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Summary: Recent advances in synthetic biology are enabling exciting technologies, including the next generation of biosensors, the rational design of cell memory, modulated synthetic cell differentiation, and generic multifunctional biocircuits. These novel applications require the design of gene circuits leading to sophisticated behaviors and functionalities. At the same time, designs need to be kept minimal to avoid compromising cell viability. Bifurcation theory addresses such challenges by associating circuit dynamical properties with molecular details of its design. Nevertheless, incorporating bifurcation analysis into automated design processes has not been accomplished yet. This work presents an optimization-based method for the automated design of synthetic gene circuits with specified bifurcation diagrams that employ minimal network topologies. Using this approach, we designed circuits exhibiting the mushroom bifurcation, distilled the most robust topologies, and explored its multifunctional behavior. We then outline potential applications in biosensors, memory devices, and synthetic cell differentiation.

Abstract Background Optimality principles have been used to explain the structure and behavior of living matter at different levels of organization, from basic phenomena at the molecular level, up to complex dynamics in whole populations. Most of these studies have assumed a single-criteria approach. Such optimality principles have been justified from an evolutionary perspective. In the context of the cell, previous studies have shown how dynamics of gene expression in small metabolic models can be explained assuming that cells have developed optimal adaptation strategies. Most of these works have considered rather simplified representations, such as small linear pathways, or reduced networks with a single branching point, and a single objective for the optimality criteria. Results Here we consider the extension of this approach to more realistic scenarios, i.e. biochemical pathways of arbitrary size and structure. We first show that exploiting optimality principles for these networks poses great challenges due to the complexity of the associated optimal control problems. Second, in order to surmount such challenges, we present a computational framework which has been designed with scalability and efficiency in mind, including mechanisms to avoid the most common pitfalls. Third, we illustrate its performance with several case studies considering the central carbon metabolism of S. cerevisiae and B. subtilis. In particular, we consider metabolic dynamics during nutrient shift experiments. Conclusions We show how multi-objective optimal control can be used to predict temporal profiles of enzyme activation and metabolite concentrations in complex metabolic pathways. Further, we also show how to consider general cost/benefit trade-offs. In this study we have considered metabolic pathways, but this computational framework can also be applied to analyze the dynamics of other complex pathways, such as signal transduction or gene regulatory networks.

Abstract Background Dynamic modelling is a core element in the systems biology approach to understanding complex biosystems. Here, we consider the problem of parameter estimation in models of biological oscillators described by deterministic nonlinear differential equations. These problems can be extremely challenging due to several common pitfalls: (i) a lack of prior knowledge about parameters (i.e. massive search spaces), (ii) convergence to local optima (due to multimodality of the cost function), (iii) overfitting (fitting the noise instead of the signal) and (iv) a lack of identifiability. As a consequence, the use of standard estimation methods (such as gradient-based local ones) will often result in wrong solutions. Overfitting can be particularly problematic, since it produces very good calibrations, giving the impression of an excellent result. However, overfitted models exhibit poor predictive power. Here, we present a novel automated approach to overcome these pitfalls. Its workflow makes use of two sequential optimisation steps incorporating three key algorithms: (1) sampling strategies to systematically tighten the parameter bounds reducing the search space, (2) efficient global optimisation to avoid convergence to local solutions, (3) an advanced regularisation technique to fight overfitting. In addition, this workflow incorporates tests for structural and practical identifiability. Results We successfully evaluate this novel approach considering four difficult case studies regarding the calibration of well-known biological oscillators (Goodwin, FitzHugh–Nagumo, Repressilator and a metabolic oscillator). In contrast, we show how local gradient-based approaches, even if used in multi-start fashion, are unable to avoid the above-mentioned pitfalls. Conclusions Our approach results in more efficient estimations (thanks to the bounding strategy) which are able to escape convergence to local optima (thanks to the global optimisation approach). Further, the use of regularisation allows us to avoid overfitting, resulting in more generalisable calibrated models (i.e. models with greater predictive power).

Building mathematical models of cellular networks lies at the core of systems biology. It involves, among other tasks, the reconstruction of the structure of interactions between molecular components, which is known as network inference or reverse engineering. Information theory can help in the goal of extracting as much information as possible from the available data. A large number of methods founded on these concepts have been proposed in the literature, not only in biology journals, but in a wide range of areas. Their critical comparison is difficult due to the different focuses and the adoption of different terminologies. Here we attempt to review some of the existing information theoretic methodologies for network inference, and clarify their differences. While some of these methods have achieved notable success, many challenges remain, among which we can mention dealing with incomplete measurements, noisy data, counterintuitive behaviour emerging from nonlinear relations or feedback loops, and computational burden of dealing with large data sets.

Resumen: En este trabajo se presenta una librería de unidades de operación en EcosimPro para la simulación, optimización y control de procesos térmicos en la industria alimentaria. Las plantas de procesamiento de alimentos son buenos ejemplos de sistemas híbridos donde las dinámicas continuas no lineales están acopladas con eventos discretos. El entorno EcosimPro permite trabajar con dichos sistemas de forma eï¬ciente e incorpora una interfaz gráï¬ca de usuario (EcoDiagram) que facilita el manejo de modelos matemáticos complejos a los usuarios no expertos. Para la programación de dichos modelos en el entorno EcosimPro se ha seguido el paradigma de la programación orientada a objetos (POO) que incluye características como la reutilización, herencia, abstracción o encapsulamiento. La librería de componentes se puede utilizar, por ejemplo, para analizar el efecto de tecnologías alternativas en la producción o para diseñar nuevas políticas de operación en el caso de condiciones de suministro ï¬uctuantes. Aunque este trabajo se centra en procesos de la industria conservera, se pueden añadir otras unidades para la simulación de procesos como la pasteurización o secado sin necesidad de modiï¬car los componentes ya existentes. Los modelos han sido validados utilizando una planta piloto instalada en el IIM-CSIC aunque pueden ser aplicados a otras con diferentes especiï¬caciones. Finalmente, algunas de las ventajas de disponer de esta librería de componentes se ilustran en una serie de ejemplos de uso. Palabras clave: Sistemas Híbridos, Simulación Dinámica, Procesamiento Térmico de Alimentos, Entorno de Simulación Amigable

Resumen: Los procesos de la industria química, alimentaria o biotecnológica, así como muchos de los mecanismos propios de la biología de sistemas, pertenecen a la clase de los llamados sistemas de proceso. En esta contribución se hace uso de un conjunto de resultados previos que combinan aspectos de la teoría de sistemas y grafos, con métodos de termodinámica y de redes de reacción para así sentar las bases sobre las que elaborar una representacion formal y generalizada de procesos en términos de redes complejas.Esta representación -parcialmente desarrollada por los autores- además de unificar un amplio número de procesos aparentemente diversos, proporciona una sistemática eficiente con la que abordar los problemas de control descentralizado y análisis dinámico avanzado (incluyendo el análisis de bifurcación). Palabras clave: Redes Complejas, sistemas de proceso, análisis dinámico, análisis de bifurcación, control descentralizado.

The Virtual Epileptic Patient (VEP) refers to a computer-based representation of a patient with epilepsy that combines personalized anatomical data with dynamical models of abnormal brain activities. It is capable of generating spatio-temporal seizure patterns that resemble those recorded with invasive methods such as stereoelectro EEG data, allowing for the evaluation of clinical hypotheses before planning surgery. This study highlights the effectiveness of calibrating VEP models using a global optimization approach. The approach utilizes SaCeSS, a cooperative metaheuristic algorithm capable of parallel computation, to yield high-quality solutions without requiring excessive computational time. Through extensive benchmarking on synthetic data, our proposal successfully solved a set of different configurations of VEP models, demonstrating better scalability and superior performance against other parallel solvers. These results were further enhanced using a Bayesian optimization framework for hyperparameter tuning, with significant gains in terms of both accuracy and computational cost. Additionally, we added a scalable uncertainty quantification phase after model calibration, and used it to assess the variability in estimated parameters across different problems. Overall, this study has the potential to improve the estimation of pathological brain areas in drug-resistant epilepsy, thereby to inform the clinical decision-making process.

Mechanistic dynamical models allow us to study the behavior of complex biological systems. They can provide an objective and quantitative understanding that would be difficult to achieve through other means. However, the systematic development of these models is a non-trivial exercise and an open problem in computational biology. Currently, many research efforts are focused on model discovery, i.e. automating the development of interpretable models from data. One of the main frameworks is sparse regression, where the sparse identification of nonlinear dynamics (SINDy) algorithm and its variants have enjoyed great success. SINDy-PI is an extension which allows the discovery of rational nonlinear terms, thus enabling the identification of kinetic functions common in biochemical networks, such as Michaelis-Menten. SINDy-PI also pays special attention to the recovery of parsimonious models (Occam's razor). Here we focus on biological models composed of sets of deterministic nonlinear ordinary differential equations. We present a methodology that, combined with SINDy-PI, allows the automatic discovery of structurally identifiable and observable models which are also mechanistically interpretable. The lack of structural identifiability and observability makes it impossible to uniquely infer parameter and state variables, which can compromise the usefulness of a model by distorting its mechanistic significance and hampering its ability to produce biological insights. We illustrate the performance of our method with six case studies. We find that, despite enforcing sparsity, SINDy-PI sometimes yields models that are unidentifiable. In these cases we show how our method transforms their equations in order to obtain a structurally identifiable and observable model which is also interpretable.