Topological Information Content Research Articles

Quantifying collective motion patterns in mesenchymal cell populations using topological data analysis and agent-based modeling

Fibroblasts in a confluent monolayer are known to adopt elongated morphologies in which cells are oriented parallel to their neighbors. We collected and analyzed new microscopy movies to show that confluent fibroblasts are motile and that neighboring cells often move in anti-parallel directions in a collective motion phenomenon we refer to as “fluidization” of the cell population. We used machine learning to perform cell tracking for each movie and then leveraged topological data analysis (TDA) to show that time-varying point-clouds generated by the tracks contain significant topological information content that is driven by fluidization, i.e., the anti-parallel movement of individual neighboring cells and neighboring groups of cells over long distances. We then utilized the TDA summaries extracted from each movie to perform Bayesian parameter estimation for the D’Orsgona model, an agent-based model (ABM) known to produce a wide array of different patterns, including patterns that are qualitatively similar to fluidization. Although the D’Orsgona ABM is a phenomenological model that only describes inter-cellular attraction and repulsion, the estimated region of D’Orsogna model parameter space was consistent across all movies, suggesting that a specific level of inter-cellular repulsion force at close range may be a mechanism that helps drive fluidization patterns in confluent mesenchymal cell populations.

Properties of Entropy-Based Topological Measures of Fullerenes

A fullerene is a cubic three-connected graph whose faces are entirely composed of pentagons and hexagons. Entropy applied to graphs is one of the significant approaches to measuring the complexity of relational structures. Recently, the research on complex networks has received great attention, because many complex systems can be modelled as networks consisting of components as well as relations among these components. Information—theoretic measures have been used to analyze chemical structures possessing bond types and hetero-atoms. In the present article, we reviewed various entropy-based measures on fullerene graphs. In particular, we surveyed results on the topological information content of a graph, namely the orbit-entropy Ia(G), the symmetry index, a degree-based entropy measure Iλ(G), the eccentric-entropy Ifσ(G) and the Hosoya entropy H(G).

Learning Graph Embedding With Adversarial Training Methods.

Graph embedding aims to transfer a graph into vectors to facilitate subsequent graph-analytics tasks like link prediction and graph clustering. Most approaches on graph embedding focus on preserving the graph structure or minimizing the reconstruction errors for graph data. They have mostly overlooked the embedding distribution of the latent codes, which unfortunately may lead to inferior representation in many cases. In this article, we present a novel adversarially regularized framework for graph embedding. By employing the graph convolutional network as an encoder, our framework embeds the topological information and node content into a vector representation, from which a graph decoder is further built to reconstruct the input graph. The adversarial training principle is applied to enforce our latent codes to match a prior Gaussian or uniform distribution. Based on this framework, we derive two variants of the adversarial models, the adversarially regularized graph autoencoder (ARGA) and its variational version, and adversarially regularized variational graph autoencoder (ARVGA), to learn the graph embedding effectively. We also exploit other potential variations of ARGA and ARVGA to get a deeper understanding of our designs. Experimental results that compared 12 algorithms for link prediction and 20 algorithms for graph clustering validate our solutions.

On Properties of Distance-Based Entropies on Fullerene Graphs.

In this paper, we study several distance-based entropy measures on fullerene graphs. These include the topological information content of a graph , a degree-based entropy measure, the eccentric-entropy , the Hosoya entropy and, finally, the radial centric information entropy . We compare these measures on two infinite classes of fullerene graphs denoted by and . We have chosen these measures as they are easily computable and capture meaningful graph properties. To demonstrate the utility of these measures, we investigate the Pearson correlation between them on the fullerene graphs.

TopoICSim: a new semantic similarity measure based on gene ontology

BackgroundThe Gene Ontology (GO) is a dynamic, controlled vocabulary that describes the cellular function of genes and proteins according to tree major categories: biological process, molecular function and cellular component. It has become widely used in many bioinformatics applications for annotating genes and measuring their semantic similarity, rather than their sequence similarity. Generally speaking, semantic similarity measures involve the GO tree topology, information content of GO terms, or a combination of both.ResultsHere we present a new semantic similarity measure called TopoICSim (Topological Information Content Similarity) which uses information on the specific paths between GO terms based on the topology of the GO tree, and the distribution of information content along these paths. The TopoICSim algorithm was evaluated on two human benchmark datasets based on KEGG pathways and Pfam domains grouped as clans, using GO terms from either the biological process or molecular function. The performance of the TopoICSim measure compared favorably to five existing methods. Furthermore, the TopoICSim similarity was also tested on gene/protein sets defined by correlated gene expression, using three human datasets, and showed improved performance compared to two previously published similarity measures. Finally we used an online benchmarking resource which evaluates any similarity measure against a set of 11 similarity measures in three tests, using gene/protein sets based on sequence similarity, Pfam domains, and enzyme classifications. The results for TopoICSim showed improved performance relative to most of the measures included in the benchmarking, and in particular a very robust performance throughout the different tests.ConclusionsThe TopoICSim similarity measure provides a competitive method with robust performance for quantification of semantic similarity between genes and proteins based on GO annotations. An R script for TopoICSim is available at http://bigr.medisin.ntnu.no/tools/TopoICSim.R.

Estimating Bayesian Phylogenetic Information Content.

Measuring the phylogenetic information content of data has a long history in systematics. Here we explore a Bayesian approach to information content estimation. The entropy of the posterior distribution compared with the entropy of the prior distribution provides a natural way to measure information content. If the data have no information relevant to ranking tree topologies beyond the information supplied by the prior, the posterior and prior will be identical. Information in data discourages consideration of some hypotheses allowed by the prior, resulting in a posterior distribution that is more concentrated (has lower entropy) than the prior. We focus on measuring information about tree topology using marginal posterior distributions of tree topologies. We show that both the accuracy and the computational efficiency of topological information content estimation improve with use of the conditional clade distribution, which also allows topological information content to be partitioned by clade. We explore two important applications of our method: providing a compelling definition of saturation and detecting conflict among data partitions that can negatively affect analyses of concatenated data. [Bayesian; concatenation; conditional clade distribution; entropy; information; phylogenetics; saturation.]

Structural and topological complexity of zeolites: An information-theoretic analysis

Shannon information theory is applied to the quantitative evaluation of topological and structural complexity of zeolite frameworks. Within this approach, content of the reduced unit cell volume is considered as a message with atoms as symbols. Two atoms are considered equivalent, if they belong to the same crystallographic orbit. The framework complexity is characterized by its total topological information content, IG,total. Topological complexity parameters are calculated for the 201 zeolite structure types listed in the International Zeolite Association Zeolite Structure Database. On the basis of the proposed complexity measures, zeolite frameworks can be classified into very simple, simple, intermediate, complex, and very complex. The six most complex zeolite frameworks are [IG,total in bits]: SFV [19557.629], ITV [2825.097], IMF [2614.111], CLO [2413.449], and LTN [2285.985]. The six simplest zeolite frameworks are: SOD [16.529], BCT [19.020], ABW [23.020], NPO [28.529], EDI and NAB [32.603]. The sodalite–cancrinite group of zeolite frameworks is used to investigate evolution of complexity within modular series of structurally related zeolites. The topological complexity measures can be used to investigate evolution of complexity during crystallization and transformation of zeolites.

Information-based measures of structural complexity: application to fluorite-related structures

Topological complexity of fluorite-related structures consisting of edge- and corner-sharing tetrahedra is investigated using information-based complexity measures: topological information content, IG, normalized topological information content, IG,norm, vertex-degree distribution information content, Ivd, and average edge complexity, Ea. The IG and IG,norm parameters are quite sensitive to complexity of structural units and work well for homologous series as demonstrated for finite clusters and multiple chains. In addition, these parameters have high discriminative power and can be used for identification of structural units and crystal structures in general. The Ivd and Ea parameters are additional useful measures of complexity that are sensitive to the coordination numbers of particular atoms within the structural units.

Topological complexity of crystal structures: quantitative approach

The topological complexity of a crystal structure can be quantitatively evaluated using complexity measures of its quotient graph, which is defined as a projection of a periodic network of atoms and bonds onto a finite graph. The Shannon information-based measures of complexity such as topological information content, I(G), and information content of the vertex-degree distribution of a quotient graph, I(vd), are shown to be efficient for comparison of the topological complexity of polymorphs and chemically related structures. The I(G) measure is sensitive to the symmetry of the structure, whereas the I(vd) measure better describes the complexity of the bonding network.

Topological Information Content and Expressiveness of Function Models in Mechanical Design

In this paper, two approaches for computing the topological information content of function models in mechanical engineering design are developed and compared. Previously, a metric for computing information content of functions and flows within function models was proposed. Here, this metric is evolved to include the information contained in the connections between flows and functions in a function model. The first approach is based on uniform unconditional probability of a flow connecting any two functions within the model. The second approach is based on additional knowledge that the functions and flows in a model have limited compatibility, thereby, reducing the choices for origin and destination functions for each flow. This additional knowledge is represented using a new graphical representation supported by syntactic grammar rules. Both approaches are then applied to an example function model. Comparison between the approaches shows that the inclusion of this additional knowledge increases the expressiveness by reducing the uncertainty associated with function models.

A Large Scale Analysis of Information-Theoretic Network Complexity Measures Using Chemical Structures

This paper aims to investigate information-theoretic network complexity measures which have already been intensely used in mathematical- and medicinal chemistry including drug design. Numerous such measures have been developed so far but many of them lack a meaningful interpretation, e.g., we want to examine which kind of structural information they detect. Therefore, our main contribution is to shed light on the relatedness between some selected information measures for graphs by performing a large scale analysis using chemical networks. Starting from several sets containing real and synthetic chemical structures represented by graphs, we study the relatedness between a classical (partition-based) complexity measure called the topological information content of a graph and some others inferred by a different paradigm leading to partition-independent measures. Moreover, we evaluate the uniqueness of network complexity measures numerically. Generally, a high uniqueness is an important and desirable property when designing novel topological descriptors having the potential to be applied to large chemical databases.

Mathematics of Periodic Tables for Benzenoid Hydrocarbons

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract, please click on HTML or PDF.

Mathematics of Periodic Tables for Benzenoid Hydrocarbons

The upper and lower bounds for invariants of polyhex systems based on the Harary and Harborth inequalities are studied. It is shown that these invariants are uniquely correlated by the Periodic Table for Benzenoid Hydrocarbons. A modified periodic table for total resonant sextet (TRS) benzenoids based on the invariants of Ds and r(empty) is presented; Ds is the number of disconnections among the empty rings for fused TRS benzenoid hydrocarbons. This work represents a contribution toward deciphering the topological information content of benzenoid formulas.

Inferring Global Topology from Local Juxtaposition Geometry: Interlinking Polymer Rings and Ramifications for Topoisomerase Action

Lattice modeling is applied to investigate how the configurations of local chain juxtapositions may provide information about whether two ring polymers (loops) are topologically linked globally. Given a particular juxtaposition, the conditional probability that the loops are linked is determined by exact enumeration and extensive Monte Carlo sampling of conformations satisfying excluded volume constraints. A discrimination factor f L, defined as the ratio of linked to unlinked probabilities, varies widely depending on which juxtaposition is presumed. |log f L|s that are large for small loop size n tend to decrease, signaling diminishing topological information content of the juxtapositions, with increasing n. However, some juxtaposition geometries can impose sufficient overall conformational biases such that |log f L| remains significant for large n. Notably, for two loops as large as n = 200 in the model, the probability that passing the segments of a hooked juxtaposition would unlink an originally linked configuration is remarkably high, ∼85%. In contrast, segment-passage of a free juxtaposition would link the loops from an originally unlinked configuration more than 90% of the time. The statistical mechanical principles emerging from these findings suggest that it is physically possible for DNA topoisomerases to decatenate effectively by acting selectively on juxtapositions with specific “hooked” geometries.

Physicochemical Significance of Topological Parameters, Connectivity Indices and Information Content. Part 1: Correlation Studies in the Sets with Aromatic and Aliphatic Substituents

AbstractTopological parameters like 1x, 2xv and IC1 are used in QSAR studies because of their simplicity of calculation. In the absence of their physicochemical significance, it is difficult to interpret the results of such QSAR studies in terms of mode or mechanism of action of the bioactive molecule. Keeping this in view, attempts have been made to interpret the empiricism of these parameters. The physicochemical significance of these parameters has been studied in different sets of compounds having one physicochemical parameter constant in each set. It has been observed that the connectivity index correlated to a greater extent with molar refractivity (MR) than with hydrophobic (π) or logP which may be due to the inherent relationship between MR, molecular weight, numbers of non‐hydrogen atoms in the molecule, surface, volume 1x and 2xv values. The information content did not show correlation with any of the physicochemical parameter considered.

The Topological Information Content of a Map / An Attempt At A Rehabilitation Of Information Theory In Cartography

This paper recalls promising attempts at the application of information theory in cartography and their denial by means of the concept of information increment generated in the course of map interpretation which is out of keeping with the principles of information theory. Critical analysis of the idea of information increment is presented, and applied information theory and topology are identified as a scientific environment facilitating explanation of this increment as an inherent attribute of a map. The paper introduces the topological information content of a map as an effective instrument for quantification of the increment mentioned and demonstrates its application in an experimental river basin map. Operation of this tool confirms that the concept of information increment is compatible with the principles of applied information theory which finds hardier usefulness in cartography.

ChemInform Abstract: NOTE ON THE TOPOLOGICAL INFORMATION CONTENT OF SIMPLE GRAPHS

It is shown that simple graphs gave equal topological information content if their automorphism groups are isomorphic. Further, if the automorphism groups of two graphs are represented by wreath products of which the inner groups are isomorphic, then the two graphs possess equal topological information content. Three graphs which correspond to organic molecules illustrate this finding.

Note on the topological information content of simple graphs

It is shown that simple graphs gave equal topological information content if their automorphism groups are isomorphic. Further, if the automorphism groups of two graphs are represented by wreath products of which the inner groups are isomorphic, then the two graphs possess equal topological information content. Three graphs which correspond to organic molecules illustrate this finding.

Topological information content of genetic molecules—I.

In this paper an effort has been made to obtain the topological information content of (i) the four bases of DNA and uracil, (ii) the nucleotides of DNA and RNA, (iii) the 64 nucleotide triplets of RNA and (iv) the twenty amino acids. By defining first-order neighborhoods of the vertices of the chemical graph of a molecule, a topology is established (which may be termed first-order topology). An equivalence relation is thereafter defined on the set of vertices of this graph to get the disjoint classes of equivalent atoms in the configuration, and with the help of Shannon's formula [19], first-order topological information contents of such molecules are calculated. From this measure of information content it appears that the topological information content, rather than the non-topological one, is more pronounced for bases of nucleic acids as well as for nucleotides. This result may give a clearer picture of information processing at the cellular level of a living system.

Topological considerations in protein structure. I. Disulfide linkage.

AbstractThe patterns of disulfide bridges in proteins were considered by using the concept of topological information content. It was proposed that the difference between topological informal ion content in the half‐cystine residues of the native state and of the fully reduced form of a protein is related to the problems of the renaturation of the fully reduced and denatured protein. Specifically, when there is no difference between the topological information contents of the two states, the reduced protein is able to recover its native conformation. The concept reported in the present paper is consistent without exception with reported experimental results.