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

Abstract

The organised generation of functionally distinct cell types in developing tissues depends on establishing spatial patterns of gene expression. In many cases, this is directed by spatially graded chemical signals - known as morphogens. In the influential "French Flag Model", morphogen concentration is proposed to instruct cells to acquire their specific fate. However, this mechanism has been questioned. It is unclear how it produces timely and organised cell-fate decisions, despite the presence of changing morphogen levels, molecular noise and individual variability. Moreover, feedback is present at various levels in developing tissues introducing dynamics to the process that break the link between morphogen concentration, signaling activity and position. Here we develop an alternative approach using optimal control theory to tackle the problem of morphogen-driven patterning. In this framework, intracellular signalling is derived as the control strategy that guides cells to the correct fate while minimizing a combination of signalling levels and the time taken. Applying this approach demonstrates its utility and recovers key properties of the patterning strategies that are found in experimental data. Together, the analysis offers insight into the design principles that produce timely, precise and reproducible morphogen patterning and it provides an alternative framework to the French Flag paradigm for investigating and explaining the control of tissue patterning.