The size and density of living cells are the result of passive physical constraints and active biological processes. Their interplay leads to the appearance of robust and ubiquitous scaling laws relating linearly cell size, dry mass, and nuclear size. I will discuss how the different scaling laws can be explained quantitatively by a single model of size regulation based on three simple, yet generic, physical constraints - osmotic balance, hydrostatic balance, and electro-neutrality - defining the “the Pump-Leak model” (PLM). One remarkable feature is that the protein density within a cell remains constant during cell growth. I will show how this can be understood by coupling the PLM with a simple model of gene expression. I will then discuss how cell mechanics may modify the different scaling law. I will end with the interesting case of fresh-water single celled organism, which have evolve specific ways of dealing with particularly acute osmotic challenges.
I will give examples of symmetry breakìng in epitheliums on substrates with several different topographies.
Skyrmions are of interest both from a fundamental and technological point of view, due to their potential to act as information carriers. But one challenge concerns their manipulation, especially at high temperature where thermal fluctuations eventually disintegrate them. Here we study the competition between skyrmions and a chiral spin liquid, using the latter as an entropic buffer to impose a quasivacuum of skyrmions . As a result, the temperature becomes a knob to tune the skyrmion density from a dense liquid to a diluted gas, protecting the integrity of each skyrmion from paramagnetic disintegration. With this additional knob in hand, we find at high field a topological spin glass made of zero- and one-dimensional topological defects (respectively skyrmions and bimerons). To conclude, we will investigate how these different chiral magnetic textures couple to itinerant electrons and stabilise anomalous Hall effects of different strength .  Rosales, Gómez Albarracín, Pujol & Jaubert, Phys. Rev. Lett. 130, 106703 (2023)  Gómez Albarracín, Rosales, Udagawa, Jaubert & Pujol (in preparation)