🔬 condensed matter

Cell divisions suppress dynamical correlations in solid tissues

Using a two-dimensional elastoplastic model, this study demonstrates that while cell divisions fluidize developing tissues and preserve marginal stability, they fundamentally suppress the system-spanning dynamical avalanches characteristic of passive amorphous solids by imposing a finite energy budget for rearrangements.

Original authors: Ali Tahaei, Ahandeep Manna, Marko Popović

Published 2026-05-13

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CC BY 4.0

Original authors: Ali Tahaei, Ahandeep Manna, Marko Popović

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a living tissue, like the skin on your arm or the lining of a fruit fly's wing, not as a static wall, but as a crowded, bustling city made of cells. This city is solid enough to hold its shape and transmit forces, but it's also constantly remodeling itself. Cells are dividing, moving around, and swapping neighbors.

The researchers in this paper wanted to understand how this constant "construction work" (cell division) affects the city's overall stability and how it reacts to stress. They compared this living tissue to a passive amorphous solid, which is like a pile of sand or a block of glass that isn't alive.

Here is the breakdown of their findings using simple analogies:

1. The "Avalanche" Problem in Dead Materials

In a non-living, disordered solid (like a pile of sand or a block of glass), if you push on it just enough to make it start to slide (yield), a tiny local slip can trigger a chain reaction. One grain of sand moves, which pushes its neighbor, which pushes the next, creating a massive avalanche that can span the entire material. This happens because the material is "marginally stable"—it's balanced on a knife's edge, and long-range elastic forces connect every part of it.

2. The Living City: Cell Divisions as "Active Construction"

In a living tissue, cells divide. The researchers treated these divisions as "active plastic events." Think of a cell dividing not just as a cell splitting, but as a construction crew suddenly injecting energy and reshaping the street grid, regardless of whether the street was about to collapse or not.

They asked: Does this constant construction keep the "avalanche" behavior, or does it change it?

3. The Key Findings

A. Divisions Turn the Solid into a Fluid (Below the Breaking Point)
In a dead solid, if you push it gently (below a certain stress limit), it acts like a rock and doesn't flow. But in this living tissue, the constant cell divisions act like a lubricant. They "fluidize" the tissue, allowing it to flow and reshape even under very gentle pressure. It's like having a crowd of people constantly shifting and making space for each other, allowing the whole group to move smoothly even without a strong shove.

B. The "Marginal Stability" Paradox
You might think that if you keep shaking a system with cell divisions, it would become chaotic and lose its delicate balance. Surprisingly, the tissue remains marginally stable. It still has that "knife-edge" balance where it is ready to yield, just like the passive solid. The local rules of stability haven't changed; the tissue is still poised right on the edge of breaking.

C. The Big Surprise: Avalanches are Crushed
This is the most important discovery. Even though the tissue is still marginally stable and the parts are still connected by long-range forces, the massive, system-spanning avalanches disappear.

Instead of one giant earthquake rippling through the whole city, the cell rearrangements happen in small, isolated bursts. The "avalanches" are suppressed.

Why? The Energy Budget Analogy
The authors explain this using an energy budget.

In a dead solid: When you push it, energy builds up until it releases in one giant, catastrophic avalanche.
In the living tissue: Cell divisions act like a faucet constantly dripping energy into the system. This allows the tissue to flow gently. However, this energy source is limited. It's like a finite budget.
Because the cell divisions are constantly injecting energy and resetting the local stress, they "spend" the energy budget on small, local adjustments. There isn't enough "saved up" energy left to trigger a massive, city-wide avalanche. The divisions essentially "pay for" the small rearrangements, preventing the big ones from happening.

4. Different Types of Divisions Matter

The researchers looked at two main ways cells might divide:

Random Divisions: The cell splits in a random direction. This still stops the big avalanches, but the tissue flows mostly because cells are rearranging around the random splits.
Stress-Relaxing Divisions: The cell splits in a way that specifically relieves the local stress (like a pressure valve opening). This is even more effective at stopping avalanches. It's so good at relieving pressure that it almost completely stops the "snowball effect" of rearrangements. The tissue becomes very stable locally, but the "budget" for big movements is almost zero.

The Bottom Line

Living tissues are a unique hybrid. They look like "marginal solids" (they have the structural hallmarks of a material ready to break), but they behave very differently dynamically. Because cell divisions constantly inject energy and reset local stresses, they prevent the massive, chain-reaction avalanches seen in dead, passive materials.

In short: Life keeps the tissue on the edge of breaking, but the constant activity of cell division acts as a "fire extinguisher" that stops small slips from turning into massive, system-wide collapses. This explains why tissues can be stiff and glassy (like a solid) without exhibiting the wild, unpredictable avalanches you'd expect from a non-living solid.

Technical Summary: Cell divisions suppress dynamical correlations in solid tissues

Problem Statement
Developing tissues function as amorphous solids that maintain mechanical coherence while continuously remodeling through cellular processes like neighbor exchanges, extrusions, and divisions. In passive amorphous solids, localized plastic events interact via long-ranged elastic fields, triggering system-spanning avalanches of rearrangements near the yielding transition, a phenomenon rooted in marginal stability. However, it remains unclear whether living tissues exhibit similar collective dynamics. Unlike passive materials where rearrangements are triggered by local mechanical instability, cell divisions are active events that generate stress and remodeling independently of the local mechanical state. This raises the question of whether such activity preserves the avalanche phenomenology and marginal stability characteristic of passive amorphous solids, or if it fundamentally alters the tissue's dynamical correlations.

Methodology
The authors employ a two-dimensional elastoplastic model (EPM) to simulate solid-like epithelial tissues. In this framework, the tissue is discretized into $N$ mesoscopic blocks, each characterized by a local shear stress tensor. The model incorporates:

Passive Mechanics: Blocks behave elastically until their local stress exceeds a yield surface (defined as a circle in stress space), at which point they undergo plastic rearrangements (analogous to T1 transitions). These events redistribute stress throughout the system via a long-ranged elastic propagator.
Active Remodeling: Cell divisions are treated as active plastic events that imprint an anisotropic force dipole on the surrounding tissue. The study distinguishes between three types of divisions based on their orientation relative to local stress:
- Randomly Oriented Divisions (ROD): No preferred axis; strain magnitude drawn from a bounded distribution.
- Stress-Oriented Divisions (SOD): Axis aligns with local shear stress.
- Stress-Relaxing Divisions (SRD): Reset local stress to zero in the same symmetry channel as a passive plastic event.
  The simulations analyze the steady-state flow, the distribution of local stability ( $P(x)$ ), and the statistics of avalanche sizes ( $S$ ) defined as the number of cell rearrangements triggered by a single division event.

Key Contributions and Results

Fluidization Below Yield: The study confirms that cell divisions fluidize the tissue below the passive yield stress ( $\Sigma_c$ ), generating a linear rheological response ( $\dot{\gamma} \sim \Sigma$ ) controlled by the division rate ( $k_d$ ). The origin of this flow depends on the division type: for ROD, flow is driven almost entirely by cell rearrangements, whereas for SRD and SOD, the flow is dominated by the divisions themselves at low stress.
Preservation of Marginal Stability: In the quasistatic limit ( $k_d \to 0$ ), the system retains marginal stability. The distribution of local stability $P(x)$ exhibits a pseudogap scaling as $P(x) \sim x^\theta$ with $\theta \approx 0.55$ for ROD and $\theta \approx 0.52$ for SRD, consistent with values found in passive amorphous solids. However, for SRD, the prefactor of this distribution is exponentially suppressed, significantly depleting the pool of blocks available to yield, even though the formal gap does not open.
Suppression of Avalanches: Contrary to the behavior of passive amorphous solids, the presence of cell divisions strongly suppresses system-spanning avalanches. While avalanches follow a power-law distribution $\rho(S) \sim S^{-\tau}$ (with $\tau \approx 1.36$ ) at the yield stress, they acquire a stress-dependent cutoff $S_c$ below $\Sigma_c$ . For SRD, this cutoff is severe at low stress, effectively eliminating avalanches.
Energy Balance Mechanism: The authors attribute the suppression of avalanches to an energy balance constraint. The energy injected by cell divisions allows for shear flow below the yield stress but simultaneously provides a finite "budget" for rearrangements. As the system approaches the yield stress from below, the energy dissipated by rearrangements vanishes linearly with $(\Sigma_c - \Sigma)$ , while the energy injected by divisions remains finite. This balance dictates that the average avalanche size scales as $\langle S \rangle \sim (\Sigma_c - \Sigma)^{-1}$ , leading to the observed cutoff scaling $S_c \sim (\Sigma_c - \Sigma)^{1/(2-\tau)}$ .

Significance and Claims
The paper claims that proliferating tissues display the structural hallmarks of marginal amorphous solids (specifically the density of local stability $P(x)$ ) while exhibiting significantly shorter-ranged dynamical correlations compared to their passive counterparts. The authors suggest that activity does not merely add noise to a passive yielding material; rather, it continuously reshapes the population of regions close to local instability. By limiting the availability of passive plasticity to organize into collective bursts, cell divisions prevent the emergence of system-spanning avalanches.

This work provides a potential explanation for why epithelial tissues can exhibit glassy mechanical signatures without displaying the large-scale avalanches expected in passive amorphous solids. The authors note that while other sources of active noise (e.g., molecular motors) might behave more like thermal noise, the specific mechanism of cell division acts to preserve marginal stability while sharply reducing dynamical correlations.

1. The "Avalanche" Problem in Dead Materials

2. The Living City: Cell Divisions as "Active Construction"

3. The Key Findings

4. Different Types of Divisions Matter

The Bottom Line

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