Figure 1. See text for explanation. Taken from Elhai & Khudyakov (2018). Very similar to figure in Wilcox et al (1973).
| Mathematician Alan Turing is well known for his pioneering work on computation, but near the end of his life, he also made a significant contribution to our understanding of biological pattern formation (Turing, 1952). He showed that a simple model (Figure 1) consisting of two components could in principle produce patterns starting from nothing except random fluctuation. The first component (R) determines the reaction, the biological action (e.g. pigmentation or differentiation). It feeds back positively on itself, so that a small amount of active R produces greater activity. The second component (S) is dependent on R for its synthesis, suppresses R, and diffuses away from its site of synthesis. Hans Meinhardt and co-workers expanded on the idea, for one thing allowing the R component to be totally non-diffusible, as you'd expect from a protein trapped within a cell (Meinhardt, 2008). Michael Wilcox and colleagues came up with a similar theoretical formulation and showed that heterocyst spacing in Anabaena was consistent with the model in certain respects (Wilcox et al, 1973). | Figure 1. See text for explanation. Taken from Elhai & Khudyakov (2018). Very similar to figure in Wilcox et al (1973). |
The model realized in Anabaena
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Buikema & Haselkorn (1991) identified a protein in Anabaena with the earmarks of the R component of the Turing model. It is the master regulator of heterocyst differentiation (Kumar et al, 2010) and positively regulates its own expression (Black et al, 1993). Yoon & Golden (1998) found a small protein in Anabaena that looked like the S component. Its synthesis depends on HetR (Huang et al (2004)) and it acts to block HetR action (Kumar et al, 2010). There is suggestive evidence that a small peptide derived from PatS diffuses from cells in which it is synthesized (Herrero et al, 2016). These relationships are shown in Figure 2.
Other regulatory components have found that tie the model to the specific biology of patterned heterocyst differentiation (Figure 2). HetN protein acts in a way very similar to PatS but is important in the maintenance rather then the initiation of the pattern of heterocysts (Callahan & Buikema, 2001). |  Figure 2. See text for explanation. Taken from Elhai & Khudyakov (2018). |
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