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PubMed2004

Complexity analysis of yeast proteome network.

Topological and compositional complexity of protein-protein networks is assessed in a variety of ways making use of graph theory and information theory. The methodology used is borrowed from mathematical chemistry and includes complexity descriptors such as substructure count, overall connectivity, walk count, and information on various vertex distributions. The approach is applied to the (incomplete) proteome of Saccharomyces cerevisiae containing 232 protein complexes of a total of 1,440 proteins. The proteome network and each of its nine functional subsets of protein complexes are disconnected graphs, containing a number of noninteracting species and a major component. A weighted edge between two vertices in these graphs stands for the number of shared proteins between the respective complexes. The major component is a highly connected, 'small-world' network, in which the average vertex distance between protein complexes does not exceed 2.2 (2.4 for the entire proteome), whereas the maximum distance does not exceed 4 (or 5 for the proteome). The vertex degree distribution in the major proteome component with 199 complexes follows the power law P(k) approximately k(-gamma), with gamma approximately = 1.7. The analysis of the functional organization of the yeast proteome has shown that, for any pair of biological functions, there always exist many proteins that can perform both functions. The potential application of the quantitative proteome descriptors discussed includes quantitative relationships between the structure and biological action of dynamic protein complexes in changing environment, identification of targets for markers/drugs, as well as system analysis and comparative studies of proteomes.

Fungal Proteins↗
PubMed2003

Topological rotational strengths as chirality descriptors for fullerenes.

A graph-theoretical procedure is proposed for assigning a chirality descriptor (the topological sign tau(+) or tau(-)) to each enantiomer of a chiral polyhedron, polyhedral molecule or graph, independently of any vertex labelling scheme. Model Cartesian coordinates and rotational strengths are obtained using only adjacency information; a generalised HOMO-LUMO rotational strength is used to associate a sign with a Schlegel diagram and the corresponding three-dimensional structure, polyhedron or molecule. The topological sign gives an unambiguous way of communicating the identity of an enantiomer. The mean-square topological rotational strength is a possible measure of the chirality content of a polyhedral graph or structure.

Journal Article↗
PubMed1989

Convergence and divergence in the afferent projections to cat area 17.

We have examined the topography of the afferent connections to area 17 in the cat by means of double retrograde label tracing techniques. Injections of two fluorescent retrograde tracers, diamidino yellow and fast blue, were made with variable separations in area 17 and the spatial distributions of the resulting populations of labeled cells examined in afferent cortical areas and subcortical structures. When injections were separated rostrocaudally, the topographic organizations of the projections were characterized quantitatively with two graphic methods: the labeling density curve and the connectivity graph. The labeling density curve measures labeled neuron density in successive rostrocaudal sections, whereas the connectivity graph provides a two-dimensional model of the topography of a given connectivity. The connectivity graph makes it possible to define two parameters that characterize the topography of the connection: the convergence and the divergence. The convergence is defined as the extent of an afferent structure that contains neurons converging on a line normal to the cortical surface in area 17. The divergence is the extent of area 17 that is innervated by neurons contained in an infinitely small region of the afferent structure. The results show that a number of subcortical structures project to area 17 in a nontopographic manner, i.e., that in each of these structures neurons contained in an infinitely small region send projections to the whole of area 17 and that a line normal to the surface of area 17 is innervated by neurons distributed throughout the afferent structure in question. Nontopographic projections are found from the intralaminar nuclei, the ventral mesencephalic tegmental region, the diagonal band of Broca, and the locus coeruleus. All remaining subcortical structures and cortical areas send topographically organized projections to area 17. The extent of the convergence and divergence, however, varies between structures. Only the projection from the A laminae of the LGN was found to approximate a point-to-point projection with a convergence of 0.4 mm and 2 mm in divergence. Much larger convergence and divergence values are found in the projections from the claustrum and the cortical areas. For example, the divergence reaches 20 mm for the projections from area 20 or from the anterior part of the lateral suprasylvian sulcus. Knowing the convergence and divergence values and the retinotopic organizations of area 17 and a number of its afferents, it becomes possible to test whether connections in the visual system link regions representing the same zone of the visual field.(ABSTRACT TRUNCATED AT 400 WORDS)

Afferent Pathways↗
PubMed2006

Spectral imaging microscopy web sites and data.

The Internet is enabling greater access to spectral imaging publications, spectral graphs, and data than that was available a generation ago. The spectral imaging systems discussed in this issue of Cytometry work because reagent and hardware spectra are reproducible, reusable, and provide input to spectral unmixing and spectral components recognition algorithms. These spectra need to be readily available in order to determine what to purchase, how to use it, and what the output means. We refer to several commercially sponsored and academic spectral web sites and discuss our spectral graphing and data sites. Sites include fluorescent dye graph servers from Invitrogen/Molecular Probes, BD Biosciences, Zeiss/Bio-Rad Cell Sciences, and filter set servers from Chroma Technology and Omega Optical. Several of these sites include data download capabilities. Recently, two microscope manufacturers have published on their web sites transmission curves for select objective lenses-crucial data for anyone doing multiphoton excitation microscopy. Notable among the academic sites, PhotoChemCAD 2.0 has over 200 dyes and a downloadable database/graphing program, and the USC-A Chemistry UV-vis Database displays absorption spectra of many dyes and indicators used in clinical histology and pathology. Our Fluorescent Spectra graphing/calculator site presents dyes, filters, and illumination data from many of these and additional sources. PubSpectra is our free download site which uses Microsoft Excel files as standardized human/machine readable format with over 2,000 biomedical spectra. The principle that data is not subject to copyright provides a framework in which all scientific data should be made freely accessible.

Algorithms↗
PubMed1993

On the use of dimensionless parameters in acid-base theory. V. Buffers composed of binary mixtures of monovalent weak acids and bases.

A general theory for buffers consisting of one weak acid and one weak base is developed, particular interest being devoted to the special case of doubly weak salts. The pH course as it varies with the acid/base concentration ratio is presented in equations and graphs. The influence of delta pK' = pK'b-pK'a, which can be negative as well as positive, is discussed and visualized in graphs. The buffer capacity is deduced as a function of pH. The buffer range is, at a maximum, 2.67 times that of a monovalent weak protolyte for delta pK' = 2.7 pH units. The buffer capacity curve has two maxima for delta pK' values bigger than 0.77. For negative delta pK' values the buffer capacity curve has only one maximum, and the buffer range is not better than that of a monovalent protolyte. A general equation for the ionic concentrations is deduced, and as a corollary the degree of hydrolysis of the doubly weak salt is obtained as a function of delta pK'. For solutions of this salt, the relation between concentration and pH is elucidated by equations and graphs.

Acids↗
PubMed2003

Popitam: towards new heuristic strategies to improve protein identification from tandem mass spectrometry data.

In recent years, proteomics research has gained importance due to increasingly powerful techniques in protein purification, mass spectrometry and identification, and due to the development of extensive protein and DNA databases from various organisms. Nevertheless, current identification methods from spectrometric data have difficulties in handling modifications or mutations in the source peptide. Moreover, they have low performance when run on large databases (such as genomic databases), or with low quality data, for example due to bad calibration or low fragmentation of the source peptide. We present a new algorithm dedicated to automated protein identification from tandem mass spectrometry (MS/MS) data by searching a peptide sequence database. Our identification approach shows promising properties for solving the specific difficulties enumerated above. It consists of matching theoretical peptide sequences issued from a database with a structured representation of the source MS/MS spectrum. The representation is similar to the spectrum graphs commonly used by de novo sequencing software. The identification process involves the parsing of the graph in order to emphasize relevant sections for each theoretical sequence, and leads to a list of peptides ranked by a correlation score. The parsing of the graph, which can be a highly combinatorial task, is performed by a bio-inspired algorithm called Ant Colony Optimization algorithm.

Algorithms↗
PubMed2005

Topological determinants of protein unfolding rates.

For proteins that fold by two-state kinetics, the folding and unfolding processes are believed to be closely related to their native structures. In particular, folding and unfolding rates are influenced by the native structures of proteins. Thus, we focus on finding important topological quantities from a protein structure that determine its unfolding rate. After constructing graphs from protein native structures, we investigate the relationships between unfolding rates and various topological quantities of the graphs. First, we find that the correlation between the unfolding rate and the contact order is not as prominent as in the case of the folding rate and the contact order. Next, we investigate the correlation between the unfolding rate and the clustering coefficient of the graph of a protein native structure, and observe no correlation between them. Finally, we find that a newly introduced quantity, the impact of edge removal per residue, has a good overall correlation with protein unfolding rates. The impact of edge removal is defined as the ratio of the change of the average path length to the edge removal probability. From these facts, we conclude that the protein unfolding process is closely related to the protein native structure.

Binding Sites↗
PubMed2001

SNAPping up functionally related genes based on context information: a colinearity-free approach.

We describe a computational approach for finding genes that are functionally related but do not possess any noticeable sequence similarity. Our method, which we call SNAP (similarity-neighborhood approach), reveals the conservation of gene order on bacterial chromosomes based on both cross-genome comparison and context information. The novel feature of this method is that it does not rely on detection of conserved colinear gene strings. Instead, we introduce the notion of a similarity-neighborhood graph (SN-graph), which is constructed from the chains of similarity and neighborhood relationships between orthologous genes in different genomes and adjacent genes in the same genome, respectively. An SN-cycle is defined as a closed path on the SN-graph and is postulated to preferentially join functionally related gene products that participate in the same biochemical or regulatory process. We demonstrate the substantial non-randomness and functional significance of SN-cycles derived from real genome data and estimate the prediction accuracy of SNAP in assigning broad function to uncharacterized proteins. Examples of practical application of SNAP for improving the quality of genome annotation are described.

Algorithms↗
PubMed2001

Topological nature of the genetic code.

A model for topological coding of proteins is proposed. The model is based on the capacity of hydrogen bonds (property of connectivity) to fix conformations of protein molecules. The protein chain is modeled by an n -arc graph with the following elements: vertices (alpha -carbon atoms), structural edges (peptide bonds) and connectivity edges (virtual edges connecting non-adjacent atoms). It was shown that 64 conformations of the 4-arc graph can be described in the binary system by matrices of six variables which form a supermatrix containing four blocks. On the basis of correspondences between the pairs of variables in matrices and four letters of the genetic code matrices and supermatrix are converted, respectively, into the triplets and the table of the genetic code. An algorithm admitting computer programming is proposed for coding the n -arc graph and protein chain. Connectivity operators (polar amino acids) are assigned to blocks of triplets coding for cyclic conformations (G, A-in the second position), while anti-connectivity operators (non-polar amino acids) correspond to blocks of triplets coding for open conformations (C, U-in the second position). Amino acids coded by triplets differing by the first base have different structures. The third base for C, U and G, A is degenerated. Properties of the real genetic code are in full agreement with the model. The model provides an insight into the topological nature of the genetic code and can be used for development of algorithms for the prediction of the protein structure.

Algorithms↗
PubMed1976

Graphic representation of the epileptic focus.

On the basis of systematic examinations of electrical activity of brain deep structures in 87 epileptic patients, an experiment was carried out to replace the concept of the epileptic focus by the graph of functional grouping of structures with epileptic activity. In order to make the graph as realistic as possible, the multi-lead electrodes have to be introduced into the brain systematically and under standard conditions. In this case, the results obtained are comparable. At the same time, the graph proves to be the basis of indications for stereotactic treatment.

Amygdala↗
PubMed1995

The atom assignment problem in automated de novo drug design. 1. Transferability of molecular fragment properties.

This paper is the first of a series which examines the problems of atom assignment in automated de novo drug design. In subsequent papers, a combinatoric optimization method for fragment placement onto 3D molecular graphs is provided. Molecules are built from molecular graphs by placing fragments onto the graph. Here we examine the transferability of atomic residual charge, by fragment placement, with respect to the electrostatic potential. This transferability has been tested on 478 molecular structures extracted from the Cambridge Structural Database. The correlation found between the electrostatic potential computed from composite fragments and that computed for the whole molecule was encouraging, except for extended conjugated systems.

Computer Simulation↗
PubMed1995

Detecting higher-order interactions among the spiking events in a group of neurons.

We propose a formal framework for the description of interactions among groups of neurons. This framework is not restricted to the common case of pair interactions, but also incorporates higher-order interactions, which cannot be reduced to lower-order ones. We derive quantitative measures to detect the presence of such interactions in experimental data, by statistical analysis of the frequency distribution of higher-order correlations in multiple neuron spike train data. Our first step is to represent a frequency distribution as a Markov field on the minimal graph it induces. We then show the invariance of this graph with regard to changes of state. Clearly, only linear Markov fields can be adequately represented by graphs. Higher-order interdependencies, which are reflected by the energy expansion of the distribution, require more complex graphical schemes, like constellations or assembly diagrams, which we introduce and discuss. The coefficients of the energy expansion not only point to the interactions among neurons but are also a measure of their strength. We investigate the statistical meaning of detected interactions in an information theoretic sense and propose minimum relative entropy approximations as null hypotheses for significance tests. We demonstrate the various steps of our method in the situation of an empirical frequency distribution on six neurons, extracted from data on simultaneous multineuron recordings from the frontal cortex of a behaving monkey and close with a brief outlook on future work.

Action Potentials↗
PubMed1982

Seasonality of pre-ovulatory non-disjunction and the aetiology of Down syndrome. A European collaborative study.

Six series of patients with Down syndrome (DS) from different European countries, altogether 287 cases, were divided into four categories according to parental origin of the additional chromosome 21 and meiotic division in which the nondisjunction had occurred. The monthly birth or conception frequencies per category were analysed by graph and compared with the total birth curve by Watson's adaptation of the Kolmogorov-Smirnov statistic for cyclic trends. Unexpectedly, the non-disjunctions during maternal meiosis I (63%), by far the largest category, occurred more frequently during the seasonal "restoration" and "inhibition" phase of the "ovulatory seasons" and less frequently when the ovulation rate is stabilized. The graph of the maternal meiosis II patients (17%) also seemed to conform to this phenomenon, though less obviously. In contrast to this, the paternal DS graph (20%) was very divergent, although a seasonal cluster of non-disjunctions may also occur here. From these findings a seasonal disturbance of preovulatory ripening of the ovum emerges as a possible cause of the first (and second) meiotic non-disjunction. Seasonal periodicity of the prolactin concentration in women and "transient hyperprolactinaemia", shown to be allied to delayed ovulation, may be related to these seasonal DS conception clusters.

Down Syndrome↗
PubMed1985

In vitro evaluation of CSF shunt function by radionuclides.

An in vitro study of clearance of a radiolabeled marker was conducted on nine commonly used shunting devices. Clearance of 0.5 ml of 113mIn-diethylenetriamine-pentaacetic acid (DTPA) injected into the chamber, by water infused through the system at constant rate (0.034-0.46 ml/min), was measured by monitoring activity over the chamber and accumulating counts at 5-s intervals on a multichannel analyzer. Each flow rate was triplicated, and a graph of log value of counts versus time made. A mean t1/2 was computed for each flow rate and a new graph constructed. A best-fit curve constructed for the graph of each shunt system allows determination of flow rate for a known half time of isotope clearance.

Cerebrospinal Fluid Shunts↗
PubMed2001

Autoreproductive cells and plant meristem construction: the case of the tomato cap meristem.

Root apical meristems are composed of two zones in which either formative or proliferative cell divisions occur. Within the formative zone, autoreproductive initial cells (a-cells) occupy distinctive locations. By means of graph-L-systems, the behavior of one such type of a-cells has been investigated, with particular reference to root caps within the developing primordia of lateral roots of Lycopersicon esculentum cultivated in vitro. Here, the a-cells constitute the "protoderm initials", cells which are found also in the root cap of many angiosperm species. A set of cuboidal (i.e., six-sided) a-cells develops early in the ontogeny of a lateral-root primordium. Then, according to both anatomical observations and theoretical simulations obtained by the application of graph-L-systems, sequential production of descendents from each a-cell leads to the formation of a new autoreproductive cell (a), a cap columella initial (c), and two mother cells (e and f) whose respective descendents differentiate as root epidermis and cap flank cells. In this graph-L-system, there is specification of the location of sister cells with respect to the three orthogonal directions of a cuboidal. In the early stage of root cap formation, only a few rounds of these formative cell divisions by each a-cell and its four types of descendents are required to provide the basic set of cells necessary for full cap development. After the lateral root emerges from the parent root, there may be a temporary cessation of the formative divisions of the a-cells which give rise to columella initials. Columella production is then supported entirely by its own independent set of autoreproductive c-initials. At the same time, division of the autoreproductive protoderm initial cell is directed towards maintaining the cap flank and the epidermal cell files. The regulation of the types of formative division by the a-cell may be represented by means of a division counter which may be specific for a given species.

Algorithms↗
PubMed1996

CT-target determination in postero-ventral pallidotomy: a universal method. Technical note.

Stereotactic targeting of the postero-ventral pallidum (PVP) presents special challenges to the surgeon 1) The target is in intimate relation to the optic tract and the internal capsule. 2) Proper angulation of the trajectory is crucial to achieve optimal effects given the long craniocaudal extension of the PVP. 3) The PVP is difficult to identify on computerized tomography (CT): the border between the internal capsule and the pallidum is usually not apparent. Potential sources of error in target determination include: - angulation of the scanning plane in relation to the intercommissural plane; - projection of the reference points (anterior commissure/posterior commissure [AC/PC]) results in the foreshortened intercommissural line, affecting the Y co-ordinate; - small tilts between the CT gantry and the stereotactic frame affect determination of the X and Z co-ordinates. Correction of these sources of error is done with basic trigonometric algorithms. The authors have developed a rapid method of stereotactic co-ordinate calculation which avoids the need to perform error-prone calculations under the pressure of operating room conditions. 1) The frame is applied with its basal plane corresponding roughly to the orbito-meatal line. 2) Thin CT slices (2 mm increments) are obtained through the area of interest and the slices are printed. 3) The major reference points (Foramen of Monro, AC, PC) are identified and marked. The PC point is projected onto the film containing AC (or viceversa if the PC slice is caudal to AC). 4) The intercommissural distance is measured, and the true length is obtained from a correction graph. The Y co-ordinate is then calculated as 1/2 ICL + 2 mm [towards AC]. 5) The slice corresponding to the target [Z co-ordinate] is obtained from a correction graph that takes into consideration the gap [number of slices] between AC and PC. 6) The X co-ordinate is placed 20 to 22 mm from midline. A graph that takes into consideration the coronal tilt of the stereotactic frame in relation to the CT gantry allows for final corrections of the X and Z co-ordinates. This step-by-step simple method of co-ordinate calculation can be used with any CT-compatible stereotactic frame.

Brain Mapping↗
PubMedDate not supplied

TransMiner: mining transitive associations among biological objects from text.

Associations among biological objects such as genes, proteins, and drugs can be discovered automatically from the scientific literature. TransMiner is a system for finding associations among objects by mining the Medline database of the scientific literature. The direct associations among the objects are discovered based on the principle of co-occurrence in the form of an association graph. The principle of transitive closure is applied to the association graph to find potential transitive associations. The potential transitive associations that are indeed direct are discovered by iterative retrieval and mining of the Medline documents. Those associations that are not found explicitly in the entire Medline database are transitive associations and are the candidates for hypothesis generation. The transitive associations were ranked based on the sum of weight of terms that co-occur with both the objects. The direct and transitive associations are visualized using a graph visualization applet. TransMiner was tested by finding associations among 56 breast cancer genes and among 24 objects in the calpain signal transduction pathway. TransMiner was also used to rediscover associations between magnesium and migraine.

Abstracting and Indexing↗
PubMed1996

A new bell-shaped function for idiotypic interactions based on cross-linking.

Most recent models of the immune network are based upon a phenomenological log bell-shaped interaction function. This function depends on a single parameter, the "field," which is the sum of all ligand concentrations weighted by their respective affinities. The typical behavior of these models is dominated by percolation, a phenomenon in which a local stimulus spreads globally throughout the network. The usual reason for employing a log bell-shaped interaction function is that B cells are activated by cross-linking of their surface immunoglobulin receptors. Here we formally derive a new phenomenological log bell-shaped function from the chemistry of receptor cross-linking by bivalent ligand. Specifying how this new function depends on the ligand concentrations requires two fields: a binding field and a cross-linking field. When we compare the activation functions for ligand-receptor pairs with different affinities, the one-field and the two-field functions differ markedly. In the case of the one-field activation function, its graph is shifted to increasingly higher concentration as the affinity decreases but keeps its width and height. In the case of the two-field activation function, the graph of a low-affinity interaction is nested within the graphs of all higher-affinity interactions. We show that this difference in the relations among activation functions for different affinities radically changes the network behavior. In models that described B cell proliferation using the one-field activation function, network behavior was dominated by low-affinity interactions. Conversely, in our new model, the high-affinity interactions are the most significant. As a consequence, percolation is no longer the only typical network behavior.

Animals↗