Assessing the role of initial conditions in the local structural identifiability of large dynamic models (original) (raw)
Related papers
Structural Identifiability of Dynamic Systems Biology Models
PLoS computational biology, 2016
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 unidentifiabl...
Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods
PLoS ONE, 2011
Analysing the properties of a biological system through in silico experimentation requires a satisfactory mathematical representation of the system including accurate values of the model parameters. Fortunately, modern experimental techniques allow obtaining time-series data of appropriate quality which may then be used to estimate unknown parameters. However, in many cases, a subset of those parameters may not be uniquely estimated, independently of the experimental data available or the numerical techniques used for estimation. This lack of identifiability is related to the structure of the model, i.e. the system dynamics plus the observation function. Despite the interest in knowing a priori whether there is any chance of uniquely estimating all model unknown parameters, the structural identifiability analysis for general non-linear dynamic models is still an open question. There is no method amenable to every model, thus at some point we have to face the selection of one of the possibilities. This work presents a critical comparison of the currently available techniques. To this end, we perform the structural identifiability analysis of a collection of biological models. The results reveal that the generating series approach, in combination with identifiability tableaus, offers the most advantageous compromise among range of applicability, computational complexity and information provided.
Bioinformatics, 2009
Motivation: Mathematical description of biological reaction networks by differential equations leads to large models whose parameters are calibrated in order to optimally explain experimental data. Often only parts of the model can be observed directly. Given a model that sufficiently describes the measured data, it is important to infer how well model parameters are determined by the amount and quality of experimental data. This knowledge is essential for further investigation of model predictions. For this reason a major topic in modeling is identifiability analysis. Results: We suggest an approach that exploits the profile likelihood. It enables to detect structural non-identifiabilities, which manifest in functionally related model parameters. Furthermore, practical non-identifiabilities are detected, that might arise due to limited amount and quality of experimental data. Last but not least confidence intervals can be derived. The results are easy to interpret and can be used f...
Comparison of approaches for parameter identifiability analysis of biological systems
Bioinformatics, 2014
Modeling of dynamical systems using ordinary differential equations is a popular approach in the field of Systems Biology. The amount of experimental data that are used to build and calibrate these models is often limited. In this setting, the model parameters may not be uniquely determinable. Structural or a priori identifiability is a property of the system equations that indicates whether, in principle, the unknown model parameters can be determined from the available data. We performed a case study using three current approaches for structural identifiability analysis for an application from cell biology. The approaches are conceptually different and are developed independently. The results of the three approaches are in agreement. We discuss strength and weaknesses of each of them and illustrate how they can be applied to real world problems. For application of the approaches to further applications, code representations (DAISY, Mathematica and MATLAB) for benchmark model and data are provided on the authors webpage. andreas.raue@fdm.uni-freiburg.de.
Methods for Checking Structural Identifiability of Nonlinear Biosystems: A Critical Comparison
Proceedings of the 18th IFAC World Congress, 2011
Model parametric identification is a critical yet often overlooked step for the modelling of biosystems. Modern experimental techniques can be used to obtain time-series data which may then be used to estimate model parameters. However, in many cases, a subset of model parameters may not be uniquely estimated, independently of the quantity and quality of data available or the numerical techniques used for estimation. This lack of identifiability is related to the structure of the model. This work presents a review and a critical comparison of methods to analyze the structural identifiability of non-linear models. Three examples, of increasing level of complexity, related to the modelling of biochemical networks, will be used to illustrate advantages and disadvantages of the available techniques. Results reveal that the generating series approach combined with the identifiability tableau is the most promising to analyze large scale highly nonlinear models.
Identifiability and Regression Analysis of Biological Systems Models
SpringerBriefs in Statistics, 2020
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
A new computational tool for establishing model parameter identifiability
2009
Abstract We describe a novel method to establish a priori whether the parameters of a nonlinear dynamical system are identifiable—that is, whether they can be deduced from output data (experimental observations). This is an important question as usually identifiability is assumed, and parameters are sought without first establishing whether these can be inferred from a set of measurements. We highlight the connections between parameter identifiability and state observability.
Determination of parameter identifiability in nonlinear biophysical models: A Bayesian approach
The Journal of General Physiology, 2014
A major goal of biophysics is to understand the physical mechanisms of biological molecules and systems. Mechanistic models are evaluated based on their ability to explain carefully controlled experiments. By fitting models to data, biophysical parameters that cannot be measured directly can be estimated from experimentation. However, it might be the case that many different combinations of model parameters can explain the observations equally well. In these cases, the model parameters are not identifiable: the experimentation has not provided sufficient constraining power to enable unique estimation of their true values. We demonstrate that this pitfall is present even in simple biophysical models. We investigate the underlying causes of parameter non-identifiability and discuss straightforward methods for determining when parameters of simple models can be inferred accurately. However, for models of even modest complexity, more general tools are required to diagnose parameter non-...
AMIGO, a toolbox for advanced model identification in systems biology using global optimization
Bioinformatics, 2011
Motivation: Mathematical models of complex biological systems usually consist of sets of differential equations which depend on several parameters which are not accessible to experimentation. These parameters must be estimated by fitting the model to experimental data. This estimation problem is very challenging due to the non-linear character of the dynamics, the large number of parameters and the frequently poor information content of the experimental data (poor practical identifiability). The design of optimal (more informative) experiments is an associated problem of the highest interest. Results: This work presents AMIGO, a toolbox which facilitates parametric identification by means of advanced numerical techniques which cover the full iterative identification procedure putting especial emphasis on robust methods for parameter estimation and practical identifiability analyses, plus flexible capabilities for optimal experimental design.
GenSSI 2.0: multi-experiment structural identifiability analysis of SBML models
Bioinformatics, 2017
Motivation Mathematical modeling using ordinary differential equations is used in systems biology to improve the understanding of dynamic biological processes. The parameters of ordinary differential equation models are usually estimated from experimental data. To analyze a priori the uniqueness of the solution of the estimation problem, structural identifiability analysis methods have been developed. Results We introduce GenSSI 2.0, an advancement of the software toolbox GenSSI (Generating Series for testing Structural Identifiability). GenSSI 2.0 is the first toolbox for structural identifiability analysis to implement Systems Biology Markup Language import, state/parameter transformations and multi-experiment structural identifiability analysis. In addition, GenSSI 2.0 supports a range of MATLAB versions and is computationally more efficient than its previous version, enabling the analysis of more complex models. Availability and implementation GenSSI 2.0 is an open-source MATLAB...