Reaction-diffusion model of hair-bundle morphogenesis

Abstract

The hair bundle, an apical specialization of the hair cell composed of several rows of regularly organized stereocilia and a kinocilium, is essential for mechanotransduction in the ear. Its precise organization allows the hair bundle to convert mechanical stimuli to electrical signals; mutations that alter the bundle's morphology often cause deafness. However, little is known about the proteins involved in the process of morphogenesis and how the structure of the bundle arises through interactions between these molecules. We present a mathematical model based on simple reaction-diffusion mechanisms that can reproduce the shape and organization of the hair bundle. This model suggests that the boundary of the cell and the kinocilium act as signaling centers that establish the bundle's shape. The interaction of two proteins forms a hexagonal Turing pattern - a periodic modulation of the concentrations of the morphogens, sustained by local activation and long-range inhibition of the reactants - that sets a blueprint for the location of the stereocilia. Finally we use this model to predict how different alterations to the system might impact the shape and organization of the hair bundle.