Geometrical properties of gel and fluid clusters in DMPC/DSPC bilayers: Monte Carlo simulation approach using a two-state model

In this paper the geometrical properties of gel and fluid clusters of equim olar dimyristoylphosphatidylcholine/ distearoylphosphatidylcholine (DMPC/DS PC) lipid bilayers are calculated by using an Ising-type model (Sugar, I. P ., T. E. Thompson, and R. L. Biltonen. 1999. Biophys. J. 76:2099-2110). The model is able to predict the following properties in agreement with the re spective experimental data: the excess heat capacity curves, fluorescence r ecovery after photobleaching (FRAP) threshold temperatures at different mix ing ratios, the most frequent center-to -center distance between DSPC clust ers, and the fractal dimension of gel clusters. In agreement with the neutr on diffraction and fluorescence microscopy data, the simulations show that below the percolation threshold temperature of gel clusters many nanometer- size gel clusters co-exist with one large gel cluster of size comparable wi th the membrane surface area. With increasing temperature the calculated ef fective fractal dimension and capacity dimension of gel and fluid clusters decrease and increase, respectively, within the (0, 2) interval. In the reg ion of the gel-to-fluid transition the following geometrical properties are independent from the temperature and the state of the cluster: 1) the clus ter perimeter linearly increases with the number of cluster arms at a rate of 8.2 nm/arm; 2) the average number of inner islands in a cluster increase s with increasing cluster size, S, according to a power function of 0.00427 X S-1.3; 3) the following exponential function describes the average size of an inner island versus the size of the host cluster, S: 1 + 1.09(1 - e(- 0.0072XS)). By means of the equations describing the average geometry of th e clusters the process of the association of clusters is investigated.