The graphical methods described in this article are the results of classroom experience by one of the authors (EG) who regularly teaches the subject to a relatively large class of senior undergraduate, master's, and graduate students. First, we describe the nature of the physical phenomena we intend to address then we propose graphical methods that should be understandable by the general reader.

The corresponding author (EG) has used part of the material of this article in the course BME 138 (Biospectroscopy for Undergraduates) and for the graduate course BME 238 (Biospectroscopy for Graduates).

In compartments, biochemical reactions can be accelerated in one compartment and kept separated from other compartments. How molecules diffuse in biological systems is necessary for the introduction of the concept of compartments in cells and in tissues. We believe that the subject is important for modelers and to biologists in general. This article is intended as a guide for teachers in a course describing the motion of molecules in cells in the presence of obstacles small and large found in the cell. We also observe a gradual increase in the connectivity for longer distances or times, presumably because of molecular trajectories around the nucleolus. 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. 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 this situation the pair correlation function introduced in this article is independent of the direction and is uniform in all directions. If there are no barriers to diffusion, particles could diffuse equally in all directions. 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. We describe an approach based on the 2-dimensional pair correlation function (2D-pCF) analysis of the spatial connectivity in a cell. However, because of the transient nature and the lack of a visible barrier, the existence of phase separation is difficult to demonstrate experimentally. Discontinuities between spaces can be generated by a physical barrier but also by thermodynamic barriers achieved by phase separation of molecules. Transient barriers are fundamental to cell supramolecular organization and assembly.

Barriers to diffusion of disease