Algae from the viewpoint of mathematics

The multicellular organisms we shall treat in this chapter range from unicellular Gonium to Volvox having thousands of cells. By introducing a seminal notion of complexity hierarchy, we have constructed a simple classification of extracellular matrices in the framework of formal language theory. Then, this classification has enabled us to understand the necessity of various forms of multicells. We have also constructed another model for generalized Anabaena, which is a genus of filamentous cyanobacteria or blue-green algae, using a Lindenmayer system (an L-system). An L-system is a parallel rewriting system that was introduced originally to model the development of multicellular organisms. The aim of this model is the derivation of exact algebraic equations between the proliferation and transition rates for high cell-type diversity. For simplicity, we have studied 'generalized Anabaena' having three cell types: A, B and C on the assumption of A ⇒ B ⇒ C cell lineage. In this model, the high cell-type diversity corresponds to the condition that A, B and C cells are well mingled. This model has revealed that the condition for high cell-type diversity can be described as an elliptic curve under a certain condition that is deeply related to 'Fermat's last theorem.