Universal Features of Non-equilibrium Ionic Currents through Perm-Selective Membranes: Gating by Charged...

The presence of a small number (∼1000) of charged nanoparticles or macromolecules on the surface of an oppositely charged perm-selective membrane is shown to sensitively gate the ionic current through the membrane at a particular voltage, thus producing a voltage signal much larger than thermal noise. We show that, at sufficiently high voltages, surface vortices appear on the membrane surface and sustain an ion-depleted boundary layer that controls the diffusion length and ion current. An asymmetric vortex bifurcation occurs beyond a critical voltage to reduce the diffusion length and the differential resistance by half. Surface nanoparticles and molecules only affect this transition voltage in the membrane I-V curve. It is shown to shift by 2 ln10 (RT/F) ∼ 0.12 V for every decade increase in bulk target concentration, independent of sensor dimension and target/probe pair. Such universal features of the surface charge-sensitive nonlinear and nonequilibrium conductance allow us to develop very robust (a 2-3 decade dynamic range for highly heterogeneous samples with built-in control) yet sensitive (subpicomolar) and selective biosensors for highly charged molecules like nucleic acids and endotoxins-and for proteins with charged nanoparticle reporters.