Logarithmic Picard groups, chip firing, and the combinatorial rank

Illusie has suggested that one should think of the classifying group of M_X^{gp}-torsors on a logarithmically smooth curve $X$ over a standard logarithmic point as a logarithmic analogue of the Picard group of $X$. This logarithmic Picard group arises naturally as a quotient of the algebraic Picard group by lifts of the chip firing relations of the associated dual graph. We connect this perspective to Baker and Norine’s theory of ranks of divisors on a finite graph, and to Amini and Baker’s metrized complexes of curves. Moreover, we propose a definition of a combinatorial rank for line bundles on $X$ and prove that an analogue of the Riemann–Roch formula holds for our combinatorial rank. Our proof proceeds by carefully describing the relationship between the logarithmic Picard group on a logarithmic curve and the Picard group of the associated metrized complex. This approach suggests a natural categorical framework for metrized complexes, namely the category of logarithmic curves

Logarithmic Picard groups, chip firing, and the combinatorial rank

Illusie has suggested that one should think of the classifying group of MgpX -torsors on a logarithmically smooth curve X over a standard logarithmic point as a logarithmic analogue of the Picard group of X. This logarithmic Picard group arises naturally as a quotient of the algebraic Picard group by lifts of the chip firing relations of the associated dual graph. We connect this perspective to Baker and Norine’s theory of ranks of divisors on a finite graph, and to Amini and Baker’s metrized complexes of curves. Moreover, we propose a definition of a combinatorial rank for line bundles on X and prove that an analogue of the Riemann–Roch formula holds for our combinatorial rank. Our proof proceeds by carefully describing the relationship between the logarithmic Picard group on a logarithmic curve and the Picard group of the associated metrized complex. This approach suggests a natural categorical framework for metrized complexes, namely the category of logarithmic curves

Vimentin DNA methylation predicts survival in breast cancer

The Vimentin gene plays a pivotal role in epithelial-to-mesenchymal transition and is known to be overexpressed in the prognostically poor basal-like breast cancer subtype. Recent studies have reported Vimentin DNA methylation in association with poor clinical outcomes in other solid tumors, but not in breast cancer. We therefore quantified Vimentin DNA methylation using MALDI-TOF mass spectrometry in breast tumors and matched normal pairs in association with gene expression and survival in a hospital-based study of breast cancer patients. Gene expression data via qRT-PCR in cell lines and oligomicroarray data from breast tissues were correlated with percent methylation in the Vimentin promoter. A threshold of 20 percent average methylation compared with matched normal pairs was set for bivariate and multivariate tests of association between methylation and tumor subtype, tumor histopathology, and survival. Vimentin was differentially methylated in luminal breast cancer cell lines, and in luminal A, luminal B, and HER2-enriched breast tumor subtypes, but was rare in basal-like cell lines and tumors. Increased methylation was strongly correlated with decreased mRNA expression in cell lines, and had a moderate inverse correlation in breast tumors. Vimentin methylation predicted poor overall survival independent of race, subtype, stage, nodal status, or metastatic disease and holds promise as a new prognostic biomarker for breast cancer patients

Comprehensive population-based genome sequencing provides insight into hematopoietic regulatory mechanisms

Genetic variants affecting hematopoiesis can influence commonly measured blood cell traits. To identify factors that affect hematopoiesis, we performed association studies for blood cell traits in the population-based Estonian Biobank using high-coverage whole-genome sequencing (WGS) in 2,284 samples and SNP genotyping in an additional 14,904 samples. Using up to 7,134 samples with available phenotype data, our analyses identified 17 associations across 14 blood cell traits. Integration of WGS-based fine-mapping and complementary epigenomic datasets provided evidence for causal mechanisms at several loci, including at a previously undiscovered basophil count-associated locus near the master hematopoietic transcription factor CEBPA. The fine-mapped variant at this basophil count association near CEBPA overlapped an enhancer active in common myeloid progenitors and influenced its activity. In situ perturbation of this enhancer by CRISPR/Cas9 mutagenesis in hematopoietic stem and progenitor cells demonstrated that it is necessary for and specifically regulates CEBPA expression during basophil differentiation. We additionally identified basophil count-associated variation at another more pleiotropic myeloid enhancer near GATA2, highlighting regulatory mechanisms for ordered expression of master hematopoietic regulators during lineage specification. Our study illustrates how population-based genetic studies can provide key insights into poorly understood cell differentiation processes of considerable physiologic relevance.Peer reviewe

Genome-wide enhancer maps link risk variants to disease genes

Genome-wide association studies (GWAS) have identified thousands of noncoding loci that are associated with human diseases and complextraits, each of which could reveal insights into the mechanisms of disease(1). Many ofthe underlying causal variants may affect enhancers(2,3), but we lack accurate maps of enhancers and their target genes to interpret such variants. We recently developed the activity-by-contact (ABC) model to predict which enhancers regulate which genes and validated the model using CRISPR perturbations in several cell types(4). Here we apply this ABC model to create enhancer-gene maps in 131 human cell types and tissues, and use these maps to interpret the functions of GWAS variants. Across 72 diseases and complex traits, ABC links 5,036 GWAS signals to 2,249 unique genes, including a class of 577genesthat appear to influence multiple phenotypes through variants in enhancers that act in different cell types. In inflammatory bowel disease (IBD), causal variants are enriched in predicted enhancers by more than 20-fold in particular cell types such as dendritic cells, and ABC achieves higher precision than other regulatory methods at connecting noncoding variants to target genes. These variant-to-function maps reveal an enhancer that contains an IBD risk variant and that regulates the expression of PPIF to alter the membrane potential of mitochondria in macrophages. Our study reveals principles of genome regulation, identifies genes that affect IBD and provides a resource and generalizable strategy to connect risk variants of common diseases to their molecular and cellular functions.Peer reviewe

Gene-centric functional dissection of human genetic variation uncovers regulators of hematopoiesis

Genome-wide association studies (GWAS) have identified thousands of variants associated with human diseases and traits. However, the majority of GWAS-implicated variants are in non-coding regions of the genome and require in depth follow-up to identify target genes and decipher biological mechanisms. Here, rather than focusing on causal variants, we have undertaken a pooled loss-of-function screen in primary hematopoietic cells to interrogate 389 candidate genes contained in 75 loci associated with red blood cell traits. Using this approach, we identify 77 genes at 38 GWAS loci, with most loci harboring 1-2 candidate genes. Importantly, the hit set was strongly enriched for genes validated through orthogonal genetic approaches. Genes identified by this approach are enriched in specific and relevant biological pathways, allowing regulators of human erythropoiesis and modifiers of blood diseases to be defined. More generally, this functional screen provides a paradigm for gene-centric follow up of GWAS for a variety of human diseases and traits

Association of Epidemiologic Factors and Genetic Variants Influencing Hypothalamic-Pituitary-Adrenocortical Axis Function With Postconcussive Symptoms After Minor Motor Vehicle Collision

To determine the influence of epidemiologic factors and the influence of genetic variants affecting FKBP5, a protein known to modulate hypothalamic-pituitary-adrenocortical (HPA) axis function, on the severity of somatic symptoms commonly termed “post-concussive” six and twelve months after motor-vehicle collision (MVC)

Prioritizing disease and trait causal variants at the TNFAIP3 locus using functional and genomic features

Genome-wide association studies have associated thousands of genetic variants with complex traits and diseases, but pinpointing the causal variant(s) among those in tight linkage disequilibrium with each associated variant remains a major challenge. Here, we use seven experimental assays to characterize all common variants at the multiple disease-associated TNFAIP3 locus in five disease-relevant immune cell lines, based on a set of features related to regulatory potential. Trait/disease-associated variants are enriched among SNPs prioritized based on either: (1) residing within CRISPRi-sensitive regulatory regions, or (2) localizing in a chromatin accessible region while displaying allele-specific reporter activity. Of the 15 trait/disease-associated haplotypes at TNFAIP3, 9 have at least one variant meeting one or both of these criteria, 5 of which are further supported by genetic fine-mapping. Our work provides a comprehensive strategy to characterize genetic variation at important disease-associated loci, and aids in the effort to identify trait causal genetic variants

The NORAD lncRNA assembles a topoisomerase complex critical for genome stability

The human genome contains thousands of long non-coding RNAs, but specific biological functions and biochemical mechanisms have been discovered for only about a dozen. A specific long non-coding RNA—non-coding RNA activated by DNA damage (NORAD)—has recently been shown to be required for maintaining genomic stability, but its molecular mechanism is unknown. Here we combine RNA antisense purification and quantitative mass spectrometry to identify proteins that directly interact with NORAD in living cells. We show that NORAD interacts with proteins involved in DNA replication and repair in steady-state cells and localizes to the nucleus upon stimulation with replication stress or DNA damage. In particular, NORAD interacts with RBMX, a component of the DNA-damage response, and contains the strongest RBMX-binding site in the transcriptome. We demonstrate that NORAD controls the ability of RBMX to assemble a ribonucleoprotein complex—which we term NORAD-activated ribonucleoprotein complex 1 (NARC1)—that contains the known suppressors of genomic instability topoisomerase I (TOP1), ALYREF and the PRPF19–CDC5L complex. Cells depleted for NORAD or RBMX display an increased frequency of chromosome segregation defects, reduced replication-fork velocity and altered cell-cycle progression—which represent phenotypes that are mechanistically linked to TOP1 and PRPF19–CDC5L function. Expression of NORAD in trans can rescue defects caused by NORAD depletion, but rescue is significantly impaired when the RBMX-binding site in NORAD is deleted. Our results demonstrate that the interaction between NORAD and RBMX is important for NORAD function, and that NORAD is required for the assembly of the previously unknown topoisomerase complex NARC1, which contributes to maintaining genomic stability. In addition, we uncover a previously unknown function for long non-coding RNAs in modulating the ability of an RNA-binding protein to assemble a higher-order ribonucleoprotein complex

The NORAD lncRNA assembles a topoisomerase complex critical for genome stability

The human genome contains thousands of long non-coding RNAs, but specific biological functions and biochemical mechanisms have been discovered for only about a dozen. A specific long non-coding RNA—non-coding RNA activated by DNA damage (NORAD)—has recently been shown to be required for maintaining genomic stability, but its molecular mechanism is unknown. Here we combine RNA antisense purification and quantitative mass spectrometry to identify proteins that directly interact with NORAD in living cells. We show that NORAD interacts with proteins involved in DNA replication and repair in steady-state cells and localizes to the nucleus upon stimulation with replication stress or DNA damage. In particular, NORAD interacts with RBMX, a component of the DNA-damage response, and contains the strongest RBMX-binding site in the transcriptome. We demonstrate that NORAD controls the ability of RBMX to assemble a ribonucleoprotein complex—which we term NORAD-activated ribonucleoprotein complex 1 (NARC1)—that contains the known suppressors of genomic instability topoisomerase I (TOP1), ALYREF and the PRPF19–CDC5L complex. Cells depleted for NORAD or RBMX display an increased frequency of chromosome segregation defects, reduced replication-fork velocity and altered cell-cycle progression—which represent phenotypes that are mechanistically linked to TOP1 and PRPF19–CDC5L function. Expression of NORAD in trans can rescue defects caused by NORAD depletion, but rescue is significantly impaired when the RBMX-binding site in NORAD is deleted. Our results demonstrate that the interaction between NORAD and RBMX is important for NORAD function, and that NORAD is required for the assembly of the previously unknown topoisomerase complex NARC1, which contributes to maintaining genomic stability. In addition, we uncover a previously unknown function for long non-coding RNAs in modulating the ability of an RNA-binding protein to assemble a higher-order ribonucleoprotein complex