Intersecting Families of Permutations

A set of permutations $I \subset S_n$ is said to be {\em k-intersecting} if any two permutations in $I$ agree on at least $k$ points. We show that for any $k \in \mathbb{N}$, if $n$ is sufficiently large depending on $k$, then the largest $k$-intersecting subsets of $S_n$ are cosets of stabilizers of $k$ points, proving a conjecture of Deza and Frankl. We also prove a similar result concerning $k$-cross-intersecting subsets. Our proofs are based on eigenvalue techniques and the representation theory of the symmetric group.Comment: 'Erratum' section added. Yuval Filmus has recently pointed out that the 'Generalised Birkhoff theorem', Theorem 29, is false for k > 1, and so is Theorem 27 for k > 1. An alternative proof of the equality part of the Deza-Frankl conjecture is referenced, bypassing the need for Theorems 27 and 2

A catalog of stability-associated sequence elements in 3' UTRs of yeast mRNAs

BACKGROUND: In recent years, intensive computational efforts have been directed towards the discovery of promoter motifs that correlate with mRNA expression profiles. Nevertheless, it is still not always possible to predict steady-state mRNA expression levels based on promoter signals alone, suggesting that other factors may be involved. Other genic regions, in particular 3' UTRs, which are known to exert regulatory effects especially through controlling RNA stability and localization, were less comprehensively investigated, and deciphering regulatory motifs within them is thus crucial. RESULTS: By analyzing 3' UTR sequences and mRNA decay profiles of Saccharomyces cerevisiae genes, we derived a catalog of 53 sequence motifs that may be implicated in stabilization or destabilization of mRNAs. Some of the motifs correspond to known RNA-binding protein sites, and one of them may act in destabilization of ribosome biogenesis genes during stress response. In addition, we present for the first time a catalog of 23 motifs associated with subcellular localization. A significant proportion of the 3' UTR motifs is highly conserved in orthologous yeast genes, and some of the motifs are strikingly similar to recently published mammalian 3' UTR motifs. We classified all genes into those regulated only at transcription initiation level, only at degradation level, and those regulated by a combination of both. Interestingly, different biological functionalities and expression patterns correspond to such classification. CONCLUSION: The present motif catalogs are a first step towards the understanding of the regulation of mRNA degradation and subcellular localization, two important processes which - together with transcription regulation - determine the cell transcriptome

No nonlocal box is universal

We show that standard nonlocal boxes, also known as Popescu-Rohrlich machines, are not sufficient to simulate any nonlocal correlations that do not allow signalling. This was known in the multipartite scenario, but we extend the result to the bipartite case. We then generalize this result further by showing that no finite set containing any finite-output-alphabet nonlocal boxes can be a universal set for nonlocality.Comment: Additions to the acknowledgements sectio

Messenger RNA Fluctuations and Regulatory RNAs Shape the Dynamics of Negative Feedback Loop

Single cell experiments of simple regulatory networks can markedly differ from cell population experiments. Such differences arise from stochastic events in individual cells that are averaged out in cell populations. For instance, while individual cells may show sustained oscillations in the concentrations of some proteins, such oscillations may appear damped in the population average. In this paper we investigate the role of RNA stochastic fluctuations as a leading force to produce a sustained excitatory behavior at the single cell level. Opposed to some previous models, we build a fully stochastic model of a negative feedback loop that explicitly takes into account the RNA stochastic dynamics. We find that messenger RNA random fluctuations can be amplified during translation and produce sustained pulses of protein expression. Motivated by the recent appreciation of the importance of non--coding regulatory RNAs in post--transcription regulation, we also consider the possibility that a regulatory RNA transcript could bind to the messenger RNA and repress translation. Our findings show that the regulatory transcript helps reduce gene expression variability both at the single cell level and at the cell population level.Comment: 87.18.Vf --> Systems biology 87.10.Mn --> Stochastic models in biological systems 87.18.Tt --> Noise in biological systems http://www.ncbi.nlm.nih.gov/pubmed/20365787 http://www.weizmann.ac.il/complex/tlusty/papers/PhysRevE2010.pd

Extraction of transcription regulatory signals from genome-wide DNA–protein interaction data

Deciphering gene regulatory network architecture amounts to the identification of the regulators, conditions in which they act, genes they regulate, cis-acting motifs they bind, expression profiles they dictate and more complex relationships between alternative regulatory partnerships and alternative regulatory motifs that give rise to sub-modalities of expression profiles. The ‘location data’ in yeast is a comprehensive resource that provides transcription factor–DNA interaction information in vivo. Here, we provide two contributions: first, we developed means to assess the extent of noise in the location data, and consequently for extracting signals from it. Second, we couple signal extraction with better characterization of the genetic network architecture. We apply two methods for the detection of combinatorial associations between transcription factors (TFs), the integration of which provides a global map of combinatorial regulatory interactions. We discover the capacity of regulatory motifs and TF partnerships to dictate fine-tuned expression patterns of subsets of genes, which are clearly distinct from those displayed by most genes assigned to the same TF. Our findings provide carefully prioritized, high-quality assignments between regulators and regulated genes and as such should prove useful for experimental and computational biologists alike