Pathway-dependent nonequilibrium conformations of a polymer globule as a model for chromatin organization

The spatial organization of chromatin in nucleus resembles a fractal globule, of which structure differs from an equilibrium polymer globule. Even though there have been efforts to develop a polymer model to describe nonequilibrium structure of tightly-packed chromatin, the dependence of a transition pathway toward a globule has been often ignored. Because biological systems are often in nonequilibrium states, the transition pathway the chromatin would take before it reaches the densely-packaged globule would be important. In this study, by using a simple polymer model and Langevin dynamics simulations, we investigate the conformational transition of a single polymer from swollen coil to compact globule in order to elucidate the effect of transition pathway on the final globular structure. We show that a fast collapse induces a nonequilibrium fractal-like structure, whose relaxation toward an equilibrium globule is extremely slow. Moreover, in strong confinement, polymer conformation never relaxes into equilibrium state, thus the structure of the globule becoming dependent on the transition pathway.