3D Pressure Field in Lipid Membranes and Membrane-Protein Complexes

We calculate full 3D pressure fields for inhomogeneous nanoscale systems using molecular dynamics simulation data. The fields represent systems with increasing level of complexity, ranging from semivesicles and vesicles to membranes characterized by coexistence of two phases, including also a protein-membrane complex. We show that the 3D pressure field is distinctly different for curved and planar bilayers, the pressure field depends strongly on the phase of the membrane, and that an integral protein modulates the tension and elastic properties of the membrane.

Figure 1

The $p_T(r)$ for the DPPC semivesicle as a function of $r$ calculated using mean-field and virial methods.

Figure 2

Pressure profiles for DOPC bilayers and vesicles. (a) For the bilayer, the solid line and dashed green line stand for $p_L$ and $p_{zz}$, respectively. For the vesicle, the solid line and dashed black line correspond to $p_T$ and $p_{rr}$ with $\Delta P\approx -30\mathrm{bar}$, in respective order. (b) Results for the vesicle with $\Delta P\approx 130\mathrm{bar}$. Solid line and dashed red line correspond to $p_T$ and $p_{rr}$, respectively. Black lines are as in panel (a). Vertical dotted lines show the location of intersections between acyl chain and water density.

Figure 3

Pressure profile of a membrane-protein system. (a) Horizontal axis is the distance from protein center, vertical axis is the normal component of the bilayer (protein center at $z=0$). The lower and upper leaflets are characterized by $z\in [-4,-1)\mathrm{nm}$ and $z\in [-1,2]\mathrm{nm}$, respectively, and color represents the local pressure (in units of bar). The approximate boundary of the protein region is presented with a full black line (see the SM [19]). (b) Surface tension $\gamma$ as a function of distance from the protein center $r$. (c) Product $\kappa c_0$ vs $r$. Pivotal planes are located in $z_0=-2\mathrm{nm}$ and $z_0=0\mathrm{nm}$, for lower and upper [see order in panel (a) leaflets], respectively.

Figure 4

Pressure tensor components in (a) liquid and (b) gel phases. (c) Pressure as a function of normal to the phase boundary $\mathbf{P}(x)$ (see text). The pure liquid phase is located between $x=2–6\mathrm{nm}$ and the pure gel between 7.5–10.5 nm.