Combinatorics of giant hexagonal bilayer hemoglobins

The paper discusses combinatorial and probabilistic models allowing to char acterize various aspects of spacial symmetry and structural heterogeneity o f the giant hexagonal bilayer hemoglobins (HBL Hb). Linker-dodecamer config urations of HBL are described for two and four linker types (occurring in t he two most studied HBL Hb of Arenicola and Lumbricus, respectively), and t he most probable configurations are found. It is shown that, for HBL with m arked dodecamers, the number of 'normal-marked' pairs of dodecamers in homo logical position follows a binomial distribution. The group of symmetries o f the dodecamer substructure of HBL is identified with the dihedral group D g Under natural symmetry assumptions, the total dipole moment of the dodeca mer substructure of HBL is shown to be zero. Biological implications of the mathematical findings are discussed. (C) 2000 Elsevier Science Inc. All ri ghts reserved.