Probing chromosome structure using multidimensional scaling of DNA contact matrices

Chromosome conformation capture technology has provided a route to studying genome structure through DNA-DNA contact-counts. An iteration of chromosome conformation capture technology is Hi-C, which provides genome wide two dimensional contact-count data. The contact-count data from Hi-C can be viewed as a proxy for distance and using some transform function can be transformed into estimated distances. These estimated distances can be fitted into Euclidean space using the statistical tools of multidimensional scaling to give estimated chromosome or genome configurations. The first part of this thesis takes the Hi-C contact-count data for Chromosome 14, transforms it into estimated distances which are fitted into Euclidean space to give an estimated chromosome configuration. Steps are also taken to pre-process the genome contact-count matrix to refine the information held within it. The pre-processed genome contact-count matrix is transformed into estimated distances, which are fitted into Euclidean space to give an estimated genome configuration. The estimated chromosome and genome configurations are investigated, to find if known features of these structures are captured through fitting the Hi-C data. The second part of this thesis simulates contact-count data from simple configurations. Using the inverse of the transform functions the distances between points in a configuration can be transformed into mean contact-counts. The mean contact-counts are perturbed using a suitable distribution function to provide perturbed contact-counts, which are transformed into perturbed distances. The perturbed distances can be fitted into Euclidean space to give a fitted configurations. The properties of the fitted configurations are investigated and compared with the original configurations, and the properties of the perturbed distances are also investigated. Then steps are taken to improve the fitted configurations using information from the properties of the perturbed distances, with the successful techniques applied to estimating the chromosome configuration.