Quantum Tunneling Enables High-Flux Transport in Ion Channels

Abstract

Classical molecular dynamics and electro-diffusion theories have achieved profound success in elucidating ion selectivity and gating mechanisms. However, reconciling strict selectivity with high flux permeation in Angstrom-scaled biological ion channels poses a universal challenge in nanoscale physics, as classical models consistently underestimate single-channel conductance. Using a non perturbative quantum transport framework, we calculate the ion permeation dynamics through the selectivity filter within a transfer matrix formalism. We demonstrate that quantum tunneling allows ions to bypass classical Arrhenius suppression, quantitatively recovering the experimental conductance of Na+ and K+ channels. Crucially, our findings reveal that the exploitation of quantum mechanics is a fundamental prerequisite for achieving macroscopic physiological efficiency. By reframing ion channels as mesoscopic quantum conductors, this work establishes a transformative paradigm in quantum biology and predicts distinct transport resonances in the terahertz regime.

Figures (5)

• Figure 1: Schematic illustration of the quantum transport model for biological ion channels. The system models an ion traversing the narrow selectivity filter of a transmembrane channel. The yellow curve depicts the effective one-dimensional potential landscape $V(x)$. The red curve represents the probability density amplitude of the incident ion wave packet.
• Figure 2: Spatiotemporal visualization of sub-barrier tunneling. Time-evolution of the potassium ion wave function $|\psi(x,t)|^2$ (colored solid curves) interacting with the selectivity filter potential (grey dashed line). Panels (a)-(d) correspond to incident kinetic energies of $3.6, 4.7, 5.6,$ and $7.0 k_{\rm B} T$. Arrows indicate the propagation direction of the wave packet components.
• Figure 3: The transmission probability $P_T(v)$ as a function of incident ion velocity for transport of (a) K$^+$ and (b) Na$^{+}$ ions. The transition from opaque ($T\approx0$) to transparent ($T\approx 1$) follows a smooth sigmoid profile, contrasting with the sharp step-function predicted by classical mechanics.
• Figure 4: Thermodynamic validation of the quantum model. (a, b) Bidirectional ion fluxes for Na$^+$ and K$^+$ vs. voltage. The intersection points ($I_{\rm net}=0$) indicates resting potentials of $+50$ mV and $-64$ mV, respectively. (c, d) Dependence of the resting potential on temperature and concentration gradient. The quantum model predictions (symbols) strictly align with the classical Nernst equation (solid lines) at respective physiological concentration range, confirming adherence to thermodynamic equilibrium.
• Figure 5: Resolution of the conductance deficit. (a, b) $I$-$V$ profiles for Na$^+$ and K$^+$ channels. Solid lines: Quantum model; Dashed lines: Classical model. (c, d) Conductance comparison. The quantum predictions (solid bars) quantitatively match experimental benchmarks, whereas classical MD simulations underestimate the flux by an order of magnitude.