Building Subtraction Operators and Controllers via Molecular Sequestration

We show how subtraction can be performed via a simple chemical reaction network that includes molecular sequestration. The network computes the difference between the production rate parameters of the two mutually 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 subtraction occurs when the inputs are constant or time varying. Through simulations, we discuss two sequestration-based architectures for feedback control in light of the subtraction operations they perform.