Barriers to Diffusion in Cells: Visualization of Membraneless Particles in the Nucleus

Transient barriers are fundamental to cell supramolecular organization and assembly. Discontinuities between spaces can be generated by a physical barrier but also by thermodynamic barriers achieved by phase separation of molecules. However, because of the transient nature and the lack of a visible barrier, the existence of phase separation is difficult to demonstrate experimentally. We describe an approach based on the 2-dimensional pair correlation function (2D-pCF) analysis of the spatial connectivity in a cell. The educational aim of the article is to present both a model suitable for explaining diffusion barrier measurements to a broad range of courses and examples of biological situations. If there are no barriers to diffusion, particles could diffuse equally in all directions. In this situation the pair correlation function introduced in this article is independent of the direction and is uniform in all directions. However, in the presence of obstacles, the shape of the 2D-pCF is distorted to reflect how the obstacle position and orientation change the flow of molecules. In the example shown in this article, measurements of diffusion of enhanced green fluorescent protein moving in live cells show the lack of connectivity at the nucleolus surface for shorter distances. We also observe a gradual increase in the connectivity for longer distances or times, presumably because of molecular trajectories around the nucleolus.