Figure 1.
Schematic of Lipid Clustering in Different Membrane Configurations
(A) A homogeneous mixture of two lipid components (type A in blue, B in red) has a high energy because of the abundance of unlike nearest-neighbor pairs, each contributing an energy ε (see Materials and Methods).
(B) Same as (A), except the cell wall has higher curvature; this results in a slight reduction in the energy of lipids of type A, which have higher intrinsic curvature.
(C) A cluster of lipids of type A is accompanied by membrane curvature (∇2h(r)). Though the elastic energy of the membrane increases relative to (A), the formation of clusters eliminates unlike nearest-neighbor pairs and so reduces the total energy.
(D) The same configuration in (C) shifted to a region of cell wall with higher curvature experiences a large reduction in energy, leading to cluster localization at the poles.
Figure 2.
Lipid Cluster Size as a Function of Short-Range Attractive Interaction and Intrinsic Lipid Curvature
(A–F) Representative distribution in a mixed membrane of lipids A and B, where lipid A has intrinsic curvature γ, lipid B has no intrinsic curvature, and immediately neighboring lipids of the same type experience an attractive interaction ɛ. The stiffness modulus (κ = 25 kBT), pinning modulus (λ = 0.25 kBT/nm4), and fraction of lipid A (ϕ = 0.075) are the same in all panels. Blue indicates the presence of lipid A, while red represents the height of the membrane relative to the cell wall. (A–C) ɛ = 2.5 kBT, and γ = 0.2 nm−1, 0.4 nm−1, 0.6 nm−1, respectively
(D,E) ɛ = 3 kBT, and γ = 0.4 nm−1, 0.6 nm−1, respectively.
(F) ɛ = 4 kBT and γ = 0.6 nm−1.
(G) Height profile of the membrane along the dashed black line in (B).
(H) The long-range repulsive elastic interaction between two lipids is well fit by a Gaussian.
(I) Average cluster size as a function of ɛ/γ2. Results of simulations are shown with blue dots, while the black line represents the theoretical prediction based on minimizing free energy per lipid.
Figure 3.
Polar Localization of Lipid Clusters
Elastic energy parameters are fixed (κ = 25 kBT, λ = 0.25 kBT/nm4, γ = 0.4 nm−1), with varying short-range attraction (A) ɛ = 1 kBT, (B) ɛ = 1.5 kBT, and (C) ɛ = 2.5 kBT. The rectangles on the left and right represent the cell poles and have slightly enhanced cell-wall curvature, γpole = 0.04 nm−1. The three-dimensional figure in (D) represents the lipid position and the membrane height in (C) mapped onto the surface of a capped cylinder. The color scheme and fraction of lipid A (ϕ = 0.075) are the same as in Figure 2.
Figure 4.
Effect of Membrane Composition on Cluster Formation
(A,C) The percentage of lipid A is ϕ = 0.15; the clusters remain approximately the same size as in Figure 2B, with the same lipid and elastic parameters.
(C) The rectangles at the left and right represent the poles of the cell with slightly higher curvature γpole = 0.04 nm−1, as in Figure 3.
(B,D) Identical to (A) and (C), respectively, except that ϕ = 0.3.
Figure 5.
Localization of Lipid Clusters by Heterogeneous Membrane Pinning
Membrane with uniform cell-wall curvature, fixed stiffness modulus κ = 25kBT and lipid A intrinsic curvature γ = 0.4 nm−1, and varying short-range attraction (A) ɛ = 1 kBT, (B) ɛ = 1.5 kBT, and (C) ɛ = 2.5 kBT. The pinning modulus of the left half of the membrane is lower by a factor of two (λ = λ0/2 = 0.125 kBT/nm4) relative to the right half of the cell (λ = λ0). The color scheme and fraction of lipid A (ϕ = 0.075) are the same as in Figure 2.
Figure 6.
Competition between Curvature and Osmotic Localization of Lipid Clusters during Sporulation and Cell Division
(A) During exponential growth, high-intrinsic-curvature lipid clusters localize to the poles of the inner leaflet (solid black curve), driven by differences in membrane curvature. All curvatures are shown relative to curvature in the cylindrical region of the cell. The cell-wall curvature experienced by the outer leaflet (solid gray curve) is opposite in sign to the intrinsic lipid curvature. Orange regions denote cardiolipin localization.
(B) A lower osmotic-pressure differential across the septal/forespore-engulfing membrane corresponds to a reduced value of the pinning modulus λ and induces relocalization of the lipid clusters to the septal membrane (see Figure 5).
(C) As the spore is engulfed, the clusters can migrate along the continuous leaflet consisting of the inner leaflet of the mother cell and the outer leaflet of the forespore-engulfing membrane to localize around the spore due to low osmotic-pressure differential.