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

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 469 ◽  
Author(s):  
Gemma Massonis ◽  
Alejandro F. Villaverde
Keyword(s):  
Nonlinear Models ◽  
Rational Functions ◽  
Lie Symmetries ◽  
Structural Identifiability ◽  
Unknown Parameters ◽  
Identifiability Analysis ◽  
Model Equations ◽  
Rational Expressions ◽  
Model Reformulation ◽  
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.

scholarly journals SIAN: software for structural identifiability analysis of ODE models

2019 ◽  
Vol 35 (16) ◽  
pp. 2873-2874 ◽  
Author(s):  
Hoon Hong ◽  
Alexey Ovchinnikov ◽  
Gleb Pogudin ◽  
Chee Yap
Keyword(s):  
Open Source Software ◽  
A Priori ◽  
Supplementary Information ◽  
Biological Processes ◽  
Structural Identifiability ◽  
Unknown Parameters ◽  
Identifiability Analysis ◽  
Ode Models ◽  
Free Data ◽  
Continuous Noise

Abstract Summary Biological processes are often modeled by ordinary differential equations with unknown parameters. The unknown parameters are usually estimated from experimental data. In some cases, due to the structure of the model, this estimation problem does not have a unique solution even in the case of continuous noise-free data. It is therefore desirable to check the uniqueness a priori before carrying out actual experiments. We present a new software SIAN (Structural Identifiability ANalyser) that does this. Our software can tackle problems that could not be tackled by previously developed packages. Availability and implementation SIAN is open-source software written in Maple and is available at https://github.com/pogudingleb/SIAN. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals GenSSI 2.0: multi-experiment structural identifiability analysis of SBML models

2017 ◽  
Vol 34 (8) ◽  
pp. 1421-1423 ◽  
Author(s):  
Thomas S Ligon ◽  
Fabian Fröhlich ◽  
Oana T Chiş ◽  
Julio R Banga ◽  
Eva Balsa-Canto ◽  
...  
Keyword(s):  
Structural Identifiability ◽  
Identifiability Analysis ◽  
Structural Identifiability Analysis

scholarly journals Full observability and estimation of unknown inputs, states and parameters of nonlinear biological models

2019 ◽  
Vol 16 (156) ◽  
pp. 20190043 ◽  
Author(s):  
Alejandro F. Villaverde ◽  
Nikolaos Tsiantis ◽  
Julio R. Banga
Keyword(s):  
Recent Literature ◽  
State Parameter ◽  
Identification Problem ◽  
Input State ◽  
Biological Models ◽  
Theoretical Possibility ◽  
Model Equations ◽  
Differential Equations Models ◽  
Biological Modelling ◽  
Simultaneous Assessment

In this paper, we address the system identification problem in the context of biological modelling. We present and demonstrate a methodology for (i) assessing the possibility of inferring the unknown quantities in a dynamic model and (ii) effectively estimating them from output data. We introduce the term Full Input-State-Parameter Observability (FISPO) analysis to refer to the simultaneous assessment of state, input and parameter observability (note that parameter observability is also known as identifiability). This type of analysis has often remained elusive in the presence of unmeasured inputs. The method proposed in this paper can be applied to a general class of nonlinear ordinary differential equations models. We apply this approach to three models from the recent literature. First, we determine whether it is theoretically possible to infer the states, parameters and inputs, taking only the model equations into account. When this analysis detects deficiencies, we reformulate the model to make it fully observable. Then we move to numerical scenarios and apply an optimization-based technique to estimate the states, parameters and inputs. The results demonstrate the feasibility of an integrated strategy for (i) analysing the theoretical possibility of determining the states, parameters and inputs to a system and (ii) solving the practical problem of actually estimating their values.

Comment on "Parameter and structural identifiability concepts and ambiguities: a critical review and analysis"

1982 ◽  
Vol 242 (5) ◽  
pp. R421-R422
Author(s):  
K. R. Godfrey
Keyword(s):  
Glucose Tolerance ◽  
Laplace Transform ◽  
Glucose Tolerance Test ◽  
Transfer Functions ◽  
External Perturbation ◽  
Tolerance Test ◽  
Structural Identifiability ◽  
Identifiability Analysis ◽  
The Laplace Transform ◽  
The Individual

Identifiability of a model for the glucose tolerance test, considered by Cobelli and DiStefano [Am. J. Physiol. 239 (Regulatory Integrative Comp. Physiol. 8): R7-R24, 1980], is shown to depend on the shape of the external perturbation. For systems with two or more inputs applied simultaneously, it is essential in Laplace transform identifiability analysis to examine the Laplace transform(s) of the observation(s) rather than the individual transfer functions, which are not measurable separately.

scholarly journals An Optimal Estimation Method for Nonlinear Models of Mechanical Systems

1994 ◽  
Vol 116 (4) ◽  
pp. 805-810 ◽  
Author(s):  
M. J. G. van de Molengraft ◽  
F. E. Veldpaus ◽  
J. J. Kok
Keyword(s):  
Nonlinear Models ◽  
A Priori ◽  
Mechanical Systems ◽  
Estimation Method ◽  
Optimal Estimation ◽  
Model Structure ◽  
Unknown Parameters ◽  
Starting Point ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical Systems

This paper presents an optimal estimation method for nonlinear mechanical systems. The a priori knowledge of the system in the form of a nonlinear model structure is taken as a starting point. The method determines estimates of the parameters and estimates of the positions, velocities, accelerations, and inputs of the system. The optimal estimation method is applied to an experimental mechanical system. The unknown parameters in this system relate to inertia, friction and elastic deformation. It is shown that the optimal estimation method on the basis of a relatively simple model structure can lead to a useful description of the system.

scholarly journals Structural identifiability analysis of a cardiovascular system model

2016 ◽  
Vol 38 (5) ◽  
pp. 433-441 ◽  
Author(s):  
Antoine Pironet ◽  
Pierre C. Dauby ◽  
J. Geoffrey Chase ◽  
Paul D. Docherty ◽  
James A. Revie ◽  
...  
Keyword(s):  
Cardiovascular System ◽  
System Model ◽  
Structural Identifiability ◽  
Identifiability Analysis ◽  
Cardiovascular System Model ◽  
Structural Identifiability Analysis

scholarly journals Identifiability analysis for models of the translation kinetics after mRNA transfection

2021 ◽  
Author(s):  
Susanne Pieschner ◽  
Jan Hasenauer ◽  
Christiane Fuchs
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Ode Model ◽  
Kinetic Rate ◽  
Identifiability Analysis ◽  
Parameter Identifiability ◽  
Ode Models ◽  
Kinetic Rate Constants ◽  
Mrna Transfection ◽  
Model Equations

Mechanistic models are a powerful tool to gain insights into biological processes. The parameters of such models, e.g. kinetic rate constants, usually cannot be measured directly but need to be inferred from experimental data. In this article, we study dynamical models of the translation kinetics after mRNA transfection and analyze their parameter identifiability. Previous studies have considered ordinary differential equation (ODE) models of the process, and here we formulate a stochastic differential equation (SDE) model. For both model types, we consider structural identifiability based on the model equations and practical identifiability based on simulated as well as experimental data and find that the SDE model provides better parameter identifiability than the ODE model. Moreover, our analysis shows that even for those parameters of the ODE model that are considered to be identifiable, the obtained estimates are sometimes unreliable. Overall, our study clearly demonstrates the relevance of considering different modeling approaches and that stochastic models can provide more reliable and informative results.

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