Geometry Graphics Research Articles

Atomic Level Insight into the Oxidative Half-reaction of Aromatic Amine Dehydrogenase

The quinoprotein aromatic amine dehydrogenase (AADH) uses a covalently bound tryptophan tryptophylquinone (TTQ) cofactor to oxidatively deaminate primary aromatic amines. Recent crystal structures have provided insight into the reductive half-reaction. In contrast, no atomic details are available for the oxidative half-reaction. The TTQ O7 hydroxyl group is protonated during reduction, but it is unclear how this proton can be removed during the oxidative half-reaction. Furthermore, compared with the electron transfer from the N-quinol form, electron transfer from the non-physiological O-quinol form to azurin is significantly slower. Here we report crystal structures of the O-quinol, N-quinol, and N-semiquinone forms of AADH. A comparison of oxidized and substrate reduced AADH species reveals changes in the TTQ-containing subunit, extending from residues in the immediate vicinity of the N-quinol to the putative azurin docking site, suggesting a mechanism whereby TTQ redox state influences interprotein electron transfer. In contrast, chemical reduction of the TTQ center has no significant effect on protein conformation. Furthermore, structural reorganization upon substrate reduction places a water molecule near TTQ O7 where it can act as proton acceptor. The structure of the N-semiquinone, however, is essentially similar to oxidized AADH. Surprisingly, in the presence of substrate a covalent N-semiquinone substrate adduct is observed. To our knowledge this is the first detailed insight into a complex, branching mechanism of quinone oxidation where significant structural reorganization upon reduction of the quinone center directly influences formation of the electron transfer complex and nature of the electron transfer process.

The Crystal and Solution Structures of Glyceraldehyde-3-phosphate Dehydrogenase Reveal Different Quaternary Structures

The presence of an isoform of glyceraldehyde-3-phosphate dehydrogenase (kmGAPDH1p) associated with the cell wall of a flocculent strain of Kluyveromyces marxianus was the first report of a non-cytosolic localization of a glycolytic enzyme, but the mechanism by which the protein is transported to the cell surface is not known. To identify structural features that could account for the multiple localizations of the protein, the three-dimensional structure of kmGAPDH1p was determined by x-ray crystallography and small angle x-ray scattering. The x-ray crystallographic structure of kmGAPDH1p revealed a dimer, although all GAPDH homologs studied thus far have a tetrameric structure with 222 symmetry. Interestingly, the structure of kmGAPDH1p in solution revealed a tetramer with a 70 degrees tilt angle between the dimers. Moreover, the separation between the centers of the dimers composing the kmGAPDH1p tetramer diminished from 34 to 30 A upon NAD(+) binding, this latter value being similar to the observed in the crystallographic models of GAPDH homologs. The less compact structure of apo-kmGAPDH1p could already be the first image of the transition intermediate between the tetramer observed in solution and the dimeric form found in the crystal structure, which we postulate to exist in vivo because of the protein's multiple subcellular localizations in this yeast species.

Catalytic Mechanism and Structure of Viral Flavin-dependent Thymidylate Synthase ThyX

By using biochemical and structural analyses, we have investigated the catalytic mechanism of the recently discovered flavin-dependent thymidylate synthase ThyX from Paramecium bursaria chlorella virus-1 (PBCV-1). Site-directed mutagenesis experiments have identified several residues implicated in either NADPH oxidation or deprotonation activity of PBCV-1 ThyX. Chemical modification by diethyl pyrocarbonate and mass spectroscopic analyses identified a histidine residue (His53) crucial for NADPH oxidation and located in the vicinity of the redox active N-5 atom of the FAD ring system. Moreover, we observed that the conformation of active site key residues of PBCV-1 ThyX differs from earlier reported ThyX structures, suggesting structural changes during catalysis. Steady-state kinetic analyses support a reaction mechanism where ThyX catalysis proceeds via formation of distinct ternary complexes without formation of a methyl enzyme intermediate.

Predicting calcium‐binding sites in proteins—A graph theory and geometry approach

Identifying calcium-binding sites in proteins is one of the first steps towards predicting and understanding the role of calcium in biological systems for protein structure and function studies. Due to the complexity and irregularity of calcium-binding sites, a fast and accurate method for predicting and identifying calcium-binding protein is needed. Here we report our development of a new fast algorithm (GG) to detect calcium-binding sites. The GG algorithm uses a graph theory algorithm to find oxygen clusters of the protein and a geometric algorithm to identify the center of these clusters. A cluster of four or more oxygen atoms has a high potential for calcium binding. High performance with about 90% site sensitivity and 80% site selectivity has been obtained for three datasets containing a total of 123 proteins. The results suggest that a sphere of a certain size with four or more oxygen atoms on the surface and without other atoms inside is necessary and sufficient for quickly identifying the majority of the calcium-binding sites with high accuracy. Our finding opens a new avenue to visualize and analyze calcium-binding sites in proteins facilitating the prediction of functions from structural genomic information.

Structures of the Carbohydrate Recognition Domain of Ca2+-independent Cargo Receptors Emp46p and Emp47p

Emp46p and Emp47p are type I membrane proteins, which cycle between the endoplasmic reticulum (ER) and the Golgi apparatus by vesicles coated with coat protein complexes I and II (COPI and COPII). They are considered to function as cargo receptors for exporting N-linked glycoproteins from the ER. We have determined crystal structures of the carbohydrate recognition domains (CRDs) of Emp46p and Emp47p of Saccharomyces cerevisiae, in the absence and presence of metal ions. Both proteins fold as a beta-sandwich, and resemble that of the mammalian ortholog, p58/ERGIC-53. However, the nature of metal binding is distinct from that of Ca(2+)-dependent p58/ERGIC-53. Interestingly, the CRD of Emp46p does not bind Ca(2+) ion but instead binds K(+) ion at the edge of a concave beta-sheet whose position is distinct from the corresponding site of the Ca(2+) ion in p58/ERGIC-53. Binding of K(+) ion to Emp46p appears essential for transport of a subset of glycoproteins because the Y131F mutant of Emp46p, which cannot bind K(+) ion fails to rescue the transport in disruptants of EMP46 and EMP47 genes. In contrast the CRD of Emp47p binds no metal ions at all. Furthermore, the CRD of Emp46p binds to glycoproteins carrying high mannosetype glycans and the is promoted by binding not the addition of Ca(2+) or K(+) ion in These results suggest that Emp46p can be regarded as a Ca(2+)-independent intracellular lectin at the ER exit sites.

Expanders, rank and graphs of groups

LetG be a finitely presented group, and let {G i } be a collection of finite index normal subgroups that is closed under intersections. Then, we prove that at least one of the following must hold: 1.G i is an amalgamated free product or HNN extension, for infinitely manyi; 2. the Cayley graphs ofG/G i (with respect to a fixed finite set of generators forG) form an expanding family; 3. infi(d(G i )−1)/[G:G i ]=0, whered(G i ) is the rank ofG i . The proof involves an analysis of the geometry and topology of finite Cayley graphs. Several applications of this result are given.

Structural Basis of Cellulosome Efficiency Explored by Small Angle X-ray Scattering

Cellulose, the main structural component of plant cell walls, is the most abundant carbohydrate polymer in nature. To break down plant cell walls, anaerobic microorganisms have evolved a large extracellular enzyme complex termed cellulosome. This megadalton catalytic machinery organizes an enzymatic assembly, tenaciously bound to a scaffolding protein via specialized intermodular "cohesin-dockerin" interactions that serve to enhance synergistic activity among the different catalytic subunits. Here, we report the solution structure properties of cellulosome-like assemblies analyzed by small angle x-ray scattering and molecular dynamics. The atomic models, generated by our strategy for the free chimeric scaffoldin and for binary and ternary complexes, reveal the existence of various conformations due to intrinsic structural flexibility with no, or only coincidental, inter-cohesin interactions. These results provide primary evidence concerning the mechanisms by which these protein assemblies attain their remarkable synergy. The data suggest that the motional freedom of the scaffoldin allows precise positioning of the complexed enzymes according to the topography of the substrate, whereas short-scale motions permitted by residual flexibility of the enzyme linkers allow "fine-tuning" of individual catalytic domains.

Crystal Structure of the Actinomadura R39 DD-peptidase Reveals New Domains in Penicillin-binding Proteins

Actinomadura sp. R39 produces an exocellular DD-peptidase/penicillin-binding protein (PBP) whose primary structure is similar to that of Escherichia coli PBP4. It is characterized by a high beta-lactam-binding activity (second order rate constant for the acylation of the active site serine by benzylpenicillin: k2/K = 300 mm(-1) s(-1)). The crystal structure of the DD-peptidase from Actinomadura R39 was solved at a resolution of 1.8 angstroms by single anomalous dispersion at the cobalt resonance wavelength. The structure is composed of three domains: a penicillin-binding domain similar to the penicillin-binding domain of E. coli PBP5 and two domains of unknown function. In most multimodular PBPs, additional domains are generally located at the C or N termini of the penicillin-binding domain. In R39, the other two domains are inserted in the penicillin-binding domain, between the SXXK and SXN motifs, in a manner similar to "Matryoshka dolls." One of these domains is composed of a five-stranded beta-sheet with two helices on one side, and the other domain is a double three-stranded beta-sheet inserted in the previous domain. Additionally, the 2.4-angstroms structure of the acyl-enzyme complex of R39 with nitrocefin reveals the absence of active site conformational change upon binding the beta-lactams.

Structure of Escherichia coli UMP Kinase Differs from That ofOther Nucleoside Monophosphate Kinases and Sheds New Light on EnzymeRegulation

Structure of Escherichia coli UMP Kinase Differs from That ofOther Nucleoside Monophosphate Kinases and Sheds New Light on EnzymeRegulation

Approximating the isoperimetric number of strongly regular graphs

A factor 2 and a factor 3 approximation algorithm are given for the isoperimetricnumber of Strongly Regular Graphs. One approach involves eigenvalues of the combinatorial laplacian of such graphs. In this approach, both the upper and lower bounds involve the spectrum of the combinatorial laplacian. An interesting inequality is proven between the second smallest and the largest eigenvalue of combinatorial laplacian of strongly regular graphs. This yields a factor 3 approximation of the isoperimetric number. The second approach, firstly, finds properties of the metric which is returned by the linear programming formulation of [Linial et. al, The geometry of graphs and some of its algorithmic applications, Combinatorica, vol. 15(2) (1995), pp. 215–245] and secondly, gives an explicit cut which is within factor 2 of the optimal value of the linear program. The spectral algorithm can be generalized to get a factor 3 approximation for a variant of the isoperimetric number for Strongly Regular Graphs.

Evidence for Domain-specific Recognition of SK and Kv Channels by MTX and HsTx1 Scorpion Toxins

Maurotoxin (MTX) and HsTx1 are two scorpion toxins belonging to the alpha-KTx6 structural family. These 34-residue toxins, cross-linked by four disulfide bridges, share 59% sequence identity and fold along the classical alpha/beta scaffold. Despite these structural similarities, they fully differ in their pharmacological profiles. MTX is highly active on small (SK) and intermediate (IK) conductance Ca(2+)-activated (K(+)) channels and on voltage-gated Kv1.2 channel, whereas HsTx1 potently blocks voltage-gated Kv1.1 and Kv1.3 channels only. Here, we designed and chemically produced MTX-HsTx1, a chimera of both toxins that contains the N-terminal helical region of MTX (sequence 1-16) and the C-terminal beta-sheet region of HsTx1 (sequence 17-34). The three-dimensional structure of the peptide in solution was solved by (1)H NMR. MTX-HsTx1 displays the activity of MTX on SK channel, whereas it exhibits the pharmacological profile of HsTx1 on Kv1.1, Kv1.2, Kv1.3, and IK channels. These data demonstrate that the helical region of MTX exerts a key role in SK channel recognition, whereas the beta-sheet region of HsTx1 is crucial for activity on all other channel types tested.

Syntactic and Network Pattern Structures of City

This paper analyzes the relationship between livability and structure of two towns in Sumida city, Tokyo. Being historically and spatially contrasted despite located nearby, Kyojima and Honjo are comparatively analyzed under two different methods. According to a well-established topological analysis of city by Hillier (1998), Space Syntax′s Axial Map is applied to evaluate ′syntactic intelligibility′ and the degree of ′natural movement′ at both towns. Based upon ′Graph Geometry′ proposed by Nophaket (2004 a), the towns′ minimum-path structures are also detected. The network analysis applies Dijkstra algorithm to visualize the ′Network Pattern′ of street structure via C-language computer simulation (Nophaket, 2004 b). Comparison between topological-syntactic structure and geometrical-network pattern testifies not only significant contrasts in street patterns of Kyojima and Honjo, but also the different logic between two analytical models. Whilst Axial Map specifically shows the quantitative correlation between ′integration value′ and pedestrian or vehicle flow rate on each straight line, the new Path Map of Network Pattern detects an overall ′qualitative pattern′, the organic grid of winding streets in particular. Importantly, it shows the vital linkage of city. This study can conclude that Space Syntax model based on depth analysis implies a macro structure of city. Network Pattern, by contrast, represents the metrical significance of street at a more detailed level. The research findings, therefore, challenge an accepted generalization of applying Space Syntax across different cultures, archetypes and scales of street patterns. Moreover, it includes the geometrical analysis into basic graph-network study of urban form. As we believe, it is this metrical importance of street pattern that has been lost, perhaps not fully justifiably, within traditional Space Syntax analysis of the city.

The Graph Geometry for Architectural Planning

This paper introduces new graph geometric measures and models for architectural planning. Based upon geometrical distance among nodes, the ′minimum-path graph′ is proposed to analyse all shortest-path traversal from every to every other space in a network. By applying the geometric graph, two spatial models are created in order to represent node′s centrality and edge′s optimal passage capacity. They describe specific values for each individual space with regards to the overall system.The graph geometry primarily aims to assist architect planners to clarify the underlying geometric potential of space with more accuracy. In a near future, it is also hoped that the new geometric measures and models will further deepen, and widen, our planning knowledge for architectural and urban space network.

Generalized Graph Matrix, Graph Geometry, Quantum Chemistry, and Optimal Description of Physicochemical Properties

The generalized graph matrix Γ(x,v) (Estrada, E. Chem. Phys. Lett. 2001, 336, 247) is shown to encompass several of the applications of graph theory in physical chemistry in a more compact and effective way. It defines several n-Euclidean graph metrics, which simulate a graph defolding by changing the exponent v from 0 to 0.5 in a continuous way. This matrix is included in the formalism of the Huckel molecular orbital approach by considering that the resonance integrals between nonneighbor atoms are a function of the topological distance in terms of β. In doing so, the isospectrality between graphs disappears by changing the x parameter in this matrix as a consequence of considering the interactions between nonneighbor atoms. The Γ(x,v) matrix permits several of the “classical” topological indices to be (re)defined using only one graph invariant. These indices include the connectivity index, Balaban J index, Zagreb indices, Wiener index, and Harary indices, which are represented in an 8-dimensional space ...

The geometry of profinite graphs with applications to free groups and finite monoids

We initiate the study of the class of profinite graphsΓ\Gammadefined by the following geometric property: for any two verticesvvandwwofΓ\Gamma, there is a (unique) smallest connected profinite subgraph ofΓ\Gammacontaining them; such graphs are calledtree-like. Profinite trees in the sense of Gildenhuys and Ribes are tree-like, but the converse is not true. A profinite group is then said to bedendralif it has a tree-like Cayley graph with respect to some generating set; a Bass-Serre type characterization of dendral groups is provided. Also, such groups (including free profinite groups) are shown to enjoy a certain small cancellation condition. We define a pseudovariety of groupsH\mathbf {H}to bearboreousif all finitely generated free pro-H\mathbf {H}groups are dendral (with respect to a free generating set). Our motivation for studying such pseudovarieties of groups is to answer several open questions in the theory of profinite topologies and the theory of finite monoids. We prove, for arboreous pseudovarietiesH\mathbf {H}, a pro-H\mathbf {H}analog of the Ribes and Zalesskiĭ product theorem for the profinite topology on a free group. Also, arboreous pseudovarieties are characterized as precisely the solutionsH\mathbf {H}to the much studied pseudovariety equation\mathbf {J}\ast \mathbf {H}= \mathbf {J} \text {\textcircled {m}} \mathbf {H}.

Ample Parameterization of Variational Inclusions

For a general category of variational inclusions in finite dimensions, a class of parameterizations, called "ample" parameterizations, is identified that is rich enough to provide a full theory of Lipschitz-type properties of solution mappings without the need to resort to the auxiliary introduction of canonical parameters. Ample parameterizations also support a detailed description of the graphical geometry that underlies generalized differentiation of solutions mappings. A theorem on proto-derivatives is thereby obtained. The case of a variational inequality over a polyhedral convex set is given special treatment along with an application to minimizing a parameterized function over such a set.

X-ray Crystal Structure of the Trimeric N-terminal Domain of Gephyrin

Gephyrin is a ubiquitously expressed protein that, in the central nervous system, forms a submembraneous scaffold for anchoring inhibitory neurotransmitter receptors in the postsynaptic membrane. The N- and C-terminal domains of gephyrin are homologous to the Escherichia coli enzymes MogA and MoeA, respectively, both of which are involved in molybdenum cofactor biosynthesis. This enzymatic pathway is highly conserved from bacteria to mammals, as underlined by the ability of gephyrin to rescue molybdenum cofactor deficiencies in different organisms. Here we report the x-ray crystal structure of the N-terminal domain (amino acids 2-188) of rat gephyrin at 1.9-A resolution. Gephyrin-(2-188) forms trimers in solution, and a sequence motif thought to be involved in molybdopterin binding is highly conserved between gephyrin and the E. coli protein. The atomic structure of gephyrin-(2-188) resembles MogA, albeit with two major differences. The path of the C-terminal ends of gephyrin-(2-188) indicates that the central and C-terminal domains, absent in this structure, should follow a similar 3-fold arrangement as the N-terminal region. In addition, a central beta-hairpin loop found in MogA is lacking in gephyrin-(2-188). Despite these differences, both structures show a high degree of surface charge conservation, which is consistent with their common catalytic function.

The geometry of graphs and some of its algorithmic applications

In this paper we explore some implications of viewing graphs asgeometric objects. This approach offers a new perspective on a number of graph-theoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that respect themetric of the (possibly weighted) graph. Given a graphG we map its vertices to a normed space in an attempt to (i) keep down the dimension of the host space, and (ii) guarantee a smalldistortion, i.e., make sure that distances between vertices inG closely match the distances between their geometric images. In this paper we develop efficient algorithms for embedding graphs low-dimensionally with a small distortion. Further algorithmic applications include: Given faithful low-dimensional representations of statistical data, it is possible to obtain meaningful and efficientclustering. This is one of the most basic tasks in pattern-recognition. For the (mostly heuristic) methods used in the practice of pattern-recognition, see [20], especially chapter 6. Our studies of multicommodity flows also imply that every embedding of (the metric of) ann-vertex, constant-degree expander into a Euclidean space (of any dimension) has distortion Ω(logn). This result is tight, and closes a gap left open by Bourgain [12].

The Distance Between Two Points Moving On A Graph

This work considers the problem of calculating the average distance between two points moving on a directed graph whose arcs are straight line segments. The points are supposed to move independently from each other according to a stationary stochastic model. The average and variance of the distance between the points are determined by the graph geometry and the mobility parameters.

Damaging 2D quantum gravity

We investigate numerically the behaviour of damage spreading in a Kauffman cellular automaton with quenched rules on a dynamical φ 3 graph, which is equivalent to coupling the model to discretized 2D gravity. The model is interesting from the cellular automaton point of view as it lies midway between a fully quenched automaton with fixed rules and fixed connectivity and a (soluble) fully annealed automaton with varying rules and varying connectivity. In addition, we simulate the automaton on a fixed φ 3 graph coming from a 2D gravity simulation as a means of exploring the graph geometry.