. In contrast, neither 1 m nor 1 w show cooperative thermal melting; instead, their structures appear intact at temperatures as high as 65 °C; this observation suggests that steric constraint is dominant in stabilizing these structures. Finally, the ¹H NMR CαH spectroscopic resonances of 1 m are downfield‐shifted with respect to random‐coil values, a hitherto unreported property for β helices that appears to be a general feature of these structures. These results show for the first time that an appropriately designed β‐helical peptide can fold stably in a polar solvent; furthermore, the structural and spectroscopic data reported should prove useful in the future design and characterization of water‐soluble β helices.     

Analysis of stacking overlap in nucleic acid structures: algorithm and application

RNA contains different secondary structural motifs like pseudo-helices, hairpin loops, internal loops, etc. in addition to anti-parallel double helices and random coils. The secondary structures are mainly stabilized by base-pairing and stacking interactions between the planar aromatic bases. The hydrogen bonding strength and geometries of base pairs are characterized by six intra-base pair parameters. Similarly, stacking can be represented by six local doublet parameters. These dinucleotide step parameters can describe the quality of stacking between Watson–Crick base pairs very effectively. However, it is quite difficult to understand the stacking pattern for dinucleotides consisting of non canonical base pairs from these parameters. Stacking interaction is a manifestation of the interaction between two aromatic bases or base pairs and thus can be estimated best by the overlap area between the planar aromatic moieties. We have calculated base pair overlap between two consecutive base pairs as the buried van der Waals surface between them. In general, overlap values show normal distribution for the Watson–Crick base pairs in most double helices within a range from 45 to 50 Å² irrespective of base sequence. The dinucleotide steps with non-canonical base pairs also are seen to have high overlap value, although their twist and few other parameters are rather unusual. We have analyzed hairpin loops of different length, bulges within double helical structures and pseudo-continuous helices using our algorithm. The overlap area analyses indicate good stacking between few looped out bases especially in GNRA tetraloop, which was difficult to quantitatively characterise from analysis of the base pair or dinucleotide step parameters. This parameter is also seen to be capable to distinguish pseudo-continuous helices from kinked helix junctions.     

Secondary globular structure of copolymers containing amphiphilic and hydrophilic units: Computer simulation analysis

The coil-globule transition in copolymers composed of amphiphilic and hydrophilic monomer units has been studied by the computer simulation technique. It has been shown that the structure of globules formed in such systems substantially depends on the rate at which the solvent quality worsens. The globule resulting from slow cooling is cylindrical, and its core contains a large amount of hydrophilic groups. The globule formed upon rapid cooling takes the helical conformation, in which all hydrophilic groups are displaced to the periphery. One helix turn of such globules contains 3–5 units. In both cases, the backbone of the polymer chain forms a typical zigzag-shaped structure with an average angle between neighboring bond vectors of about 60°. This fact implies that globules of copolymers consisting of amphiphilic and hydrophilic units comprise secondary structure components.     

Effects of hydrophobic and dipole-dipole interactions on the conformational transitions of a model polypeptide

We studied the effects of hydrophobicity and dipole-dipole interactions between the nearest-neighbor amide planes on the secondary structures of a model polypeptide by calculating the free energy differences between different peptide structures. The free energy calculations were performed with low computational costs using the accelerated Monte Carlo simulation (umbrella sampling) method, with a bias-potential method used earlier in our accelerated molecular dynamics simulations. It was found that the hydrophobic interaction enhances the stability of alpha helices at both low and high temperatures but stabilizes beta structures only at high temperatures at which alpha helices are not stable. The nearest-neighbor dipole-dipole interaction stabilizes beta structures under all conditions, especially in the low temperature region where alpha helices are the stable structures. Our results indicate clearly that the dipole-dipole interaction between the nearest neighboring amide planes plays an important role in determining the peptide structures. Current research provides a more unified and quantitative picture for understanding the effects of different forms of interactions on polypeptide structures. In addition, the present model can be extended to describe DNA/RNA, polymer, copolymer, and other chain systems.     

Delta-peptides and delta-amino acids as tools for peptide structure design--a theoretical study

An overview on all possible helix types in oligomers of delta-amino acids (delta-peptides) and their stabilities is given on the basis of a systematic conformational analysis employing various methods of ab initio MO theory (HF/6-31G*, B3LYP/6-31G*, PCM//HF/6-31G*). A wide variety of novel helical structures with hydrogen-bonded pseudocycles of different size are predicted. Since a delta-amino acid constituent may replace a dipeptide unit in alpha-peptides, there are close relationships between the secondary structures of peptides with delta-amino acid residues and typical secondary structures of alpha-peptides. However, the preference of gauche conformations at the central C(beta)-C(gamma) bonds of delta-amino acids, which correspond to the peptide linkages in alpha-peptides, over staggered ones makes completely novel structure alternatives for helices and turns more probable. The peculiarities of beta-turn formation by sugar amino acids derived from delta-amino acids are compared with the turn formation in delta-amino acid residues and in alpha-peptides. The considerable potential of secondary structure formation in delta-peptides and single delta-amino acid constituents predicted by ab initio MO theory may stimulate experimental work in the field of peptide and foldamer design.     

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.     

A general procedure for building the transmembrane domains of G‐protein coupled receptors

The only results available at present about the structural features of G‐protein coupled receptors are the low resolution electron projection maps obtained from microscopy studies carried out on two‐dimensional crystals of rhodopsin. These studies support previous suggestions that these integral proteins are constituted by seven transmembrane domains. The low resolution electron density map of rhodopsin can be used to extract information about helix relative positions and tilt. This information, together with a reliable procedure to assess the residues involved in each of the transmembrane regions, can be used to construct a model of rhodopsin at atomic resolution. We have developed an algorithm that can be used to generate such a model in a completely automated fashion. The steps involved are: (i) locate the centers of the helices according to the low resolution electron density map; (ii) compute the tilt of each helix based on the elliptical shape observed by each helix in the map; (iii) define a local coordinate system for each of the helices; (iv) bring them together in an antiparallel orientation; (v) rotate each helix through the helical axis in such a way that its hydrophobic moment points in the same direction as the bisector formed between three consecutive helices in the bundle; (vi) rotate each helix through an axis perpendicular to the helical one to assign a proper tilt; (vii) translate each of the helix to its center deduced from the projection map. A major advantage of the procedure presented is its generality and consequently can be used to obtain a model of any G‐protein coupled receptor with the only assumption that the shape of the bundle is the same as found in rhodopsin. This avoids uncertainties found in other procedures that construct models of G‐protein coupled receptors based on sequence homology using rhodopsin as template. This revised version was published online in July 2006 with corrections to the Cover Date.     

Flaws in foldamers: conformational uniformity and signal decay in achiral helical peptide oligomers

Although foldamers, by definition, are extended molecular structures with a well-defined conformation, minor conformers must be populated at least to some extent in solution. We present a quantitative analysis of these minor conformers for a series of helical oligomers built from achiral but helicogenic α-amino acids. By measuring the chain length dependence or chain position dependence of NMR or CD quantities that measure screw-sense preference in a helical oligomer, we quantify values for the decay constant of a conformational signal as it passes through the molecular structure. This conformational signal is a perturbation of the racemic mixture of M and P helices that such oligomers typically adopt by the inclusion of an N or C terminal chiral inducer. We show that decay constants may be very low (<1% signal loss per residue) in non-polar solvents, and we evaluate the increase in decay constant that results in polar solvents, at higher temperatures, and with more conformationally flexible residues such as Gly. Decay constants are independent of whether the signal originates from the N or the C terminus. By interpreting the decay constant in terms of the probability with which conformations containing a screw-sense reversal are populated, we quantify the populations of these alternative minor conformers within the overall ensemble of secondary structures adopted by the foldamer. We deduce helical persistence lengths for Aib polymers that allow us to show that in a non-polar solvent a peptide helix, even in the absence of chiral residues, may continue with the same screw sense for approximately 200 residues.     

The generic geometry of helices and their close-packed structures

The formation of helices is an ubiquitous phenomenon for molecular structures whether they are biological, organic, or inorganic, in nature. Helical structures have geometrical constraints analogous to close-packing of three-dimensional crystal structures. For helical packing the geometrical constraints involve parameters such as the radius of the helical cylinder, the helical pitch angle, and the helical tube radius. In this communication, the geometrical constraints for single helix, double helix, and for double helices with minor and major grooves are calculated. The results are compared with values from the literature for helical polypeptide backbone structures, the α-, π-, 3₁₀-, and γ-helices. The α-helices are close to being optimally packed in the sense of efficient use of space, i.e. close-packed. They are also more densely packed than the other three types of helices. For double helices comparisons are made to the A, B, and Z forms of DNA. The helical geometry of the A form is nearly close-packed. The packing density for the B and Z forms of DNA are found to be approximately equal to each other.     

Tight β-turns in peptides. DFT-based study of infrared absorption and vibrational circular dichroism for various conformers including solvent effects

Vibrational circular dichroism (VCD) has had a large impact on configurational studies of organic molecules largely due to the theoretical advances made by Philip Stephens and co-workers. For peptides, the structural issue is not one of the configuration, but of conformation, and the flexibility of the oligomeric structure raises major computational challenges. Turns are a vital aspect of peptide and protein conformation that allow such structures to fold into a compact unit. However, unlike helices and sheets, they are not extended repeating structures, but each residue has a different local conformation. Also, when turns are part of larger peptides their termini are connected to completely different structural elements. We have done extended comparative density functional theory (DFT) computations to characterize the expected spectral contributions of selected turn structures to the amide IR and VCD spectra of peptides. The isolated vacuum results for tri-amide turns (Ac-X-Y-NH₂) of a few different sequences are compared with calculations involving correction for solvation effects. In particular, we looked at the sequence variation in spectra and structure between Ala-Ala, Aib-Gly and D-Pro-Gly for the turn-specific X–Y residues. The nature of some turn-associated, amide originating, spectral transitions are developed and tested.     

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.     

A novel type of optically active helical polymers: Synthesis and characterization of poly(N‐propargylureas)

This article presents two novel artificial helical polymers, substituted polyacetylenes with urea groups in side chains. Poly( 4 ) and poly( 5 ) can be obtained in high yields (≥97%) and with moderate molecular weights (11,000–14,000). Poly( 4 ) contains chiral centers in side chains, and poly( 5 ) is an achiral polymer. Both of the two polymers adopted helical structures under certain conditions. More interestingly, poly( 4 ) exhibited large specific optical rotations, resulting from the predominant one‐handed screw sense. The helical conformation in poly( 5 ) was stable against heat, while poly( 4 ) underwent conformational transition from helix to random coil upon increasing temperature from 0 to 55 °C. Solvents had considerable influence on the stability of the helical conformation in poly( 4 ). The screw sense adopted by the helices was also largely affected by the nature of the solvent. Poly( 4 ‐co‐ 5 )s formed helical conformation and showed large optical rotations, following the Sergeants and Soldiers rule. By comparing the present two polymers (with one ? N? H groups) with the three polymers previously reported (with two ? N? H groups in side chains), the nature of the hydrogen bonds formed between the neighboring urea groups played big roles in the formation of stable helical conformation. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 4112–4121, 2008     

Theoretical study of helix formation in substituted phenylene ethynylene oligomers

Theoretical investigations of the relative stabilities of helical vs extended forms of phenylene ethynylene oligomers established that MMFF molecular mechanics was more useful than AM1 or DFT for calculating helical structures and for estimating relative energies. At the level of MMFF, theory predicts that for o- or m-oligophenylene ethynylenes, helix formation is enthalpically favored for ester and ether-substituted oligomers. In contrast to simple electron-demand predictions, we predict that the position of substituents can make a substantial difference in the tendency to form helices.     

MD simulations of homomorphous PNA, DNA, and RNA single strands: characterization and comparison of conformations and dynamics

MD simulations of homomorphous single-stranded PNA, DNA, and RNA with the same base sequence have been performed in aqueous solvent. For each strand two separate simulations were performed starting from a (i) helical conformation and (ii) random coiled state. Comparisons of the simulations with the single-stranded helices (case i) show that the differences in the covalent nature of the backbones cause significant differences in the structural and dynamical properties of the strands. It is found that the PNA strand maintains its nice base-stacked initial helical structure throughout the 1.5-ns MD simulation at 300 K, while DNA/RNA show relatively larger fluctuations in the structures with a few local unstacking events during -ns MD simulation each. It seems that the weak physical coupling between the bases and the backbone in PNA causes a loss of correlation between the dynamics of the bases and the backbone compared to the DNA/RNA and helps maintain the base-stacked helical conformation. The global flexibility of a single-stranded PNA helix was also found to be lowest, while RNA appears to be the most flexible single-stranded helix. The sugar pucker of several nucleotides in single-stranded DNA and RNA was found to adopt both C2'-endo and C3'-endo conformations for significant times. This effect is more pronounced for single strands in completely coiled states. The simulations with single-stranded coils as the initial structure also indicate that a PNA can adopt a more compact globular structure, while DNA/RNA of the same size adopts a more extended coil structure. This allows even a short PNA in the coiled state to form a significantly stable nonsequentially base-stacked globular structure in solution. Due to the hydrophobic nature of the PNA backbone, it interacts with surrounding water rather weakly compared to DNA/RNA.     

Probing possible left- and right-handed poly(dinucleotide) helical conformations from (n–h) plots. models for polysequential nucleotides

Introducing the concept of the “dinucleotide” as the helical repeat, theoretical attempts have been made to determine possible single and double stranded helical structures by using helical parameter calculations and model building investigations. By virtue of its flexible framework, the dinucleotide repeat offers a much greater scope of finding new secondary structural forms for nucleic acids. Considering only those conformations which show tendency for at least partial base overlap as does the dinucleotide helical repeat, it has been possible to predict poly(dinucleotide) helical models in which successive phosphodiesters as well as nucleotide conformations alternate. More important, the recently found left-handed Z-type polynucleotide helix is characterized rather uniquely on the helical parameter plot. The results further suggest the possibility of other Z-type helices obtainable by alternative conformations for the exocyclic C4'–C5' bond and sugar pucker. Near neighbor long range conformational correlations between the dinucleotide repeat and the phosphodiester linking them have been established similar to poly(mononucleotide) helices. Need for considering higher repeats such as trinucleotide has been suggested to obtain models for looped out helical conformations.     

Relative helix-helix conformations in branched aromatic oligoamide foldamers

The de novo design and synthesis of large and well-organized, tertiary-like, α-peptidic folded architectures is difficult because it relies on multiple cooperative interactions within and between secondary folded motifs of relatively weak intrinsic stability. The very stable helical structures of oligoamides of 8-amino-2-quinoline carboxylic acid offer a way to circumvent this difficulty thanks to their ability to fold into predictable and stable secondary motifs. Branched architectures comprised of two pairs of tetrameric (1), pentameric (2), or octameric (3) oligomers connected via an ethylene glycol spacer were designed and synthesized. The short spacer holds two helices in close proximity, thus enabling interactions between them. Degrees of freedom allowed in the system are well-defined: the relative P or M handedness of the two helices; the relative orientation of the helix axes; and the gauche or anti conformation of the ethylene spacer. Investigating the structures of 1-3 in the solid state and in solution allowed a detailed picture to be drawn of their conformational preferences and dynamics. The high variability of the solid state structures provides many snapshots of possible solution conformations. Helix-helix handedness communication was evidenced and shown to depend both on solvent and on a defined set of side chains at the helix-helix interface. Interdigitation of the side chains was found to restrict free rotation about the ethylene spacer. One solid state structure shows a high level of symmetry and provides a firm basis to further design specific side chain/side chain directional interactions.     

Proteins that convert from alpha helix to beta sheet: implications for folding and disease

The sequence of a protein normally determines which amino acid residues will form alpha helices, and which one beta sheets, to an extent that allows secondary structure prediction to be made with a reasonable reliability. Nevertheless, non-native helical structures are observed during in vitro folding of several model proteins and may even occur during protein biosynthesis within the ribosomal exit tunnel. Moreover, non-native beta sheet structures are common in amyloid fibrils formed by a variety of pathogenic and even non-pathogenic proteins and peptides. In all of these cases, the formation of alpha helix precedes the appearance of beta sheet, which suggests that conversion from the simpler, more local helix structure to the often more convoluted sheet architecture during folding and pathogenic misfolding processes could be a unifying principle of general importance. A better understanding of this switching process, and the ability to design molecular systems which can be induced to switch between these conformations will have a significant impact on fields ranging from fundamental biochemistry through to applied technology and medicine.