Figure 6.

Engulfment model with signaling. (A) Sketch of the model which, in addition to the receptor density ρ, contains a signaling molecule with density S. Receptors can only diffuse (with diffusion constant D) and drift (with speed v), whereas the signaling molecule is produced within the cup with rate βρ_L, degraded everywhere with lifetime τ, and diffuses with diffusion constant D_S. (B) In contrast to other models, the rate of engulfment can now accelerate if the drift velocity depends linearly on S via v = v₁S, tending to a constant as t → ∞. Parameters are v₁ = 20 μm³ s⁻¹, β = 0.1 s⁻¹, τ = 10 s, and R = 2 μm, no diffusion. (C) In the full model, with a drift velocity that depends on the signaling molecule via a threshold, S₀, and an initial latent period, t₀, a sharp increase in engulfment rate can be obtained, which matches well with the measured data. Here the measured data is the average of the upper and lower lobes for the 4.6-μm bead shown in Fig. 2C. Parameters are D = 3.8 μm² s⁻¹, v₁ = 6 μm³ s⁻¹, S₀ = 0.498 μm⁻², β = 0.4 s⁻¹, τ = 0.5 s, t₀ = 10 s, and R = 2.75 μm. (D) The dependence of the full-engulfment time on the ligand density, ρ_L, showing a minimum at intermediate ρ_L. Parameters as in panel C. Additional parameters are ρ₀ = 50 μm⁻², $\mathcal{E}$ = 3, $\mathcal{B}$ = 20, D_S = 1 μm² s⁻¹, and L = 50 μm. To see this figure in color, go online.