Measurements of eight frog neural crest cell clusters migrating toward stiffer gel reveal asymmetric height profiles with rearward peaks. The authors extend active-wetting theory so basal cell motion drives internal flow, pressure differences and surface curvature, and fit the numerical model to the averaged measured profile. The fit gives a capillary number of 0.29 ± 0.03 and an estimated viscosity of about 8.2 kPa·s. The viscosity estimate depends on the assumed amplitude of basal velocity variations, which were not directly measured.

SOFT MATTER / LIVING SYSTEMS

A migrating cell cluster looks like a droplet. Its uneven shape tells a story about the forces within.

An interactive reading of Hennighausen et al. · 2026

THE IDEA IN ONE LINE

Cells pull. Flow builds pressure. Pressure shapes the tissue.

01 / THE LIVING DROPLET LAB

Watch a tissue move.

Watch the cluster travel forward with its peak behind the center. Change the flow to see what shapes that asymmetry.

Increase flow’s influence relative to surface tension, keeping the normalized basal velocity profile fixed.

The basal layer is the bottom layer of cells in contact with the gel.

Uneven basal motion creates a rearward peak. At Ca = 0.29, the model’s peak is 15.8 µm behind the center.

02 / WHAT THE CELLS ACTUALLY DO

A steeper back. A gentler front.

Eight neural crest cell clusters from frog embryos migrated across gels that became stiffer in one direction. Moving toward a stiffer region is called durotaxis.

After migration, the clusters were fixed and imaged by confocal microscopy, which measured their height. The surface was asymmetric: a high point behind the center, with different angles where the front and rear meet the gel.

Choose an edge to reveal its tangent.

Rear: 25 ± 2°. The back meets the gel at a steeper angle.

The supplement fits a straight line near each edge, above a 4.5 µm height cutoff. That line is the tangent; its angle is the contact angle.

TWO WAYS TO AVERAGE

Measurements from the averaged height profile of eight clusters. Peak height: 30 ± 3 µm; half-length: 110 ± 11 µm.

03 / FOLLOW THE FORCES

From a pull to a profile.

A droplet’s surface holds the signature of what is happening beneath it. Follow the causal chain.

In the model, basal cells pull more strongly at the front than the rear: 15 Pa versus 5 Pa. This traction—the force per area transmitted to the substrate—sets up an uneven velocity profile along the cluster.

WHY THIS CONNECTION MATTERS

A living surface, read from within.

Instead of prescribing a lopsided outline, the researchers predict it from internal flow. The same physical connection could help explain the shapes of other migrating tissues driven by chemical, electrical or mechanical guidance.

That extension is a proposal: this paper studies durotactic neural crest clusters and models how their asymmetric shape emerges.

A thin-film view

The calculation treats the cluster as a two-dimensional slice with fixed length and area. The bottom layer is active; the tissue above it is treated as a passive, incompressible viscous fluid. The 3D lab extrudes the calculated cross section to make the mechanism visible. Playback translates that steady shape at the model’s 50 µm/h, with time accelerated. The view follows the cluster; gel markers pass beneath it. Flow arrows show laboratory-frame velocity, while tracers move relative to the cluster.

One ratio, many shapes

The capillary number is Ca = viscosity × migration speed / surface tension. Higher viscosity or speed makes flow more influential; higher surface tension favors a smoother, more symmetric shape. The lab varies Ca at a fixed normalized velocity profile.

The shape equation

h‴ = 3 Ca (1 − v/VT) / h²

Equation (8) links how curvature changes along the height profile h to the difference between the bottom-layer velocity v and the migration speed VT. Pressure is connected to curvature by surface tension.

What is estimated

The fit gives Ca = 0.29 ± 0.03 and a viscosity near 8.2 kPa·s under the chosen parameter assumptions. Supplementary Appendix C explains how that viscosity estimate depends on the strength of the basal flow modulation.

THE RESEARCH

Migrating cell clusters as active droplets with asymmetric shape and contact angles

Hanno I. Hennighausen · Jaime A. Espina · Elias H. Barriga · Ricard Alert arXiv preprint · 2026

Scientific basis: Figure 1 and Appendix A (measurements), Figures 2–3 and Equations (1), (2), (8) (model), Appendix C (parameter estimates). Lab curves are a numerical reconstruction, not microscopy data. All interactive diagrams are original. Source manuscript: arXiv perpetual, non-exclusive distribution license. Figures and supplementary material are credited through the source links.