Topological Defects Mediate Collective Transport of Confluent Cells

Abstract

Collective cell migration governs a range of physiological and pathological processes, from tissue morphogenesis to cancer invasion, in which topological defects arise as an inevitable consequence of frequent cellular rearrangement and migration. Here, we employ an Active Vertex Model to investigate structural defects generated in the wake of transported cells. We find that while the drag coefficient of a cell in a perfect lattice is anisotropic, the threshold drag force required to mobilize the cell is isotropic. Remarkably, we find that dragging two neighboring cells along the direction of least-resistance minimizes lattice disruption. By comparing defect-healing behaviors across different physical models, we disentangle the contributions of cell adhesion and many-body interactions. Together, our findings provide new insights into the topological organization of confluent tissues during collective migration, advancing our physical understanding of cellular transport processes such as wound healing, tissue repair, and cancer metastasis.

Figures (8)

• Figure 1: Topological defects in the AVM model.a Representative pictures of structural defects and nematic defects. b A snapshot of the system (left) and the corresponding director field (right) in the solid state with $\bar{v}_0=0.3$ and $p_0=3.55$. c A snapshot of the system (left) and the corresponding director field (right) in the liquid state with $\bar{v}_0=0.3$ and $p_0=3.85$. $+$ and $-$ defect cells are marked purple and yellow, respectively, and $+1/2$ and $-1/2$ defects are marked by blue lines and red trefoils, respectively.
• Figure 2: Statistics of different types of cells. (a--d) Violin plots of the average cell area $\bar{A}$ for $+$ defect, $-$ defect, and hexagonal cells. (e--h) Violin plots of the average shape-parameter $\bar{p}$ for $+$ defect, $-$ defect, and hexagonal cells. The dashed lines mark the transition point between the solid and liquid phase.
• Figure 3: Statistics of cells and topological defects.a Schematic definitions of two angles. Left: angle between a cell's velocity vector and its long axis, $\phi_{c}$; right: angle between a $+1/2$ defect's velocity vector and its orientation direction, $\phi_{+1/2}$. b Rose-plot of the histogram of $\phi_{c}$ at $\bar{v}_0 = 0.3$. c Rose-plot of the histogram of $\phi_{+1/2}$ at $\bar{v}_0 = 0.3$. Different colored curves are for different $p_0$. The liquid--solid transition point is $p_0 \approx 3.7$. d Heatmap of the distribution of $+1/2$ defects around an average $+$ defect cell (purple) and an average $-$ defect cell (yellow) in the solid (upper) and liquid (lower) state. The white arrows indicate the average orientation of the $+1/2$ defects at that point. e Schematic diagrams showing how $+1/2$ defects tend to orient and spatially distribute around $\pm$ defects. f The distribution of $\pm$ defects around an average $+1/2$ defect in the solid ($\bar{v}_0=0.3$, $p_0=3.55$) and liquid ($\bar{v}_0=0.3$, $p_0=3.85$) state. g A schematic explanation of the spatio-orientational correlation between $\pm$ defects and $+1/2$ defects by looking at how a cell invades an otherwise hexagonal lattice.
• Figure 4: Single-cell drag simulation.a Snapshots of the system when a cell is dragged with $\bar{F}_\text{d}=6$ and $\Psi_\text{d}=0^\circ$. Insets: cell dragging is realized by applying additional forces to its vertices. b The velocity--force relation for the dragged cell at different force angles in the solid state ($\bar{v}_0=0.1$ and $p_0=3.65$), the hexatic state ($\bar{v}_0=0.3$ and $p_0=3.65$), and liquid state ($\bar{v}_0=0.5$ and $p_0=3.65$); right four panels: steady-state snapshots of the system for different parameter sets $(\bar{F}_\text{d},\Psi_\text{d})$. The threshold force for both the solid and hexatic state is $\bar{F}_\text{c}\simeq 4$. c The average velocity $\bar{v}$ of the dragged cell plotted against force angle $\Psi_\text{d}$ for different $\bar{F}_\text{d}$.
• Figure 5: Double-cell drag simulation.a Snapshots of dragging two neighboring cells at $\Psi_\text{d}=0^\circ$, $\bar{F}_\text{d}=6$. The blue vectors are the Burger's vectors around a packet of the moving cells containing structural defects. To clearly distinguish the displacement vector field of the cells, we use random colored arrows pointing from the initial position at $t/\tau_0=10$ to the current position. b Snapshots of the packet undergoing self-healing of structural defects, along with the displacement vectors for black-outlined cells across different layers before and after the packet passes through.