title: Comprehensive estimation of input signals and dynamics in biochemical reaction networks.
abstract: BACKGROUND
  Cellular information processing can be described mathematically using differential equations. Often, external stimulation of cells by compounds such as drugs or hormones leading to activation has to be considered. Mathematically, the stimulus is represented by a time-dependent input function. Parameters such as rate constants of the molecular interactions are often unknown and need to be estimated from experimental data, e.g. by maximum likelihood estimation. For this purpose, the input function has to be defined for all times of the integration interval. This is usually achieved by approximating the input by interpolation or smoothing of the measured data. This procedure is suboptimal since the input uncertainties are not considered in the estimation process which often leads to overoptimistic confidence intervals of the inferred parameters and the model dynamics.
  
  
  RESULTS
  This article presents a new approach which includes the input estimation into the estimation process of the dynamical model parameters by minimizing an objective function containing all parameters simultaneously. We applied this comprehensive approach to an illustrative model with simulated data and compared it to alternative methods. Statistical analyses revealed that our method improves the prediction of the model dynamics and the confidence intervals leading to a proper coverage of the confidence intervals of the dynamic parameters. The method was applied to the JAK-STAT signaling pathway.
  
  
  BACKGROUND
  MATLAB code is available on the authors' website http://www.fdmold.uni-freiburg.de/~schelker/.
  
  
  BACKGROUND
  max.schelker@fdm.uni-freiburg.de
  
  
  BACKGROUND
  Additional information is available at Bioinformatics Online.
authors.affiliation: Institute for Physics, University of Freiburg, D-79104 Freiburg, Germany. max.schelker@fdm.uni-freiburg.de
authors.forename: M
authors.initials: M
authors.lastname: Schelker
authors.forename: A
authors.initials: A
authors.lastname: Raue
authors.forename: J
authors.initials: J
authors.lastname: Timmer
authors.forename: C
authors.initials: C
authors.lastname: Kreutz
mesh_terms: D000465:Algorithms; D053612:Janus Kinases / Q000378:metabolism; D016013:Likelihood Functions; D008954:Models, Biological; D050791:STAT Transcription Factors / Q000378:metabolism; D015398:Signal Transduction
chemical_list: D050791:STAT Transcription Factors; D053612:Janus Kinases