The observed form of coated vesicles and a mathematical covering problem.
A connection is made between (1) the observed structures of clathrin cages and (2) the mathematical problem of determination of the smallest diameter of n equal circles by which the surface of a sphere can be covered without gaps. For different numbers n of circles, it is found that the various clathrin polyhedra identified so far provide topologically the same configurations as the proven solutions of the sphere-covering problem for some n or improve on the currently best conjectured solutions for other n. Thus a study of some biological structures has, in this case, given additional insight into a mathematical problem.
Tarnai
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University of Cambridge, Engineering Department, England.
D002966:Clathrin; D003034:Coated Pits, Cell-Membrane; D008433:Mathematics; D008954:Models, Biological
D002966:Clathrin