Snowflakes could explain how tooth enamel is formed

Researchers from the University of Helsinki and Aalto University have used the way that snowflakes form to explain how tooth enamel gets distributed over the crown during growth

Physicists and mathematicians use the classical ‘Stefan problem’ to explain the principles of crystal formation, such as snowflakes.

The newly published work provides a theoretical basis for the developmental regulation of enamel formation, and helps to uncover why even closely-related species such as humans and orangutans have very different looking teeth.

Tooth enamel matrix is soft when freshly laid down but it starts to harden immediately and once mature, enamel is the most mineralised and hardest part of the mammalian body.

The hardness of the enamel makes teeth capable of lasting a lifetime – or longer and enamel cannot be repaired or remodelled, making the growth of the enamel matrix a critical step in tooth formation.

The researchers at the University of Helsinki and Aalto University propose that differences in enamel thickness are regulated by the nutrient diffusion rate – the rate that individual regions on a crown receive the required nutrients and substances needed to make the enamel.

The same principles apply

Starting from a model that is used to simulate snowflake formation, the researchers built a new model that instead of ice, mimics the formation of enamel matrix.

Teemu Häkkinen from the Aalto University in Finland explains: ‘Whereas enamel is not obviously as intriguingly shaped as snowflakes, it is interesting that the same physical principles can account for the increase in complexity in both systems.’

The new model can be used to investigate both evolutionary species differences, and medical defects in enamel formation.

Starting from CT-imaged real teeth from which enamel was digitally removed, enamel matrix was reloaded on underlying dentin surfaces by computer simulations.

Only when simulating the matrix secretion as a diffusion-limited process, were the researchers able to make the subtle enamel features found on a human cheek tooth i.e. a molar.

In contrast to humans, orangutan molar teeth have complex ridges and grooves that could be simulated by lowering the diffusion rate of enamel-forming nutrients even further.

Thus, orangutans, which eat also hard foods such as unripe fruits and bark, may have evolved their wrinkly enamel with a relatively simple developmental change.

‘There are huge amounts of different data available on enamel, and now we have the tools of physicists to make testable predictions,’ explains Professor Jukka Jernvall from the Institute of Biotechnology, University of Helsinki, Finland.

The research was a collaboration between the University of Helsinki and Aalto University.


Häkkinen TJ, Sova SS, Corfe IJ, Tjäderhane L, Hannukainen A, Jernvall J (2019) Modeling enamel matrix secretion in mammalian teeth. PLoS Comput Biol 15(5): e1007058. https://


Research group page:
Helsinki EVO-DEVO group

University of Helsinki

Aalto University

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