Cellular interfacial and surface tensions determined from aggregate compression tests using a finite element model

Although previous studies suggested that the interfacial tension γ _cc acting along cell‐cell boundaries and the effective viscosity μ of the cell cytoplasm could be measured by compressing a spherical aggregate of cells between parallel plates, the mechanical understanding necessary to extract this information from these tests—tests that have provided the surface tension σ_cm acting along cell‐medium interfaces—has been lacking. These tensions can produce net forces at the subcellular level and give rise to cell motions and tissue reorganization, the rates of which are regulated by μ. Here, a three‐dimensional (3D) cell‐based finite element model provides insight into the mechanics of the compression test, where these same forces are at work, and leads to quantitative relationships from which the effective viscosity μ of the cell cytoplasm, the tension γ _cc that acts along internal cell‐cell interfaces and the surface tension σ_cp along the cell‐platen boundaries can be determined from force‐time curves and aggregate profiles. Tests on 5‐day embryonic chick mesencephalon, neural retina, liver, and heart aggregates show that all of these properties vary significantly with cell type, except γ_cc, which is remarkably constant. These properties are crucial for understanding cell rearrangement and tissue self‐organization in contexts that include embryogenesis, cancer metastases, and tissue engineering.