Spatial extent of a single lipid's influence on bilayer mechanics

To what spatial extent does a single lipid affect the mechanical properties of the membrane that surrounds it? The lipid composition of a membrane determines its mechanical properties. The shapes available to the membrane depend on its compositional material properties, and therefore, the lipid environment. Because each individual lipid species' chemistry is different, it is important to know its range of influence on membrane mechanical properties. This is defined herein as the lipid's mechanical extent. Here, a lipid's mechanical extent is determined by quantifying lipid redistribution and the average curvature that lipid species experience on fluctuating membrane surfaces. A surprising finding is that, unlike unsaturated lipids, saturated lipids have a complicated, nonlocal effect on the surrounding surface, with the interaction strength maximal at a finite length-scale. The methodology provides the means to substantially enrich curvature-energy models of membrane structures, quantifying what was previously only conjecture.

Figure 1

Top: A cartoon illustrating the curvature-sampling bias created by tracking a lipid's position away from the neutral surface. Colored arrows indicate how measuring a lipid's position off the neutral surface (dashed black line) biases either toward negative curvature when sampled too close to the head groups (red arrows) or toward positive curvature when sampled too far into the acyl chain region (blue arrows). Bottom: Transverse curvature bias profiles, $\langle c_{\mathbf{q}}\rangle \left(z\right)$, for mixtures including DOPC, DOPE, and DOPS. Profiles including all lipids are shown in black. The average curvature per lipid (vertical axis) is reported as a function of the atom used to measure a lipid's lateral position. The atom's identity is mapped to its height in a nearly planar initial state (horizontal axis). The lipid's average curvature is recorded at the neutral surface determined using the average over all lipids. The arrow for DOPE in the center panel indicates the shift due to lipid spontaneous curvature. The red and blue colors indicate the sign of curvature according to the cartoon above. Note that the data points for each lipid's profile are not independent; they are correlated by being spatially fixed by the molecular geometry. Error bars are standard errors of the mean.

Figure 2

${\overline{F}}_c^{\prime }\left(0\right)$versus percentage of PSM in a POPC bilayer. Error bars are standard errors of the mean. The dark shaded regions are within one standard deviation for a linear fit of their respective data with PSM $>60\%$. The lighter shaded regions are two standard deviations.

Figure 3

Spontaneous curvature spectra sampled from PC${}_{55}$PS${}_{45}$, PC${}_{25}$PE${}_{30}$PS${}_{45}$, and PE${}_{55}$PS${}_{45}$. DOPC is shown in black triangles, DOPS in gray circles, and DOPE in lighter gray squares. Open circles at $q=0$ are computed from the LPP. The data is a histogram of values. Error bars are $\pm$ the standard error of the histogram bin mean.

Figure 4

Spontaneous curvature spectra sampled from simulations of PSM in POPC. POPC is shown in blue. PSM is colored red. Open circles at $q=0$ are computed from the LPP. Each data point is the average over modes within a narrow range of $q$. The dashed line indicates an exponential fit to the spectra as discussed in the text. Points outlined in black in the intermediate range of $q$ indicate where saturated lipids appear to have increased positive curvature. Error bars are $\pm$ the standard error of the histogram bin mean.

Figure 5

Spontaneous curvature spectra sampled from DPPC${}_{20}$POPC${}_{80}$. POPC is shown in blue. DPPC is colored red. The data is a histogram of values. Points outlined in black in the intermediate range of $q$ indicate where saturated lipids appear to have increased positive curvature. Error bars are $\pm$ the standard error of the histogram bin mean.