GALCIT Colloquium

The thermal fluctuations of lipid bilayer membranes are key to their interaction with cellular components as well as the measurement of their mechanical properties. Typically, membrane  fluctuations are analyzed by decomposing into normal modes or by molecular simulations. We propose a new approach to calculate the partition function of a membrane. We view the membrane as a fluctuating von Karman plate and discretize it into triangular elements. We express its energy as a function of nodal displacements, and then compute the partition function and covariance matrix using Gaussian integrals. We recover well-known results for the dependence of the projected area of the membrane on the applied tension and recent simulation results on the dependence of membrane free energy on geometry, spontaneous curvature and tension. As new applications we compute the fluctuations of the membrane of a malaria infected cell and analyze the effects of boundary conditions on fluctuations. We also apply our methods to quantitatively explain the negative thermal expansion coefficient of graphene. In contrast to lipid bilayers, which are liquid in-plane, graphene is a solid plate of atomic thickness. Thus, its out-of-plane bending fluctuations are coupled with in-plane strains. This constrains the number of configurations that a graphene sheet can explore and has consequences on the magnitude of its fluctuations. We will show how we account for this constraint in our calculations.