Universal Persistent Brownian Motions in Confluent Tissues

TL;DR

This work uses a two-dimensional active foam model to demonstrate that persistent Brownian motion provides a minimal framework for describing tissue dynamics, while distinct active forces leave identifiable structural and dynamical signatures, thereby enabling inference of the dominant active force in fluid state tissues.

Abstract

Biological tissues are active materials whose non-equilibrium dynamics emerge from distinct cellular force-generating mechanisms. Using a two-dimensional active foam model, we compare the effects of traction forces and junctional tension fluctuations on confluent tissue dynamics. While these two modes of activity produce qualitatively different cell shapes, rearrangement statistics, and spatiotemporal correlations in fluid states, we find that the long-time cellular motion universally converges to persistent Brownian dynamics. This universal feature contrasts with the non-universal correlations between cell geometry, rearrangement rate, and fluidity, which depend sensitively on the underlying modes of active force. Our results demonstrate that persistent Brownian motion provides a minimal framework for describing tissue dynamics, while distinct active forces leave identifiable structural and dynamical signatures, thereby enabling inference of the dominant active force in fluid state tissues.

Figures (6)

• Figure 1: Modeling framework and phase transition behaviors. (a) Representative tissue snapshot, showing distinct types of vertices. (b) Traction force as a self-propelling force, whose polarity $\theta_i$ diffuses over time. (c) Edge tension $T_{ij}$ fluctuates around a fixed point $T_0$. Phase diagram of (d) traction force, and (e) tension fluctuations, based on long-time MSRD.
• Figure 2: Cell geometry in fluid states. Schematic representation of (a) shape factor $q$ and (b) aspect ratio $\alpha$. Cell anisotropy changes for traction (left) and tension fluctuations (right) in terms of (c) shape factor and (d) aspect ratio. The dashed line in (c) indicates $q_c = 3.81$. Triangles, circles, and squares respectively represent solid, fluid(traction), and fluid(tension fluctuations) states, as defined in Fig. \ref{['fig:1']}(d)(e). (e) Correlations between shape factor, aspect ratio, and MSRD, exhibiting non-universal features.
• Figure 3: Cell geometry in fluid states. (a) Representative cell shapes for distinct $q$. (b) Correlations between $q$ and $\alpha$ for fluid states with experimental data saraswathibhatla2020spatiotemporalmalinverno2017endocytic shown as black markers. Error bars indicate the standard error of the mean. The insets illustrate the different morphologies at large $q$.
• Figure 4: T1 dynamics. (a) Schematics of a successful (left) and an unsuccessful (right) T1 transition. (b) Representative edge length evolution during a T1 transition for traction (purple) and tension fluctuations (green). Solid and dashed lines represent successful and unsuccessful T1 events, respectively. The gray line marks $l_c$. (c) Mean stalling time, and (d) T1 success rate for tension fluctuations. (e) Mean expected change in defect density for unsuccessful T1 transitions.
• Figure 5: Spatio-temporal correlations in cell dynamics. Normalized mean squared velocity for (a) traction (linear scale) and (b) tension fluctuations (log scale). (c) Effective persistence $\tau_\text{eff}$ and (d) correlation length $l_v$. The dashed line in (c) represents unity.