Combinatorics of giant hexagonal bilayer hemoglobins

The paper discusses combinatorial and probabilistic models allowing to characterize various aspects of spacial symmetry and structural heterogeneity of the giant hexagonal bilayer hemoglobins (HBL Hb). Linker–dodecamer configurations of HBL are described for two and four linker types (occurring in the two most studied HBL Hb of Arenicola and Lumbricus, respectively), and the most probable configurations are found. It is shown that, for HBL with marked dodecamers, the number of `normal-markedʹ pairs of dodecamers in homological position follows a binomial distribution. The group of symmetries of the dodecamer substructure of HBL is identified with the dihedral group D6. Under natural symmetry assumptions, the total dipole moment of the dodecamer substructure of HBL is shown to be zero. Biological implications of the mathematical findings are discussed.