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Treball de fi de grau en Biomèdica Tutors: Jordi Gacía Ojalvo, Alfonso Martínez Arias Small aggregates of 300-500 mouse embryonic stem cells are able to self-organize into polarized structures that exhibit collective behavior that mirrors those observed in early mouse embryos. This includes symmetry breaking, axial organization, germ layer specification and axis elongation on a time-scale similar to that of the mouse embryo. These embryonic organoids are called Gastruloids and are a reproducible model system to understand the processes underlying early mouse development. These Gastruloids were formed from mouse embryonic stem cells containing reporters for T-Brachyury, and FGF Signaling. We were able to quantitatively assess the contribution of these signaling pathways to the establishment of a pattern in early gastrulogenesis through single time-point and live-cell fluorescence microscopy. We found that during the first 24h-48h of culture, interactions between the Wnt/- Catenin signaling pathways promote the initial symmetry-breaking event (elongation), manifested through polarized T-Brachyury expression. Our experiments also show that FGF/MEK signaling pathway does not play an important role in pattern formation or in Gastruloid elongation although we suspect that another FGF signaling pathway might be crucial for these events to happen. However, more experimental work should be done to better understand which FGF pathway is really involved in early gastrulogenesis. We can conclude that chemical signaling plays an important role in pattern formation but the mechanical interactions between cells is also relevant for this process to take place. From these experimental observations, we tried to model T-Brachyury pattern formation in Gastruloids using the reaction-di↵usion model from Alan Turing, which is the best known theoretical model used to explain self-regulated pattern formation in the developing animal embryo. We performed the stability analysis for a two component and a three component system were we imposed that only two molecules were able to di↵use. Also, we included time delay in the typical Gierer-Meinhardt models to see whether pattern could still be able to form. As a result, we showed that any two component reaction di↵usion system with only one di↵user cannot exhibit Turing instabilities and the addition of a third di↵user in our system failed to become a Turing system because of our network structure. With all the stability analysis performed, we created a tool used to reject three component systems with two di↵users from being Turing patterns just by looking at the network structure. Finally, we were able to observe how a small time delay in protein production was able to avoid pattern formation in the most used reaction-di↵usion systems. The experimental and computational results suggest that pattern formation is a process that requires mechanical transduction and time delay due to protein formation, so as a future work we shall focus on a di↵erent modeling approach.