Physical origin of the contact frequency in chromosome conformation capture data

Physical proximity between each pair of genomic loci in a nucleus is measured as a form of contact frequency in chromosome conformation capture-based methods. Complexity of chromosome structure in interphase can be characterized by measuring a statistical property of physical distance between genomic loci according to genomic separation along single chromatids. To find a relationship between the physical distance and the contact frequency, we propose a polymer model derived from the Langevin equation. The model is derived by considering a structure of a chromosome as a trajectory of a particle, where each consecutive segment in the chromosome corresponds to a transient position in the trajectory over time. Using chromosome conformation capture data, we demonstrate the functional relationship between the two quantities. The physical distances derived from the mean contact frequencies by the model show a good correlation with those from experimental data. From the model, we present that the mean contact frequency curve can be divided into three components that arise from different physical origins and show that the contact frequency is proportional to the contact surface area, not to the volume of segments suggested by the fractal globule model. The model explains both a decaying pattern of the contact frequency and the biphasic relationship between the physical distance and the genomic length.