The Gated Tube

Diffusion into a stochastically gated tube depends on whether the tube is open when the molecule arrives — not just on how often it opens.

Ion channels, nuclear pores, and enzyme active sites open and close stochastically. A molecule diffusing in the bulk must not only reach the entrance but arrive while the gate is open. The classical problem assumes a narrow pore: the diffusive flux depends on the pore’s open probability and the bulk diffusion coefficient. But real pores aren’t always narrow, and the diffusivity inside may differ from the bulk.

Berezhkovskii and Szabo (arXiv:2603.09841) extend the gated-flux framework to tubes that are not necessarily narrow, with distinct diffusion coefficients inside and outside. The result separates into factors: the ungated flux (what you’d get without gating), the open probability (how often the gate is open), and a correction factor that couples the gating dynamics to the diffusive transport.

The correction factor is the interesting part. When gating is fast relative to diffusion, it approaches one — the molecule sees the time-averaged open probability. When gating is slow, the correction deviates from one because the molecule’s arrival is correlated with the gate state. A molecule that finds the gate closed must wait and may diffuse away; a molecule that finds it open enters immediately. Slow gating creates an effective selection: only molecules that happen to arrive during an open period contribute to the flux.

The tube width matters because a wide tube accepts molecules from a larger solid angle, increasing the attempt rate. The diffusivity ratio matters because a slow tube interior creates a bottleneck that interacts with the gating timescale. Neither factor appears in the narrow-pore limit.

Berezhkovskii and Szabo, “Diffusive flux into a stochastically gated tube,” arXiv:2603.09841 (2026).