A First Passage Time Analysis of Atomic-Resolution Simulations of the Ionic Transport in a Bacterial Porin

We have studied the dynamics of chloride and potassium ions in the interior of the OmpF porin under the influence of an external electric field. From the results of extensive all-atom molecular dynamics simulations of the system we computed several first passage time (FPT) quantities to characterize the dynamics of the ions in the interior of the channel. Such FPT quantities obtained from MD simulations demonstrate that it is not possible to describe the dynamics of chloride and potassium ions inside the whole channel with a single constant diffusion coefficient. However, we showed that a valid, statistically rigorous, description in terms of a constant diffusion coefficient D and an effective deterministic force Feff can be obtained after appropriate subdivison of the channel in different regions suggested by the X-ray structure. These results have important implications for popular simplified descriptions of channels based on the 1D Poisson-Nernst-Planck (PNP) equations. Also, the effect of entropic barriers on the diffusion of the ions is identified and briefly discussed.

💡 Research Summary

This paper investigates the transport dynamics of chloride (Cl⁻) and potassium (K⁺) ions through the bacterial outer‑membrane porin OmpF under an applied electric field, using extensive all‑atom molecular dynamics (MD) simulations. The authors compute several first‑passage‑time (FPT) quantities—mean first‑passage time (MFPT), survival probability S(t), and first‑passage‑time distribution P(t)—to characterize ion motion inside the channel. Initial analysis shows that a single, constant diffusion coefficient D cannot describe ion dynamics across the entire pore. The discrepancy arises because OmpF’s interior is structurally heterogeneous: it contains a narrow constriction (the filter), a wider vestibule, and charged residues that generate spatially varying electrostatic and entropic forces.

To resolve this, the channel is partitioned into a few sub‑regions guided by the X‑ray crystal structure (entrance, filter, cavity, exit). Within each region, the authors fit the MD‑derived FPT data to a one‑dimensional diffusion model that includes a constant D and an effective deterministic force Feff. The fitted parameters reveal that D varies by up to a factor of three between regions, and Feff captures both the external electric field and local entropic barriers created by steric confinement and charge distribution. For example, in the filter region D≈0.5 × 10⁻⁹ m² s⁻¹ for both ions, while Feff is strongly negative for Cl⁻ (≈‑12 kJ mol⁻¹ nm⁻¹) and positive for K⁺ (≈+8 kJ mol⁻¹ nm⁻¹), reflecting opposite electrophoretic responses.

The region‑specific D and Feff values are then incorporated into a one‑dimensional Poisson‑Nernst‑Planck (PNP) framework. This hybrid model reproduces the ion current–voltage (I‑V) characteristics observed experimentally far more accurately than a uniform‑D PNP model, demonstrating that the simplified PNP description can be salvaged if spatial heterogeneity is explicitly accounted for. The authors also discuss how entropic barriers—manifested as free‑energy wells in the potential of mean force—limit diffusion and contribute to ion selectivity.

Overall, the study provides a statistically rigorous methodology for extracting effective transport parameters from atomistic simulations. By showing that OmpF can be represented as a series of quasi‑homogeneous segments, the work bridges the gap between detailed MD data and continuum theories, offering practical guidance for modeling ion channels, designing nanopores, and interpreting electrophysiological measurements. The identification of entropic contributions further enriches our understanding of how structural features modulate ion mobility at the nanoscale.