Mathematical framework for analysing and improving the controllability of gene regulatory networks

The disruption of gene regulation is often a hallmark of weakened cellular control, and renders organisms predisposed to numerous complex diseases. The ability to characterise and quantify this phenomenon within a mathematical framework will improve our understanding of the causality relationships between what happens within the cell and how the cellular rewiring manifests itself in the form of a phenotype. Such an understanding could then be employed for systematic testing and identification of possible intervention points for the treatment of complex diseases, which constitute nearly all human disorders that display high prevalence.

A quantitative genetics theory should link genetic variation to phenotypic variation in a causally cohesive way based on how genes work and interact. This necessitates the adoption of a theoretical framework for predicting and understanding the manifestation of genetic variation in regulatory networks with feedback structures and functional dependencies. Through networks and graph theory, a propagation function can describe how genetic variation is propagated through the network and show how their derivatives are related to the network's feedback structure. Similarly, feedback functions can describe the effect of genotypic variation of a gene on itself, either directly or mediated by the network.

Our current investigation of gene regulatory networks (GRNs) relies on how gene expression is affected by a set of regulatory inputs specified by interactions between proteins and DNA. These networks are comprised of two different types of nodes; genes and proteins; may even comprise a gene and the protein encoded from that same gene simultaneously, necessitating a clear need for bi-modality, and the information flow in the interactions represented in these networks has a direction. These unique characteristics render their analysis challenging, and substantially limited to the utilisation of standard graph theoretical methods that focus on network structure.

This project aims to address this challenge by moving away from structural GRN analysis towards formulating a quantitative framework: The goal is to develop an alternative strategy by modelling the relationship between genes using ordinary differential equations, which will allow changes in the expression of a gene to propagate to other genes along paths in the network by taking into account the strengths of the interactions between genes and their transcription factors. The proposed approach mimics the modelling of ecological food web networks through community (Jacobian) matrices. The construction of this matrix will allow a platform to conduct the stability analysis of these networks through positive and negative feedback loops, in order to explore gene-regulatory protein dependencies at the global scale.

The mathematical framework for analysing mammalian gene regulatory networks, which will be developed, will be readily available for addressing drug target identification problems as described above. The tool will then be integrated with mathematical frameworks that are available for analysing metabolic pathways such as dynamic flux balance analysis and metabolic control analysis to extend the capabilities of model-based investigation of cellular events. There is a growing interest in utilising information available at the cellular in the implementation of smart control actions to ensure robust upstream bioprocessing. The modelling frameworks described here will be used to feed into these bioprocess control actions.
This project is in alignment with the following research theses and current research priorities of EPSRC: Research themes of healthcare technologies and manufacturing the future, and with the following research areas: Biological informatics, manufacturing technologies, mathematical biology, and operational research. It also aligns with EPSRC's current research priorities in Digital Manufacturing and Sustainable Industries