Dehydration as a Universal Mechanism for Ion Selectivity in Graphene and Other Atomically Thin Pores

Abstract

Ion channels play a key role in regulating cell behavior and in electrical signaling. In these settings, polar and charged functional groups – as well as protein response – compensate for dehydration in an ion-dependent way, giving rise to the ion selective transport critical to the operation of cells. Dehydration, though, yields ion-dependent free-energy barriers and thus is predicted to give rise to selectivity by itself. However, these barriers are typically so large that they will suppress the ion currents to undetectable levels. Here, we establish that graphene displays a measurable dehydration-only mechanism for selectivity of K+ over Cl−. This fundamental mechanism – one that depends only on the geometry and hydration – is the starting point for selectivity for all channels and pores. Moreover, while we study selectivity of K+ over Cl−, we find that dehydration-based selectivity functions for all ions, i.e., cation over cation selectivity (e.g., K+ over Na+). Its likely detection in graphene pores resolves conflicting experimental results, as well as presents a new paradigm for characterizing the operation of ion channels and engineering molecular/ionic selectivity in filtration and other applications.

Maxwell-Hall access resistance in graphene nanopores

“…In linear response, the pore resistance should be independent of the applied field. While we have a 1 V potential, the main findings hold for smaller voltages, as continuum simulations demonstrate, and there is roughly linear behavior of the graphene I-V curve at this voltage [29].…”

“…In linear response, the pore resistance should be independent of the applied field. While we have a 1 V potential, the main findings hold for smaller voltages, as continuum simulations demonstrate, and there is roughly linear behavior of the graphene I-V curve at this voltage [29].Since all three corrections depend on 1/L, we can combine them into a single term, yieldingwhere R ∞ is the combined access and pore resistance when all the linear dimensions of the cell are balanced and large compare to the pore radius. The behavior of R ∞ is expected to be R ∞ = 2R MH + R pore from Hall's theroy, which we will show later to hold for graphene pores down to the dehydration limit.…”

“…Moreover, their single atom thickness makes these systems ideal for interrogating ion dehydration [29,30], which both sheds light on recent experiments on ion selectivity in porous graphene [25,26,28] and will help analyze the behavior of biological pores [29,30]. Dehydration has been predicted to give rise to ion selectivity and quantized conductance in long, narrow pores [31][32][33][34][35] but the energy barriers are typically so large that the currents are minuscule, which is rectified by the use of membranes with single-atom thickness [29,30].Despite the intense and broad interest in ion transport, one of its most fundamental aspects, the convergence of the bulk to the pore, is essentially not computable with all-atom molecular dynamics (MD) [36], yet is very important for understanding in vivo operation and characteristics of ion channels [37]. Experiments on mono-or bi-layer graphene, show a dominant 1/a access resistance for a pore of radius a [19,38,39] as expected for an atomically thin pore.…”

“…Novel fabrication strategies and designs are under development to create large-scale, controllable porous membranes [25,26,28] and graphene laminate devices [23,24]. Moreover, their single atom thickness makes these systems ideal for interrogating ion dehydration [29,30], which both sheds light on recent experiments on ion selectivity in porous graphene [25,26,28] and will help analyze the behavior of biological pores [29,30]. Dehydration has been predicted to give rise to ion selectivity and quantized conductance in long, narrow pores [31][32][33][34][35] but the energy barriers are typically so large that the currents are minuscule, which is rectified by the use of membranes with single-atom thickness [29,30].…”

“…Experimentally, there are many sources of ambiguity: Uncertainties in measured values and in the pore depth (for example, multi-layer versus single layer graphene) and pore size (and aspect ratio / non-circularity), plus unknown charged functional groups or dipoles (that would enhance 1/a behavior by creating excess density at the membrane surface that "feeds" the current through the pore via its circumference), all affect either the balance of 1/a and 1/a 2 behavior, or how well one can extract that behavior. This list can also include nonlinearities (for example, MD simulations show the onset of polarizationinduced chaperoning of ions [29], which can tilt the balance in favor of access resistance as the dominant resistance). Different membranes and conditions can thus display diverse behavior, but "ideal" graphene membranes with pores larger than the dehydration limit have both access and pore contributions.…”