Lecture 10: Comprehensive Study Notes on Hemoglobin and Myoglobin Structure, Function, and Kinetics

Physiological Necessity of Oxygen Transport Proteins

• Respiration and Energy Generation:

  • Most cellular adenosine triphosphate ($\text{ATP}$) is generated via oxidative respiration, a biological process that strictly requires molecular oxygen ($O_2$).
  • Continuous oxygen supply is required to sustain cellular ATP production and maintain organismal viability.

• Solubility Constraints of Oxygen:

  • Molecular oxygen has extremely low solubility in aqueous solutions such as blood plasma.
  • Oxygen solubility is even lower in dense, fibrous tissues such as skeletal muscle.
  • Passive diffusion of dissolved oxygen is physically insufficient to sustain metabolic exertion in any living organism larger than $1 accession\,\text{mm}$ ($1\,\text{mm}$).
  • Organisms exceeding $1\,\text{mm}$ in size require specialized oxygen transport and storage proteins—specifically myoglobin and hemoglobin—to make complex aerobic life possible.

• Functional Differences Between Myoglobin and Hemoglobin:

  • Myoglobin:
    • Located primarily in skeletal muscle tissue.
    • Monomeric protein consisting of a single polypeptide chain with a single oxygen-binding site.
    • Functions independently of other myoglobin molecules within the cell.
    • Increases the effective concentration of oxygen inside skeletal muscle cells to power muscular exertion.
    • Binds oxygen non-cooperatively.
    • Lacks quaternary structure and allosteric regulation.
  • Hemoglobin:
    • Packaged within red blood cells inside the circulatory system.
    • Each red blood cell contains approximately $300,000,000$ to $800,000,000$ ($3 \times 10^8$ to $8 \times 10^8$) hemoglobin molecules.
    • Tetrameric protein composed of two alpha ($\alpha$) subunits and two beta ($\beta$) subunits ($\alpha_2\beta_2$).
    • Contains four distinct oxygen-binding sites (one per subunit).
    • Possesses quaternary structure mediated by non-covalent interactions between the four subunits.
    • Binds and releases oxygen with positive cooperativity.
    • Undergoes allosteric regulation by small metabolic effectors.

Structural Organization and Sequence Homology

• Myoglobin Architecture:

  • Composed of a single polypeptide chain of $153$ amino acids containing a distinct N-terminus and C-terminus.
  • Secondary structure is comprised entirely of $8$ alpha helices ($\alpha$-helices), labeled alphabetically from $A$ through $H$.
  • Employs a repeating structural motif: $A\text{ helix} \rightarrow AB\text{ corner} \rightarrow B\text{ helix} \rightarrow BC\text{ corner} \rightarrow C\text{ helix} \rightarrow CD\text{ corner} \rightarrow D\text{ helix} \rightarrow DE\text{ corner} \rightarrow E\text{ helix} \rightarrow EF\text{ corner} \rightarrow F\text{ helix} \rightarrow FG\text{ corner} \rightarrow G\text{ helix} \rightarrow GH\text{ corner} \rightarrow H\text{ helix}$.
  • Contains a tightly bound non-protein prosthetic group called heme, situated in a hydrophobic binding pocket, which stabilizes the biologically active three-dimensional tertiary conformation.

• Positional Nomenclature System:

  • Residue positions within myoglobin and hemoglobin subunits are identified by helix letter and sequence position number within that specific helix.
  • Distal Histidine ($\text{His } E7$): The $7\text{th}$ amino acid residue of the $E$ helix.
  • Proximal Histidine ($\text{His } F8$): The $8\text{th}$ amino acid residue of the $F$ helix (also referred to as residue position $93$ or $193$ from the N-terminus).
  • Example: An designation of $A7$ indicates the $7\text{th}$ amino acid residue located within the $A$ helix.

• Quaternary Structure Nomenclature:

  • In protein structural biology, distinct polypeptide chains within a oligomeric complex are assigned distinct Greek letters ($\alpha$, $\beta$, $\gamma$, $\delta$, $\epsilon$).
  • Greek letter assignments denote distinct gene products and subunits; they do not refer to secondary structure elements (e.g., $\alpha$-subunit does not mean $\alpha$-helix, and $\beta$-subunit does not mean $\beta$-sheet).
  • Hemoglobin possesses an $\alpha_2\beta_2$ quaternary structure consisting of two identical $\alpha$ chains and two identical $\beta$ chains.

• Sequence Alignment and Evolutionary Homology:

  • Myoglobin, the $\alpha$ subunit of hemoglobin, and the $\beta$ subunit of hemoglobin share conserved primary sequences and virtually identical tertiary structures.
  • Sequence comparison statistics:
    • Strict sequence identity across all three proteins (myoglobin, $\alpha$-subunit, $\beta$-subunit): $13\%$ of residue positions are identical.
    • Sequence identity between $\alpha$ subunit and $\beta$ subunit: $46\%$ identical residues (high sequence homology).
    • Sequence identity between myoglobin and $\alpha$ subunit: $26\%$ identical residues.
    • Sequence identity between myoglobin and $\beta$ subunit: $22\%$ identical residues.
  • High structural identity and sequence conservation demonstrate that all three proteins evolved from a single ancient ancestral oxygen-binding gene.
  • Positions lacking strict identity frequently display conservative amino acid replacements (e.g., substitution of valine for alanine, preserving hydrophobic character, or substitutions maintaining hydrogen-bond donor capacity to stabilize helices).

• Pathological Mutations and Specific Residue Functions:

  • Sickle Cell Anemia:
    • A point mutation converting a single surface glutamate ($\text{Glu}$) residue to valine ($\text{Val}$) in the $\beta$ subunit generates an abnormal hydrophobic patch on the protein surface.
    • Under conditions of low oxygen tension or high proton concentration ($\text{low } pH$), deoxyhemoglobin molecules aggregate into linear polymer fibers.
    • Aggregation distorts red blood cells into a rigid, sickle-like morphology that occludes capillary blood flow, producing painful vaso-occlusive crises.
    • Genetic disorders affecting hemoglobin structure or synthesis are classified as hemoglobinopathies.
  • Proton Binding Site for the Bohr Effect:
    • The C-terminal residue of the $\beta$ subunit, Histidine 146 ($\text{His } 146$), binds the proton ($H^+$) responsible for mediating the Bohr effect.
  • Fetal Hemoglobin Modification:
    • In fetal hemoglobin, Histidine 143 ($\text{His } 143$) of the $\beta$ subunit is replaced by a Serine ($\text{Ser}$) residue.
    • This amino acid substitution reduces the binding affinity for the negative allosteric effector 2,3-bisphosphoglycerate ($2,3\text{-BPG}$), increasing the oxygen affinity of fetal hemoglobin relative to maternal hemoglobin.

Coordination Chemistry of the Heme Prosthetic Group

• Heme Chemical Structure and Oxidation States:

  • The heme group consists of an aromatic tetrapyrrole porphyrin ring with a central iron atom.
  • Delocalization of $4n + 2$ $\pi$-electrons confers aromaticity and planarity to the porphyrin ring.
  • Ferrous State ($Fe^{2+}$):
    • The iron atom must remain in the $+2$ oxidation state ($Fe^{2+}$) to reversibly bind molecular oxygen.
    • Oxygen binds as a ligand without permanently altering the ferrous oxidation state under normal physiological conditions.
  • Ferric State ($Fe^{3+}$):
    • Occasionally, an electron is transferred from the ferrous iron to bound oxygen, releasing a superoxide anion radical ($O_2^-$) and oxidizing iron to the ferric ($Fe^{3+}$) state.
    • Ferric iron ($Fe^{3+}$) cannot reversibly bind molecular oxygen; instead, it irreversibly coordinates a water ($H_2O$) molecule at the axial ligand site.

• Oxidized Hemeprotein Derivatives and Cellular Repair Systems:

  • Metmyoglobin and Methemoglobin:
    • Oxidation of iron to $Fe^{3+}$ converts myoglobin to metmyoglobin and hemoglobin to methemoglobin.
    • Both oxidized forms hold water tightly at the axial position, rendering them completely non-functional for oxygen transport.
  • Methemoglobin Reductase System:
    • Red blood cell cytosol contains the enzyme methemoglobin reductase.
    • Methemoglobin reductase utilizes reduced nicotinamide adenine dinucleotide phosphate ($\text{NADPH}$) as a cofactor to reduce ferric iron ($Fe^{3+}$) back to functional ferrous iron ($Fe^{2+}$).
    • No equivalent metmyoglobin reductase enzyme exists in muscle cells; oxidized metmyoglobin is marked by ubiquitination and degraded into constituent amino acids.

• Spectral and Color Properties of Hemoglobin:

  • Deoxyhemoglobin:
    • Unoxygenated state in venous blood.
    • Specific electronic distribution across the porphyrin $\pi$-system absorbs light such that the blood exhibits a purplish-blue color.
  • Oxyhemoglobin:
    • Oxygenated state in arterial blood.
    • Binding of oxygen alters the electronic cloud density of the porphyrin ring without altering the $Fe^{2+}$ oxidation state, shifting light absorption to yield a bright red color.
  • Pulse Oximetry:
    • Measures light absorption differences between oxyhemoglobin (bright red) and deoxyhemoglobin (purplish-blue) to determine arterial oxygen saturation percentage (physiologically targeted near $98\%$).

• Octahedral Coordination Geometry of Iron:

  • Iron prefers an octahedral coordination sphere possessing $6$ total coordination sites:
    • $4$ Equatorial Positions: Occupied by the four pyrrole nitrogens of the porphyrin ring.
    • $1$ Axial Position: Occupied by the imidazole nitrogen of the proximal histidine ($\text{His } F8$ / $\text{His } 93$).
    • $1$ Axial Position: Reserved for reversible binding of molecular oxygen ($O_2$).
  • Competitive Ligands and Poisons:
    • Small gaseous molecules such as carbon monoxide ($CO$), nitric oxide ($NO$), and hydrogen sulfide ($H_2S$) compete directly with oxygen for binding at the un-occupied axial position.

Structural Dynamics and Molecular Mechanism of Cooperativity

• Conformational States: Low Affinity (Deoxy) vs. High Affinity (Oxy):

  • Deoxy State Geometry:
    • In the absence of oxygen, the porphyrin ring adopts a distorted, non-planar, dome-like (bowl-like) conformation.
    • The central $Fe^{2+}$ atom sits displaced out of the porphyrin plane by $0.3\,\text{\AA}$ toward the proximal histidine.
    • Steric repulsion between oxygen and the domed porphyrin ring creates a long, structurally weak $Fe-O_2$ bond, defining the low-affinity state.
  • Structural Movements Upon Oxygen Binding:
    1. Oxygen binding pulls the iron atom $0.3\,\text{\AA}$ into the plane of the porphyrin ring toward planarity.
    2. The bond between iron and the proximal histidine nitrogen shortens by $0.1\,\text{\AA}$.
    3. The proximal histidine ($\text{His } F8$) is physically pulled toward the heme ring by a total displacement of $0.4\,\text{\AA}$ ($0.3\,\text{\AA} + 0.1\,\text{\AA}$).
    4. Because hydrophobic side chains (leucine, isoleucine, valine) surrounding $\text{His } F8$ are tightly packed against the porphyrin ring at their van der Waals limits, movement of $\text{His } F8$ forces a spatial translation of the entire $F$ helix by $1.0\,\text{\AA}$.
    5. Translation of the $F$ helix shifts the adjacent $FG$ corner by $6.0\,\text{\AA}$.

• Energetic Barriers and Quaternary Rearrangement:

  • In Myoglobin:
    • Being monomeric, myoglobin faces no structural quaternary barrier. The $0.4\,\text{\AA}$ shift of the proximal histidine occurs continuously upon oxygen binding.
  • In Hemoglobin:
    • The $6.0\,\text{\AA}$ movement of the $FG$ corner requires breaking an extensive network of inter-subunit non-covalent contacts at the subunit interfaces.
    • Transitioning from the low-affinity state to the high-affinity state requires breaking $19$ specific quaternary interactions stabilizing the deoxy state and forming $19$ new quaternary interactions stabilizing the oxy state.
    • This substantial energy barrier prevents individual subunits from switching conformations independently, forming the physical basis for cooperative oxygen binding and release.

• Role of the Distal Histidine ($\text{His } E7$):

  • Prevention of Spontaneous Oxidation:
    • Presents a positively charged environment that helps maintain iron in the ferrous ($Fe^{2+}$) oxidation state, preventing irreversible conversion to methemoglobin/metmyoglobin.
  • Steric Selectivity and Carbon Monoxide Mitigation:
    • Free model heme systems (lacking distal histidine) bind carbon monoxide ($CO$) linearly at an angle of $180^\text{o}$, resulting in an affinity $100,000$ times ($10^5\times$) greater than that for oxygen ($O_2$).
    • Oxygen naturally prefers a bent binding geometry with a bond angle of $60^\text{o}$.
    • In hemoglobin and myoglobin, the side chain of $\text{His } E7$ sterically clashes with linearly bound ligands, forcing $CO$ to bind at a bent $60^\text{o}$ angle.
    • Forcing $CO$ into this sterically unfavorable bent geometry reduces its relative binding affinity from $100,000\times$ down to only $100\times$ relative to oxygen.
    • This steric restriction renders endogenous $CO$ binding fully reversible, allowing survival despite continuous metabolic generation and atmospheric exposure to carbon monoxide.

Allosteric Regulation of Oxygen Affinity

• Allosteric Regulation Principle:

  • Hemoglobin is an allosterically regulated oligomer whose oxygen affinity is modulated by negative allosteric effectors.
  • Negative allosteric effectors bind to sites distinct from the oxygen-binding heme pockets, stabilizing the low-affinity deoxy quaternary conformation and promoting oxygen release to respiring tissues.
  • Prevents toxic over-saturation of respiring tissues with free oxygen, which would otherwise form cell-damaging reactive oxygen species (ROS).

• Physiological Negative Allosteric Effectors:

  1. Protons ($H^+$ / Decreasing pH): Mediates the Bohr effect; high proton concentration (low pH) in metabolically active tissues promotes oxygen release by protonating $\text{His } 146$ of the $\beta$ subunit.
  2. Carbon Dioxide ($CO_2$): Elevated in rapidly respiring tissues; directly lowers oxygen affinity.
  3. Chloride Ions ($Cl^-$): Anionic effector stabilizing the deoxy quaternary state.
  4. 2,3-Bisphosphoglycerate ($2,3\text{-BPG}$): Highly charged organic phosphate that binds the central cavity of the deoxyhemoglobin tetramer.

• Metabolic Fine-Tuning:

  • Higher metabolic rates in active tissues increase local concentrations of $H^+$, $CO_2$, $Cl^-$, and $2,3\text{-BPG}$.
  • Enhanced effector concentrations force hemoglobin to dump its bound oxygen specifically where metabolic demand is highest.
  • Principles of allosteric regulation established in hemoglobin serve as the foundational model for metabolic enzyme regulation.

Mathematical Derivation of Binding Kinetics and Fractional Saturation

• Historical Biochemical Framing:

  • Biochemical equilibrium for ligand binding is historically written using a dissociation framework based on classic acid-base disassociation models ($\text{HA} \rightleftharpoons \text{A}^- + \text{H}^+$).
  • The reversible dissociation reaction for a monomeric oxygen binding protein (Myoglobin, $\text{Mb}$) is formally defined as:         $\text{Mb}O_2 \rightleftharpoons \text{Mb} + O_2$
  • The corresponding equilibrium dissociation constant ($K_d$) is expressed as:         $K_d = \frac{[\text{Mb}][O_2]}{[\text{Mb}O_2]}$

• Derivation of Fractional Saturation ($Y$):

  • Fractional saturation ($Y$) represents the fraction of total protein binding sites occupied by oxygen:         $Y = \frac{[\text{Mb}O_2]}{[\text{Mb}]_{\text{total}}} = \frac{[\text{Mb}O_2]}{[\text{Mb}] + [\text{Mb}O_2]}$
  • Expressing bound protein ($[\text{Mb}O_2]$) in terms of free protein ($[\text{Mb}]$), free ligand ($[O_2]$), and $K_d$:         $[\text{Mb}O_2] = \frac{[\text{Mb}][O_2]}{K_d}$
  • Substituting this expression into the fractional saturation formula:         $Y = \frac{\frac{[\text{Mb}][O_2]}{K_d}}{[\text{Mb}] + \frac{[\text{Mb}][O_2]}{K_d}}$
  • Factoring out and canceling free myoglobin concentration ($[\text{Mb}]$) yields:         $Y = \frac{[O_2]}{K_d + [O_2]}$

• Conversion to Partial Pressure Terms:

  • Because oxygen is a gas, its molar concentration ($[O_2]$) is directly proportional to its partial pressure ($pO_2$) via the Ideal Gas Law:         $PV = nRT \implies [O_2] = \frac{n}{V} = \frac{pO_2}{RT}$
  • By biochemical convention, partial pressures ($pO_2$) are retained directly in place of molar concentrations without dividing by RT$.\n * P_{50}$is defined as the specific partial pressure of oxygen required to achieve half-maximal fractional saturation ($Y = 0.5).\n * Under these conditions, the dissociation constant is numerically equivalent to P_{50}:\n        K_d = P_{50}\n * Substituting partial pressures yields the hyperbolic binding equation for non-cooperative, monomeric oxygen binding proteins:\n        Y = \frac{pO_2}{P_{50} + pO_2}$$