Fig. 5.

Effect of varying Michaelis constant, a_k. (A) Dependence of expansion speed on the chemotactic sensitivity, $\varphi$, for different values of a_k and $D_{\rho }=50 \mathrm{\mu }{\mathrm{m}}^2/\mathrm{s}$. Solid lines indicate analytical solutions for corresponding best fit values of η, and markers denote the numerical solutions. Results for $a_k=0.1 \mathrm{\mu }\mathrm{M},\hspace{0.17em}1 \mathrm{\mu }\mathrm{M}$, and $10 \mathrm{\mu }\mathrm{M}$ are shown in yellow, red, and blue, respectively. (B) Dependence of the expansion speed on model parameter a_k. The numerical solutions obtained for $D_{\rho }=50 \mathrm{\mu }{\mathrm{m}}^2/\mathrm{s},\hspace{0.17em}\varphi =5$ are represented by yellow triangles, and the analytic solution found in Eq. 21 for $a_k=a_m={10}^{-3} \text{mM}$ is shown by the red line. Parameters have the default values from SI Appendix, Table S1, unless specified.