Figure 1.
The rates of nascent adhesion formation and turnover depend on the velocity of membrane protrusion (v), and the formation rate depends also on the density and composition of ECM. Nascent adhesions promote further protrusion by mediating activation of Rac, utilizing a pathway that is reinforced by positive feedback as shown. Those nascent adhesions that are not turned over mature to form stable adhesions, a process that is reinforced by myosin-mediated feedback in our model. We also include a mechanism whereby stable adhesions directly antagonize protrusion. Stable adhesions disassemble over a relatively long time scale, and their influence on processes at the leading edge is also diminished by convective (v-dependent) transport.
Figure 2.
Qualitative dependence of CHO.K1 cell motility on ECM density.
CHO.K1 cells expressing GFP-paxillin were filmed using TIRF microscopy as they migrated on the indicated densities of fibronectin ([FN], expressed as the coating concentration in µg/ml) for a period of 30 minutes. As the representative time courses show, only the intermediate concentration of 2 µg/ml supports a broad zone of persistent membrane protrusion. The images also show the monotonically positive dependence of stable adhesion abundance on [FN]. The illustrative plots show the predicted effects of myosin IIA (MIIA) depletion or overexpression.
Figure 3.
Exploration of model parameter space by phase plane analysis.
The nullclines for n (green) and s (magenta) are plotted in (v, s) space. For the n-nullclines, the values of the ECM parameter are 0.03 (light green), 0.1 (green), and 0.3 (dark green) min−1. Intersections of the n- and s-nullclines are fixed points of the system. The values of Es and In are varied as indicated, and all other parameters are assigned base case values (Supplementary Table S1).
Figure 4.
In each plot, the shaded region of (, Es) parameter space indicates where there are multiple fixed points (
values given in units of min−1). Outside of these regions, the model is monostable, supporting either low (low
or high Es) or high (high
or low Es) protrusion. The values of Cs and In are varied as indicated, and all other parameters are assigned base case values (Supplementary Table S1).
Figure 5.
Characterization of protrusion/adhesion phenotypes through stochastic simulations.
The model system was allowed to evolve stochastically, with all species numbers equal to zero initially. a. Protrusion velocity v is plotted as a function of time for = 0.3 min−1, N* = 3, and a matrix of Es and In values as indicated. b. The same (Es, In) matrix was repeated for different values of
and N* as indicated, and each simulation was coded according to the apparent phenotype. The matrix framed with a thicker border corresponds to the simulations shown in a. The raw data for each of these simulations, v(t) and s(t), are provided in Supplementary Figs. S1 and S2, respectively.
Figure 6.
Alternating spatial waves of protrusion and adhesion.
Spatially extended simulations were performed using the Next Subvolume Method, accounting for lateral diffusion of active Rac. Protrusion velocity is indicated in grayscale (white: v = 0; black: v = 1) as a function of time and position; the virtual leading edge is subdivided into 20 subvolumes, each 1.94 µm in length. Corresponding stable adhesion density maps are given in Supplementary Fig. S3. a. Propagating waves are perceived as contiguous regions radiating from the point of initiation. Evidence of membrane protrusion waves, each halted by a wave of adhesion maturation (arrowheads), is found in the cell from Fig. 2 plated on 20 µg/ml fibronectin. b. Velocity maps for a matrix of (Es, In) values, parametrically consistent with the one-compartment simulations shown in Fig. 5 a.
Figure 7.
Effects of myosin IIA knockdown or overexpression assessed by protrusion velocity mapping.
CHO.K1 cells expressing fluorescently labeled paxillin were filmed using TIRF microscopy as they migrated on the indicated densities of fibronectin ([FN], expressed as the coating concentration in µg/ml). Myosin IIA levels were knocked down by RNA interference or increased by overexpression as indicated. a. For each condition, the velocity of protrusion is mapped for a representative cell as a function of time and position around the cell periphery. A gray area indicates a region of the cell periphery where protrusion velocity could not be determined. b. A protrusion event is marked as a contiguous region in space and time with protrusion velocity exceeding 1 nm/s and containing at least one instance where the protrusion velocity exceeded 5 nm/s (Supplemental Fig. S4). The total area of such protrusions on the velocity map (in units of length*time), normalized by the duration of the experiment, is plotted for normal and myosin IIA knockdown conditions from a.