A simple model of active shape fluctuations of thin elastic shells swollen by hydrostatic pressure

Many organisms have an elastic hydrostatic skeleton (shell) that often consists of epithelial cells, and is filled with fluid. Living systems (such as hydra) can regulate both elastic forces and hydrostatic pressure by energy consuming (via ATP/GTP hydrolysis) active processes such as contraction of supracellular actomyosin fibers, and by osmotic control of the hydrostatic pressure inside the shell, respectively. 

 In this work we use computer simulations to study a simple network of springs model of such systems. We introduce hydrostatic, elastic and frictional forces that act on each of the vertices of the network. We model active deformations by changing the equilibrium lengths and the spring constants of randomly selected springs at periodic or at random time intervals. Inspired by recent experiments of Erez Braun and his group, we study the resulting non-thermal fluctuations of the total surface area A of the system both at constant hydrostatic pressure and in the case when pressure and area are coupled. We elucidate the statistical properties of these fluctuations by computing the distribution of A values at different times, and the relaxation of the autocorrelation function of A.