The velocity-density relation in the spherical model

We study the cosmic velocity-density relation using the spherical collapse model (SCM) as a proxy to non-linear dynamics. Although the dependence of this relation on cosmological parameters is known to be weak, we retain the density parameter Omega_m in SCM equations, in order to study the limit Omega_m -> 0. We show that in this regime the considered relation is strictly linear, for arbitrary values of the density contrast, on the contrary to some claims in the literature. On the other hand, we confirm that for realistic values of Omega_m the exact relation in the SCM is well approximated by the classic formula of Bernardeau (1992), both for voids (delta<0) and for overdensities up to delta ~ 3. Inspired by this fact, we find further analytic approximations to the relation for the whole range delta from -1 to infinity. Our formula for voids accounts for the weak Omega_m-dependence of their maximal rate of expansion, which for Omega_m < 1 is slightly smaller that 3/2. For positive density contrasts, we find a simple relation div v = 3 H_0 (Omega_m)^(0.6) [ (1+delta)^(1/6) - (1+delta)^(1/2) ], that works very well up to the turn-around (i.e. up to delta ~ 13.5 for Omega_m = 0.25 and neglected Omega_Lambda). Having the same second-order expansion as the formula of Bernardeau, it can be regarded as an extension of the latter for higher density contrasts. Moreover, it gives a better fit to results of cosmological numerical simulations.Comment: 11 pages, 6 figures. Accepted for publication in MNRA

Nonlinearity and stochasticity in the density--velocity relation

We present results of the investigations of the statistical properties of a joint density and velocity divergence probability distribution function (PDF) in the mildly non-linear regime. For that purpose we use both perturbation theory results, extended here for a top-hat filter, and numerical simulations. In particular we derive the quantitative (complete as possible up to third order terms) and qualitative predictions for constrained averages and constrained dispersions -- which describe the nonlinearities and the stochasticity properties beyond the linear regime -- and compare them against numerical simulations. We find overall a good agreement for constrained averages; however, the agreement for constrained dispersions is only qualitative. Scaling relations for the Omega-dependence of these quantities are satisfactory reproduced. Guided by our analytical and numerical results, we finally construct a robust phenomenological description of the joint PDF in a closed analytic form. The good agreement of our formula with results of N-body simulations for a number of cosmological parameters provides a sound validation of the presented approach. Our results provide a basis for a potentially powerful tool with which it is possible to analyze galaxy survey data in order to test the gravitational instability paradigm beyond the linear regime and put useful constraints on cosmological parameters. In particular we show how the nonlinearity in the density--velocity relation can be used to break the so-called Omega-bias degeneracy in cosmic density-velocity comparisons.Comment: 12 pages, 11 figures; revised version with minor changes in the presentation, accepted for publication in MNRA

Power spectrum for the small-scale Universe

The first objects to arise in a cold dark matter universe present a daunting challenge for models of structure formation. In the ultra small-scale limit, CDM structures form nearly simultaneously across a wide range of scales. Hierarchical clustering no longer provides a guiding principle for theoretical analyses and the computation time required to carry out credible simulations becomes prohibitively high. To gain insight into this problem, we perform high-resolution (N=720^3 - 1584^3) simulations of an Einstein-de Sitter cosmology where the initial power spectrum is P(k) propto k^n, with -2.5 < n < -1. Self-similar scaling is established for n=-1 and n=-2 more convincingly than in previous, lower-resolution simulations and for the first time, self-similar scaling is established for an n=-2.25 simulation. However, finite box-size effects induce departures from self-similar scaling in our n=-2.5 simulation. We compare our results with the predictions for the power spectrum from (one-loop) perturbation theory and demonstrate that the renormalization group approach suggested by McDonald improves perturbation theory's ability to predict the power spectrum in the quasilinear regime. In the nonlinear regime, our power spectra differ significantly from the widely used fitting formulae of Peacock & Dodds and Smith et al. and a new fitting formula is presented. Implications of our results for the stable clustering hypothesis vs. halo model debate are discussed. Our power spectra are inconsistent with predictions of the stable clustering hypothesis in the high-k limit and lend credence to the halo model. Nevertheless, the fitting formula advocated in this paper is purely empirical and not derived from a specific formulation of the halo model.Comment: 30 pages including 10 figures; accepted for publication in MNRA

The Optimal Exponent Base for emPAI Is 6.5

Exponentially Modified Protein Abundance Index (emPAI) is an established method of estimating protein abundances from peptide counts in a single LC-MS/MS experiment. EmPAI is defined as 10PAI minus one, where PAI (Protein Abundance Index) denotes the ratio of observed to observable peptides. EmPAI was first proposed by Ishihama et al [1] who found that PAI is approximately proportional to the logarithm of absolute protein concentration. I define emPAI65 = 6.5PAI-1 and show that it performs significantly better than emPAI, while it is equally easy to compute. The higher accuracy of emPAI65 is demonstrated by analyzing three data sets, including the one used in the original study [1]. I conclude that emPAI65 ought to be used instead of the original emPAI for protein quantitation

Comprehensive Structural and Substrate Specificity Classification of the Saccharomyces cerevisiae Methyltransferome

Methylation is one of the most common chemical modifications of biologically active molecules and it occurs in all life forms. Its functional role is very diverse and involves many essential cellular processes, such as signal transduction, transcriptional control, biosynthesis, and metabolism. Here, we provide further insight into the enzymatic methylation in S. cerevisiae by conducting a comprehensive structural and functional survey of all the methyltransferases encoded in its genome. Using distant homology detection and fold recognition, we found that the S. cerevisiae methyltransferome comprises 86 MTases (53 well-known and 33 putative with unknown substrate specificity). Structural classification of their catalytic domains shows that these enzymes may adopt nine different folds, the most common being the Rossmann-like. We also analyzed the domain architecture of these proteins and identified several new domain contexts. Interestingly, we found that the majority of MTase genes are periodically expressed during yeast metabolic cycle. This finding, together with calculated isoelectric point, fold assignment and cellular localization, was used to develop a novel approach for predicting substrate specificity. Using this approach, we predicted the general substrates for 24 of 33 putative MTases and confirmed these predictions experimentally in both cases tested. Finally, we show that, in S. cerevisiae, methylation is carried out by 34 RNA MTases, 32 protein MTases, eight small molecule MTases, three lipid MTases, and nine MTases with still unknown substrate specificity

Repression of Mitochondrial Translation, Respiration and a Metabolic Cycle-Regulated Gene, SLF1, by the Yeast Pumilio-Family Protein Puf3p

Synthesis and assembly of the mitochondrial oxidative phosphorylation (OXPHOS) system requires genes located both in the nuclear and mitochondrial genomes, but how gene expression is coordinated between these two compartments is not fully understood. One level of control is through regulated expression mitochondrial ribosomal proteins and other factors required for mitochondrial translation and OXPHOS assembly, which are all products of nuclear genes that are subsequently imported into mitochondria. Interestingly, this cadre of genes in budding yeast has in common a 3′-UTR element that is bound by the Pumilio family protein, Puf3p, and is coordinately regulated under many conditions, including during the yeast metabolic cycle. Multiple functions have been assigned to Puf3p, including promoting mRNA degradation, localizing nucleus-encoded mitochondrial transcripts to the outer mitochondrial membrane, and facilitating mitochondria-cytoskeletal interactions and motility. Here we show that Puf3p has a general repressive effect on mitochondrial OXPHOS abundance, translation, and respiration that does not involve changes in overall mitochondrial biogenesis and largely independent of TORC1-mitochondrial signaling. We also identified the cytoplasmic translation factor Slf1p as yeast metabolic cycle-regulated gene that is repressed by Puf3p at the post-transcriptional level and promotes respiration and extension of yeast chronological life span when over-expressed. Altogether, these results should facilitate future studies on which of the many functions of Puf3p is most relevant for regulating mitochondrial gene expression and the role of nuclear-mitochondrial communication in aging and longevity

Chromatin loop anchors are associated with genome instability in cancer and recombination hotspots in the germline

Abstract Background Chromatin loops form a basic unit of interphase nuclear organization, with chromatin loop anchor points providing contacts between regulatory regions and promoters. However, the mutational landscape at these anchor points remains under-studied. Here, we describe the unusual patterns of somatic mutations and germline variation associated with loop anchor points and explore the underlying features influencing these patterns. Results Analyses of whole genome sequencing datasets reveal that anchor points are strongly depleted for single nucleotide variants (SNVs) in tumours. Despite low SNV rates in their genomic neighbourhood, anchor points emerge as sites of evolutionary innovation, showing enrichment for structural variant (SV) breakpoints and a peak of SNVs at focal CTCF sites within the anchor points. Both CTCF-bound and non-CTCF anchor points harbour an excess of SV breakpoints in multiple tumour types and are prone to double-strand breaks in cell lines. Common fragile sites, which are hotspots for genome instability, also show elevated numbers of intersecting loop anchor points. Recurrently disrupted anchor points are enriched for genes with functions in cell cycle transitions and regions associated with predisposition to cancer. We also discover a novel class of CTCF-bound anchor points which overlap meiotic recombination hotspots and are enriched for the core PRDM9 binding motif, suggesting that the anchor points have been foci for diversity generated during recent human evolution. Conclusions We suggest that the unusual chromatin environment at loop anchor points underlies the elevated rates of variation observed, marking them as sites of regulatory importance but also genomic fragility