Origin of lipid tilt in flat monolayers and bilayers

This paper continues the series of our works devoted to the liquid-gel phase transition in lipid membranes. Previously we described a variation of area per lipid, membrane thickness, and diffusion coefficient at the temperature-driven liquid-gel phase transition in bilayers. Here we expand the application of our analytic model approach to include a description of the lipid tilt and also extend the investigation to include Langmuir and self-assembled monolayers. The theory describes tilt formation at the temperature-driven liquid-gel phase transition in bilayers and the pressure-driven phase transition in Langmuir monolayers. Neither uniform tilt nor liquid-gel phase transition is found in self-assembled monolayers chemically bonded to the substrate.

Figure 1

Origin of the tilt. The lipid can lower its free energy by getting tails closer to each other, thereby increasing van der Waals attraction. However, if the area per tails is sufficiently small, due to the glycerol “neck” this is possible only by tilting the tails together.

Figure 2

Hydrocarbon tails of the lipid molecule are modeled as a flexible string. Schematic representation.

Figure 3

Collisions with neighboring lipids are modeled by self-consistent confining potential. Potential is a parabolic function of the string deviation amplitude from axis $z$ (arrow sizes mimic local force strength).

Figure 4

Main phase transition in DPPC bilayer.

Figure 5

DPPC bilayer mean order parameter dependence on the temperature.

Figure 6

Lipid monolayer with a tilt.

Figure 7

Solid line with empty triangles shows computed tilt angle for DPPC bilayer. Filled triangles show measured DPPC bilayer tilt angle values [17]. Line with empty circles shows calculated cross-section area of DPPC tails. Area per lipid is defined by the lipid tails as long as cross-section area per tail exceeds the area per lipid head. Filled circles show experimental data for area per lipid in DPPC [17].

Figure 8

Langmuir monolayer setup. Area per lipid is set by the external pressure applied to barriers.

Figure 9

Liquid-to-gel pressure-driven DPPC phase transition at 297 K (Langmuir setup, see Fig. 8). Equation of state is the same as for a bilayer, Eq. (17), with external pressure (see Fig. 8) $P_L$ taking part of hydrophobic tension $\gamma$. Dashed line shows area per tails in the gel phase.

Figure 10

Calculated free energy of hydrocarbon tails of DPPC Langmuir monolayer at 297 K and external pressure of 18 dyn/cm. Experimental area per lipid under these conditions is about 46 Å${}^2$ (shown here with dashed line, also see Fig. 9).

Figure 11

Pressure-driven liquid-to-gel phase transition pressure dependence on temperature for DPPC. Experimental data from [18, 19].

Figure 12

Neither uniform tilt, nor temperature- or pressure-driven liquid-gel phase transition are found for a lipid monolayer chemically bonded to a substrate.

Figure 13

The only displacement type of the bonded rigid rod.