arXiv subjects

Irene Otero-Muras

Publications and source records attributed to Irene Otero-Muras.

6 recordsLinked to original sources

arXiv2026

Predictive-Switching Control of Stochastic Gene Regulatory Networks: A Contractive PIDE Framework

This paper develops a predictive switching control algorithm for stochastic gene regulatory networks described by a Partial Integro-Differential Equation (PIDE) model, which enables direct shape control of the probability density function. Control inputs are selected from a finite candidate set to minimize a prescribed cost functional. A hybrid framework is proposed for scalability in higher-dimensional systems, using neural networks to approximate the control policy. A central theoretical contribution is a contraction-based analysis of the closed-loop PIDE dynamics. The paper establishes $L^ 1$-contractivity under the proposed control scheme, yielding formal stability guarantees and showing that the evolution of the probability density becomes progressively independent of the initial condition. Moreover, under strictly positive leakage terms, exponential convergence is obtained. The effectiveness and flexibility of the approach, together with the theoretical contractivity results, are illustrated through numerical simulations on three representative examples of increasing dimensionality.

math.DS↗

arXiv2026

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↗

arXiv2025

Turing Patterns in a Morphogenetic Model with Single Regulatory Function

Confirming Turing's theory of morphogens in developmental processes is challenging, and synthetic biology has opened new avenues for testing Turing's predictions. Synthetic mammalian pattern formation has been recently achieved through a reaction-diffusion system based on the short-range activator (Nodal) and the long-range inhibitor (Lefty) topology, where a single function regulates both morphogens. In this paper, we investigate the emergence of Turing patterns in the synthetic Nodal-Lefty system. First, we prove the existence of a global solution and derive conditions for Turing instability through linear stability analysis. Subsequently, we examine the behavior of the system near the bifurcation threshold, employing weakly nonlinear analysis, and using multiple time scales, we derive the amplitude equations for supercritical and subcritical cases. The results demonstrate the ability of the system to support various patterns, with the subcritical Turing instability playing a crucial role in the formation of dissipative structures observed experimentally.

nlin.PS↗

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↗

arXiv2019

Transient hysteresis and inherent stochasticity in gene regulatory networks

Cell fate determination, the process through which cells commit to differentiated states is commonly mediated by gene regulatory motifs with mutually exclusive expression states. The classical deterministic picture for cell fate determination includes bistability and hysteresis, which enables the persistence of the acquired cellular state after withdrawal of the stimulus, ensuring a robust cellular response. However, the stochasticity inherent to gene expression dynamics is not compatible with hysteresis, since the stationary solution of the governing Chemical Master Equation does not depend on the initial conditions. In this work, we provide a quantitative description of a transient hysteresis phenomenon that reconciles experimental evidence of hysteretic behaviour in gene regulatory networks with their inherent stochasticity. Under sufficiently slow dynamics, the dependency of the non-stationary solutions on the initial state of the cells can lead to what we denote here as transient hysteresis. To quantify this phenomenon, we provide an estimate of the convergence rate to the equilibrium. We also introduce the equation of a natural landscape capturing the evolution of the system that, unlike traditional cell fate potential landscapes, is compatible with the notion of coexistence at the microscopic level.

q-bio.MN↗

arXiv2014

Multicriteria global optimization for biocircuit design

One of the challenges in Synthetic Biology is to design circuits with increasing levels of complexity. While circuits in Biology are complex and subject to natural tradeoffs, most synthetic circuits are simple in terms of the number of regulatory regions, and have been designed to meet a single design criterion. In this contribution we introduce a multiobjective formulation for the design of biocircuits. We set up the basis for an advanced optimization tool for the modular and systematic design of biocircuits capable of handling high levels of complexity and multiple design criteria. Our methodology combines the efficiency of global Mixed Integer Nonlinear Programming solvers with multiobjective optimization techniques. Through a number of examples we show the capability of the method to generate non intuitive designs with a desired functionality setting up a priori the desired level of complexity. The presence of more than one competing objective provides a realistic design setting where every design solution represents a trade-off between different criteria. The tool can be useful to explore and identify different design principles for synthetic gene circuits.

math.OC↗