Finding and breaking lie symmetries: implications for structural identifiability and observability in biological modelling

A dynamic model is structurally identifiable (respectively, observable) if it is theoretically possible to infer its unknown parameters (respectively, states) by observing its output over time. The two properties, structural identifiability and observability, are completely determined by the model equations. Their analysis is of interest for modellers because it informs about the possibility of gaining insight into a model’s unmeasured variables. Here we cast the problem of analysing structural identifiability and observability as that of finding Lie symmetries. We build on previous results that showed that structural unidentifiability amounts to the existence of Lie symmetries. We consider nonlinear models described by ordinary differential equations and restrict ourselves to rational functions. We revisit a method for finding symmetries by transforming rational expressions into linear systems. We extend the method by enabling it to provide symmetry-breaking transformations, which allows for a semi-automatic model reformulation that renders a non-observable model observable. We provide a MATLAB implementation of the methodology as part of the STRIKE-GOLDD toolbox for observability and identifiability analysis. We illustrate the use of the methodology in the context of biological modelling by applying it to a set of problems taken from the literature.Ministerio de Ciencia, Innovación y Universidades | Ref. DPI2017-82896-C2-2-

AutoRepar: a method to obtain identifiable and observable reparameterizations of dynamic models with mechanistic insights

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGMechanistic dynamic models of biological systems allow for a quantitative and systematic interpretation of data and the generation of testable hypotheses. However, these models are often over-parameterized, leading to nonidentifiability and nonobservability, that is, the impossibility of inferring their parameters and state variables. The lack of structural identifiability and observability (SIO) compromises a model's ability to make predictions and provide insight. Here we present a methodology, AutoRepar, that corrects SIO deficiencies of nonlinear ODE models automatically, yielding reparameterized models that are structurally identifiable and observable. The reparameterization preserves the mechanistic meaning of selected variables, and has the exact same dynamics and input-output mapping as the original model. We implement AutoRepar as an extension of the STRIKE-GOLDD software toolbox for SIO analysis, applying it to several models from the literature to demonstrate its ability to repair their structural deficiencies. AutoRepar increases the applicability of mechanistic models, enabling them to provide reliable information about their parameters and dynamics.Consejo Superior de Investigaciones Científicas https://doi.org/10.13039/501100003339 | Ref. PIE 202070E062MCIN/AEI/10.13039/501100011033 | Ref. RYC-2019-027537-IMCIN/AEI/10.13039/501100011033 | Ref. PID2020-113992RA-I00MCIN/AEI/ 10.13039/501100011033 | Ref. PID2020-117271RB-C2MCIN/AEI/ 10.13039/501100011033 | Ref. DPI2017-82896-C2-2-RXunta de Galicia | Ref. ED431F 2021/00

Improving dynamic predictions with ensembles of observable models

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGMotivation: Dynamic mechanistic modelling in systems biology has been hampered by the complexity and variability associated with the underlying interactions, and by uncertain and sparse experimental measurements. Ensemble modelling, a concept initially developed in statistical mechanics, has been introduced in biological applications with the aim of mitigating those issues. Ensemble modelling uses a collection of different models compatible with the observed data to describe the phenomena of interest. However, since systems biology models often suffer from lack of identifiability and observability, ensembles of models are particularly unreliable when predicting non-observable states. Results: We present a strategy to assess and improve the reliability of a class of model ensembles. In particular, we consider kinetic models described using ordinary differential equations (ODEs) with a fixed structure. Our approach builds an ensemble with a selection of the parameter vectors found when performing parameter estimation with a global optimization metaheuristic. This technique enforces diversity during the sampling of parameter space and it can quantify the uncertainty in the predictions of state trajectories. We couple this strategy with structural identifiability and observability analysis, and when these tests detect possible prediction issues we obtain model reparameterizations that surmount them. The end result is an ensemble of models with the ability to predict the internal dynamics of a biological process. We demonstrate our approach with models of glucose regulation, cell division, circadian oscillations, and the JAK-STAT signalling pathway. Availability: The code that implements the methodology and reproduces the results is available at https://doi.org/10.5281/zenodo.6782638. Supplementary information: Supplementary data are available at Bioinformatics online.MCIN/AEI/ 10.13039/501100011033 | Ref. PID2020-117271RBC22MCIN/AEI/ 10.13039/501100011033 | Ref. PID2020-113992RA-I00MCIN/AEI/ 10.13039/501100011033 | Ref. RYC-2019-027537-IXunta de Galicia | Ref. ED431F 2021/00

Contribuciones al modelado para conjuntos en biologia de sistemas: de la identificación a la cuantificación de la incertidumbre en la estructura y las predicciones

Jornada Virtual de Doctorandos en MSO 2021, 12 de abrilN

Contribucións ao modelado mecanístico en bioloxía de sistemas: identificabilidade, simetrías e cuatificación da incerteza

This thesis is framed in the context of dynamic modelling of biological systems. As dynamic models we will mainly use non-linear models in common differential equations. The objective is the development and application of computational methodologies that facilitate such modelling. These methodologies are of general purpose, applicable to biological problems in different fields (biomedicine, biotechnology industrial, food technology, ecology, etc.). Several lines of research are envisaged complementary in two respects: on the one hand, the identification of systems; on the other hand, the analysis of the uncertainty associated with model predictions. The first aspect, the identification of the system, refers to the construction and calibration of dynamic models from experimental data. These models have the capacity to make predictions about conditions not included in the experimental data. However, there is always some uncertainty associated with these predictions, which is important to quantify; this is the second aspect to consider in this thesis. The two aspects are related. In turn, within each of them we can distinguish several objectives or tasks. In this way, the objectives of this thesis can be framed in four large blocks: 1.- Analysis of the structural systemic properties of dynamic models: identifiability, observability and controllability and the relationship between them. 2.- Study of the distinction between dynamic models and their relationship with the inference of these models. 3.- Construction of sets ("ensembles") of models, and application to the analysis of uncertainty of the predictions. 4.- Machine learning of dynamic models from experimental dataEsta tesis se enmarca en el contexto del modelado dinámico de sistemas biológicos. Como modelos dinámicos utilizaremos, principalmente, modelos no lineales en ecuaciones diferenciales ordinarias. El objetivo es el desarrollo y aplicación de metodologías computacionales que faciliten tal modelado. Estas metodologías son de propósito general, aplicables a problemas biológicos de diferentes campos (biomedicina, biotecnología industrial, tecnología alimentaria, ecología, etc.). Se contemplan varias líneas de investigación complementarias relacionadas con dos aspectos: por una parte, la identificación de sistemas; por otro, el análisis de la incertidumbre asociada a las predicciones de los modelos. El primer aspecto, la identificación del sistema, se refiere a la construcción y calibración de modelos dinámicos a partir de datos experimentales. Estos modelos tienen la capacidad de hacer predicciones sobre condiciones no recogidas en los datos experimentales. No obstante, siempre hay cierta incertidumbre asociada la estas predicciones, que es importante cuantificar; este es el segundo aspecto a considerar en esta tesis. Los dos aspectos están relacionados. A su vez, dentro de cada uno de ellos podemos distinguir varios objetivos o tareas. De este modo, los objetivos de este de la tesis se pueden enmarcar en cuatro grandes bloques: 1.- Análisis de las propiedades sistémicas estructurales de modelos dinámicos: identificabilidad, observabilidad y controlabilidad y relación entre ellos. 2.- Estudio de la distinción de los modelos dinámicos y de su relación con la inferencia de los dichos modelos. 3.- Construcción de conjuntos (" ensembles") de modelos, y aplicación al análisis de la incertidumbre de las predicciones. 4.- Machine learning de modelos dinámicos a partir de datos experimentales.Esta tese enmárcase no contexto do modelado dinámico de sistemas biolóxicos. Como modelos dinámicos utilizaremos, principalmente, modelos non lineares en ecuacións diferenciais ordinarias. O obxectivo é o desenvolvemento e aplicación de metodoloxías computacionais que faciliten tal modelado. Estas metodoloxías son de propósito xeral, aplicables a problemas biolóxicos de diferentes campos (biomedicina, biotecnoloxía industrial, tecnoloxía alimentaria, ecoloxía, etc.). Contémplanse varias liñas de investigación complementarias relacionadas con dous aspectos: por unha banda, a identificación de sistemas; por outro, a análise da incerteza asociada ás predicións dos modelos. O primeiro aspecto, a identificación do sistema, refírese á construción e calibración de modelos dinámicos a partir de datos experimentais. Estes modelos teñen a capacidade de facer predicións sobre condicións non recollidas nos datos experimentais. Non obstante, sempre hai certa incerteza asociada a estas predicións, que é importante cuantificar; este é o segundo aspecto a considerar nesta tese. Os dous aspectos están relacionados. Á súa vez, dentro de cada un deles podemos distinguir varios obxectivos ou tarefas. Deste xeito, os obxectivos deste da tese pódense enmarcar en catro grandes bloques: 1.- Análise das propiedades sistémicas estruturais de modelos dinámicos: identificabilidade, observabilidade e controlabilidade e relación entre eles. 2.- Estudo da distinción dos modelos dinámicos e da súa relación coa inferencia dos devanditos modelos. 3.- Construción de conxuntos ("ensembles") de modelos, e aplicación á análise da incerteza das predicións. 4.- Aprendizaxe automática de modelos dinámicos a partir de datos experimentais.Ministerio de Ciencia e Innovación | Ref. PID2020-117271RB-C22Ministerio de Ciencia e Innovación | Ref. PID2020-113992RA-I00Xunta de Galicia | Ref. ED431F 2021/003CSIC | Ref. PIE 202070E062 (MOEBIUS

Finding and Breaking Lie Symmetries: Implications for Structural Identifiability and Observability in Biological Modelling

© 2020 by the authors.A dynamic model is structurally identifiable (respectively, observable) if it is theoretically possible to infer its unknown parameters (respectively, states) by observing its output over time. The two properties, structural identifiability and observability, are completely determined by the model equations. Their analysis is of interest for modellers because it informs about the possibility of gaining insight into a model’s unmeasured variables. Here we cast the problem of analysing structural identifiability and observability as that of finding Lie symmetries. We build on previous results that showed that structural unidentifiability amounts to the existence of Lie symmetries. We consider nonlinear models described by ordinary differential equations and restrict ourselves to rational functions. We revisit a method for finding symmetries by transforming rational expressions into linear systems. We extend the method by enabling it to provide symmetry-breaking transformations, which allows for a semi-automatic model reformulation that renders a non-observable model observable. We provide a MATLAB implementation of the methodology as part of the STRIKE-GOLDD toolbox for observability and identifiability analysis. We illustrate the use of the methodology in the context of biological modelling by applying it to a set of problems taken from the literature.This research was funded by the Spanish Ministry of Science, Innovation and Universities through the project SYNBIOCONTROL (ref. DPI2017-82896-C2-2-R).Peer reviewe

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

8 pages.-- This is an open access article distributed under the terms of the Creative Commons Attribution LicenseA recent paper published in PLOS Computational Biology [1] 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 lead one to conclude that the model is identifiable and observable when it is actually notAFV has received funding from a Ramón y Cajal Fellowship (RYC-2019-027537-I) and from the Spanish Ministry of Science, Innovation and Universities and the European Union FEDER under project grant SYNBIOCONTROL (DPI2017-82896-C2-2-R). GM was funded by the CSIC intramural project grant MOEBIUS (PIE 202070E062)Peer reviewe

Distilling identifiable and interpretable dynamic models from biological data

<p><strong>This repository contains the accompanying code to the paper:</strong></p><p> </p><p><strong>Massonis, G., Villaverde, A.F., Banga, J.R. (2023). Distilling identifiable and interpretable dynamic models from biological data. PLOS Computational Biology 19(10): e1011014</strong>. <a href="https://doi.org/10.1371/journal.pcbi.1011014">https://doi.org/10.1371/journal.pcbi.1011014 </a><strong>([email protected], [email protected], </strong><a href="mailto:[email protected]"><strong>[email protected]</strong></a><strong>)</strong></p><p><strong>which presents a methodology to ensure that models discovered via sparse regression (using SINDy-PI) are structurally identifiable, observable and interpretable.</strong></p><p><strong>Requirements:</strong></p><p><strong>MATLAB (tested with version R2020b under Win10), including:</strong></p><p><strong>Symbolic Math Toolbox.</strong></p><p><strong>Parallel Computing Toolbox (optional)</strong></p><p><strong>STRIKE-GOLDD (tested with version 4.0.2); </strong><a href="https://github.com/afvillaverde/strike-goldd.git"><strong>https://github.com/afvillaverde/strike-goldd.git</strong></a><strong>)</strong></p><p><strong>SINDy-PI (</strong><a href="https://github.com/dynamicslab/SINDy-PI.git"><strong>https://github.com/dynamicslab/SINDy-PI.git</strong></a><strong>).</strong></p><p><strong>Installation: please follow the instructions in the README_install.txt file</strong></p>This research has received support from grant PID2020-117271RB-C22 (BIODYNAMICS) funded by MCIN/AEI/ 10.13039/501100011033; from the CSIC intramural project grant PIE 202070E062 (MOEBIUS); from grant PID2020-113992RA-I00 funded by MCIN/AEI/ 10.13039/501100011033 (PREDYCTBIO); from grant ED431F 2021/003 funded by Consellería de Cultura, Educación e Ordenación Universitaria, Xunta de Galicia; and from grant RYC-2019-027537-I funded by MCIN/AEI/ 10.13039/501100011033 and by "ESF Investing in your future''. The funding bodies played no role in the design of the study, the collection and analysis of data

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 (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