Figure 4.

Optimal cluster size is robust to model assumptions and agrees with experiments. (A) Optimum persists both when we vary the minimal cluster size $j_{\text{min}}$ that can propagate the signal downstream (open symbols) and we allow the total number of active Ras molecules to fluctuate, with deactivation rate γ, adding input noise to the system (solid symbols). (Black dashed line) Fidelity when only monomers are present (see Discussion). (B) Distribution of optimal cluster size ${\nu }^{\ast }$ for 100 cooperativity values sampled from b = 1.25–100 (uniformly in log space). The most frequent ${\nu }^{\ast }$ values also have the highest mean fidelity (colors) and are contained within the range $5\le {\nu }^{\ast }\lesssim 10$, in good agreement with the observed ranges for Ras (6–8 (1) and 4–10 molecules (36)) and CD59 clusters (3–9 molecules (3, 4)). Parameters: (A) β = 3 (solid symbols), b = 3, and T = 10⁴ s; (B) T = 10 s (sufficient to identify the optima); and in both, $N_{\text{max}}$ = 100, α = 10 s⁻¹, and μ = 10³ s⁻¹. To see this figure in color, go online.