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### Abstract

A coarse-grained molecular model, which consists of a spherical particle and an orientation vector, is proposed to simulate lipidmembrane on a large length scale. The solvent is implicitly represented by an effective attractive interaction between particles. A bilayer structure is formed by orientation-dependent (tilt and bending) potentials. In this model, the membrane properties (bending rigidity, line tension of membrane edge, area compression modulus, lateral diffusion coefficient, and flip-flop rate) can be varied over broad ranges. The stability of the bilayer membrane is investigated via droplet-vesicle transition. The rupture of the bilayer and worm-like micelle formation can be induced by an increase in the spontaneous curvature of the monolayermembrane.

This work is supported by KAKENHI (21740308) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

I. INTRODUCTION

II. MODEL AND METHOD

A. Molecular model

B. Brownian dynamics

III. RESULTS AND DISCUSSION

A. Self-assembly and membrane stability

B. Calculation of membrane properties

C. Parameter dependence of membrane properties

IV. SUMMARY

## Figures

The cutoff function , the compact Gaussian weight function , and the repulsive potential . Schematic drawing of molecules is shown in the inset.

The cutoff function , the compact Gaussian weight function , and the repulsive potential . Schematic drawing of molecules is shown in the inset.

Probability distribution of (a) the positions and (b) the orientation of the molecules in the planar membrane at *N* = 512, , ε = 2, , and . (a) The *z* components of and are shown with respect to the center of mass of the membrane () for . The dashed line represents of the molecules at . (b) The *z* component of the molecular orientation is shown for , 2, 4, and 8. The error bars are displayed at several data points.

Probability distribution of (a) the positions and (b) the orientation of the molecules in the planar membrane at *N* = 512, , ε = 2, , and . (a) The *z* components of and are shown with respect to the center of mass of the membrane () for . The dashed line represents of the molecules at . (b) The *z* component of the molecular orientation is shown for , 2, 4, and 8. The error bars are displayed at several data points.

Sequential snapshots of the molecular self-assembly at *N* = 2000, , ε = 2, , , , and . (a) . (b) . (c) . (d) .

Sequential snapshots of the molecular self-assembly at *N* = 2000, , ε = 2, , , , and . (a) . (b) . (c) . (d) .

Droplet-vesicle transition at *N* = 500, ε = 2, , , and . The lower and upper lines represent the radius of gyration in increasing or decreasing, respectively. Sliced snapshots are also shown at .

Droplet-vesicle transition at *N* = 500, ε = 2, , , and . The lower and upper lines represent the radius of gyration in increasing or decreasing, respectively. Sliced snapshots are also shown at .

Formation of vesicles from a droplet at *N* = 4000, ε = 2, , , and . The tilt coefficient is gradually increased as . Sliced snapshots are shown at (a) (), (b) , (c) , (d) , and (e) (). All molecules are also shown for in (c).

Formation of vesicles from a droplet at *N* = 4000, ε = 2, , , and . The tilt coefficient is gradually increased as . Sliced snapshots are shown at (a) (), (b) , (c) , (d) , and (e) (). All molecules are also shown for in (c).

Shape transition points of molecular aggregates between the droplet and the bilayer membrane (vesicles and disks) for various (a) *N*, (b) , (c) ε, and (d) . If not specified, *N* = 500, ε = 2, , and . The solid and dashed lines represent data with increasing and decreasing , respectively. The open and filled symbols represent data with fixed and , respectively.

Shape transition points of molecular aggregates between the droplet and the bilayer membrane (vesicles and disks) for various (a) *N*, (b) , (c) ε, and (d) . If not specified, *N* = 500, ε = 2, , and . The solid and dashed lines represent data with increasing and decreasing , respectively. The open and filled symbols represent data with fixed and , respectively.

Surface tension γ of a flat membrane at *N* = 512, , ε = 2, , and . Dependence of γ on (a) the projected area per molecule and (b) the intrinsic area per molecule . The squares, triangles, and circles represent γ for , and 8, respectively. The error bars are smaller than the line thickness.

Surface tension γ of a flat membrane at *N* = 512, , ε = 2, , and . Dependence of γ on (a) the projected area per molecule and (b) the intrinsic area per molecule . The squares, triangles, and circles represent γ for , and 8, respectively. The error bars are smaller than the line thickness.

Spectra of undulation modes of nearly planar, tensionless membranes (γ = 0) at *N* = 8192, , ε = 2, , and . Results for calculated from the molecular positions (+) and from the averaged positions on a square mesh (×) are shown. The inset shows the dependence of on , which is used to extract the bending rigidity κ.

Spectra of undulation modes of nearly planar, tensionless membranes (γ = 0) at *N* = 8192, , ε = 2, , and . Results for calculated from the molecular positions (+) and from the averaged positions on a square mesh (×) are shown. The inset shows the dependence of on , which is used to extract the bending rigidity κ.

Line tension Γ of membrane edge at ε = 2, , , , and . The circles represent Γ calculated from a pore on the flat membrane at *N* = 2048. The solid line represents Γ calculated from the striped membrane at *N* = 512: .

Line tension Γ of membrane edge at ε = 2, , , , and . The circles represent Γ calculated from a pore on the flat membrane at *N* = 2048. The solid line represents Γ calculated from the striped membrane at *N* = 512: .

Time development of the probability difference of the molecules in the upper and lower monolayers at *N* = 512, , ε = 2, , and . At the initial states (*t* = 0), and . The error bars are displayed at several data points.

Time development of the probability difference of the molecules in the upper and lower monolayers at *N* = 512, , ε = 2, , and . At the initial states (*t* = 0), and . The error bars are displayed at several data points.

Parameter dependence of (a) the intrinsic area per molecule, (b) area compression modulus , (c) bending rigidity κ, (d) line tension Γ, and (e) diffusion coefficient *D* for the tensionless membrane at , , and . The circles and squares represent data for ε = 2 and 8, respectively.

Parameter dependence of (a) the intrinsic area per molecule, (b) area compression modulus , (c) bending rigidity κ, (d) line tension Γ, and (e) diffusion coefficient *D* for the tensionless membrane at , , and . The circles and squares represent data for ε = 2 and 8, respectively.

Parameter ε dependence of (a) , (b) , (c) κ, (d) Γ, and (e) *D* for , , and . The triangles, circles, and squares represent data for , 4, and 8, respectively.

Parameter ε dependence of (a) , (b) , (c) κ, (d) Γ, and (e) *D* for , , and . The triangles, circles, and squares represent data for , 4, and 8, respectively.

Bending rigidity κ dependence on (a) , (b) , and (c) for , ε = 2, and . The solid lines with squares, circles, and triangles represent data for , , and , respectively. The dashed lines with crosses and diamonds represent data for and 8, respectively.

Bending rigidity κ dependence on (a) , (b) , and (c) for , ε = 2, and . The solid lines with squares, circles, and triangles represent data for , , and , respectively. The dashed lines with crosses and diamonds represent data for and 8, respectively.

Parameter dependence of (a) , (b) , (c) Γ, and (d) *D* for , ε = 2, and . The squares, circles, and triangles represent data for , , and , respectively.

Parameter dependence of (a) , (b) , (c) Γ, and (d) *D* for , ε = 2, and . The squares, circles, and triangles represent data for , , and , respectively.

Parameter dependence of (a) , (b) , (c) Γ, and (d) *D* for , ε = 2, and . The squares and circles represent data for and 8, respectively.

Parameter dependence of (a) , (b) , (c) Γ, and (d) *D* for , ε = 2, and . The squares and circles represent data for and 8, respectively.

Line tension Γ dependence on at ε = 2 or 8, or , and . (a) The diamonds, squares, triangles, and circles represent data for , and 8, respectively. (b), (c) The squares, triangles, and circles represent data for , and 8, respectively.

Line tension Γ dependence on at ε = 2 or 8, or , and . (a) The diamonds, squares, triangles, and circles represent data for , and 8, respectively. (b), (c) The squares, triangles, and circles represent data for , and 8, respectively.

Parameter dependence of (a) , (b) , (c) κ, and (d) *D* for , ε = 2, and . The squares and circles represent data for and 8, respectively.

Parameter dependence of (a) , (b) , (c) κ, and (d) *D* for , ε = 2, and . The squares and circles represent data for and 8, respectively.

Half lifetime of flip-flop motion. (a) Dependence on at , ε = 2, and . The dashed lines represent the free-energy barrier estimated by the orientation distribution shown in Fig. 2(b). (b) Dependence on at and ε = 2. (c) Dependence on ε at , , and . (d) Dependence on at and .

Half lifetime of flip-flop motion. (a) Dependence on at , ε = 2, and . The dashed lines represent the free-energy barrier estimated by the orientation distribution shown in Fig. 2(b). (b) Dependence on at and ε = 2. (c) Dependence on ε at , , and . (d) Dependence on at and .

Sequential snapshots of vesicle rupture at *N* = 2000, ε = 2, , , , and . (a) . (b) . (c) .

Sequential snapshots of vesicle rupture at *N* = 2000, ε = 2, , , , and . (a) . (b) . (c) .

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