Analytical approximations for the amplitude and period of a relaxation oscillator

<p>Abstract</p> <p>Background</p> <p>Analysis and design of complex systems benefit from mathematically tractable models, which are often derived by approximating a nonlinear system with an effective equivalent linear system. Biological oscillators with coupled positive and negative feedback loops, termed hysteresis or relaxation oscillators, are an important class of nonlinear systems and have been the subject of comprehensive computational studies. Analytical approximations have identified criteria for sustained oscillations, but have not linked the observed period and phase to compact formulas involving underlying molecular parameters.</p> <p>Results</p> <p>We present, to our knowledge, the first analytical expressions for the period and amplitude of a classic model for the animal circadian clock oscillator. These compact expressions are in good agreement with numerical solutions of corresponding continuous ODEs and for stochastic simulations executed at literature parameter values. The formulas are shown to be useful by permitting quick comparisons relative to a negative-feedback represillator oscillator for noise (10× less sensitive to protein decay rates), efficiency (2× more efficient), and dynamic range (30 to 60 decibel increase). The dynamic range is enhanced at its lower end by a new concentration scale defined by the crossing point of the activator and repressor, rather than from a steady-state expression level.</p> <p>Conclusion</p> <p>Analytical expressions for oscillator dynamics provide a physical understanding for the observations from numerical simulations and suggest additional properties not readily apparent or as yet unexplored. The methods described here may be applied to other nonlinear oscillator designs and biological circuits.</p

Genetic interaction motif finding by expectation maximization – a novel statistical model for inferring gene modules from synthetic lethality

BACKGROUND: Synthetic lethality experiments identify pairs of genes with complementary function. More direct functional associations (for example greater probability of membership in a single protein complex) may be inferred between genes that share synthetic lethal interaction partners than genes that are directly synthetic lethal. Probabilistic algorithms that identify gene modules based on motif discovery are highly appropriate for the analysis of synthetic lethal genetic interaction data and have great potential in integrative analysis of heterogeneous datasets. RESULTS: We have developed Genetic Interaction Motif Finding (GIMF), an algorithm for unsupervised motif discovery from synthetic lethal interaction data. Interaction motifs are characterized by position weight matrices and optimized through expectation maximization. Given a seed gene, GIMF performs a nonlinear transform on the input genetic interaction data and automatically assigns genes to the motif or non-motif category. We demonstrate the capacity to extract known and novel pathways for Saccharomyces cerevisiae (budding yeast). Annotations suggested for several uncharacterized genes are supported by recent experimental evidence. GIMF is efficient in computation, requires no training and automatically down-weights promiscuous genes with high degrees. CONCLUSION: GIMF effectively identifies pathways from synthetic lethality data with several unique features. It is mostly suitable for building gene modules around seed genes. Optimal choice of one single model parameter allows construction of gene networks with different levels of confidence. The impact of hub genes the generic probabilistic framework of GIMF may be used to group other types of biological entities such as proteins based on stochastic motifs. Analysis of the strongest motifs discovered by the algorithm indicates that synthetic lethal interactions are depleted between genes within a motif, suggesting that synthetic lethality occurs between-pathway rather than within-pathway

RNA-Seq optimization with eQTL gold standards.

BackgroundRNA-Sequencing (RNA-Seq) experiments have been optimized for library preparation, mapping, and gene expression estimation. These methods, however, have revealed weaknesses in the next stages of analysis of differential expression, with results sensitive to systematic sample stratification or, in more extreme cases, to outliers. Further, a method to assess normalization and adjustment measures imposed on the data is lacking.ResultsTo address these issues, we utilize previously published eQTLs as a novel gold standard at the center of a framework that integrates DNA genotypes and RNA-Seq data to optimize analysis and aid in the understanding of genetic variation and gene expression. After detecting sample contamination and sequencing outliers in RNA-Seq data, a set of previously published brain eQTLs was used to determine if sample outlier removal was appropriate. Improved replication of known eQTLs supported removal of these samples in downstream analyses. eQTL replication was further employed to assess normalization methods, covariate inclusion, and gene annotation. This method was validated in an independent RNA-Seq blood data set from the GTEx project and a tissue-appropriate set of eQTLs. eQTL replication in both data sets highlights the necessity of accounting for unknown covariates in RNA-Seq data analysis.ConclusionAs each RNA-Seq experiment is unique with its own experiment-specific limitations, we offer an easily-implementable method that uses the replication of known eQTLs to guide each step in one's data analysis pipeline. In the two data sets presented herein, we highlight not only the necessity of careful outlier detection but also the need to account for unknown covariates in RNA-Seq experiments

Dynamic Networks from Hierarchical Bayesian Graph Clustering

Biological networks change dynamically as protein components are synthesized and degraded. Understanding the time-dependence and, in a multicellular organism, tissue-dependence of a network leads to insight beyond a view that collapses time-varying interactions into a single static map. Conventional algorithms are limited to analyzing evolving networks by reducing them to a series of unrelated snapshots

Fast Association Tests for Genes with FAST

Gene-based tests of association can increase the power of a genome-wide association study by aggregating multiple independent effects across a gene or locus into a single stronger signal. Recent gene-based tests have distinct approaches to selecting which variants to aggregate within a locus, modeling the effects of linkage disequilibrium, representing fractional allele counts from imputation, and managing permutation tests for p-values. Implementing these tests in a single, efficient framework has great practical value. Fast ASsociation Tests (Fast) addresses this need by implementing leading gene-based association tests together with conventional SNP-based univariate tests and providing a consolidated, easily interpreted report. Fast scales readily to genome-wide SNP data with millions of SNPs and tens of thousands of individuals, provides implementations that are orders of magnitude faster than original literature reports, and provides a unified framework for performing several gene based association tests concurrently and efficiently on the same data. Availability: https://bitbucket.org/baderlab/fast/downloads/FAST.tar.gz, with documentation at https://bitbucket.org/baderlab/fast/wiki/Hom

NeMo: Network Module identification in Cytoscape

© 2010 Rivera et al; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution Licens

Commensurate distances and similar motifs in genetic congruence and protein interaction networks in yeast

BACKGROUND: In a genetic interaction, the phenotype of a double mutant differs from the combined phenotypes of the underlying single mutants. When the single mutants have no growth defect, but the double mutant is lethal or exhibits slow growth, the interaction is termed synthetic lethality or synthetic fitness. These genetic interactions reveal gene redundancy and compensating pathways. Recently available large-scale data sets of genetic interactions and protein interactions in Saccharomyces cerevisiae provide a unique opportunity to elucidate the topological structure of biological pathways and how genes function in these pathways. RESULTS: We have defined congruent genes as pairs of genes with similar sets of genetic interaction partners and constructed a genetic congruence network by linking congruent genes. By comparing path lengths in three types of networks (genetic interaction, genetic congruence, and protein interaction), we discovered that high genetic congruence not only exhibits correlation with direct protein interaction linkage but also exhibits commensurate distance with the protein interaction network. However, consistent distances were not observed between genetic and protein interaction networks. We also demonstrated that congruence and protein networks are enriched with motifs that indicate network transitivity, while the genetic network has both transitive (triangle) and intransitive (square) types of motifs. These results suggest that robustness of yeast cells to gene deletions is due in part to two complementary pathways (square motif) or three complementary pathways, any two of which are required for viability (triangle motif). CONCLUSION: Genetic congruence is superior to genetic interaction in prediction of protein interactions and function associations. Genetically interacting pairs usually belong to parallel compensatory pathways, which can generate transitive motifs (any two of three pathways needed) or intransitive motifs (either of two pathways needed)

Where Have All the Interactions Gone? Estimating the Coverage of Two-Hybrid Protein Interaction Maps

Yeast two-hybrid screens are an important method for mapping pairwise physical interactions between proteins. The fraction of interactions detected in independent screens can be very small, and an outstanding challenge is to determine the reason for the low overlap. Low overlap can arise from either a high false-discovery rate (interaction sets have low overlap because each set is contaminated by a large number of stochastic false-positive interactions) or a high false-negative rate (interaction sets have low overlap because each misses many true interactions). We extend capture–recapture theory to provide the first unified model for false-positive and false-negative rates for two-hybrid screens. Analysis of yeast, worm, and fly data indicates that 25% to 45% of the reported interactions are likely false positives. Membrane proteins have higher false-discovery rates on average, and signal transduction proteins have lower rates. The overall false-negative rate ranges from 75% for worm to 90% for fly, which arises from a roughly 50% false-negative rate due to statistical undersampling and a 55% to 85% false-negative rate due to proteins that appear to be systematically lost from the assays. Finally, statistical model selection conclusively rejects the Erdös-Rényi network model in favor of the power law model for yeast and the truncated power law for worm and fly degree distributions. Much as genome sequencing coverage estimates were essential for planning the human genome sequencing project, the coverage estimates developed here will be valuable for guiding future proteomic screens. All software and datasets are available in Datasets S1 and S2, Figures S1–S5, and Tables S1−S6, and are also available from our Web site, http://www.baderzone.org