Fig. 2: Methodology for the characterization of nonlinearities using time-varying voltage drop across single- and multi-pore membranes.

a, Triangular forcing at 2 Hz, 200 mV, with 6 aerolysin wt nanopores used to extract the single open-pore IV curve. b, IV characteristics of a single aerolysin wt nanopore in the lipid membrane measured with sinusoidal potential (0.1 Hz). Fifty consecutive cycles are summed to retrieve the smooth hysteresis loop. c, Normalized IV characteristics of 26 pores in the same membrane showing the smooth hysteresis loop (0.1 Hz). Pores in the membrane close and open in a voltage-dependent manner, giving rise to the hysteresis loop. Arrows indicate the direction of the sweep. Inset: gating quantification. The solid blue line represents the closed-state probability, p, and the solid black line represents the sinusoidal voltage. The calculation of p is ill-defined around the origin, resulting in a discontinuous line in the probability plot, which did not affect our conclusions (‘Data analysis’ in Methods). The maximum slope indicated by the red lines and dots corresponds to k_X for both polarities, where k_X is the maximum closing rate. All experiments were conducted in 1 M KCl buffered with 10 mM phosphate to pH 6.2.