Phase diagram resulting from cohesion [Eq. (4)] in the plane of potential width and temperature at zero lateral tension. Each symbol corresponds to one simulation and identifies different bilayer phases: (×) gel, (●) fluid, and (+) unstable. The lines are merely guides to the eye. The inset shows the pair potential between tail lipids (solid line) and the purely repulsive head-head and head-tail interactions (dashed line).
Phase diagram resulting from cohesion [Eq. (5)] in the plane of potential width and temperature at zero lateral tension. The meaning of all symbols is the same as in Fig. 1.
Self-assembly sequence for the bilayer system with 1000 lipids in a cubic box of side length . Lipid cohesion was set to and temperature to . A random gas of lipids quickly forms small clusters which slowly coarsen and eventually “zip up” to form a box-spanning bilayer sheet. The numbers indicate the MD time.
Profile of the density as a function of vertical distance from the bilayer midplane for a system of 4000 lipids at constant zero tension and with simulation parameters and . The plotted lines are bead densities for head beads (long dashed), first tail beads (short dashed), terminal tail beads (dotted), and the sum of all beads (solid).
Asymptotic scaling of the power spectrum for the bilayer system with and .
Scaled distribution of squared displacements of lipid molecules for the system with , and (crosses), (open circles), and (filled circles). The lines are fits to Eq. (12). These always yield and values of the two diffusion constants as given in the inset. While is constant, the data are compatible with approaching with a asymptotics (inset, dashed line).
Basic static properties of the fluid bilayer phase as a function of and , where indicates a rescaled attractive potential . is the value of on the liquid-unstable (gas) transition line. Each plot shows four isotherms: (filled squares), (asterisks), (open circles), and (filled circles). The values of for each of these isotherms were 0.815, 1.025, 1.2, and 1.27, respectively. In all cases statistical errors were smaller than the size of the plotted points.
Diffusion constant as a function of rescaled potential width . The symbols and shifts are the same as in Fig. 7.
Flip-flop rate as a function of rescaled potential width . The symbols and shifts are the same as in Fig. 7.
Variation of the area per lipid across the gel-fluid-phase boundary. Each figure shows a cooling-heating hysteresis for a particular value of . From top to bottom the values of used were 1.0, 1.4, and 1.6. The arrows indicate the direction of temperature change. The rate of temperature change was for the top plot and for the bottom two plots. The three vertical lines in the uppermost plot indicate the temperatures where the order parameter of Fig. 11 has been measured.
Probability density of the height difference between a lipid and its six immediate neighbors. The solid, dashed, and dotted curves correspond to the temperatures indicated by lines 1, 2, and 3 in Fig. 10, respectively.
Bilayer tension as a function of (projected) area A for a flat membrane sheet with at . The bold solid line is a fit to the model of Farago (Ref. 19) and Tolpekina et al. (Ref. 26) [see also Eq. (B5) in Appendix B]; the fine solid and dashed curves indicate the metastable and unstable branches, respectively.
Article metrics loading...
Full text loading...