Ion channels open and close stochastically. The flux of ions through a channel depends on the channel’s geometry (how wide, how long), the diffusion coefficient of the ions (how fast they move), and the gating dynamics (how often and how long the channel is open). Previous estimates in the physics literature have treated these factors separately or combined them approximately.

The paper derives an explicit flux estimate that accounts for all three — gating, geometry, and heterogeneous diffusion — simultaneously. The estimate is exact in certain parameter ranges and accurate across the full parameter space, as validated by stochastic simulations.

The results diverge from previously published estimates. The discrepancy is not a refinement — it’s a correction. Earlier results made approximations in combining the geometric and gating contributions that fail when the gating rate and the diffusion timescale are comparable. The channel opens and closes on a timescale that interferes with the time it takes an ion to traverse the channel; the interaction between these two timescales produces a flux that neither factor alone predicts.

The biological implication: channel conductance is not simply the product of an open-channel conductance and an open probability. The gating dynamics interact with the transport dynamics, and the interaction can increase or decrease the effective flux depending on the geometry. A shorter channel with fast gating behaves differently from a longer channel with the same average open probability because the transit time and gating time compete differently. The channel’s function depends on the ratio of its timescales, not just their values.