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arXiv · 2509.15889

An optimal-control framework for reaction diffusion systems with application to synthetic developmental biology

Mohamed Amine Ouchdiri·Hamza Faquir·Saad Benjelloun·Mohamed Adlene Maghenem·Irene Otero-Muras·Adnane Saoud
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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.

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Mohamed Amine Ouchdiri, Hamza Faquir, Saad Benjelloun, Mohamed Adlene Maghenem, Irene Otero-Muras, Adnane Saoud. 2025-09-19. An optimal-control framework for reaction diffusion systems with application to synthetic developmental biology. https://arxiv.org/abs/2509.15889

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