# Mathematical models of the gene regulatory networks underlying mesendoderm formation in amphibians

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## Abstract

An early event in embryo development is the formation of mesoderm, endoderm and ectoderm, known as the primary germ layers. The gene regulatory network (GRN) consisting of the regulatory mechanisms underlying the formation of mesoderm and endoderm (the mesendoderm GRN) has been extensively studied both experimentally and using mathematical models. The Xenopus GRN is complex, with much of this complexity due to large numbers of Mix and Nodal genes. Mice and humans have only single Mix and Nodal genes, meaning that the Xenopus GRN is overly complex compared with higher vertebrates. Urodele amphibians, for example the axolotl, have single Mix and Nodal genes required for mesoderm and endoderm formation giving a model organism for the study of a simplified mesendoderm GRN. We study the axolotl mesendoderm GRN by developing mathematical models that encompass the time evolution of transcription factors in a cell. A detailed investigation reveals that, despite differences in the axolotl mesendoderm GRN compared with the Xenopus, the model can qualitatively reproduce experimental observations. We obtain experimental data to estimate model parameters using a computational algorithm, then test the behaviour of the resulting mathematical model using independent data. We extend mathematical models of the Xenopus mesendoderm GRN to include transcription factors involved in patterning the DV axis. An investigation of this model shows that it can account for the formation of mesoderm, endoderm and anterior mesendoderm forming in regions of the embryo consistent wth experimental data. In the final section of this thesis, we extend a multicellular model of the Xenopus mesendoderm GRN into a grid of cells.

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