A mathematical analysis of developmental gene regulatory networks

Student thesis: Doctoral ThesisDoctor of Philosophy


The specification of cell fates is a central aspect of multicellular development. In order to understand this complex phenomenon, mathematical models combined with experimental perturbations have been used. In this thesis we were motivated by the vertebrate neural tube to develop mathematical tools and models that explain the emergence of discrete domains of gene expression as well as the precision of the boundaries between them.

We developed two dimensionality reduction methods based on the Zwanzig-Mori projection that allow a dynamical system to be divided into an arbitrary subnetwork and bulk. The bulk is then replaced by memory functions which correct for the baseline approximation of each method. For the first method the bulk is assumed to be at Steady State; for the second method the bulk is assumed to be at Quasi-Steady State. Using these methods, we were able to accurately capture the dynamics and properties of the original systems. Furthermore, after reducing the dimensionality of the system we show how these methods provide insight into the functioning of biologically relevant networks and we demonstrate how the methods can be used in a complementary way to gain an understanding of the importance of individual reactions in the Gene Regulatory Network (GRN) that patterns the ventral neural tube.

To understand how the boundaries between domains of distinct cell fates are established, we developed a stochastic model of ventral neural tube patterning. This model recapitulated the precision and positioning of wild type and mutant domain boundaries. We modelled perturbations of coding and regulatory regions, and found that the GRN contributes to boundary precision. We performed a computational screen in parameter space that demonstrates that boundary precision can emerge from two dynamical properties that modulate the changes in transition time between steady states in the system. Supported by experimental results, this established design principles for the generation of precise domains between gene expression domains in developing tissues.
Date of Award1 Mar 2020
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorJames Briscoe (Supervisor) & Peter Sollich (Supervisor)

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