Incremental mutual information: a new method for characterizing the strength and dynamics of connections in neuronal circuits

Understanding the computations performed by neuronal circuits requires characterizing the strength and dynamics of the connections between individual neurons. This characterization is typically achieved by measuring the correlation in the activity of two neurons. We have developed a new measure for studying connectivity in neuronal circuits based on information theory, the incremental mutual information (IMI). By conditioning out the temporal dependencies in the responses of individual neurons before measuring the dependency between them, IMI improves on standard correlation-based measures in several important ways: 1) it has the potential to disambiguate statistical dependencies that reflect the connection between neurons from those caused by other sources (e.g. shared inputs or intrinsic cellular or network mechanisms) provided that the dependencies have appropriate timescales, 2) for the study of early sensory systems, it does not require responses to repeated trials of identical stimulation, and 3) it does not assume that the connection between neurons is linear. We describe the theory and implementation of IMI in detail and demonstrate its utility on experimental recordings from the primate visual system.     

Improved scoring of functional groups from gene expression data by decorrelating GO graph structure

MOTIVATION: The result of a typical microarray experiment is a long list of genes with corresponding expression measurements. This list is only the starting point for a meaningful biological interpretation. Modern methods identify relevant biological processes or functions from gene expression data by scoring the statistical significance of predefined functional gene groups, e.g. based on Gene Ontology (GO). We develop methods that increase the explanatory power of this approach by integrating knowledge about relationships between the GO terms into the calculation of the statistical significance. RESULTS: We present two novel algorithms that improve GO group scoring using the underlying GO graph topology. The algorithms are evaluated on real and simulated gene expression data. We show that both methods eliminate local dependencies between GO terms and point to relevant areas in the GO graph that remain undetected with state-of-the-art algorithms for scoring functional terms. A simulation study demonstrates that the new methods exhibit a higher level of detecting relevant biological terms than competing methods.     

A biologically inspired measure for coexpression analysis

Two genes are said to be coexpressed if their expression levels have a similar spatial or temporal pattern. Ever since the profiling of gene microarrays has been in progress, computational modeling of coexpression has acquired a major focus. As a result, several similarity/distance measures have evolved over time to quantify coexpression similarity/dissimilarity between gene pairs. Of these, correlation coefficient has been established to be a suitable quantifier of pairwise coexpression. In general, correlation coefficient is good for symbolizing linear dependence, but not for nonlinear dependence. In spite of this drawback, it outperforms many other existing measures in modeling the dependency in biological data. In this paper, for the first time, we point out a significant weakness of the existing similarity/distance measures, including the standard correlation coefficient, in modeling pairwise coexpression of genes. A novel measure, called BioSim, which assumes values between -1 and +1 corresponding to negative and positive dependency and 0 for independency, is introduced. The computation of BioSim is based on the aggregation of stepwise relative angular deviation of the expression vectors considered. The proposed measure is analytically suitable for modeling coexpression as it accounts for the features of expression similarity, expression deviation and also the relative dependence. It is demonstrated how the proposed measure is better able to capture the degree of coexpression between a pair of genes as compared to several other existing ones. The efficacy of the measure is statistically analyzed by integrating it with several module-finding algorithms based on coexpression values and then applying it on synthetic and biological data. The annotation results of the coexpressed genes as obtained from gene ontology establish the significance of the introduced measure. By further extending the BioSim measure, it has been shown that one can effectively identify the variability in the expression patterns over multiple phenotypes. We have also extended BioSim to figure out pairwise differential expression pattern and coexpression dynamics. The significance of these studies is shown based on the analysis over several real-life data sets. The computation of the measure by focusing on stepwise time points also makes it effective to identify partially coexpressed genes. On the whole, we put forward a complete framework for coexpression analysis based on the BioSim measure.     

Describing and quantifying interspecific interactions: a commentary on recent approaches

There has been a recent resurgence of attempts to measure the strengths of interspecific interactions in biological communities. Two recent reviews have compared the performances of different measures of interaction strength using simulations. The goal of obtaining measures of interaction strength is based on the premise that such measures will achieve a closer connection between theory and experiment in community ecology. The present article disputes this premise. Because interactions are typically nonlinear, single numerical measures are generally poor characterizations. Typically, the functional dependencies of growth rates on population densities are unknown. Lacking more information about the form of these functions, the results of most population manipulations make very limited contributions to the construction of dynamic models of communities. Even if all effects of population densities on per capita growth rates were linear, performing all possible removal experiments will frequently fail to identify the constants of proportionality. Many misconceptions about the meaning and measurement of interaction coefficient persist. More extensive natural history observations and use of more flexible short-term experiments are advocated as approaches that will aid in constructing mathematical models of interspecific interactions.     

Pharmacogenomics - it''s not just pharmacogenetics

New technologies in both combinatorial chemistry and combinatorial biology promise to unlock new opportunities for drug discovery and lead optimisation. Using such genome-based technologies to measure the dynamic properties of pharmacological systems, pharmacogenomics can now provide an objective measure of a drug's biological efficacy, including its potential adverse effects.     

Novel search method for the discovery of functional relationships

MOTIVATION: Numerous annotations are available that functionally characterize genes and proteins with regard to molecular process, cellular localization, tissue expression, protein domain composition, protein interaction, disease association and other properties. Searching this steadily growing amount of information can lead to the discovery of new biological relationships between genes and proteins. To facilitate the searches, methods are required that measure the annotation similarity of genes and proteins. However, most current similarity methods are focused only on annotations from the Gene Ontology (GO) and do not take other annotation sources into account. RESULTS: We introduce the new method BioSim that incorporates multiple sources of annotations to quantify the functional similarity of genes and proteins. We compared the performance of our method with four other well-known methods adapted to use multiple annotation sources. We evaluated the methods by searching for known functional relationships using annotations based only on GO or on our large data warehouse BioMyn. This warehouse integrates many diverse annotation sources of human genes and proteins. We observed that the search performance improved substantially for almost all methods when multiple annotation sources were included. In particular, our method outperformed the other methods in terms of recall and average precision.     

Modularization of biochemical networks based on classification of Petri net t-invariants

Background  

Structural analysis of biochemical networks is a growing field in bioinformatics and systems biology. The availability of an increasing amount of biological data from molecular biological networks promises a deeper understanding but confronts researchers with the problem of combinatorial explosion. The amount of qualitative network data is growing much faster than the amount of quantitative data, such as enzyme kinetics. In many cases it is even impossible to measure quantitative data because of limitations of experimental methods, or for ethical reasons. Thus, a huge amount of qualitative data, such as interaction data, is available, but it was not sufficiently used for modeling purposes, until now. New approaches have been developed, but the complexity of data often limits the application of many of the methods. Biochemical Petri nets make it possible to explore static and dynamic qualitative system properties. One Petri net approach is model validation based on the computation of the system's invariant properties, focusing on t-invariants. T-invariants correspond to subnetworks, which describe the basic system behavior.     

Precursors to natural grammar learning: preliminary evidence from 4-month-old infants

When learning a new language, grammar--although difficult--is very important, as grammatical rules determine the relations between the words in a sentence. There is evidence that very young infants can detect rules determining the relation between neighbouring syllables in short syllable sequences. A critical feature of all natural languages, however, is that many grammatical rules concern the dependency relation between non-neighbouring words or elements in a sentence i.e. between an auxiliary and verb inflection as in is singing. Thus, the issue of when and how children begin to recognize such non-adjacent dependencies is fundamental to our understanding of language acquisition. Here, we use brain potential measures to demonstrate that the ability to recognize dependencies between non-adjacent elements in a novel natural language is observable by the age of 4 months. Brain responses indicate that 4-month-old German infants discriminate between grammatical and ungrammatical dependencies in auditorily presented Italian sentences after only brief exposure to correct sentences of the same type. As the grammatical dependencies are realized by phonologically distinct syllables the present data most likely reflect phonologically based implicit learning mechanisms which can serve as a precursor to later grammar learning.     

Accounting for Redundancy when Integrating Gene Interaction Databases

During the last years gene interaction networks are increasingly being used for the assessment and interpretation of biological measurements. Knowledge of the interaction partners of an unknown protein allows scientists to understand the complex relationships between genetic products, helps to reveal unknown biological functions and pathways, and get a more detailed picture of an organism''s complexity. Being able to measure all protein interactions under all relevant conditions is virtually impossible. Hence, computational methods integrating different datasets for predicting gene interactions are needed. However, when integrating different sources one has to account for the fact that some parts of the information may be redundant, which may lead to an overestimation of the true likelihood of an interaction. Our method integrates information derived from three different databases (Bioverse, HiMAP and STRING) for predicting human gene interactions. A Bayesian approach was implemented in order to integrate the different data sources on a common quantitative scale. An important assumption of the Bayesian integration is independence of the input data (features). Our study shows that the conditional dependency cannot be ignored when combining gene interaction databases that rely on partially overlapping input data. In addition, we show how the correlation structure between the databases can be detected and we propose a linear model to correct for this bias. Benchmarking the results against two independent reference data sets shows that the integrated model outperforms the individual datasets. Our method provides an intuitive strategy for weighting the different features while accounting for their conditional dependencies.     

SIDEseq: A Cell Similarity Measure Defined by Shared Identified Differentially Expressed Genes for Single-Cell RNA sequencing Data

One goal of single-cell RNA sequencing (scRNA seq) is to expose possible heterogeneity within cell populations due to meaningful, biological variation. Examining cell-to-cell heterogeneity, and further, identifying subpopulations of cells based on scRNA seq data has been of common interest in life science research. A key component to successfully identifying cell subpopulations (or clustering cells) is the (dis)similarity measure used to group the cells. In this paper, we introduce a novel measure, named SIDEseq, to assess cell-to-cell similarity using scRNA seq data. SIDEseq first identifies a list of putative differentially expressed (DE) genes for each pair of cells. SIDEseq then integrates the information from all the DE gene lists (corresponding to all pairs of cells) to build a similarity measure between two cells. SIDEseq can be implemented in any clustering algorithm that requires a (dis)similarity matrix. This new measure incorporates information from all cells when evaluating the similarity between any two cells, a characteristic not commonly found in existing (dis)similarity measures. This property is advantageous for two reasons: (a) borrowing information from cells of different subpopulations allows for the investigation of pairwise cell relationships from a global perspective and (b) information from other cells of the same subpopulation could help to ensure a robust relationship assessment. We applied SIDEseq to a newly generated human ovarian cancer scRNA seq dataset, a public human embryo scRNA seq dataset, and several simulated datasets. The clustering results suggest that the SIDEseq measure is capable of uncovering important relationships between cells, and outperforms or at least does as well as several popular (dis)similarity measures when used on these datasets.     

Electrophysiological measures of regional neural interactive coupling. Linear and non-linear dependence relationships among multiple channel electroencephalographic recordings

Linear spectral coherence (Sklat et al., 1973) measures have been used in the neurosciences to test hypotheses which address the question of whether multiple EEG recording sites are independent or whether they are activated by common sources of neurophysiological activity. This measure is appropriate when regional neural sources interact and thereby electrically activate several recording sites through linear transmission pathways which may or may not be different in their linear transformation properties. However, if the transmission media are non-linear, then interactive dependency is not necessarily revealed by a linear coherence test. Therefore, if common sources are activating EEG recording sites through nonlinear media, evaluating the resulting relationships among the signals recorded from these sites requires a test which reveals the presence of such nonlinear relationships. In neurophysiological applications, a polycoherence cross-spectral measure provides such a test for nonlinear dependency (similar to the linear coherence test) among EEG recording sites. The data requirements and statistical properties of these linear and non-linear measures are described and results of a linear coherence analysis are presented in the context of an EEG pilot study of learning diabled children.     

Causal inference in biomolecular pathways using a Bayesian network approach and an Implicit method

We introduce here the concept of Implicit networks which provide, like Bayesian networks, a graphical modelling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We show that Implicit networks, when used in conjunction with appropriate statistical techniques, are very attractive for their ability to understand and analyze biological data. Particularly, we consider here the use of Implicit networks for causal inference in biomolecular pathways. In such pathways, an Implicit network encodes dependencies among variables (proteins, genes), can be trained to learn causal relationships (regulation, interaction) between them and then used to predict the biological response given the status of some key proteins or genes in the network. We show that Implicit networks offer efficient methodologies for learning from observations without prior knowledge and thus provide a good alternative to classical inference in Bayesian networks when priors are missing. We illustrate our approach by an application to simulated data for a simplified signal transduction pathway of the epidermal growth factor receptor (EGFR) protein.     

An information theoretic exploratory method for learning patterns of conditional gene coexpression from microarray data

In this article, we introduce an exploratory framework for learning patterns of conditional co-expression in gene expression data. The main idea behind the proposed approach consists of estimating how the information content shared by a set of M nodes in a network (where each node is associated to an expression profile) varies upon conditioning on a set of L conditioning variables (in the simplest case represented by a separate set of expression profiles). The method is non-parametric and it is based on the concept of statistical co-information, which, unlike conventional correlation based techniques, is not restricted in scope to linear conditional dependency patterns. Moreover, such conditional co-expression relationships can potentially indicate regulatory interactions that do not manifest themselves when only pair-wise relationships are considered. A moment based approximation of the co-information measure is derived that efficiently gets around the problem of estimating high-dimensional multi-variate probability density functions from the data, a task usually not viable due to the intrinsic sample size limitations that characterize expression level measurements. By applying the proposed exploratory method, we analyzed a whole genome microarray assay of the eukaryote Saccharomices cerevisiae and were able to learn statistically significant patterns of conditional co-expression. A selection of such interactions that carry a meaningful biological interpretation are discussed.     

MDR and PRP: a comparison of methods for high-order genotype-phenotype associations

Complex diseases such as cardiovascular disease are likely due to the effects of high-order interactions among multiple genes and demographic factors. Therefore, in order to understand their underlying biological mechanisms, we need to consider simultaneously the effects of genotypes across multiple loci. Statistical methods such as multifactor dimensionality reduction (MDR), the combinatorial partitioning method (CPM), recursive partitioning (RP), and patterning and recursive partitioning (PRP) are designed to uncover complex relationships without relying on a specific model for the interaction, and are therefore well-suited to this data setting. However, the theoretical overlap among these methods and their relative merits have not been well characterized. In this paper we demonstrate mathematically that MDR is a special case of RP in which (1) patterns are used as predictors (PRP), (2) tree growth is restricted to a single split, and (3) misclassification error is used as the measure of impurity. Both approaches are applied to a case-control study assessing the effect of eleven single nucleotide polymorphisms on coronary artery calcification in people at risk for cardiovascular disease.     

Analisi informazionale degli schemi di dinamica della vegetazione. Un esempio sul popolamento vegetale delle dune del litorale di Venezia

Abstract

A method to quantify the dynamic schemes of vegetation based on information functions.—The dynamic schemes of vegetation as proposed by Braun-Blanquet have been never quantified with the aim to give indirect measures of the probability of transition between the types. This work presents a method that quantifies the arrows between the types by means of a redundancy measure. This is calculated by comparing the phytosociological types two by two. Redundancy, as proposed here, measures the similarity between the tables not only based on species composition but also on the basis of species cooccurrence. The method relies on the assumption that in a succession the higher is the redundancy between the types, that are presumably in sequence, the higher is the probability and then the velocity of transition from one type to another one. An example is given with data from coastal dune grasslands of the Venice Lagoon.     

Quantitative Genome-Wide Genetic Interaction Screens Reveal Global Epistatic Relationships of Protein Complexes in Escherichia coli

Large-scale proteomic analyses in Escherichia coli have documented the composition and physical relationships of multiprotein complexes, but not their functional organization into biological pathways and processes. Conversely, genetic interaction (GI) screens can provide insights into the biological role(s) of individual gene and higher order associations. Combining the information from both approaches should elucidate how complexes and pathways intersect functionally at a systems level. However, such integrative analysis has been hindered due to the lack of relevant GI data. Here we present a systematic, unbiased, and quantitative synthetic genetic array screen in E. coli describing the genetic dependencies and functional cross-talk among over 600,000 digenic mutant combinations. Combining this epistasis information with putative functional modules derived from previous proteomic data and genomic context-based methods revealed unexpected associations, including new components required for the biogenesis of iron-sulphur and ribosome integrity, and the interplay between molecular chaperones and proteases. We find that functionally-linked genes co-conserved among γ-proteobacteria are far more likely to have correlated GI profiles than genes with divergent patterns of evolution. Overall, examining bacterial GIs in the context of protein complexes provides avenues for a deeper mechanistic understanding of core microbial systems.