Mathematical models of RNA and protein dynamics and their integration with gene expression data

A gene regulatory network involves a set of genes interacting with each other to control cellular functions. For example, in autoregulation, a protein expressed from a gene activates or suppresses its own transcription, thereby regulating the number of proteins through negative or positive feedback [1].

Mathematical models of stochastic gene expression have provided insight into how intrinsic noise (due to transcriptional and translational processes) can be controlled via feedback mechanisms [1]. These models also have shown how noise can generate oscillations and multi-stable states. However, these models ignore important sources of fluctuations such as those due to cell growth, cell division, DNA replication and cell size dependent transcription.

In this project, the student will build on recent advances [2] to construct a detailed stochastic model of gene regulation that includes these noise sources. A first aim is the approximate analytical solution of this stochastic model and its use to precisely quantify how each different source of noise contributes to emergent phenomena observed at the single-cell level.

A secondary aim is to obtain a reduced version of this detailed model by the modification of recently proposed AI techniques [3]. A final aim involves the use of the analytical solution within a Bayesian inference framework to estimate the parameters of gene regulatory networks from single cell data.

The project will give the student a solid foundation in the basic molecular biology of transcription, and its modelling using stochastic simulations, the chemical master equation and techniques from machine learning.