2024-07-10 –, While Loop (4.2)
Biological systems often include complicated combinations of positive and negative feedback control. Recovering this control network is often difficult, because of both limitations in biological knowledge and available data. In this poster, we present the use of SciML's universal differential equation framework, uniquely available in Julia, for uncovering and personalising mathematical equations for biological modulation points and mechanisms.
Biological regulation is the result of the interplay between many molecules in a network of chemical reactions. Through mathematical modelling, parts of the system can be simulated in silico to quickly match biological hypotheses with experimental evidence.
However, many components of subsystems of human regulation are often unknown, or cannot be directly measured. Therefore, simplifications are required to keep the model both mathematically identifiable from the available data, as well as biologically meaningful. This process can take a long time, and simplified solutions may work on population averages, but fail more often when applied to personalised data directly.
Modelling unknown terms using a neural network, creating a universal differential equation (UDE), and combining this with symbolic regression can enable the data-driven discovery of mathematical model terms that describe the data.
This poster describes the systematic application of these universal differential equations in context of control loops and modulation points found in biological models, presenting the use of neural networks to both locate and recover missing modulation points in biological models. Furthermore, it highlights limitations of the inclusion of neural networks related to data sparsity and identifiability.
I’m a PhD candidate in systems biology for metabolic disease at the Department of Biomedical Engineering at Eindhoven University of Technology. I am working on model personalisation with scientific machine learning.