# PID Control of Biochemical Reaction Networks

## TL;DR

This paper introduces a novel derivative component in biochemical reaction networks, enabling PID control in synthetic biological systems, demonstrated by regulating gene expression in a microRNA model.

## Contribution

First implementation of a derivative component in CRNs, facilitating PID control for biochemical systems.

## Key findings

- Successfully implemented a derivative component in CRNs.
- Demonstrated PID control in gene expression regulation.
- Showed potential for advanced control in synthetic biology.

## Abstract

Principles of feedback control have been shown to naturally arise in biological systems and successfully applied to build synthetic circuits. In this work we consider Biochemical Reaction Networks (CRNs) as a paradigm for modelling biochemical systems and provide the first implementation of a derivative component in CRNs. That is, given an input signal represented by the concentration level of some species, we build a CRN that produces as output the concentration of two species whose difference is the derivative of the input signal. By relying on this component, we present a CRN implementation of a feedback control loop with Proportional-Integral-Derivative (PID) controller and apply the resulting control architecture to regulate the protein expression in a microRNA regulated gene expression model.