# Dynamical compensation and structural identifiability of biological models: Analysis, implications, and reconciliation

@article{Villaverde2017DynamicalCA, title={Dynamical compensation and structural identifiability of biological models: Analysis, implications, and reconciliation}, author={Alejandro Fern{\'a}ndez Villaverde and Julio R. Banga}, journal={PLoS Computational Biology}, year={2017}, volume={13} }

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. However, the original definition of dynamical compensation amounts to lack of structural identifiability. This is relevant if model parameters need to be estimated, as is often the case in biological modelling. Care should we taken when using an unidentifiable model to extract biological insight: the estimated…

## 20 Citations

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## References

SHOWING 1-10 OF 48 REFERENCES

Dynamical compensation in biological systems as a particular case of structural non-identifiability

- BiologyArXiv
- 2017

It is argued that the similitude between DC and Structural Identifiability (SI) can be explained in terms of (lack of) the latter, and it is proposed to exploit this fact by using currently existing tools for SI analysis to perform DC analysis.

Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood

- Computer ScienceBioinform.
- 2009

This work suggests an approach that exploits the profile likelihood that enables to detect structural non-identifiabilities, which manifest in functionally related model parameters, that might arise due to limited amount and quality of experimental data.

Structural Identifiability of Dynamic Systems Biology Models

- Computer SciencePLoS Comput. Biol.
- 2016

This paper shows how to analyse the structural identifiability of a very general class of nonlinear models by extending methods originally developed for studying observability by implementing STRIKE-GOLDD, a method implemented in a MATLAB toolbox.

Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods

- MathematicsPloS one
- 2011

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.

A note on dynamical compensation and its relation to parameter identifiability

- MathematicsbioRxiv
- 2017

This work clarifies the apparent discrepancy by requiring that the parameters of DC circuits be identifiable both away from steady-state and when measuring other system variables.

Parameter and structural identifiability concepts and ambiguities: a critical review and analysis.

- BiologyThe American journal of physiology
- 1980

The importance of identifiability analysis prior to performing a parameter estimation experiment, the algebraic difficulties, possible pitfalls, and not-so-apparent ambiguities that may be encountered--even for simple models--and the utility of the concept in experiment design are illustrated.

Comparison of approaches for parameter identifiability analysis of biological systems

- Computer ScienceBioinform.
- 2014

A case study using three current approaches for structural identifiability analysis for an application from cell biology, discussing strength and weaknesses of each of them and illustrating how they can be applied to real world problems.

Parameter Identifiability of Fundamental Pharmacodynamic Models

- MathematicsFront. Physiol.
- 2016

Issues of parameter identifiability of routinely used pharmacodynamics models are considered and a case study was performed applying an unidentifiable model to real experimental data to show how performing such an analysis prior to parameter estimation can improve the parameter estimation process and model performance.

Delineating parameter unidentifiabilities in complex models.

- Computer SciencePhysical review. E
- 2017

This work describes a scalable method for detecting unidentifiabilities, as well as the functional relations defining them, for generic models, and demonstrates the duality between multiscale sloppiness and the geometry of confidence regions surrounding parameter estimates made where measurement uncertainty is non-negligible.

Higher-order Lie symmetries in identifiability and predictability analysis of dynamic models.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

A direct search algorithm is established for the determination of admitted Lie group symmetries and it is shown how models with nonidentifiable parameters can still be employed to make reliable predictions.