Reply to Missner et al.: Timescale for passive diffusion across bilayer lipid membranes

A fundamental flaw in the analysis of Missner et al. (1) is evident from inspection of the equation presented in their letter, in which the overwhelming mass transport resistance for passive diffusion is from an unstirred layer on the trans side of the membrane. This is not a realistic representation of the experimental situation in a microelectrochemical system, where 2-dimensional diffusion greatly enhances mass transport, leads to the establishment of steady-state conditions on a rapid timescale (2–4), and allows the measurement of fast processes (2, 5, 6).

In Fig. 1 we show snapshots of the time-dependent pH response, obtained by simulation for the parameters pertinent to acetic acid (see ref. 2), after switching on an anodic electrode current of 5 nA (see figure 7 in ref. 2 for the axisymmetric cylindrical geometry of our experiments). There is no discernible difference in the profiles for 1.5 s and steady state. Thus, when Missner et al. (1) calculate that 1,200 s would be needed to achieve a steady state, they are wrong by ≈3 orders of magnitude. The experiments reported were at steady state, and it is entirely appropriate to solve the steady-state mass transport problem described (2). Fig. 1 also highlights the step in pH at the membrane boundary, indicating a clear kinetic barrier that can be measured by our technique; Missner et al. are incorrect when they claim that the membrane resistance reported would be difficult to detect because they have grossly underestimated mass transport rates.

Fig. 1.

Finite element simulations of the pH profile (in the axisymmetric cylindrical coordinate system similar to that defined in figure 7 of ref. 2) for an ultramicroelectrode-confocal microscopy measurement of membrane permeation (2). The simulations are for acetic acid permeation through a lipid bilayer at different times after the application of a 5-nA anodic current to the ultramicroelectrode. The electrode is at a distance of 20 μm from the lipid bilayer membrane. The data demonstrate that the system rapidly reaches a steady state. In all frames the contours represent lines of equal pH (5, 5.5, 6, and 6.5). The profiles correspond to times of 0.1 s (A), 0.5 s (B), 1.5 s (C), and steady state (D). Details of the simulation were as given in ref. 2. For A–C the time-dependent version of the diffusion equation was solved; i.e., equation 5 in ref. 2, with the right hand side replaced with ∂c_i/∂t.