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The distribution of voltage in sub-micron cellular domains remains poorlyunderstood. In neurons, the voltage results from the difference in ionicconcentrations which are continuously maintained by pumps and exchangers.However, it not clear how electro-neutrality could be maintained by an excessof fast moving positive ions that should be counter balanced by slow diffusingnegatively charged proteins. Using the theory of electro-diffusion, we studyhere the voltage distribution in a generic domain, which consists of twoconcentric disks (resp. ball) in two (resp. three) dimensions, where a negativecharge is fixed in the inner domain. When global but not localelectro-neutrality is maintained, we solve the Poisson-Nernst-Planck equationboth analytically and numerically in dimension 1 (flat) and 2 (cylindrical) andfound that the voltage changes considerably on a spatial scale which is muchlarger than the Debye screening length, which assumes electro-neutrality. Thepresent result suggests that long-range voltage drop changes are expected inneuronal microcompartments, probably relevant to explain the activation of faraway voltage-gated channels located on the surface.

Voltage distribution in a non-locally but globally electroneutral confined electrolyte medium: applications for nanophysiology