title: Estimating confidence intervals in predicted responses for oscillatory biological models.
abstract: BACKGROUND
  The dynamics of gene regulation play a crucial role in a cellular control: allowing the cell to express the right proteins to meet changing needs. Some needs, such as correctly anticipating the day-night cycle, require complicated oscillatory features. In the analysis of gene regulatory networks, mathematical models are frequently used to understand how a network's structure enables it to respond appropriately to external inputs. These models typically consist of a set of ordinary differential equations, describing a network of biochemical reactions, and unknown kinetic parameters, chosen such that the model best captures experimental data. However, since a model's parameter values are uncertain, and since dynamic responses to inputs are highly parameter-dependent, it is difficult to assess the confidence associated with these in silico predictions. In particular, models with complex dynamics - such as oscillations - must be fit with computationally expensive global optimization routines, and cannot take advantage of existing measures of identifiability. Despite their difficulty to model mathematically, limit cycle oscillations play a key role in many biological processes, including cell cycling, metabolism, neuron firing, and circadian rhythms.
  
  
  RESULTS
  In this study, we employ an efficient parameter estimation technique to enable a bootstrap uncertainty analysis for limit cycle models. Since the primary role of systems biology models is the insight they provide on responses to rate perturbations, we extend our uncertainty analysis to include first order sensitivity coefficients. Using a literature model of circadian rhythms, we show how predictive precision is degraded with decreasing sample points and increasing relative error. Additionally, we show how this method can be used for model discrimination by comparing the output identifiability of two candidate model structures to published literature data.
  
  
  CONCLUSIONS
  Our method permits modellers of oscillatory systems to confidently show that a model's dynamic characteristics follow directly from experimental data and model structure, relaxing assumptions on the particular parameters chosen. Ultimately, this work highlights the importance of continued collection of high-resolution data on gene and protein activity levels, as they allow the development of predictive mathematical models.
authors.affiliation: Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-5080, USA.
authors.forename: Peter C
authors.initials: PC
authors.lastname: St John
authors.forename: Francis J
authors.initials: FJ
authors.lastname: Doyle
mesh_terms: D019295:Computational Biology / Q000379:methods*; D005786:Gene Expression Regulation; D008954:Models, Biological; D010507:Periodicity; D035501:Uncertainty
references.citation: Biotechnol Bioeng. 1977 Dec;19(12):1831-50
references.pmid: 563249
references.citation: Hum Mol Genet. 2006 Oct 15;15 Spec No 2:R271-7
references.pmid: 16987893
references.citation: PLoS Comput Biol. 2007 Oct;3(10):1871-78
references.pmid: 17922568
references.citation: Proc Natl Acad Sci U S A. 2008 Dec 30;105(52):20746-51
references.pmid: 19104043
references.citation: Science. 2012 Aug 31;337(6098):1094-7
references.pmid: 22798407
references.citation: Cell. 2001 Dec 28;107(7):855-67
references.pmid: 11779462
references.citation: PLoS Biol. 2010 Dec 14;8(12):e1000559
references.pmid: 21179498
references.citation: Metab Eng. 2006 Sep;8(5):447-55
references.pmid: 16793301
references.citation: PLoS Genet. 2009 Apr;5(4):e1000442
references.pmid: 19343201
references.citation: Nat Rev Neurosci. 2007 Oct;8(10):790-802
references.pmid: 17882255
references.citation: Proc Natl Acad Sci U S A. 2003 Jun 10;100(12):7051-6
references.pmid: 12775757
references.citation: Bioinformatics. 2009 Aug 1;25(15):1923-9
references.pmid: 19505944
references.citation: Cell. 2009 Oct 2;139(1):199-210
references.pmid: 19765810
references.citation: Proc Natl Acad Sci U S A. 2003 Dec 9;100(25):14806-11
references.pmid: 14657377
references.citation: Proc Natl Acad Sci U S A. 2009 Jul 7;106(27):11107-12
references.pmid: 19549830
references.citation: SIAM J Sci Comput. 2009 Jun;31(4):2706-2732
references.pmid: 23296349
references.citation: Genome Res. 2003 Nov;13(11):2396-405
references.pmid: 14597654