Sigma: multiple alignment of weakly-conserved non-coding DNA sequence

BACKGROUND: Existing tools for multiple-sequence alignment focus on aligning protein sequence or protein-coding DNA sequence, and are often based on extensions to Needleman-Wunsch-like pairwise alignment methods. We introduce a new tool, Sigma, with a new algorithm and scoring scheme designed specifically for non-coding DNA sequence. This problem acquires importance with the increasing number of published sequences of closely-related species. In particular, studies of gene regulation seek to take advantage of comparative genomics, and recent algorithms for finding regulatory sites in phylogenetically-related intergenic sequence require alignment as a preprocessing step. Much can also be learned about evolution from intergenic DNA, which tends to evolve faster than coding DNA. Sigma uses a strategy of seeking the best possible gapless local alignments (a strategy earlier used by DiAlign), at each step making the best possible alignment consistent with existing alignments, and scores the significance of the alignment based on the lengths of the aligned fragments and a background model which may be supplied or estimated from an auxiliary file of intergenic DNA. RESULTS: Comparative tests of sigma with five earlier algorithms on synthetic data generated to mimic real data show excellent performance, with Sigma balancing high "sensitivity" (more bases aligned) with effective filtering of "incorrect" alignments. With real data, while "correctness" can't be directly quantified for the alignment, running the PhyloGibbs motif finder on pre-aligned sequence suggests that Sigma's alignments are superior. CONCLUSION: By taking into account the peculiarities of non-coding DNA, Sigma fills a gap in the toolbox of bioinformatics

PhyloGibbs-MP: Module Prediction and Discriminative Motif-Finding by Gibbs Sampling

PhyloGibbs, our recent Gibbs-sampling motif-finder, takes phylogeny into account in detecting binding sites for transcription factors in DNA and assigns posterior probabilities to its predictions obtained by sampling the entire configuration space. Here, in an extension called PhyloGibbs-MP, we widen the scope of the program, addressing two major problems in computational regulatory genomics. First, PhyloGibbs-MP can localise predictions to small, undetermined regions of a large input sequence, thus effectively predicting cis-regulatory modules (CRMs) ab initio while simultaneously predicting binding sites in those modules—tasks that are usually done by two separate programs. PhyloGibbs-MP's performance at such ab initio CRM prediction is comparable with or superior to dedicated module-prediction software that use prior knowledge of previously characterised transcription factors. Second, PhyloGibbs-MP can predict motifs that differentiate between two (or more) different groups of regulatory regions, that is, motifs that occur preferentially in one group over the others. While other “discriminative motif-finders” have been published in the literature, PhyloGibbs-MP's implementation has some unique features and flexibility. Benchmarks on synthetic and actual genomic data show that this algorithm is successful at enhancing predictions of differentiating sites and suppressing predictions of common sites and compares with or outperforms other discriminative motif-finders on actual genomic data. Additional enhancements include significant performance and speed improvements, the ability to use “informative priors” on known transcription factors, and the ability to output annotations in a format that can be visualised with the Generic Genome Browser. In stand-alone motif-finding, PhyloGibbs-MP remains competitive, outperforming PhyloGibbs-1.0 and other programs on benchmark data

Dynamical Mean-Field Theory of Resonating Valence Bond Antiferromagnets

We propose a theory of the spin dynamics of frustrated quantum antiferromagnets, which is based on an effective action for a plaquette embedded in a self-consistent bath. This approach, supplemented by a low-energy projection, is applied to the kagome antiferromagnet. We find that a spin-liquid regime extends to very low energy, in which local correlation functions have a slow decay in time, well described by a power law behaviour and $\omega/T$ scaling of the response function: $\chi''(\omega)\propto \omega^{-\alpha}F(\omega/T)$.Comment: 5 pages, 3 figures; contains some clarifications on the role of the triplet states and the triplet ga

MMM and MMMSynth: Clustering of heterogeneous tabular data, and synthetic data generation

We provide new algorithms for two tasks relating to heterogeneous tabular datasets: clustering, and synthetic data generation. Tabular datasets typically consist of heterogeneous data types (numerical, ordinal, categorical) in columns, but may also have hidden cluster structure in their rows: for example, they may be drawn from heterogeneous (geographical, socioeconomic, methodological) sources, such that the outcome variable they describe (such as the presence of a disease) may depend not only on the other variables but on the cluster context. Moreover, sharing of biomedical data is often hindered by patient confidentiality laws, and there is current interest in algorithms to generate synthetic tabular data from real data, for example via deep learning. We demonstrate a novel EM-based clustering algorithm, MMM (``Madras Mixture Model''), that outperforms standard algorithms in determining clusters in synthetic heterogeneous data, and recovers structure in real data. Based on this, we demonstrate a synthetic tabular data generation algorithm, MMMsynth, that pre-clusters the input data, and generates cluster-wise synthetic data assuming cluster-specific data distributions for the input columns. We benchmark this algorithm by testing the performance of standard ML algorithms when they are trained on synthetic data and tested on real published datasets. Our synthetic data generation algorithm outperforms other literature tabular-data generators, and approaches the performance of training purely with real data.Comment: 16 pages, 4 figure

Dinucleotide Weight Matrices for Predicting Transcription Factor Binding Sites: Generalizing the Position Weight Matrix

Background: Identifying transcription factor binding sites (TFBS) in silico is key in understanding gene regulation. TFBS are string patterns that exhibit some variability, commonly modelled as ‘‘position weight matrices’ ’ (PWMs). Though convenient, the PWM has significant limitations, in particular the assumed independence of positions within the binding motif; and predictions based on PWMs are usually not very specific to known functional sites. Analysis here on binding sites in yeast suggests that correlation of dinucleotides is not limited to near-neighbours, but can extend over considerable gaps. Methodology/Principal Findings: I describe a straightforward generalization of the PWM model, that considers frequencies of dinucleotides instead of individual nucleotides. Unlike previous efforts, this method considers all dinucleotides within an extended binding region, and does not make an attempt to determine a priori the significance of particular dinucleotide correlations. I describe how to use a ‘‘dinucleotide weight matrix’ ’ (DWM) to predict binding sites, dealing in particular with the complication that its entries are not independent probabilities. Benchmarks show, for many factors, a dramatic improvement over PWMs in precision of predicting known targets. In most cases, significant further improvement arises by extending the commonly defined ‘‘core motifs’ ’ by about 10bp on either side. Though this flanking sequence shows no strong motif at the nucleotide level, the predictive power of the dinucleotide model suggests that the ‘‘signature’ ’ in DNA sequence of protein-binding affinity extends beyond the core protein-DNA contact region

Quantizing the Toda lattice

In this work we study the quantum Toda lattice, developing the asymptotic Bethe ansatz method first used by Sutherland. Despite its known limitations we find, on comparing with Gutzwiller's exact method, that it works well in this particular problem and in fact becomes exact as ħ grows large. We calculate ground state and excitation energies for finite-sized lattices, identify excitations as phonons and solitons on the basis of their quantum numbers, and find their dispersions. These are similar to the classical dispersions for small ħ, and remain similar all the way up to ħ=1, but then deviate substantially as we go farther into the quantum regime. On comparing the sound velocities for various ħ obtained thus with that predicted by conformal theory we conclude that the Bethe ansatz gives the energies per particle accurate to O(1/N2). On that assumption we can find correlation functions. Thus the Bethe ansatz method can be used to yield much more than the thermodynamic properties which previous authors have calculated

PhyloGibbs: A Gibbs Sampling Motif Finder That Incorporates Phylogeny

A central problem in the bioinformatics of gene regulation is to find the binding sites for regulatory proteins. One of the most promising approaches toward identifying these short and fuzzy sequence patterns is the comparative analysis of orthologous intergenic regions of related species. This analysis is complicated by various factors. First, one needs to take the phylogenetic relationship between the species into account in order to distinguish conservation that is due to the occurrence of functional sites from spurious conservation that is due to evolutionary proximity. Second, one has to deal with the complexities of multiple alignments of orthologous intergenic regions, and one has to consider the possibility that functional sites may occur outside of conserved segments. Here we present a new motif sampling algorithm, PhyloGibbs, that runs on arbitrary collections of multiple local sequence alignments of orthologous sequences. The algorithm searches over all ways in which an arbitrary number of binding sites for an arbitrary number of transcription factors (TFs) can be assigned to the multiple sequence alignments. These binding site configurations are scored by a Bayesian probabilistic model that treats aligned sequences by a model for the evolution of binding sites and “background” intergenic DNA. This model takes the phylogenetic relationship between the species in the alignment explicitly into account. The algorithm uses simulated annealing and Monte Carlo Markov-chain sampling to rigorously assign posterior probabilities to all the binding sites that it reports. In tests on synthetic data and real data from five Saccharomyces species our algorithm performs significantly better than four other motif-finding algorithms, including algorithms that also take phylogeny into account. Our results also show that, in contrast to the other algorithms, PhyloGibbs can make realistic estimates of the reliability of its predictions. Our tests suggest that, running on the five-species multiple alignment of a single gene's upstream region, PhyloGibbs on average recovers over 50% of all binding sites in S. cerevisiae at a specificity of about 50%, and 33% of all binding sites at a specificity of about 85%. We also tested PhyloGibbs on collections of multiple alignments of intergenic regions that were recently annotated, based on ChIP-on-chip data, to contain binding sites for the same TF. We compared PhyloGibbs's results with the previous analysis of these data using six other motif-finding algorithms. For 16 of 21 TFs for which all other motif-finding methods failed to find a significant motif, PhyloGibbs did recover a motif that matches the literature consensus. In 11 cases where there was disagreement in the results we compiled lists of known target genes from the literature, and found that running PhyloGibbs on their regulatory regions yielded a binding motif matching the literature consensus in all but one of the cases. Interestingly, these literature gene lists had little overlap with the targets annotated based on the ChIP-on-chip data. The PhyloGibbs code can be downloaded from http://www.biozentrum.unibas.ch/~nimwegen/cgi-bin/phylogibbs.cgi or http://www.imsc.res.in/~rsidd/phylogibbs. The full set of predicted sites from our tests on yeast are available at http://www.swissregulon.unibas.ch

Exact ground state and kink-like excitations of a two dimensional Heisenberg antiferromagnet

A rare example of a two dimensional Heisenberg model with an exact dimerized ground state is presented. This model, which can be regarded as a variation on the kagome lattice, has several features of interest: it has a highly (but not macroscopically) degenerate ground state; it is closely related to spin chains studied by earlier authors; in particular, it is probably the first genuinely two-dimensional quantum system to exhibit domain-wall-like ``kink'' excitations normally found only in one-dimensional systems. In some limits it decouples into non-interacting chains, purely dynamically and not because of weakening of interchain couplings: indeed, paradoxically, this happens in the limit of strong coupling of the chains.Comment: 4 pages, revtex, 5 figures included via epsfi