Simulation of the distribution of chromosome targets in cell nuclei under topological constraints

Abstract

Several models for the distribution of subchromosomal targets under topological constraints were developed which take into account that chromosomes occupy distinct, mutually exclusive territories in the cell nucleus. Nuclei and two pairs of chromosome territories of various size were modeled by spheres or ellipsoids under the simplified assumption that the entire set of chromosome territories present in a diploid cell nucleus completely fills the nuclear interior and that each territory occupies a fraction of the nuclear volume proportional to its DNA content. Monte Carlo simulations of the distribution of the territory gravity centers were performed taking into account the constraint of territory extension by the nuclear boundary and the constraint of territory self avoidance, i.e. territories should not intersect each other. In addition, various assumptions were made with regard to the location of point-like targets either within or at the surface of two ‘homologous’ model territories. For each assumption the distance between the two point-like targets and between each target and the center of the model nucleus was calculated in Monte Carlo simulations and in part also analytically. The distribution of point-like targets in model nuclei under the influence of these topological constraints depends on the shape of the model nucleus and shows strong deviations from a model often applied in previous studies. In this model the random distribution of point-like targets was described under the assumption that such targets are distributed uniformly and independently from each other within the nuclear space without any constraints except for the nuclear boundary. All models were applied to experimentally measured distributions of chromosomal subregions delineated by fluorescence in situ hybridization with subregion specific probes. We demonstrate that a neglect of geometrical constraints in the simulation of target distributions can lead to erroneous conclusions of whether experimental target distributions occur in a random manner or not.