Experimental confirmation of tissue liquidity based on the exact solution of the Laplace equation

TL;DR

This study derives an exact analytical solution to measure tissue surface tension, confirming that tissues behave like incompressible liquids with consistent surface tension regardless of compression or volume.

Contribution

The paper introduces an exact solution to the Laplace equation for tissue surface tension measurement, improving accuracy over previous approximations.

Findings

Tissues exhibit constant surface tension independent of compression.

Tissues behave similarly to true liquids in surface tension properties.

The method accurately measures tissue surface tension using geometric parameters.

Abstract

The notion of tissue surface tension has provided a physical understanding of morphogenetic phenomena such as tissue spreading or cell sorting. The measurement of tissue surface tension so far relied on strong approximations on the geometric profile of a spherical droplet compressed between parallel plates. We solved the Laplace equation for this geometry and tested its solution on true liquids and embryonic tissue fragments as well as multicellular aggregates. The analytic solution provides the surface tension in terms of easily and accurately measurable geometric parameters. Experimental results show that the various tissues and multicellular aggregates studied here are incompressible and, similarly to true liquids, possess effective surface tensions that are independent of the magnitude of the compressive force and the volume of the droplet.