Morphology of the lamellipodium and organization of actin filaments at the leading edge of crawling cells

Abstract

Lamellipodium extension, incorporating actin filament dynamics and the cell membrane, is simulated in three dimensions. The actin filament network topology and the role of actin-associated proteins such as Arp2/3 are examined. We find that the orientational pattern of the filaments is in accord with the experimental data only if the spatial orientation of the Arp2/3 complex is restricted during each branching event. We hypothesize that branching occurs when Arp2/3 is bound to Wiskott-Aldrich syndrome protein (WASP), which is in turn bound to Cdc42 signaling complex; Arp2/3 binding geometry is restricted by the membrane-bound complex. Using mechanical and energetic arguments, we show that any membrane protein that is conical or trapezoidal in shape preferentially resides at the curved regions of the plasma membrane. We hypothesize that the transmembrane receptors involved in the recruitment of Cdc42/WASP complex has this property and concentrate at the leading edge. These features, combined with the mechanical properties of the cell membrane, explain why lamellipodium is a flat organelle.

FIGURE 1

Geometrical patterns of actin filaments at the leading edge of a crawling cell. The lamellipodium is a broad and extremely flat organelle filled with a dense actin filament network. The lamellipodium thickness is not drawn to scale with the rest of the cell. Looking from above, the actin filaments are polarized. The angle, α, is defined as the angle between the filament and the vertical normal. EM of the lamellipodium suggests that the angular probability distribution, P(α), has distinct peaks at ±35°.

FIGURE 2

Transmembrane proteins such as G protein-coupled receptors (GPCR) can be asymmetrical in shape. The hydrophobic contact energy between the membrane and the protein enforces a boundary condition at the protein-lipid interface. We compute the solvation energy of such a protein into a flat/curved membrane region, Δμ_1,2, which is the difference between free energies, F₂ − F₁. The symbols in the upper-panel are explained in the text.

FIGURE 3

Solvation free energy, Δμ, of membrane proteins as a function of the membrane curvature, 1/R. The protein is ≈5 nm in diameter and has a shape shown in the figure. All four interfaces with the membrane make an angle ψ with respect to N. For ψ = 70°, the most favorable curvature corresponds to a radius of 50 nm. In this case, the free energy difference between solvating in a flat region versus a curved one is ≈4 k_BT. Thus, the relative probability of seeing the protein in the flat region versus the leading edge (R = 50 nm) is low, i.e., e⁻⁴ = 0.02.

FIGURE 4

Solvation free energy of an asymmetric protein in a curved membrane. Two of the membrane interfaces impose an angle of ψ = π/2. The two other interfaces impose an angle of ψ = π/2 − 25°. We see that the membrane protein has a preferred orientation so that is perpendicular to the y-axis. For a membrane curvature of 1/50 nm⁻¹, the protein energy difference between two orientations is >6 k_BT.

FIGURE 5

Order of the actin monomers in the helical filament structure and branching geometry. D_m, D_d are the direction vectors of mother and daughter filaments. O_m, O_d are the orientation vectors of mother and daughter monomers. All the vectors D_m, D_d and O_m, O_d lie in the same plane. O_m, O_d and D_m, D_d also define the orientation of the Arp2/3 complex at the branching point. Note that D_m⊥O_m and D_d⊥O_d and ∠(D_d, D_m) = 70°.

FIGURE 6

The definitions of the variables used to describe the orientation of Arp2/3 with respect to the leading edge normal, N. {θ, φ, ω} are used in our model to define the geometry of a branching event. (a) Regardless of how Arp2/3 is attached to the membrane complex, the orientation of Arp2/3 can be specified by either (D_m, O_m) or (D_d, O_d). We chose (D_d, O_d), which are defined by {θ, φ, ω} with respect to the normal vector N. (b and c) The three-dimensional definitions of {θ, φ, ω}. The curved surface in c is the leading-edge membrane. (d) In our simulation, the average shape of the leading edge remains constant and N is defined with respect to the lab-frame, {x, y, z}.

FIGURE 7

Branching can only occur if the filament and Arp2/3 orientation are compatible with each other. Structure of WASP-Cdc42 complex is not known. We describe the orientation of Arp2/3 using probability distributions P(θ), P(φ), and P(ω). The orientation of the F-actin tip, described by (θ′, φ′, ω′), must fall within the nonzero regions of the probability distribution.

FIGURE 8

The probability distribution, P(α), for growing actin filaments in the lamellipodium. The dashed line is the experimental data from Maly and Borisy (11), which shows the histogram of α with respect to the normal of the leading edge. The angle α is computed from the projection of the filaments in the xy plane. The distributions are normalized. The solid lines are the results from our simulations. (a) Case 1: no geometrical restriction on the values of θ and φ. Arp2/3 branching occurs with the rate k_b in a region 50-nm from the leading edge. (b) Case 1: no restriction on θ, φ, and ω, but branching occurs directly underneath the membrane, i.e., within 5 nm. (c and d) Two successful examples from Case 2. (e and f) Two failed examples from Case 2. See Table 1 for the values of θ₀, φ₀, Δθ, and Δφ. (g and h) Case 3: θ₀ = 45°, φ₀ = 45°, and ω is constrained. ω₀ = ±90° and Δω = 45°. (g) Δθ = Δφ = 45°. (h) Δθ = Δφ = 90°. We see that agreement between simulation and experiment is achieved in c–f. The detailed description of these panels are given in the text.

FIGURE 9

A representative three-dimensional actin filament network from our simulation (upper panel). The projection of three-dimensional filament in the xy-plane is shown (lower panel). Case 2 conditions are applied (see Fig. 8). The red filaments are uncapped and growing. The black filaments are no longer growing. The actively growing region is the 200–300-nm zone directly behind the leading edge. The filament diameters are not to scale.

FIGURE 10

The process of lamellipodium initiation can be related to curvature sensitivity of the membrane receptors. Our scenario: Initially receptors are distributed on the surfaces of the cell body. Cell sticks to the substrate and that results in high curved regions closer to the substrate. If the receptor proteins are asymmetrical in shape as shown in Fig. 3 or Fig. 4, then they are localized at the regions close to the substrate. Signaling occurs and the recruitment of Cdc42, WASP, and Arp2/3 initiates lamellipodium protrusion. During the protrusion process, the transmembrane receptors resides in the curved region due to favorable solvation energy (Fig. 4). These combination of factors maintains lamellipodium thickness and growth.

FIGURE 11

Representative configurations of the membrane with a transmembrane protein at the center. The triangular finite elements are shown, along with the transmembrane protein (depicted as the shaded box). Panels a and b are different views of the same curved membrane. Panels c and d are different views of the same flat membrane. The boundary condition of Eq. 5 is applied to the triangles immediately next to the central hole.