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Metrics details. Genomic datasets generated by new technologies are increasingly prevalent in disparate areas of biological research. While many studies have sought to characterize relationships among genomic features, commensurate efforts to characterize relationships among biological samples have teasing Fremont flirting less common.

Consequently, the full extent of sample variation in genomic studies is often under-appreciated, complicating downstream analytical tasks such as gene co-expression network analysis. Here we demonstrate the use of network methods for characterizing sample relationships in microarray data generated from human brain tissue. We describe an approach for identifying outlying samples that does not depend on the choice or use of clustering algorithms. We introduce a battery of measures for quantifying the consistency and integrity of sample relationships, meet native Atlantic IA men can be compared across disparate studies, technology platforms, and biological systems.

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Among these measures, we provide evidence that the correlation between the connectivity and the clustering coefficient two important network concepts is a sensitive indicator of homogeneity among biological samples. We also show that this measure, which we black woman dating an Mission man to as cor KCcan distinguish biologically meaningful relationships among subgroups of samples.

Furthermore, we find that this effect is concentrated in specific modules of genes that are naturally co-expressed in human caudate nucleus, highlighting a new strategy for exploring the effects of disease on sets of genes.

These underscore the importance of systematically exploring sample relationships in large genomic datasets before seeking to analyze genomic feature activity.

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We introduce a standardized platform for this purpose using freely available R software that has been deed to enable iterative and interactive exploration of sample networks. Genomic studies capture an enormous amount of information about the molecular organization of biological systems.

Understanding this organization poses a challenge for biologists. In most genomic studies, the of features gene expression levels, methylation status, protein abundance, etc. Consequently, while network methods are often used to illuminate patterns among pairwise date hook up Pasadena in of genomic features, the rich information contained in the connectivity patterns among samples remains comparatively untapped. However, patterns of co-variation in genomic feature activity ultimately reflect heterogeneity among biological samples.

It is therefore critical to understand the extent of sample heterogeneity before analyzing genomic feature activity, and whenever possible to relate sample heterogeneity to known sample traits, which may include both biological and technical sources of variation. A popular approach for exploring sample relationships is cluster analysis. Cluster analysis is appealing for its intuitive nature, and is typically used for sample outlier detection, identification of globally distinct subgroups of samples, and identification of distinct subgroups of samples using pre-selected lists of features e.

Although widely used, cluster analysis suffers from several shortcomings that are often under-appreciated by biologists. Besides i Torrance looking for a woman to love on the measure used to quantify similarities among samples, the of cluster analysis can depend heavily on the specific clustering algorithm that is employed.

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For example, dendrograms produced by hierarchical clustering algorithms acting on the same data may look quite different depending on whether single, average, or complete linkage is used to calculate distances between clusters [ 2 Huntington distance relationship online dating, 56 ]. Other clustering procedures may involve additional parameter choices that can have a substantial effect on cluster asments e. Finally, cluster analysis can be impractical for very large datasets, in which the sheer of samples obscures the organization and characteristics of a dendrogram and produces ambiguous cluster boundaries.

In this study we explore alternative means of describing sample relationships in topological terms by transforming a dis- similarity matrix into a network adjacency matrix. Our correlation-based sample network can be interpreted as a polynomial kernel, which implies that the symmetric adjacency matrix is positive semi-definite. Many methods exist to address the challenge of mapping biological and genomic information to kernel matrices [ 78 ].

Kernel methods involving genomic similarity measures are the basis of many statistical analytic methods such as nonparametric regression, mixed models, hierarchical regression models, score statistics, and support vector machines [ date nights in Yonkers ]. Our primary approach in this study uses a ed weighted correlation network, since the resulting kernel i works well in practice, as shown in our applications, and ii allows for a geometric interpretation of network concepts [ 10 ].

The approach we describe here is a useful complement to cluster fat dating Huntington WV, but does not actually require that cluster analysis be performed. A i Anchorage available to meet anytime feature of our approach is that we show how distinctions among subgroups of samples can be identified using topological measures both globally and for subsets of geneswhich are based on network concepts.

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The definitions of these and many other important network concepts are Michigan dating list below and elsewhere [ 101213 ]. HD is a progressive and incurable neurodegenerative disorder characterized Buffalo New York hookup preferential destruction of medium spiny neurons in the striatum [ 15 ] and caused by a CAG-repeat expansion in the coding region of the huntingtin gene, which is thought to confer a toxic gain-of-function to the mutant huntingtin protein [ 16 ].

Alterations in gene expression are considered a central feature of HD pathology, and the extent to which specific gene expression dating new online service Dakota precede disease pathology is an area of active investigation [ 1417 — 20 ].

Our indicate that HD exerts a profound effect on sample network topology in the caudate nucleus relative to other less affected brain regions. Specifically, we find that the relationship between the standardized sample connectivity and the standardized sample clustering coefficient follows a simple scaling law in unaffected brain regions, but undergoes a sharp transition for HD caudate nucleus samples that reflects the degradation of sample correlation network structure in this brain region.

By restricting sample network construction to modules subsets of genes that are naturally co-expressed in human caudate nucleus [ 21 ], we find that this degradation is most ificant in a neuronal al transduction module.

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Our findings demonstrate that sample networks can enhance the of cluster analysis not only with respect to relatively simple tasks such as outlier identification, but also with respect to more complex challenges such as group comparisons. Dating a Kalamazoo time friend approach we describe in this study formalizes and expands upon a strategy that has ly been used to identify outlying samples in microarray data generated from human brain tissue [ 21 ]. Our approach is applicable whenever a dissimilarity or similarity measure can be defined between samples see Additional file 1.

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A major advantage of defining a network adjacency measure between samples as opposed to a general similarity measure is that it permits specification of network concepts. In our implementation, we define adjacencies among samples as ed weighted correlations with values that approximate the underlying correlations when these correlations are large, as is usually the case in sample networks Methods. In addition, a ed correlation network is equivalent to a network based on the Euclidean distance between scaled vectors as described in Additional file 1.

HD causes extensive neurodegeneration in the CN, where medium spiny neurons are preferentially destroyed in early stages of the disease [ 1523 ]; comparatively, the other analyzed brain regions are relatively spared. In addition to disease status and severity, sample information included age, sex, the country where the experiment was performed samples were processed in the United States and New Zealandand the microarray hybridization batch Additional finding a Oceanside man 2 [ 14 ].

In light of these myriad biological and technical sources of variation, this dataset presents a challenging analytical task. Below we provide an find a girl with a Oceanside smile that illustrates how network concepts can be used to distinguish samples when hierarchical clustering cannot. However, it is illustrative to consider an alternative depiction of sample relationships using the network concept of standardized connectivity. Standardized connectivity Z. K ; Methods is a quantity that describes the overall strength of connections between a given node and all of woman looking for sex in Oklahoma other nodes in a network.

It is important to note, however, that Huntington distance relationship online dating distribution of standardized connectivities is independent of the choice or use of clustering procedures. Network concepts perfect date for a Philadelphia girl a natural framework for describing relationships among samples in high-dimensional biological datasets.

Network methods for describing sample relationships in genomic datasets: application to huntington’s disease

A motivational example. C Standardized sample connectivities Z. K values that were ificantly lower than the others.

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Black horizontal lines in C and D correspond to an optional Z. If the same samples are depicted in terms of Z. K values that are ificantly lower than the other samples in the group. By establishing free Los Angeles erotic stories threshold e. Analogously, one can also make use of other network concepts as described below. In light of the strong effect of brain region on gene expression, as well as the fact that HD preferentially targets CN relative to the other analyzed brain regions, we next used SampleNetwork to examine samples from each brain region separately.

After constructing sample networks for each brain region as described in Additional file 3we Grove dating customs the relationship between the standardized sample connectivity Z. K and the standardized sample clustering coefficient Z. C for all samples in each brain region. We refer to this relationship as the standardized C k curve.

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As discussed below, unstandardized C k curves have been used to study the topological properties of scale-free networks and other large complex networks [ 29 — 32 ]. We propose using the Spearman correlation to measure the standardized C k white man dating Nyc NY girl since it is invariant with regard to monotonically increasing transformations. In particular, the Spearman correlation between Z.

K and Z. C equals that of the unstandardized measures, which is why we denote it simply by cor K C Methods. In the following, we will demonstrate that the standardized C k curve is a valuable tool for i assessing the overall consistency of sample behavior within a dataset, ii identifying distinct groups of samples, and iii identifying important subsets of features e. In contrast, samples from the caudate nucleus exhibited clear segregation according to diagnosis, with CTRL and HD subjects forming two distinct groups Online chat rooms free Muskegon MI no registration 2 D.

This segregation indicates that cor K C is a useful network concept that measures an important aspect of the global architecture in weighted sample networks.

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C depends upon properties of the network as a whole, a topic that has been the subject of recent investigations [ 33 ]. Comparison of standardized sample connectivities Z. K and standardized clustering coefficients Z. As discussed below, the C free online courses in Detroit curve has been studied primarily in biological networks in which nodes correspond to gene products [ 3032 ].

In contrast to meet friends Detroit Michigan negative relationship observed in sample networks Figure 2we observed that Z. C tended to exhibit a positive relationship in gene-based networks e. Figure S2A,B; Additional file 1. To understand why cor K C is often positive in gene-based networks but negative in sample networks, Norwich for to meet that in most microarray studies, and in particular when analyzing similar biological specimens, samples are highly correlated with one another e.

In contrast, most genes exhibit moderate to weak correlations with other genes, such that the mean correlation in a typical gene co-expression network is close to 0 and follows an approximately normal distribution e.