Evolution of three-dimensional folds for a non-Newtonian plate in a viscous medium

We derive analytical solutions for the three-dimensional time-dependent buckling of a non-Newtonian viscous plate in a less viscous medium. For the plate we assume a power-law rheology. The principal, axes of the stretching D-ij in the homogeneously deformed ground state are parallel and orthogonal to the bounding surfaces of the plate in the flat state. In the model formulation the action of the less viscous medium is replaced by equivalent reaction forces. The reaction forces are assumed to be parallel to the normal vector of the deformed plate surfaces. As a consequence, the buckling process is driven by the differences between the in-plane stresses and out of plane stress, and not by the in-plane stresses alone as assumed in previous models. The governing differential equation is essentially an orthotropic plate equation for rate dependent material, under biaxial pre-stress, supported by a viscous medium. The differential problem is solved by means of Fourier transformation and largest growth coefficients and corresponding wavenumbers are evaluated. We discuss in detail fold evolutions for isotropic in-plane stretching (D-11 = D-22), uniaxial plane straining (D-22 = 0) and in-plane flattening (D-11 = -2D(22)). Three-dimensional plots illustrate the stages of fold evolution for random initial perturbations or initial embryonic folds with axes non-parallel to the maximum compression axis. For all situations, one dominant set of folds develops normal to D-11, although the dominant wavelength differs from the Biot dominant wavelength except when the plate has a purely Newtonian viscosity. However, in the direction parallel to D-22, there exist infinitely many modes in the vicinity of the dominant wavelength which grow only marginally slower than the one corresponding to the dominant wavelength. This means that, except for very special initial conditions, the appearance of a three-dimensional fold will always be governed by at least two wavelengths. The wavelength in the direction parallel to D-11 is the dominant wavelength, and the wavelength(s) in the direction parallel to D-22 is determined essentially by the statistics of the initial state. A comparable sensitivity to the initial geometry does not exist in the classic two-dimensional folding models. In conformity with tradition we have applied Kirchhoff's hypothesis to constrain the cross-sectional rotations of the plate. We investigate the validity of this hypothesis within the framework of Reissner's plate theory. We also include a discussion of the effects of adding elasticity into the constitutive relations and show that there exist critical ratios of the relaxation times of the plate and the embedding medium for which two dominant wavelengths develop, one at ca. 2.5 of the classical Biot dominant wavelength and the other at ca. 0.45 of this wavelength. We propose that herein lies the origin of parasitic folds well known in natural examples.

The solution structure of the N-terminal zinc finger of GATA-1 reveals a specific binding face for the transcriptional co-factor FOG

Zinc fingers (ZnFs) are generally regarded as DNA-binding motifs. However, a number of recent reports have implicated particular ZnFs in the mediation of protein-protein interactions. The N-terminal ZnF of GATA-1 (NF) is one such finger, having been shown to interact with a number of other proteins, including the recently discovered transcriptional co-factor FOG. Here we solve the three-dimensional structure of the NF in solution using multidimensional H-1/N-15 NMR spectroscopy, and we use H-1/N-15 spin relation measurements to investigate its backbone dynamics. The structure consists of two distorted beta-hairpins and a single alpha-helix, and is similar to that of the C-terminal ZnF of chicken GATA-1. Comparisons of the NF structure with those of other C-4-type zinc binding motifs, including hormone receptor and LIM domains, also reveal substantial structural homology. Finally, we use the structure to map the spatial locations of NF residues shown by mutagenesis to be essential for FOG binding, and demonstrate that these residues all lie on a single face of the NE Notably, this face is well removed from the putative DNA-binding face of the NE an observation which is suggestive of simultaneous roles for the NF; that is, stabilisation of GATA-1 DNA complexes and recruitment of FOG to GATA-1-controlled promoter regions.

Detection of lead(II) and silver(I) in aqueous solution using a piezoelectric device

The gold surface of a quartz crystal microbalance was modified by the attachment of silica particles derivatised with N-[(3-trimethoxysilyl)propyl] ethylenediaminetriacetic acid. The device was employed to study the kinetics of the interaction of aqueous solutions of lead(II) nitrate and silver(I) nitrate with the surface and for the selective separation of the metal ions.

Solution structure of alpha-conotoxin ImI by H-1 nuclear magnetic resonance

alpha-Conotoxin ImI derives from the venom of Conus imperialis and is the first and only small-peptide ligand that selectively binds to the neuronal alpha(7) homopentameric subtype of the nicotinic acetylcholine receptor (nAChR). This receptor subtype is a possible drug target for several neurological disorders. The cysteines are connected in the pairs Cys2-Cys8 and Cys3-Cys12, To date it is the only alpha-conotoxin with a 4/3 residue spacing between the cysteines, The structure of ImI has been determined by H-1 NMR spectroscopy in aqueous solution, The NMR structure is of high quality, with a backbone pairwise rmsd of 0.34 Angstrom for a family of 19 structures, and comprises primarily a series of nested beta turns. Addition of organic solvent does not perturb the solution structure. The first eight residues of ImI are identical to the larger, but related, conotoxin EpI and adopt a similar structure, despite a truncated second loop. Residues important for binding of ImI to the alpha 7 nAChR are all clustered on one face of the molecule. Once further binding data for EPI and ImI are available, the ImI structure will allow for design of novel alpha(7) nAChR-specific agonists and antagonists with a wide range of potential pharmaceutical applications.

A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements

To translate and transfer solution data between two totally different meshes (i.e. mesh 1 and mesh 2), a consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements is presented in this paper. The proposed algorithm has the following significant advantages: (1) The use of a point-searching strategy allows a point in one mesh to be accurately related to an element (containing this point) in another mesh. Thus, to translate/transfer the solution of any particular point from mesh 2 td mesh 1, only one element in mesh 2 needs to be inversely mapped. This certainly minimizes the number of elements, to which the inverse mapping is applied. In this regard, the present algorithm is very effective and efficient. (2) Analytical solutions to the local co ordinates of any point in a four-node quadrilateral element, which are derived in a rigorous mathematical manner in the context of this paper, make it possible to carry out an inverse mapping process very effectively and efficiently. (3) The use of consistent interpolation enables the interpolated solution to be compatible with an original solution and, therefore guarantees the interpolated solution of extremely high accuracy. After the mathematical formulations of the algorithm are presented, the algorithm is tested and validated through a challenging problem. The related results from the test problem have demonstrated the generality, accuracy, effectiveness, efficiency and robustness of the proposed consistent point-searching algorithm. Copyright (C) 1999 John Wiley & Sons, Ltd.

Solution structure of a defensin-like peptide from platypus venom

Three defensin-like peptides (DLPs) were isolated from platypus venom and sequenced. One of these peptides, DLP-1, was synthesized chemically and its three-dimensional structure was determined using NMR spectroscopy. The main structural elements of this 42-residue peptide were an anti-parallel beta-sheet comprising residues 15-18 and 37-40 and a small 3(10) helix spanning residues 10-12. The overall three-dimensional fold is similar to that of beta-defensin-12, and similar to the sodium-channel neurotoxin ShI (Stichodactyla helianthus neurotoxin I). However, the side chains known to be functionally important in beta-defensin-12 and ShI are not conserved in DLP-1, suggesting that it has a different biological function. Consistent with this contention, we showed that DLP-1 possesses no anti-microbial properties and has no observable activity on rat dorsal-root-ganglion sodium-channel currents.

Solution structures in aqueous SDS micelles of two amyloid beta peptides of A beta(1-28) mutated at the alpha-secretase cleavage site (K16E, K16F)

NMR solution structures are reported for two mutants (K16E, K16F) of the soluble amyloid beta peptide A beta(1-28). The structural effects of these mutations of a positively charged residue to anionic and hydrophobic residues at the alpha-secretase cleavage site (Lys16-Leu17) were examined in the membrane-simulating solvent aqueous SDS micelles. Overall the three-dimensional structures were similar to that for the native A beta(1-28) sequence in that they contained an unstructured N-terminus and a helical C-terminus. These structural elements are similar to those seen in the corresponding regions of full-length A beta peptides A beta(1-40) and A beta(1-42), showing that the shorter peptides are valid model systems. The K16E mutation, which might be expected to stabilize the macrodipole of the helix, slightly increased the helix length (residues 13-24) relative to the K16F mutation, which shortened the helix to between residues 16 and 24. The observed sequence-dependent control over conformation in this region provides an insight into possible conformational switching roles of mutations in the amyloid precursor protein from which A beta peptides are derived. In addition, if conformational transitions from helix to random coil to sheet precede aggregation of A beta peptides in vivo, as they do in vitro, the conformation-inducing effects of mutations at Lys16 may also influence aggregation and fibril formation. (C) 2000 Academic Press.

Three-dimensional structure of RK-1: A novel alpha-defensin peptide

NMR spectroscopy and simulated annealing calculations have been used to determine the three-dimensional structure of RK-1, an antimicrobial peptide from rabbit kidney recently discovered from homology screening based on the distinctive physicochemical properties of the corticostatins/defensins. RK-1 consists of 32 residues, including six cysteines arranged into three disulfide bonds. It exhibits antimicrobial activity against Escherichia coli and activates Ca2+ channels in vitro. Through its physicochemical similarity, identical cysteine spacing, and linkage to the corticostatins/defensins, it was presumed to be a member of this family. However, RK-1 lacks both a large number of arginines in the primary sequence and a high overall positive charge, which are characteristic of this family of peptides. The three-dimensional solution structure, determined by NMR, consists of a triple-stranded antiparallel beta -sheet and a series of turns and is similar to the known structures of other alpha -defensins. This has enabled the definitive classification of RK-1 as a member of this family of antimicrobial peptides. Ultracentrifuge measurements confirmed that like rabbit neutrophil defensins, RK-1 is monomeric in solution, in contrast to human neutrophil defensins, which are dimeric.

Circular proteins in plants - Solution structure of a novel macrocyclic trypsin inhibitor from Momordica cochinchinensis

Much interest has been generated by recent reports on the discovery of circular (i.e. head-to-tail cyclized) proteins in plants. Here we report the three-dimensional structure of one of the newest such circular proteins, MCoTI-II, a novel trypsin inhibitor from Momordica cochinchinensis, a member of the Cucurbitaceae plant family. The structure consists of a small beta -sheet, several turns, and a cystine knot arrangement of the three disulfide bonds. Interestingly, the molecular topology is similar to that of the plant cyclotides (Craik, D. J., Daly, N. L., Bond, T., and Waine, C. (1999) J. Mol. Biol, 294, 1327-1336), which derive from the Rubiaceae and Violaceae plant families, have antimicrobial activities, and exemplify the cyclic cystine knot structural motif as part of their circular backbone. The sequence, biological activity, and plant family of MCoTI-II are all different from known cyclotides. However, given the structural similarity, cyclic backbone, and plant origin of MCoTI-II, we propose that MCoTI-II can be classified as a new member of the cyclotide class of proteins. The expansion of the cyclotides to include trypsin inhibitory activity and a new plant family highlights the importance and functional variability of circular proteins and the fact that they are more common than has previously been believed, Insights into the possible roles of backbone cyclization have been gained by a comparison of the structure of MCoTI-II with the homologous acyclic trypsin inhibitors CMTI-I and EETI-II from the Cucurbitaceae plant family.

Conformations of platypus venom C-type natriuretic peptide in aqueous solution and sodium dodecyl sulfate micelles

Nuclear magnetic resonance spectroscopy was used to investigate the conformations of the platypus venom C-type natriuretic peptide A (OvCNPa) in aqueous solutions and in solutions containing sodium dodecyl sulfate (SDS) micelles. The chemically synthesized OvCNPa showed a substantial decrease in flexibility in aqueous solution at 10 degreesC, allowing the observation of medium- and long-range nuclear Overhauser enhancement (NOE) connectivities. Three-dimensional structures calculated using these data showed flexible and reasonably well-defined regions, the locations of which were similar in the two solvents. In aqueous solution, the linear part that spans residues 3-14 was basically an extended conformation while the cyclic portion, defined by residues 23-39, contained a series of beta-turns. The overall shape of the cyclic portion was similar to that observed for an atrial natriuretic peptide (ANP) variant in aqueous solution. OvCNPa adopted a different conformation in SDS micelles wherein the N-terminal region, defined by residues 2-10, was more compact, characterised by turns and a helix, while the cyclic region had turns and an overall shape that was fundamentally different from those structures observed in aqueous solution. The hydrophobic cluster, situated at the centre of the ring of the structure in aqueous solution, was absent in the structure in the presence of SDS micelles. Thus, OvCNPa interacts with SDS micelles and can possibly form ion-channels in cell membranes. (C) 2002 Elsevier Science Ltd. All rights reserved.

Signature of mott-insulator transition with ultracold fermions in a one-dimensional optical lattice

Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultracold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.

Solution structure of χ-conopeptide MrIA, a modulator of the human norepinephrine transporter

The chi-conopeptides MrIA and MrIB are 13-residue peptides with two disulfide bonds that inhibit human and rat norepinephrine transporter systems and are of significant interest for the design of novel drugs involved in pain treatment. In the current study we have determined the solution structure of MrIA using NMR spectroscopy. The major element of secondary structure is a hairpin with the two strands connected by an inverse gamma-turn. The residues primarily involved in activity have previously been shown to be located in the turn region (Sharpe, I. A.; Palant, E.: Schroder, C. L; Kaye, D. M.; Adams, D. I.; Alewood, P. F.; Lewis, R. J. J Biol Client 2003, 278, 40317-40323), which appears to be more flexible than the beta-strands based on disorder in the ensemble of calculated structures. Analogues of MrIA with N-terminal truncations indicate that the N-terminal residues play a role in defining a stable conformation and the native disulfide connectivity. In particular, noncovalent interactions between Val3 and Hypl2 are likely to be involved in maintaining a stable conformation. The N-terminus also affects activity, as a single N-terminal deletion introduced additional pharmacology at rat vas deferens, while deleting the first two amino acids reduced chi-conopeptide potency. This article was originally published online as an accepted preprint. The Published Online date corresponds to the preprint version. You can request a copy of the preprint by entailing the Biopolymers editorial office at biopolymers@wiley.com (c) 2005 Wiley Periodicals, Inc.

Determination of the solution structures of conantokin-G and conantokin-T by CD and NMR spectroscopy

Conantokin-G and conantokin-T are two paralytic polypeptide toxins originally isolated from the venom of the fish-hunting cone snails of the genus Conus. Conantokin-G and conantokin-T are the only naturally occurring peptidic compounds which possess N-methyl-D-aspartate receptor antagonist activity, produced by a selective non-competitive antagonism of polyamine responses, They are also structurally unusual in that they contain a disproportionately large number of acid labile post-translational gamma-carboxyglutamic acid (Gla) residues, Although no precise structural information has previously been published for these peptides, early spectroscopic measurements have indicated that both conantokin-G and conantokin-T form alpha-helical structures, although there is some debate whether the presence of calcium ions is required for these peptides to adopt this fold, We now report a detailed structural study of synthetic conantokin-G and conantokin-T in a range of solution conditions using CD and H-1 NMR spec troscopy. The three-dimensional structures of conantokin-T and conantokin-G were calculated from H-1 NMR-derived distance and dihedral restraints. Both conantokins were found to contain a mixture of alpha- and 3(10) helix, that give rise to curved and straight helical conformers. Conantokin-G requires the presence of divalent cations (Zn2+, Ca2+, Cu2+, Or Mg2+) to form a stable iv-helix, while conantokin-T adopts a stable alpha-helical structure in aqueous conditions, in the presence or absence of divalent cations (Zn2+, Ca2+, Cu2+, Or Mg2+).

Solution structure of the sodium channel antagonist conotoxin GS: A new molecular caliper for probing sodium channel geometry

Background: The venoms of Conus snails contain small, disulfide-rich inhibitors of voltage-dependent sodium channels. Conotoxin GS is a 34-residue polypeptide isolated from Conus geographus that interacts with the extracellular entrance of skeletal muscle sodium channels to prevent sodium ion conduction. Although conotoxin GS binds competitively with mu conotoxin GIIIA to the sodium channel surface, the two toxin types have little sequence identity with one another, and conotoxin GS has a four-loop structural framework rather than the characteristic three-loop mu-conotoxin framework. The structural study of conotoxin GS will form the basis for establishing a structure-activity relationship and understanding its interaction with the pore region of sodium channels. Results: The three-dimensional structure of conotoxin GS was determined using two-dimensional NMR spectroscopy. The protein exhibits a compact fold incorporating a beta hairpin and several turns. An unusual feature of conotoxin GS is the exceptionally high proportion (100%) of cis-imide bond geometry for the three proline or hydroxyproline residues. The structure of conotoxin GS bears little resemblance to the three-loop mu conotoxins, consistent with the low sequence identity between the two toxin types and their different structural framework. However, the tertiary structure and cystine-knot motif formed by the three disulfide bonds is similar to that present in several other polypeptide ion channel inhibitors. Conclusions: This is the first three-dimensional structure of a 'four-loop' sodium channel inhibitor, and it represents a valuable new structural probe for the pore region of voltage-dependent sodium channels. The distribution of amino acid sidechains in the structure creates several polar and charged patches, and comparison with the mu conotoxins provides a basis for determining the binding surface of the conotoxin GS polypeptide.

Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity

We consider solutions to the second-harmonic generation equations in two-and three-dimensional dispersive media in the form of solitons localized in space and time. As is known, collapse does not take place in these models, which is why the solitons may be stable. The general solution is obtained in an approximate analytical form by means of a variational approach, which also allows the stability of the solutions to be predicted. Then, we directly simulate the two-dimensional case, taking the initial configuration as suggested by the variational approximation. We thus demonstrate that spatiotemporal solitons indeed exist and are stable. Furthermore, they are not, in the general case, equivalent to the previously known cylindrical spatial solitons. Direct simulations generate solitons with some internal oscillations. However, these oscillations neither grow nor do they exhibit any significant radiative damping. Numerical solutions of the stationary version of the equations produce the same solitons in their unperturbed form, i.e., without internal oscillations. Strictly stable solitons exist only if the system has anomalous dispersion at both the fundamental harmonic and second harmonic (SH), including the case of zero dispersion at SH. Quasistationary solitons, decaying extremely slowly into radiation, are found in the presence of weak normal dispersion at the second-harmonic frequency.