_{II}mesophase of monoolein

^{1,2,a)}, Anela Ivanova

^{3}, Galia Madjarova

^{3}, Abraham Aserin

^{1}and Nissim Garti

^{1}

### Abstract

The goal of the present work is to study theoretically the structure of water inside the water cylinder of the inverse hexagonal mesophase (H_{II}) of glyceryl monooleate (monoolein, GMO), using the method of molecular dynamics. To simplify the computational model, a fixed structure of the GMO tube is maintained. The non-standard cylindrical geometry of the system required the development and application of a novel method for obtaining the starting distribution of water molecules. A predictor-corrector schema is employed for generation of the initial density of water. Molecular dynamics calculations are performed at constant volume and temperature (*NVT* ensemble) with 1D periodic boundary conditions applied. During the simulations the lipidstructure is kept fixed, while the dynamics of water is unrestrained. Distribution of hydrogen bonds and density as well as radial distribution of water molecules across the water cylinder show the presence of water structure deep in the cylinder (about 6 Å below the GMO heads). The obtained results may help understanding the role of water structure in the processes of insertion of external molecules inside the GMO/water system. The present work has a semi-quantitative character and it should be considered as the initial stage of more comprehensive future theoretical studies.

I. INTRODUCTION

II. INITIAL MODEL OF THE GMO/WATER STRUCTURE

III. CONSTRUCTION OF THE INITIAL STATE AND MD SETUP

A. Construction of the GMO tube

B. Construction of the initial water structure

C. MD setup

IV. RESULTS AND DISCUSSION

V. CONCLUSIONS

### Key Topics

- Lipids
- 20.0
- Hydrogen bonding
- 15.0
- Hydrophilic interactions
- 14.0
- Molecular dynamics
- 14.0
- Rings
- 8.0

##### C12

## Figures

Schematic representation of the inverse hexagonal (H_{II}) mesophase of monoolein and its crystal lattice parameters (left), and the structural formulas of GMO and tricaprylin (right).

Schematic representation of the inverse hexagonal (H_{II}) mesophase of monoolein and its crystal lattice parameters (left), and the structural formulas of GMO and tricaprylin (right).

(a) Structure of the GMO molecule used throughout the process of building the GMO tubes. Axis (*x*) is the longest axis of rotation. Axes (*y*) and (*z*) are presented for completeness; (b) Graphical representation of a generated GMO ring with notations of the radius of the internal empty circle and the pivotal radius *R* _{w} and *R* _{p}; (c) Skewed side view of a constructed GMO tube (see Sec. III A for detailed explanations).

(a) Structure of the GMO molecule used throughout the process of building the GMO tubes. Axis (*x*) is the longest axis of rotation. Axes (*y*) and (*z*) are presented for completeness; (b) Graphical representation of a generated GMO ring with notations of the radius of the internal empty circle and the pivotal radius *R* _{w} and *R* _{p}; (c) Skewed side view of a constructed GMO tube (see Sec. III A for detailed explanations).

(a) Pivotal surface, *A* _{p}, as a criterion for determination of the distance between GMO rings – 2*R* _{p} (for parameter definitions, see Sec. III A and Eqs. (10) and (11); (b) Explanation of the process of GMO ring sectorization using the sector angle *θ*. (see Sec. III A for details).

(a) Pivotal surface, *A* _{p}, as a criterion for determination of the distance between GMO rings – 2*R* _{p} (for parameter definitions, see Sec. III A and Eqs. (10) and (11); (b) Explanation of the process of GMO ring sectorization using the sector angle *θ*. (see Sec. III A for details).

Initial distribution of water molecules obtained by the Monte Carlo rejection sampling routine (see Sec. III B for details). The cylindrical volume of the distribution is rotated about the *y*-axis for a better view.

Initial distribution of water molecules obtained by the Monte Carlo rejection sampling routine (see Sec. III B for details). The cylindrical volume of the distribution is rotated about the *y*-axis for a better view.

The effective part of a single GMO ring, which is initially hydrated; the same structural unit is used for calculation of the positions of the GMO molecules along the ring.

The effective part of a single GMO ring, which is initially hydrated; the same structural unit is used for calculation of the positions of the GMO molecules along the ring.

The pivotal area and the pivotal volume estimation by fitting an appropriate dataset with Eq. (11). The values of *R* _{w} and *A* _{w} are taken from Table I.

The pivotal area and the pivotal volume estimation by fitting an appropriate dataset with Eq. (11). The values of *R* _{w} and *A* _{w} are taken from Table I.

(a) Probability mass function and (b) cumulative distribution function of the distances between 1514 oxygen atoms of water molecules inside the water cylinder of a GMO/water structure. The oxygen lattice forms a cylindrical volume with no submerged GMO heads within (*R* _{w} = 12 Å, *h* = 100 Å) (see Sec. III B for explanations).

(a) Probability mass function and (b) cumulative distribution function of the distances between 1514 oxygen atoms of water molecules inside the water cylinder of a GMO/water structure. The oxygen lattice forms a cylindrical volume with no submerged GMO heads within (*R* _{w} = 12 Å, *h* = 100 Å) (see Sec. III B for explanations).

Front (a) and side (b) visualization of the coordinate set of the initial structure of a GMO/water system. The first GMO ring of the structure is removed to satisfy the PBC requirements.

Front (a) and side (b) visualization of the coordinate set of the initial structure of a GMO/water system. The first GMO ring of the structure is removed to satisfy the PBC requirements.

An illustrative example of the GMO/water structure obtained after the MD simulation of system with *N* _{l} = 17 (Table I): (a) radial view; (b) side view with periodic boundary conditions applied. Due to the careful initial arrangement of water molecules and their quantity (fitting of water density), there is no depletion or significant excess of molecules.

An illustrative example of the GMO/water structure obtained after the MD simulation of system with *N* _{l} = 17 (Table I): (a) radial view; (b) side view with periodic boundary conditions applied. Due to the careful initial arrangement of water molecules and their quantity (fitting of water density), there is no depletion or significant excess of molecules.

Probability mass function of hydrogen bond distances between the GMO and the water molecules (G/W) and between the water molecules themselves (W/W).

Probability mass function of hydrogen bond distances between the GMO and the water molecules (G/W) and between the water molecules themselves (W/W).

Distribution of water density across the three cylinders with different radii: (a), (c), and (e) – radial distribution (*xy*-coordinates); (b), (d), and (f) – longitudinal distribution (*z-*coordinate). All *z*-positions of the planes of the GMO circles are marked with arrows.

Distribution of water density across the three cylinders with different radii: (a), (c), and (e) – radial distribution (*xy*-coordinates); (b), (d), and (f) – longitudinal distribution (*z-*coordinate). All *z*-positions of the planes of the GMO circles are marked with arrows.

Radial distribution function, , of the distance between the hydroxyl oxygen of GMO, , directed towards the water cylinder, and oxygen atoms of the water molecules. Only the *xy*-component of the distance is used.

Radial distribution function, , of the distance between the hydroxyl oxygen of GMO, , directed towards the water cylinder, and oxygen atoms of the water molecules. Only the *xy*-component of the distance is used.

## Tables

Parameters of the studied systems at various water weight fractions and GMO/tricaprylin weight ratios^{26} (dilution line) at *t* = 25 °C: the hexagonal lattice parameter of the inverse hexagonal phase, *α* (Eq. (1)); the lipid volume ratio, *ϕ* _{l}; the radius of the water cylinder, *R* _{w} (Eq. (2)); area at the Luzatti interface, *A* _{0} (Eq. (3)); the number of lipid molecules in a GMO ring, *N* _{l} (Eq. (8)); the effective sector angle, *θ* _{eff} (Eq. (9)), and the radius of the pivotal area, *R* _{p}.

Parameters of the studied systems at various water weight fractions and GMO/tricaprylin weight ratios^{26} (dilution line) at *t* = 25 °C: the hexagonal lattice parameter of the inverse hexagonal phase, *α* (Eq. (1)); the lipid volume ratio, *ϕ* _{l}; the radius of the water cylinder, *R* _{w} (Eq. (2)); area at the Luzatti interface, *A* _{0} (Eq. (3)); the number of lipid molecules in a GMO ring, *N* _{l} (Eq. (8)); the effective sector angle, *θ* _{eff} (Eq. (9)), and the radius of the pivotal area, *R* _{p}.

List of rejection sampling rules used to determine the coordinates of oxygen atoms in a randomized water lattice and to fix the positions of the hydrogen atoms of water molecules. See Sec. III B for details.

List of rejection sampling rules used to determine the coordinates of oxygen atoms in a randomized water lattice and to fix the positions of the hydrogen atoms of water molecules. See Sec. III B for details.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content