Building subtraction operators and controllers via molecular sequestration

Abstract

We show how subtraction can be performed via a simple chemical reaction network that includes molec- ular sequestration. The network computes the difference between the production rate parameters of the two mutu- ally sequestering species. We benefit from introducing a simple change of variables, that facilitates the derivation of an approximate solution for the differential equations modeling the chemical reaction network, under a time scale separation assumption that is valid when the sequestration rate parameter is sufficiently fast. Our main result is that we provide simple expressions confirming that temporal sub- traction occurs when the inputs are constant or time vary- ing. Through simulations, we discuss two sequestration- based architectures for feedback control in light of the subtraction operations they perform.