Does the Geometric Location of Odontoblast Differentiation and Dentinal Tubules Depend on a Reaction-Diffusion System between BMP2 and Noggin? A Mathematical Model

Abstract Introduction The mesenchymal differentiation to odontoblasts is a complex process that determines the formation of dentinal tubules. This process involves a carefully regulated sequence of changes in the behavior of mesenchymal cells coordinated by the expression of different molecular factors that includes mainly the Noggin and bone morphogenetic protein type 2 (BMP2). Methods We investigated a bioregulatory mathematic model based on a set of equations of reaction-diffusion to predict the geometry of the formation of the dentinal tubules. Results We found that odontoblast location and the dentinal tubules formation are determined by the spatial distribution of a set of molecular signals that compete among themselves to maintain places of the greatest concentration of BMP2, which determines the step from mesenchymal cells to odontoblasts and the formation of the dentinal tubules. Conclusions This mathematic model suggests a regulatory loop between BMP2 and Noggin, which is highly stable and repeatable and determines the right location patterns of the odontoblasts and the formation of dentinal tubules. This mathematic approach allows us to understand biological phenomena and biochemical activity during the period of pulp differentiation.