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Modelling and analysis of oscillations in gene expression through neural development

Phillips, Nick

[Thesis]. Manchester, UK: The University of Manchester; 2016.

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Abstract

The timing of differentiation underlies the development of any organ system. In neural development, the expression of the transcription factor Hes1 has been shown to be oscillatory in neural progenitors, but at a low steady state in differentiated neurons. This change in the dynamics of expression marks the timing of differentiation. We previously constructed a mathematical model to test the experimental hypothesis that the topology of the miR-9/Hes1 network and specifically the accumulation of the micro-RNA, miR-9, could terminate Hes1 oscillations and account for the timing of neuronal differentiation, using deterministic delay differential equations.However, biochemical reactions are the result of random encounters between discrete numbers of molecules, and some of these molecules may be present at low numbers. The finite number of molecules interacting within the system leads to inherent randomness, and this is known as intrinsic stochasticity. The stochastic model predicts that low molecular number causes the time to differentiation to be distributed, which is in agreement with recent experimental evidence and considered important to generate cell type diversity. For the exact same model, fewer reacting molecules causes a decrease in the average time to differentiation, showing that the number of molecules can systematically change the timing of differentiation.Oscillations are important for a wide range of biological processes, but current methods for discovering oscillatory genes have primarily been designed for measurements performed on a population of cells. We introduce a new approach for analysing biological time series data designed for cases where the underlying dynamics of gene expression is inherently noisy at a single cell level. Our analysis method combines mechanistic stochastic modelling with the powerful methods of Bayesian nonparametric regression, and can distinguish oscillatory expression in single cell data from random fluctuations of nonoscillatory gene expression, despite peak-to-peak variability in period and amplitude of single cell oscillations.Models of gene expression commonly involve delayed biological processes, but the combination of stochasticity, delay and nonlinearity lead to emergent dynamics that are not understood at a theoretical level. We develop a theory to explain these effects, and apply it to a simple model of gene regulation. The new theory can account for long time-scale dynamics and nonlinear character of the system that emerge when the number of interacting molecules becomes low. Both the absolute length and the uncertainty in the delay time are shown to be crucial in controlling the magnitude of nonlinear effects.

Layman's Abstract

During neural development stem cells produce neurons through the process of differentiation. During differentiation, the expression of key genes controlling the stem cell state change from oscillatory to a low steady state. We use mathematical modelling to understand how the dynamics of this transition is regulated, and how the randomness caused by few reacting molecules within a cell affects this process.