Mechanical determinants of epithelium thickness in early-stage embryos.

To address the fundamental question, "How is the thickness of an embryonic epithelium determined?" equations of force equilibrium are derived and used to construct a theory applicable to embryonic epithelia and other labile monolayers, including confluent cultured cells. Under typical physiological conditions, the underlying mathematical relationships can be reworked into one simple algebraic equation. The theory shows that sheet thickness is determined by mechanical interactions between microfilaments, microtubules, cell adhesion systems and in-plane loading. It also explains the perplexing negative in-plane Poisson's ratio observed in some uniaxial tensile tests of embryonic epithelia. Thickness anomalies can affect phenotype, and the equations make it possible to calculate the degree to which gene expression, signalling pathways or other factors must alter the forces at work in order to produce a specified change in sheet thicknesses. Key findings are confirmed using a cell-based finite element model.