  A two-dimensional (2D) model is developed to describe the growth of spotty
patterns (domains) in the lipid membranes which result from the coagulation of
ion channels. It is assumed that the ion channels can coagulate when activated,
e.g. the neurotransmitter may act as the surface-active substance for some ion
channels in the lipid matrix or the activation may result in increase of
polarity of the ion channels that give rise to their coagulation process due to
the Brownian diffusive motion. The results show that the domain radius rD of
the ion channels scales with time as rD~time^0.4.The slowing and subsequent
saturation of the domain radius at longer time periods are in qualitative
agreement with experiments.
