Optimal control of gene regulatory networks for morphogen-driven tissue patterning.

The generation of distinct cell types in developing tissues depends on establishing spatial patterns of gene expression. Often, this is directed by spatially graded chemical signals-known as morphogens. In the "French Flag model," morphogen concentration instructs cells to acquire specific fates. How this mechanism produces timely and organized cell-fate decisions, despite the presence of changing morphogen levels, molecular noise, and individual variability, is unclear. Moreover, feedback is present at various levels in developing tissues, breaking the link between morphogen concentration, signaling activity, and position. Here, we develop an alternative framework using optimal control theory to tackle the problem of morphogen-driven patterning: intracellular signaling is derived as the control strategy that guides cells to the correct fate while minimizing a combination of signaling levels and time. This approach recovers experimentally observed properties of patterning strategies and offers insight into design principles that produce timely, precise, and reproducible morphogen patterning.