3-manifolds efficiently bound 4-manifolds

It is known since 1954 that every 3-manifold bounds a 4-manifold. Thus, for instance, every 3-manifold has a surgery diagram. There are several proofs of this fact, including constructive proofs, but there has been little attention to the complexity of the 4-manifold produced. Given a 3-manifold M of complexity n, we show how to construct a 4-manifold bounded by M of complexity O(n^2). Here we measure ``complexity'' of a piecewise-linear manifold by the minimum number of n-simplices in a triangulation. It is an open question whether this quadratic bound can be replaced by a linear bound. The proof goes through the notion of "shadow complexity" of a 3-manifold M. A shadow of M is a well-behaved 2-dimensional spine of a 4-manifold bounded by M. We prove that, for a manifold M satisfying the Geometrization Conjecture with Gromov norm G and shadow complexity S, c_1 G <= S <= c_2 G^2 for suitable constants c_1, c_2. In particular, the manifolds with shadow complexity 0 are the graph manifolds.Comment: 39 pages, 21 figures; added proof for spin case as wel

Single-cell RNA-seq reveals intratumoral heterogeneity in osteosarcoma patients: A review

While primary bone malignancies make up just 0.2% of all cancers, osteosarcoma (OS) is the third most common cancer in adolescents. Due to its highly complex and heterogeneous tumor microenvironment (TME), OS has proven difficult to treat. There has been little to no improvement in therapy for this disease over the last 40 years. Even the recent success of immunotherapies in other blood-borne and solid malignancies has not translated to OS. With frequent recurrence and lung metastases continuing to pose a challenge in the clinic, recent advancements in molecular profiling, such as single-cell RNA sequencing (scRNA-seq), have proven useful in identifying novel biomarkers of OS tumors while providing new insight into this TME that could potentially lead to new therapeutic options. This review combines the analyses of over 150,000 cells from 18 lesions ranging from primary, recurrent, and metastatic OS lesions, revealing distinct cellular populations and gene signatures that exist between them. Here, we detail these previous findings and ultimately convey the intratumoral heterogeneity that exists within OS tumor specimens

Integrative epigenetic and genetic pan-cancer somatic alteration portraits

Genetic and epigenetic alterations are required for carcinogenesis and the mutation burden across tumor types has been investigated. Here, we investigate epigenetic alterations with a novel measure of global DNA methylation dysregulation, the methylation dysregulation index (MDI), across 14 cancer types in The Cancer Genome Atlas (TCGA) database. DNA methylation data—obtained using Illumina HumanMethylation450 BeadChip—was accessed from TCGA. We calculated the MDI in 14 tumor types (n = 5,592 tumors), using adjacent normal tissues (n = 701) from each tumor site. Copy number alteration, and mutation burden were retrieved from cBioportal (n = 5,152). We tested the relation of subject MDI across tumors and with age, gender, tumor stage, estimated tumor purity, and copy number alterations for both overall MDI and genomic-context-specific MDI. We also investigated the top most dysregulated loci shared across tumor types. There was a broad range of extent in methylation dysregulation across tumor types (P < 2.2E-16). However, a consistent pattern of methylation dysregulation stratified by genomic context was observed across tumor types where the highest dysregulation occurred at non-CpG island regions. Considering other summary measures of somatic alteration, MDI was correlated with copy number alterations but not with mutation burden. Using the top dysregulated CpG sites in common across tumors, 4 classes of cancer types were observed, and the functional consequences of these alterations to gene expression were confirmed. This work identified the global DNA methylation dysregulation patterns across 14 cancer types showing a higher impact for the non-CpG island areas. The most dysregulated loci across cancer types identified common clusters across cancer types that may have implications for future treatment and prevention measures

Epigenetic and genetic burden measures are associated with tumor characteristics in invasive breast carcinoma

<p>The development and progression of invasive breast cancer is characterized by alterations to the genome and epigenome. However, the relationship between breast tumor characteristics, disease subtypes, and patient outcomes with the cumulative burden of these molecular alterations are not well characterized. We determined the average departure of tumor DNA methylation from adjacent normal breast DNA methylation using Illumina 450K methylation data from 700 invasive breast tumors and 90 adjacent normal breast tissues in The Cancer Genome Atlas. From this we generated a novel summary measure of altered DNA methylation, the DNA methylation dysregulation index (MDI), and examined the relation of MDI with tumor characteristics and summary measures that quantify cumulative burden of genetic mutation and copy number alterations. Our analysis revealed that MDI was significantly associated with tumor stage (<i>P</i> = 0.017). Across invasive breast tumor subtypes we observed significant differences in genome-wide DNA MDIs (<i>P</i> = 4.9E–09) and in a fraction of the genome with copy number alterations (FGA) (<i>P</i> = 4.6E–03). Results from a linear regression adjusted for subject age, tumor stage, and estimated tumor purity indicated a positive significant association of MDI with both MCB and FGA (<i>P</i> = 0.036 and <i>P</i> < 2.2E–16). A recursively partitioned mixture model of all 3 somatic alteration burden measures resulted in classes of tumors whose epigenetic and genetic burden profile were associated with the PAM50 subtype and mutations in <i>TP53, PIK3CA, and CDH1</i>. Together, our work presents a novel framework for characterizing the epigenetic burden and adds to the understanding of the aggregate impact of epigenetic and genetic alterations in breast cancer.</p

Aligned Networks of Engineered Fibrillar Fibronectin Guide Cellular Orientation and Motility

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/168273/1/sstr202000137.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/168273/2/sstr202000137_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/168273/3/sstr202000137-sup-0001-SuppData-S1.pd

Aligned Networks of Engineered Fibrillar Fibronectin Guide Cellular Orientation and Motility

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/168273/1/sstr202000137.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/168273/2/sstr202000137_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/168273/3/sstr202000137-sup-0001-SuppData-S1.pd