An Active Surface Model Explains W-Shaped Folding of the Forebrain Roof Plate

During vertebrate embryonic development, the roof plate of the forebrain invaginates, separating the two cerebral hemispheres, which is an essential step for proper brain formation. However, this mechanical process remains poorly understood. We use chick embryos to study this process. Observations of the cross-sections along the dorsal-ventral axis reveal that the roof plate forms a characteristic W-shaped profile that deepens until the opposing fronts meet, completing the hemispherical separation. This process correlates with differential adhesion molecule expression and spatial variation in cell proliferation, suggesting the generation of anisotropic active tensions between the apical and basal surfaces of the neuroepithelium, as well as anchoring to the surrounding mesenchyme. To explain this process mechanistically, we developed an active gel model that treats the roof plate as a two-dimensional epithelial surface with finite thickness, subject to apical, basal, and lateral tensions. Our approach bridges vertex models and continuum mechanics, linking model parameters (tensions, volume and area density) to measurable quantities. Using this framework, we recapitulate the characteristic W-shaped folding and attribute it to gradients in active tension or proliferation modulated by mesenchymal anchoring.