Efficient parameter estimation for ODE models of cellular processes using semi-quantitative data

Quantitative dynamical models facilitate the understanding of biological processes and the prediction of their dynamics. The parameters of these models are commonly estimated from experimental data. Yet, experimental data generated from different techniques do not provide direct information about the state of the system but a non-linear (monotonic) transformation of it. For such semi-quantitative data, when this transformation is unknown, it is not apparent how the model simulations and the experimental data can be compared. Here, we propose a versatile spline-based approach for the integration of a broad spectrum of semi-quantitative data into parameter estimation. We derive analytical formulas for the gradients of the hierarchical objective function and show that this substantially increases the estimation efficiency. Subsequently, we demonstrate that the method allows for the reliable discovery of unknown measurement transformations. Furthermore, we show that this approach can significantly improve the parameter inference based on semi-quantitative data in comparison to available methods. Modelers can easily apply our method by using our implementation in the open-source Python Parameter EStimation TOolbox (pyPESTO). ### Competing Interest Statement The authors have declared no competing interest.