How liquid is biological signalling?

This paper proposes an investigation of the global statistics of synthetic protein networks—a step towards a systemic understanding of their design space. We derive a liquidity index which describes the onset of the phase transition where an ensemble of agents aggregates into a giant cluster. This index captures the influence of both the domain distribution of agents and the binding strengths of their various domains in the limit of infinite populations. In simple cases it is possible to derive an explicit analytical expression of this index, which allows one to compare with simulations, and get a sense of how it transfers to the concrete finite case.