  The distributions of many proteins in rod-shaped bacteria are far from
homogenous. Often they accumulate at the cell poles or in the cell center. At
the same time, the copy number of proteins in a single cell is relatively small
making the patterns noisy. To explore limits to protein patterns due to
molecular noise, we studied a generic mechanism for spontaneous polar protein
assemblies in rod-shaped bacteria, which is based on cooperative binding of
proteins to the cytoplasmic membrane. For mono-polar assemblies, we find that
the switching time between the two poles increases exponentially with the cell
length and with the protein number.
