Diffusion limitation in the block by symmetric tetraalkylammonium ions of anthrax toxin channels in planar phospholipid bilayer membranes

Current flow through the channel formed in planar phospholipid bilayer membranes by the PA₆₅ fragment of anthrax toxin is blocked, in a voltage-dependent manner, by tetraalkylammonium ions (at micromolar concentrations), which bind to a blocking site within the channel lumen. We have presented evidence that diffusion plays a significant role in the kinetics of blocking by tetrabutylammonium ion (Bu₄N⁺) from the cis (toxin-containing) side of the membrane (Blaustein, R. O., E. J. A. Lea, and A. Finkelstein. 1990. J. Gen. Physiol. 96:921-942); in this paper we examine the implications and consequences of diffusion control for binding kinetics. As expected for a diffusion-affected reaction, both the entry rate constant (k₁^cis) of Bu₄N⁺ from the cis solution to the blocking site and the exit rate constant (k_-1^cis) of Bu₄N⁺ from the blocking site to the ciss solution arc reduced if the viscosity of that medium is increased by the addition of dextran. In conformity with both thermodynamics and kinetic arguments, however, the voltage-dependent equilibrium binding constant, K_eq (=k_-1^cis/k₁^cis), is not altered by the dextran-induced viscosity increase of the cis solution. The entry rate constants (k₁^cis) for tetrapentylammonium (Pe₄N⁺), tetrahexylammonium (Hx₄N⁺), and tetraheptylammonium (Hp₄N⁺) are also diffusion controlled, and all of them, including that for Bu₄N⁺, attain a voltage-independent plateau value at large positive cis voltages consistent with diffusion limitation. Although the plateau value of k₁^cis for Hx₄N⁺ is only a factor of 3 less than that for Bu₄N⁺, the plateau value for Hp₄N⁺ is a factor of 35 less. This precipitous fall in value indicates, from diffusion-limitation theory, that the diameter of the channel entrance facing the cis solution is not much larger than the diameter of Hp₄N⁺, i.e., ∼12 Å.