🔬 physics

Shape matters: Inferring the motility of confluent cells from static images

This study demonstrates that machine learning models trained on individual cell shape features extracted from static images can accurately predict single-cell motility in dense, heterogeneous collectives, offering a physics-inspired approach to inferring dynamic behaviors from histological data.

Original authors: Quirine J. S. Braat, Giulia Janzen, Bas C. Jansen, Vincent E. Debets, Simone Ciarella, Liesbeth M. C. Janssen

Published 2026-02-26

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CC BY 4.0

Original authors: Quirine J. S. Braat, Giulia Janzen, Bas C. Jansen, Vincent E. Debets, Simone Ciarella, Liesbeth M. C. Janssen

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 you are a detective trying to solve a mystery in a crowded room. The room is packed shoulder-to-shoulder with people (cells). Some of these people are sprinting around the room (active, motile cells), while others are standing still or shuffling very slowly (passive, non-motile cells).

The problem? You can only take one single photograph of the room. You can't see who is moving; you can only see who is standing where.

Your goal is to look at that frozen photo and point out exactly who is the sprinter and who is the stander, just by looking at their shape and how they are squeezed by their neighbors.

This is exactly what the scientists in this paper did, but instead of people, they studied cells in a tissue, and instead of a camera, they used a computer simulation.

The Big Idea: "Shape Tells the Story"

In biology, we often know that cells move differently when they are sick (like in cancer spreading) or healing a wound. But watching them move in real-time is hard. Doctors usually only have static pictures (like a snapshot from a microscope).

The researchers asked: "Can we guess how fast a cell is moving just by looking at its shape in a still picture?"

They found that yes, we can. A cell that is trying to push its way through a crowd looks different from a cell that is just sitting there.

How They Did It (The Recipe)

The Simulation (The Virtual Crowd):
They didn't use real cells first; they built a virtual world using a computer model called the Cellular Potts Model. Imagine a giant grid of pixels. They filled this grid with 144 "digital cells."
- Some cells were programmed to be sprinters (Active).
- Some were programmed to be sluggards (Passive).
- They took "snapshots" of this digital crowd at random moments.
The Detective Work (Machine Learning):
They taught a computer (a simple AI called a Neural Network) to look at these snapshots. They gave the computer a list of clues to look for, such as:
- How long is the cell? (Is it stretched out?)
- How round is it?
- How many neighbors does it have?
- Is it squished by the people next to it?
The Training:
The computer looked at thousands of these snapshots, learning that "Oh, if a cell is long and skinny and pushing against its neighbors, it's probably a sprinter!"

The Surprising Findings

Here is where the story gets interesting:

The "Solo Sprinter" Effect: When there was only one sprinter in a crowd of standers, the computer could spot it instantly. The sprinter looked very different because it was stretching and distorting the crowd around it.
The "Crowded Party" Effect: As they added more sprinters, it got harder to tell them apart. However, the computer was still surprisingly good at it, even with just one single snapshot.
The Secret Weapon: The most powerful clue wasn't the complex math of the whole crowd. It was simply the shape of the individual cell. If you just looked at the shape of one specific cell, the AI could tell you if it was a sprinter or a stander with high accuracy.

Why This Matters (The Real-World Application)

Think of a pathologist (a doctor who looks at tissue samples) trying to diagnose cancer. They have a slide with a picture of tumor cells. They can't see the cells moving because the cells are frozen on the slide.

Before this paper: They had to guess which cells were aggressive based on general patterns or complex, hard-to-see features.
After this paper: They can use a simple AI tool to look at the shape of each cell in the picture. If a cell looks "stretched" or "distorted" in a specific way, the AI can flag it: "Hey, this cell is likely the aggressive, moving type that might spread cancer."

The Takeaway Metaphor

Imagine a dance floor.

Passive cells are like people standing in a tight circle, holding hands, not moving much. They look round and compact.
Active cells are like people trying to break through the circle to get to the exit. They look stretched, elongated, and they push their neighbors out of the way.

This paper proves that if you take a photo of the dance floor, you don't need to see the movement to know who is trying to escape. You just need to look at who is stretched out and who is squished. The shape itself holds the secret to the movement.

In short: The researchers built a digital microscope that can "read" the future movement of cells just by looking at their current shape, offering a new, powerful tool for understanding diseases like cancer.

1. Problem Statement

Cell motility within dense, confluent tissues is a critical factor in physiological processes (e.g., wound healing) and pathological conditions (e.g., cancer metastasis, asthma). A major challenge in this field is the heterogeneity of cell motility within a tissue; some cells are highly motile (active), while others are less motile or non-motile (passive).

The Core Challenge: Identifying the motility phenotype of individual cells is difficult because standard histological analysis relies on static images, whereas motility is a dynamic property.
The Gap: While previous research has established links between average cell shape and collective dynamics (e.g., jamming/unjamming transitions), it remains largely unexplored whether static, single-cell shape features can predict the individual motility of a specific cell within a heterogeneous layer.

2. Methodology

The authors employed a physics-informed machine learning (ML) approach combining simulations and classification algorithms.

A. Simulation Model (Cellular Potts Model - CPM)

Framework: They utilized the Cellular Potts Model (CPM) implemented in CompuCell3D to simulate a 2D confluent layer of cells on a $300 \times 300$ lattice.
Hamiltonian: The system dynamics are governed by an energy function ( $H$ $H$ ) comprising:
- Adhesion energy ( $H_{adh}$ ).
- Area constraint ( $H_{area}$ ) to maintain cell size.
- Perimeter constraint ( $H_{perimeter}$ ) to prevent non-physical shapes.
- Active Force ( $H_{active}$ ): This term drives motility. The strength of the active force ( $\kappa$ ) distinguishes cell types.
Scenarios: Two distinct regimes were simulated:
1. Binary Motility: Passive cells are non-motile ( $\kappa_p = 0$ ), while active cells are highly motile ( $\kappa_a = 1500$ ).
2. Heterogeneous Motility: Both cell types are motile, but active cells are significantly more motile ( $\kappa_a > \kappa_p > 0$ ).
Data Generation: Static snapshots were extracted every 1000 Monte Carlo Steps (MCS). The number of active cells ( $N_a$ ) was varied from 0 to 60 in a total population of 144 cells.

B. Feature Extraction

Instead of using raw images, the authors extracted 145 interpretable physical features for each cell, categorized into:

Shape Features: Geometric properties derived from the cell's pixel boundary (e.g., area, perimeter, eccentricity, semi-major/minor axes, alignment with neighbors).
Structural Features: Properties derived from the centers of mass (COM) of the cell and its neighbors (e.g., bond order parameters $\psi_n$ , neighbor distances, moments of mass).

Local vs. Non-Local: Features were further divided into local (single-cell properties) and non-local (averages/max/min of neighboring cells).

C. Machine Learning Model

Algorithm: A Multilayer Perceptron (MLP) (a simple neural network with one hidden layer) was used for binary classification (Active vs. Passive).
Training: The dataset was split into 80% training and 20% testing. To handle class imbalance, subsets of passive cells were randomly selected to match the number of active cells.
Validation: The model's performance was evaluated using accuracy.
Feature Importance Analysis: Three methods were used to understand which features drove the predictions:
1. Manual removal of feature subsets.
2. SHAP (Shapley Additive Explanations) to quantify feature contribution.
3. PCA (Principal Component Analysis) to reduce dimensionality and identify variance.

3. Key Contributions

Proof of Concept for Single-Cell Inference: The study demonstrates that static shape features alone are sufficient to accurately predict the motility phenotype of an individual cell in a confluent layer, without needing time-lapse data.
Dominance of Local Shape: A key finding is that local shape features (information intrinsic to the single cell) are nearly as effective as using the full set of 145 features (including complex structural and non-local neighbor data).
Robustness to Heterogeneity: The model successfully generalizes across different ratios of active-to-passive cells and varying motility strengths, provided the motility difference is significant.
Physics-Informed ML: The work bridges the gap between physical modeling (CPM) and data-driven classification, showing that physical shape distortions caused by active forces are detectable in static snapshots.

4. Key Results

High Accuracy in Extreme Cases: When passive cells are non-motile ( $\kappa_p=0$ ) and active cells are highly motile, the model achieves near-perfect accuracy ( $\approx 1.0$ ) when $N_a$ is low (e.g., 1 active cell). Accuracy remains above 0.7 even as $N_a$ increases to 60.
Local vs. Non-Local: Models trained only on local shape features performed almost identically to models trained on all features (shape + structure). This suggests that the cell's own geometry contains the primary signal of its motility.
Structural Features are Secondary: Using only structural features (neighbor distances, bond orders) resulted in significantly lower accuracy compared to shape-based models.
Generalization Capabilities:
- A model trained on a specific number of active cells ( $N_a$ ) can generalize to unseen $N_a$ values, with models trained on intermediate $N_a$ (e.g., 15) showing the best overall robustness.
- Models generalize well across different motility ratios ( $\gamma = \kappa_p/\kappa_a$ ) as long as the active cell motility ( $\kappa_a$ ) remains high. However, predictive power drops if the active cells in the training set are significantly less motile than those in the test set.
Failure Modes: The model tends to fail when the emergent long-time diffusion coefficients of active and passive cells become too similar (i.e., when the motility difference is small).

5. Significance and Implications

Diagnostic Potential: This approach offers a pathway to infer cell dynamics from routine static histological images (e.g., H&E stained slides) used in pathology. This could be crucial for estimating the aggressiveness of tumors or the progression of epithelial-to-mesenchymal transition (EMT) without requiring live-cell imaging.
Simplicity and Efficiency: The finding that simple local shape features are sufficient makes the method computationally efficient and easier to implement in clinical settings compared to complex, multi-feature deep learning models.
Theoretical Insight: The work reinforces the concept of "morphodynamics," confirming that the instantaneous shape of a cell is a direct physical manifestation of its internal motility forces, even in a crowded, confluent environment.
Future Applications: The authors suggest this framework could be adapted for experimental data analysis to diagnose disease progression or study cell behavior in complex tissues where time-lapse imaging is not feasible.