The vertebral column develops during early embryogenesis. It is formed from a periodic pattern of somites along the anterior- posterior axis of an organism. These somites are rounded structures formed after compaction and segmentation of mesenchymal cells. There is an intricate pattern of gene activity and protein expression which appears to be involved in the rounding process. However, here we consider the physical aspects of the mechanism. Current theory is that increased cell-cell adhesion induces minimization of the tissue surface tension, yielding rounded tissue. We investigate this behaviour using a viscous liquid model of tissue dynamics. Given the relatively brief time in which somite formation occurs, and the high bulk viscosities of tissues, the basic model is unconvincing. We propose a simple chemotactic mechanism to extend the model. This new model successfully produces rounding within the timeframe found in vivo.
This work was recently published in Developmental Biology. The reference is:
R. Grima, S. Schnell (2007). Can tissue surface tension drive somite formation? Developmental Biology 307, 248-257.
This manuscript doesn't have any hard mathematics. We have published a number of papers on somitogenesis, a number of them are for a mathematical inclined audience. The most recent mathematical model we developed is the clock and wavefront model for somite formation. The references with the mathematical model and its analysis are:
- R. E. Baker, S. Schnell, P. K. Maini (2006). A clock and wavefront mechanism for somite formation. Developmental Biology 293, 116-126.
- R. E. Baker, S. Schnell, P. K. Maini (2006). A mathematical investigation of a new model for somitogenesis. Journal of Mathematical Biology 52, 458-482 .
These two papers are related to the topic of my talk (somitogenesis), though there are not directly dealing with the same problem. I'll explain what we have done and show some of the models. Then I'll go to our new theories, which at the moment we haven't developed yet into full mathematical models. We simply have done physio-chemical calculations to test different theories. This will give a flavour of the new biological problems and the opportunities open to applied mathematicians.
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