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### Abstract

Self-assembly dynamics in binary surfactant mixtures and structure changes of lipid vesicles induced by detergent solution are studied using coarse-grained molecular simulations. Disk-shaped micelles, the bicelles, are stabilized by detergents surrounding the rim of a bilayer disk of lipids. The self-assembled bicelles are considerably smaller than bicelles formed from vesicle rupture, and their size is determined by the concentrations of lipids and detergents and the interactions between the two species. The detergent-adsorption induces spontaneous curvature of the vesicle bilayer and results in vesicle division into two vesicles or vesicle rupture into worm-like micelles. The division occurs mainly via the inverse pathway of the modified stalk model. For large spontaneous curvature of the monolayers of the detergents, a pore is often opened, thereby leading to vesicle division or worm-like micelle formation.

The computation in this work was partially done using the facilities of the supercomputer Center, Institute for Solid State Physics, University of Tokyo. This study is partially supported by a Grant-in-Aid for Scientific Research on Priority Area “Molecular Science of Fluctuations toward Biological Functions” from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

I. INTRODUCTION

II. MODEL AND METHOD

III. SELF-ASSEMBLY INTO BICELLES

IV. SURFACTANT ABSORPTION INTO VESICLES

V. SUMMARY

##### C11D

## Figures

Dependence of (a) the lateral diffusion coefficient *D* and (b) the effective line tension Γ of the membrane edges on ɛ_{AB} at *N* _{A} = *N* _{B}. (a) The symbols with lines represent data for (⋄), 0.4 (□), 0.8 (○), and 1.2 (△) at . The diffusion coefficient *D* is normalized using the diffusion coefficient *D* _{0} = σ^{2}/τ_{0} of an isolated molecule. (b) The symbols with solid lines represent data at . The symbols with dashed lines represent data at (▽) and 1 (×).

Dependence of (a) the lateral diffusion coefficient *D* and (b) the effective line tension Γ of the membrane edges on ɛ_{AB} at *N* _{A} = *N* _{B}. (a) The symbols with lines represent data for (⋄), 0.4 (□), 0.8 (○), and 1.2 (△) at . The diffusion coefficient *D* is normalized using the diffusion coefficient *D* _{0} = σ^{2}/τ_{0} of an isolated molecule. (b) The symbols with solid lines represent data at . The symbols with dashed lines represent data at (▽) and 1 (×).

Sequential snapshots of self-assembly into bicelles at *N* _{A} = *N* _{B} = 2000 and ɛ_{AB} = 1. (a)–(d) All molecules in the simulation are shown at (a) *t* = 0, (b) 1000τ_{0}, (c) 100 000τ_{0}, and (d) 1 000 000τ_{0}. (e)–(g) The largest cluster is shown at (e) *t* = 1000τ_{0}, (f) 10 000τ_{0}, and (g) 1 000 000τ_{0}. The red (yellow) and light blue (light yellow) hemispheres represent the hydrophilic (hydrophobic) parts of type A and type B molecules, respectively.

Sequential snapshots of self-assembly into bicelles at *N* _{A} = *N* _{B} = 2000 and ɛ_{AB} = 1. (a)–(d) All molecules in the simulation are shown at (a) *t* = 0, (b) 1000τ_{0}, (c) 100 000τ_{0}, and (d) 1 000 000τ_{0}. (e)–(g) The largest cluster is shown at (e) *t* = 1000τ_{0}, (f) 10 000τ_{0}, and (g) 1 000 000τ_{0}. The red (yellow) and light blue (light yellow) hemispheres represent the hydrophilic (hydrophobic) parts of type A and type B molecules, respectively.

Sequential snapshots of self-assembly into a vesicle and micelles at *N* _{A} = *N* _{B} = 2000 and ɛ_{AB} = 3. (a)–(d) All molecules in the simulation are shown at (a) *t* = 5000τ_{0}, (b) 100 000τ_{0}, (c) 803 000τ_{0}, and (d) 1 000 000τ_{0}. (e)–(g) The largest cluster is shown at (e) *t* = 5000τ_{0}, (f) 30 000τ_{0}, and (g) 100 000τ_{0}.

Sequential snapshots of self-assembly into a vesicle and micelles at *N* _{A} = *N* _{B} = 2000 and ɛ_{AB} = 3. (a)–(d) All molecules in the simulation are shown at (a) *t* = 5000τ_{0}, (b) 100 000τ_{0}, (c) 803 000τ_{0}, and (d) 1 000 000τ_{0}. (e)–(g) The largest cluster is shown at (e) *t* = 5000τ_{0}, (f) 30 000τ_{0}, and (g) 100 000τ_{0}.

Snapshots of self-assembled micelles for (a) ɛ_{AB} = 0 and (b) ɛ_{AB} = 2 at *N* _{A} = *N* _{B} = 2000 and *t* = 1 000 000τ_{0}.

Snapshots of self-assembled micelles for (a) ɛ_{AB} = 0 and (b) ɛ_{AB} = 2 at *N* _{A} = *N* _{B} = 2000 and *t* = 1 000 000τ_{0}.

Time development of the mean cluster size ⟨*n* _{cl}⟩. (a) *N* _{B}/*N* = 1. (b) *N* _{B}/*N* = 0.25, 0.5, 0.75, 0.9, and 1 at ɛ_{AB} = 1. (c) ɛ_{AB} = 0, 1, 2, and 3 at *N* _{B}/*N* = 0.5. The error-bars are shown at several data points.

Time development of the mean cluster size ⟨*n* _{cl}⟩. (a) *N* _{B}/*N* = 1. (b) *N* _{B}/*N* = 0.25, 0.5, 0.75, 0.9, and 1 at ɛ_{AB} = 1. (c) ɛ_{AB} = 0, 1, 2, and 3 at *N* _{B}/*N* = 0.5. The error-bars are shown at several data points.

Time development of the mean asphericity ⟨α_{sp}⟩ of clusters at *N* _{B}/*N* = 0.5, (a) Averaged for all clusters with *i* _{cl} > 10 at ɛ_{AB} = 0, 1, 2, and 3. (b) Averaged for clusters with 10 < *i* _{cl} ⩽ 50, 50 < *i* _{cl} ⩽ 100, and *i* _{cl} > 100 at ɛ_{AB} = 3. The error-bars are shown at several data points.

Time development of the mean asphericity ⟨α_{sp}⟩ of clusters at *N* _{B}/*N* = 0.5, (a) Averaged for all clusters with *i* _{cl} > 10 at ɛ_{AB} = 0, 1, 2, and 3. (b) Averaged for clusters with 10 < *i* _{cl} ⩽ 50, 50 < *i* _{cl} ⩽ 100, and *i* _{cl} > 100 at ɛ_{AB} = 3. The error-bars are shown at several data points.

Sequential snapshots of vesicle division due to surfactant adsorption at and ɛ_{AB} = −5. (a) *t* = 0 (b) *t* = 8550τ_{0}. (c) *t* = 8563τ_{0}. (d) *t* = 8570τ_{0}. (a) All molecules in the simulation are shown. (b)–(d) Upper and lower snapshots show whole and cross-sectional views of vesicles, respectively.

Sequential snapshots of vesicle division due to surfactant adsorption at and ɛ_{AB} = −5. (a) *t* = 0 (b) *t* = 8550τ_{0}. (c) *t* = 8563τ_{0}. (d) *t* = 8570τ_{0}. (a) All molecules in the simulation are shown. (b)–(d) Upper and lower snapshots show whole and cross-sectional views of vesicles, respectively.

Sequential snapshots of vesicle rupturing into worm-like micelles at and ɛ_{AB} = −5. (a) *t* = 7600τ_{0}. (b) *t* = 8200τ_{0}. (c) *t* = 9500τ_{0}. (d) *t* = 30 000τ_{0}. (a)–(c) Only the largest cluster is shown. The lower snapshot in (a) shows the cross-sectional view of the vesicle. (d) All molecules in the simulation are shown.

Sequential snapshots of vesicle rupturing into worm-like micelles at and ɛ_{AB} = −5. (a) *t* = 7600τ_{0}. (b) *t* = 8200τ_{0}. (c) *t* = 9500τ_{0}. (d) *t* = 30 000τ_{0}. (a)–(c) Only the largest cluster is shown. The lower snapshot in (a) shows the cross-sectional view of the vesicle. (d) All molecules in the simulation are shown.

Time development of (a) the number *N* _{clus} of molecules in the first and second largest clusters and (b) the aspericity α_{sp} of the largest cluster for (•) and 1.2 (×). The cluster size is normalized by the initial vesicle size, *N* _{int} = 2000. The same data are shown in Figs. 7 and 8 .

Time development of (a) the number *N* _{clus} of molecules in the first and second largest clusters and (b) the aspericity α_{sp} of the largest cluster for (•) and 1.2 (×). The cluster size is normalized by the initial vesicle size, *N* _{int} = 2000. The same data are shown in Figs. 7 and 8 .

Detergent-adsorption-induced vesicle division and worm-like micelle formation. (a) Probability of structure changes at for (○), 1 (△), and 1.2 (□). The solid lines represent the sum of vesicle division and micelle formation. The dashed lines represent worm-like micelle formation. (b) Phase diagram of vesicle structure for (○), 0.8 (△), and 1 (□). The vesicle maintains its shape for ɛ_{AB} values above the solid line. The vesicle is divided into two vesicles or transforms into worm-like micelles below the line.

Detergent-adsorption-induced vesicle division and worm-like micelle formation. (a) Probability of structure changes at for (○), 1 (△), and 1.2 (□). The solid lines represent the sum of vesicle division and micelle formation. The dashed lines represent worm-like micelle formation. (b) Phase diagram of vesicle structure for (○), 0.8 (△), and 1 (□). The vesicle maintains its shape for ɛ_{AB} values above the solid line. The vesicle is divided into two vesicles or transforms into worm-like micelles below the line.

Time development of the mean number ⟨*N* _{ves}⟩ of molecules in the vesicle. (a) ɛ_{AB} = 0, −1, −2, −3, −4, and −5 at . (b) , 0.2, 0.4, 0.6, 0.8, 1, and 1.2 at ɛ_{AB} = −4. Divided vesicles are not taken into account for the average in (b).

Time development of the mean number ⟨*N* _{ves}⟩ of molecules in the vesicle. (a) ɛ_{AB} = 0, −1, −2, −3, −4, and −5 at . (b) , 0.2, 0.4, 0.6, 0.8, 1, and 1.2 at ɛ_{AB} = −4. Divided vesicles are not taken into account for the average in (b).

Vesicle initial growth rate *k* _{ad} = ⟨*N* _{ves}⟩τ_{0}/*dt*|_{ t = 0} at (□), 0.8 (△), 1.2 (○) and ɛ_{AB} = −4. The rate is normalized by the initial monomer concentration ρ_{1} in (b).

Vesicle initial growth rate *k* _{ad} = ⟨*N* _{ves}⟩τ_{0}/*dt*|_{ t = 0} at (□), 0.8 (△), 1.2 (○) and ɛ_{AB} = −4. The rate is normalized by the initial monomer concentration ρ_{1} in (b).

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