The presence of a small number (similar to 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 iondepleted 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) similar to 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.