The global architecture of the cell nucleus and the spatial organization of chromatin play important roles in gene expression and nuclear function. Single-cell imaging and chromosome conformation capture-based techniques provide a wealth of information on the spatial organization of chromosomes. However, a mechanistic model that can account for all observed scaling behaviors governing long-range chromatin interactions is missing. Here we describe a model called constrained self-avoiding chromatin (C-SAC) for studying spatial structures of chromosomes, as the available space is a key determinant of chromosome folding. We studied large ensembles of model chromatin chains with appropriate fiber diameter, persistence length and excluded volume under spatial confinement. We show that the equilibrium ensemble of randomly folded chromosomes in the confined nuclear volume gives rise to the experimentally observed higher-order architecture of human chromosomes, including average scaling properties of mean-square spatial distance, end-to-end distance, contact probability and their chromosome-to-chromosome variabilities. Our results indicate that the overall structure of a human chromosome is dictated by the spatial confinement of the nuclear space, which may undergo significant tissue- and developmental stage-specific size changes.
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