  The spatial organization of complex biochemical reactions is essential for
the regulation of cellular processes. Membrane-less structures called foci
containing high concentrations of specific proteins have been reported in a
variety of contexts, but the mechanism of their formation is not fully
understood. Several competing mechanisms exist that are difficult to
distinguish empirically, including liquid-liquid phase separation, and the
trapping of molecules by multiple binding sites. Here we propose a theoretical
framework and outline observables to differentiate between these scenarios from
single molecule tracking experiments. In the binding site model, we derive
relations between the distribution of proteins, their diffusion properties, and
their radial displacement. We predict that protein search times can be reduced
for targets inside a liquid droplet, but not in an aggregate of slowly moving
binding sites. These results are applicable to future experiments and suggest
different biological roles for liquid droplet and binding site foci.
