Dynamic modelling of signalling pathways when ODEs are not feasible

Abstract

AbstractMotivationMathematical modelling plays a crucial role in understanding of inter- and intracellular signalling processes. Currently, ordinary differential equations (ODEs) are the predominant approach utilized in systems biology for modelling such pathways. While such mechanistic ODE models offer interpretability, they also suffer from limitations, including the need to consider all relevant compounds, resulting in large models that are difficult to handle numerically and require extensive data.ResultsIn our previous work, we introduced theretarded transient function (RTF)as an alternative method for modelling the temporal response of signalling pathways. In this work, we extend the RTF approach to also integrate concentration or dose-dependencies of dynamics to fully cover the application range of ordinary differential equation (ODE) models. This extension enables time- and dose-dependent predictions and offers an intuitive means to investigate and characterize signalling differences between biological conditions or cell types. To demonstrate the applicability of our extended RTF approach, we employ data from time- and dose-dependent inflammasome activation in primary murine bone marrow-derived dendritic cells (BMDCs) treated with tyrosine kinase inhibitors. Our results show the effectiveness of the extended RTF approach as a generic framework for modelling dose-dependent kinetic data as they typically occur in cellular signalling. The presented approach offers intuitive interpretability of signal dynamics and enables predictive modelling of time- and dose-dependencies even if only individual cellular components are quantified.AvailabilityThe presented approach is available within the MATLAB-basedData2Dynamicsmodelling toolbox athttps://github.com/Data2Dynamicsand as R code athttps://github.com/kreutz-lab/RTF.Contactclemens.kreutz@uniklinik-freiburg.de