A computational model of teeth and the developmental origins of morphological variation

Journal name:
Date published:
Published online

The relationship between the genotype and the phenotype, or the genotype–phenotype map, is generally approached with the tools of multivariate quantitative genetics and morphometrics1, 2, 3, 4. Whereas studies of development5, 6, 7 and mathematical models of development4, 8, 9, 10, 11, 12 may offer new insights into the genotype–phenotype map, the challenge is to make them useful at the level of microevolution. Here we report a computational model of mammalian tooth development that combines parameters of genetic and cellular interactions to produce a three-dimensional tooth from a simple tooth primordia. We systematically tinkered with each of the model parameters to generate phenotypic variation and used geometric morphometric analyses to identify, or developmentally ordinate, parameters best explaining population-level variation of real teeth. To model the full range of developmentally possible morphologies, we used a population sample of ringed seals (Phoca hispida ladogensis)13. Seal dentitions show a high degree of variation, typically linked to the lack of exact occlusion13, 14, 15, 16. Our model suggests that despite the complexity of development and teeth, there may be a simple basis for dental variation. Changes in single parameters regulating signalling during cusp development may explain shape variation among individuals, whereas a parameter regulating epithelial growth may explain serial, tooth-to-tooth variation along the jaw. Our study provides a step towards integrating the genotype, development and the phenotype.

At a glance


  1. A model integrating gene networks and tissue mechanics.
    Figure 1: A model integrating gene networks and tissue mechanics.

    a, Nine parameters regulating gene network properties and ten parameters regulating cellular properties integrate the behaviour of cells. Act induces the differentiation of epithelial cells into enamel knots (white arrow), which results in the production of Inh and also Sec regulating tissue growth. b, Tissue morphology is modelled for the cells of the inner enamel epithelium. The underlying mesenchyme is a three-dimensional space in which molecules and mechanical stresses diffuse. Molecular diffusion between the immediate surroundings of two epithelial cells is calculated using Fick’s law of diffusion (diffusing inhibitor shown in colour). A triangular mesh connects cells centres (black lines) and the position of each corner is calculated as a Voronoi node (blue mesh). Cell shape depends on the positions and number of neighbouring cells. c, The initial conditions consists of seven epithelial cells representing the tip of the oral epithelium invagination and developing tooth shape can be visualized at any time point, here shown at 1,000 time intervals. At each interval, all equations are integrated using the Euler method and all variation simulations used 10,000 time points. Anterior towards the left. a–d denote cusp names used to identify seal tooth cusps.

  2. Shape of variation in real and in silico seal teeth.
    Figure 2: Shape of variation in real and in silico seal teeth.

    a, The fourth postcanine tooth of Lake Ladoga seals varies from three to five cusped shapes. b, Systematical tinkering with each model parameter (shown at 20% intervals for the three examples) produces variation in cusp shape, size and number. c, Component loadings based on procrustes superimposition (variance-covariance matrix) and principal component analyses of the four tallest cusp positions (teeth with four and five cusps, n = 67) and of each simulated tooth population after changing each parameter (n = 22 to 99 depending on how many teeth had at least four cusps). Loadings shown for the first two components together with percentages of variance explained. The whiskers show the direction and relative strength that the first two components affect variation (the whisker lengths of the second components, dashed black line, are scaled based on variance explained relative to the first component, orange line). The grey outline shows the mean cusp pattern of the real teeth (Phoca). Anterior towards the left. For parameter names, see Methods Summary.

  3. Variation in cusp position and number implicate the same patterning kernel parameters.
    Figure 3: Variation in cusp position and number implicate the same patterning kernel parameters.

    a, Differences in the first two principal component loadings (plotted for all four cusps) between real seal teeth and in silico teeth show that genetic parameters belonging to the activator–inhibitor loop regulating enamel knot formation produce the most realistic variation. Boxes enclose 50% of cusps; the median and the mean are indicated with a horizontal bar and a circle, respectively, and whiskers denote range. b, Tinkering systematically with each model parameter (shown at 20% intervals) produces variation in cusp number in 13 of the 19 parameters. We note the tendency for increasing top-cusp angle with increasing number of cusps in real seal teeth and in silico teeth varied with the patterning kernel parameters. Genetic parameters are in red, cellular parameters are in blue. Error bars denote s.d.

  4. Serial tooth-to-tooth variation implicates a cellular parameter.
    Figure 4: Serial tooth-to-tooth variation implicates a cellular parameter.

    a, The four ringed seal (Phoca) postcanines (P2–P5) show a gradual change in morphology, whereas the grey seal (Halichoerus) tooth row has a transition from a three- to a one-cusped shape. b, Constant change in parameter Egr, the epithelial growth rate, produces change in relative cusp height similar to the morphological change observed in the ringed seal tooth row. We note the curvature of the in silico P2 main cusp, resembling that of real teeth. Three parameters (Act, Egr and Pbi) can be used to turn an in silico ringed seal tooth into a grey seal tooth, and constant changes in two parameters (Egr and Act) produce changes reminiscent of changes along the grey seal tooth row, despite the heterodont change in morphology. Grey seal was produced by manually tinkering with ringed seal parameters. Scale bar, 10 mm.

Author information


  1. Departament de Genètica i Microbiologia, Facultat de Biociències, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

    • Isaac Salazar-Ciudad
  2. Developmental Biology Program, Institute of Biotechnology, University of Helsinki, PO Box 56, FIN-00014 Helsinki, Finland

    • Isaac Salazar-Ciudad &
    • Jukka Jernvall
  3. Department of Ecology and Evolution, Stony Brook University, Stony Brook, New York 11794, USA

    • Jukka Jernvall

Competing financial interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary Information (580K)

    This file contains Supplementary Figures 1-6 with legends, and Supplementary Tables 1-6.

Additional data