Systems biology is largely becoming transformed by the fourth industrial revolution; the integration of artificial intelligence and machine-learning within scientific research practice. Parameter estimation within enzyme kinetics entails determining the values of the parameters in a kinetic model that best fit the experimental data. However, experimentally, this process can be laborious, prone to error, and expensive. Therefore, a machine-learning system approach might provide some benefits.

We here address these challenges by implementing the use of Neural Differential Equations (NDEs) for modeling experimental enzymatic time series data, using the phosphoglycerate mutase (PGM) and enolase enzymes in the glycolytic pathway as an example model system. NDEs combine deep learning with differential equations by modeling the change of a neural network’s unknown position repeatedly over time. This allows the handling of convoluted, irregular and time-dependent time series data. This research utilized 52 experimental time-series datasets from our own laboratory. Validation of the NDE models is performed through classic machine learning procedures in order to test integrity and reliability. This includes a 20/80 test/train dataset split, to evaluate model performance, cross validation using k-fold cross validation methods as well as comparisons to established baseline models.

NDEs present numerous advantages in comparison to traditional Bayesian parameter estimation techniques. These include greater efficiency, enhanced scalability for handling large and complex datasets and the ability to accurately represent and capture underlying processes of dynamical systems in a continuous manner.

This research utilizes the application of Catalax, a JAX-based framework developed by Jan Range at the University of Stuttgart, Germany, which supports simulation and parameter inference through Bayesian parameter estimation. Catalax leverages Markov Chain Monte Carlo (MCMC) sampling to infer posterior distributions of model parameters with the inclusion of the training framework for the NDEs.