A mathematical model of fractone-controlled morphogenesis

It has been hypothesized that the generation of new neural cells (neurogenesis) resulting from stem and progenitor cell proliferation and differentiation in the developing and adult brain is guided by the extracellular matrix. The extracellular matrix of the neurogenic niches comprises specialized structures termed fractones, which are scattered in between stem/progenitor cells. Growing evidence indicates that fractones of the adult brain bind and activate growth factors at the surface of stem/progenitor cells to influence their proliferation. It has been shown that neuroepithelial cell proliferation is also associated with fractones during early brain development, although the functional links between fractones and neuroepithelial cells have not been elucidated. We present a mathematical model that considers the role of fractones as captors and activators of growth factors that influence the rate of proliferation and the location of the newly generated neuroepithelial cells in the forming brain. This model allows for the dynamic placement and removal of fractones into the evolving cell mass, giving us control over its developing shape. Using this model, we simulate early brain morphogenesis, focusing on the formation of the lateral ventricle walls from the anterior portion of the neural tube.