Mathematical modeling improves EC50 estimations from classical dose-response curves

FEBS J. 2015 Mar;282(5):951-62. doi: 10.1111/febs.13194. Epub 2015 Feb 6.


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.

Database: The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database, and may be accessed at

Keywords: EC 50; adrenaline; cardiac β-adrenergic signaling; dynamic mathematical modeling; ordinary differential equations.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Adrenergic beta-Agonists / administration & dosage
  • Adrenergic beta-Agonists / pharmacology*
  • Animals
  • Chickens
  • Dose-Response Relationship, Drug*
  • Epinephrine / administration & dosage
  • Epinephrine / pharmacology
  • Models, Theoretical*
  • Muscle Contraction / drug effects


  • Adrenergic beta-Agonists
  • Epinephrine