Abstract
A recent paper by Karin et al. introduced a mathematical notion called dynamical compensation (DC) of biological circuits. DC was shown to play an important role in glucose homeostasis as well as other key physiological regulatory mechanisms. Karin et al. went on to provide a sufficient condition to test whether a given system has the DC property. Here, we show how DC can be formulated in terms of a well-known concept in systems biology, statistics, and control theory—that of parameter structural non-identifiability. Viewing DC as a parameter identification problem enables one to take advantage of powerful theoretical and computational tools to test a system for DC. We obtain as a special case the sufficient criterion discussed by Karin et al. We also draw connections to system equivalence and to the fold-change detection property.
Highlights
The recent paper [1] argued that physiological control systems should ensure a precise dynamical response despite variations in certain parameters, lest pathological conditions arise
A recently introduced mathematical notion called dynamical compensation of biological circuits was shown to play an important role in glucose homeostasis and other key physiological regulatory mechanisms
This paper explains how dynamical compensation can be formulated in terms of a well-known concept in systems biology, statistics, and control theory—that of parameter structural non-identifiability
Summary
The recent paper [1] argued that physiological control systems should ensure a precise dynamical response despite variations in certain parameters, lest pathological conditions arise. The authors highlighted the biological significance of this robustness property through the analysis of several biological systems, including models of plasma glucose response in the face of changes in insulin sensitivity, parathyroid hormone control of calcium homeostasis, and arterial oxygen regulation in response to hypoxia. They formally introduced the system property of dynamical compensation (DC) with respect to variations in a parameter p, meaning that the complete output dynamics is exactly the same, for any time dependent input, independently of the precise value of p. From the systems and parameter identification (“reverse engineering”) point of view, the more that a parameter affects behavior, the easier it is to estimate it, and poor sensitivity is taken as an indication of a poorly parametrized model
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