The t-stability number of a random graph

Given a graph G = (V,E), a vertex subset S is called t-stable (or t-dependent) if the subgraph G[S] induced on S has maximum degree at most t. The t-stability number of G is the maximum order of a t-stable set in G. We investigate the typical values that this parameter takes on a random graph on n vertices and edge probability equal to p. For any fixed 0 < p < 1 and fixed non-negative integer t, we show that, with probability tending to 1 as n grows, the t-stability number takes on at most two values which we identify as functions of t, p and n. The main tool we use is an asymptotic expression for the expected number of t-stable sets of order k. We derive this expression by performing a precise count of the number of graphs on k vertices that have maximum degree at most k. Using the above results, we also obtain asymptotic bounds on the t-improper chromatic number of a random graph (this is the generalisation of the chromatic number, where we partition of the vertex set of the graph into t-stable sets).Comment: 25 pages; v2 has 30 pages and is identical to the journal version apart from formatting and a minor amendment to Lemma 8 (and its proof on p. 21

Largest sparse subgraphs of random graphs

For the Erd\H{o}s-R\'enyi random graph G(n,p), we give a precise asymptotic formula for the size of a largest vertex subset in G(n,p) that induces a subgraph with average degree at most t, provided that p = p(n) is not too small and t = t(n) is not too large. In the case of fixed t and p, we find that this value is asymptotically almost surely concentrated on at most two explicitly given points. This generalises a result on the independence number of random graphs. For both the upper and lower bounds, we rely on large deviations inequalities for the binomial distribution.Comment: 15 page

Fermented beverages with health-promoting potential: Past and future perspectives

peer-reviewedFermentation is an ancient form of food preservation, which also improves the nutritional content of foods. In many regions of the world, fermented beverages have become known for their health-promoting attributes. In addition to harnessing traditional beverages for commercial use, there have recently been innovative efforts to develop non-dairy probiotic fermented beverages from a variety of substrates, including soy milk, whey, cereals and vegetable and fruit juices. On the basis of recent developments, it is anticipated that fermented beverages will continue to be a significant component within the functional food market

The t-improper chromatic number of random graphs

We consider the $t$-improper chromatic number of the Erd{\H o}s-R{\'e}nyi random graph $G(n,p)$. The t-improper chromatic number $\chi^t(G)$ of $G$ is the smallest number of colours needed in a colouring of the vertices in which each colour class induces a subgraph of maximum degree at most $t$. If $t = 0$, then this is the usual notion of proper colouring. When the edge probability $p$ is constant, we provide a detailed description of the asymptotic behaviour of $\chi^t(G(n,p))$ over the range of choices for the growth of $t = t(n)$.Comment: 12 page

Sequencing-Based Analysis of the Bacterial and Fungal Composition of Kefir Grains and Milks from Multiple Sources

peer-reviewedKefir is a fermented milk-based beverage to which a number of health-promoting properties have been attributed. The microbes responsible for the fermentation of milk to produce kefir consist of a complex association of bacteria and yeasts, bound within a polysaccharide matrix, known as the kefir grain. The consistency of this microbial population, and that present in the resultant beverage, has been the subject of a number of previous, almost exclusively culture-based, studies which have indicated differences depending on geographical location and culture conditions. However, culture-based identification studies are limited by virtue of only detecting species with the ability to grow on the specific medium used and thus culture-independent, molecular-based techniques offer the potential for a more comprehensive analysis of such communities. Here we describe a detailed investigation of the microbial population, both bacterial and fungal, of kefir, using high-throughput sequencing to analyse 25 kefir milks and associated grains sourced from 8 geographically distinct regions. This is the first occasion that this technology has been employed to investigate the fungal component of these populations or to reveal the microbial composition of such an extensive number of kefir grains or milks. As a result several genera and species not previously identified in kefir were revealed. Our analysis shows that the bacterial populations in kefir are dominated by 2 phyla, the Firmicutes and the Proteobacteria. It was also established that the fungal populations of kefir were dominated by the genera Kazachstania, Kluyveromyces and Naumovozyma, but that a variable sub-dominant population also exists.The Alimentary Pharmabiotic Centre is a research centre funded by Science Foundation Ireland (SFI), through the Irish Government’s National Development Plan. The authors and their work were supported by SFI CSET grant APC CSET 2 grant 07/CE/B1368

In silico identification of bacteriocin gene clusters in the gastrointestinal tract, based on the Human Microbiome Project’s reference genome database

peer-reviewedBackground The human gut microbiota comprises approximately 100 trillion microbial cells which significantly impact many aspects of human physiology - including metabolism, nutrient absorption and immune function. Disturbances in this population have been implicated in many conditions and diseases, including obesity, type-2 diabetes and inflammatory bowel disease. This suggests that targeted manipulation or shaping of the gut microbiota, by bacteriocins and other antimicrobials, has potential as a therapeutic tool for the prevention or treatment of these conditions. With this in mind, several studies have used traditional culture-dependent approaches to successfully identify bacteriocin-producers from the mammalian gut. In silico-based approaches to identify novel gene clusters are now also being utilised to take advantage of the vast amount of data currently being generated by next generation sequencing technologies. In this study, we employed an in silico screening approach to mine potential bacteriocin clusters in genome-sequenced isolates from the gastrointestinal tract (GIT). More specifically, the bacteriocin genome-mining tool BAGEL3 was used to identify potential bacteriocin producers in the genomes of the GIT subset of the Human Microbiome Project’s reference genome database. Each of the identified gene clusters were manually annotated and potential bacteriocin-associated genes were evaluated. Results We identified 74 clusters of note from 59 unique members of the Firmicutes, Bacteroidetes, Actinobacteria, Fusobacteria and Synergistetes. The most commonly identified class of bacteriocin was the >10 kDa class, formerly known as bacteriolysins, followed by lantibiotics and sactipeptides. Conclusions Multiple bacteriocin gene clusters were identified in a dataset representative of the human gut microbiota. Interestingly, many of these were associated with species and genera which are not typically associated with bacteriocin production.CJW, CMG and PDC are supported by a SFI PI award to PDC “Obesibiotics” (11/PI/1137)

Expression of KOC, S100P, mesothelin and MUC1 in pancreatico-biliary adenocarcinomas: development and utility of a potential diagnostic immunohistochemistry panel

&lt;b&gt;Background&lt;/b&gt; Pancreatico-biliary adenocarcinomas (PBA) have a poor prognosis. Diagnosis is usually achieved by imaging and/or endoscopy with confirmatory cytology. Cytological interpretation can be difficult especially in the setting of chronic pancreatitis/cholangitis. Immunohistochemistry (IHC) biomarkers could act as an adjunct to cytology to improve the diagnosis. Thus, we performed a meta-analysis and selected KOC, S100P, mesothelin and MUC1 for further validation in PBA resection specimens.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Methods&lt;/b&gt; Tissue microarrays containing tumour and normal cores in a ratio of 3:2, from 99 surgically resected PBA patients, were used for IHC. IHC was performed on an automated platform using antibodies against KOC, S100P, mesothelin and MUC1. Tissue cores were scored for staining intensity and proportion of tissue stained using a Histoscore method (range, 0–300). Sensitivity and specificity for individual biomarkers, as well as biomarker panels, were determined with different cut-offs for positivity and compared by summary receiver operating characteristic (ROC) curve.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Results&lt;/b&gt; The expression of all four biomarkers was high in PBA versus normal ducts, with a mean Histoscore of 150 vs. 0.4 for KOC, 165 vs. 0.3 for S100P, 115 vs. 0.5 for mesothelin and 200 vs. 14 for MUC1 (p &lt; .0001 for all comparisons). Five cut-offs were carefully chosen for sensitivity/specificity analysis. Four of these cut-offs, namely 5%, 10% or 20% positive cells and Histoscore 20 were identified using ROC curve analysis and the fifth cut-off was moderate-strong staining intensity. Using 20% positive cells as a cut-off achieved higher sensitivity/specificity values: KOC 84%/100%; S100P 83%/100%; mesothelin 88%/92%; and MUC1 89%/63%. Analysis of a panel of KOC, S100P and mesothelin achieved 100% sensitivity and 99% specificity if at least 2 biomarkers were positive for 10% cut-off; and 100% sensitivity and specificity for 20% cut-off.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Conclusion&lt;/b&gt; A biomarker panel of KOC, S100P and mesothelin with at least 2 biomarkers positive was found to be an optimum panel with both 10% and 20% cut-offs in resection specimens from patients with PBA.&lt;p&gt;&lt;/p&gt

Isolation of a Novel Phage with Activity against Streptococcus mutans Biofilms

peer-reviewedStreptococcus mutans is one of the principal agents of caries formation mainly, because of its ability to form biofilms at the tooth surface. Bacteriophages (phages) are promising antimicrobial agents that could be used to prevent or treat caries formation by S. mutans. The aim of this study was to isolate new S. mutans phages and to characterize their antimicrobial properties. A new phage, ɸAPCM01, was isolated from a human saliva sample. Its genome was closely related to the only two other available S. mutans phage genomes, M102 and M102AD. ɸAPCM01 inhibited the growth of S. mutans strain DPC6143 within hours in broth and in artificial saliva at multiplicity of infections as low as 2.5x10-5. In the presence of phage ɸAPCM01 the metabolic activity of a S. mutans biofilm was reduced after 24 h of contact and did not increased again after 48 h, and the live cells in the biofilm decreased by at least 5 log cfu/ml. Despite its narrow host range, this newly isolated S. mutans phage exhibits promising antimicrobial properties