Monte Carlo calculations of the free-energy landscape of vesicle formation and growth

A flat-histogram Monte Carlo sampling method is used to calculate the free-energy landscape of a simple semi-flexible triangulated membrane model as a function of the number of vertices and the number of free edges. Results yield the equilibrium ratio of open (disk) and closed (vesicle) states, the free-energy barrier between these states, and the scaling of vesicle free energy with size N in the range from 6 to 200 vertices. Deviations from the predictions of a simple model for the disk-vesicle transition are found to result from the fluctuations of the edge. Vesicle free energies are fit to the form BN + vk(B)T lnN, with coefficient v = 1.6 +/- 0.1 for flexible membranes (consistent with self- avoiding branched polymer statistics) and 1.2 +/- 0.1 for semi flexible membranes.