Domain formation in membranes caused by lipid wetting of protein

Formation of rafts and other domains in cell membranes is considered as wetting of proteins by lipids. The membrane is modeled as a continuous elastic medium. Thermodynamic functions of the lipid films that wet proteins are calculated using a mean-field theory of liquid crystals as adapted to biomembranes. This approach yields the conditions necessary for a macroscopic wetting film to form; its thickness could also be determined. It is shown that films of macroscopic thicknesses form around large (tens nanometers in diameter) lipid-protein aggregates; only thin adsorption films form around single proteins or small complexes. The means by which wetting films can facilitate the merger of these aggregates is considered. It is shown that a wetting film prevents a protein from leaving an aggregate. Using experimentally derived values of elastic moduli and spontaneous curvatures as well as height mismatch between aggregates and bulk membrane, we obtained numerical results, which can be compared with the experimental data.

Figure 1

Schematic representation of a protein or an aggregate of radius $r_p$ wetted by a lipid film of thickness $l$.

Figure 2

Compensation of hydrophobic mismatch between the surrounding bilayer membrane and a protein transmembrane domain (gray). (a) Compensation is achieved by deformation of the liquid-disordered membrane without formation of a film. (b) Compensation with the formation of a thin film. The film is in a liquid-ordered state. For both (a) and (b), the hydrophobic mismatch at the protein surface is completely compensated by membrane deformations. The notations are described in the body of the text.

Figure 3

Deformations of elements of a monolayer: (a) the initial undistorted state, (b) the deformation of tilt, (c) the deformation of splay. See text for details.

Figure 4

The dependence of chemical potential of the film $\mu$ on film thickness $l=r-r_p$. Here, zero spontaneous curvatures $J_r=J_s=0$ and zero protein-film mismatch $h_p=h_r$ are assumed. This allows the influence of the mismatch between the film and surround on chemical potential to be directly illustrated by curves $A–D$: curve $A$, $h_p=h_r=2.3\mathrm{nm}$; curve $B$, $h_p=h_r=2.4\mathrm{nm}$; curve $C$, $h_p=h_r=2.5\mathrm{nm}$; curve $D$, $h_p=h_r=2.6\mathrm{nm}$. $h_s=2.0\mathrm{nm}$ and $r_p=20\mathrm{nm}$ for all four curves. The horizontal dashed lines correspond to the chemical potentials of the surrounding membrane at subsaturations $\Delta =0.2\%$, 0.4%, 0.5%, and 1%.

Figure 5

The work $E$ to create a film of thickness $l$. Curves $A–C$ represent different membrane subsaturations corresponding to those of the horizontal dashed lines in Fig. 4: curve $A$, $\Delta =1\%$; curve $B$, $\Delta =0.4\%$; curve $C$, $\Delta =0.2\%$. The parameters are those of curve $C$ of Fig. 4, $J_r=J_s=0$, $h_p=h_r=2.5\mathrm{nm}$, $h_s=2.0\mathrm{nm}$, and $r_p=20\mathrm{nm}$.

Figure 6

The dependence of boundary energy $W$ (per monolayer) on $l$. All parameters for curves $A–D$ are the same as in Fig. 4.

Figure 7

(a) The dependence of chemical potential of the film $\mu$ on film thickness $l=r-r_p$. The spontaneous curvatures are set equal to zero, $J_r=J_s=0$, but in contrast to Fig. 4, the length of the protein transmembrane domain is varied to create a height mismatch between the protein and film. Curve $A$, $h_p=2.0\mathrm{nm}$; curve $B$, $h_p=2.5\mathrm{nm}$; curve $C$, $h_p=2.7\mathrm{nm}$; curve $D$, $h_p=2.9\mathrm{nm}$. (b) The dependence of the boundary energy $W$ (per monolayer) on $l$. All parameters for curves $A–D$ are the same as in (a). For (a) and (b), $h_r=2.5\mathrm{nm}$, $h_s=2.0\mathrm{nm}$, and $r_p=20\mathrm{nm}$.

Figure 8

Work $E$ for creating a film of thickness $l$ for the case of curve $C$ in Fig. 7: $J_r=J_s=0$, $h_p=2.7\mathrm{nm}$, $h_r=2.5\mathrm{nm}$, $h_s=2.0\mathrm{nm}$, and $r_p=20\mathrm{nm}$. Zero subsaturation is assumed, $\Delta =0\%$.

Figure 9

Work $E$ for creating a film of thickness $l$ for the case of curve $A$ in Fig. 7: $J_r=J_s=0$, $h_p=2.0\mathrm{nm}$, $h_r=2.5\mathrm{nm}$, $h_s=2.0\mathrm{nm}$, and $r_p=20\mathrm{nm}$. Subsaturation is $\Delta =0\%$.

Figure 10

The dependence of chemical potential of the film $\mu$ on film width $l=r-r_p$ for varied protein radii $r_p$. Curve $A$, $r_p=5\mathrm{nm}$; curve $B$; $r_p=10\mathrm{nm}$; curve $C$; $r_p=20\mathrm{nm}$; curve $D$; $r_p=30\mathrm{nm}$, curve $E$, $r_p=\infty$. Spontaneous curvatures are zero, $J_r=J_s=0$, and $h_p=h_r=2.5\mathrm{nm}$, $h_s=2.0\mathrm{nm}$.

Figure 11

(a) The dependence of chemical potential of the film $\mu$ on film thickness $l=r-r_p$ for varied spontaneous curvatures. Curve $A$, $J_r=J_s=0$; curve $B$, $J_r=-1∕14{\mathrm{nm}}^{-1}$, $J_s=-1∕8{\mathrm{nm}}^{-1}$; curve $C$, $J_r=0$, $J_s=-1∕8{\mathrm{nm}}^{-1}$. The equilibrium width of the film is largest for maximum $\mid J_r-J_s\mid$. (b) The dependence of the boundary energy $W$ (per monolayer) on $l$. All parameters for curves $A–D$ are the same as in (a). In all curves of panels (a) and (b), $h_p=2.5\mathrm{nm}$, $h_r=2.5\mathrm{nm}$, $h_s=2.0\mathrm{nm}$, $r_p=20\mathrm{nm}$.

Figure 12

The dependence of the free energy $E_{\mathit{min}}\left(r_p\right)$ of the equilibrium film on the radius of an aggregate $r_p$.

Figure 13

The dependence of chemical potential of a film, $\mu$, on film thickness $l=r-r_p$. Curve $A$ calculated the chemical potential by using the energy of fluctuations, $V_{\mathit{fl}}$, at a boundary. Curve $B$ (which is the same as curve $D$ in Fig. 4) uses the mean-field theory. For both curves $h_s=2.0\mathrm{nm}$ and $r_p=20\mathrm{nm}$.

Figure 14

Dependence of the free energy of a film, $E\left(r\right)$, on film thickness $l=r-r_p$. The parameters are the same as for curve $D$ of Fig. 4, subsaturation $\Delta =0.1\%$.