Demonstrating Single and Multiple Currents Through theE. coli-SecYEG-Pore: Testing for the Number of Modes of Noisy Observations

Abstract

We analyze a new dataset from an electrophysiological recording of transmembrane currents through a bacterial membrane channel to demonstrate the existence of single and multiple channel currents. Protein channels mediate transport through biological membranes; knowledge of the channel properties gained from electrophysiological recordings is important for a targeted drug design. We investigate the bacterial membrane protein SecYEG which is of essential importance for the secretory pathway for sorting of newly synthesized proteins to their place of function in the cell. Our results strongly indicate that in the SecYEG pore the different modes of the density of channel currents are approximately equidistant and correspond to different numbers of open channels in the membrane. A current of ≈12 pA under the present experimental conditions turns out to be characteristic of the presence of a single open SecYEG pore, a fact that had not been electrophysiologically characterized so far. Electrophysiological recordings of single protein channels show a substantial amount of background noise. The data at our disposal can be modeled as the independent sum of an error variable and the realization of the ionic current. Thus, we are led to deconvoluting the density of the observations in order to recover the density f of the ionic currents, and then investigating the number of modes of f . To this end we propose an extension of Silverman’s (1981) test for the number of modes to deconvolution kernel density estimation, and develop the relevant theory. The finite sample performance of the test is investigated in a simulation study. Technical details for the proofs in this article are available as supplementary material online.