13.9 Spirometry, Dead Space, Gas Exchange & Haemoglobin Allostery

13.9 Spirometry, Dead Space, Gas Exchange & Haemoglobin Allostery

Spirometry: Lung Volumes, Capacities & Dead Space

Pulmonary ventilation is assessed clinically using spirometry, which records the movement of air into and out of the lungs:

Fundamental Lung Volumes

• Tidal Volume ($TV$): The volume of air inspired or expired during a normal, quiet breath at rest (typically ~500 mL).
• Inspiratory Reserve Volume ($IRV$): The maximal additional volume of air that can be inspired forcefully above the end of a normal tidal inspiration (typically ~3,000 mL).
• Expiratory Reserve Volume ($ERV$): The maximal additional volume of air that can be expired forcefully below the end of a normal tidal expiration (typically ~1,100 mL).
• Residual Volume ($RV$): The volume of gas remaining in the lungs following a maximal forced exhalation (typically ~1,200 mL). Residual volume cannot be measured by direct spirometry because the air cannot be exhaled; it requires indirect helium dilution or body plethysmography.

Calculated Lung Capacities

A capacity is the sum of two or more individual volumes:

• Vital Capacity ($VC$): The maximal volume of air that can be expired after a maximal inspiration: $$VC = TV + IRV + ERV \approx 500 + 3,000 + 1,100 = 4,600\text{ mL}$$
• Total Lung Capacity ($TLC$): The total volume of gas contained in the lungs following a maximal inspiration: $$TLC = VC + RV = TV + IRV + ERV + RV \approx 5,800\text{ mL}$$
• Functional Residual Capacity ($FRC$): The volume of gas remaining in the lungs at the end of a normal, quiet tidal expiration: $$FRC = ERV + RV \approx 1,100 + 1,200 = 2,300\text{ mL}$$ Biophysical Significance of $FRC$: At $FRC$, the respiratory system is in resting mechanical equilibrium: the outward elastic recoil of the chest wall is exactly equal and opposite to the inward elastic recoil of the lungs, establishing the baseline -5 cm H2O intrapleural pressure.
• Inspiratory Capacity ($IC$): The maximal volume inspired from resting $FRC$: $$IC = TV + IRV \approx 3,500\text{ mL}$$

Minute Ventilation vs. Alveolar Ventilation

• Minute (Total) Ventilation ($\dot{V}_E$): Total volume of gas moved into and out of the lungs per minute: $$\dot{V}_E = TV \times RR$$ For a subject with $TV = 500\text{ mL}$ and respiratory rate $RR = 12\text{ breaths/min}$: $\dot{V}_E = 500 \times 12 = 6,000\text{ mL/min} = 6.0\text{ L/min}$.
• Alveolar Ventilation ($\dot{V}_A$): The true volume of fresh air that reaches the gas-exchanging respiratory zone per minute, accounting for anatomical dead space ($V_D \approx 150\text{ mL}$): $$\dot{V}_A = (TV - V_D) \times RR$$ For the same subject: $\dot{V}_A = (500 - 150) \times 12 = 350 \times 12 = 4,200\text{ mL/min} = 4.2\text{ L/min}$.
• MCAT Physiological Deduction: Rapid, shallow breathing (e.g., $TV = 200\text{ mL}, RR = 30$) produces the same minute ventilation (6.0 L/min), but alveolar ventilation drops precipitously to $(200 - 150) \times 30 = 1,500\text{ mL/min}$, inducing severe hypoxemia and hypercapnia!

---

Gas Exchange Dynamics Across the Alveolar-Capillary Barrier

Passive diffusion of $O_2$ and $CO_2$ across the blood-gas barrier is governed by Fick's Law of Diffusion:

$$\dot{V}_{gas} = \frac{A \times D \times \Delta P}{T}$$

(where $A$ is surface area, $D$ is the gas diffusion coefficient, $\Delta P$ is the partial pressure gradient, and $T$ is membrane diffusion thickness).

• Structural Optimizations: The human lung maximizes diffusion rate by presenting an enormous surface area ($A \approx 100\text{ square meters}$) and an extraordinarily thin membrane ($T \approx 0.2-0.5\,\mu\text{m}$, consisting only of the Type I alveolar epithelial cell, fused extracellular basement membranes, and the capillary endothelial cell).
• Diffusion Constants: Carbon dioxide is 20 to 24 times more soluble in aqueous tissue than oxygen ($D_{CO_2} \gg D_{O_2}$). Therefore, despite a much smaller partial pressure gradient for $CO_2$ ($\Delta P_{CO_2} = 45 - 40 = 5\text{ mmHg}$) compared to oxygen ($\Delta P_{O_2} = 104 - 40 = 64\text{ mmHg}$), $CO_2$ diffuses across the blood-gas barrier just as rapidly, equilibrating within 0.25 seconds (well within the normal 0.75-second erythrocyte transit time).

---

Hemoglobin Allostery & The Oxygen-Hemoglobin Dissociation Curve

Oxygen is poorly soluble in aqueous plasma (0.003 mL O2 / 100 mL plasma / mmHg PO2). Over 98.5% of all oxygen in blood is carried bound to Hemoglobin (HbA):

• Structure: A heterotetramer consisting of two $\alpha$-globin and two $\beta$-globin subunits. Each subunit envelops a planar protoporphyrin IX heme ring coordinating a central ferrous iron atom ($Fe^{2+}$), which reversibly binds a single $O_2$ molecule (total capacity = $4\text{ }O_2$ molecules per Hb tetramer).
• Positive Cooperativity: The oxygen-hemoglobin binding curve exhibits a distinctive sigmoidal (S-shaped) morphology driven by allosteric cooperativity (Hill coefficient $n_H \approx 2.8$):
  • In deoxygenated tissue ($PO_2 < 30\text{ mmHg}$), hemoglobin exists in the low-affinity T (Tense) state, stabilized by inter-subunit salt bridges.
  • Binding of the first $O_2$ molecule pulls the $Fe^{2+}$ atom into the plane of the porphyrin ring, triggering a cascade of tertiary and quaternary structural shifts that break salt bridges and convert adjacent subunits to the high-affinity R (Relaxed) state.
  • Each successive $O_2$ molecule binds with progressively higher affinity, ensuring near-complete loading at pulmonary alveolar $PO_2$ ($100\text{ mmHg} \implies 98-100\%$ saturation) while facilitating rapid unloading along the steep slope in peripheral tissues ($PO_2 = 40\text{ mmHg} \implies 75\%$ saturation; $PO_2 = 20\text{ mmHg} \implies 35\%$ saturation).
• $P_{50}$ Metric: The partial pressure of oxygen at which hemoglobin is 50% saturated with oxygen (normally 26.6 mmHg). Changes in $P_{50}$ quantify shifts in oxygen affinity.

Allosteric Modulation: Right vs. Left Shifts

• Molecular Mechanics of the Bohr Effect: In metabolically active skeletal muscle, accelerated cellular respiration generates high $CO_2$, lactic acid ($H^+$), and heat. Protons bind specific histidine residues (e.g., His-146 on $\beta$-chains), forming salt bridges that lock hemoglobin into the low-affinity T state, physically forcing the release of bound $O_2$ into the tissue bed.
• 2,3-Bisphosphoglycerate (2,3-DPG): An allosteric byproduct of erythrocyte glycolysis (via the Rapoport-Luebering shunt). A single 2,3-DPG molecule binds the central cavity of the deoxygenated Hb tetramer, cross-linking the two $\beta$-subunits and stabilizing the T state. 2,3-DPG synthesis increases under chronic hypoxia (e.g., high altitude adaptation, chronic anemia), shifting the curve rightward to facilitate peripheral oxygen release.
• Fetal Hemoglobin (HbF): Composed of two $\alpha$ and two $\gamma$ globin chains ($\alpha_2\gamma_2$). The $\gamma$-chains replace a critical positively charged histidine residue with a neutral serine, substantially weakening the binding of negatively charged 2,3-DPG. Consequently, HbF remains predominantly in the high-affinity R state, shifting its dissociation curve to the left relative to maternal adult HbA ($P_{50} \approx 19\text{ mmHg}$). This affinity differential enables the fetus to extract oxygen across the placental villi down an affinity gradient.
• Carbon Monoxide (CO) Toxicity: CO binds ferrous heme with an affinity 200 to 250 times greater than oxygen, forming carboxyhemoglobin. Not only does CO occupy oxygen-binding sites, but the binding of CO to one or two subunits locks the remaining subunits into the ultra-high-affinity R state, shifting the curve violently to the left and abolishing cooperativity. Hemoglobin becomes entirely incapable of releasing oxygen to hypoxic tissues.

---