Combining Shapley value and statistics to the analysis of gene expression data in children exposed to air pollution

Utilization of Computer Classification Methods for Exposure Prediction and Gene Selection in Daphnia magna Toxicogenomics

Zinc (Zn) is an essential element that influences many cellular functions. Depending on bioavailability, Zn can cause both deficiency and toxicity. Zn bioavailability is influenced by water hardness. Therefore, water quality analysis for health-risk assessment should consider both Zn concentration and water hardness. However, exposure media selection for traditional toxicology tests are set to defined hardness levels and do not represent the diverse water chemistry compositions observed in nature. Moreover, these tests commonly use whole organism endpoints, such as survival and reproduction, which require high numbers of test animals and are labor intensive. Gene expression stands out as a promising alternative to provide insight into molecular events that can be used for risk assessment. In this work, we apply machine learning techniques to classify the Zn concentrations and water hardness from Daphnia magna gene expression by using quantitative PCR. A method for gene ranking was explored using techniques from game theory, namely, Shapley values. The results show that standard machine learning classifiers can classify both Zn concentration and water hardness simultaneously, and that Shapley values are a versatile and useful alternative for gene ranking that can provide insight about the importance of individual genes.

Redundancy-aware unsupervised ranking based on game theory: Ranking pathways in collections of gene sets

In Genetics, gene sets are grouped in collections concerning their biological function. This often leads to high-dimensional, overlapping, and redundant families of sets, thus precluding a straightforward interpretation of their biological meaning. In Data Mining, it is often argued that techniques to reduce the dimensionality of data could increase the maneuverability and consequently the interpretability of large data. In the past years, moreover, we witnessed an increasing consciousness of the importance of understanding data and interpretable models in the machine learning and bioinformatics communities. On the one hand, there exist techniques aiming to aggregate overlapping gene sets to create larger pathways. While these methods could partly solve the large size of the collections' problem, modifying biological pathways is hardly justifiable in this biological context. On the other hand, the representation methods to increase interpretability of collections of gene sets that have been proposed so far have proved to be insufficient. Inspired by this Bioinformatics context, we propose a method to rank sets within a family of sets based on the distribution of the singletons and their size. We obtain sets' importance scores by computing Shapley values; Making use of microarray games, we do not incur the typical exponential computational complexity. Moreover, we address the challenge of constructing redundancy-aware rankings where, in our case, redundancy is a quantity proportional to the size of intersections among the sets in the collections. We use the obtained rankings to reduce the dimension of the families, therefore showing lower redundancy among sets while still preserving a high coverage of their elements. We finally evaluate our approach for collections of gene sets and apply Gene Sets Enrichment Analysis techniques to the now smaller collections: As expected, the unsupervised nature of the proposed rankings allows for unremarkable differences in the number of significant gene sets for specific phenotypic traits. In contrast, the number of performed statistical tests can be drastically reduced. The proposed rankings show a practical utility in bioinformatics to increase interpretability of the collections of gene sets and a step forward to include redundancy-awareness into Shapley values computations.

Systemic CLIP-seq analysis and game theory approach to model microRNA mode of binding

microRNAs (miRNAs) associate with Ago proteins to post-transcriptionally silence gene expression by targeting mRNAs. To characterize the modes of miRNA-binding, we developed a novel computational framework, called optiCLIP, which considers the reproducibility of the identified peaks among replicates based on the peak overlap. We identified 98 999 binding sites for mouse and human miRNAs, from eleven Ago2 CLIP-seq datasets. Clustering the binding preferences, we found heterogeneity of the mode of binding for different miRNAs. Finally, we set up a quantitative model, named miRgame, based on an adaptation of the game theory. We have developed a new algorithm to translate the miRgame into a score that corresponds to a miRNA degree of occupancy for each Ago2 peak. The degree of occupancy summarizes the number of miRNA-binding sites and miRNAs targeting each binding site, and binding energy of each miRNA::RNA heteroduplex in each peak. Ago peaks were stratified accordingly to the degree of occupancy. Target repression correlates with higher score of degree of occupancy and number of miRNA-binding sites within each Ago peak. We validated the biological performance of our new method on miR-155-5p. In conclusion, our data demonstrate that miRNA-binding sites within each Ago2 CLIP-seq peak synergistically interplay to enhance target repression.

Game theoretic centrality: a novel approach to prioritize disease candidate genes by combining biological networks with the Shapley value

Background

Complex human health conditions with etiological heterogeneity like Autism Spectrum Disorder (ASD) often pose a challenge for traditional genome-wide association study approaches in defining a clear genotype to phenotype model. Coalitional game theory (CGT) is an exciting method that can consider the combinatorial effect of groups of variants working in concert to produce a phenotype. CGT has been applied to associate likely-gene-disrupting variants encoded from whole genome sequence data to ASD; however, this previous approach cannot take into account for prior biological knowledge. Here we extend CGT to incorporate a priori knowledge from biological networks through a game theoretic centrality measure based on Shapley value to rank genes by their relevance–the individual gene’s synergistic influence in a gene-to-gene interaction network. Game theoretic centrality extends the notion of Shapley value to the evaluation of a gene’s contribution to the overall connectivity of its corresponding node in a biological network.

Results

We implemented and applied game theoretic centrality to rank genes on whole genomes from 756 multiplex autism families. Top ranking genes with the highest game theoretic centrality in both the weighted and unweighted approaches were enriched for pathways previously associated with autism, including pathways of the immune system. Four of the selected genes HLA-A, HLA-B, HLA-G, and HLA-DRB1–have also been implicated in ASD and further support the link between ASD and the human leukocyte antigen complex.

Conclusions

Game theoretic centrality can prioritize influential, disease-associated genes within biological networks, and assist in the decoding of polygenic associations to complex disorders like autism.

Coalitional Game Theory Facilitates Identification of Non-Coding Variants Associated With Autism

Studies on autism spectrum disorder (ASD) have amassed substantial evidence for the role of genetics in the disease's phenotypic manifestation. A large number of coding and non-coding variants with low penetrance likely act in a combinatorial manner to explain the variable forms of ASD. However, many of these combined interactions, both additive and epistatic, remain undefined. Coalitional game theory (CGT) is an approach that seeks to identify players (individual genetic variants or genes) who tend to improve the performance-association to a disease phenotype of interest-of any coalition (subset of co-occurring genetic variants) they join. This method has been previously applied to boost biologically informative signal from gene expression data and exome sequencing data but remains to be explored in the context of cooperativity among non-coding genomic regions. We describe our extension of previous work, highlighting non-coding chromosomal regions relevant to ASD using CGT on alteration data of 4595 fully sequenced genomes from 756 multiplex families. Genomes were encoded into binary matrices for three types of non-coding regions previously implicated in ASD and separated into ASD (case) and unaffected (control) samples. A player metric, the Shapley value, enabled determination of individual variant contributions in both sets of cohorts. A total of 30 non-coding positions were found to have significantly elevated player scores and likely represent significant contributors to the genetic coordination underlying ASD. Cross-study analyses revealed that a subset of mutated non-coding regions (all of which are in human accelerated regions (HARs)) and related genes are involved in biological pathways or behavioral outcomes known to be affected in autism, suggesting the importance of single nucleotide polymorphisms (SNPs) within HARs in ASD. These findings support the use of CGT in identifying hidden yet influential non-coding players from large-scale genomic data, to better understand the precise underpinnings of complex neurodevelopmental disorders such as autism.

Coalitional game theory as a promising approach to identify candidate autism genes

Despite mounting evidence for the strong role of genetics in the phenotypic manifestation of Autism Spectrum Disorder (ASD), the specific genes responsible for the variable forms of ASD remain undefined. ASD may be best explained by a combinatorial genetic model with varying epistatic interactions across many small effect mutations. Coalitional or cooperative game theory is a technique that studies the combined effects of groups of players, known as coalitions, seeking to identify players who tend to improve the performance--the relationship to a specific disease phenotype--of any coalition they join. This method has been previously shown to boost biologically informative signal in gene expression data but to-date has not been applied to the search for cooperative mutations among putative ASD genes. We describe our approach to highlight genes relevant to ASD using coalitional game theory on alteration data of 1,965 fully sequenced genomes from 756 multiplex families. Alterations were encoded into binary matrices for ASD (case) and unaffected (control) samples, indicating likely gene-disrupting, inherited mutations in altered genes. To determine individual gene contributions given an ASD phenotype, a "player" metric, referred to as the Shapley value, was calculated for each gene in the case and control cohorts. Sixty seven genes were found to have significantly elevated player scores and likely represent significant contributors to the genetic coordination underlying ASD. Using network and cross-study analysis, we found that these genes are involved in biological pathways known to be affected in the autism cases and that a subset directly interact with several genes known to have strong associations to autism. These findings suggest that coalitional game theory can be applied to large-scale genomic data to identify hidden yet influential players in complex polygenic disorders such as autism.

Translational Meta-analytical Methods to Localize the Regulatory Patterns of Neurological Disorders in the Human Brain

The task of mapping neurological disorders in the human brain must be informed by multiple measurements of an individual's phenotype - neuroimaging, genomics, and behavior. We developed a novel meta-analytical approach to integrate disparate resources and generated transcriptional maps of neurological disorders in the human brain yielding a purely computational procedure to pinpoint the brain location of transcribed genes likely to be involved in either onset or maintenance of the neurological condition.

Global transcriptome analysis reveals small RNAs affecting Neisseria meningitidis bacteremia

Most bacterial small RNAs (sRNAs) are post-transcriptional regulators involved in adaptive responses, controlling gene expression by modulating translation or stability of their target mRNAs often in concert with the RNA chaperone Hfq. Neisseria meningitides, the leading cause of bacterial meningitis, is able to adapt to different host niches during human infection. However, only a few sRNAs and their functions have been fully described to date. Recently, transcriptional expression profiling of N. meningitides in human blood ex vivo revealed 91 differentially expressed putative sRNAs. Here we expanded this analysis by performing a global transcriptome study after exposure of N. meningitides to physiologically relevant stress signals (e.g. heat shock, oxidative stress, iron and carbon source limitation). and we identified putative sRNAs that were differentially expressed in vitro. A set of 98 putative sRNAs was obtained by analyzing transcriptome data and 8 new sRNAs were validated, both by Northern blot and by primer extension techniques. Deletion of selected sRNAs caused attenuation of N. meningitides infection in the in vivo infant rat model, leading to the identification of the first sRNAs influencing meningococcal bacteremia. Further analysis indicated that one of the sRNAs affecting bacteremia responded to carbon source availability through repression by a GntR-like transcriptional regulator. Both the sRNA and the GntR-like regulator are implicated in the control of gene expression from a common network involved in energy metabolism.

DoGeNetS: using optimisation to discriminate regulatory network topologies based on gene expression data

Gene regulatory networks (GRNs) determine the dynamics of gene expression. Interest often focuses on the topological structure of a GRN while numerical parameters (e.g. decay rates) are unknown and less important. For larger GRNs, inference of structure from gene expression data is prohibitively difficult. Models are often proposed based on integrative interpretation of multiple sources of information. We have developed DoGeNetS (Discrimination of Gene Network Structures), a method to directly assess candidate models of GRN structure against a target gene expression data set. The transsys language serves to model GRN structures. Numeric parameters are optimised to approximate the target data. Multiple restarts of optimisation yield score sets that provide a basis to statistically discriminate candidate models according to their potential to explain the target data. We demonstrate discrimination power of the DoGeNetS method by relating structural divergence to divergence between gene expression data sets. Known models are used to generate target expression data, and a set of candidate models with a defined structural divergence to the true model is produced. Structural divergence and divergence of expression profiles after optimisation are strongly correlated. We further show that discrimination is possible at noise levels exceeding those typical of contemporary microarray data. DoGeNetS is capable of discriminating the best GRN structure from among a small number of candidates. p values indicate whether differences in divergence of expression are significant. Although this study uses single gene knockouts, the DoGeNetS method can be adapted to simulate a virtually unlimited range of experimental conditions. [Includes supplementary material].

Restricted cooperative games on metabolic networks reveal functionally important reactions

Understanding the emerging properties of complex biological systems is in the crux of systems biology studies. Computational methods for elucidating the role of each component in the synergetic interplay can be used to identify targets for genetic and metabolic engineering. In particular, we aim at determining the importance of reactions in a metabolic network with respect to a specific biological function. Therefore, we propose a novel game-theoretic framework which integrates restricted cooperative games with the outcome of flux balance analysis. We define productivity games on metabolic networks and present an analysis of their unrestricted and restricted variants based on the game-theoretic solution concept of the Shapley value. Correspondingly, this concept provides a characterization of the robustness and functional centrality for each enzyme involved in a given metabolic network. Furthermore, the comparison of two different environments - feast and famine - demonstrates the dependence of the results on the imposed flux capacities.

Using coalitional games on biological networks to measure centrality and power of genes

MOTIVATION

The interpretation of gene interaction in biological networks generates the need for a meaningful ranking of network elements. Classical centrality analysis ranks network elements according to their importance but may fail to reflect the power of each gene in interaction with the others.

RESULTS

We introduce a new approach using coalitional games to evaluate the centrality of genes in networks keeping into account genes' interactions. The Shapley value for coalitional games is used to express the power of each gene in interaction with the others and to stress the centrality of certain hub genes in the regulation of biological pathways of interest. The main improvement of this contribution, with respect to previous applications of game theory to gene expression analysis, consists in a finer resolution of the gene interaction investigated in the model, which is based on pairwise relationships of genes in the network. In addition, the new approach allows for the integration of a priori knowledge about genes playing a key function on a certain biological process. An approximation method for practical computation on large biological networks, together with a comparison with other centrality measures, is also presented.

Gene expression endpoints following chronic waterborne copper exposure in a genomic model organism, the zebrafish, Danio rerio

Although copper (Cu) is an essential micronutrient for all organisms, in excess, waterborne Cu poses a significant threat to fish from the cellular to population level. We examined the physiological and gene expression endpoints that chronic waterborne Cu exposure (21 d) imposes on soft-water acclimated zebrafish at two environmentally relevant concentrations: 8 microg/l (moderate) and 15 microg/l (high). Using a 16,730 65-mer oligonucleotide customized zebrafish microarray chip related to metal metabolism and toxicity to assess the transcriptomic response, we found that 573 genes in the liver responded significantly to Cu exposure. These clustered into three distinct patterns of expression. There was distinct upregulation of a majority of these genes under moderate Cu exposure and a significant downregulation under high Cu exposure. Microarray results were validated by qPCR of eight genes; two genes, metallothionein 2 (mt2) and Na(+)-K(+)-ATPase 1a1 (atp1a1), displayed increased expression under both Cu exposures, indicative of potential genetic endpoints of Cu toxicity, whereas the remaining six genes demonstrated opposing effects at each Cu exposure. Na(+)-K(+)-ATPase enzyme activity decreased during Cu exposure, which may be linked to Cu's competitive effects with Na(+). Whole body cortisol levels were significantly increased in Cu-exposed fish, which prompted an analysis of the promoter region of all significantly regulated genes for glucocorticoid (GRE) and metal (MRE) response elements to dissociate metal- and stress-specific gene responses. Of the genes significantly regulated, 30% contained only a GRE sequence, whereas 2.5% contained only a consensus MRE. We conclude that the indirect effects of Cu exposure regulate gene expression to a much greater degree than the direct effects.