  Cells store information in DNA and in stable programs of gene expression,
which thereby implement forms of long-term cellular memory. Cells must also
possess short-term forms of information storage, implemented
post-translationally, to transduce and interpret external signals. CaMKII, for
instance, is thought to implement a one-bit (bistable) short-term memory
required for learning at post-synaptic densities. Here we show by mathematical
analysis that multisite protein phosphorylation, which is ubiquitous in all
eukaryotic signalling pathways, exhibits multistability for which the maximal
number of steady states increases with the number of sites. If there are n
sites, the maximal information storage capacity is at least log_2 (n+2)/2 bits
when n is even and log_2 (n+1)/2 bits when n is odd. Furthermore, when
substrate is in excess, enzyme saturation together with an alternating low/high
pattern in the site-specific relative catalytic efficiencies, enriches for
multistability. That is, within physiologically plausible ranges for
parameters, multistability becomes more likely than monostability. We discuss
the experimental challenges in pursuing these predictions and in determining
the biological role of short-term information storage.
