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Nucleocytoplasmic transport is essential for cellular function, presenting a canonical example of rapid molecular sorting inside cells. It consists of a coordinated interplay between import/export of molecules in/out the cell nucleus. Here, we investigate the role of spatiotemporal dynamics of the nucleocytoplasmic transport and its regulation. We develop a biophysical model that captures the main features of the nucleocytoplasmic transport, in particular, its regulation through the Ran cycle. Our model yields steady-state profiles for the molecular components of the Ran cycle, their relaxation times, as well as the nuclear-to-cytoplasmic molecule ratio. We show that these quantities are affected by their spatial dynamics and heterogeneity within the nucleus. Specifically, we find that the spatial nonuniformity of Ran guanine exchange factor (RanGEF)—particularly its proximity to the nuclear envelope—increases the Ran content in the nucleus. We further show that RanGEF's accumulation near the nuclear envelope results from its intrinsic dynamics as a nuclear cargo, transported by the Ran cycle itself. Overall, our work highlights the critical role of molecular spatial dynamics in cellular processes and proposes new avenues for theoretical and experimental inquiries into the nucleocytoplasmic transport. Published by the American Physical Society2024 

Chromatin – the functional form of DNA in the cell – exists in the form of a polymer immersed in a nucleoplasmic fluid inside the cell nucleus. Both chromatin and nucleoplasm are subject to active forces resulting from local biological processes. This activity leads to non-equilibrium phenomena, affecting chromatin organization and dynamics, yet the underlying physics is far from understood. Here, we expand upon a previously developed two-fluid model of chromatin and nucleoplasm by considering three types of activity in the form of force dipoles – two with both forces of the dipole acting on the same fluid (either polymer or nucleoplasm) and a third, with two forces pushing chromatin and solvent in opposite directions. We find that this latter type results in the most significant flows, dominating over most length scales of interest. Due to the friction between the fluids and their viscosity, we observe emergent screening length scales in the active flows of this system. We predict that the presence of different activity types and their relative strengths can be inferred from observing the power spectra of hydrodynamic fluctuations in the chromatin and the nucleoplasm.