Lov\`{a}sz's hom-counting theorem by inclusion-exclusion principle

Let ${\mathcal C}$ be the category of finite graphs. Lov\`{a}sz (1967) shows that if $|\mathrm{Hom}(X,A)|=|\mathrm{Hom}(X,B)|$ holds for any $X$, then $A$ is isomorphic to $B$. Pultr (1973) gives a categorical generalization using a similar argument. Both proofs assume that each object has a finite number of isomorphism classes of subobjects. Generalizations without this assumption are given by Dawar, Jakl, and Reggio (2021) and Regio (2021). Here another generalization without this assumption is given, with a shorter proof. Examples of categories are given, for which our theorem is applicable, but the existing theorems are not

Testis size variation within sneaker males of the dusky frillgoby Bathygobius fuscus (Gobiidae): effects of within-tactic competition

A ‘sneaking tactic’ is an alternative reproductive strategy that usually results in sperm competition among males with different tactics. Relatively large testes are a sneaker-specific trait that has generally been thought to have evolved due to sperm competition between sneaker males and bourgeois (guarding) males. However, here we show that competition among sneaker males can also affect testis enlargement in the dusky frillgoby (Bathygobius fuscus) sneaker males. The competitive advantage of focal sneaker males was experimentally manipulated by placing them in tanks with either relatively smaller or larger males. Testis enlargement was conspicuous in focal males that were cohoused with larger males. Smaller sneaker males may invest more in testicular growth because they are at a competitive disadvantage in physical contests for sneaking opportunities among sneaker males and consequently may be confined to making relatively late intrusions during spawning into nests that have a higher risk of sperm competition. Another possible reason for the relative size-dependent energy investment in testes may be increased investment by large sneaker males in aggressive interactions for sneaking opportunities. This is the first evidence that testis size variation among sneaker males is affected by the competition among sneaker males

Establishment of macaque trophoblast stem cell lines derived from cynomolgus monkey blastocysts

The placenta forms a maternal-fetal junction that supports many physiological functions such as the supply of nutrition and exchange of gases and wastes. Establishing an in vitro culture model of human and non-human primate trophoblast stem/progenitor cells is important for investigating the process of early placental development and trophoblast differentiation. In this study, we have established five trophoblast stem cell (TSC) lines from cynomolgus monkey blastocysts, named macTSC #1-5. Fibroblast growth factor 4 (FGF4) enhanced proliferation of macTSCs, while other exogenous factors were not required to maintain their undifferentiated state. macTSCs showed a trophoblastic gene expression profile and trophoblast-like DNA methylation status and also exhibited differentiation capacity towards invasive trophoblast cells and multinucleated syncytia. In a xenogeneic chimera assay, these stem cells contributed to trophectoderm (TE) development in the chimeric blastocysts. macTSC are the first primate trophoblast cell lines whose proliferation is promoted by FGF4. These cell lines provide a valuable in vitro culture model to analyze the similarities and differences in placental development between human and non-human primates

Ultra-Deep Bisulfite Sequencing to Detect Specific DNA Methylation Patterns of Minor Cell Types in Heterogeneous Cell Populations: An Example of the Pituitary Tissue

<div><p>DNA methylation is an epigenetic modification important for cell fate determination and cell type-specific gene expression. Transcriptional regulatory regions of the mammalian genome contain a large number of tissue/cell type-dependent differentially methylated regions (T-DMRs) with DNA methylation patterns crucial for transcription of the corresponding genes. In general, tissues consist of multiple cell types in various proportions, making it difficult to detect T-DMRs of minor cell types in tissues. The present study attempts to detect T-DMRs of minor cell types in tissues by ultra-deep bisulfite sequencing of cell type-restricted genes and to assume proportions of minor cell types based on DNA methylation patterns of sequenced reads. For this purpose, we focused on transcriptionally active hypomethylated alleles (Hypo-alleles), which can be recognized by the high ratio of unmethylated CpGs in each sequenced read (allele). The pituitary gland contains multiple cell types including five hormone-expressing cell types and stem/progenitor cells, each of which is a minor cell type in the pituitary tissue. By ultra-deep sequencing of more than 100 reads for detection of Hypo-alleles in pituitary cell type-specific genes, we identified T-DMRs specific to hormone-expressing cells and stem/progenitor cells and used them to estimate the proportions of each cell type based on the Hypo-allele ratio in pituitary tissue. Therefore, introduction of the novel Hypo-allele concept enabled us to detect T-DMRs of minor cell types with estimation of their proportions in the tissue by ultra-deep bisulfite sequencing.</p></div

Validation of hypomethylated alleles (Hypo-alleles) by MiSeq ultra-deep sequencing.

<p>≥75% unmethylated CpG sites (3 or 4 out of the 4 CpGs shown) are defined as Hypo-alleles. Among the five reads, reads 1 and 2 are Hypo-alleles, and the Hypo-allele ratio is 40% (2 reads/5 reads). Left panel: conventional CpG methylation analysis data; white and black circles indicate unmethylated and methylated CpGs, respectively. Right panel: MiSeq ultra-deep bisulfite analysis; white and black bars indicate unmethylated and methylated CpGs, respectively. (B) Validation of Hypo-allele ratio analysis by MiSeq ultra-deep bisulfite sequencing at the <i>Sall4</i> T-DMR using mixtures of genomic DNAs from PFF and iPSC. Sequenced reads above the dotted lines are Hypo-alleles. White and black bars indicate unmethylated and methylated CpGs, respectively. Mixtures of genomic DNAs of PFF and iPSC (0:100, 25:75, 50:50, 75:25, or 100:0) would exhibit the expected respective Hypo-allele ratios (100%, 75%, 50%, 25%, or 0%) for the <i>Sall4</i> T-DMR. (C) Hypo-allele ratios of the <i>Sall4</i> T-DMR analyzed by ultra-deep sequencing. Hypo-allele ratios were calculated from the PFF/iPSC mixtures (expected Hypo-allele ratios of 100%, 75%, 50%, 25%, and 0%) shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146498#pone.0146498.g001" target="_blank">Fig 1B</a>. The Hypo-allele ratios from three independent experiments are shown as mean ± SE (n = 3). (D) Accuracy of detecting Hypo-allele ratio (10%) in relation to sequenced read numbers based on the MiSeq data at the <i>Sall4</i> T-DMR. For this analysis, genomic DNAs of PFF and iPSC were mixed at 90:10 for a Hypo-allele ratio of 10%. From two independent MiSeq analyses, 1,109 reads (Exp. 1) and 1,447 reads (Exp. 2) were obtained. Hypo-allele ratios of each trial are plotted (filled circles, n = 5), and mean ± SD for five trials each for 10, 20, 50, 100, or 200 reads are plotted as triangles with lines. (E) Examination of detection accuracy of Hypo-allele (10% or 50%) by conventional analysis of small numbers of sequencing reads based on the MiSeq data at the <i>Sall4</i> T-DMR. Genomic DNAs of PFF and iPSC were mixed at 90:10 or 50:50 for samples exhibiting Hypo-allele ratios of 10% or 50%, respectively. From the raw data, 20 successive reads were grouped from the first through 100th read. The Hypo-allele ratios of 20-read groups were calculated. Asterisks indicate Hypo-alleles. White and black bars indicate unmethylated CpGs and methylated CpGs, respectively.</p

Comparison of DNA methylation profiles of pituitary-related genes in porcine tissues by ultra-deep bisulfite sequencing between the conventional DNA methylation analysis and a novel Hypo-allele ratio analysis.

<p>Hypo-allele ratios of 37 pituitary-related genes were analyzed in pituitary (#1 and #2), liver, brain, and PFF samples using a MiSeq sequencer. The Hypo-allele data for each tissue are shown as a heatmap after hierarchical clustering based on Euclidean distance (left panel). Using the same bisulfite sequencing data, the conventional DNA methylation degrees calculated by methyl-CpGs/total CpGs are also shown as a heatmap with hierarchical clustering (right panel). ND, No data.</p

Schematic diagram of predicted proportions of pituitary cell types in adult porcine pituitary tissue.

<p>Proportions of several pituitary cell types were estimated based on the Hypo-allele ratios of the pituitary cell type-restricted genes (white).</p

Detection of Hypo-alleles of endogenous imprinted genes in porcine pituitary and liver.

<p>Bisulfite ultra-deep sequencing was performed for differentially methylated regions of imprinted <i>Meg3</i> and <i>Peg10</i> genes, and their Hypo-allele ratios were calculated as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146498#pone.0146498.g001" target="_blank">Fig 1</a>. Sequenced reads above the dotted lines are Hypo-alleles. White and black bars indicate unmethylated and methylated CpGs, respectively.</p