Peter Huggins

Cross species analysis of microarray expression data

MOTIVATION Many biological systems operate in a similar manner across a large number of species or conditions. Cross-species analysis of sequence and interaction data is often applied to determine the function of new genes. In contrast to these static measurements, microarrays measure the dynamic, condition-specific response of complex biological systems. The recent exponential growth in microarray expression datasets allows researchers to combine expression experiments from multiple species to identify genes that are not only conserved in sequence but also operated in a similar way in the different species studied. RESULTS In this review we discuss the computational and technical challenges associated with these studies, the approaches that have been developed to address these challenges and the advantages of cross-species analysis of microarray data. We show how successful application of these methods lead to insights that cannot be obtained when analyzing data from a single species. We also highlight current open problems and discuss possible ways to address them.

THE HYPERDETERMINANT AND TRIANGULATIONS OF THE 4-CUBE

PETER HUGGINS, BERND STURMFELS,JOSEPHINE YU AND DEBBIE S. YUSTERAbstract. The hyperdeterminant of format 2×2×2×2 is a polynomialof degree 24 in 16 unknowns which has 2894276 terms. We compute theNewton polytope of this polynomial and the secondary polytope of the 4-cube. The 87959448 regular triangulations of the 4-cube are classified into25448 D-equivalence classes, one for each vertex of the Newton polytope.The 4-cube has 80876 coarsest regular subdivisions, one for each facet of thesecondary polytope, but only 268 of them come from the hyperdeterminant.

Short rational functions for toric algebra and applications

Abstract We encode the binomials belonging to the toric ideal I A associated with an integral d × n matrix A using a short sum of rational functions as introduced by Barvinok (Math. Operations Research 19 (1994) 769) and Barvinok and Woods (J. Amer. Math. Soc. 16 (2003) 957). Under the assumption that d and n are fixed, this representation allows us to compute a universal Grobner basis and the reduced Grobner basis of the ideal I A , with respect to any term order, in time polynomial in the size of the input. We also derive a polynomial time algorithm for normal form computations which replaces in this new encoding the usual reductions typical of the division algorithm. We describe other applications, such as the computation of Hilbert series of normal semigroup rings, and we indicate applications to enumerative combinatorics, integer programming, and statistics.

Parametric Alignment of Drosophila Genomes

The classic algorithms of Needleman–Wunsch and Smith–Waterman find a maximum a posteriori probability alignment for a pair hidden Markov model (PHMM). To process large genomes that have undergone complex genome rearrangements, almost all existing whole genome alignment methods apply fast heuristics to divide genomes into small pieces that are suitable for Needleman–Wunsch alignment. In these alignment methods, it is standard practice to fix the parameters and to produce a single alignment for subsequent analysis by biologists. As the number of alignment programs applied on a whole genome scale continues to increase, so does the disagreement in their results. The alignments produced by different programs vary greatly, especially in non-coding regions of eukaryotic genomes where the biologically correct alignment is hard to find. Parametric alignment is one possible remedy. This methodology resolves the issue of robustness to changes in parameters by finding all optimal alignments for all possible parameters in a PHMM. Our main result is the construction of a whole genome parametric alignment of Drosophila melanogaster and Drosophila pseudoobscura. This alignment draws on existing heuristics for dividing whole genomes into small pieces for alignment, and it relies on advances we have made in computing convex polytopes that allow us to parametrically align non-coding regions using biologically realistic models. We demonstrate the utility of our parametric alignment for biological inference by showing that cis-regulatory elements are more conserved between Drosophila melanogaster and Drosophila pseudoobscura than previously thought. We also show how whole genome parametric alignment can be used to quantitatively assess the dependence of branch length estimates on alignment parameters.

Identification of differentially expressed thyroid hormone responsive genes from the brain of the Mexican Axolotl (Ambystoma mexicanum)

The Mexican axolotl (Ambystoma mexicanum) presents an excellent model to investigate mechanisms of brain development that are conserved among vertebrates. In particular, metamorphic changes of the brain can be induced in free-living aquatic juveniles and adults by simply adding thyroid hormone (T4) to rearing water. Whole brains were sampled from juvenile A. mexicanum that were exposed to 0, 8, and 18 days of 50 nM T4, and these were used to isolate RNA and make normalized cDNA libraries for 454 DNA sequencing. A total of 1,875,732 high quality cDNA reads were assembled with existing ESTs to obtain 5884 new contigs for human RefSeq protein models, and to develop a custom Affymetrix gene expression array (Amby_002) with approximately 20,000 probe sets. The Amby_002 array was used to identify 303 transcripts that differed statistically (p<0.05, fold change >1.5) as a function of days of T4 treatment. Further statistical analyses showed that Amby_002 performed concordantly in comparison to an existing, small format expression array. This study introduces a new A. mexicanum microarray resource for the community and the first lists of T4-responsive genes from the brain of a salamander amphibian.

DECOD: fast and accurate discriminative DNA motif finding

MOTIVATION Motif discovery is now routinely used in high-throughput studies including large-scale sequencing and proteomics. These datasets present new challenges. The first is speed. Many motif discovery methods do not scale well to large datasets. Another issue is identifying discriminative rather than generative motifs. Such discriminative motifs are important for identifying co-factors and for explaining changes in behavior between different conditions. RESULTS To address these issues we developed a method for DECOnvolved Discriminative motif discovery (DECOD). DECOD uses a k-mer count table and so its running time is independent of the size of the input set. By deconvolving the k-mers DECOD considers context information without using the sequences directly. DECOD outperforms previous methods both in speed and in accuracy when using simulated and real biological benchmark data. We performed new binding experiments for p53 mutants and used DECOD to identify p53 co-factors, suggesting new mechanisms for p53 activation. AVAILABILITY The source code and binaries for DECOD are available at http://www.sb.cs.cmu.edu/DECOD CONTACT: zivbj@cs.cmu.edu SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

iB4e : a software framework for parametrizing specialized LP problems

Given a polytope P, the classical linear programming (LP) problem asks us to find a point in P which attains maximal inner product with a given real objective vector c. When the objective is a vector of unknown parameters, the LP problem amounts to computing certain information about the polytope P, such as its vertices and normal fan.

Reconstruction of composite regulator-target splicing networks from high-throughput transcriptome data

We present a computational framework tailored for the modeling of the complex, dynamic relationships that are encountered in splicing regulation. The starting point is whole-genome transcriptomic data from high-throughput array or sequencing methods that are used to quantify gene expression and alternative splicing across multiple contexts. This information is used as input for state of the art methods for Graphical Model Selection in order to recover the structure of a composite network that simultaneously models exon co-regulation and their cognate regulators. Community structure detection and social network analysis methods are used to identify distinct modules and key actors within the network. As a proof of concept for our framework we studied the splicing regulatory network for Drosophila development using the publicly available modENCODE data. The final model offers a comprehensive view of the splicing circuitry that underlies fly development. Identified modules are associated with major developmental hallmarks including maternally loaded RNAs, onset of zygotic gene expression, transitions between life stages and sex differentiation. Within-module key actors include well-known developmental-specific splicing regulators from the literature while additional factors previously unassociated with developmental-specific splicing are also highlighted. Finally we analyze an extensive battery of Splicing Factor knock-down transcriptome data and demonstrate that our approach captures true regulatory relationships.

First Steps toward the Geometry of Cophylogeny

Here we introduce researchers in algebraic biology to the exciting new field of cophylogenetics. Cophylogenetics is the study of concomitantly evolving organisms (or genes), such as host and parasite species. Thus the natural objects of study in cophylogenetics are tuples of related trees, instead of individual trees. We review various research topics in algebraic statistics for phylogenetics, and propose analogs for cophylogenetics. In particular we propose spaces of cophylogenetic trees, cophylogenetic reconstruction, and cophylogenetic invariants. We conclude with open problems.

Three Kinds of Integer Programming Algorithms Based on Barvinok’s Rational Functions

This paper presents three kinds of algebraic-analytic algorithms for solving integer and mixed integer programming problems. We report both theoretical and experimental results. We use the generating function techniques introduced by A. Barvinok.