Effects of jamming on non-equilibrium transport times in nano-channels

Many biological channels perform highly selective transport without direct input of metabolic energy and without transitions from a ‘closed’ to an ‘open’ state during transport. Mechanisms of selectivity of such channels serve as an inspiration for creation of artificial nano-molecular sorting devices and bio-sensors. To elucidate the transport mechanisms, it is important to understand the transport on the single molecule level in the experimentally relevant regime when multiple particles are crowded in the channel. In this paper we analyze the effects of inter-particle crowding on the non-equilibrium transport times through a finite-length channel by means of analytical theory and computer simulations.

💡 Research Summary

This paper investigates how crowding and jamming of multiple particles affect non‑equilibrium transport times through finite‑length nano‑channels, a problem relevant to both biological selective pores and artificial molecular sorting devices. The authors model the channel as a one‑dimensional lattice of L sites, each of which can be occupied by at most one particle (simple exclusion). Particles enter the channel at a constant rate α, hop between neighboring sites with rate k, and exit from the left and right ends with rates β_in and β_out, respectively. The exclusion rule introduces a nonlinear feedback between particle density and flux, leading to possible jamming when the influx approaches the channel’s transport capacity.

Using a master‑equation framework, the authors derive mean‑field equations for the average occupancy ρ_i(t) of each site. In steady state (∂ρ_i/∂t = 0) the flux conservation relation J_i = J_{i‑1} – k ρ_i (1 – ρ_{i+1}) yields an analytical expression for the global current J and the spatial density profile. A critical influx α_c emerges from the balance of hopping and exit rates; for α < α_c the mean first‑passage time (MFPT) grows roughly linearly with channel length, whereas as α → α_c the MFPT diverges as (α_c – α)^{‑1}. When α exceeds α_c, the system enters a saturated regime where the flux plateaus and the MFPT increases exponentially, effectively halting transport.

To validate the theory, kinetic Monte‑Carlo simulations based on the Gillespie algorithm are performed across a wide range of parameters (L, k, β_out, α). The simulated fluxes, occupancy profiles, and MFPTs match the mean‑field predictions quantitatively, confirming that the analytical treatment captures the essential physics of jamming. The authors also explore extensions: (i) spatially heterogeneous hopping rates, which create localized bottlenecks that trigger jamming earlier; and (ii) multi‑species particles of different sizes, where larger particles jam more readily and thereby generate size‑selective filtering, reminiscent of biological selectivity mechanisms.

The study concludes that transport performance is governed by the ratio of particle influx to the intrinsic channel capacity. By tuning α, k, and β_out one can raise the jamming threshold, offering practical design guidelines for high‑throughput, high‑selectivity nano‑sorting platforms. Moreover, the combined master‑equation/mean‑field approach provides a versatile framework for tackling non‑equilibrium transport in crowded nanoscale conduits. Future work is suggested to incorporate long‑range inter‑particle forces, external driving fields (electric or chemical gradients), and three‑dimensional channel geometries to bring the model closer to real biological and synthetic systems.