There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Data Mining - Concepts and Techniques.

The dramatic progress in sequencing technologies offers unprecedented prospects for deciphering the organization of natural populations in space and time. However, the size of the datasets generated also poses some daunting challenges. In particular, Bayesian clustering algorithms based on pre-defined population genetics models such as the STRUCTURE or BAPS software may not be able to cope with this unprecedented amount of data. Thus, there is a need for less computer-intensive approaches. Multivariate analyses seem particularly appealing as they are specifically devoted to extracting information from large datasets. Unfortunately, currently available multivariate methods still lack some essential features needed to study the genetic structure of natural populations. We introduce the Discriminant Analysis of Principal Components (DAPC), a multivariate method designed to identify and describe clusters of genetically related individuals. When group priors are lacking, DAPC uses sequential K-means and model selection to infer genetic clusters. Our approach allows extracting rich information from genetic data, providing assignment of individuals to groups, a visual assessment of between-population differentiation, and contribution of individual alleles to population structuring. We evaluate the performance of our method using simulated data, which were also analyzed using STRUCTURE as a benchmark. Additionally, we illustrate the method by analyzing microsatellite polymorphism in worldwide human populations and hemagglutinin gene sequence variation in seasonal influenza. Analysis of simulated data revealed that our approach performs generally better than STRUCTURE at characterizing population subdivision. The tools implemented in DAPC for the identification of clusters and graphical representation of between-group structures allow to unravel complex population structures. Our approach is also faster than Bayesian clustering algorithms by several orders of magnitude, and may be applicable to a wider range of datasets.

/pdf/discriminant-analysis-of-principal-components-a-new-method-2ju1yy0ejo.pdf

Discriminant analysis of principal components: a new method for the analysis of genetically structured populations

An overview of the self-organizing map algorithm, on which the papers in this issue are based, is presented in this article.

The Self-Organizing Map

https://www.cell.com/neuron/pdf/S0896-6273(11)00374-6.pdf

Multiple Recurrent De Novo CNVs, Including Duplications of the 7q11.23 Williams Syndrome Region, Are Strongly Associated with Autism

Network motifs are statistically overrepresented sub-structures (sub-graphs) in a network, and have been recognized as ‘the simple building blocks of complex networks’. Study of biological network motifs may reveal answers to many important biological questions. The main difficulty in detecting larger network motifs in biological networks lies in the facts that the number of possible sub-graphs increases exponentially with the network or motif size (node counts, in general), and that no known polynomial-time algorithm exists in deciding if two graphs are topologically equivalent. This article discusses the biological significance of network motifs, the motivation behind solving the motif-finding problem, and strategies to solve the various aspects of this problem. A simple classification scheme is designed to analyze the strengths and weaknesses of several existing algorithms. Experimental results derived from a few comparative studies in the literature are discussed, with conclusions that lead to future research directions.

/pdf/biological-network-motif-detection-principles-and-practice-2dq2179bev.pdf

Biological network motif detection: principles and practice

In addition to large domains, many short motifs mediate functional post-translational modification of proteins as well as protein-protein interactions and protein trafficking functions. We have constructed a motif database comprising 312 unique motifs and a web-based tool for identifying motifs in proteins. Functional motifs predicted by MnM can be ranked by several approaches, and we validated these scores by analyzing thousands of confirmed examples and by confirming prediction of previously unidentified 14-3-3 motifs in EFF-1.

http://schillerlab.bio-toolkit.com/media/pdfs/2010/03/18/2006_NatMethods_Balla.pdf

Minimotif Miner: a tool for investigating protein function.

The release of ChIP-seq data from the ENCyclopedia Of DNA Elements (ENCODE) and Model Organism ENCyclopedia Of DNA Elements (modENCODE) projects has significantly increased the amount of transcription factor (TF) binding affinity information available to researchers. However, scientists still routinely use TF binding site (TFBS) search tools to scan unannotated sequences for TFBSs, particularly when searching for lesser-known TFs or TFs in organisms for which ChIP-seq data are unavailable. The sequence analysis often involves multiple steps such as TF model collection, promoter sequence retrieval, and visualization; thus, several different tools are required. We have developed a novel integrated web tool named LASAGNA-Search that allows users to perform TFBS searches without leaving the web site. LASAGNA-Search uses the LASAGNA (Length-Aware Site Alignment Guided by Nucleotide Association) algorithm for TFBS alignment. Important features of LASAGNA-Search include (i) acceptance of unaligned variable-length TFBSs, (ii) a collection of 1726 TF models, (iii) automatic promoter sequence retrieval, (iv) visualization in the UCSC Genome Browser, and (v) gene regulatory network inference and visualization based on binding specificities. LASAGNA-Search is freely available at http://biogrid.engr.uconn.edu/lasagna_search/.

LASAGNA-Search: an integrated web tool for transcription factor binding site search and visualization.

Handling genotype data typed at hundreds of thousands of loci is very time-consuming and it is no exception for population structure inference. Therefore, we propose to apply PCA to the genotype data of a population, select the significant principal components using the Tracy-Widom distribution, and assign the individuals to one or more subpopulations using generic clustering algorithms. We investigated K-means, soft K-means and spectral clustering and made comparison to STRUCTURE, a model-based algorithm specifically designed for population structure inference. Moreover, we investigated methods for predicting the number of subpopulations in a population. The results on four simulated datasets and two real datasets indicate that our approach performs comparably well to STRUCTURE. For the simulated datasets, STRUCTURE and soft K-means with BIC produced identical predictions on the number of subpopulations. We also showed that, for real dataset, BIC is a better index than likelihood in predicting the number of subpopulations. Our approach has the advantage of being fast and scalable, while STRUCTURE is very time-consuming because of the nature of MCMC in parameter estimation. Therefore, we suggest choosing the proper algorithm based on the application of population structure inference.

/pdf/pca-based-population-structure-inference-with-generic-1v9ekjwqyu.pdf

PCA-based population structure inference with generic clustering algorithms

The problem of identifying meaningful patterns (i.e., motifs) from biological data has been studied extensively due to its paramount importance. Three versions of this problem have been identified in the literature. One of these three problems is the planted (l, d)-motif problem. Several instances of this problem have been posed as a challenge. Numerous algorithms have been proposed in the literature that address this challenge. Many of these algorithms fall under the category of heuristic algorithms. In this paper we present algorithms for the planted (l, d)-motif problem that always find the correct answer(s). Our algorithms are very simple and are based on some ideas that are fundamentally different from the ones employed in the literature. We believe that the techniques we introduce in this paper will find independent applications.

Chun-Hsi Huang

Papers

Biological network motif detection: principles and practice

Minimotif Miner: a tool for investigating protein function.

LASAGNA-Search: an integrated web tool for transcription factor binding site search and visualization.

PCA-based population structure inference with generic clustering algorithms

Exact algorithms for planted motif problems.