Confinement-induced glassy dynamics in a model for chromosome organization

Recent experiments showing scaling of the intrachromosomal contact probability, $P(s)\sim s^{-1}$ with the genomic distance $s$, are interpreted to mean a self-similar fractal-like chromosome organization. However, scaling of $P(s)$ varies across organisms, requiring an explanation. We illustrate dynamical arrest in a highly confined space as a discriminating marker for genome organization, by modeling chromosome inside a nucleus as a homopolymer confined to a sphere of varying sizes. Brownian dynamics simulations show that the chain dynamics slows down as the polymer volume fraction ($\phi$) inside the confinement approaches a critical value $\phi_c$. The universal value of $\phi_c^{\infty}\approx 0.44$ for a sufficiently long polymer ($N\gg 1$) allows us to discuss genome dynamics using $\phi$ as a single parameter. Our study shows that the onset of glassy dynamics is the reason for the segregated chromosome organization in human ($N\approx 3\times 10^9$, $\phi\gtrsim\phi_c^{\infty}$), whereas chromosomes of budding yeast ($N\approx 10^8$, $\phi<\phi_c^{\infty}$) are equilibrated with no clear signature of such organization.