School of Mathematics

Karen Page

Karen Page abstract

Karen M Page, Department of Mathematics, UCL

Mathematical modelling of vertebrate neural tube patterning

A major challenge in developmental biology is to understand the mechanisms of pattern formation. Morphogens provide the positional information that organises gene expression and cell differentiation in many developing tissues. Conventional views say they induce distinct responses in a concentration-dependent manner. But signal duration has also been implicated in determining cellular responses. Here we establish how both the level and duration of signaling by the morphogen Sonic Hedgehog (Shh) control patterning in the vertebrate neural tube. Morphogen signaling is interpreted by a transcriptional regulatory circuit that links Shh signaling to three transcription factors. We present the circuit and equations to describe the levels of the transcription factors within a cell. We show that the design of this circuit unifies the temporal and graded response to Shh signaling. It also renders cells insensitive to transient increases in Shh signalling and confers hysteresis - memory of the signal. These results are experimentally verified. We discuss alternative behaviours of the gene regulatory network.