Mathematical modeling improves EC50 estimations from classical dose–response curves

Elin Nyman, Isa Lindgren, William Lövfors, Karin Lundengård, Ida Cervin, Theresia Arbring Sjöström, Jordi Altimiras, Gunnar Cedersund

The beta-adrenergic response is impaired in failing hearts. When studying beta-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, but noted a decreasing response at high concentrations. The classical interpretation of such data would be to assume maximal response before the decrease and fit a sigmoid curve to the remaining data to determine EC50 . We have applied a mathematical modeling approach to instead interpret the full dose-response curve in a new way. The developed model predicts a non-steady-state caused by short resting time between increased concentrations of agonist, which affect the dose-response characterization. Therefore, an improved estimate of EC50 can be calculated using steady-state simulations of the model. The model-based estimation of EC50 is further refined with additional time-resolved data to decrease the uncertainty of the prediction. The resulting model-based EC50 (180-525 nM) is higher than the classical interpreted EC50 (46-191 nM). Mathematical modeling thus makes it possible to reinterpret already obtained datasets, and to make accurate estimates of EC50 even when steady-state measurements are not experimentally feasible. This article is protected by copyright. All rights reserved.