Single-cell analysis of the 3D topologies of genomic loci using genome architecture mapping

Although each cell within an organism contains a nearly identical genome sequence, the three-dimensional (3D) packing of the genome varies among individual cells, influencing cell-type-specific gene expression. Genome Architecture Mapping (GAM) is the first genome-wide experimental method for capturing 3D proximities between any number of genomic loci without ligation. GAM overcomes several limitations of 3C-based methods by sequencing DNA from a large collection of thin sections sliced from individual nuclei. The GAM technique measures locus co-segregation, extracts radial positions, infers chromatin compaction, requires small numbers of cells, does not depend on ligation, and provides rich single-cell information. However, previous analyses of GAM data focused exclusively on population averages, neglecting the variation in 3D topology among individual cells. We present the first single-cell analysis of GAM data, demonstrating that the slices from individual cells reveal intercellular heterogeneity in chromosome conformation. By simultaneously clustering both slices and genomic loci, we identify topological variation among single cells, including differential compaction of cell cycle genes. We also develop a geometric model of the nucleus, allowing prediction of the 3D positions of each slice. Using GAM data from mouse embryonic stem cells, we make new discoveries about the structure of the major mammalian histone gene locus, which is incorporated into the Histone Locus Body (HLB), including structural fluctuations and putative causal molecular mechanisms. Our methods are packaged as SluiceBox, a toolkit for mining GAM data. Our approach represents a new method of investigating variation in 3D genome topology among individual cells across space and time

The road to deterministic matrices with the restricted isometry property

The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some novel, and we evaluate their performance. In evaluating some techniques, we apply random matrix theory and inadvertently find a simple alternative proof that certain random matrices are RIP. Later, we propose a particular class of matrices as candidates for being RIP, namely, equiangular tight frames (ETFs). Using the known correspondence between real ETFs and strongly regular graphs, we investigate certain combinatorial implications of a real ETF being RIP. Specifically, we give probabilistic intuition for a new bound on the clique number of Paley graphs of prime order, and we conjecture that the corresponding ETFs are RIP in a manner similar to random matrices.Comment: 24 page

Enhancement of Magneto-Optic Effects via Large Atomic Coherence

We utilize the generation of large atomic coherence to enhance the resonant nonlinear magneto-optic effect by several orders of magnitude, thereby eliminating power broadening and improving the fundamental signal-to-noise ratio. A proof-of-principle experiment is carried out in a dense vapor of Rb atoms. Detailed numerical calculations are in good agreement with the experimental results. Applications such as optical magnetometry or the search for violations of parity and time reversal symmetry are feasible

Multiplex-GAM: genome-wide identification of chromatin contacts yields insights overlooked by Hi-C

Technology for measuring 3D genome topology is increasingly important for studying gene regulation, for genome assembly and for mapping of genome rearrangements. Hi-C and other ligation-based methods have become routine but have specific biases. Here, we develop multiplex-GAM, a faster and more affordable version of genome architecture mapping (GAM), a ligation-free technique that maps chromatin contacts genome-wide. We perform a detailed comparison of multiplex-GAM and Hi-C using mouse embryonic stem cells. When examining the strongest contacts detected by either method, we find that only one-third of these are shared. The strongest contacts specifically found in GAM often involve ‘active’ regions, including many transcribed genes and super-enhancers, whereas in Hi-C they more often contain ‘inactive’ regions. Our work shows that active genomic regions are involved in extensive complex contacts that are currently underestimated in ligation-based approaches, and highlights the need for orthogonal advances in genome-wide contact mapping technologies

Meta-analysis of type 2 Diabetes in African Americans Consortium

Type 2 diabetes (T2D) is more prevalent in African Americans than in Europeans. However, little is known about the genetic risk in African Americans despite the recent identification of more than 70 T2D loci primarily by genome-wide association studies (GWAS) in individuals of European ancestry. In order to investigate the genetic architecture of T2D in African Americans, the MEta-analysis of type 2 DIabetes in African Americans (MEDIA) Consortium examined 17 GWAS on T2D comprising 8,284 cases and 15,543 controls in African Americans in stage 1 analysis. Single nucleotide polymorphisms (SNPs) association analysis was conducted in each study under the additive model after adjustment for age, sex, study site, and principal components. Meta-analysis of approximately 2.6 million genotyped and imputed SNPs in all studies was conducted using an inverse variance-weighted fixed effect model. Replications were performed to follow up 21 loci in up to 6,061 cases and 5,483 controls in African Americans, and 8,130 cases and 38,987 controls of European ancestry. We identified three known loci (TCF7L2, HMGA2 and KCNQ1) and two novel loci (HLA-B and INS-IGF2) at genome-wide significance (4.15 × 10(-94)<P<5 × 10(-8), odds ratio (OR)  = 1.09 to 1.36). Fine-mapping revealed that 88 of 158 previously identified T2D or glucose homeostasis loci demonstrated nominal to highly significant association (2.2 × 10(-23) < locus-wide P<0.05). These novel and previously identified loci yielded a sibling relative risk of 1.19, explaining 17.5% of the phenotypic variance of T2D on the liability scale in African Americans. Overall, this study identified two novel susceptibility loci for T2D in African Americans. A substantial number of previously reported loci are transferable to African Americans after accounting for linkage disequilibrium, enabling fine mapping of causal variants in trans-ethnic meta-analysis studies.Peer reviewe