Figure 5.

Quantifying polar receptor clustering. (a) Cluster-membrane energy density, i.e., energy per trimer as a function of cluster size N. Total energy density ɛ (black) is the sum of repulsive elastic energy density ɛ_el (blue) and attractive cluster energy density ɛ_a (red). Solid lines correspond to cell poles and dashed lines to lateral positions. Thin solid and dashed blue lines indicate asymptotic limits of the elastic energy density for $N\to \mathrm{\infty }$ at the poles and lateral positions, respectively. Polar clusters are stabilized by energy density Δɛ. (b) Distribution of cluster sizes for three values of the trimer density (occupancy fraction), ρ = 0.4, 0.1, and 0.025 at the poles (solid lines) and lateral positions (dashed lines). (c) Average cluster radius 〈R〉 at the poles (black solid line) and lateral area (black dashed line) as a function of trimer density, ρ, based on standard parameters, including trimer-trimer coupling, J₀, trimer curvature, C_T, and cluster bending stiffness, κ_c from Table 1. Error bars indicate robustness to parameter changes: upper error bars for poles and lateral area are 1.1 for J₀ (red), 0.98 for C_T (dimer-dimer distance reduced by 1 nm (green)), and 0.92 for κ_c (blue); lower error bars for poles and lateral area are 0.9 for J₀ (red), 1.03 for C_T (dimer-dimer distance increased by 1 nm (green)), and 1.09 for κ_c (blue). (Inset) Average cluster size (number of trimers) 〈N〉 as a function of trimer density for standard parameters.