A fractal polymer with loops recapitulates key features of chromosome organization

Chromosomes are exceedingly long polymers compacted in a cell nucleus. While it was long suggested that mammalian chromosomes are folded into loops, experimental detection of such loops has remained a daunting task. The most comprehensive experimental information about chromosome spatial organization is provided by Hi-C experiments that measure the frequency of contacts between all chromosomal positions. The lack of a tractable physical model of a polymer folded into loops limits our ability to interpret experimental data. It thus remains unknown how to obtain accurate and quantitative information about the nature of chromosomal looping from Hi-C. Here, we introduce a model of a polymer with random loops, solve it analytically and extend it by simulations for real chains. Remarkably, our model faithfully reproduces complex shapes of experimental contact probability curves universal among mammalian cells. This agreement suggests that chromosomes are indeed organized into a sequence of randomly positioned loops and allows to estimate loop sizes. We further show that excluded volume in real chains can induce osmotic and topological repulsion between loops. Thus, our new framework allows interpretation of experimental data and suggests that interphase chromosomes are crumpled polymers further folded into a sequence of randomly positioned loops. ### Competing Interest Statement The authors have declared no competing interest.