A kinetic model for fluorescence microscopy experiments in disordered media that contains binding sites and obstacles

A model is proposed that describes the diffusion of molecules in a disordered medium with binding sites (traps) and obstacles (barriers). The equations of the model are obtained using the subordination method. As the parent process, random walks on a disordered lattice are taken, described by the random barriers model. As the leading process, the renewal process that corresponds to the multiple-trapping model is taken. Theoretical expressions are derived for the curves obtained in experiments using fluorescence microscopy (FRAP, FCS and SPT). Generalizations of the model are proposed, allowing to take into account correlations in the mutual arrangement of traps and barriers. The model can be used to find parameters characterizing the diffusion and binding properties of biomolecules in living cells.