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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.

Engineered genetic circuits with tailored functions that mimic how cells process information in changing environments (e.g. cell fate decision, chemotaxis, immune response) have great applications in biomedicine and synthetic biology. Although there is a lot of progress toward the design of gene circuits yielding desired steady states (e.g. logic-based networks), building synthetic circuits for dynamic signal processing (e.g. filters, frequency modulation, and controllers) is still challenging. Here, we provide a model-based approach to build gene networks that can operate as band-pass filters by taking advantage of molecular sequestration. By suitably approximating the dynamics of molecular sequestration, we analyze an Incoherent Feed-Forward Loop (IFFL) and a Negative Feedback (NF) circuit and illustrate how they can achieve band-pass filter behavior. Computational analysis shows that a circuit that incorporates both IFFL and NF motifs improves the filter performance. Our approach facilitates the design of sequestration-based filters, and may support the synthesis of molecular controllers with desired specifications.