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This lecture covers the concept of random walks in biological systems, focusing on protein abundances in single cells and population genetics. The Moran process in population genetics is explained, detailing the selection, elimination, and reproduction of individuals in a population. The lecture discusses the importance of thermal fluctuations at the cellular scale and their impact on biological processes. Various chemical bonds' strength, biopolymers' flexibility, and biomembranes are explored in the context of thermal fluctuations. The presentation includes simulations of simple models for protein abundance and the Moran model in population genetics.