Diffusion, exclusion, and specific binding in a large channel: a study of OmpF selectivity inversion

Abstract

We find that moderate cationic selectivity of the general bacterial porin OmpF in sodium and potassium chloride solutions is inversed to anionic selectivity in concentrated solutions of barium, calcium, nickel, and magnesium chlorides. To understand the origin of this phenomenon, we consider several factors, which include the binding of divalent cations, electrostatic and steric exclusion of differently charged and differently sized ions, size-dependent hydrodynamic hindrance, electrokinetic effects, and significant "anionic" diffusion potential for bulk solutions of chlorides of divalent cations. Though all these factors contribute to the measured selectivity of this large channel, the observed selectivity inversion is mostly due to the following two. First, binding divalent cations compensates, or even slightly overcompensates, for the negative charge of the OmpF protein, which is known to be the main cause of cationic selectivity in sodium and potassium chloride solutions. Second, the higher anionic (versus cationic) transport rate expected for bulk solutions of chloride salts of divalent cations is the leading cause of the measured anionic selectivity of the channel. Interestingly, at high concentrations the binding of cations does not show any pronounced specificity within the divalent series because the reversal potentials measured in the series correlate well with the corresponding bulk diffusion potentials. Thus our study shows that, in contrast to the highly selective channels of neurophysiology that employ mostly the exclusion mechanism, quite different factors account for the selectivity of large channels. The elucidation of these factors is essential for understanding large channel selectivity and its regulation in vivo.

Figure 1

(A) Schematic illustration of the electric elements contributing to the measured potential V_exp (after Finkelstein and Mauro (25)). The goal is to measure zero-current potential between the cis and trans solutions of the cell. At equal concentrations and same salt types in the bridges, the electrochemical potentials E_Ag/Bridge and E_Bridge/Ag compensate each other because they are equal in modulus and opposite in sign. These are equilibrium silver/silver chloride electrode potentials. Potentials between the agarose bridges are nonequilibrium and stem from the differences in diffusion coefficients of the involved ionic species and can be estimated from Henderson's equation (50). Depending on experimental conditions, they can be either of the same or opposite sign (see Appendix). The internal resistances of the elements representing contacts between silver/silver chloride electrodes and solutions in bridges are not shown, as they are much smaller than all other resistances in the system. Current traces of spontaneous channel insertion at 20-fold gradients of CaCl₂ (B) and KCl (C). The potentials that should be applied to zero currents in the two cases are of opposite signs.

Figure 2

OmpF channel reversal potential measured in monovalent (KCl, NaCl) and divalent salts (CaCl₂, MgCl₂) at pH 6. Salt concentration is 0.1 M on the trans side, and concentration on the cis side varies up to a 20-fold concentration ratio. Error bars are smaller than the symbol size. Each point was measured for at least three different channels in three different experiments.

Figure 3

Reversal potential as a function of bulk diffusion potential expected for different salts at their concentration gradients varied up to a 20-fold ratio (Fig. 2). Bulk diffusion potential is calculated for each pair of concentrations of every salt according to Planck's equation (see main text).

Figure 4

Reversal potential as a function of the cis/trans concentration ratio for KCl (circles) and NaCl (solid squares) at pH 6. Solution concentration on the trans side was fixed at 0.1 M, whereas the concentration on the cis side was increased from 0.1 M to 3 M. Membranes were formed from DPhPC. The difference between the values of reversal potential in NaCl and KCl solutions (open squares) scales with the natural logarithm of the concentration ratio (r = 0.99).

Figure 5

Reversal potential measured in salts of monovalent and divalent cations at the inverted (0.1 M cis | 1 M trans) gradient at different pH. The corresponding bulk diffusion potentials for this gradient are also shown. Over a broad range of pH, the reversal potential in 2-1 salts is only weakly sensitive to channel residue ionization. This contrasts with the known titration behavior of OmpF in monovalent salts where increasing proton concentration beyond pH 4 results in the inversion of both reversal potential and the channel effective charge (11,16,29).

Figure 6

(Right) Reversal potential measured in salts of divalent cations at high concentrations (1.0 M cis | 0.1 M trans) displays correlation between the reversal potential and the corresponding bulk diffusion potentials for the 1.0|0.1 gradient. Although binding properties of these four divalent cations are very different in other systems (neutral lipid bilayers, for instance), here the reversal potential seems to be sensitive only to cation diffusivity. (Left) At small concentrations of divalent cations (15 mM cis | 10 mM trans), the channel regains its cationic selectivity. Correlation between reversal potential and bulk diffusion potential is lost. Both sets of measurements are performed at pH 6.

Figure 7

(A) Reversal potential measured at a 10-fold cis/trans concentration ratio but different absolute concentrations of KCl (circles) and CaCl₂ (triangles) at pH 6. In KCl the channel shows cationic selectivity that is enhanced at low concentrations. In CaCl₂ the channel does not increase its anionic selectivity at low concentrations but becomes less selective to anions. At low enough CaCl₂ concentrations (see insets that show measurements at 1.5-fold cis/trans concentration ratio), OmpF seems to recover its “normal” negative fixed charge since the reversal potential is lower in magnitude than the free solution diffusion potential and, for the smallest concentrations, the selectivity gets cationic again. (B) Selectivity of the channel, calculated from data in (A).