Use of the Poisson−Boltzmann Equation To Estimate The Electrostatic Free Energy Barrier for Dielectric Models of Biological Ion Channels

We have obtained the electrostatic free energy profile of a univalent positive ion as it is moved from a bulk electrolyte solution into a biological ion channel of various model forms. The form of the results was unaffected by the method of calculation. We used a fully consistent nonlinearized Poisson−Boltzmann scheme, a fully consistent linearized Poisson−Boltzmann scheme, and a hybrid scheme. The channel models we used were designed to (crudely) mimic the shape and imbedded charge and dipolar distributions for biological ion-selective channels (such as the voltage-gated K + “shaker” channel). The results obtained were accounted for on simple physical grounds.