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Length scale of cellular activity determines signatures of epithelial remodeling

Using an active vertex model, this study demonstrates that while four distinct modes of cellular activity (apolar motility, polar motility, fluctuating contractility, and mechanochemical regulation) all drive epithelial fluidization, they produce unique signatures in tissue dynamics and architecture that can be specifically identified by analyzing the correlation length and functional form of spatial velocity correlations.

Original authors: Sahil Islam, Anupam Gupta, Mohd. Suhail Rizvi

Published 2026-08-17

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CC BY 4.0

Original authors: Sahil Islam, Anupam Gupta, Mohd. Suhail Rizvi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine a bustling city made entirely of living cells, packed so tightly that they form a continuous, flexible sheet. This is an epithelial tissue, the kind of material that lines your skin, your gut, and your lungs. In the world of physics, these tissues are "active materials," meaning they aren't just sitting there; they are constantly generating their own energy and moving. Sometimes, this tissue acts like a solid brick wall, holding its shape firmly. Other times, it suddenly turns into a fluid, flowing and reshaping itself like honey. This transformation is called "fluidization," and it's the secret sauce behind how embryos grow into complex shapes, how wounds heal, and unfortunately, how cancer spreads.

But here's the mystery: just because a tissue turns into a fluid doesn't mean we know how it happened. Think of it like a traffic jam clearing up. The cars might start moving because a traffic light turned green (a signal), because a driver decided to speed up (motility), or because the road itself started vibrating (contractility). In biology, scientists have long suspected that different "engines" drive this fluidization, but for a long time, models treated all these engines as if they were the same generic motor. The big question is: if you see a tissue flowing, can you tell which specific engine is running underneath, or is the flow just a generic result of any engine working hard?

This paper dives into that question by building a digital simulation of a tissue and testing four different "engines" of cellular activity. The researchers, using a computer model where cells are treated as polygons, asked: if we turn on different types of cellular activity, does the tissue behave differently, even if the end result looks the same? They tested four distinct modes:

Apolar Motility: Like tiny, random jitters at the edge of a cell, with no specific direction.
Polar Motility: Like a cell deciding to march in a specific direction, pushing all its edges forward.
Fluctuating Contractility: Like a cell randomly squeezing and relaxing its muscles without a pattern.
Mechanochemical Regulation: A complex feedback loop where a cell senses its own size and adjusts its squeezing power, creating waves of activity that ripple across the whole tissue.

The simulations revealed a fascinating truth: while all four engines successfully turned the solid tissue into a fluid circle, they did it in completely different ways. It's as if four different groups of people all managed to clean up a messy room, but one group did it by dancing, another by shouting, a third by randomly throwing things, and the fourth by following a synchronized wave. The final room looked clean in all cases, but the path to get there was unique to each group.

The study found that these different engines leave behind distinct "fingerprints" in how the cells move and rearrange themselves. For instance, the random jitters (Apolar Motility) caused cells to shuffle around quickly but chaotically. The marching cells (Polar Motility) moved together in a coordinated way but only over short distances. The random squeezers (Fluctuating Contractility) got stuck in a sort of "cage," moving a bit and then stopping. The wave-followers (Mechanochemical Regulation) moved in large, rhythmic pulses that traveled across the tissue, sometimes causing cells to vanish entirely as they shrank too much.

Crucially, the paper suggests that you can't just look at the final shape or how fast the tissue flows to figure out which engine is running. Instead, the key is to look at spatial velocity correlations—a fancy way of asking, "If I watch one cell move, how does a neighbor cell move?" The simulations showed that this single measurement acts like a master key. It can tell you exactly which of the four engines is driving the tissue. For example, if the correlation between moving cells drops off quickly and never goes negative, it's likely random jitters. If it shows a wave-like pattern where cells move in opposite directions at certain distances, it's the mechanochemical feedback loop.

The authors emphasize that these findings come from computer simulations, not direct experiments on living tissue yet, but they point out that the tools to measure these velocity patterns already exist in labs using standard live-cell imaging. By simply watching how cells move relative to each other, scientists might soon be able to diagnose the physical origin of tissue remodeling without needing to poke the cells or look for specific molecular markers. It's a new way to read the story of a tissue's life just by watching its dance.

Technical Summary: Length scale of cellular activity determines signatures of epithelial remodeling

Problem Statement
Epithelial tissues undergo fluidization—a transition from solid-like to fluid-like states—during development, wound healing, and disease. While this macroscopic outcome is well-documented, the underlying physical origins of the active forces driving it are diverse. Cells can generate forces through subcellular stochastic protrusions, cell-scale polarity-driven migration, fluctuating cortical contractility, or tissue-scale mechanochemical feedback. Current theoretical models often represent these distinct mechanisms using a single generic active stress or self-propelled motility, implicitly assuming mechanical equivalence. Consequently, it remains unclear whether different force-generation mechanisms produce unique structural, dynamical, and mechanical signatures that can be experimentally distinguished, or if they all converge to indistinguishable tissue-scale behaviors.

Methodology
The authors employ an active vertex model to simulate confluent epithelial tissues, representing cells as polygons governed by a mechanical energy function dependent on area and perimeter. To investigate the role of spatial organization, they extend the passive model with four distinct classes of activity, each operating at a different length scale:

Apolar Motility (AM): Subcellular scale ( $< l_0$ ). Modeled as spatially uncorrelated, temporally fluctuating white noise forces applied directly to cell vertices.
Polar Motility (PM): Cellular scale ( $\sim l_0$ ). Modeled as coherent, directed forces applied to all vertices of a cell based on an intrinsic, uncorrelated polarity vector.
Fluctuating Contractility (FC): Cellular scale ( $\sim l_0$ ). Modeled as temporally varying, isotropic contractile stresses within each cell, driven by Ornstein–Uhlenbeck processes, without spatial correlation between cells.
Mechanochemical Regulation (MR): Tissue scale ( $\gg l_0$ ). Modeled via a feedback loop where cell area deviation drives Rho–ROCK–myosin signaling, generating spatially and temporally correlated contractile waves.

The study systematically compares these classes by analyzing their ability to drive tissue fluidization (spontaneous rounding of a rectangular tissue), topological rearrangements (T1 and T2 transitions), cell dynamics (Mean Squared Displacement), structural heterogeneity (shape factor and area distributions), rheological responses (stress relaxation), and spatial velocity correlations.

Key Contributions and Results
The study establishes that while all four activity classes drive the same global transition to a fluid-like circular morphology, they do so through fundamentally distinct microscopic pathways that leave distinguishable signatures:

Dynamics of Remodeling: The time to reach the fluidized state varies significantly. Mechanochemical regulation (MR) is the fastest, driven by a two-stage process involving the self-organization of contractile waves that accelerate T1 and T2 events. Apolar (AM) and Polar (PM) motility relax on comparable timescales, while Fluctuating Contractility (FC) is the slowest due to weak, unstructured tension fluctuations.
Topological Pathways:
- T1 Transitions: AM shows steady accumulation; PM shows a delayed onset; FC is slowest; MR exhibits a rapid, two-stage accumulation driven by coherent waves.
- T2 Transitions (Cell Elimination): MR uniquely drives a burst of cell elimination via coordinated area reduction, providing an additional, rapid route to fluidization. FC produces very few T2 events.
Structural and Rheological Signatures:
- Shape and Area: Motility-driven classes (AM, PM) broaden cell shape distributions toward anisotropy while preserving mean area. Contractility-driven classes (FC, MR) maintain isotropic shapes but shift mean area to smaller values due to shrinkage and cell loss.
- Stress Relaxation: AM and PM show rapid, monotonic stress decay. FC shows slower decay. MR exhibits non-monotonic, oscillatory relaxation with a distinct spectral peak corresponding to the mechanochemical feedback frequency.
Spatial Velocity Correlations (The Unifying Fingerprint): The authors identify spatial velocity correlations, $C(r)$ $C (r)$ , as the most robust observable for distinguishing all four mechanisms:
- AM: Short correlation length ( $\xi \sim 0.5\sqrt{A_0}$ ), strictly positive, monotonic decay.
- PM: Extended correlation length ( $\xi > \sqrt{A_0}$ ), monotonic decay, reflecting cell-scale coherence.
- FC: Short correlation length ( $\xi < \sqrt{A_0}$ ) but with a negative lobe (anticorrelation) arising from local contraction/expansion kinematics.
- MR: Long correlation length ( $\xi \sim 3\sqrt{A_0}$ ) with a pronounced negative lobe, directly reflecting the wavelength of mechanochemical waves.
- Robustness: These qualitative signatures (correlation length and the presence/absence of anticorrelation) remain robust across varying activity strengths.

Significance
The paper claims to provide a physical framework linking the scale and organization of active force generation to macroscopic tissue behavior. Its primary significance lies in demonstrating that tissue fluidization is not a unique mechanical state but a common outcome reachable via different modes of force generation, each leaving a specific "fingerprint."

Crucially, the authors argue that spatial velocity correlations offer an experimentally accessible means to identify the physical origin of epithelial activity using only live-cell imaging (via particle image velocimetry or cell tracking), without requiring mechanical perturbations or molecular reporters. This allows researchers to infer whether observed tissue remodeling is driven by motility, contractility, or mechanochemical feedback based on the spatial structure of cell motion. The work suggests that the diversity of velocity correlation profiles observed in various experimental epithelial systems can be interpreted through this unified lens of activity length scales.

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