A computational modeling of invadopodia protrusion into an extracellular matrix fiber network

Abstract

Invadopodia are dynamic actin-rich membrane protrusions that have been implicated in cancer cell invasion and metastasis. In addition, invasiveness of cancer cells is strongly correlated with invadopodia formation, which are observed during extravasation and colonization of metastatic cancer cells at secondary sites. However, quantitative understanding of the interaction of invadopodia with extracellular matrix (ECM) is lacking, and how invadopodia protrusion speed is associated with the frequency of protrusion-retraction cycles remains unknown. Here, we present a computational framework for the characterization of invadopodia protrusions which allows two way interactions between intracellular branched actin network and ECM fibers network. We have applied this approach to predicting the invasiveness of cancer cells by computationally knocking out actin-crosslinking molecules, such as α-actinin, filamin and fascin. The resulting simulations reveal distinct invadopodia dynamics with cycles of protrusion and retraction. Specifically, we found that (1) increasing accumulation of MT1-MMP at tips of invadopodia as the duration of protrusive phase is increased, and (2) the movement of nucleus toward the leading edge of the cell becomes unstable as duration of the retractile phase (or myosin turnover time) is longer than 1 min.

Figure 1

Dynamic model of cancer invadopodia protrusion in a viscoelastic ECM fiber network. (a) Integrated cancer cell migration model consisting of invadopodia membrane (yellow), force transduction layer (green), actin cortex layer, branched actin network, perinuclear actin layer, and nuclear membrane (blue). Viscoelastic behaviors in all of them are modeled using Kelvin-Voigt model. (b) The free body diagram of the i-th invadopodial node in the circle marked in (a) where four external forces are acting.

Figure 2

Computational model of invadopodia protrusion. (a) Schematic of invadopodia protrusions into stiff and soft ECMs showing the adaptation of branched actin network by surrounding ECM stiffness or density. (b) A schematic showing viscoelastic behaviors in the branched actin network, actin cortex layer (ACL), force transduction layer (FTL), cellular membrane, and ECM fiber network, which are modeled using Kelvin-Voight model (a spring and a dashpot together in parallel). (c) Schematic shows mechanical interactions between intracellular branched actin filaments and ECM fiber network via invadopodia protrusion. Three kinds of actin-crosslinkers, such as filamin, α-actinin, and fascin, connect two neighboring actin filaments. Additionally, actin filament and perinuclear actin layer (PAL) on the nuclear membrane surface (NMS) can be also connected by filamin and α-actinin. ARP2/3 complex nucleates a new branched actin filament (daughter) from the existing filament (mother), and bipolar myosin filaments slide on two neighboring actin filaments to gain contractile forces. (d) Invadopodia protrusion dynamics showing protrusive, retractile, and severing phases.

Figure 3

Mechanical interactions in viscoelastic actin filaments. (a) A schematic representation of single actin filament with series of springs and dashpots for the calculation of two kinds of elastic forces due to stretching and bending actin filament. (b) A schematic representation of branched actin filament for the calculation of two kinds of elastic forces due to branched and dihedral angles. ${\mathit{x}}_{i,j}^{\mathit{AF}}$ and ${\mathit{x}}_{k,1}^{\mathit{AF}}$ indicate binding sites of ARP2/3 complex. (c) A schematic representation of cross-linked actin filaments. ${\mathit{x}}_{i,l}^{\mathit{AF}}$ and ${\mathit{x}}_{k,l}^{\mathit{AF}}$ indicate binding sites of actin-crosslinker.

Figure 4

Characterization of invadopodia protrusion. (a) Selected still shots of simulated invadopodia protrusion into ECM under three different duration times in the protrusive phase, such as 60, 120, and 240 s. Blue, red, yellow, dark blue, and black lines indicate F-actin, bipolar myosin filament, α-actinin, filamin, and fascin, respectively. (b) Selected MMP-2 contour plots under three different duration times in the protrusive phase, such as 60, 120, and 240 s. (c) A graph showing speed of invadopodia verses duration time of retractile phase. (d) A graph showing z coordinate of invadopodia tip by time, and (e) linear regression (r² = 0.992) between migrated distance of invadopodial tip and duration time of protrusive phase.

Figure 5

Experimental observation of invadopodia mechanosensing. GFP expressing MDA-MB-231 (MDA231) cells were cultured within a collagen I ECM, and the movement of the invadopodia were imaged and quantified by confocal time-lapse microscopy. (a) MDA231 (green) cells cultured in collagen I ECM (white) sends out elongated invadopodia (red arrows) to probe the ECM (scale bar = 30 μm). Quantification (b), mean; (c), frequency distribution) of the invadopodia speed from cells treated with antibody against MT1-MMP (a-MT1-MMP) and cells treated with IgG control (Ctrl). For (b), data shown are means (displayed above the bar) ± s.e.m from invadopodia from n = 50–54 cells. ****, p < 0.0001 from unpaired student t-test. (d) A selected still shot of simulated cancer cell with MT1-MMP knockout and Arp2/3 inhibition in ECM fiber network at the time-point of 500 s. (e) Bar graphs showing time-averaged speeds and s.e.m at the tip of invadopodium for three different cases of Ctrl, KO MT1-MMP only, and KO MT1-MMP and Arp2/3 inhibition. [*P < 0.05, n = 12, 11, 11, one-way ANOVA, posthoc Tukey’s test].

Figure 6

Cancer cell simulations with knockout (KO) of actin-crosslinking molecules. Selected plots of simulation for invadopodia protrusion in ECM with two cases of (a) KO α-actinin, and (b) KO filamin and fascin. Blue, red, yellow, dark blue, and black lines indicate F-actin, bipolar myosin filament, α-actinin, filamin and fascin, repectively. (c) Trajectory of invadopodial tip about three cases of control, KO α-actinin, and KO filamin and fascin. (d) Bar graphs showing time-averaged speeds and s.e.m at the tip of invadopodium for three different cases of control, KO α-actinin, and KO filamin and fascin. [*P < 0.05, n = 9, 9, 9, one-way ANOVA, posthoc Tukey’s test].

Figure 7

Cyclic motion of invadopodia dynamics during the directed cell migration towards stiffer ECM. Selected still shots of simulated cell migration toward stiffer ECM at time points of (a) 300 s (at the end of 1^st protrusive phase), (b) 355 s (at the end of 1st retractile phase), and (c) 560 s (at the end of 2^nd protrusive phase). Three graphs in (d), (e), and (f) show time-varying traction (extracellular) force, intracellular force, and trajectory at the tip of invadopodium, respectively.