Cell-Cell Adhesion as a Double-Edged Sword in Tissue Fluidity

Abstract

Cell migration plays a fundamental role in numerous physiological processes, including embryonic development, wound healing, and cancer metastasis. While cell-cell adhesion is known to regulate motion by shaping cell morphology and intercellular force balance, its dynamic, rate-dependent contributions to tissue behavior remain poorly understood. In this study, we examine how the dissipative nature of cell-cell adhesion influences tissue dynamics and collective migration using an extended vertex model with explicit junctional viscosity. Our findings reveal a nontrivial interplay between two distinct components of adhesion: an interfacial adhesion energy (energetic, rate-independent) contribution, which sets the effective junctional tension, and a dissipative (rate-dependent) contribution, which controls resistance to relative motion during cell rearrangements. We show that increasing the energetic component promotes migration by modifying cell shape and lowering the barrier to neighbor exchanges, whereas strengthening the dissipative component induces jamming and suppresses cell motion. Linear rheological analysis further demonstrates that, in the unjammed regime, vertex-model tissues exhibit power-law viscoelastic behavior, with adhesion modulating the power-law exponent and thereby controlling the spread of relaxation timescales. Together, these findings clarify the dual role of adhesion in governing tissue mechanics and rheology and provide a mechanistic framework for understanding the balance between fluidity and rigidity in epithelial monolayers.

Figures (11)

• Figure 1: Modeling cell-cell adhesion force in vertex model. a) A microscopic model of cell-cell adhesion force. b) Schematic of adhesion force implementation in vertex model
• Figure 2: Glassy dynamics analysis: (a) Mean squared displacement (MSD) for $p_0 = 3.81$ and $v_0 = 0.05$, showing suppressed long-time diffusion with increasing $\xi_0$. (b) Self-intermediate scattering function $F_s(k,t)$ at the same parameters as in panel (a), evaluated at $k = \pi/\sqrt{A_0}$, illustrating the extension of the plateau and increase in relaxation time. (c) Effective diffusivity $D_{\text{eff}}$ and $\alpha$-relaxation time $\tau_\alpha$ as functions of $\xi_0$, obtained from panel (a) and (b), highlight the approach to a jammed state. (d) Dependence of $D_{\text{eff}}$ on $\xi_0$ and $p_0$ while keeping $v_0 = 0.05$, demonstrating how both energetic and viscous adhesion mechanisms influence tissue dynamics (bottom to top: $p_0=3.81, \ 3.87, \ 3.9, \ 3.99$).
• Figure 3: A jamming phase diagram governed by cell–cell adhesion. Tissue states are quantified using the effective diffusivity $D_{\text{eff}}$, with the jamming–unjamming boundary defined by the equi-diffusivity contour $D_{\text{eff}} = 0.001$ (white dashed curve). The phase diagram is constructed from simulations with $v_0=0.05$ and $D_r=0.5$
• Figure 4: Linear rheology of model tissue in fluid regime at $p_0=3.9$ suggests a broad spectrum of relaxation times: (a) The average complex modulus obtained from simulations at $\xi_0 = 0$ was fitted to both the classical Burgers model and the fractional Burgers model. The curve represent the mean over eight independent initial conditions, and the error bars denote the standard deviation of $G'$ and $G"$ at each frequency $\omega$. (b) The complex modulus measured at different $\xi_0$. Error bars indicate the mean $\pm$ standard deviation of $G'$ and $G"$ at each $\omega$, reflecting the variability across simulations. Solid and dashed lines correspond to fits using the fractional Burgers model and the classical Burgers model, respectively. (c) The collapse of different moduli curves for varying cell-cell adhesion $\xi_0$. (d) Viscoelastic parameters of the conventional Maxwell branch in fractional Burgers model as a function of $\xi_0$. (e) Viscoelastic parameters of the fractional Maxwell branch.
• Figure 5: Linear rheology of model tissue in solid regime at $p_0=3.72$ provides another evidence for the presence of multiple timescales in the system. (a,b) At $\xi_0=0$, the average storage ($G'$) and loss ($G"$) moduli are fitted using the fractional SLS and standard SLS models. The curves in panels (a) and (b) were obtained by averaging over eight different initial conditions; error bars represent the standard deviation. (c) Data collapse of different moduli curves for varying cell-cell adhesion $\xi_0$. (d) Viscoelastic parameters as a function of $\xi_0$.