  It is well known that at the gel-liquid phase transition temperature a lipid
bilayer membrane exhibits an increased ion permeability. We analyze the
quantized currents in which the increased permeability presents itself. The
open time histogram shows a "-3/2" power law which implies an open-closed
transition rate that decreases like $k(t) \propto t^{-1}$ as time evolves. We
propose a "pore freezing" model to explain the observations. We discuss how
this model also leads to the $1/f^{\alpha}$ noise that is commonly observed in
currents across biological and artificial membranes.
