In an earlier study (Xue et al. Nature Materials 2018), stem cells differentiated into one of two cell types, neural plate border (NPB) or neural plate (NP), in vitro with the NP forming a central circular domain. This previous study demonstrated that this differentiation is likely mechanics-guided. Part of this demonstration was measurements of the displacement of microposts under the cell layer as the cells differentiate. These measurements suggested that the NPB cells are more contractile than NP cells (see Dataset of cell layers on micro-patterned substrates compost of posts). The authors of the 2018 study and of a follow-up study further explored how the size of the NPB domain depends on experimental conditions (see Dataset of stem cell colonies differentiating in neural induction medium and code for analysis of resulting fate pattern). To further understand what factors could be driving NPB formation, we estimated cell area at the colony edge (see Dataset on cell areas and nuclear densities in differentiating stem cell colonies). This analysis inspired a mathematical model of mechanical patterning: fate affects cell contractility, and pressure in the cell layer biases fate. Cells at the colony edge, more contractile than cells at the center, seed a pattern that propagates via force transmission. We simulated the model in various cell geometries and for different substrates (see Code for simulating NP/NPB fate patterning in stem cell colonies). Strikingly, our model implies that the width of the outer fate domain varies non-monotonically with substrate stiffness, a prediction that we confirm experimentally. Our findings thus support the idea that mechanical stress can mediate patterning in the complete absence of chemical morphogens, even in non-motile cell layers, thus expanding the repertoire of possible roles for mechanical signals in development and morphogenesis.
