Abstract Background Permutation testing is often considered the “gold standard” for multi-test significance analysis, as it is an exact test requiring few assumptions about the distribution being computed. However, it can be computationally very expensive, particularly in its naive form in which the full analysis pipeline is re-run after permuting the phenotype labels. This can become intractable in multi-locus genome-wide association studies (GWAS), in which the number of potential interactions to be tested is combinatorially large. Results In this paper, we develop an approach for permutation testing in multi-locus GWAS, specifically focusing on SNP–SNP-phenotype interactions using multivariable measures that can be computed from frequency count tables, such as those based in Information Theory. We find that the computational bottleneck in this process is the construction of the count tables themselves, and that this step can be eliminated at each iteration of the permutation testing by transforming the count tables directly. This leads to a speed-up by a factor of over 103 for a typical permutation test compared to the naive approach. Additionally, this approach is insensitive to the number of samples making it suitable for datasets with large number of samples. Conclusions The proliferation of large-scale datasets with genotype data for hundreds of thousands of individuals enables new and more powerful approaches for the detection of multi-locus genotype-phenotype interactions. Our approach significantly improves the computational tractability of permutation testing for these studies. Moreover, our approach is insensitive to the large number of samples in these modern datasets. The code for performing these computations and replicating the figures in this paper is freely available at https://github.com/kunert/permute-counts .

BACKGROUND: Biomolecular pathways and networks are dynamic and complex, and the perturbations to them which cause disease are often multiple, heterogeneous and contingent. Pathway and network visualizations, rendered on a computer or published on paper, however, tend to be static, lacking in detail, and ill-equipped to explore the variety and quantities of data available today, and the complex causes we seek to understand. RESULTS: RCytoscape integrates R (an open-ended programming environment rich in statistical power and data-handling facilities) and Cytoscape (powerful network visualization and analysis software). RCytoscape extends Cytoscape's functionality beyond what is possible with the Cytoscape graphical user interface. To illustrate the power of RCytoscape, a portion of the Glioblastoma multiforme (GBM) data set from the Cancer Genome Atlas (TCGA) is examined. Network visualization reveals previously unreported patterns in the data suggesting heterogeneous signaling mechanisms active in GBM Proneural tumors, with possible clinical relevance. CONCLUSIONS: Progress in bioinformatics and computational biology depends upon exploratory and confirmatory data analysis, upon inference, and upon modeling. These activities will eventually permit the prediction and control of complex biological systems. Network visualizations--molecular maps--created from an open-ended programming environment rich in statistical power and data-handling facilities, such as RCytoscape, will play an essential role in this progression.

It is not obvious what fraction of all the potential information residing in the molecules and structures of living systems is significant or meaningful to the system. Sets of random sequences or identically repeated sequences, for example, would be expected to contribute little or no useful information to a cell. This issue of quantitation of information is important since the ebb and flow of biologically significant information is essential to our quantitative understanding of biological function and evolution. Motivated specifically by these problems of biological information, we propose here a class of measures to quantify the contextual nature of the information in sets of objects, based on Kolmogorov's intrinsic complexity. Such measures discount both random and redundant information and are inherent in that they do not require a defined state space to quantify the information. The maximization of this new measure, which can be formulated in terms of the universal information distance, appears to have several useful and interesting properties, some of which we illustrate with examples.

Extraction of all the biological information inherent in large-scale genetic interaction datasets remains a significant challenge for systems biology. The core problem is essentially that of classification of the relationships among phenotypes of mutant strains into biologically informative "rules" of gene interaction. Geneticists have determined such classifications based on insights from biological examples, but it is not clear that there is a systematic, unsupervised way to extract this information. In this paper we describe such a method that depends on maximizing a previously described context-dependent information measure to obtain maximally informative biological networks. We have successfully validated this method on two examples from yeast by demonstrating that more biological information is obtained when analysis is guided by this information measure. The context-dependent information measure is a function only of phenotype data and a set of interaction rules, involving no prior biological knowledge. Analysis of the resulting networks reveals that the most biologically informative networks are those with the greatest context-dependent information scores. We propose that these high-complexity networks reveal genetic architecture at a modular level, in contrast to classical genetic interaction rules that order genes in pathways. We suggest that our analysis represents a powerful, data-driven, and general approach to genetic interaction analysis, with particular potential in the study of mammalian systems in which interactions are complex and gene annotation data are sparse.

MOTIVATION: There has been considerable interest in developing computational techniques for inferring genetic regulatory networks from whole-genome expression profiles. When expression time series data sets are available, dynamic models can, in principle, be used to infer correlative relationships between gene expression levels, which may be causal. However, because of the range of detectable expression levels and the current quality of the data, the predictive nature of such inferred, quantitative models is questionable. Network models derived from simple rate laws offer an intermediate level analysis, going beyond simple statistical analysis, but falling short of a fully quantitative description. This work shows how such network models can be constructed and describes the global properties of the networks derived from such a model. These global properties are statistically robust and provide insights into the design of the underlying network. RESULTS: Several whole-genome expression time series data sets from yeast microarray experiments were analyzed using a Markov-modeling method (Dewey and Galas, FUNC: Integr. Genomics, 1, 269-278, 2001) to infer an approximation to the underlying genetic network. We found that the global statistical properties of all the resulting networks are similar. The overall structure of these biological networks is distinctly different from that of other recently studied networks such as the Internet or social networks. These biological networks show hierarchical, hub-like structures that have some properties similar to a class of graphs known as small world graphs. Small world networks exhibit local cliquishness while exhibiting strong global connectivity. In addition to the small world properties, the biological networks show a power law or scale free distribution of connectivities. An inverse power law, N(k) approximately k(-3/2), for the number of vertices (genes) with k connections was observed for three different data sets from yeast. We propose network growth models based on gene duplication events. Simulations of these models yield networks with the same combination of global graphical properties that we inferred from the expression data.