The dose-dependent retarded transient function: a novel approach for modelling cellular signalling dynamics

Mathematical modelling is essential for understanding both intercellular and intracellular signalling processes. Currently, modelling in systems biology predominantly relies on ordinary differential equations (ODEs), e.g., for the modelling of signalling pathways. These mechanistic ODE models offer interpretability, but have certain limitations: it is necessary to include all pathway compounds, which results in complex, large-scale models that are numerically intensive and require extensive data that may not be available. Recently, the retarded transient function (RTF) was introduced as an alternative for modelling the temporal dynamics of signalling pathways. In this study, we enhance the RTF approach to incorporate concentration or dose dependencies, thus extending its applicability to the full application range of ODE models since this enhancement allows for both time- and dose-dependent predictions. With its intuitive parameters, it is providing a tool for exploring and comparing signalling across different biological conditions or cell types. To validate this extended RTF method, we apply it to data of time- and dose-dependent inflammasome activation in primary murine bone marrow-derived dendritic cells (BMDCs) treated with tyrosine kinase inhibitors. Our findings demonstrate that the extended RTF method is an effective, general framework for modelling dose- and time-dependent data for typical dynamics of cellular signalling. This approach offers clear interpretability of signal dynamics and enables predictive modelling of time- and dose-dependencies, even when only specific cellular components are measured. The developed method is accessible via the MATLAB-based modelling toolbox Data2Dynamics at https://github.com/Data2Dynamics, and a paper about it is currently under revision. As a second part of the thesis, the RTF approach is employed to achieve a low-dimensional representation of an ODE model. This representation facilitates the investigation of how specific pathway compounds' dynamics change under various biological conditions. By fitting the RTF to solutions of an existing ODE model and then using the estimated parameters for UMAP creation, we can visually cluster and compare the dynamics of different compounds and between dynamics for different conditions of the same compound. This method is applied to a published model of the NFκB signalling pathway, to illustrate how such low-dimensional representations of the dynamics of pathway components can be used for the investigation of different biological conditions. This analysis is feasible for a pathway condition in terms of external activation and also for characterizing the pathway response in terms of dependencies on the strength of the external activation. Together, the two parts of this work demonstrate the potential and versatility of the RTF approach for modelling of signalling processes and as a tool for the interpretation of ODE models.