ODE modelling and hypothesis testing

Our roots come from mathematical modelling – where we use these models as a tool to analyze biological data and help us derive knowledge from the system. To be more precise, these models have generally been based on ordinary differential equations (ODEs). Following is a general overview of or modelling approach and how we typically work, for a more detailed explanation we refer the reader to one doctorial thesis of a previous PhD in our group, Model-Based Hypothesis Testing in Biomedicine: How Systems Biology Can Drive the Growth of Scientific Knowledge.

In practice, there are two key components to our modelling: experimental data and a mechanistic hypothesis. In contrast to black-box modelling, we strive for our mathematical models to be explainable and expand upon our biological knowledge. Therefore, the mechanistic hypothesis is of importance to ensure that the model describes the studied system. The experimental data's role is to validate the mechanistic hypotheses and can be of different formats, but time series are typically desired. To end up with a robust model more data is always better. In figure 1 down below, we can see a schematic overview of the iterative process of developing a model. The starting mechanistic explanation and experimental data are inputs to the process. As a first step, a model is developed to describe the behavior in the data. If an explanation is unable to describe the data, this hypothesis is rejected, and the mechanistic explanation needs to be revisited and reformulated. This loop continues until one or more mechanistic explanations can describe the data, and then we proceed to the core prediction analysis. Here, the value of big data comes to show, as we want to test our model against new data (validation data) that is unseen to the model. The idea is that if the model formulation is close to the true system, then the model hypothesis should be able to explain unseen data from different experiments (on the same system). Here, again, the hypothesis can be rejected as data might not be described and the iterative process continues. Once a model formulation passes this validation data, this is a core prediction. However, new data and hypotheses can always be added to further develop the model formulation, to come closer to a model formulation that can describe the true system.