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This lecture covers the concept of genetic circuits with negative feedback and their relation to mechanical analogies for spatial problems. It discusses the synchronization of genetic clocks and the coupling between cells. The presentation delves into the correlation between mRNA levels and histone acetylation, providing insights into genetic regulation mechanisms. Additionally, it explores the logistics growth model and the propagation of solutions in 1D spatial systems. The lecture concludes with a detailed analysis of phase portraits and the behavior of trajectories in different scenarios.