Main transition in the Pink membrane model: finite-size scaling and the influence of surface roughness

We consider the main transition in single-component membranes using computer simulations of the Pink model [D. A. Pink et al., Biochemistry 19, 349 (1980)]. We first show that the accepted parameters of the Pink model yield a main transition temperature that is systematically below experimental values. This resolves an issue that was first pointed out by Corvera and co-workers [Phys. Rev. E 47, 696 (1993)]. In order to yield the correct transition temperature, the strength of the van der Waals coupling in the Pink model must be increased; by using finite-size scaling, a set of optimal values is proposed. We also provide finite-size scaling evidence that the Pink model belongs to the universality class of the two-dimensional Ising model. This finding holds irrespective of the number of conformational states. Finally, we address the main transition in the presence of quenched disorder, which may arise in situations where the membrane is deposited on a rough support. In this case, we observe a stable multidomain structure of gel and fluid domains, and the absence of a sharp transition in the thermodynamic limit.