An optimal-control framework for reaction diffusion systems with application to synthetic developmental biology
Abstract
Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of optimal control for a class of coupled reaction-diffusion systems. The couplings are justified by the shared regulatory mechanisms encountered in synthetic biology. Furthermore, we introduce inputs and polynomial input-gain functions to guarantee well-posedness of the control system while maintaining biological relevance. As a result, we formulate an optimal control problem and derive necessary optimality conditions. We demonstrate our framework on an instance of such equations modeling the Nodal-Lefty interactions in mammalian cells. Numerical simulations showcase the effectiveness in directing pattern towards diverse targeted ones.
Cite
@article{arxiv.2509.15889,
title = {An optimal-control framework for reaction diffusion systems with application to synthetic developmental biology},
author = {Mohamed Amine Ouchdiri and Hamza Faquir and Saad Benjelloun and Mohamed Adlene Maghenem and Irene Otero-Muras and Adnane Saoud},
journal= {arXiv preprint arXiv:2509.15889},
year = {2026}
}