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.

MOTIVATION: One of the main causes hampering predictability during the model identification and automated design of gene circuits in synthetic biology is the effect of molecular noise. Stochasticity may significantly impact the dynamics and function of gene circuits, specially in bacteria and yeast due to low mRNA copy numbers. Standard stochastic simulation methods are too computationally costly in realistic scenarios to be applied to optimization-based design or parameter estimation. RESULTS: In this work, we present IDESS (Identification and automated Design of Stochastic gene circuitS), a software toolbox for optimization-based design and model identification of gene regulatory circuits in the stochastic regime. This software incorporates an efficient approximation of the Chemical Master Equation as well as a stochastic simulation algorithm-both with GPU and CPU implementations-combined with global optimization algorithms capable of solving Mixed Integer Nonlinear Programming problems. The toolbox efficiently addresses two types of problems relevant in systems and synthetic biology: the automated design of stochastic synthetic gene circuits, and the parameter estimation for model identification of stochastic gene regulatory networks. AVAILABILITY AND IMPLEMENTATION: IDESS runs under the MATLAB environment and it is available under GPLv3 license at https://doi.org/10.5281/zenodo.7788692.

Motivation: Gene regulation is inherently stochastic. In many applications concerning Systems and Synthetic Biology such as the reverse engineering and the de novo design of genetic circuits, stochastic effects (yet potentially crucial) are often neglected due to the high computational cost of stochastic simulations. With advances in these fields there is an increasing need of tools providing accurate approximations of the stochastic dynamics of gene regulatory networks (GRNs) with reduced computational effort. Results: This work presents SELANSI (SEmi-LAgrangian SImulation of GRNs), a software toolbox for the simulation of stochastic multidimensional gene regulatory networks. SELANSI exploits intrinsic structural properties of gene regulatory networks to accurately approximate the corresponding Chemical Master Equation with a partial integral differential equation that is solved by a semi-lagrangian method with high efficiency. Networks under consideration might involve multiple genes with self and cross regulations, in which genes can be regulated by different transcription factors. Moreover, the validity of the method is not restricted to a particular type of kinetics. The tool offers total flexibility regarding network topology, kinetics and parameterization, as well as simulation options. Availability and implementation: SELANSI runs under the MATLAB environment, and is available under GPLv3 license at https://sites.google.com/view/selansi. Contact: [email protected].