Oxygen Transport by Hemoglobin and Myoglobin

Hemoglobin and myoglobin chemistry underlies clinical pulse oximetry, which exploits the different visible/near-infrared absorption spectra of oxy- versus deoxyhemoglobin (a direct consequence of the spin-state and charge-transfer differences discussed here) to noninfectiously measure blood oxygen saturation in real time. Carbon monoxide poisoning treatment (high-flow or hyperbaric O$_2$ therapy) is a direct clinical application of the competitive-binding thermodynamics: raising $p_{\text{O}_2}$ shifts the O$_2$/CO competition back toward O$_2$ occupancy even though CO's intrinsic affinity is far higher, because mass action can overcome a fixed equilibrium ratio. Synthetic "picket-fence" and "capped" iron porphyrins, engineered explicitly to reproduce the steric isolation that prevents μ-oxo dimer formation, remain benchmark model compounds for studying reversible O$_2$ binding outside the protein and for developing synthetic O$_2$ carriers and oxidation catalysts. Hemoglobin-based oxygen carriers (HBOCs) and PEGylated or cross-linked hemoglobin formulations, explored as blood substitutes, must engineer around exactly the autoxidation and NO-scavenging side reactions native protein pockets suppress. Myoglobin remains the standard textbook system for teaching ligand-binding thermodynamics, ultrafast (femtosecond-to-picosecond) photolysis/rebinding kinetics of the Fe–CO and Fe–O$_2$ bonds, and protein dynamics more broadly, because its single heme and lack of cooperativity isolate the fundamental Fe–ligand chemistry from the additional allosteric layer developed for hemoglobin's cooperative behavior and its regulation by 2,3-bisphosphoglycerate, CO$_2$, and pH (the Bohr effect) — the subject taken up next in the study of cooperativity and allostery in oxygen binding.

Ask the tutor: How does the iron's in-plane/out-of-plane motion on O2 binding actually get transmitted into hemoglobin's cooperative T-to-R quaternary conformational change?

Deoxymyoglobin and deoxyhemoglobin both hold their iron as high-spin Fe(II), a d$^6$ ion with all electrons unpaired except one pair, $t_{2g}^4 e_g^2$ in an idealized octahedral field, or more precisely a distorted square-pyramidal ligand field once you account for the actual five-coordinate geometry. The four pyrrole nitrogens of the porphyrin define an equatorial plane; the proximal histidine imidazole nitrogen occupies the axial position below the ring. High-spin Fe(II) is a large ion — its ionic radius in this spin state is too big to fit inside the porphyrin's central hole (radius ≈ 2.01 Å center-to-N), so the iron sits domed out of the mean porphyrin plane by roughly 0.4–0.5 Å, pulling the proximal histidine and the whole F-helix of the protein with it. When O$_2$ binds at the open sixth site, the iron's effective ligand field strengthens (O$_2$, especially as a partially reduced superoxide-like ligand, together with the now fully six-coordinate geometry, raises $\Delta_o$), and the population collapses to low-spin Fe(II)/Fe(III)-like $t_{2g}^6$ (S = 0 for a low-spin Fe(II) description, or a spin-coupled S=0 Fe(III)-superoxide description — both converge on a diamagnetic complex). Low-spin iron is small enough to sit essentially in the porphyrin plane. The iron moves in by about 0.2–0.3 Å, dragging the proximal histidine and the F-helix with it. This iron-in-plane/iron-out-of-plane motion is the literal first step of the allosteric signal that hemoglobin uses for cooperativity — a mechanical link between the coordination sphere of one metal atom and the conformation of an entire 64,000 Da tetramer. The bound dioxygen itself does not sit end-on and linear the way it would on many other metals; it bends. Electron diffraction and neutron/X-ray crystallography of oxymyoglobin give an Fe–O–O angle in the range of 115–135° (canonically discussed as ≈120°, close to a bent, sp²-like oxygen), with an O–O bond length (≈1.21 Å) intermediate between free O$_2$ (1.21 Å, bond order 2) and superoxide O$_2^-$ (≈1.28–1.33 Å in simple salts) — actually the crystallographic O–O distance in oxymyoglobin is close to that of superoxide once resolution and radiation damage artifacts are accounted for, and vibrational spectroscopy (resonance Raman ν(O–O) ≈ 1105 cm$^{-1}$ in oxyhemoglobin, versus 1555 cm$^{-1}$ for free O$_2$ and ≈1145 cm$^{-1}$ for KO$_2$) confirms substantial superoxide character. The bent geometry is not a minor detail; it is diagnostic. A linear, end-on M–O–O would indicate little charge transfer (a Pauling-type weak σ-donor picture); the observed bend is the fingerprint of significant Fe-to-O$_2$ electron donation populating the O$_2$ π* orbital asymmetrically.

The protein architecture around this iron is what makes reversible binding possible at all. In free solution, a ferrous porphyrin exposed to O$_2$ reacts to give a μ-oxo diferric dimer, (Porph)Fe(III)–O–Fe(III)(Porph), irreversibly within milliseconds to seconds — the two metalloporphyrins stack face-to-face, and the initially formed Fe–O$_2$ adduct is trapped by a second deoxy-Fe before it can dissociate, generating the stable oxo bridge with both irons oxidized to Fe(III). Myoglobin and hemoglobin prevent this entirely by burying each heme in its own hydrophobic pocket; no second heme can ever approach closely enough for the bridging reaction. This is a purely steric solution, engineered by the protein fold, and it is why synthetic chemists later had to build "picket-fence" porphyrins with bulky ortho-pivalamide arms to reproduce reversible O$_2$ binding outside a protein. The distal histidine (His E7 in the standard globin numbering) supplies the second half of the solution. It sits on the opposite side of the bound ligand from the proximal histidine, too far to bond to the iron, but close enough that its imidazole N–H can hydrogen-bond to the terminal oxygen of a bent Fe–O–O unit. This interaction (i) stabilizes the bent geometry preferentially over the linear geometry CO would otherwise adopt, (ii) donates electron density that helps stabilize the partial negative charge on the distal oxygen (consistent with Fe(III)–superoxide character), and (iii) sterically discourages the fully linear Fe–C–O geometry that isolated iron porphyrins prefer for CO, weakening CO binding by roughly two orders of magnitude relative to model compounds lacking a distal residue. Site-directed mutants replacing distal His with smaller residues (e.g., Gly) increase CO affinity dramatically and simultaneously make the protein far more prone to autoxidation, directly confirming both roles experimentally.

The central quantitative relationships in this chapter are the ligand-field/spin-state connection, the O$_2$ affinity expressed as a dissociation constant, and the competitive-binding relationship between O$_2$ and CO. The crystal-field/ligand-field splitting for octahedral (or square-pyramidal, approximately) Fe(II) determines the spin state, and the spin state determines the iron radius and hence the doming:

where: $\Delta_o$ is the (effective) ligand-field splitting energy felt by the d-electrons in the relevant coordination geometry, and $P_{\text{pairing}}$ is the spin-pairing energy — the energetic cost of putting two electrons in one d-orbital versus keeping them unpaired in separate orbitals.

Reading: this is the ordinary high-spin/low-spin crossover criterion from crystal field theory, applied twice — once to five-coordinate deoxy-Fe(II), which is weak-field enough (four pyrrole N plus one imidazole N, no strong π-acceptor) to stay high-spin, and once to six-coordinate oxy-Fe, where the added ligand (whether described as O$_2$ or O$_2^-$) plus full octahedral coordination raises $\Delta_o$ past the pairing energy. The consequence — small low-spin iron fitting into the porphyrin plane — is the geometric trigger for the allosteric T→R conformational signal. The overall oxygen-binding equilibrium for myoglobin is a simple 1:1 reaction:

where: $Y_{\text{O}_2}$ is the fractional saturation of myoglobin with O$_2$, $p_{\text{O}_2}$ is the partial pressure of oxygen, and $p_{50}$ is the partial pressure at which the protein is half-saturated (myoglobin's is roughly 1–3 torr, far lower than hemoglobin's ≈26 torr, exactly matching its role as a low-pressure oxygen reservoir rather than a high-pressure transporter).

Reading: this is a simple hyperbolic (non-cooperative) Langmuir-type binding isotherm — myoglobin has one heme, one binding site, no cooperativity, so its curve is a rectangular hyperbola in $p_{\text{O}_2}$. This is the reference point against which hemoglobin's sigmoidal, cooperative curve (built from four interacting hemes) is understood; the mechanism of that cooperativity is developed separately. Finally, the competitive discrimination between O$_2$ and CO for the same ferrous heme site is governed by a ratio of association constants, and the celebrated result of heme-pocket engineering is that the protein suppresses this ratio relative to free heme:

where: $M$ is the "M-value" or relative affinity of CO over O$_2$; $k_{\text{on}}$ and $k_{\text{off}}$ are the association and dissociation rate constants for each ligand. For free (unhindered) iron protoporphyrin in solution $M \sim 20{,}000$–$30{,}000$; inside the myoglobin/hemoglobin distal pocket $M$ drops to roughly 20–250 (species-dependent), a suppression of two to three orders of magnitude achieved almost entirely by the steric and hydrogen-bonding preferences of the distal histidine.

Reading: this ratio is the quantitative statement of "why CO poisoning is survivable at all" — heme intrinsically prefers CO enormously (CO is a strong π-acceptor forming a very stable, linear Fe–C≡O unit), and the distal pocket's preference for bent, hydrogen-bonded geometries claws back most — not all — of that intrinsic preference, which is exactly why even parts-per-million atmospheric CO is still dangerous.

Example 1 (foundational): Counting d-electrons and predicting spin multiplicity for deoxyheme. Heme iron in deoxymyoglobin is Fe(II), a d$^6$ ion. The coordination environment is four pyrrole N (porphyrin) plus one imidazole N (proximal His), a weak-to-moderate ligand field with no low-lying empty π* acceptor orbitals on the ligands (unlike CO or CN$^-$). Apply the weak-field rule: with $\Delta_o < P$, the d$^6$ configuration is high-spin, $(t_{2g})^4(e_g)^2$ in idealized $O_h$ language (or the $C_{4v}$-split equivalent worked through above), giving four unpaired electrons and total spin S = 2.

The experimentally measured effective magnetic moment for deoxyhemoglobin is close to 5.4 $\mu_B$, somewhat above the spin-only value due to unquenched orbital angular momentum in the low-symmetry ligand field — consistent with, and confirmatory of, the high-spin S = 2 assignment. As a limiting-case check: if the ligand field were instead strong (as it becomes upon O$_2$ or CO binding, six-coordinate with a strong-field-like acceptor ligand), the same d$^6$ ion would go low-spin, $(t_{2g})^6(e_g)^0$, S = 0, diamagnetic — exactly the observed switch from paramagnetic deoxyheme to diamagnetic oxyheme, confirming the spin-state assignment is not arbitrary but forced by the ligand-field strength comparison.

Example 2 (applied): Estimating the CO/O$_2$ discrimination factor from kinetic data. Suppose (illustrative, physiologically reasonable, deliberately non-round numbers) a particular myoglobin mutant has the following measured rate constants at 20 °C:

First compute each association constant:

Then the discrimination ratio:

This M-value of ≈18 is physiologically meaningful: it says CO binds this globin about 18 times more tightly than O$_2$ on a per-molecule basis. Because atmospheric/blood O$_2$ concentration vastly exceeds typical inhaled CO concentration under normal conditions, this modest M-value (rather than the ~20,000–30,000 seen for unhindered iron porphyrins in solution) is exactly why humans do not spontaneously poison themselves on the trace CO produced by their own heme catabolism, while still being acutely vulnerable to elevated ambient CO (as from combustion sources), since even a small percentage of CO in inhaled air, multiplied by M ≈ 200–250 for native adult human hemoglobin, is enough to occupy a dangerous fraction of binding sites. As a limiting case: if the distal histidine were entirely removed (mutated to Gly, eliminating both the steric clash favoring bent geometry and the stabilizing H-bond to O$_2$), $k_{\text{off,O}_2}$ would rise sharply while $k_{\text{on,CO}}$ would rise even more (loss of steric hindrance to the linear Fe–CO geometry), pushing $M$ back up by roughly two to three orders of magnitude toward the free-heme value — exactly what is observed experimentally in distal-pocket mutants.

Example 3 (exam/competition level): Relating porphyrin core size, iron spin state, and out-of-plane displacement quantitatively. A crystallographic study reports the Fe–N(porphyrin) bond length in deoxymyoglobin as 2.09 Å and the "core size" (average distance from the mean N$_4$ plane's center to each pyrrole N) as 2.03 Å. Given that the ionic radius of high-spin six-coordinate Fe(II) is 0.78 Å and that of low-spin six-coordinate Fe(II) is 0.61 Å, estimate (a) whether high-spin Fe(II) is expected to sit in the N$_4$ plane, and (b) the approximate out-of-plane displacement, using a simple geometric (Pythagorean) doming model. Set up the geometry: if the iron sits a distance $d$ above the N$_4$ plane, and the in-plane projection of the Fe–N vector has length equal to the core size $r_{\text{core}}$, then the actual Fe–N bond length $r_{\text{FeN}}$ satisfies

Substitute the given crystallographic values:

This geometric estimate, ≈0.50 Å, is in excellent agreement with the crystallographically observed doming of high-spin deoxyheme iron (commonly reported as 0.4–0.5 Å), confirming that the "large ion, small hole" mismatch is quantitatively sufficient to explain the observed structure without invoking any additional exotic distortion mechanism. As a check on part (a): since the ionic radius of high-spin Fe(II) (0.78 Å) considerably exceeds the porphyrin core size (2.03 Å is the N–N-plane radius, and comparing radii on a consistent basis shows the ion is oversized relative to the cavity that would keep it exactly in-plane with normal Fe–N bond lengths of order 2.0 Å), the iron cannot sit in the plane without either stretching the Fe–N bonds unfavorably or ruffling the porphyrin core — displacement out of plane toward the fifth ligand is the lower-energy relaxation, consistent with observation. For the limiting case of the six-coordinate low-spin oxy form, repeating the same calculation with a typical oxyheme Fe–N(porphyrin) distance of 2.00 Å and a relaxed, less-domed core size of 1.99 Å gives $d = \sqrt{2.00^2 - 1.99^2} = \sqrt{4.00-3.96} \approx 0.20$ Å, matching the smaller but nonzero residual displacement seen in oxy structures and confirming that low-spin iron, while much closer to the plane, is not perfectly coplanar either.

Max Ferdinand Perutz spent over two decades solving the crystal structure of hemoglobin, publishing the first atomic-resolution model in 1959–1960 after starting the project in the 1930s. Working at the Cavendish Laboratory and later the MRC Laboratory of Molecular Biology in Cambridge, Perutz used isomorphous replacement with heavy-atom derivatives to solve the phase problem for a molecule far larger than anything crystallographers had tackled before — hemoglobin's four subunits and roughly 10,000 non-hydrogen atoms represented a leap in scale from the small-molecule and fiber-diffraction studies that preceded it. His structures directly revealed the heme pocket geometry, the position of the proximal and distal histidines, and — crucially — the conformational differences between oxy (R-state) and deoxy (T-state) hemoglobin that explained cooperativity structurally for the first time. John Kendrew, working alongside Perutz, solved the myoglobin structure slightly earlier (1958), providing the simpler single-chain reference structure against which hemoglobin's four-chain cooperative behavior could be understood. Perutz and Kendrew shared the 1962 Nobel Prize in Chemistry for these structures. Later spectroscopic and physical-organic work — by Linus Pauling on the bonding model, and by many subsequent groups using resonance Raman, Mössbauer, and picosecond spectroscopy — refined the bonding picture from Perutz's static crystal structures into the dynamic, electronic-structure account presented here.