4. Protein Function: Hemoglobin & Myoglobin
How oxygen-binding proteins illustrate fundamental principles of ligand binding, cooperativity, and allosteric regulation.
Myoglobin: A Simple O$_2$ Carrier
Myoglobin (Mb) is a single-polypeptide oxygen-binding protein found predominantly in muscle tissue, where it serves as an intracellular oxygen reservoir. Its study by John Kendrew (1958 Nobel Prize) produced the first high-resolution protein crystal structure.
Structure and Heme Group
Myoglobin consists of 153 amino acids folded into 8 $\alpha$-helices (labeled A through H) surrounding a single heme prosthetic group. The heme is a protoporphyrin IX ring coordinating a central iron atom:
Fe$^{2+}$ Coordination Geometry
- Positions 1-4: Four pyrrole nitrogen atoms of the porphyrin ring (equatorial plane)
- Position 5: Proximal histidine (His F8) -- the imidazole N$_\varepsilon$ coordinates to Fe$^{2+}$ from below the ring
- Position 6: O$_2$ binding site -- when occupied, O$_2$ binds in a bent end-on geometry (~120 degree Fe-O-O angle)
The distal histidine (His E7) does not directly coordinate Fe$^{2+}$ but stabilizes bound O$_2$ via a hydrogen bond and discriminates against CO binding by steric hindrance.
Hyperbolic O$_2$ Binding
Because myoglobin has a single binding site, its oxygen-binding curve is a simple rectangular hyperbola described by the equilibrium:
The fractional saturation $Y$ is given by:
where $Y$ is the fractional saturation (fraction of myoglobin molecules with bound O$_2$),$p\text{O}_2$ is the partial pressure of oxygen, and $P_{50} \approx 2.8$ mmHg is the partial pressure at which half the myoglobin molecules are oxygenated. The low $P_{50}$ indicates very high oxygen affinity, making myoglobin an effective oxygen storage protein in muscle.
Example:
In resting muscle, $p\text{O}_2 \approx 40$ mmHg. Myoglobin saturation:
Even at relatively low tissue $p\text{O}_2$, myoglobin remains nearly fully saturated, releasing O$_2$ only under extreme metabolic demand.
Hemoglobin: Cooperative O$_2$ Binding
Hemoglobin (Hb) is an $\alpha_2\beta_2$ tetrameric protein in red blood cells responsible for transporting O$_2$ from the lungs to peripheral tissues. Unlike myoglobin, hemoglobin exhibits cooperative binding: the binding of O$_2$ to one subunit increases the affinity of the remaining subunits.
T-State and R-State
T-State (Tense)
Deoxy conformation. Low O$_2$ affinity. Stabilized by intersubunit salt bridges and hydrogen bonds. Fe$^{2+}$ is displaced ~0.4 A out of the porphyrin plane (toward His F8). The central cavity is wider and can accommodate 2,3-BPG.
R-State (Relaxed)
Oxy conformation. High O$_2$ affinity. O$_2$ binding pulls Fe$^{2+}$ into the porphyrin plane, which pulls His F8 and the F-helix, triggering a 15 degree rotation of the $\alpha_1\beta_1$ dimer relative to $\alpha_2\beta_2$. Salt bridges are broken.
Sigmoidal Binding Curve
The cooperative binding of O$_2$ to hemoglobin produces a sigmoidal (S-shaped) oxygen dissociation curve, described by the Hill equation:
where $n$ is the Hill coefficient. For hemoglobin, $n \approx 2.8$ (maximum possible for a tetramer is 4, indicating high but not perfectly concerted cooperativity) and $P_{50} \approx 26$ mmHg.
Physiological Significance
Example:
The sigmoidal curve enables efficient O$_2$ transport:
- In the lungs ($p\text{O}_2 \approx 100$ mmHg): $Y \approx 0.98$ -- hemoglobin is ~98% saturated
- In resting tissues ($p\text{O}_2 \approx 40$ mmHg): $Y \approx 0.75$ -- releases ~23% of its O$_2$
- In active muscle ($p\text{O}_2 \approx 20$ mmHg): $Y \approx 0.32$ -- releases ~66% of its O$_2$
A hypothetical non-cooperative carrier (hyperbolic curve with the same $P_{50}$) would deliver far less O$_2$ over the same pressure range. Cooperativity maximizes the difference in saturation between lungs and tissues.
The Hill Equation and Cooperativity
Derivation and the Hill Plot
Starting from the Hill equation, we can linearize it by rearranging and taking logarithms:
Taking the logarithm of both sides:
A plot of $\log\!\bigl(\frac{Y}{1-Y}\bigr)$ versus $\log(p\text{O}_2)$ is the Hill plot. The slope at $Y = 0.5$ (i.e., where $\log\frac{Y}{1-Y} = 0$) gives the Hill coefficient $n$:
Interpreting the Hill Coefficient
- $n = 1$: No cooperativity (hyperbolic binding, like myoglobin)
- $n > 1$: Positive cooperativity (sigmoidal curve; hemoglobin: $n \approx 2.8$)
- $n < 1$: Negative cooperativity (binding of one ligand decreases affinity for subsequent ligands)
- $n = N$ (number of subunits): Infinitely cooperative (all-or-none binding; theoretical maximum)
Models of Cooperativity
Concerted (MWC) Model
Proposed by Monod, Wyman, and Changeux (1965). All subunits exist in the same conformational state -- either all T or all R. The equilibrium constant $L = [\text{T}]/[\text{R}]$ shifts toward R as ligand binds. No hybrid T/R states exist. Explains positive cooperativity but not negative cooperativity.
Sequential (KNF) Model
Proposed by Koshland, Nemethy, and Filmer (1966). Ligand binding induces a conformational change in the bound subunit, which sequentially influences neighboring subunits. Hybrid conformational states are allowed. Can explain both positive and negative cooperativity. More general than MWC.
Allosteric Effectors
The oxygen affinity of hemoglobin is modulated by several physiological effectors that right-shift the O$_2$ dissociation curve (increasing $P_{50}$, decreasing affinity), promoting O$_2$ release in metabolically active tissues.
The Bohr Effect
A decrease in pH (increase in [H$^+$]) promotes O$_2$ release. Protons stabilize the T-state by forming salt bridges (e.g., His 146 of the $\beta$-chain):
In actively metabolizing tissues, CO$_2$ production lowers pH (via carbonic anhydrase: CO$_2$ + H$_2$O $\rightleftharpoons$ H$_2$CO$_3$ $\rightleftharpoons$ HCO$_3^-$ + H$^+$). The resulting protons shift the equilibrium toward deoxyhemoglobin, facilitating O$_2$ delivery precisely where it is needed.
CO$_2$ Effect
In addition to its indirect effect via pH, CO$_2$ directly binds to the N-terminal amino groups of hemoglobin to form carbamino compounds:
The negative charge of the carbamate favors salt bridge formation, stabilizing the T-state. About 15-20% of CO$_2$ is transported this way; the remainder travels as dissolved CO$_2$ or bicarbonate.
2,3-Bisphosphoglycerate (2,3-BPG)
2,3-BPG is present in red blood cells at approximately equimolar concentration with hemoglobin (~5 mM). It binds in the central cavity of deoxyhemoglobin between the two $\beta$-subunits, interacting with positively charged residues (His 2, His 143, Lys 82 of both $\beta$-chains). This stabilizes the T-state and reduces O$_2$ affinity.
Without 2,3-BPG, hemoglobin $P_{50} \approx 12$ mmHg (too high affinity for efficient tissue delivery). With 2,3-BPG, $P_{50} \approx 26$ mmHg.
Fetal Hemoglobin (HbF)
Example:
HbF ($\alpha_2\gamma_2$) has $\gamma$-subunits instead of $\beta$-subunits. The $\gamma$-chain has Ser at position 143 instead of His, eliminating a key 2,3-BPG binding contact. Consequently:
- HbF binds 2,3-BPG less tightly than HbA
- HbF has higher O$_2$ affinity ($P_{50} \approx 19$ mmHg) than HbA ($P_{50} \approx 26$ mmHg)
- This enables O$_2$ transfer from maternal HbA to fetal HbF across the placenta
Sickle Cell Disease
Sickle cell disease is a molecular disease caused by a single point mutation in the $\beta$-globin gene. It was the first genetic disease to be understood at the molecular level (Linus Pauling, 1949).
The Mutation
A single nucleotide change (GAG $\to$ GTG) at position 6 of the $\beta$-globin gene replaces glutamic acid (Glu, charged, hydrophilic) with valine (Val, nonpolar, hydrophobic): Glu6 $\to$ Val. The resulting hemoglobin variant is designated HbS.
Molecular Mechanism
The Val6 side chain creates a hydrophobic patch on the surface of the deoxy-HbS molecule. This patch fits into a complementary hydrophobic pocket on an adjacent deoxy-HbS tetramer (between Phe 85 and Leu 88 of the$\beta$-chain). The result is polymerization of deoxy-HbS into long, rigid fibers that distort red blood cells into the characteristic sickle shape.
Key features of sickling:
- Polymerization is O$_2$-dependent: Only deoxy-HbS polymerizes; oxy-HbS does not have the exposed hydrophobic pocket.
- Nucleation-dependent: A critical concentration of deoxy-HbS must be reached before fiber formation begins (delay time).
- Consequences: Vaso-occlusive crises, hemolytic anemia, organ damage, and reduced RBC lifespan (~20 days vs. normal ~120 days).
Heterozygote Advantage
Sickle cell trait (HbAS heterozygotes) confers resistance to Plasmodium falciparum malaria. The parasite-infected red blood cells sickle preferentially and are cleared by the spleen. This balanced polymorphism explains the high frequency of the HbS allele (~10%) in malaria-endemic regions of sub-Saharan Africa, the Mediterranean, and South Asia.
Carbon Monoxide Poisoning
Carbon monoxide (CO) is a colorless, odorless gas that competes with O$_2$ for binding at the Fe$^{2+}$ of heme. CO exerts its toxicity through two mechanisms:
High-Affinity Binding
CO binds Fe$^{2+}$ approximately 200-250 times more strongly than O$_2$. Even low environmental concentrations of CO (0.1%) can occupy a significant fraction of heme binding sites. The relative affinity is quantified by the Haldane coefficient:
Left-Shift of O$_2$ Curve
CO binding to one or more subunits locks those subunits in the R-state, increasing the O$_2$ affinity of the remaining subunits. This left-shifts the O$_2$ dissociation curve, meaning that the remaining bound O$_2$ is held more tightly and is not effectively released to tissues -- a double insult.
Clinical Presentation and Treatment
Symptoms range from headache and confusion (COHb 20-30%) to seizures, coma, and death (COHb >60%). Classic "cherry-red" coloration of skin is due to the bright red color of carboxyhemoglobin. Pulse oximetry is unreliable because it cannot distinguish HbO$_2$ from HbCO.
Treatment: Administer 100% O$_2$ via non-rebreather mask (reduces CO half-life from ~5 hours on room air to ~1 hour). Severe cases: hyperbaric oxygen therapy (2.5-3 atm, reduces half-life to ~20 minutes) to accelerate CO displacement by mass action.
Why doesn't CO bind even more strongly?
Free heme binds CO ~20,000 times more strongly than O$_2$. In hemoglobin, the distal histidine (His E7) sterically forces CO to bind at a bent angle rather than its preferred linear geometry, reducing the Hb affinity for CO from 20,000-fold to ~210-fold over O$_2$. This is a crucial protective adaptation.
Key Concepts
- *Myoglobin is a monomeric O$_2$-storage protein with a hyperbolic binding curve and $P_{50} \approx 2.8$ mmHg.
- *Hemoglobin is an $\alpha_2\beta_2$ tetramer with cooperative O$_2$ binding (sigmoidal curve, Hill coefficient $n \approx 2.8$).
- *The T-state (deoxy, low affinity) and R-state (oxy, high affinity) interconversion is the structural basis of cooperativity.
- *The Hill equation $Y = (p\text{O}_2)^n / (P_{50}^n + (p\text{O}_2)^n)$ quantifies cooperativity; the Hill plot linearizes this relationship.
- *The MWC (concerted) model assumes all-or-none T$\to$R transitions; the KNF (sequential) model allows hybrid states.
- *The Bohr effect: lower pH and higher CO$_2$ reduce hemoglobin O$_2$ affinity, promoting O$_2$ delivery to active tissues.
- *2,3-BPG binds in the central cavity of the T-state, reducing O$_2$ affinity; its absence in HbF gives fetal hemoglobin higher O$_2$ affinity.
- *Sickle cell disease (HbS): Glu6$\to$Val in $\beta$-globin creates a hydrophobic patch causing deoxy-HbS polymerization into fibers.
- *CO binds Fe$^{2+}$ ~210x stronger than O$_2$ and left-shifts the dissociation curve; treated with 100% O$_2$ or hyperbaric oxygen.