Kinetic models based on ordinary differential equations (ODEs) are widely used to study the dynamics of mRNA/pre-mRNA and proteins/mRNA interactions. These models provide valuable insights into gene expression regulation. In this talk, I will present an enhanced approach to ODE modelling by incorporating Gaussian processes. By extending ODEs with Gaussian processes and assuming a Gaussian likelihood, the system of ODEs can be represented as a Gaussian process with biologically interpretable hyperparameters. This enables us to capture additional complexities in the modelling process. Moreover, I will discuss two extensions. Firstly, I will explain how this approach can account for data overdispersion by adopting negative binomial likelihood, although at the expense of losing analytical tractability. Nonetheless, we can employ variational inference techniques to approximate the posterior distribution of interest. Secondly, I will explore the incorporation of change point kernels to model time variation in the parameters.
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