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Abstract
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 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.
Highlights
Some biological systems are capable of maintaining an approximatively constant output despite environmental fluctuations
Given that deficiencies in identifiability may lead to wrong reconstructions of a system’s behaviour, and that parameter identification is an ubiquitous need in biological modelling, it is necessary to assess the structural identifiability of a model before using it to extract insights about the corresponding biological system
The fact that DC1 is essentially equivalent to structural unidentifiability when examined from the viewpoint of model identification, as noted in [19, 20], is a source of potential confusion: it opens the door to (i) interpreting as dynamical compensation what might be a case of structural unidentifiability, and to (ii) inadvertently using structurally unidentifiable models
Summary
Some biological systems are capable of maintaining an approximatively constant output despite environmental fluctuations. Karin et al [6] addressed the problem of finding mechanisms that allowed to maintain the transient response unchanged in the face of environmental disturbances To describe this phenomenon they coined the term dynamical compensation with respect to a parameter, which they defined as the property that the output of a system does not depend on the value of that parameter. Their estimated values are biologically meaningless [14], and the use of a structurally unidentifiable model for predicting the time course of system variables that cannot be directly measured can produce wrong results [15]. The correspondence between dynamical compensation and structural unidentifiability is relevant in realistic situations, in which the parameters of interest can be unknown
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