Reversal potential of a wide ion channel. Nonuniform charge distribution effects

A theory for the reversal potential V, in a wide, charged ion channel (i.e. , with radius comparable to channel length and Debye's length) embedded in a planar membrane is developed. We analyze the influence of a nonuniform ch annel charge distribution along, the channel axis on V,. The analysis is pe rformed in the framework of the space charge model, which is generalized fo r axial nonuniform charge distributions. Two kinds of nonhomogeneity are co nsidered: (1) a symmetrical nonhomogeneous distribution when channel charge is uniformly smeared over the inner surface of channel wall, but it does n ot extend over the whole surface, and (2) an asymmetrical nonhomogeneous di stribution corresponding to some part of the total charge uniformly smeared over the channel wall and some other located on one of the channel entranc es. Forthe first distribution it is shown that even a small deviation from a uniform distribution leads to a significant change in the reversal potent ial. In particular, the experimentally observed nonmonotonic behavior of V, for the voltage-dependent anion channel from mitochondria (VDAC) as a func tion of concentration gradient [Zambrowicz, E. B.; Colombini, M.; Biophys. J. 1993, 65, 1093.] is explained by invoking the axial nonhomogeneity of ch annel charge. For the second kind of distribution (which resembles that in VDAC closed states) it is shown that the sign and value of the reversal pot ential depends on the location of the mobile part of the channel charge. Th eoretical results are compared with previously reported experimental data f or VDAC but they are valid for any charged multiionic channel where the Ner nst-Planck formalism can be applied.