Influence of nonequilibrium lipid transport, membrane compartmentalization, and membrane proteins on the lateral organization of the plasma membrane

Compositional lipid domains (lipid rafts) in plasma membranes are believed to be important components of many cellular processes. The mechanisms by which cells regulate the sizes, lifetimes, and spatial localization of these domains are rather poorly understood at the moment. We propose a robust mechanism for the formation of finite-sized lipid raft domains in plasma membranes, the competition between phase separation in an immiscible lipid system and active cellular lipid transport processes naturally leads to the formation of such domains. Simulations of a continuum model reveal that the raft size distribution is broad and the average raft size is strongly dependent on the rates of cellular and interlayer lipid transport processes. We demonstrate that spatiotemporal variations in the recycling may enable the cell to localize larger raft aggregates at specific parts along the membrane. Moreover, we show that membrane compartmentalization may further facilitate spatial localization of the raft domains. Finally, we demonstrate that local interactions with immobile membrane proteins can spatially localize the rafts and lead to further clustering.

Figure 1

(Color online) Schematic presentation of the nonequilibrium lipid transport processes considered here. Both protein-facilitated flip-flop events (upper pathway) and vesicle trafficking events between the plasma membrane and internal organelles (lower pathway) lead to an effective rearrangement of the lipid composition over a scale $\sim \ell$ in the exoplasmic leaflet. The gray tubes represent membrane compartmentalization.

Figure 2

(Color online) Instantaneous recycling noise term realizations with different recycling lengths: (a) $\ell =0.01$, (b) $\ell =2$, and (c) $\ell =128$. The red, light grey in print (blue, dark grey in print) patches represent a local depletion (increase) of the raft component. The data has been locally averaged over a circular area of radius $r=10$ to highlight the differences in the large scale behavior between the three examples. Note that an increase in $\ell$ results in larger patches of the same color.

Figure 3

(Color online) Snapshots of domain configurations with different $\Delta x$ and $\Delta \tau$ in steady state. Raft and nonraft phases are shown in black and copper, respectively. (a) $\Delta x=0.5,\Delta t=0.0013$ and (b) $\Delta x=1.0,\Delta t=0.005$. The other parameters were set to $H=1.41$, $\ell =\infty$, and $\varphi =0$ for both simulations. (c) The asymptotic domain size converges for different choices of the grid spacing $\Delta x$ and time step $\Delta \tau$ within error bars, which are shown for the three data points corresponding to the end of the simulations.

Figure 4

(Color online) Snapshots of domain configurations with different recycling lengths with $\ell =1$ (a) and (b) and $\ell =64$ (c) and (d). Raft (nonraft) phase is shown in black (copper). The snapshot times are $\tau =2000$ (a) and (c) and $\tau =7500$ (b) and (D=d). For both systems, $\varphi =0.5$ and $H=0.71$.

Figure 5

(Color online) The time evolution of the mean domain size corresponding to Fig. 4. Continuous domain coarsening is observed for $\ell =1$ with $R\sim t^{0.29\pm 0.02}$, while for $\ell =64$ domain coarsening is suppressed and the system enters a steady-state due to sufficiently strong recycling processes.

Figure 6

(Color online) Snapshots of domain structures in steady state with recycling lengths (a) $\ell =2$, (b) $\ell =16$, and (c) $\ell =1280$. For all cases, $\varphi =0.25$ and $H=1.41$. Again, the raft (nonraft) phase is shown in black (copper). (d) The average domain size in steady state increases as $\ell$ increases.

Figure 7

(Color online) The behavior of domain size distribution for lipid raft area fraction $\varphi =0.25$ and $H=1.41$ for several values of the recycling length $\ell$ on a logarithmic scale. The data in (b) have been shifted vertically to highlight the observations that (1) the different curves have the same slope, as can be seen in (a), and (2) the main effect of increasing the recycling length $\ell$ is to allow for the formation of larger domains, highlighted in (b).

Figure 8

(Color online) Snapshots of domain structures in steady state. The recycling rate $H=1.41$ (a) and (c) and $H=0.71$ (b). The nominal lipid raft area fraction was set to $\varphi =0.15$ (a) and (b) or 0.25 (c), with the recycling length $\ell =16$. Again, the raft (non raft) phase is shown in black (copper). The average domain size plotted in (d) shows that the average domain size decreases as the recycling rate increases and/or area fraction decreases.

Figure 9

(Color online) Steady state domain size $\overline{R}$ as a function of $H$, $\varphi$, and the scaling of the data. (a) $\overline{R}$ vs $H$ for a fixed $\varphi$; (b) $\overline{R}$ vs $\varphi$ for a fixed $H$; (c) $K\left(H\right)$ vs $H$. The red line is a fitting function for $K\left(H\right)$; (d) $\overline{R}\left(\varphi ,H\right)/K\left(H\right)$ vs $\varphi$. Recycling length $\ell =20$ for all simulations.

Figure 10

(Color online) Steady-state average linear domain size as a function of the recycling rate $H$ and length $\ell$ for a fixed nominal lipid raft area fraction $\varphi =0.15$. Note that H increases from right to left in the plot. The two frames on the right display slices through the data at fixed $H$ and $\ell$, respectively.

Figure 11

(Color online) Effect of spatiotemporally varying $H$ on local raft domain properties. At the center of the system inside a disk of radius $r=50$, $H^{in}=0.25$ for $1250\le \tau \le 2500$, while $H^{in}=1.41$ at all other times; outside the disk, $H^{out}=1.414$ always. The lipid raft area fraction $\varphi =0.3$ and the recycling length $\ell =4$ everywhere. The plot in (d) shows the time development of $R\left(\tau \right)$ inside and outside the disk region [$R^{in}\left(\tau \right)$ and $R^{out}\left(\tau \right)$, respectively]. The snapshots were taken at (a) $\tau =1000$, (b) $\tau =2400$, and (c) $\tau =2525$, respectively. Note that $R^{in}\left(\tau \right)$ rapidly increases in the time window when $H^{in}$ is reduced, and rapidly decreases toward the steady-state value when $H^{in}$ is reset to its original value.

Figure 12

(Color online) Snapshots of domain structures and the mean domain size evolution in the presence of compartments of characteristic linear dimension (a) $L_c=64$ and (b) $L_c=32$ with compartment boundaries described by a reduced mobility. In the simulations $\varphi =0.25$, $H=0.85$, and $\ell =10$. The mobility $M$ reduces from a value of $M=1$ inside the compartments to $M=0.1$ at the compartment boundaries, whose thickness was set to 6 grid spacings. As can be seen from (c), the domain size decreases as $L_c$ decreases, corresponding to an increase in the total compartment boundary length.

Figure 13

(Color online) Snapshots of domain configurations in the presence of compartment boundaries (not drawn to scale), represented by a nonzero value of $g\left(r\right)$, which either attract $\left[\text{(a)}\sim \text{(c)}\right]$ or repel $\left[\text{(d)}\sim \text{(f)}\right]$ the raft phase. $g\left(r\right)=0.8$ for $\left[\text{(a)}\sim \text{(c)}\right]$ and $g\left(r\right)=-0.8$ for $\left[\text{(d)}\sim \text{(f)}\right]$. Except for the boundaries represented by the blue mesh, $g\left(r\right)=0$ elsewhere. No recycling is present in (a) and (d), while $H=1.13$ and $\ell =10$ in (b), (c), (e), and (f); furthermore, to assist in viewing, (c) and (f) display only the local composition from snapshots (b) and (e), respectively, with compartment boundaries excluded. Compartment boundary thickness is 3, and the nominal raft area fraction $\varphi =0.4$. Note that the boundary-lipid interaction has shifted the equilibrium compositions of the raft and nonraft phases, and thus, the effective raft area fraction varies between frames.

Figure 14

(Color online) Average domain size in the presence of compartments with attractive or repulsive raft-boundary interactions.

Figure 15

(Color online) Spatial localization and aggregation of lipid rafts due to membrane proteins. Here, white crosses indicate the locations of immobile membrane proteins. (a) Raft distribution in the presence of 15 randomly distributed proteins. Notice how each protein is surrounded by a raft domain. (b) Raft distribution in the presence 15 weakly clustered proteins. (c) Raft distribution in the presence of 15 strongly clustered proteins. Note the appearance of an extended raft centered around the protein aggregate in the right panel.