Hastings, Cato; (2024) Mathematical modelling of primitive streak formation in chick embryos. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The site of primitive streak formation is the first anatomical sign which defines the anterior and posterior sides of the embryo. In some embryos, two primitive streaks are initiated spontaneously which could lead to the formation of identical twins. We use different methods of mathematical modelling to study how the site of primitive streak formation is established, comparing our results with those of experiments performed in chick embryos. First, we use Bayesian parameter estimation to compare two mathematical models probing how the site of streak formation is established. We find that a model in which cells assess levels of streak-inducing and streak-inhibiting signals relative to their neighbours explains experimental results better than a model in which cells assess signals independently. Second, it is proposed that a signal involving long-range transmission of short bursts of calcium firing activity prevents the formation of multiple primitive streaks in most embryos. We propose a model for how a calcium-based signal might interact with other streak-inhibiting signals. Solving a set of ordinary differential equations, we show that such a model can explain the dynamics of streak formation in the normal embryo as well as the behaviour of isolated embryo fragments. The final part of the thesis studies how a calcium-based signal might vary and propagate between cells. We describe a 2–dimensional model of intercellular calcium signalling and find that increasing connectivity of cells might explain changing calcium firing activity observed in the developing chick embryo.

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