DNA copy number aberrations (CNAs) are of biological and medical interest because they help identify regulatory mechanisms underlying tumor initiation and evolution. Identification of tumor-driving CNAs (driver CNAs) however remains a challenging task, because they are frequently hidden by CNAs that are the product of random events that take place during tumor evolution. Experimental detection of CNAs is commonly accomplished through array comparative genomic hybridization (aCGH) assays followed by supervised and/or unsupervised statistical methods that combine the segmented profiles of all patients to identify driver CNAs. Here, we extend a previously-presented supervised algorithm for the identification of CNAs that is based on a topological representation of the data. Our method associates a two-dimensional (2D) point cloud with each aCGH profile and generates a sequence of simplicial complexes, mathematical objects that generalize the concept of a graph. This representation of the data permits segmenting the data at different resolutions and identifying CNAs by interrogating the topological properties of these simplicial complexes. We tested our approach on a published dataset with the goal of identifying specific breast cancer CNAs associated with specific molecular subtypes. Identification of CNAs associated with each subtype was performed by analyzing each subtype separately from the others and by taking the rest of the subtypes as the control. Our results found a new amplification in 11q at the location of the progesterone receptor in the Luminal A subtype. Aberrations in the Luminal B subtype were found only upon removal of the basal-like subtype from the control set. Under those conditions, all regions found in the original publication, except for 17q, were confirmed; all aberrations, except those in chromosome arms 8q and 12q were confirmed in the basal-like subtype. These two chromosome arms, however, were detected only upon removal of three patients with exceedingly large copy number values. More importantly, we detected 10 and 21 additional regions in the Luminal B and basal-like subtypes, respectively. Most of the additional regions were either validated on an independent dataset and/or using GISTIC. Furthermore, we found three new CNAs in the basal-like subtype: a combination of gains and losses in 1p, a gain in 2p and a loss in 14q. Based on these results, we suggest that topological approaches that incorporate multiresolution analyses and that interrogate topological properties of the data can help in the identification of copy number changes in cancer.

The timing of DNA replication is largely regulated by the location and timing of replication origin firing. Therefore, much effort has been invested in identifying and analyzing human replication origins. However, the heterogeneous nature of eukaryotic replication kinetics and the low efficiency of individual origins in metazoans has made mapping the location and timing of replication initiation in human cells difficult. We have mapped early-firing origins in HeLa cells using Optical Replication Mapping, a high-throughput single-molecule approach based on Bionano Genomics genomic mapping technology. The single-molecule nature and 290-fold coverage of our dataset allowed us to identify origins that fire with as little as 1% efficiency. We find sites of human replication initiation in early S phase are not confined to well-defined efficient replication origins, but are instead distributed across broad initiation zones consisting of many inefficient origins. These early-firing initiation zones co-localize with initiation zones inferred from Okazaki-fragment-mapping analysis and are enriched in ORC1 binding sites. Although most early-firing origins fire in early-replication regions of the genome, a significant number fire in late-replicating regions, suggesting that the major difference between origins in early and late replicating regions is their probability of firing in early S-phase, as opposed to qualitative differences in their firing-time distributions. This observation is consistent with stochastic models of origin timing regulation, which explain the regulation of replication timing in yeast.