4.18: Structural Basis of Ligand Affinities of Oxygen Carriers

The interaction of ligands, such as dioxygen, with metal complexes, such as iron-porphyrinato systems, and the means by which this interaction is characterized, have been covered in broad outline in the previous sections. As noted earlier, the affinities of hemoglobins for carbon monoxide and dioxygen span a wide range (see Table 4.2 and Figure 4.24). In this section the active site is examined in much finer detail than before in order to develop relationships between perturbations in structure and affinity (and hence function)—so called structure-function relationships. The reference point is the somewhat hypothetical situation where the dioxygen binder is in the gas phase and independent of interactions with solvent molecules, solute molecules, and itself, and where dioxygen, carbon monoxide, and other small molecules may bind without steric constraints—in other words, a state where intrinsic affinity is measured. In this section attention is focused exclusively on the hemoglobin family and on iron- and cobalt-porphyrinato systems. In recent years structural data on hemoglobin, myoglobin, and their derivatives have become available with a precision that permits meaningful comparison with the more precisely determined model or synthetic systems. In addition, the various hemoglobins and myoglobins, and especially the naturally occurring mutants of hemoglobin A (human Hb), have provided a sort of poor man's site-directed mutagenesis. Now the techniques of molecular biology permit the site of mutation to be selected, the altered gene to be inserted into E. coli, and the mutant protein to be expressed in large (mg) quantities. With the conditions for crystallization of hemoglobins now well-established, we can discover quite rapidly what structural perturbations are caused by the substitution of one amino acid for another, and can relate these to the perturbations in properties, such as cooperativity, dioxygen affinity, and kinetics of ligand binding.

The principles enunciated here are applicable generally to hemerythrin and hemocyanin; however, we currently lack the thermodynamic and especially structural data we would like to have for these systems.

Ligand Affinities in Hemoglobins and Their Models

The O2 affinities in biological carriers span five orders of magnitude, which at room temperature corresponds to a difference in the free energy of oxygen binding

\[\delta \Delta G = -RTln(K_{max}/K_{min}) = -RTln(P_{1/2min}/P_{1/2max}) \tag{4.47}\]

of about 6.0 kcal/mol. This wide range of O₂ and CO affinities has not yet been paralleled in synthetic systems; the values for O₂ affinity do not exceed those for R-state human hemoglobin. A selection of values from model systems is given in Table 4.5.^{23,31,160-165} For the flat-open porphyrin system (Figure 4.23) the dioxygen ostensibly binds in an unconstrained manner, but is actually subject to solvent influences. In order to obtain thermodynamic constants on these "unhindered" systems, one must gather data at several low temperatures and then extrapolate to room temperature, or obtain them from kinetic measurements, K = k_on/k_off, at room temperature.

For the picket-fence porphyrins, dioxygen binds in a protected pocket that is deep enough to accommodate it and to prevent the dimerization that leads to irreversible oxidation, provided that there is a slight excess of base to ensure full saturation of the coordination sites on the unprotected face of the porphyrin.⁷² Thus the picket-fence, the capped, and the bis-pocket porphyrins reversibly bind dioxygen at room temperature with little oxidation over many cycles. This stability facilitated isolation of crystals of a synthetic iron-dioxygen species of the picket-fence porphyrin. The capped porphyrin offers a more highly protected site. The low affinity these latter systems have for dioxygen indicates that the binding cavity is so small that repulsive steric interactions between coordinated dioxygen and the cap are unavoidable. The left-hand side of Figure 4.24 depicts on a logarithmic scale the range of O₂ affinities. Each power of 10 corresponds to around 1.2 kcal/mol at 25 °C.

The right-hand side of Figure 4.24 illustrates the range of affinities for CO binding. For many synthetic systems the CO affinities are orders of magnitude greater than in the biological systems that have an O₂ affinity similar to the synthetic; for example, see the entries for the picket-fence porphyrin. Comparison of the left- and right-hand sides of Figure 4.24 reveals that the strongest O₂ binder, hemoglobin Ascaris, is one of the weakest CO binders. The O₂ affinity of the picket-fence porphyrins is very similar to that of myoglobin, but, as will be detailed shortly, one cannot infer from this that the binding sites are strictly comparable. Indeed, similar affinities have been observed with a non-porphyrin iron complex.^121,162 Moreover, if the CO affinity of myoglobin paralleled that of the picket-fence porphyrins, some 20 percent of myoglobin (and hemoglobin) would be in the carbonmonoxy form (in contrast to the approximately 3 percent that occurs naturally), a level that could render reading this section while chewing gum physically taxing.¹¹⁷

Figure 4.24 - CO and O₂ affinities of a selection of hemoglobins and model systems. Affinities are given as P_1/2, and the scale is logarithmic. One order of magnitude corresponds to 1.2 kcal/mol at 25 °C.

Table 4.5 - Thermodynamics and kinetics of ligand binding to synthetic oxygen carriers at 20-25 ºC

a) When available P_1/2 are from thermodynamic measurements, otherwise from k_on/k_off, where solubility of O₂ in toluene is 1.02 x 10⁵ M/Torr and of CO in toluene is 1.05 x 10^-2; solubilities in benzene are very similar.

b) Some k_off are calculated from K(O₂), k_on(CO), and M.

Carrier	P1/2(O2) Torr	\(\Delta\)H kcal/mol	Dioxygen \(\Delta\)S eu	Binding kon \(\mu\)M^-1s^-1	koff s^-1	P1/2(CO) Torr	Carbon \(\Delta\)H kcal/mol	Monoxide \(\Delta\)S eu	Binding kon \(\mu\)M^-1s^-1	koff s^-1
Toluene/benzene solvent
Picket fence, pocket
Fe(PF-Im)	0.58	-16.3	-40	430	2,900	0.000022	—	—	36	0.0078
Fe(PF)(1,2-Me2Im)	38	-14.3	-42	106	46,000	0.0089	—	—	1.4	0.14
Fe(Poc-PF)(1-MeIm)	0.36	—	—	2.2	9	0.0015	—	—	0.58	0.0086
Fe(Poc-PF) (1, 2-Me2lm)	12.6	-13.9	-28	1.9	280	0.067	—	—	0.098	0.055
Fe(Bis-Poc) (1, 2-Me2Im)	508	-14.4	-47	—	—	0.0091	—	—	—	—
Cap
Fe(C2Cap) (1-MeIm)	23	-10.5	-28	—	—	0.0054	—	—	0.95	0.05
Fe(C2Cap) (1, 2-Me2Im)	4,000	-9.7	-36	—	—	0.20	—	—	—	—
Strapped
Fe(7, 7-CP) (1, 5-Cy2Im)	1.4	—	—	65	1,000	0.00091	—	—	6	0.05
Fe(6, 6-CP) (1, 5-Cy2Im)	700	—	—	0.1	800	0.17	—	—	0.03	0.05
Flat open
Fe(PPIX-Im)	5.6	—	—	62	4,200	0.00025	—	—	11	0.025
Bis-strapped
Fe(Amide-Im)	0.29	—	—	310	620	0.000017	—	—	40	0.067
Fe(Amide-Py)	2.0	—	—	360	5,000	0.00009	—	—	35	0.03
Fe(Ether-Py)	18	—	—	300	40,000	0.0001	—	—	68	0.069
H2O, alkylammonium micelles, pH 7.3
Fe(PPIX-Im)	1.0	-14.0	-3.5	26	4.7	0.002	-17.5	-34	3.6	0.009
Fe(MPIX-Im)	0.57	—	—	22	23	0.0013	—	—	11	0.019
Fe(MPIX-Py)	12.2	—	—	1	380	0.0021	—	—	12	0.035

There is a convenient index to summarize the extent to which CO (or O₂) binding is discriminated against for a given iron-porphyrin system. M is defined as the ratio of O₂ affinity (as P_1/2) to CO affinity for a particular system and experimental conditions:

\[M = \frac{P_{1/2}(O_{2})}{P_{1/2}(CO)} \tag{4.48}\]

From Figure 4.24 and from Tables 4.2 and 4.5 the M values calculated may be somewhat arbitrarily divided into three classes: those where M > 2 x 10⁴ (good CO binder); those where 2 x 10² < M < 2 x 10⁴; and those where M < 2 x 10² (good O₂ binder). An analogous parameter, N, may be defined to summarize the differences in the O₂ affinity between an iron-porphyrin system and its cobalt analogue:

\[M = \frac{P_{1/2}(O_{2}—Co)}{P_{1/2}(O_{2}—Fe)} \ldotp \tag{4.49}\]

For the picket-fence porphyrins and for vertebrate hemoglobins N is in the range 10 to 250, whereas for the flat-open porphyrins and for some hemoglobins that lack a distal histidine (e.g., hemoglobin Glycera and hemoglobin Aplysia), N is at least an order of magnitude larger, indicating for these latter species that the cobalt analogue binds O₂ relatively poorly^167,168 (see Table 4.6).

Note that whereas the O₂ binding of the picket-fence porphyrins is similar to that for myoglobin, the kinetics of the process are very different; the synthetic system is more than an order of magnitude faster in k₁ and k_-1 (often also referred to as k_on and k_off). On the other hand, O₂ binding to the pocket porphyrin is similar to that for the biological system. The factors by which ligand affinities are modulated, generally to the benefit of the organism, are subtle and varied, and their elucidation requires the precise structural information that is currently available only from x-ray diffraction experiments. Figure 4.25 shows the structural features of interest that will be elaborated upon in the next subsections.^110,169

Table 4.6 - Relative affinities (M) of iron-porphyrinato systems for O₂ and CO, and relative affinities (N) for O₂ of iron and cobalt-porphyrinato systems.

Compound	P1/2(Fe—CO) Torr	P1/2(Fe—O2) Torr	M P1/2(Fe—O2)/P1/2(Fe—CO)	P1/2(Co—O2) Torr	N P1/2(Co—O2)/P1/2(Fe—O2)
H2O, pH 7
Whale Mb	0.018	0.51	28	57	110
Whale Mb (E7His→Gly)	0.0049	6.2	1,300	—	—
Aplysia Mb	0.013	2.7	200	50 x CoMb	> 1,000
Glycera Mb	0.00089	5.2	5,800	50 x CoMb	> 1,000
Fe(PPIX-Im)	0.002	1.0	500	—	—
Toluene/Benzene
Fe(PF-Im)/ Co(PF) (1-MeIm)	0.000022	0.58	27,000	140	240
M(PF)(1, 2-Me2Im)	0.0089	38	4,300	900	24
M(Bis-Poc)- (1, 2-Me2Im)	0.0091	508	55,800	—	—
Fe(PPIX-Im)/ Co(PPIX) (1-Melm)	0.00025	5.6	22,000	18,000	3,200
M(C2-Cap)(1-Melm)	0.0054	23	4,200	140,000	6,100