Geometrical Properties of Gel and Fluid Clusters in DMPC/DSPC Bilayers: Monte Carlo Simulation Approach Using a Two-State Model  István P. Sugár, Ekaterina Michonova-Alexova, Parkson Lee-Gau Chong  Biophysical Journal  Volume 81, Issue 5, Pages 2425-2441 (November 2001) DOI: 10.1016/S0006-3495(01)75890-0 Copyright © 2001 The Biophysical Society Terms and Conditions

Figure 1 A typical gel state cluster with one inner island. Closed circles: gel state lattice point; open circles: fluid state lattice point. Gel-fluid nearest-neighbor lattice points are interconnected by solid lines at the outer periphery of the cluster. The shaded area in the upper corner marks a unit cell of the lattice. ls1, ls2, and ls3 are the lengths of the projections of the cluster in the three characteristic directions of the lattice. The arrow marks the center of the cluster, C, calculated by Eqs. 4 and 5. Biophysical Journal 2001 81, 2425-2441DOI: (10.1016/S0006-3495(01)75890-0) Copyright © 2001 The Biophysical Society Terms and Conditions

Figure 2 Calculated and experimental excess heat capacity curves of equimolar DMPC/DSPC bilayers. Dotted line: experimental excess heat capacity curve; open circles: calculated values. All calorimetric scans were performed on a home-made high-sensitivity scanning calorimeter (Suurkuusk et al., 1976) at scan rates from 0.1 to 5°C/h. In this scan the lipid concentration was 20mM with a scan rate of 5°C/h. To obtain the calculated excess heat capacity, CP, the variance of the lattice energy E was determined at each temperature, T, and then the following equation was used: CP ≈CV=〈(E−〈E〉)2〉)/(RT2N), where R=2 cal/mol−chain/deg, and N is the number of lattice points. A straight line is fitted to the inflection points of the excess heat capacity curve at its low- and high-temperature edges. The intercepts of the straight lines with the line at zero excess heat capacity define the onset and completion temperatures of the gel-to-fluid transition (see crosses at 299.2 and 322.9K, respectively). Biophysical Journal 2001 81, 2425-2441DOI: (10.1016/S0006-3495(01)75890-0) Copyright © 2001 The Biophysical Society Terms and Conditions

Figure 3 Calculated size distributions of fluid state clusters of equimolar DMPC/DSPC bilayers. (A) 302K; (B) 305.3K; (C) 306K; (D) 306K; where open circles mark the size distribution of the largest fluid cluster in each snapshot and closed circles show the size distribution of all the fluid clusters except the largest ones. The average size of these smaller clusters is 〈s〉=3.19. Biophysical Journal 2001 81, 2425-2441DOI: (10.1016/S0006-3495(01)75890-0) Copyright © 2001 The Biophysical Society Terms and Conditions

Figure 4 Calculated size, number, and center-to-center distance of clusters in equimolar DMPC/DSPC mixtures. (A) Calculated average linear size 〈ls〉 of gel (closed circles) and fluid clusters (open circles) at 305.3K is plotted against the cluster size S. The linear cluster size is defined by Eq. 2. (B) Calculated temperature dependence of the average total size and average number of all the clusters except the largest one in each snapshot. Open squares: average total size; open triangles: average number of the clusters. Solid and dashed lines refer to fluid and gel clusters, respectively. (C) Calculated center-to-center distributions of DSPC clusters in equimolar DMPC/DSPC mixtures at 314K (squares), 311K (circles), and 283K (diamonds). In each simulation 6000 equilibration cycles were followed by 1.2million Monte Carlo cycles. The center-to-center distance is measured in lattice units. (D) Calculated temperature dependence of the average size of the largest cluster of the lattice. Solid line: fluid cluster; dashed line: gel cluster. Biophysical Journal 2001 81, 2425-2441DOI: (10.1016/S0006-3495(01)75890-0) Copyright © 2001 The Biophysical Society Terms and Conditions

Figure 5 Percolation frequency curves and percolation threshold temperatures. (A) Calculated percolation frequency curves of gel and fluid clusters of equimolar DMPC/DSPC bilayers. Dashed line: fluid clusters; solid line: gel cluster. A straight line is fitted to the inflection point of the percolation frequency curve of fluid clusters and its intercept with the zero frequency line defines the percolation threshold temperature of fluid clusters (see cross at 304.6K). The percolation threshold temperature of gel clusters is marked by a cross at 317.5K. (B) Calculated percolation threshold temperatures versus FRAP threshold temperatures measured at different DMPC/DSPC mole fractions. Closed circles: percolation threshold temperatures of gel clusters; open circles: percolation threshold temperatures of fluid clusters; closed squares: temperatures at 0.36 percolation frequency of gel clusters. Biophysical Journal 2001 81, 2425-2441DOI: (10.1016/S0006-3495(01)75890-0) Copyright © 2001 The Biophysical Society Terms and Conditions

Figure 6 Clusters’ outer perimeter and fractal dimensions. (A) Calculated average outer perimeter of fluid clusters of equimolar DMPC/DSPC bilayers. The average outer perimeter is plotted against the cluster size, S. Temperature: 306K; open circles: simulated data; solid line: Eq. 6 is fitted to the ascending section of the simulated data. Estimated model parameters: Feff=1.552±0.007, A=7.68±0.12. Error bars show the calculated standard deviations of the outer perimeter at certain cluster sizes. (B) Calculated effective fractal dimensions of fluid (open circles) and gel clusters (closed circles) of equimolar DMPC/DSPC bilayers are plotted against the temperature. Crosses and the connecting solid line mark the result of the obstacle aggregation model of Schram et al. (1996). Open squares connected by a solid line mark the upper and lower limit of the effective fractal dimension of gel clusters of an AFM scan (not shown). The scan, provided by Drs. Ka Yee Lee and Adrian Muresan (University of Chicago), was taken from a supported, equimolar DMPC/DSPC bilayer at 313K, while the sample was in a solution of 8mM MgCl2. (C) Calculated capacity dimensions of fluid (dashed line) and gel clusters (solid line) of equimolar DMPC/DSPC bilayers are plotted against the temperature. The closed circle marks the capacity dimension of gel clusters obtained from the analysis of the same AFM scan mentioned in the legend to B. Error bars show the calculated standard deviations. Biophysical Journal 2001 81, 2425-2441DOI: (10.1016/S0006-3495(01)75890-0) Copyright © 2001 The Biophysical Society Terms and Conditions

Figure 7 Calculated average number and average size of inner islands in the fluid clusters of equimolar DMPC/DSPC bilayers. (A) Average number of inner islands versus size of the host fluid cluster. Equation 8 is fitted to the simulated data (solid line). Estimated parameters are D1=0.00427±0.00009 and D2=1.304±0.0034. The correlation coefficient is r=0.9994. Error bars show the calculated standard deviations. (B) Average size of inner islands versus size of the host fluid cluster. Equation 9 is fitted to the simulated data (solid line). Estimated parameters are E1=1.09±0.01 and E2=0.0072±0.0002. The correlation coefficient is r=0.977. Cross: 302K; open triangles: 305.3K; open circles: 306K. Biophysical Journal 2001 81, 2425-2441DOI: (10.1016/S0006-3495(01)75890-0) Copyright © 2001 The Biophysical Society Terms and Conditions

Figure 8 Calculated average number of arms of fluid clusters of equimolar DMPC/DSPC bilayers. Temperature: 306K; open circles: simulated data. Error bars show the calculated standard deviations. (A) Average number of arms versus cluster's average outer perimeter. Solid line: Eq. 10 is fitted to the straight section of the simulated curve. Estimated model parameters: B=29.82±0.05, C=1.25±0.01. (B) Average number of arms versus cluster size. The solid line is calculated from Eq. 11 by using the above values for B and C, while the values for A and Feff are given in the legend to Fig. 6 A. Biophysical Journal 2001 81, 2425-2441DOI: (10.1016/S0006-3495(01)75890-0) Copyright © 2001 The Biophysical Society Terms and Conditions