Dynamic compensation, parameter identifiability, and equivariances. Sontag, E. PLoS Computational Biology, 13:e1005447, 2017. Preprint was in bioRxiv https://doi.org/0.1101/095828, 2016.
Dynamic compensation, parameter identifiability, and equivariances [link]Paper  abstract   bibtex   
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 is a reformulation 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.
@ARTICLE{plos2017_dynamic_compensation,
   AUTHOR       = {E.D. Sontag},
   JOURNAL      = {PLoS Computational Biology},
   TITLE        = {Dynamic compensation, parameter identifiability, and 
      equivariances},
   YEAR         = {2017},
   OPTMONTH     = {},
   NOTE         = {Preprint was in bioRxiv https://doi.org/0.1101/095828, 2016.},
   OPTNUMBER    = {},
   PAGES        = {e1005447},
   VOLUME       = {13},
   KEYWORDS     = {fcd, fold-change detection, scale invariance, 
      dynamic compensation, identifiability, observability},
   URL          = {https://doi.org/10.1371/journal.pcbi.1005447},
   PDF          = {../../FTPDIR/dynamic_compensation_parameter_identifiability_equivariances_sontag_plos2017.pdf},
   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 is a reformulation 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.}
}

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