Diffusion of DNA-Binding Species in the Nucleus: A Transient Anomalous Subdiffusion Model.

Single-particle tracking experiments have measured escape times of DNA-binding species diffusing in living cells: CRISPR-Cas9, TetR, and LacI. The observed distribution is a truncated power law. Working backward from the experimental results, the observed distribution appears inconsistent with a Gaussian distribution of binding energies.

Wanted: scalable tracers for diffusion measurements.

Scalable tracers are potentially a useful tool to examine diffusion mechanisms and to predict diffusion coefficients, particularly for hindered diffusion in complex, heterogeneous, or crowded systems. Scalable tracers are defined as a series of tracers varying in size but with the same shape, structure, surface chemistry, deformability, and diffusion mechanism. Both chemical homology and constant dynamics are required.

Wanted: a positive control for anomalous subdiffusion.

Anomalous subdiffusion in cells and model systems is an active area of research. The main questions are whether diffusion is anomalous or normal, and if it is anomalous, its mechanism. The subject is controversial, especially the hypothesis that crowding causes anomalous subdiffusion.

Two-dimensional continuum percolation threshold for diffusing particles of nonzero radius.

Lateral diffusion in the plasma membrane is obstructed by proteins bound to the cytoskeleton. The most important parameter describing obstructed diffusion is the percolation threshold. The thresholds are well known for point tracers, but for tracers of nonzero radius, the threshold depends on the excluded area, not just the obstacle concentration.

Modeling 2D and 3D diffusion.

Modeling obstructed diffusion is essential to the understanding of diffusion-mediated processes in the crowded cellular environment. Simple Monte Carlo techniques for modeling obstructed random walks are explained and related to Brownian dynamics and more complicated Monte Carlo methods. Random number generation is reviewed in the context of random walk simulations.

A biological interpretation of transient anomalous subdiffusion. II. Reaction kinetics.

Reaction kinetics in a cell or cell membrane is modeled in terms of the first passage time for a random walker at a random initial position to reach an immobile target site in the presence of a hierarchy of nonreactive binding sites. Monte Carlo calculations are carried out for the triangular, square, and cubic lattices. The mean capture time is expressed as the product of three factors: the analytical expression of Montroll for the capture time in a system with a single target and no binding sites; an exact expression for the mean escape time from the set of lattice points; and a correction factor for the number of targets present.

A biological interpretation of transient anomalous subdiffusion. I. Qualitative model.

Anomalous subdiffusion has been reported for two-dimensional diffusion in the plasma membrane and three-dimensional diffusion in the nucleus and cytoplasm. If a particle diffuses in a suitable infinite hierarchy of binding sites, diffusion is well known to be anomalous at all times. But if the hierarchy is finite, diffusion is anomalous at short times and normal at long times.

Unexpected mobility variation among individual secretory vesicles produces an apparent refractory neuropeptide pool.

Most stored neuropeptide cannot be released from nerve terminals suggesting the existence of a refractory pool of dense core vesicles (DCVs). Past fluorescence photobleaching recovery, single particle tracking and release experiments suggested that the refractory neuropeptide pool corresponds to a distinct immobile fraction of cytoplasmic DCVs. However, tracking of hundreds of individual green fluorescent protein-labeled neuropeptidergic vesicles by wide-field or evanescent-wave microscopy shows that a separate immobile fraction is not evident.