A Computational Framework for Optimal and Model Predictive Control of Stochastic Gene Regulatory Networks

Engineering biology demands precise control over biomolecular circuits, a central objective in the field of Cybergenetics. A major challenge in designing controllers for cellular functions is developing systems capable of effectively managing molecular noise. To address this, efforts have focused on model-based controllers for stochastic biomolecular systems, with a key bottleneck being the accurate and efficient solution of the Chemical Master Equation. In this work we develop a framework for optimal and Model Predictive Control of stochastic gene regulatory networks that offers three key advantages: high computational efficiency, precise control over the probability density function to fine-tune cell populations for complex behaviors (including bimodal distributions and other emergent properties), and robust handling of intrinsic molecular noise. Our approach relies on an efficient approximation of the Chemical Master Equation using Partial Integro-Differential Equations, enabling the implementation of an effective adjoint-based optimization method. We demonstrate the effectiveness of our methods with two key applications in Synthetic Biology: inducing and shaping bimodality in cell populations and tracking dynamic target distributions using inducible gene regulatory circuits.