Topological side-chain classification of beta-turns: Ideal motifs for peptidomimetic development

beta-turns are important topological motifs for biological recognition of proteins and peptides. Organic molecules that sample the side chain positions of beta-turns have shown broad binding capacity to multiple different receptors, for example benzodiazepines. beta-turns have traditionally been classified into various types based on the backbone dihedral angles (phi 2, psi 2, phi 3 and psi 3). Indeed, 57-68% of beta-turns are currently classified into 8 different backbone families (Type I, Type II, Type I', Type II', Type VIII, Type VIa1, Type VIa2 and Type VIb and Type IV which represents unclassified beta-turns). Although this classification of beta-turns has been useful, the resulting beta-turn types are not ideal for the design of beta-turn mimetics as they do not reflect topological features of the recognition elements, the side chains. To overcome this, we have extracted beta-turns from a data set of non-homologous and high-resolution protein crystal structures. The side chain positions, as defined by C-alpha-C-beta vectors, of these turns have been clustered using the kth nearest neighbor clustering and filtered nearest centroid sorting algorithms. Nine clusters were obtained that cluster 90% of the data, and the average intra-cluster RMSD of the four C-alpha-C-beta vectors is 0.36. The nine clusters therefore represent the topology of the side chain scaffold architecture of the vast majority of beta-turns. The mean structures of the nine clusters are useful for the development of beta-turn mimetics and as biological descriptors for focusing combinatorial chemistry towards biologically relevant topological space.

The relationship between hetero-oligomer formation and function of the topological specificity domain of the Escherichia coli MinE protein

MinE is an oligomeric protein that, in conjunction with other Min proteins, is required for the proper placement of the cell division site of Escherichia coli. We have examined the self-association properties of MinE by analytical ultracentrifugation and by studies of hetero-oligomer formation in non-denaturing polyacrylamide gets. The self-association properties of purified MinE predict that cytoplasmic MinE is likely to exist as a mixture of monomers and dimers. Consistent with this prediction, the C-terminal MinE(22-88) fragment forms hetero-oligomers with MinE(+) when the proteins are co-expressed. In contrast, the MinE(36-88) fragment does not form MinE(+)/MinE(36-88) hetero-oligomers, although MinE36-88 affects the topological specificity of septum placement as shown by its ability to induce minicell formation when co-expressed with MinE(+) in wild-type cells. Therefore, hetero-oligomer formation is not necessary for the induction of mini-celling by expression of MinE(36-88) in wild-type cells. The interference with normal septal placement is ascribed to competition between MinE(36-88),nd the corresponding domain in the complete MinE protein for a component required for the topological specificity of septal placement.

The dimerization and topological specificity functions of MinE reside in a structurally autonomous C-terminal domain

Correct placement of the division septum in Escherichia coli requires the co-ordinated action of three proteins, MinC, MinD and MinE. MinC and MinD interact to form a non-specific division inhibitor that blocks septation at all potential division sites. MinE is able to antagonize MinCD in a topologically sensitive manner, as it restricts MinCD activity to the unwanted division sites at the cell poles, Here, we show that the topological specificity function of MinE residues in a structurally autonomous, trypsin-resistant domain comprising residues 31-88, Nuclear magnetic resonance (NMR) and circular dichroic spectroscopy indicate that this domain includes both alpha and beta secondary structure, while analytical ultracentrifugation reveals that it also contains a region responsible for MinE homodimerization. While trypsin digestion indicates that the anti-MinCD domain of MinE (residues 1-22) does not form a tightly folded structural domain, NMR analysis of a peptide corresponding to MinE(1-22) indicates that this region forms a nascent helix in which the peptide rapidly interconverts between disordered (random coil) and alpha-helical conformations, This suggests that the N-terminal region of MinE may be poised to adopt an alpha-helical conformation when it interacts with the target of its anti-MinCD activity, presumably MinD.

Unitary R-matrices for topological quantum computing

The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding-the R-matrix-be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.

Topological charge and angular momentum of light beams carrying optical vortices

We analyze the properties of light beams carrying phase singularities, or optical vortices. The transformations of topological charge during free-space propagation of a light wave, which is a combination of a Gaussian beam and a multiple charged optical vortex within a Gaussian envelope, are studied both in theory and experiment. We revise the existing knowledge about topological charge conservation, and demonstrate possible scenarios where additional vortices appear or annihilate during free propagation of such a combined beam. Coaxial interference of optical vortices is also analyzed, and the general rule for angular-momentum density distribution in a combined beam is established. We show that, in spite of any variation in the number of vortices in a combined beam, the total angular momentum is constant during the propagation. [S1050-2947(97)09910-1].

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Affective and evaluative descriptors of pain in the McGill Pain Questionnaire: reduction and reorganization

Recent reports indicate that several descriptors of pain sensations in the McGill Pain Questionnaire (MPQ) are difficult to classify within MPQ sensory subcategories because of incomprehension, underuse, or ambiguity of usage. Adopting the same methodology of recent studies, the present investigation focused on the affective and evaluative subcategories of the MPQ. A decision rule revealed that only 6 of 18 words met criteria for the affective category and 5 of 11 words met criteria for the evaluative category, thus warranting a reduced list of words in these categories. This reduction, however, led to negligible loss of information transmitted. Despite notable changes in classification, the intensity ratings of the retained words correlated very highly with those originally reported for the MPQ. In conclusion, although the intensity ratings of MPQ affective and evaluative descriptors need no revision, selective reduction and reorganization of these descriptors can enhance the efficiency of this approach to pain assessment. [copy ] 2001 by the American Pain Society

Various topological excitations in the SO(4) gauge field in higher dimensions

Following the original analysis Of Zhang and Hu for the 4-dimensional generalization of Quantum Hall effect, there has been much work from different viewpoints on the higher dimensional condensed matter systems. In this paper, we discuss three kinds of topological excitations in the SO(4) gauge field of condensed matter systems in 4-dimension-the instantons and anti-instantons, the 't Hooft-Polyakov monopoles, and the 2-membranes. Using the phi-mapping topological theory, it is revealed that there are 4-, 3-, and 2-dimensional topological currents inhering in the SO (4) gauge field, and the above three kinds of excitations can be directly and explicitly derived from these three kinds of currents, respectively. Moreover, it is shown that the topological charges of these excitations are characterized by the Hopf indices and Brouwer degrees of phi-mapping. (c) 2005 Elsevier Inc. All rights reserved.

Artificial neural network modeling of phytoestrogen binding to estrogen receptors

Differential pathophysiological roles of estrogen receptors alpha (ERα) and beta (ERβ) are of particular interest for phytochemical screening. A QSAR incorporating theoretical descriptors was developed in the present study utilizing sequential multiple-output artificial neural networks. Significant steric, constitutional, topological and electronic descriptors were identified enabling ER affinity differentiation.

Cyclic MrIA: A stable and potent cyclic conotoxin with a novel topological fold that targets the norepinephrine transporter

Conotoxins, disulfide-rich peptides from the venom of cone snails, have created much excitement over recent years due to their potency and specificity for ion channels and their therapeutic potential. One recently identified conotoxin, MrIA, a 13-residue member of the chi-conotoxin family, inhibits the human norepinephrine transporter (NET) and has potential applications in the treatment of pain. In the current study, we show that the, beta-hairpin structure of native MrIA is retained in a synthetic cyclic version, as is biological activity at the NET. Furthermore, the cyclic version has increased resistance to trypsin digestion relative to the native peptide, an intriguing result because the cleavage site for the trypsin is not close to the cyclization site. The use of peptides as drugs is generally hampered by susceptibility to proteolysis, and so, the increase in enzymatic stability against trypsin observed in the current study may be useful in improving the therapeutic potential of MrIA. Furthermore, the structure reported here for cyclic MrIA represents a new topology among a growing number of circular disulfide-rich peptides.

Developmental Pathways in Microcerotermes turneri (Termitidae: Termitinae): Biometric Descriptors of Worker Caste and Instar

The foraging process of location and exploitation of food in complex termite societies is in part reliant upon unequal division of specific tasks amongst its members (polyethism). To conduct studies assessing the role of individuals in foraging activities it is necessary to have descriptors of worker caste and instar. Here we provide biometric descriptors of specific caste and instar for worker caste and instars of Microcerotermes turneri (Froggatt) (Termitidae: Termitinae) for the worker castes (male and female) for the identification of individuals in laboratory assays applicable across multiple nests. The use of head width for determining sex of workers was successful across multiple nests. The length of the first three flagellum segments of the antenna and tibia three could be used to determine worker instar.

Summarizing level-two topological relations in large spatial datasets

Summarizing topological relations is fundamental to many spatial applications including spatial query optimization. In this article, we present several novel techniques to effectively construct cell density based spatial histograms for range (window) summarizations restricted to the four most important level-two topological relations: contains, contained, overlap, and disjoint. We first present a novel framework to construct a multiscale Euler histogram in 2D space with the guarantee of the exact summarization results for aligned windows in constant time. To minimize the storage space in such a multiscale Euler histogram, an approximate algorithm with the approximate ratio 19/12 is presented, while the problem is shown NP-hard generally. To conform to a limited storage space where a multiscale histogram may be allowed to have only k Euler histograms, an effective algorithm is presented to construct multiscale histograms to achieve high accuracy in approximately summarizing aligned windows. Then, we present a new approximate algorithm to query an Euler histogram that cannot guarantee the exact answers; it runs in constant time. We also investigate the problem of nonaligned windows and the problem of effectively partitioning the data space to support nonaligned window queries. Finally, we extend our techniques to 3D space. Our extensive experiments against both synthetic and real world datasets demonstrate that the approximate multiscale histogram techniques may improve the accuracy of the existing techniques by several orders of magnitude while retaining the cost efficiency, and the exact multiscale histogram technique requires only a storage space linearly proportional to the number of cells for many popular real datasets.

Multiscale histograms: Summarizing topological relations in large spatial datasets

Summarizing topological relations is fundamental to many spatial applications including spatial query optimization. In this paper, we present several novel techniques to eectively construct cell density based spatial histograms for range (window) summarizations restricted to the four most important topological relations: contains, contained, overlap, and disjoint. We rst present a novel framework to construct a multiscale histogram composed of multiple Euler histograms with the guarantee of the exact summarization results for aligned windows in constant time. Then we present an approximate algorithm, with the approximate ratio 19/12, to minimize the storage spaces of such multiscale Euler histograms, although the problem is generally NP-hard. To conform to a limited storage space where only k Euler histograms are allowed, an effective algorithm is presented to construct multiscale histograms to achieve high accuracy. Finally, we present a new approximate algorithm to query an Euler histogram that cannot guarantee the exact answers; it runs in constant time. Our extensive experiments against both synthetic and real world datasets demonstrated that the approximate mul- tiscale histogram techniques may improve the accuracy of the existing techniques by several orders of magnitude while retaining the cost effciency, and the exact multiscale histogram technique requires only a storage space linearly proportional to the number of cells for the real datasets.