title: Mathematical modeling improves EC50 estimations from classical dose-response curves.
abstract: The β-adrenergic response is impaired in failing hearts. When studying β-adrenergic function in vitro, the half-maximal effective concentration (EC50 ) is an important measure of ligand response. We previously measured the in vitro contraction force response of chicken heart tissue to increasing concentrations of adrenaline, and observed a decreasing response at high concentrations. The classical interpretation of such data is to assume a maximal response before the decrease, and to fit a sigmoid curve to the remaining data to determine EC50 . Instead, we have applied a mathematical modeling approach to interpret the full dose-response curve in a new way. The developed model predicts a non-steady-state caused by a short resting time between increased concentrations of agonist, which affect the dose-response characterization. Therefore, an improved estimate of EC50 may be calculated using steady-state simulations of the model. The model-based estimation of EC50 is further refined using additional time-resolved data to decrease the uncertainty of the prediction. The resulting model-based EC50 (180-525 nm) is higher than the classically interpreted EC50 (46-191 nm). Mathematical modeling thus makes it possible to re-interpret previously obtained datasets, and to make accurate estimates of EC50 even when steady-state measurements are not experimentally feasible.
  
  
  METHODS
  The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database, and may be accessed at http://jjj.bio.vu.nl/database/nyman.
authors.affiliation: Integrative Systems Biology, Department of Biomedical Engineering, Linköping University, Linköping, Sweden; CVMD iMED DMPK AstraZeneca R&D, Mölndal, Sweden.
authors.forename: Elin
authors.initials: E
authors.lastname: Nyman
authors.forename: Isa
authors.initials: I
authors.lastname: Lindgren
authors.forename: William
authors.initials: W
authors.lastname: Lövfors
authors.forename: Karin
authors.initials: K
authors.lastname: Lundengård
authors.forename: Ida
authors.initials: I
authors.lastname: Cervin
authors.forename: Theresia Arbring
authors.initials: TA
authors.lastname: Sjöström
authors.forename: Jordi
authors.initials: J
authors.lastname: Altimiras
authors.forename: Gunnar
authors.initials: G
authors.lastname: Cedersund
mesh_terms: D000318:Adrenergic beta-Agonists / Q000008:administration & dosage / Q000494:pharmacology*; D000818:Animals; D002645:Chickens; D004305:Dose-Response Relationship, Drug; D004837:Epinephrine / Q000008:administration & dosage / Q000494:pharmacology; D008962:Models, Theoretical; D009119:Muscle Contraction / Q000187:drug effects
chemical_list: D000318:Adrenergic beta-Agonists; D004837:Epinephrine
keywords: EC
  50; adrenaline; cardiac β-adrenergic signaling; dynamic mathematical modeling; ordinary differential equations