Boolean Dynamics with Random Couplings

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d, the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical Sciences Serie

Predicting Target DNA Sequences of DNA-Binding Proteins Based on Unbound Structures

DNA-binding proteins such as transcription factors use DNA-binding domains (DBDs) to bind to specific sequences in the genome to initiate many important biological functions. Accurate prediction of such target sequences, often represented by position weight matrices (PWMs), is an important step to understand many biological processes. Recent studies have shown that knowledge-based potential functions can be applied on protein-DNA co-crystallized structures to generate PWMs that are considerably consistent with experimental data. However, this success has not been extended to DNA-binding proteins lacking co-crystallized structures. This study aims at investigating the possibility of predicting the DNA sequences bound by DNA-binding proteins from the proteins' unbound structures (structures of the unbound state). Given an unbound query protein and a template complex, the proposed method first employs structure alignment to generate synthetic protein-DNA complexes for the query protein. Once a complex is available, an atomic-level knowledge-based potential function is employed to predict PWMs characterizing the sequences to which the query protein can bind. The evaluation of the proposed method is based on seven DNA-binding proteins, which have structures of both DNA-bound and unbound forms for prediction as well as annotated PWMs for validation. Since this work is the first attempt to predict target sequences of DNA-binding proteins from their unbound structures, three types of structural variations that presumably influence the prediction accuracy were examined and discussed. Based on the analyses conducted in this study, the conformational change of proteins upon binding DNA was shown to be the key factor. This study sheds light on the challenge of predicting the target DNA sequences of a protein lacking co-crystallized structures, which encourages more efforts on the structure alignment-based approaches in addition to docking- and homology modeling-based approaches for generating synthetic complexes

Temperature, recreational fishing and diapause egg connections : dispersal of spiny water fleas (Bythotrephes longimanus)

© The Author(s), 2011. This article is distributed under the terms of the Creative Commons Attribution Noncommercial License. The definitive version was published in Biological Invasions 13 (2011): 2513-2531, doi:10.1007/s10530-011-0078-8.The spiny water flea (Bythotrephes longimanus) is spreading from Great Lakes coastal waters into northern inland lakes within a northern temperature-defined latitudinal band. Colonization of Great Lakes coastal embayments is assisted by winds and seiche surges, yet rapid inland expansion across the northern states comes through an overland process. The lack of invasions at Isle Royale National Park contrasts with rapid expansion on the nearby Keweenaw Peninsula. Both regions have comparable geology, lake density, and fauna, but differ in recreational fishing boat access, visitation, and containment measures. Tail spines protect Bythotrephes against young of the year, but not larger fish, yet the unusual thick-shelled diapausing eggs can pass through fish guts in viable condition. Sediment traps illustrate how fish spread diapausing eggs across lakes in fecal pellets. Trillions of diapausing eggs are produced per year in Lake Michigan and billions per year in Lake Michigamme, a large inland lake. Dispersal by recreational fishing is linked to use of baitfish, diapausing eggs defecated into live wells and bait buckets, and Bythothephes snagged on fishing line, anchor ropes, and minnow seines. Relatively simple measures, such as on-site rinsing of live wells, restricting transfer of certain baitfish species, or holding baitfish for 24 h (defecation period), should greatly reduce dispersal.Study of Lakes Superior and Michigan was funded from NSF OCE-9726680 and OCE-9712872 to W.C.K., OCE-9712889 to J. Churchill. Geographic survey sampling and Park studies in the national parks during 2008-2010 were funded by a grant from the National Park Service Natural Resource Preservation Program GLNF CESU Task Agreement No. J6067080012

Discriminative motif discovery in DNA and protein sequences using the DEME algorithm

<p>Abstract</p> <p>Background</p> <p>Motif discovery aims to detect short, highly conserved patterns in a collection of unaligned DNA or protein sequences. Discriminative motif finding algorithms aim to increase the sensitivity and selectivity of motif discovery by utilizing a second set of sequences, and searching only for patterns that can differentiate the two sets of sequences. Potential applications of discriminative motif discovery include discovering transcription factor binding site motifs in ChIP-chip data and finding protein motifs involved in thermal stability using sets of orthologous proteins from thermophilic and mesophilic organisms.</p> <p>Results</p> <p>We describe DEME, a discriminative motif discovery algorithm for use with protein and DNA sequences. Input to DEME is two sets of sequences; a "positive" set and a "negative" set. DEME represents motifs using a probabilistic model, and uses a novel combination of global and local search to find the motif that optimally discriminates between the two sets of sequences. DEME is unique among discriminative motif finders in that it uses an informative Bayesian prior on protein motif columns, allowing it to incorporate prior knowledge of residue characteristics. We also introduce four, synthetic, discriminative motif discovery problems that are designed for evaluating discriminative motif finders in various biologically motivated contexts. We test DEME using these synthetic problems and on two biological problems: finding yeast transcription factor binding motifs in ChIP-chip data, and finding motifs that discriminate between groups of thermophilic and mesophilic orthologous proteins.</p> <p>Conclusion</p> <p>Using artificial data, we show that DEME is more effective than a non-discriminative approach when there are "decoy" motifs or when a variant of the motif is present in the "negative" sequences. With real data, we show that DEME is as good, but not better than non-discriminative algorithms at discovering yeast transcription factor binding motifs. We also show that DEME can find highly informative thermal-stability protein motifs. Binaries for the stand-alone program DEME is free for academic use and is available at <url>http://bioinformatics.org.au/deme/</url></p

A Predictive Model of the Oxygen and Heme Regulatory Network in Yeast

Deciphering gene regulatory mechanisms through the analysis of high-throughput expression data is a challenging computational problem. Previous computational studies have used large expression datasets in order to resolve fine patterns of coexpression, producing clusters or modules of potentially coregulated genes. These methods typically examine promoter sequence information, such as DNA motifs or transcription factor occupancy data, in a separate step after clustering. We needed an alternative and more integrative approach to study the oxygen regulatory network in Saccharomyces cerevisiae using a small dataset of perturbation experiments. Mechanisms of oxygen sensing and regulation underlie many physiological and pathological processes, and only a handful of oxygen regulators have been identified in previous studies. We used a new machine learning algorithm called MEDUSA to uncover detailed information about the oxygen regulatory network using genome-wide expression changes in response to perturbations in the levels of oxygen, heme, Hap1, and Co2+. MEDUSA integrates mRNA expression, promoter sequence, and ChIP-chip occupancy data to learn a model that accurately predicts the differential expression of target genes in held-out data. We used a novel margin-based score to extract significant condition-specific regulators and assemble a global map of the oxygen sensing and regulatory network. This network includes both known oxygen and heme regulators, such as Hap1, Mga2, Hap4, and Upc2, as well as many new candidate regulators. MEDUSA also identified many DNA motifs that are consistent with previous experimentally identified transcription factor binding sites. Because MEDUSA's regulatory program associates regulators to target genes through their promoter sequences, we directly tested the predicted regulators for OLE1, a gene specifically induced under hypoxia, by experimental analysis of the activity of its promoter. In each case, deletion of the candidate regulator resulted in the predicted effect on promoter activity, confirming that several novel regulators identified by MEDUSA are indeed involved in oxygen regulation. MEDUSA can reveal important information from a small dataset and generate testable hypotheses for further experimental analysis. Supplemental data are included

Inferring the role of transcription factors in regulatory networks

<p>Abstract</p> <p>Background</p> <p>Expression profiles obtained from multiple perturbation experiments are increasingly used to reconstruct transcriptional regulatory networks, from well studied, simple organisms up to higher eukaryotes. Admittedly, a key ingredient in developing a reconstruction method is its ability to integrate heterogeneous sources of information, as well as to comply with practical observability issues: measurements can be scarce or noisy. In this work, we show how to combine a network of genetic regulations with a set of expression profiles, in order to infer the functional effect of the regulations, as inducer or repressor. Our approach is based on a consistency rule between a network and the signs of variation given by expression arrays.</p> <p>Results</p> <p>We evaluate our approach in several settings of increasing complexity. First, we generate artificial expression data on a transcriptional network of <it>E. coli </it>extracted from the literature (1529 nodes and 3802 edges), and we estimate that 30% of the regulations can be annotated with about 30 profiles. We additionally prove that at most 40.8% of the network can be inferred using our approach. Second, we use this network in order to validate the predictions obtained with a compendium of real expression profiles. We describe a filtering algorithm that generates particularly reliable predictions. Finally, we apply our inference approach to <it>S. cerevisiae </it>transcriptional network (2419 nodes and 4344 interactions), by combining ChIP-chip data and 15 expression profiles. We are able to detect and isolate inconsistencies between the expression profiles and a significant portion of the model (15% of all the interactions). In addition, we report predictions for 14.5% of all interactions.</p> <p>Conclusion</p> <p>Our approach does not require accurate expression levels nor times series. Nevertheless, we show on both data, real and artificial, that a relatively small number of perturbation experiments are enough to determine a significant portion of regulatory effects. This is a key practical asset compared to statistical methods for network reconstruction. We demonstrate that our approach is able to provide accurate predictions, even when the network is incomplete and the data is noisy.</p

Network deconvolution as a general method to distinguish direct dependencies in networks

Recognizing direct relationships between variables connected in a network is a pervasive problem in biological, social and information sciences as correlation-based networks contain numerous indirect relationships. Here we present a general method for inferring direct effects from an observed correlation matrix containing both direct and indirect effects. We formulate the problem as the inverse of network convolution, and introduce an algorithm that removes the combined effect of all indirect paths of arbitrary length in a closed-form solution by exploiting eigen-decomposition and infinite-series sums. We demonstrate the effectiveness of our approach in several network applications: distinguishing direct targets in gene expression regulatory networks; recognizing directly interacting amino-acid residues for protein structure prediction from sequence alignments; and distinguishing strong collaborations in co-authorship social networks using connectivity information alone. In addition to its theoretical impact as a foundational graph theoretic tool, our results suggest network deconvolution is widely applicable for computing direct dependencies in network science across diverse disciplines.National Institutes of Health (U.S.) (grant R01 HG004037)National Institutes of Health (U.S.) (grant HG005639)Swiss National Science Foundation (Fellowship)National Science Foundation (U.S.) (NSF CAREER Award 0644282

Embedding mRNA Stability in Correlation Analysis of Time-Series Gene Expression Data

Current methods for the identification of putatively co-regulated genes directly from gene expression time profiles are based on the similarity of the time profile. Such association metrics, despite their central role in gene network inference and machine learning, have largely ignored the impact of dynamics or variation in mRNA stability. Here we introduce a simple, but powerful, new similarity metric called lead-lag R2 that successfully accounts for the properties of gene dynamics, including varying mRNA degradation and delays. Using yeast cell-cycle time-series gene expression data, we demonstrate that the predictive power of lead-lag R2 for the identification of co-regulated genes is significantly higher than that of standard similarity measures, thus allowing the selection of a large number of entirely new putatively co-regulated genes. Furthermore, the lead-lag metric can also be used to uncover the relationship between gene expression time-series and the dynamics of formation of multiple protein complexes. Remarkably, we found a high lead-lag R2 value among genes coding for a transient complex

Learning a Prior on Regulatory Potential from eQTL Data

Genome-wide RNA expression data provide a detailed view of an organism's biological state; hence, a dataset measuring expression variation between genetically diverse individuals (eQTL data) may provide important insights into the genetics of complex traits. However, with data from a relatively small number of individuals, it is difficult to distinguish true causal polymorphisms from the large number of possibilities. The problem is particularly challenging in populations with significant linkage disequilibrium, where traits are often linked to large chromosomal regions containing many genes. Here, we present a novel method, Lirnet, that automatically learns a regulatory potential for each sequence polymorphism, estimating how likely it is to have a significant effect on gene expression. This regulatory potential is defined in terms of “regulatory features”—including the function of the gene and the conservation, type, and position of genetic polymorphisms—that are available for any organism. The extent to which the different features influence the regulatory potential is learned automatically, making Lirnet readily applicable to different datasets, organisms, and feature sets. We apply Lirnet both to the human HapMap eQTL dataset and to a yeast eQTL dataset and provide statistical and biological results demonstrating that Lirnet produces significantly better regulatory programs than other recent approaches. We demonstrate in the yeast data that Lirnet can correctly suggest a specific causal sequence variation within a large, linked chromosomal region. In one example, Lirnet uncovered a novel, experimentally validated connection between Puf3—a sequence-specific RNA binding protein—and P-bodies—cytoplasmic structures that regulate translation and RNA stability—as well as the particular causative polymorphism, a SNP in Mkt1, that induces the variation in the pathway