Modeling Spatial Genomic Interactions with the Hawkes model
The spatial localization of many DNA-protein interactions is now available thanks to the development of ChIP-Seq, and their investigation calls for adapted statistical methods. Many methods were developped for peak calling, but few were proposed for the downstream analysis of peak-like data, whereas the spatial structure of such data may contain relevant biological information, like binding constraints for instance. Associations between the occurrences of two genomic features are usually assessed by overlaps, but here we propose a statistical model to precisely quantify the spatial interactions between the location of binding events. Our methodology relies on a multivariate spatial process, the Hawkes model, that can also be interpreted in terms of a graphical model to highlight spatial dependencies between genomic features. Using our method, we explore the chromatinian landscape of replication origins, and we highlight attractive and repulsive patterns that can be related to the regulation of the spatial program of replication.