Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics

Tobias Gulden,Alex Kamenev

doi:10.3390/e23010125

Tobias Gulden, Alex Kamenev

Open Access

https://doi.org/10.3390/e23010125

Copy DOI

Abstract

We study dynamics and thermodynamics of ion transport in narrow, water-filled channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and the surrounding medium, confining the electric filed to stay mostly within the water-filled channel. Statistical mechanics of such Coulomb systems is dominated by entropic effects which may be accurately accounted for by mapping onto an effective quantum mechanics. In presence of multivalent ions the corresponding quantum mechanics appears to be non-Hermitian. In this review we discuss a framework for semiclassical calculations for the effective non-Hermitian Hamiltonians. Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. We circumvent this issue by applying tools from algebraic topology, such as the Picard-Fuchs equation. We discuss how its solutions relate to the thermodynamics and correlation functions of multivalent solutions within narrow, water-filled channels.

Highlights

Transport of ions through narrow channels plays a big role in many biological and technological systems
We discuss how its solutions relate to the thermodynamics and correlation functions of multivalent solutions within narrow, water-filled channels
In particular we focus on semiclassical methods applicable for relatively large concentrations of the dissociated salts

Summary

Introduction

Transport of ions through narrow channels plays a big role in many biological and technological systems. Many pathogens attack cells by forming nanopores in the cell membrane by using pore-forming toxins (PFTs) [1,2] This punches holes in the cell membrane through which ions diffuse to the outside, effectively killing the cell. This is similar to artificial nanopores in, e.g., silicon [3,4]. Other similar examples include free-standing silicon nanowires [6,7] and waterfilled nanotubes [8,9]. These systems play various different roles in biology and technology

Objectives

Results

Conclusion