Hierarchical Dirichlet Process-Based Models For Discovery of Cross-species Mammalian Gene Expression

An important research problem in computational biology is theidentification of expression programs, sets of co-activatedgenes orchestrating physiological processes, and thecharacterization of the functional breadth of these programs. Theuse of mammalian expression data compendia for discovery of suchprograms presents several challenges, including: 1) cellularinhomogeneity within samples, 2) genetic and environmental variationacross samples, and 3) uncertainty in the numbers of programs andsample populations. We developed GeneProgram, a new unsupervisedcomputational framework that uses expression data to simultaneouslyorganize genes into overlapping programs and tissues into groups toproduce maps of inter-species expression programs, which are sortedby generality scores that exploit the automatically learnedgroupings. Our method addresses each of the above challenges byusing a probabilistic model that: 1) allocates mRNA to differentexpression programs that may be shared across tissues, 2) ishierarchical, treating each tissue as a sample from a population ofrelated tissues, and 3) uses Dirichlet Processes, a non-parametricBayesian method that provides prior distributions over numbers ofsets while penalizing model complexity. Using real gene expressiondata, we show that GeneProgram outperforms several popularexpression analysis methods in recovering biologically interpretablegene sets. From a large compendium of mouse and human expressiondata, GeneProgram discovers 19 tissue groups and 100 expressionprograms active in mammalian tissues. Our method automaticallyconstructs a comprehensive, body-wide map of expression programs andcharacterizes their functional generality. This map can be used forguiding future biological experiments, such as discovery of genesfor new drug targets that exhibit minimal "cross-talk" withunintended organs, or genes that maintain general physiologicalresponses that go awry in disease states. Further, our method isgeneral, and can be applied readily to novel compendia of biologicaldata

Vortex lattice stability and phase coherence in three-dimensional rapidly rotating Bose condensates

We establish the general equations of motion for the modes of a vortex lattice in a rapidly rotating Bose-Einstein condensate in three dimensions, taking into account the elastic energy of the lattice and the vortex line bending energy. As in two dimensions, the vortex lattice supports Tkachenko and gapped sound modes. In contrast, in three dimensions the Tkachenko mode frequency at long wavelengths becomes linear in the wavevector for any propagation direction out of the transverse plane. We compute the correlation functions of the vortex displacements and the superfluid order parameter for a homogeneous Bose gas of bounded extent in the axial direction. At zero temperature the vortex displacement correlations are convergent at large separation, but at finite temperatures, they grow with separation. The growth of the vortex displacements should lead to observable melting of vortex lattices at higher temperatures and somewhat lower particle number and faster rotation than in current experiments. At zero temperature a system of large extent in the axial direction maintains long range order-parameter correlations for large separation, but at finite temperatures the correlations decay with separation.Comment: 10 pages, 2 figures, Changes include the addition of the particle density - vortex density coupling and the correct value of the shear modulu

Dislocation-Mediated Melting in Superfluid Vortex Lattices

We describe thermal melting of the two-dimensional vortex lattice in a rotating superfluid by generalizing the Halperin and Nelson theory of dislocation-mediated melting. and derive a melting temperature proportional to the renormalized shear modulus of the vortex lattice. The rigid-body rotation of the superfluid attenuates the effects of lattice compression on the energy of dislocations and hence the melting temperature, while not affecting the shearing. Finally, we discuss dislocations and thermal melting in inhomogeneous rapidly rotating Bose-Einstein condensates; we delineate a phase diagram in the temperature -- rotation rate plane, and infer that the thermal melting temperature should lie below the Bose-Einstein transition temperature.Comment: 9 pages, 2 figure

An improved map of conserved regulatory sites for Saccharomyces cerevisiae

BACKGROUND: The regulatory map of a genome consists of the binding sites for proteins that determine the transcription of nearby genes. An initial regulatory map for S. cerevisiae was recently published using six motif discovery programs to analyze genome-wide chromatin immunoprecipitation data for 203 transcription factors. The programs were used to identify sequence motifs that were likely to correspond to the DNA-binding specificity of the immunoprecipitated proteins. We report improved versions of two conservation-based motif discovery algorithms, PhyloCon and Converge. Using these programs, we create a refined regulatory map for S. cerevisiae by reanalyzing the same chromatin immunoprecipitation data. RESULTS: Applying the same conservative criteria that were applied in the original study, we find that PhyloCon and Converge each separately discover more known specificities than the combination of all six programs in the previous study. Combining the results of PhyloCon and Converge, we discover significant sequence motifs for 36 transcription factors that were previously missed. The new set of motifs identifies 636 more regulatory interactions than the previous one. The new network contains 28% more regulatory interactions among transcription factors, evidence of greater cross-talk between regulators. CONCLUSION: Combining two complementary computational strategies for conservation-based motif discovery improves the ability to identify the specificity of transcriptional regulators from genome-wide chromatin immunoprecipitation data. The increased sensitivity of these methods significantly expands the map of yeast regulatory sites without the need to alter any of the thresholds for statistical significance. The new map of regulatory sites reveals a more elaborate and complex view of the yeast genetic regulatory network than was observed previously

Automated Discovery of Functional Generality of Human Gene Expression Programs

An important research problem in computational biology is the identification of expression programs, sets of co-expressed genes orchestrating normal or pathological processes, and the characterization of the functional breadth of these programs. The use of human expression data compendia for discovery of such programs presents several challenges including cellular inhomogeneity within samples, genetic and environmental variation across samples, uncertainty in the numbers of programs and sample populations, and temporal behavior. We developed GeneProgram, a new unsupervised computational framework based on Hierarchical Dirichlet Processes that addresses each of the above challenges. GeneProgram uses expression data to simultaneously organize tissues into groups and genes into overlapping programs with consistent temporal behavior, to produce maps of expression programs, which are sorted by generality scores that exploit the automatically learned groupings. Using synthetic and real gene expression data, we showed that GeneProgram outperformed several popular expression analysis methods. We applied GeneProgram to a compendium of 62 short time-series gene expression datasets exploring the responses of human cells to infectious agents and immune-modulating molecules. GeneProgram produced a map of 104 expression programs, a substantial number of which were significantly enriched for genes involved in key signaling pathways and/or bound by NF-κB transcription factors in genome-wide experiments. Further, GeneProgram discovered expression programs that appear to implicate surprising signaling pathways or receptor types in the response to infection, including Wnt signaling and neurotransmitter receptors. We believe the discovered map of expression programs involved in the response to infection will be useful for guiding future biological experiments; genes from programs with low generality scores might serve as new drug targets that exhibit minimal “cross-talk,” and genes from high generality programs may maintain common physiological responses that go awry in disease states. Further, our method is multipurpose, and can be applied readily to novel compendia of biological data

A Multi-Wavelength Mass Analysis of RCS2 J232727.6-020437, a ~3x1015^{15}M⊙_{\odot} Galaxy Cluster at z=0.7

We present an initial study of the mass and evolutionary state of a massive and distant cluster, RCS2 J232727.6-020437. This cluster, at z=0.6986, is the richest cluster discovered in the RCS2 project. The mass measurements presented in this paper are derived from all possible mass proxies: X-ray measurements, weak-lensing shear, strong lensing, Sunyaev Zel'dovich effect decrement, the velocity distribution of cluster member galaxies, and galaxy richness. While each of these observables probe the mass of the cluster at a different radius, they all indicate that RCS2 J232727.6-020437 is among the most massive clusters at this redshift, with an estimated mass of M_200 ~3 x10^15 h^-1 Msun. In this paper, we demonstrate that the various observables are all reasonably consistent with each other to within their uncertainties. RCS2 J232727.6-020437 appears to be well relaxed -- with circular and concentric X-ray isophotes, with a cool core, and no indication of significant substructure in extensive galaxy velocity data.Comment: 19 pages, 15 figures, submitted to ApJ on March 5, 2015; in press. Manuscript revised following the referee revie

Probing theories of gravity with phase space-inferred potentials of galaxy clusters

Modified theories of gravity provide us with a unique opportunity to generate innovative tests of gravity. In Chameleon f(R) gravity, the gravitational potential differs from the weak-field limit of general relativity (GR) in a mass dependent way. We develop a probe of gravity which compares high mass clusters, where Chameleon effects are weak, to low mass clusters, where the effects can be strong. We utilize the escape velocity edges in the radius/velocity phase space to infer the gravitational potential profiles on scales of 0.3–1 virial radii. We show that the escape edges of low mass clusters are enhanced compared to GR, where the magnitude of the difference depends on the background field value |fR0¯¯¯¯¯|. We validate our probe using N-body simulations and simulated light cone galaxy data. For a Dark Energy Spectroscopic Instrument Bright Galaxy Sample, including observational systematics, projection effects, and cosmic variance, our test can differentiate between GR and Chameleon f(R) gravity models, |fR0¯¯¯¯¯|=4×10−6 (2×10−6) at >5σ (>2σ), more than an order of magnitude better than current cluster-scale constraints