On the inner structure and topology of clusters in two-component lipid bilayers. Comparison of monomer and dimer Ising models.

It has been shown on model and biological systems that membrane clusters can affect in-plane membrane reactions and can control biochemical reaction cascades. Clusters of two-component phospholipid bilayers have been simulated by two Ising-type lattice models: the monomer and the dimer model. In each model the plane of one layer of the bilayer is represented by a triangular lattice, each site of which is occupied by an acyl chain of either a component 1 or a component 2 lipid molecule. The dimer model assumes that pairs of acyl chains (lipid molecules) are permanently connected, forming dimers on the lattice, while in the case of the monomer model this covalent connection between acyl chains is ignored. Phase diagrams of two-component phospholipid bilayers were successfully calculated by both models. In this work, we use Monte Carlo techniques to calculate thermodynamic averages of global and local characteristics of the largest component 2 cluster (such as outer/inner perimeter, percolation, minimal linear size, and local density) and compare the results obtained by the two models. A new method is developed to characterize the inner structure of the clusters. Each point of a cluster is classified based on its shortest distance (or depth) from the cluster's outer perimeter. Then local cluster properties, such as density, are calculated as a function of the depth. The depth analysis reveals that toward the cluster interior the average density usually decreases in midsize clusters and remains constant in very large clusters. On the basis of the simulations the following typical cluster topologies are identified at different cluster sizes and cooperativity parameter values: (i) branch-like, (ii) circular, (iii) band-like, and (iv) planar.We did not find qualitative differences between the cluster structures in the dimer and monomer model. However, at the same cluster size and cooperativity parameter value the cluster of the dimer model is more compact. The cluster properties of the dimer model are different from that of the monomer model because of the lower mixing entropy and higher formation energy of an elementary inner island.