Competing forces of polarization and adhesion generate directional migration bias in a minimal model

Abstract

Left-right axis specification establishes embryonic laterality through asymmetric signaling cascades originating at the cellular scale. We previously reported the presence of a directionality bias in confined pairs of endothelial (and fibroblast) cells exhibiting persistent circular motion, with cytoskeletal contractility modulating the direction. The relative simplicity of the experimental setup makes it a perfect testing ground for the physical forces that could endow this system with a tunable directional migration bias. We model self-propelling biological cells migrating in response to confinement, polarity, and pairwise repulsive forces. Our framework reproduces three key experimental observations: spontaneous coherent circular movement of confined cell pairs, emergence of directional bias when cells have asymmetric properties, and contractility-modulated switching of the rotation direction. Two key assumptions are required: an internal torque arising from cytoskeletal organization (previously observed in other cellular systems), and an asymmetric polarity response between cells, which introduces a difference in how quickly each cell reorients its migration direction. New experiments on daughter cell pairs support this asymmetry requirement in cellular properties. Tuning the polarity response timescale (or strength) relative to centering forces from confinement and cell-cell adhesion can amplify or reverse the directional migration bias.

Figures (6)

• Figure 1: Summary of our experimental results in Badih2025 on the movement of HUVEC pairs confined to a disk-shaped geometry. (A) Schematic of the experimental setup illustrating two HUVEC cells confined to a disk-shaped adherent geometry with $R=60~\mu m$. (B) Summary of experimental results illustrating a three-state migratory system: doublets rotating coherently (R) in either the clockwise (CW) or counterclockwise (CCW) direction or non-rotating (NR). (C) The doublets are characterized by an asymmetry in the stored mechanical energy as reported by traction force measurements and in the angular speed; Statistical significance was assessed using an unpaired t-test ($p=0.0087$ for left plot; $p=0.0110$ for right plot). $N=3$ independent experiments, and $n=98$ doublets for both plots. (D) Percentage of rotational doublets and (E) percentage of CW-rotational doublets, both showing directional biases modulated by contractility. Quantified in control versus treated, from decreasing concentrations of CalyA to increasing concentrations of ROCKI. Statistical significance was assessed using Chi-squared test (Fischer's exact; Significance testing: *$=0.01238$; **$=0.0087$; ***$=0.0007$; ****$\leq0.0001$). $N$ indicates the number of individual experiments and $n$ the total number of doublets used for quantification.
• Figure 2: Model of a pair of cells confined to a disk and their circular movement dynamics. (A) Doublet model schematic. (B) Sample CW, CCW, and NC trajectories over one rotational cycle. (C) Angular velocity over 2 arbitrary time units for cells that move persistently in the CW (blue) and CCW (red) directions or move non-coherently by switching directionality (black dots). (D) Averaged number of rotating doublets and their distribution into the three motility states: CW (49%), CCW (51%), and NC (21%) out of 3200 model simulations.
• Figure 3: Motility outcomes show no directional bias with symmetric or asymmetric parameter regime changes. Heatmaps showing the percentage of coherent and persistent rotations (left) and CW rotations (right) of cell doublets across model parameter variations (A) in both cells, and (B) in one cell only.
• Figure 4: By introducing an intrinsic bias, model reproduces persistent circular movement in confinement with a parameter-tunable bias in either direction. (A) Heatmaps showing the percentage of coherent rotations (left) and CW rotations (right) for parameter sweeps of doublets with intrinsic CW polarity tilt. Dashed black region indicates default values for properties across the pair, blue dashed region marks elevated CW bias ($\geq$60%), and red dashed region marks elevated CCW bias ($\leq$40%). Inset: Summary of three-state motility distribution across the dashed black region. (B) Three-state motility distribution and (C) mean angular speed for CW and CCW rotating doublets with asymmetry in velocity alignment timescale in cell 1 (left) or cell 2 (right). The model parameters correspond to an average of the mild parameter difference (-) in Fig. S4. (D) Schematic of the 'tilting dumbbell' mechanism for reversing the CW intrinsic tilt to a CCW bias. (E) Experimental results for the percentage of coherent rotations (left) and CW rotations (right) for HUVEC daughter cell pairs with equal stored mechanical energy. Statistical significance was assessed using an unpaired student's t-test ($^{*}$ indicates $p<0.01$, $^{****}$ indicates $p<0.0001$).
• Figure 5: Directionality of rotational bias is the result of an interplay between skewed cell polarity and mechanical contributions of frictional drag and cell-cell coupling. (A) Heatmap of symmetric parameter sweeps in frictional drag coefficient ($\xi$) and polarization timescale ($\tau_\text{VA}$). The dashed purple line marks the 50/50 CW/CCW (unbiased) region. Dashed blue region marks $\geq 60$ CW rotating doublets and dashed red region marks $\geq 40$ CCW doublets. (B) Histogram of the percentage of rotating and CW rotating doublets for parameters choices that correspond to default, high (red) and low (blue) contractility cases. (C) Model results for a simulated heterotypic cell doublet composed of the default CW biased cell (HUVEC-like) together with a CCW biased cell (MEF-like).