Narrow Results

Phyllotaxis of plant organs, bacterial ordering and animal coat patterns are analyzed for homogeneity and density. The patterns are approximated by 15 tiles and characterized by the self-coordination numbers T₁, T₂, T₃ of the nearest, next-nearest and third neighbors of the vertices of the tiles. Homogeneous structures with integer T_i values and maximum densities are obtained for distichous, whorled or spiral growth of leaves. Similar T₁ values, such as T₁=5 and 6 of sunflower seeds or bacteriae, give rise to maximum density. Inhomogeneous structures like the striped patterns of zebras with T₁=1, 2 and 3 connections have a higher density than homogeneous stripes with T₁=2. Maximum density is also obtained in icosahedral viruses.

Crystallization is recognized among structural biologists as a necessary process before three-dimensional structure can be solved at an atomic level. Crystallization has a dose of mysticism among protein chemist. Some treats it as an “art” and others as “black magic”. These concepts aroused from a limited knowledge in the physical chemistry of proteins in solution. Crystallization appears only in a metastable state. To define crystallization conditions the experiments are guided either by a chance search or by dedicated factorial design. Here we will briefly describe a factorial design method to rationally approach the metastable state. In summary, there is nothing mysterious in crystallization of biological macromolecules, and the success can often be achieved within a limited number of experiments.