Early stages of collective cell invasion: Biomechanics

TL;DR

The paper develops a biomechanical framework for the early, proliferation-free invasion of cancer cell aggregates using a cellular Potts model that distinguishes epithelial (E), mesenchymal (M), and hybrid E/M phenotypes. It introduces a fractional time-step scheme to separately handle stiffness-driven traction (durotaxis) and active migration forces, enabling robust single- and collective-cell invasion across diverse adhesion and stiffness parameters. Simulations reveal that M and E/M cells near the aggregate edge invade toward attraction points, with hybrid E/M cells often achieving faster, more effective migration than pure M cells; patterns depend sensitively on cell-cell and cell-substrate adhesions. The model provides qualitative insights into early invasion dynamics and offers a platform for incorporating EMT, Notch signaling, and cancer stem cell interactions in future work, with potential implications for understanding metastasis initiation.

Abstract

The early stages of the collective invasion may occur by single mesenchymal cells or hybrid epithelial-mesenchymal cell groups that detach from cancerous tissue. Tumors may also emit invading protrusions of epithelial cells, which could be led (or not) by a basal cell. Here we devise a fractional step cellular Potts model comprising passive and active cells able to describe these different types of collective invasion before cells start proliferating. Durotaxis and active forces have different symmetry properties and are included in different half steps of the fractional step method. Compared with a single step method, fractional step produces more realistic cellular invasion scenarios with little extra computational effort. Biochemical mechanisms that determine how cells acquire their different phenotypes and cellular proliferation will be incorporated to the model in future publications.

Figures (12)

• Figure 1: Simulated active and passive cells. Dynamics of red cells (passive, $E_{\theta c}=1$ kPa) and blue cells (active, embedded into a disk of passive cells, $E_{\theta m}=15$ kPa), with substrate strains (black arrows). Initial condition: circle-shaped distribution with 10 randomly placed blue cells. Panels show different iterations: (a) t=50, (b) t=500, (c) t=1000. See Video S1. Line segments indicate strain magnitude and orientation above a given threshold vanOers.
• Figure 2: Simulated migration force. Migration of active blue cells ($E_{\theta m}=15$ kPa) and passive red cells ($E_{\theta c}=1$ kPa). Substrate strains are shown by black arrows. Blue cells are attracted to the lower left corner. The initial condition is the same as in Fig \ref{['fig1']}. Panels at iterations: (a) t=1000, (b) t=1500, (c) t=3000. See Video S2.
• Figure 3: Changes in adhesion parameters. A total of $N_{total}=111$ cells are randomly placed inside a circular enclosure, with $N_m$ active cells (in blue) and passive adhesive cells (red). (a) $E_{\theta c}=E_{\theta m}=1$kPa, $j_{cs}=1$, $j_{cc}=1/2$, $j_{cm}=2$, $j_{ms}=1$, $j_{mm}=2$, $N_m=56$. (b) same as (a) except $j_{cm}=11$. (c) $E_{\theta c}=1$ kPa, $E_{\theta m}=15$ kPa, $j_{cs}=1$, $j_{cc}=1$, $j_{cm}=4$, $j_{ms}=1/4$, $j_{mm}=6$, $N_m=56$. (d) same as (a) except $j_{mm}=10$. (e) $E_{\theta c}=1$ kPa, $E_{\theta m}=15$ kPa, $j_{cs}=1$, $j_{cc}=1/2$, $j_{cm}=2$, $j_{ms}=1$, $j_{mm}=12$, $N_m=10$. (f) $E_{\theta c}=1$ kPa, $E_{\theta m}=15$ kPa, $j_{cs}=1$, $j_{cc}=1$, $j_{cm}=4$, $j_{ms}=1/4$, $j_{mm}=6$, $N_m=10$. (g) same as (f) except $j_{cm}=10$, $j_{ms}=1/2$, $j_{mm}=1/2$. (h) same as (a) except $j_{mm}= 3$. (i) same as (e) except $j_{cm}=10$, $j_{ms}=1/4$. At $t=3000$, the corresponding pattern types are: (a) 1, (b) 2, (c) 3, (d) 4, (e) 5, (f) 6, (g) 7, (h) 1,2,3, and (i) 3,6.
• Figure 4: Comparison of migration force implementations. A total of $N_{total}=111$ cells are randomly placed inside a circular enclosure, with $N_m=19$ M cells (blue) and passive E cells (red). Parameter configuration as in Fig. \ref{['fig3']}(f): $E_{\theta c}=1$ kPa, $E_{\theta m}=15$ kPa, $j_{cs}=1$, $j_{cc}=1$, $j_{cm}=4$, $j_{ms}=1/4$, and $j_{mm}=6$. (a) Initial configuration. At $t=3000$: (b) No migration force, (c) migration forces with the single time step approach, and (d) migration forces with the fractional time step approach. The attraction point is located in the bottom-left corner.
• Figure 5: Forces and strains produced by the single and fractional step methods. A cluster formed by 12 passive E cells (red) with 3 M cells (blue) on its boundary has evolved 500 Monte Carlo steps either by the fractional step method, Panels (a) and (f)-(j), or by the single step method, Panels (b)-(e). For Panel (b) (single step), (c) stiffness force $f$, (d) migration force $f_m$, (e) strain on ECM associated to force $f+f_m$. For Panel (a) (fractional step), (f) stiffness force $f$, (g) migration push force $f_m$, (h) strain on ECM associated to stiffness force $f$, (i) same for the migration force $f_m$, (j) sum of strains associated to stiffness and migration forces. Parameter values are as in Fig. \ref{['fig3']}(f) and the target point (not shown) is on the upper right corner. Panels (c)-(j) are density plots of the corresponding moduli, which are larger the darker the region is. The initial configuration is similar to that of Fig. \ref{['fig4']}(a) but with $N_{total}=15$ cells.