A Geometric Mechanism for Asymmetric Diffusion and Membrane Rectification

Biological membranes commonly conduct ions freely in one direction while clogging in the other. Existing theories emphasize electrostatic binding of blocking ions in pores as a mechanism for rectification. Here we show that rectification can have a purely geometric origin, based on the interaction of shapes of diffusing particles and pore geometry. The two possibilities can be experimentally distinguished. Blocker binding based on confinement in a potential well will have a strong Arrhenius temperature dependence, whereas ``geometric binding'' will have a much smaller dependence on temperature. We present both Hamiltonian and Brownian-based computer simulations which demonstrate this effect. A rectifying membrane can maintain different concentrations on either side, resulting in a long-lived metastable state. We derive a dynamic equation of state describing the decay of this metastable system.