Aging in mortal superdiffusive Lévy walkers

A growing body of literature examines the effects of superdiffusive subballistic movement premeasurement (aging or time lag) on observations arising from single-particle tracking. A neglected aspect is the finite lifetime of these Lévy walkers, be they proteins, cells, or larger structures. We examine the effects of aging on the motility of mortal walkers, and discuss the means by which permanent stopping of walkers may be categorized as arising from "natural" death or experimental artifacts such as low photostability or radiation damage. This is done by comparison of the walkers' mean squared displacement (MSD) with the front velocity of propagation of a group of walkers, which is found to be invariant under time lags. For any running time distribution of a mortal random walker, the MSD is tempered by the stopping rate θ. This provides a physical interpretation for truncated heavy-tailed diffusion processes and serves as a tool by which to better classify the underlying running time distributions of random walkers. Tempering of aged MSDs raises the issue of misinterpreting superdiffusive motion which appears Brownian or subdiffusive over certain time scales.