Geometrical Properties of Gel and Fluid Clusters in DMPC/DSPC Bilayers: Monte Carlo Simulation Approach Using a Two-State Model

Abstract

In this paper the geometrical properties of gel and fluid clusters of equimolar dimyristoylphosphatidylcholine/distearoylphosphatidylcholine (DMPC/DSPC) 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 respective experimental data: the excess heat capacity curves, fluorescence recovery after photobleaching (FRAP) threshold temperatures at different mixing ratios, the most frequent center-to-center distance between DSPC clusters, and the fractal dimension of gel clusters. In agreement with the neutron 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 with the membrane surface area. With increasing temperature the calculated effective fractal dimension and capacity dimension of gel and fluid clusters decrease and increase, respectively, within the (0, 2) interval. In the region of the gel-to-fluid transition the following geometrical properties are independent from the temperature and the state of the cluster: 1) the cluster 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 increases 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 the clusters the process of the association of clusters is investigated.

Recurrent fractal neural networks: a strategy for the exchange of local and global information processing in the brain

“…hydrophobic or van der Waals interactions between membrane lipids, may be programmed by incoming synaptic signals that modulate the shape of a spatially extended, fractal lipid lattice or microdomain (Bieberich, 2000a). Recently, it has been found that biological membranes exhibit requisite characteristics of fractal geometry with respect to curvature, shape, and internal molecular organization (Hoop and Peng, 2000;Rabouille et al, 1992;Sugar et al, 2001). Alternatively, microtubules or other filaments of the cytoskeleton may also form a lattice structure that can be shaped into a fractal.…”

Diffuse First Order Phase Transitions

“…The difference of our approach from that used by Suger et al [3] and Heimburg [4] is the distribution of T c with a given Gauss type function f (T 0i ). The first term in (4) describes the chemical potential of a subsystem at the i-th site in the Ising network.…”

“…We consider a two-state system in a temperature dependent field as it was introduced by Suger et al [3] and Heimburg [4]:…”

“…We add to this list also a biological example, a lipid system in living cells. The main phase transition between the solid and gel states of the lipids is diffuse and the fluctuations are strong [3,4]. Recently, one more example was found in a solid solution of antiferroelectrics, NaNbO 3 :Gd [5][6][7].…”

Lateral organization of cholesterol molecules in lipid-cholesterol assemblies

“…Previous numerical studies of the gel to fluid transition in lipid-cholesterol assemblies and the formation of superlattices have used a triangular lattice description of the membrane [15][16][17][18][19][20][21][22]. While these studies were able to capture several salient features of the thermotropic transition and even the formation of superlattices, such models cannot, obviously, capture the effects of lateral mobility of the molecules.…”