The Cell Cycle Switch Computes Approximate Majority
Biological systems have been traditionally, and quite successfully, studied as 'dynamical systems', that is, as continuous systems defined by differential equation and investigated by sophisticated analysis of their continuous state space. More recently, in order to cope with the combinatorial complexity of some of these systems, they have been modeled as 'reactive systems', that is, as discrete systems defined by their patterns of interactions and investigated by techniques that come from software and hardware analysis.
There are growing formal connections being developed between those approaches, and tools and techniques that span both. The two approaches can be usefully combined to bring new insights to specific systems. In one direction we can ask 'what algorithm does a dynamical system implement' and in the opposite direction we can ask 'what is the dynamics of a reactive system as a whole'. Answers to these questions can establish links between the structure of a system, which is dictated by the algorithm it implements, and the function of the system, which is represented by its dynamic behavior. Since there is depth on both sides, in the intricacies of the algorithms, and in the complexity of the dynamics, a better understanding can emerge of whole systems.
I will focus in particular on a connection between a clever and well-studied distributed computing algorithm, and a simple chemical system (4 reactions). It leads to a connection between that algorithm and a well-known biological switch that is universally found as part of cell cycle oscillators. These connections are examples of 'network transformations' that preserve both structure and functionality across systems of different complexity.
Joint work with Attila Csikász-Nagy.