Single-Particle Tracking of DNA-Binding Biomolecules in Cells: Power-Law Distributions of Dwell Times

Abstract

Single-particle tracking (SPT) experiments have shown a truncated power-law distribution of dwell times for several DNA-binding species in the nucleus of living cells. Why this distribution? A standard explanation is Arrhenius escape from traps with exponentially distributed binding energies. But here the binding energies are roughly Gaussian, yielding roughly lognormal escape times. We therefore examine other mechanisms. The operational definition of SPT immobility is based on the dwell time within the volume of the effective SPT point spread function. The distribution of dwell times can be power-law at short times, but the exponent is constant and much less than observed. The dwell time problem has been treated in terms of revisits by a tracer to a trap, here recast as the number of revisits before the tracer leaves the volume of the effective SPT point spread function. The effect of revisits is limited because the sum of multiple escape times from a moderate trap is tame compared with single escapes from a deep trap, by the central limit theorem. Truncated power-law trapping yields transient anomalous subdiffusion, and obstructed diffusion includes two well-studied cases of this. In percolation the tracer concentration is low and the concentration of immobile obstacles is high. Anomalous subdiffusion is the result of static geometric trapping by dead ends, but how can these structures be made on the SPT length scale from DNA with a 50-nm persistence length? The other case is crowding, in which all species are mobile, the concentration is high, and the geometric traps are dynamic. We examine the effects of polydisperse crowders and of small concentrations of immobile species in a crowded system, to see whether crowding can bridge the gap between the SPT and DNA length scales.