Role of molecular tilt in thermal fluctuations of lipid membranes

Long-wavelength thermal fluctuations of lipid membranes are adequately described by the Helfrich elastic model. On the other hand, fluctuations of wavelengths comparable with bilayer thickness exhibit significant deviations from the prediction of the elastic model and are typically assumed to be dominated by microscopic surface tension due to protrusion of lipid molecules into the solvent. We present evidence that the short-wavelength modes of a lipid membrane are dominated by fluctuations of the tilt of lipid molecules with respect to the membrane normal rather than the microscopic surface tension. We obtain an expression for the spectral intensity of the thermal membrane fluctuations by appealing to the Hamm-Kozlov model, which accounts for both membrane bending and lipid tilt contributions to the total membrane energy but neglects the contributions of the microscopic surface tension. The tilt and the bending fluctuations obtained from our coarse-grained molecular dynamics simulations of a dipalmitoylphosphatidylcholine lipid bilayer show good agreement with the theory. Furthermore, the obtained tilt and bending moduli are in close agreement with experimentally determined values. The magnitude of the microscopic protrusion tension estimated from our simulations is significantly smaller than that of the tilt modulus. These results indicate that the membrane fluctuations can be adequately described by a macroscopic elastic model down to scales of interlipid distance provided one accounts for the tilt fluctuations.

Figure 1

Coarse-grained model of a DPPC lipid. The head group is modeled by two charged hydrophilic beads, representing the choline $\left({\mathrm{NC}}_3\right)$ and the phosphate $\left({\mathrm{PO}}_4\right)$ groups, the glycerol ester linkage is modeled by two beads of intermediate hydrophobicity, ${\mathrm{GL}}_1$ and ${\mathrm{GL}}_2$, and the lipid tails are modeled by chains of hydrophobic beads, $C_i$ $(i=1,\dots ,8)$.

Figure 2

Spectral intensity of tilt fluctuations for a DPPC bilayer obtained with the four different definitions of the molecular director vector $\mathbf{n}$ (see text). The solid (open) symbols show results obtained with the first (second) definition of the head group, and the circles (triangles) show the results obtained with the first (second) definition of the tail group.

Figure 3

Spectral intensity of a DPPC bilayer surface fluctuations (circles). The solid line shows a fit by Eq. (18). Dash-dotted and dashed lines show contributions of the first and second terms of Eq. (18), respectively.

Figure 4

Density ${\rho }_{jw}^i\left(r\right)$ of water beads located at distance $r$ away from the $j$th bead of a DPPC lipid within the bilayer; $j$= choline, ${\mathrm{GL}}_1$, $C_1$, $C_2$, $C_3$, and $C_4$ (see legend).