Adjacency labeling schemes and induced-universal graphs

We describe a way of assigning labels to the vertices of any undirected graph on up to $n$ vertices, each composed of $n/2+O(1)$ bits, such that given the labels of two vertices, and no other information regarding the graph, it is possible to decide whether or not the vertices are adjacent in the graph. This is optimal, up to an additive constant, and constitutes the first improvement in almost 50 years of an $n/2+O(\log n)$ bound of Moon. As a consequence, we obtain an induced-universal graph for $n$-vertex graphs containing only $O(2^{n/2})$ vertices, which is optimal up to a multiplicative constant, solving an open problem of Vizing from 1968. We obtain similar tight results for directed graphs, tournaments and bipartite graphs

Invariant Distribution of Promoter Activities in Escherichia coli

Cells need to allocate their limited resources to express a wide range of genes. To understand how Escherichia coli partitions its transcriptional resources between its different promoters, we employ a robotic assay using a comprehensive reporter strain library for E. coli to measure promoter activity on a genomic scale at high-temporal resolution and accuracy. This allows continuous tracking of promoter activity as cells change their growth rate from exponential to stationary phase in different media. We find a heavy-tailed distribution of promoter activities, with promoter activities spanning several orders of magnitude. While the shape of the distribution is almost completely independent of the growth conditions, the identity of the promoters expressed at different levels does depend on them. Translation machinery genes, however, keep the same relative expression levels in the distribution across conditions, and their fractional promoter activity tracks growth rate tightly. We present a simple optimization model for resource allocation which suggests that the observed invariant distributions might maximize growth rate. These invariant features of the distribution of promoter activities may suggest design constraints that shape the allocation of transcriptional resources

Estimating Cell Depth from Somatic Mutations

The depth of a cell of a multicellular organism is the number of cell divisions it underwent since the zygote, and knowing this basic cell property would help address fundamental problems in several areas of biology. At present, the depths of the vast majority of human and mouse cell types are unknown. Here, we show a method for estimating the depth of a cell by analyzing somatic mutations in its microsatellites, and provide to our knowledge for the first time reliable depth estimates for several cells types in mice. According to our estimates, the average depth of oocytes is 29, consistent with previous estimates. The average depth of B cells ranges from 34 to 79, linearly related to the mouse age, suggesting a rate of one cell division per day. In contrast, various types of adult stem cells underwent on average fewer cell divisions, supporting the notion that adult stem cells are relatively quiescent. Our method for depth estimation opens a window for revealing tissue turnover rates in animals, including humans, which has important implications for our knowledge of the body under physiological and pathological conditions

Wolffia globosa–Mankai Plant-Based Protein Contains Bioactive Vitamin B12 and Is Well Absorbed in Humans

Background: Rare plants that contain corrinoid compounds mostly comprise cobalamin analogues, which may compete with cobalamin (vitamin B12 (B12)) metabolism. We examined the presence of B12 in a cultivated strain of an aquatic plant: Wolffia globosa (Mankai), and predicted functional pathways using gut-bioreactor, and the effects of long-term Mankai consumption as a partial meat substitute, on serum B12 concentrations. Methods: We used microbiological assay, liquid-chromatography/electrospray-ionization-tandem-mass-spectrometry (LC-MS/MS), and anoxic bioreactors for the B12 experiments. We explored the effect of a green Mediterranean/low-meat diet, containing 100 g of frozen Mankai shake/day, on serum B12 levels during the 18-month DIRECT-PLUS (ID:NCT03020186) weight-loss trial, compared with control and Mediterranean diet groups. Results: The B12 content of Mankai was consistent at different seasons (p = 0.76). Several cobalamin congeners (Hydroxocobalamin(OH-B12); 5-deoxyadenosylcobalamin(Ado-B12); methylcobalamin(Me-B12); cyanocobalamin(CN-B12)) were identified in Mankai extracts, whereas no pseudo B12 was detected. A higher abundance of 16S-rRNA gene amplicon sequences associated with a genome containing a KEGG ortholog involved in microbial B12 metabolism were observed, compared with control bioreactors that lacked Mankai. Following the DIRECT-PLUS intervention (n = 294 participants; retention-rate = 89%; baseline B12 = 420.5 ± 187.8 pg/mL), serum B12 increased by 5.2% in control, 9.9% in Mediterranean, and 15.4% in Mankai-containing green Mediterranean/low-meat diets (p = 0.025 between extreme groups). Conclusions: Mankai plant contains bioactive B12 compounds and could serve as a B12 plant-based food source