Bayesian inference and modelling of gene expression dynamics

Student thesis: Phd

Abstract

The regulation of differentiation is essential for the growth and development of living organisms. Changes in the dynamic expression of certain genes have been associated with differentiation in multiple contexts, including development and cancer. For example, the dynamic expression of the basic helix-loop-helix transcription factors Hes5 and Her6, which are involved in neurogenesis in mice and zebrafish respectively, is mediated by auto-repressive feedback. This auto-repression, when coupled with delays, noise, and nonlinear interactions inherent to biological processes, gives rise to dynamic expression profiles, such as oscillations. Gene expression dynamics mediated by the auto-repressive feedback motif are influenced by a number of biochemical interactions, including transcription, translation, transcriptional repression and degradation. Therefore, differences in dynamic gene expression between cells that express Hes5 or Her6 may be due to variations in some or all of these interactions. The ability to perform live imaging of gene expression at single-cell resolution presents an opportunity to identify such variations using Bayesian inference methods. Bayesian inference allows us to estimate biophysical parameters by linking experimental data with mathematical models. However, Bayesian methods that combine stochasticity, delays, and nonlinearity have not been widely adopted. I present an approach for inferring parameters of an auto-negative feedback motif with delay using live-imaging time-series data. This method is applied to published data on murine neural progenitor cells, and the results are used to inform experimental design choices. I subsequently extend this approach and adopt a variational inference method in order to work with combined time-series data from multiple cells with similar dynamic expression. We see a drastic reduction in the uncertainty in our estimates, as well as speed improvements of multiple orders of magnitude. Importantly, our method provides concise and accurate estimates for multiple parameters, such as the production rates of mRNA and protein. In addition to auto-repression, Her6 dynamics are influenced by miR-9, a microRNA which acts on mRNA stability and protein translation. In a cross-disciplinary collaboration, we show that miR-9 increases in a sharp stepwise manner during zebrafish neurogenesis. To understand the impact of this mode of increase, I develop a mathematical model based on perfect adaptation and interactions between miR-9 and Her6. My results suggest that the stepwise increase facilitates the robustness of cell state transitions in the presence of small-scale fluctuations. The work in this thesis demonstrates the power of computational methods in interpreting data and understanding how changes in gene expression dynamics are regulated during development.
Date of Award31 Dec 2023
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorJochen Kursawe (Supervisor), Magnus Rattray (Supervisor) & Nancy Papalopulu (Supervisor)

Keywords

  • Stem cell differentiation
  • Variational inference
  • MCMC
  • Kalman filters
  • Bayesian methods
  • Parameter inference
  • Gene expression oscillations

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