Gaussian Process Models for Systems Identification with Applications in Systems Biology

Our goal in this project is to develop and apply new methods for inferring the parameters of mechanistic models of systems and apply these methods in a biological context in order to uncover the mechanisms of transcriptional regulation. This goal will be achieved by unifying two different approaches to network analysis: the 'systems approach' of specifying differential equation models of transcription and the 'computational approach' of constructing probabilistic models of data. The 'systems biology approach' to modelling normally involves specifying a differential equation model of the network. In differential equation models, network interactions are represented by parameterised functions that control rates of production, degradation and transformation of network components.The 'computational biology approach' to modelling normally involves specifying a simpler model of the network interactions (in the simplest case a linear model is used). The parameters of the model are then inferred in a data driven manner. An advantage of the computational biology approach is that the models are often simpler and thereby amenable to a rigorous probabilistic treatment. A disadvantage of the computational approach is that the models do not capture the more subtle interactions in the networks.In this project we aim to bring the latest techniques in probabilistic modelling together with state of the art differential equation models together in a rigorous probabilistic manner allowing principled inference of model parameters in a realistic time frame. This will be achieved through the use of Gaussian process prior distributions on functions of interest, in particular protein concentrations.