Quantified ensemble 3D surface features modeled as a window on centric diatom valve morphogenesis

Morphological surface features are a record of genetic and developmental processes as well as environmental influences. The 3D geometric “terrain” of the surface consists of slopes via tangents, peaks and valleys via normals, smoothness of the transition between peaks and valleys, and point connections as flatness or curvature among all features. Such geometric quantities can be used to indicate morphological changes in valve formation over time. Quantified 3D surface features as geometric pattern ensembles may be representative of structural snapshots of the morphogenetic process.For diatoms, valve formation and pattern morphogenesis has been modeled using Turing-like and other algorithmic techniques to mimic the way in which diatoms exhibit the highly diverse patterns on their valve surfaces. How the created surface features are related to one another is not necessarily determined via such methods. With the diatom valve face structure of layered areolae, cribra, and other morphological characters, valve formation exhibits different combined geometries unfolding as 3D structural ensembles in particular spatial arrangements. Quantifying ensemble 3D surface geometries is attainable via models devised using parametric 3D equations and extracting surface features via partial derivatives for slopes, peaks and valleys, smoothness, and flatness as feature connectedness. Differences in ensemble 3D surface features may be used to assess structural differences among selected diatom genera as indicators of different valve formation sequences in surface generation and morphogenesis.