Mathematical models are increasingly used in both academia and the pharmaceutical industry to understand how phenotypes emerge from systems of molecular interactions. However, their current construction as monolithic sets of equations presents a fund
amental barrier to progress. Overcoming this requires modularity, enabling sub-systems to be specified independently and combined incrementally, and abstraction, enabling general properties to be specified independently of specific instances. These in turn require models to be represented as programs rather than as datatypes. Programmable modularity and abstraction enables libraries of modules to be created for generic biological processes, which can be instantiated and re-used repeatedly in different contexts with different components. We have developed a computational infrastructure to support this. We show here why these capabilities are needed, what is required to implement them and what can be accomplished with them that could not be done previously.
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.
