The possibility of direct interaction between the hemes in hemoglobin.

The Problem.-Heme-heme interaction in hemoglobin may be defined briefly as the dependence of the ligand-binding properties of a particular subunit heme upon the state of liganding of other subunit hemes in the same tetramer. The existence of such dependence is clearly demonstrated by a comparison of the equilibrium ligand-binding properties of the isolated a and , subunits with that of hemoglobin.1 The nature of heme-heme interaction has not yet been elucidated, although it has been the subject of much consideration. Pauling2 attempted with limited success to implement the concept of direct ligand-dependent interactions between the hemes themselves. The currently more popular approach is to assume that the actual subunit interactions arise at the interface between the adjacent subunits and that their ligand dependence stems from ligand-induced configurational changes in the individual subunit.3 This latter approach gains appeal from its generality, since no particular property of a heme need be invoked. However, this very generality is an enormous obstacle to the formulation of a quantitative description of protein function in terms of structure. Recent attempts4' 5 to quantify or partially quantify this allosteric model, as it is called, and to apply it to hemoglobin utilize assumptions, made in the interest of mathematical tractability, that would appear to rob the model of physical meaning. In the hope of discovering a simpler alternative to this situation, Libby6 began, in 1964, to re-examine the possibility of long-range interaction between the hemes themselves, utilizing the new knowledge of hemoglobin structure obtained since the appearance of the Pauling model. 8 Since Wyman9 had shown that the diheme produced by the splitting of hemoglobin in concentrated urea displays nearly all the cooperative ligand binding characteristic of the tetraheme, Libby assumed that two of the six possible heme pairs interact much more strongly than do the other four. Wyman's value for the ligand-dependent interaction between the two hemes in diheme (3.5 kcal/mole of dihemes) was employed as an approximate value for the interaction between the two closest heme pairs. X-ray studies had revealed that the two hemes in these close pairs are approximately 25 A apart and nearly coplanar.7 Various mechanisms by which two such hemes could directly interact with the required energy were examined for feasibility. Monopole interactions were excluded because the heme carries no net charge in either the liganded or unliganded configuration. Permanent electric dipole interactions were excluded because the near-D4h symmetry of the heme would seem to rule out the existence of permanent dipoles of the requisite size. Magnetic dipoles were excluded because unrealistically large ring currents in the conjugated pi-electron system of the heme would have to be invoked. Electron exchange bonding between the