A Model for the Spatial Patterning of Teeth Primordia in the Alligator: Initiation of the Dental Determinant

We propose a mathematical model mechanism for the initiation and spatial positioning of tooth primordia in the alligator, Alligator mississippiensis. Our goal is to formulate and analyse a model that explains the spatial patterning of teeth primordia. In line with experimental evidence, jaw growth plays a crucial role in our model. This paper is concerned with the initiation of the first tooth in the lower jaw of the alligator, the dental determinant, one of the important elements in understanding dentition patterning. The model we propose is a caricature of the qualitative model proposed by Westergaard & Ferguson (1987), and describes the initiation of the dental determinant as a process controlled by jaw growth, the age structure of the epithelial cells in the developing jaw, and the age-dependent production of cellular adhesion molecules in the dental epithelium. The model incorporates both mechanochemical and reaction-diffusion mechanisms, and makes the important prediction that gradual changes in the mechanical properties of the epithelial cells are not sufficient to explain the spatial position of the dental determinant. The study of pattern formation in this growing domain demonstrates that simpler and more intuitive approaches to pattern formation can be misleading in the study of pattern formation in more complex situations such as the one studied here.