Observability and Structural Identifiability of Nonlinear Biological Systems

Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of determining the parameter values from the output. In fact, structural identifiability becomes a particular case of observability if the parameters are considered as constant state variables. It is possible to simultaneously analyse the observability and structural identifiability of a model using the conceptual tools of differential geometry. Many complex biological processes can be described by systems of nonlinear ordinary differential equations, and can therefore be analysed with this approach. The purpose of this review article is threefold: (I) to serve as a tutorial on observability and structural identifiability of nonlinear systems, using the differential geometry approach for their analysis; (II) to review recent advances in the field; and (III) to identify open problems and suggest new avenues for research in this area.Comment: Accepted for publication in the special issue "Computational Methods for Identification and Modelling of Complex Biological Systems" of Complexit

Dynamical compensation and structural identifiability: analysis, implications, and reconciliation

The concept of dynamical compensation has been recently introduced to describe the ability of a biological system to keep its output dynamics unchanged in the face of varying parameters. Here we show that, according to its original definition, dynamical compensation is equivalent to lack of structural identifiability. This is relevant if model parameters need to be estimated, which is often the case in biological modelling. This realization prompts us to warn that care should we taken when using an unidentifiable model to extract biological insight: the estimated values of structurally unidentifiable parameters are meaningless, and model predictions about unmeasured state variables can be wrong. Taking this into account, we explore alternative definitions of dynamical compensation that do not necessarily imply structural unidentifiability. Accordingly, we show different ways in which a model can be made identifiable while exhibiting dynamical compensation. Our analyses enable the use of the new concept of dynamical compensation in the context of parameter identification, and reconcile it with the desirable property of structural identifiability

Nonlinear Observability Algorithms with Known and Unknown Inputs: Analysis and Implementation

The observability of a dynamical system is affected by the presence of external inputs, either known (such as control actions) or unknown (disturbances). Inputs of unknown magnitude are especially detrimental for observability, and they also complicate its analysis. Hence, the availability of computational tools capable of analysing the observability of nonlinear systems with unknown inputs has been limited until lately. Two symbolic algorithms based on differential geometry, ORC-DF and FISPO, have been recently proposed for this task, but their critical analysis and comparison is still lacking. Here we perform an analytical comparison of both algorithms and evaluate their performance on a set of problems, while discussing their strengths and limitations. Additionally, we use these analyses to provide insights about certain aspects of the relationship between inputs and observability. We found that, while ORC-DF and FISPO follow a similar approach, they differ in key aspects that can have a substantial influence on their applicability and computational cost. The FISPO algorithm is more generally applicable, since it can analyse any nonlinear ODE model. The ORC-DF algorithm analyses models that are affine in the inputs, and if those models have known inputs it is sometimes more efficient. Thus, the optimal choice of a method depends on the characteristics of the problem under consideration. To facilitate the use of both algorithms, we implemented the ORC-DF condition in a new version of STRIKE-GOLDD, a MATLAB toolbox for structural identifiability and observability analysis. Since this software tool already had an implementation of the FISPO algorithm, the new release allows modellers and model users the convenience of choosing between different algorithms in a single tool, without changing the coding of their modelThis research was supported by the Spanish Ministry of Science, Innovation and Universities through the project SYNBIOCONTROL (reference DPI2017-82896-C2-2-R). We acknowledge support of the publication fee by the CSIC Open Access Publication Support Initiative through its Unit of Information Resources for Research (URICI) and by the Xunta de Galicia through grant ref. IN607B 2020-03S

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

Structural identifiability and observability are desirable properties of systems biology models. Many software toolboxes have been developed for their analysis in the last decades. STRIKE-GOLDD is a generally applicable tool that can analyse non-linear, non-rational ODE models with unknown inputs. However, this generality comes at the expense of a lower computational efficiency than other tools. Here we present STRIKE-GOLDD 4.0, which includes a new algorithm, ProbObsTest, specifically designed for the analysis of rational models. ProbObsTest is significantly faster than the FISPO algorithm - which was already available in older versions of the toolbox - when applied to computationally expensive models. An important feature of both algorithms is their ability to analyse models with unknown inputs. Thus, their coexistence in the same toolbox provides a combination of general applicability and computational efficiency. STRIKE-GOLDD 4.0 is implemented as a free and open-source Matlab toolbox with a user-friendly graphical interface. It is available under a GPLv3 license and it can be downloaded from GitHub at https://github.com/afvillaverde/strike-goldd.Comment: 14 pages, 1 figur

Input-dependent structural identifiability of nonlinear systems

A dynamic model is structurally identifiable if it is possible to infer its unknown parameters by observing its output. Structural identifiability depends on the system dynamics, output, and input, as well as on the specific values of initial conditions and parameters. Here we present a symbolic method that characterizes the input that a model requires to be structurally identifiable. It determines which derivatives must be non-zero in order to have a sufficiently exciting input. Our approach considers structural identifiability as a generalization of nonlinear observability and incorporates extended Lie derivatives. The methodology assesses structural identifiability for time-varying inputs and, additionally, it can be used to determine the input profile that is required to make the parameters structurally locally identifiable. Furthermore, it is sometimes possible to replace an experiment with time-varying input with multiple experiments with constant inputs. We implement the resulting method as a MATLAB toolbox named STRIKE-GOLDD2. This tool can assist in the design of new experiments for the purpose of parameter estimation

Structural identifiability of dynamic systems biology models

22 páginas, 5 figuras, 2 tablas.-- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.A powerful way of gaining insight into biological systems is by creating a nonlinear differential equation model, which usually contains many unknown parameters. Such a model is called structurally identifiable if it is possible to determine the values of its parameters from measurements of the model outputs. Structural identifiability is a prerequisite for parameter estimation, and should be assessed before exploiting a model. However, this analysis is seldom performed due to the high computational cost involved in the necessary symbolic calculations, which quickly becomes prohibitive as the problem size increases. In this paper we show how to analyse the structural identifiability of a very general class of nonlinear models by extending methods originally developed for studying observability. We present results about models whose identifiability had not been previously determined, report unidentifiabilities that had not been found before, and show how to modify those unidentifiable models to make them identifiable. This method helps prevent problems caused by lack of identifiability analysis, which can compromise the success of tasks such as experiment design, parameter estimation, and model-based optimization. The procedure is called STRIKE-GOLDD (STRuctural Identifiability taKen as Extended-Generalized Observability with Lie Derivatives and Decomposition), and it is implemented in a MATLAB toolbox which is available as open source software. The broad applicability of this approach facilitates the analysis of the increasingly complex models used in systems biology and other areasAFV acknowledges funding from the Galician government (Xunta de Galiza, Consellería de Cultura, Educación e Ordenación Universitaria http://www.edu.xunta.es/portal/taxonomy/term/206) through the I2C postdoctoral program, fellowship ED481B2014/133-0. AB and AFV were partially supported by grant DPI2013-47100-C2-2-P from the Spanish Ministry of Economy and Competitiveness (MINECO). AFV acknowledges additional funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 686282 (CanPathPro). AP was partially supported through EPSRC projects EP/M002454/1 and EP/J012041/1.Peer reviewe

Data-driven reverse engineering of signaling pathways using ensembles of dynamic models

Signaling pathways play a key role in complex diseases such as cancer, for which the development of novel therapies is a difficult, expensive and laborious task. Computational models that can predict the effect of a new combination of drugs without having to test it experimentally can help in accelerating this process. In particular, network-based dynamic models of these pathways hold promise to both understand and predict the effect of therapeutics. However, their use is currently hampered by limitations in our knowledge of the underlying biochemistry, as well as in the experimental and computational technologies used for calibrating the models. Thus, the results from such models need to be carefully interpreted and used in order to avoid biased predictions. Here we present a procedure that deals with this uncertainty by using experimental data to build an ensemble of dynamic models. The method incorporates steps to reduce overfitting and maximize predictive capability. We find that by combining the outputs of individual models in an ensemble it is possible to obtain a more robust prediction. We report results obtained with this method, which we call SELDOM (enSEmbLe of Dynamic lOgic-based Models), showing that it improves the predictions previously reported for several challenging problems.JRB and DH acknowledge funding from the EU FP7 project NICHE (ITN Grant number 289384). JRB acknowledges funding from the Spanish MINECO project SYNBIOFACTORY (grant number DPI2014-55276-C5-2-R). AFV acknowledges funding from the Galician government (Xunta de Galiza) through the I2C postdoctoral fellowship ED481B2014/133-0. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.info:eu-repo/semantics/publishedVersio