Figure 7.

The Mid-hindbrain boundary. A Expression patterns of four major factors at the mid-hindbrain boundary. The relevant part of the neural tube is subdivided into 6 compartments, each displaying a unique expression pattern. The right table represents the known expression patterns in a Boolean framework (note that the secreted variants of Fgf8 and Wnt1 are not included here). B This code snippet demonstrates the use of Odefy for model selection. We load a precalculated set of random models along with the 9 known valid models and iterate over all model equations (lines 1-2, mhbsettings is contained in the examples folder of the Odefy package). Next, we generate Boolean models from each equation and extend the model to a six cell multicompartment model (lines 3-4). The Boolean model is converted into a system of ODEs and simulated starting from the known expression state (lines 5-7). Note that we simulate a sufficient amount of time units to ensure the systems has fallen into a steady state. If the final state after simulation is still correct in terms of activity we assume to model to be valid (lines 8-10). C Three replicated cells from our hypothetical six-cell system. Note that Wnt1 and Fgf8 are secreted factors and exhibit their influence towards neighboring cells. D The nine network variants that give rise to the desired steady state pattern. All models contain the mutual activation between Fgf8 and Wnt1 (between neighboring cells), a mutual inhibition between Otx2 and Gbx2 as well as some regulatory incluence of the transcription factors towards the secreted factors.