Figure 4.

Mean filament length and changes in filament length as a function of motor parameters. Left, variation as a function of bulk motor concentration. Center, variation as a function of motor speed. Right, variation as a function of $k_{\mathrm{off}}^{\mathrm{end}}$ in the density-controlled model. This figure uses the same parameters as figure 3 except where noted in varying the bulk motor concentration and motor speed: v = 3 μm min⁻¹, u = 1 μm min⁻¹, w = 7 μm min⁻¹, minimum catastrophe frequency f_c = 0.2 min⁻¹, rescue frequency f_r = 0.05 min⁻¹, a = 8 nm, and ρ_max = 125 μm⁻¹. For the density-controlled model the parameters are k_on = 1 nM⁻¹ μm⁻¹ min⁻¹, k_off = 0.25 min⁻¹, $k_{\mathrm{off}}^{\mathrm{end}}=1.5$ min⁻¹, bulk motor concentration c = 2 nM, and α = 0.35 min⁻¹. The simulation of the density-controlled model has the same parameters except $k_{\mathrm{off}}^{\mathrm{end}}=1$ min⁻¹ and α = 0.38 min⁻¹. For the flux-controlled mean-field model the parameters are the same as for the density-controlled mean-field model except k_on = 3 nM⁻¹μm⁻¹ min⁻¹ and α = 7 × 10⁻³. The simulation of the flux-controlled model has the same parameters as the corresponding mean-field theory except k_on = 1.5 nM⁻¹μm⁻¹ min⁻¹ and α = 2 × 10⁻³.