Significance Biochemical reactions often occur in small volumes within a cell, restricting the number of molecules to the hundreds or even tens. At this scale, reactions are discrete and stochastic, making reliable signaling difficult. This paper shows that the transition between discrete, stochastic reactions and macroscopic reactions can be exploited to make a self-regulating switch. This constitutes a previously unidentified kind of reaction network that may be present in small structures, such as synapses.

Many kinds of cellular compartments comprise decision making mechanisms that control growth and shrinkage of the compartment in response to external signals. Key examples include synaptic plasticity mechanisms that regulate the size and strength of synapses in the nervous system. However, when synaptic compartments and postsynaptic densities are small such mechanisms operate in a regime where chemical reactions are discrete and stochastic due to low copy numbers of the species involved. In this regime, fluctuations are large relative to mean concentrations, and inherent discreteness leads to breakdown of mass action kinetics. Understanding how synapses and other small compartments achieve reliable switching in the low copy number limit thus remains a key open problem. We propose a novel self regulating signaling motif that exploits the breakdown of mass action kinetics to generate a reliable size-regulated switch. We demonstrate this in simple two and three-species chemical reaction systems and uncover a key role for inhibitory loops among species in generating switching behavior. This provides an elementary motif that could allow size dependent regulation in more complex reaction pathways and may explain discrepant experimental results on well-studied biochemical pathways.