Cell mechanics, environmental geometry, and cell polarity control cell-cell collision outcomes

TL;DR

This work addresses how environmental geometry and cell mechanics govern collision outcomes between migrating cells on fiber-like substrates. By formulating a two-cell, two-dimensional phase-field model with cell–cell and cell–fiber adhesion plus a simple polarity feedback, the authors simulate head-on collisions on single and two parallel fibers, mapping how line tension, polarity strength, and fiber spacing bias toward walk-past or training. A key contribution is a linear stability analysis of the symmetric cell–cell interface that predicts the transition boundary between walk-past and training, aligning with qualitative trends in the simulations and offering a mechanistic explanation for environment-driven changes in contact inhibition of locomotion. The findings provide testable predictions for how mechanical properties and nanoscale geometry influence cell interactions, with implications for understanding collective migration in constrained environments and guiding future experiments or data-driven modeling efforts.

Abstract

Interactions between crawling cells, which are essential for many biological processes, can be quantified by measuring cell-cell collisions. Conventionally, experiments of cell-cell collisions are conducted on two-dimensional flat substrates, where colliding cells repolarize and move away upon contact with one another in "contact inhibition of locomotion" (CIL). Inspired by recent experiments that show cells on suspended nanofibers have qualitatively different CIL behaviors than those on flat substrates, we develop a phase field model of cell motility and two-cell collisions in fiber geometries. Our model includes cell-cell and cell-fiber adhesion, and a simple positive feedback mechanism of cell polarity. We focus on cell collisions on two parallel fibers, finding that larger cell deformability (lower membrane tension), larger positive feedback of polarization, and larger fiber spacing promote more occurrences of cells walking past one another. We can capture this behavior using a simple linear stability analysis on the cell-cell interface upon collision.

Figures (11)

• Figure 1: Examples of cell phase field ($\phi$, left two columns) and polarization field ($\mathbb{P}$, the rightmost column) on suspended fibers (white dashed lines). Cells expand along fibers and become either spindle-like (a, on a single fiber) or parallel-cuboidal (b, on two parallel fibers). The cell boundary ($\phi=0.5$) is marked by a thin black contour. Left column shows cells with no active forces. Middle column shows the steady-state shapes of single cells with the full dynamic simulation. In the middle column, thick magenta line segments indicate the locations where motility forces are largest, where the absolute value $\lvert\mathbb{P}\phi^2(1-\phi)^2\chi\rvert>0.025$. The right column shows the polarity fields $\mathbb{P}$ associated with the cells in the middle column.
• Figure 2: Possible collision outcomes of cells on fibers. Directions of motion are marked by white arrows. (a) In our simulations, the collision of two spindle-shaped cells on a single fiber almost always results in cells sticking together and moving in the same direction ('' training''). (b) The collision of two parallel-cuboidal cells on two fibers can also result in training, or possibly reversing from each other akin to classical CIL, which is most likely to occur in simulations without cell-cell adhesion. In addition, cells can walk past each other while keeping their original directions of motion. During a walk-past, both cells shrink to a single fiber and become teardrop-like. In other collision outcomes (training and reversing), one or both of the cells can also shrink to single-fiber shape (not shown in this figure). Cell-cell collision movies for common outcomes and a few unusual cases can be seen in Movies 1-8.
• Figure 3: (a) Phase diagram showing dominant cell collision outcomes on two parallel fibers separated by a spacing $L=90l_0$ (22.5µ). (b) and (c) show the frequencies of training and walk-past results, respectively, calculated from 96 independent simulation trajectories at each point in the phase diagram. The blue dashed line in all three figures is a global fit to the linear stability analysis predicting the transition between training and walk-past.
• Figure 4: (a) Phase diagram showing dominant cell collision outcomes on two parallel fibers separated by a spacing $L=70l_0$ (17.5µ). (b) and (c) show the frequencies of training and walk-past results calculated from 96 independent simulation trajectories at each point in the phase diagram. Note that compared to the case of $L=90l_0$, more points are dominated by training and only a few are dominated by walk-past. The linear stability prediction of walk-past threshold (dashed blue line) also moves upward accordingly.
• Figure 5: (a) Phase diagram showing dominant cell collision outcomes without cell-cell adhesion, on two parallel fibers separated by a spacing $L=90l_0$ (22.5µ). The absence of cell boundary adhesion leads to the dominance of both cells reversing from each other upon collision at large $\alpha$ and small $\beta$. The linear stability prediction of walk-past threshold (dashed line) moves slightly to the left compared to the one at nonzero cell-cell adhesion in Fig. \ref{['L90']}. (b), (c) and (d) show the frequencies of training, walk-past, and reversing results, respectively, calculated from 96 independent simulation trajectories at each point in the phase diagram.