On the origins and rarity of locally but not globally identifiable parameters in biological modeling

Structural identifiability determines the possibility of estimating the parameters of a model by observing its output in an ideal experiment. If a parameter is structurally locally identifiable, but not globally (SLING), its true value cannot be uniquely inferred because several equivalent solutions exist. In biological modeling it is sometimes assumed that local identifiability entails global identifiability, which is convenient because local identifiability tests are typically less computationally demanding than global tests. However, this assumption has never been investigated beyond demonstrating the existence of counter-examples. To clarify this matter, in this paper we began by asking how often a structurally locally identifiable parameter is not globally identifiable in systems biology. To answer this question empirically we assembled a collection of 102 mathematical models from the literature, with a total of 763 parameters. We analysed their identifiability, determining that approximately 5% of the parameters are SLING. Next we investigated how the SLING parameters arise, tracing their origin to particular features of the model equations. Finally, we investigated the possibility of obtaining false estimates. Some of the solutions that are mathematically equivalent to the true one involved parameters and/or initial conditions with negative values, which are not biologically meaningful. In other cases the true solution and the equivalent one were in the same range. These results provide insight about a previously unexplored hypothesis, and suggest that in most (albeit not all) systems biology applications it suffices to test for structural local identifiability.MCIN/AEI/ 10.13039/50110001103300004837 | Ref. PID2020-113992RA-I00MCIN/AEI/ 10.13039/50110001103300004837 | Ref. RYC-2019-027537-IXunta de Galicia | Ref. ED431F 2021/00

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-

Benchmarking tools for a priori identifiability analysis

Motivation: The theoretical possibility of determining the state and parameters of a dynamic model by measuring its outputs is given by its structural identifiability and observability. These properties should be analysed before attempting to calibrate a model, but their a priori analysis can be challenging, requiring symbolic calculations that often have a high computational cost. In recent years a number of software tools have been developed for this task, mostly in the systems biology community. These tools have vastly different features and capabilities, and a critical assessment of their performance is still lacking. Results: Here we present a comprehensive study of the computational resources available for analysing structural identifiability. We consider 13 software tools developed in 7 programming languages and evaluate their performance using a set of 25 case studies created from 21 models. Our results reveal their strengths and weaknesses, provide guidelines for choosing the most appropriate tool for a given problem, and highlight opportunities for future developments. Availability: https://github.com/Xabo-RB/Benchmarking_files.Xunta de Galicia | Ref. ED431F 2021/003Agencia Estatal de Investigación | Ref. PID2020-113992RA-I00MCIN/AEI/10.13039/501100011033 | Ref. RYC-2019-027537-IFinanciado para publicación en acceso aberto: Universidade de Vigo/CISU

Smooth non linear high gain observers for a class of dynamical systems

High-gain observers are powerful tools for estimating the state of nonlinear systems. However, their design poses several challenges due to the need of dealing with phenomena such as peaking and chattering. To address these issues, we propose a differentiator operator design based on a non linear second order high-gain observer, which is suited to a class of dynamical systems. Our method includes a procedure to determine high gains in order to avoid chattering in the case of noise-free models, and cut-off frequency based gain design in the case of noisy measurements. Complementary, we suggest performing observability analyses to ensure a priori the feasibility of the estimation. The main strengths of our approach are its simplicity and robustness. We demonstrate the performance of the proposed method by applying it to two processes (chemical and biological).Xunta de Galicia | Ref. ED431F 2021/003MCIN/AEI/10.13039/501100011033 | Ref. RYC-2019-027537-

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

Structural identifiability and observability of microbial community models

Biological communities are populations of various species interacting in a common location. Microbial communities, which are formed by microorganisms, are ubiquitous in nature and are increasingly used in biotechnological and biomedical applications. They are nonlinear systems whose dynamics can be accurately described by models of ordinary differential equations (ODEs). A number of ODE models have been proposed to describe microbial communities. However, the structural identifiability and observability of most of them—that is, the theoretical possibility of inferring their parameters and internal states by observing their output—have not been determined yet. It is important to establish whether a model possesses these properties, because, in their absence, the ability of a model to make reliable predictions may be compromised. Hence, in this paper, we analyse these properties for the main families of microbial community models. We consider several dimensions and measurements; overall, we analyse more than a hundred different configurations. We find that some of them are fully identifiable and observable, but a number of cases are structurally unidentifiable and/or unobservable under typical experimental conditions. Our results help in deciding which modelling frameworks may be used for a given purpose in this emerging area, and which ones should be avoided.Xunta de Galicia | Ref. ED431F 2021/003Ministerio de Ciencia e Innovación | Ref. PID2020-113992RA-I00Ministerio de Ciencia e Innovación | Ref. RYC-2019-027537-

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

Controllability and accessibility analysis of nonlinear biosystems

Background: We address the problem of determining the controllability and accessibility of nonlinear biosystems. We consider models described by affine-in-inputs ordinary differential equations, which are adequate for a wide array of biological processes. Roughly speaking, the controllability of a dynamical system determines the possibility of steering it from an initial state to any point in its neighbourhood; accessibility is a weaker form of controllability. Methods: While the methodology for analysing the controllability of linear systems is well established, its generalization to the nonlinear case has proven elusive. Thus, a number of related but different properties – including different versions of accessibility, reachability or weak local controllability – have been defined to approach its study, and several partial results exist in lieu of a general test. Here, leveraging the applicable results from differential geometric control theory, we source sufficient conditions to assess nonlinear controllability, as well as a necessary and sufficient condition for accessibility. Results: We develop an algorithmic procedure to evaluate these conditions efficiently, and we provide its open source implementation. Using this software tool, we analyse the accessibility and controllability of a number of models of biomedical interest. While some of them are fully controllable, we find others that are not, as is the case of some models of EGF and NF����B signalling networks. Conclusions: The contributions in this paper facilitate the accessibility and controllability analysis of nonlinear models, not only in biomedicine but also in other areas in which they have been rarely performed to date.Agencia Estatal de Investigación | Ref. PID2020-113992RA-I00Agencia Estatal de Investigación | Ref. RYC-2019-027537-IXunta de Galicia | Ref. ED431F 2021/00

STRIKE-GOLDD 4.0: user-friendly, efficient analysis of structural identifiability and observability

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGMotivation: STRIKE-GOLDD is a toolbox that analyses the structural identifiability and observability of possibly non-linear, non-rational ODE models that may have known and unknown inputs. Its broad applicability comes at the expense of a lower computational efficiency than other tools. Results: STRIKE-GOLDD 4.0 includes a new algorithm, ProbObsTest, specifically designed for the analysis of rational models. ProbObsTest is significantly faster than the previously available FISPO algorithm when applied to computationally expensive models. Providing both algorithms in the same toolbox allows combining generality and computational efficiency. STRIKE-GOLDD 4.0 is implemented as a Matlab toolbox with a user-friendly graphical interface. Availability and implementation: STRIKE-GOLDD 4.0 is a free and open-source tool available under a GPLv3 license. It can be downloaded from GitHub at https://github.com/afvillaverde/strike-goldd. Supplementary information: Supplementary data are available at Bioinformatics online.MCIN/AEI/10.13039/501100011033 | Ref. PID2020-113992RA-I00MCIN/AEI/10.13039/501100011033 | Ref. RYC-2019-027537-IXunta de Galicia | Ref. ED431F 2021/00