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Separation of components in lipid membranes induced by shape transformation
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10.1063/1.4731646
/content/aip/journal/jcp/137/1/10.1063/1.4731646
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/1/10.1063/1.4731646
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The free energy as a function of the reduced volume (Eq. (9) ). The dashed lines show the free energy obtained for constant spontaneous curvature = 4 (uniform distribution of components) for the following configurations: (i) a sphere, (ii) two, (iii) three, (iv) four, and (v) five beads, respectively. The solid curves show the free energy for (a) partially budded configurations and configurations with: (b) one, (c) two, (d) three, (e) four, (f) five small beads, and for tubular shapes (g). The total concentration is ϕ = 0.5, , , κ = κ . Configurations corresponding to the lowest value of the free energy for given are thermodynamically stable, the remaining ones are metastable.

Image of FIG. 2.
FIG. 2.

Budding induced by the change of the reduced volume (Eq. (9) ). From the left to the right vesicle = 0.94, 0.95, 0.955, 0.96, 0.97, 0.975, 0.99, respectively. The total concentration is ϕ = 0.5, , , κ = κ . The colormap shows mapping of concentration values to colors.

Image of FIG. 3.
FIG. 3.

The shapes of the vesicles for the family with one small bead for different values of the reduced volume (Eq. (9) ). = 0.705, 0.745, 0.785, 0.825, 0.865, 0.91, 0.955, respectively. The total concentration is ϕ = 0.5, , , κ = κ . The color of the surface reflects the value of the concentration ϕ according to the color map in Fig. 2 .

Image of FIG. 4.
FIG. 4.

The shapes of the vesicles for different values of the reduced volume (Eq. (9) ). In the upper panel (A), the configurations with three small beads for = 0.485, 0.535, 0.585, 0.635, 0.685, 0.735, 0.785 are presented. In the lower left panel (B), the configurations with five small beads for = 0.505, 0.545, 0.585, 0.625, 0.665 are shown. In lower right panel (C), the configurations with tubular shapes for = 0.345, 0.375, 0.405, 0.435, 0.465 are shown. The total concentration is ϕ = 0.5, the spontaneous curvatures are , , and the bending rigidity is κ = κ . The color of the surface reflects the value of the concentration ϕ according to the color map in Fig. 2 .

Image of FIG. 5.
FIG. 5.

Concentration in the spherical part of the vesicle (dashed curves) and in the protrusion (solid curves) as a function of the reduced volume (Eq. (9) ) for different shapes of vesicles for (a) configurations without the beads, and configurations with: (b) one, (c) two, (d) three, (e) four, (f) five small beads. The total concentration is ϕ = 0.5, , , κ = κ .

Image of FIG. 6.
FIG. 6.

Concentration in the spherical part of the vesicle (dashed curves) and in the protrusion (solid curves) as a function of the reduced volume (Eq. (9) ) for the different shapes of vesicles for configurations with: (a) one, (b) two, (c) three beads. The total concentration is ϕ = 0.5, , , κ = κ = 30 , = 100 nm2 and = 250 nm. The vesicle shapes represent minimized configurations with the best separation of the components (for the largest for a given family of shapes), totally mixed (for the smallest for a given family of shapes) , and intermediate. The color of the surface reflects the value of the concentration ϕ according to the color map in Fig. 2 .

Image of FIG. 7.
FIG. 7.

Concentration in the spherical part of the vesicle (dashed curves) and in the protrusion (solid curves) as a function of the reduced volume (Eq. (9) ) for configurations with one bead for different sizes of nanodomains: (b) = 400 nm2, (c) = 200 nm2, (d) = 100 nm2, (e) = 50 nm2, (f) = 25 nm2, (g) = 12 nm2. The curve (a) refers to the calculations with neglected entropy of mixing. The total concentration is ϕ = 0.5, , , κ = κ = 30 , and = 250 nm.

Image of FIG. 8.
FIG. 8.

Concentration in the spherical part of the vesicle (dashed curves) and in the protrusion (solid curves) as a function of the reduced volume (Eq. (9) ) for the different shapes of vesicles for configurations with: (a) one, (b) two, (c) three beads: (A) κ = 8κ , κ = 30 , (B) κ = 30 , κ = 8κ . The total concentration is ϕ = 0.5, , , = 100 nm2, and = 250 nm. The vesicle shapes represent minimized configurations with the best separation of components (for the largest for a given family of shapes), totally mixed (for the smallest for a given family of shapes), and intermediate. The color of the surface reflects the value of the concentration ϕ according to the color map in Fig. 2 .

Image of FIG. 9.
FIG. 9.

The shapes of vesicles with lateral segregation induced by elongation: (A) κ = 2κ , κ = 30 , (B) κ = 8 κ , κ = 30 . The total concentration is ϕ = 0.5, , , = 100 nm2, and = 250  nm. The height of the vesicle = 3.1, 4.5, 5.3, 5.7, 6.3, 6.9 in units. The color of the surface reflects the value of the concentration ϕ according to the color map in Fig. 2 . The reduced volume = 0.705 (Eq. (9) ).

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/content/aip/journal/jcp/137/1/10.1063/1.4731646
2012-07-06
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Separation of components in lipid membranes induced by shape transformation
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/1/10.1063/1.4731646
10.1063/1.4731646
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