Theoretical insights into the full description of DNA target search by subdiffusing proteins

DNA binding proteins (DBPs) diffuse in the cytoplasm to recognise and bind with their respective target sites on the DNA to initiate several biologically important processes. The first passage time distributions (FPTDs) of DBPs are useful in quantifying the timescales of the most-probable search paths in addition to the mean value of the distribution which, strikingly, are decades of order apart in time. However, extremely crowded in vivo conditions or the viscoelasticity of the cellular medium among other factors causes biomolecules to exhibit anomalous diffusion which is usually overlooked in most theoretical studies. We have obtained approximate analytical expressions of a general FPTD and the two characteristic timescales that are valid for any single subdiffusing protein searching for its target in vivo. Our results can be applied to single-particle tracking experiments of target search.