arXiv subjects

Hamza Faquir

Publications and source records attributed to Hamza Faquir.

3 recordsLinked to original sources

arXiv2026

How Much Spatial Control Is Enough? Subdomain Optimal Control of Reaction-Diffusion Systems in Synthetic Developmental Biology

Reaction-diffusion systems can produce spatial patterns such as stripes and spots through diffusion-driven instability. Steering these patterns from one configuration to another can be formulated as an optimal control problem. When the control acts on the entire spatial domain, existence and optimality conditions are well understood. Yet in practice, the control can only act on a part of the domain. Taking the Nodal--Lefty reaction--diffusion system as a case study, we consider the setting where the control is restricted to a subdomain. We derive an explicit upper bound on the optimality loss, defined as the difference between the subdomain optimal cost and the full-domain optimal cost. From this bound, we obtain an explicit formula for the minimum size of the control region needed to reach a target pattern with prescribed accuracy. We also consider the case where the control is distributed over several disjoint regions instead of a single one, with the same total area, and prove that the distributed configuration gives a tighter bound under natural conditions on the spatial structure of the target. Numerical illustrations confirm the theoretical results and show that a control region covering roughly forty percent of the domain is sufficient to drive the system from stripes to spots with high accuracy.

math.OC↗

arXiv2025

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

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.

math.OC↗

arXiv2024

A computational framework for optimal and Model Predictive Control of stochastic gene regulatory networks

Engineering biology requires precise control of biomolecular circuits, and Cybergenetics is the field dedicated to achieving this goal. A significant challenge in developing controllers for cellular functions is designing systems that can effectively manage molecular noise. To address this, there has been increasing effort to develop model-based controllers for stochastic biomolecular systems, where a major difficulty lies in accurately solving the chemical master equation. In this work we develop a framework for optimal and Model Predictive Control of stochastic gene regulatory networks with three key advantageous features: high computational efficiency, the capacity to control the overall probability density function enabling the fine-tuning of the cell population to obtain complex shapes and behaviors (including bimodality and other emergent properties), and the capacity to handle high levels of intrinsic molecular noise. Our method exploits an efficient approximation of the Chemical Master Equation using Partial Integro-Differential Equations, which additionally enables the development of an effective adjoint-based optimization. We illustrate the performance of the methods presented through two relevant studies in Synthetic Biology: shaping bimodal cell populations and tracking moving target distributions via inducible gene regulatory circuits.

q-bio.QM↗