Biology subjects

Villaverde, A. F.

Publications and source records attributed to Villaverde, A. F..

5 recordsLinked to original sources

bioRxiv2025

Leveraging mathematical models to predict and control T-cell activation

T-cell receptor (TCR)-mediated T-cell activation is a key process in adaptive immune responses. The complexity of this process has led to the development of different mathematical models that seek to describe and predict the conditions of antigen-TCR interactions required for TCR triggering and T-cell activation. These models are characterized by describing different sets of sequential molecular interactions and their kinetics, positing the generation of a final product as a necessary and sufficient condition for T-cell activation. Such modeling could provide an effective tool for simulating antigen recognition by T cells and, consequently, aid in the design of effective therapeutic strategies. However, it is necessary to previously assess the predictive capabilities of the proposed models when fitted to experimental data. To achieve this goal, in this work we examine the parameter identifiability and sensitivity of the published models of TCR-based T-cell activation. For each model, we consider different, often experimentally measured, output quantities and show how their availability affects the results. These analyses allow us to determine the ability of each model to correctly describe different experimental situations, and to establish to what extent these models can be applied to reliably predict and control T-cell activation by specific therapeutic targets. Author summaryThe adaptive immune system is a highly specialized defense mechanism present in vertebrates. It produces a response that results from a complex set of interrelated cellular and molecular mechanisms. A key process is antigen-dependent activation of T lymphocytes, for which several mechanisms have been postulated. The corresponding mathematical models allow us to explore competing hypotheses, make quantitative predictions, and eventually aid in the design of strategies to control the immune response. To achieve these goals, it is essential that the models be identifiable and observable, that is, it must be possible to infer their parameters and state from output measurements. Furthermore, their response should exhibit an adequate level of sensitivity to certain key parameters. In this work, we evaluate the degree to which currently existing models possess these qualities. Our findings provide minimum requirements for the design of system identification experiments, allowing us to discard those models that cannot be successfully calibrated with a given experimental setup.

immunology↗

bioRxiv2025

Response metrics of T-cell activation models

T-cell activation models describe the way in which antigens and T-cell receptors (TCRs) interact in order to trigger an immune response. A number of mathematical models of TCR-mediated T-cell activation have been proposed in the last decades. Often, the only measurable quantities available for the identification of these models are Emax, the maximum achievable T cell activation level (over the background level), and EC50, that is, the antigen concentration that results in 50% of Emax. In order to analyse model properties such as identifiability, observability, and sensitivity, it is necessary to know how Emax and/or EC50 relate to the model parameters. However, their expressions are only available for a few of the published models of T-cell activation. Here we present a general method to derive the expressions of Emax and/or EC50, and apply it to those models for which they are yet unknown. Our results expand the range of analyses that can be performed on T-cell activation models, contributing to enable their exploitation to understand and control the immune response.

systems biology↗

bioRxiv2023

Distilling identifiable and interpretable dynamic models from biological data

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 (Occams 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. Author summaryDynamical models provide a quantitative understanding of complex biological systems. Since their development is far from trivial, in recent years many research efforts focus on obtaining these models automatically from data. One of the most effective approaches is based on implicit sparse regression. This technique is able to infer biochemical networks with kinetic functions containing rational nonlinear terms. However, as we show here, one limitation is that it may yield models that are unidentifiable. These features may lead to inaccurate mechanistic interpretations and wrong biological insights. To overcome this limitation, we propose an integrated methodology that applies additional procedures in order to ensure that the discovered models are structurally identifiable, observable, and interpretable. We demonstrate our method with six challenging case studies of increasing model complexity.

systems biology↗

bioRxiv2020

On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading

A recent paper (Castro M, de Boer RJ, "Testing structural identifiability by a simple scaling method", PLOS Computational Biology, 2020, 16(11):e1008248) introduces the Scaling Invariance Method (SIM) for analysing structural local identifiability and observability. These two properties define mathematically the possibility of determining the values of the parameters (identifiability) and states (observability) of a dynamic model by observing its output. In this note we warn that SIM considers scaling symmetries as the only possible cause of non-identifiability and non-observability. We show that other types of symmetries can cause the same problems without being detected by SIM, and that in those cases the method may yield a wrong result. Finally, we demonstrate how to analyse structural local identifiability and observability with symbolic computation tools that do not exhibit those issues.

systems biology↗

bioRxiv2018

Benchmarking optimization methods for parameter estimation in large kinetic models

MotivationMechanistic kinetic models usually contain unknown parameters, which need to be estimated by optimizing the fit of the model to experimental data. This task can be computationally challenging due to the presence of local optima and ill-conditioning. While a variety of optimization methods have been suggested to surmount these issues, it is not obvious how to choose the best one for a given problem a priori, since many factors can influence their performance. A systematic comparison of methods that are suited to parameter estimation problems of sizes ranging from tens to hundreds of optimization variables is currently missing, and smaller studies indeed provided contradictory findings.\n\nResultsHere, we use a collection of benchmark problems to evaluate the performance of two families of optimization methods: (i) a multi-start of deterministic local searches; and (ii) a hybrid metaheuristic combining stochastic global search with deterministic local searches. A fair comparison is ensured through a collaborative evaluation, involving researchers applying each method on a daily basis, and a consideration of multiple performance metrics capturing the trade-off between computational efficiency and robustness. Our results show that, thanks to recent advances in the calculation of parametric sensitivities, a multi-start of gradient-based local methods is often a successful strategy, but a better performance can be obtained with a hybrid metaheuristic. The best performer is a combination of a global scatter search metaheuristic with an interior point local method, provided with gradients estimated with adjoint-based sensitivities. We provide an implementation of this novel method in an open-source software toolbox to render it available to the scientific community.\n\nAvailability and ImplementationThe code to reproduce the results is available at Zenodo https://doi.org/10.5281/zenodo.1160343\n\nContactjan.hasenauer@helmholtz-muenchen.de, julio@iim.csic.es

systems biology↗