Recursive feedback between matrix dissipation and chemo-mechanical signaling drives oscillatory growth of cancer cell invadopodia

Abstract

Most extracellular matrices (ECMs) are known to be dissipative, exhibiting viscoelastic and often plastic behaviors. However, the influence of dissipation, in particular mechanical plasticity in 3D confining microenvironments, on cell motility is not clear. In this study, we develop a chemo-mechanical model for dynamics of invadopodia, the protrusive structures that cancer cells use to facilitate invasion, by considering myosin recruitment, actin polymerization, matrix deformation, and mechano-sensitive signaling pathways. We demonstrate that matrix dissipation facilitates invadopodia growth by softening ECMs over repeated cycles, during which plastic deformation accumulates via cyclic ratcheting. Our model reveals that distinct protrusion patterns, oscillatory or monotonic, emerge from the interplay of timescales for polymerization-associated extension and myosin recruitment dynamics. Our model predicts the changes in invadopodia dynamics upon inhibition of myosin, adhesions, and the Rho-Rho-associated kinase (ROCK) pathway. Altogether, our work highlights the role of matrix plasticity in invadopodia dynamics and can help design dissipative biomaterials to modulate cancer cell motility.

Keywords: cyclic ratcheting; invadopodia; matrix plasticity; mechano-sensitive signaling pathways; myosin recruitment; oscillations; timescales.

Figure 1.. A chemo-mechanical model that integrates the balance of mechanical forces and mechano-sensitive signaling pathways

(A) Schematic describing the model for invadopodia protrusion. Myosin motors pull actin filament bundles toward the cell center with retrograde flow velocity V_r. Adhesion molecules, connecting actin bundles to the extracellular matrix (ECM), provide a frictional force to resist retrograde flow. Actin monomers are polymerized at the tip of filament bundles (with polymerization speed V_p) against the viscoelastic cortical cytoskeleton and viscoplastic ECM forces. The invadopodia extension rate dR/dt is the difference between polymerization speed V_p and retrograde flow V_r. (B) Mechano-sensitive signaling pathways that influence dynamics of myosin recruitment. Tensile forces at the adhesion complex trigger a conformation change of vinculin, exposing binding sites of the Src family of tyrosine kinases (SFKs). SFKs promote Rho-GTPases by controlling the activity of guanine nucleotide exchange factors (GEFs) and GTPase-activating proteins (GAPs), which increases the binding of myosin motors. Rho-GTPases are downregulated by Rac1 kinases through Rac-mediated reactive oxygen species (ROS). (C) The mechanical model with elastic, viscous, and plastic components for viscoplastic matrices. (D) The creep-recovery test showing the presence of irreversible strain (ε_p) after recovery of stress in the ECM. The constitutive law is obtained by fitting a viscoplastic model (red line) to experimental data (blue circles). Data are shown as mean ± SD for nine individual tests.

Figure 2.. Mechanisms responsible for invadopodia oscillations

(A–D) Simulated invadopodia extension length R (A), myosin pulling force F_m (B), adhesion force F_a (red line) (C), retrograde flow (dashed line) (C), and matrix resistance force F_e (D) plotted as a function of time. There is a time lag between the peak extension length and the peak myosin pulling force. (E) Schematic showing interplay of intracellular processes in the different oscillation stages.

Figure 3.. Simulation shows oscillatory extension of invadopodia in viscoplastic matrices

(A–C) Simulated invadopodia extension length (A), ECM force (B), and plastic deformation (C) of ECM plotted as a function of time. (D) Schematic depicting the behavior of viscoplastic ECM in different stages of oscillation, marked in (A)–(C). (E) Confocal fluorescence time-lapse images of MDA-MB-231 cells showing similar stages of invasive protrusion as predicted by the model (RFP-labeled actin,red; fluorescein-labeled matrices, green). The plastic deformation of the ECM (yellow line in the merged panel) remains after the retraction of the invadopodium. Scale bars, 5 μm. Timescale, h:min.

Figure 4.. Model captures the impact of matrix plasticity and stiffness on invadopodia dynamics

(A) (Top panel) Simulated invadopodia extension versus time with respect to different levels of matrix plasticity, i.e., LP (low plasticity; blue line), MP (medium plasticity; yellow line), and HP (high plasticity; red line). (Bottom panel) Force exerted on the ECM by invadopodia plotted as a function of extension length for different plasticity levels. (B) (Left panel) Time-averaged invadopodia extension length for different plasticity levels. (Right panel) Oscillation amplitude with respect to different plasticity levels. Dashed lines with circles denote simulation results. Data were obtained from three to five experimental replicates. (C) The maximum bead displacement around cells plotted with different matrix plasticity levels (data extracted from Wisdom et al., 2018). The dashed line with circles denotes simulated matrix strain (right y axis). (D) Invadopodia extension measured with a 10-min time interval for one representative cell each in LP (blue), MP (yellow), and HP (red) ECMs. (E) Fluorescence images of representative RFP-LifeAct-transfected MDA-MB-231 cells in LP, MP, and HP matrices using time-lapse microscopy. Scale bars, 10 μm. (F) (Top panel) Simulated length and (bottom panel) experimentally measured invadopodia length for a representative cell in ECMs with low stiffness (light gray) and very high stiffness (black). (G) Time-averaged invadopodia extension length with respect to matrix stiffness (low stiffness 0.4 kPa [LS], medium stiffness 1.5 kPa [MS], high stiffness 4.4 kPa [HS], and very high stiffness 9.3 kPa [VHS]). Dashed line with triangles denotes simulation results. (H) Heatmap showing how initial modulus and yield stress (normalized by cytoskeleton elastic modulus) regulate time-averaged extension length $\overline{R}$ of invadopodia. The circles/triangles represent the experimental results from three to four experimental replicates. The circles from top to bottom correspond to invadopodia in LP, MP, and HP ECMs, while the triangles from left to right correspond to invadopodia in LS, MS, HS, and VHS ECMs, respectively. For (B), (C), and (G), bar plots display the number of cells analyzed per condition, and error bars indicate 95% confidence intervals (*p < 0.05, **p < 0.01, ***p < 0.001, ANOVA with Benjamini-Hochberg procedure).

Figure 5.. Model predicts changes in invadopodia dynamics upon inhibition of b1 integrin, the Rho-ROCK pathway, and myosin activity

(A) The time-averaged extension length of invadopodia for control (blue) and different inhibitor treatments. Integrin, the Rho-ROCK pathway, and myosin activity are inhibited by β1 integrin inhibitor (red), Y27632 (green), and blebbistatin (yellow), respectively. Circles denote simulation results. (B) (Top panel) Representative RFP-LifeAct fluorescence images show cells for control and different treatments. Scale bar, 10 μm. (Bottom panel) Representative curves showing the evolution of protrusion length for experiments with different treatments. (C) The amplitude ratio r_a plotted for control and different treatments. (D) Distribution of amplitude ratios for control and different treatments. The dashed lines represent fitted density functions of log-normal distribution. Three regimes indicating low (r_a < 0.25), intermediate (0.25 < r_a < 0.5), and high (r_a > 0.5) levels of oscillation are labeled. (E) Fraction of invadopodia with (left panel) low level, (middle panel) intermediate level, and (right panel) high level of oscillation for control and different treatments. (F) Phase diagram showing two types of protrusion patterns: oscillatory protrusions (regime I) and monotonically growing protrusions (regime II), based on extension-associated viscous timescale τ_e and signaling-associated myosin recruitment timescale τ_s normalized by the intrinsic myosin recruitment timescale τ_m. The arrows indicate the influence of β1 integrin blocking antibody (red), blebbistatin (yellow), and Y27632 (green) treatments on the protrusion patterns. (G) The phase space of maximum force generated by bound myosin F_M and invadopodia extension length R for oscillatory (blue line) and monotonical (red line) behavior. The black circled marker represents the steady-state point (R_s,F_Ms). In (A) and (C), a bar plot displays the number of cells analyzed per condition, taken from three to five biological replicate experiments. Error bars indicate 95% confidence intervals (*p < 0.05, ***p < 0.001, ****p < 0.0001, ANOVA with Benjamini-Hochberg procedure).