Fig. 2.

Stick–slip dynamics of cellular protrusions. (A) Possible stick–slip region in the parameter space $\left\{r_{\text{on}},{\overline{\alpha }}_1={\alpha }_1/{\alpha }_0\right\}$ for an elastic protrusion of dimensionless stiffness ${\overline{k}}_{\sigma }=k_{\sigma }/\left({\alpha }_0{k}_{\text{off}}^0\right)$. The shaded region corresponds to a nonmonotonous friction force. Black line, stick–slip boundary for infinitely fast linker kinetics (${\overline{k}}_{\sigma }\to 0$); gray lines, boundaries for ${\overline{k}}_{\sigma }=1,\hspace{0.17em}5$, and 10 (Eq. 6). (B) Force/velocity relationship in and out of the stick–slip region (for $r_{\text{on}}=5$ and ${\overline{\alpha }}_1=150$ [gray] or 450 [black]). Characteristic values of the retrograde velocity (${\overline{v}}_{\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{p}}$ and ${\overline{v}}_{\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{k}}$) and force (${\overline{f}}_{\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{p}}$ and ${\overline{f}}_{\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{k}}$) are defined. (C and D) Growth of a 1D viscoelastic protrusion (sketched) for ${\overline{\alpha }}_1=400$ and $r_{\text{on}}=5$. (C) Protrusion length with time for two viscoelastic relaxation times and the same average speed: black, ${\overline{\tau }}_{\sigma }=0.2$ and ${\overline{\sigma }}_0=300$; and gray, ${\overline{\tau }}_{\sigma }=1$ and ${\overline{\sigma }}_0=214$ (with $r_p=15$). (D) Protrusion length with time for different homeostatic tension (with ${\overline{\tau }}_{\sigma }=0.5$ and $r_p=45$).