Lecture 2: Introduction to Gas Exchange

Slide 1

• This lecture has two parts: (1) completing the introduction to comparative perspectives begun in Lecture 1, and (2) beginning the principles of gas exchange and the oxygen supply cascade.
• Several background readings are assigned this week to cover foundational material, since there is no quiz in Week 1.

---

Slide 2

Learning objectives (continued from Lecture 1)

1. Appreciate the value of the comparative method.
2. Describe the features of early tetrapods that may have limited locomotor endurance.

---

Slide 3

• Review of the two comparative approaches from Lecture 1:
  1. Model species / case studies — study species with exceptional traits or unique experimental access.
  2. Evolutionary diversity — examine variation across lineages to test whether differences are adaptive and whether unrelated species converge on similar solutions.

---

Slide 4

• All tetrapods evolved from an aquatic sarcopterygian fish ancestor that used paired fins and lateral body undulation.
• Evolution works by modifying existing structures rather than inventing from scratch — this means ancestral constraints persist in modern species.
• The physical demands of movement are strongly affected by the medium (water vs. air) in which an animal moves.

---

Slide 5

Why medium matters for exercise physiology

Property	Air	Water	Ratio	Relevance
Density (g/cm3)	0.0012	1	830x	Forces, energy demand
Dynamic viscosity (Ns/m)	18 x 10-6	1 x 10-3	55x	Forces, energy demand
O2 content (mL O2/L)	209	7	30x	Oxygen, aerobic energy supply
Heat capacity (cal/L·°C)	0.31	1000	3200x	Thermoregulation, energy demand

• Air has 30x more oxygen per unit volume than water, making aerial gas exchange more efficient.
• Thermoregulation is critical for exercise: muscles are only ~25% efficient, generating ~75% heat as waste. Exercising animals must dissipate this heat to sustain locomotion.
• Example: cheetahs can only sustain short sprint bouts because they overheat during prolonged exercise.

---

Slide 6

Forces by locomotor mode

• Aquatic — Inertial and drag forces dominate; buoyancy supports body weight (no muscular effort against gravity).
• Terrestrial — Gravity and inertia are the dominant forces; air resistance is low at typical terrestrial speeds.
• Aerial — Gravity, inertia, and drag are all significant because high flight speeds increase air resistance.

---

Slide 7

Cost of transport (review)

• Cost of transport (CoT) = energy per unit body mass per unit distance (J/kg·m). Equivalently, CoT = Power / (mass x velocity).
• Running is the most costly mode due to gravity and collisional energy losses at each footfall.
• Swimming is the least costly because buoyancy supports body weight.
• Flying is intermediate — despite drag, higher speeds reduce energy cost per unit distance.

---

Slide 8

• Central evolutionary question: How did ancestral tetrapods move and breathe on land?
• The aquatic ancestor’s body plan was not well equipped for sustained aerobic locomotion on land.

---

Slide 9

• Early tetrapods had a body plan resembling a robust fish with massive limbs — sprawling posture with lateral body undulation for propulsion.
• Modern lizards retain this ancestral locomotor pattern, bending the trunk side-to-side during running.
• The sprawling posture requires significant muscular effort to support body weight against gravity (analogous to doing push-ups with hands far apart).

---

Slide 10

• A full locomotor cycle in a lizard involves pronounced lateral bending of the trunk.
• The trunk muscles (intercostal and abdominal) involved in this bending are the same muscles used for breathing.
• Since early tetrapods lacked a diaphragm, they relied entirely on these trunk muscles for ventilation.
• Reference: Carrier (1991) Amer. Zool. 31, 644–654.

---

Slide 11

Evidence: Tidal volume decreases during locomotion

• At rest, lizards produce large, regular breaths.
• During treadmill locomotion, tidal volumes decrease with increasing speed — the opposite of what aerobic demand requires.
• This demonstrates a mechanical constraint: the trunk muscles cannot effectively serve both locomotion and ventilation simultaneously.

---

Slide 12

• Follow-up studies in monitor lizards (Varanus) and iguanas confirmed the mechanical interference.
• Tidal volumes do not increase during exercise but increase dramatically in the recovery period after exercise stops.
• These animals cannot sustain prolonged locomotion because the running-breathing conflict inhibits oxygen supply during exercise.
• Reference: Wang, Carrier, Hicks (1997) J. Exp. Biol. 200, 2629–2639.

---

Slide 13

EMG evidence for the mechanical conflict

• During locomotion (purple): intercostal muscles fire rhythmically with each stride for trunk stabilization, and tidal volumes are small and irregular.
• During rest (yellow): the same intercostal muscles fire only during breathing cycles, producing large, regular tidal volumes.
• The muscles cannot serve both functions effectively at the same time.

---

Slide 14

Summary: Early tetrapod locomotor constraints

• Sprawling posture with lateral trunk bending and massive distal limbs
• Same muscles used for ventilation and trunk stabilization during locomotion
• Mechanical interference between running and breathing
• Result: limited aerobic scope and endurance
• Modern lizards are adapted for burst locomotion (short sprints between hiding spots), not sustained aerobic activity — this reflects their evolutionary heritage, not poor adaptation.

---

Slide 15

• The ancestral conflict between running and breathing was inherited by all tetrapod lineages.
• However, several lineages have evolved solutions to overcome this constraint.

---

Slide 16

Lineages that overcame the ancestral constraint

• Archosaurs (crocodilians + birds): Evidence suggests ancestral archosaurs had high aerobic capacity, based on convergent features in hearts, bones, and musculoskeletal systems shared between modern crocodilians and birds.
• Mammals: Many species evolved high endurance, high aerobic scope, and the ability to sustain high metabolic rates under extreme conditions (drought, heat).
• The course will examine the specific adaptations that enabled these lineages to achieve sustained athletic performance.

---

Slide 17

Reflection question

What specific features do mammals have that enable sustained athletic performance?

• This question is posed as a thought exercise to inspire curiosity about upcoming course material.
• Key features to be discussed in later lectures include: the diaphragm, erect posture, four-chambered heart, and modifications to the musculoskeletal system.

---

Slide 18

Summary: Comparative perspectives

1. Many features of animal morphology and physiology (form and function) reflect adaptation for movement and energy delivery to tissues.
2. The comparative approach provides insight into fundamental mechanisms — how animals work.
3. The comparative approach provides evolutionary context to understand adaptive features and performance limits.

---

Slide 19

Learning objectives — Gas exchange

1. Review fundamental gas laws and principles: ideal gas law, partial pressures of gases, water vapor pressure.
2. Describe the steps in the oxygen supply cascade from the environment to the mitochondria.

---

Slide 20

Fundamental steps of gas exchange

Regardless of species, oxygen delivery follows the same sequence of alternating convection and diffusion steps:

1. Convection — Bulk flow of air or water to the respiratory surface
2. Diffusion — O₂ crosses the respiratory surface (skin, gill, or lung)
3. Convection — Circulatory transport via the heart and blood
4. Diffusion — O₂ crosses from capillaries to cells through the interstitium

• This pattern is conserved across all air-breathing and water-breathing vertebrates.

---

Slide 21

The five steps of the oxygen supply cascade

1. Ventilatory air convection — moving air into the lungs
2. Pulmonary oxygen diffusion — gas exchange across the alveolar membrane
3. Blood oxygen transport (convection) — cardiac output carrying O₂ in the blood
4. Capillary-tissue diffusion — O₂ crossing from capillaries to cells
5. Cellular respiration — O₂ consumed in mitochondria for ATP production (powering protein synthesis, ion pumps, actomyosin ATPase)

• Each step represents a potential bottleneck that can limit oxygen delivery and thus limit exercise capacity.

---

Slide 22

The oxygen cascade

The oxygen cascade describes the progressive decrease in P_O₂ at each step from the environment to the mitochondria:

Location	PO₂ (mmHg)
Inspired air	150–160
Alveolar gas (PAO2)	100–110
Arterial blood (PaO2)	98
Capillary blood	50–80
Tissues	30–50
Cell mitochondria	10–20

• Each step involves a drop in P_O₂ due to diffusion barriers, dilution, and metabolic consumption.
• The drop at the tissue capillary bed depends on metabolic rate — the more O₂ consumed, the lower the tissue P_O₂.
• The first step (inspired air) sets the upper limit on how much oxygen is available.

---

Slide 23

• The remainder of this lecture reviews the fundamental gas laws needed to calculate oxygen availability at each step of the cascade.

---

Slide 24

Gas pressure fundamentals

• Gas pressure is proportional to the average force exerted by gas molecules colliding with container walls.
• Pressure is proportional to kinetic energy and therefore to temperature.
• Measured in mmHg (millimeters of mercury) using a barometer.

Pressure unit equivalences

Unit	Value
1 atmosphere (atm)	760 mmHg
1 atm	760 Torr
1 atm	101.32 kPa (SI unit)

---

Slide 25

• Barometric pressure (atmospheric pressure) is the weight of the column of air above a given point, pulled down by gravity.
• Because the amount of air above decreases with altitude, barometric pressure decreases with altitude.

---

Slide 26

Barometric pressure and altitude

• At sea level: P_B = 760 mmHg, inspired P_O₂ ≈ 150 mmHg.
• At Mt. Everest (~8,848 m): P_B ≈ 250 mmHg, inspired P_O₂ is approximately one-third of sea level — not sustainable for long-term human habitation.
• The graph shows barometric pressure decreases non-linearly with altitude, and inspired P_O₂ decreases proportionally.

---

Slide 27

Extreme altitude: La Rinconada, Peru

• La Rinconada, Peru is the highest permanent human settlement in the world.
• Available oxygen is approximately 50% of sea level.
• About one-third of Peru’s population lives at high altitude.
• Residents suffer from high rates of chronic mountain sickness due to the extreme hypoxic conditions.
• This illustrates the physiological limits of human adaptation to low oxygen availability.

---

Slide 28

Boyle’s Law

• At constant temperature and number of gas molecules, pressure is inversely proportional to volume.

\[P_1 V_1 = P_2 V_2\]

• If three of the four quantities (P₁, V₁, P₂, V₂) are known, the fourth can be calculated.
• The graph shows the characteristic inverse (hyperbolic) relationship between pressure and volume.

---

Slide 29

Charles’ Law

• At constant pressure and number of gas molecules, volume is directly proportional to temperature.

\[\frac{V_1}{T_1} = \frac{V_2}{T_2}\]

• As temperature increases, gas molecules move faster and occupy a larger volume.

---

Slide 30

Gay-Lussac’s Law

• At constant volume, pressure is directly proportional to the Kelvin temperature.

\[\frac{P_1}{T_1} = \frac{P_2}{T_2}\]

---

Slide 31

Ideal Gas Law

\[PV = nRT\]

• Where: P = pressure, V = volume, n = number of gas molecules (moles), R = ideal gas constant, T = temperature (Kelvin).
• All three individual gas laws (Boyle’s, Charles’, Gay-Lussac’s) can be derived from the ideal gas law by holding certain variables constant.

---

Slide 32

Gas laws summary

Law	Relationship	Constant	Equation
Boyle’s Law	P–V (inverse)	T, n	$P_1 V_1 = P_2 V_2$
Charles’ Law	V–T (direct)	P, n	$V_1/T_1 = V_2/T_2$
Gay-Lussac’s Law	P–T (direct)	V, n	$P_1/T_1 = P_2/T_2$
Ideal Gas Law	P, V, T, n	—	$PV = nRT$

---

Slide 33

Deriving gas laws from the ideal gas law

• Write the ideal gas law for two sets of conditions (initial and final): $P_1V_1 = n_1RT_1$ and $P_2V_2 = n_2RT_2$
• Solve both for R and set equal:

\[\frac{P_1 V_1}{n_1 T_1} = \frac{P_2 V_2}{n_2 T_2}\]

• By holding specific variables constant, individual gas laws emerge.

---

Slide 34

Derivations from the combined gas law

Starting from $\frac{P_1 V_1}{n_1 T_1} = \frac{P_2 V_2}{n_2 T_2}$:

• Boyle’s Law: Hold n and T constant → n’s and T’s cancel → $P_1V_1 = P_2V_2$
• Charles’ Law: Hold n and P constant → n’s and P’s cancel → $V_1/T_1 = V_2/T_2$
• Gay-Lussac’s Law: Hold n and V constant → n’s and V’s cancel → $P_1/T_1 = P_2/T_2$

---

Slide 35

Dalton’s Law — Partial pressures

• The total pressure of a gas mixture equals the sum of the partial pressures of each component gas.

\[P_{\text{air}} = P_{O_2} + P_{CO_2} + P_{N_2}\]

• The partial pressure of any gas equals the barometric pressure multiplied by that gas’s fractional concentration:

\[P_{O_2} = P_B \times F_{O_2}\]

Partial pressures of dry air at sea level

Gas	% in air	Fraction	PB (mmHg)	Partial P (mmHg)
O2	20.93	0.2093	760	159
CO2	0.03	0.0003	760	0.3
N2	79.04	0.7904	760	600.7
Total	100			760

---

Slide 36

Water vapor pressure correction

• When air enters the lungs, it is rapidly warmed to body temperature (37°C) and saturated with water vapor.
• Water vapor pressure at 37°C = 47 mmHg (constant, independent of barometric pressure).
• This water vapor dilutes the inspired air, reducing the available oxygen.

Calculating inspired P_O₂

\[P_{I}O_2 = (P_B - P_{H_2O}) \times F_{O_2}\]

Example at sea level:

• Dry air: $P_{O_2} = 760 \times 0.21 = 159$ mmHg

• Saturated air at 37°C: $P_IO_2 = (760 - 47) \times 0.21 = 149$ mmHg

• For all calculations in this course, use 47 mmHg as the water vapor pressure (assuming body temperature of 37°C).

---

Slide 37

• To calculate P_IO₂ at altitude, substitute the appropriate barometric pressure for that altitude into the water vapor correction formula.
• The fraction of O₂ in air (20.93%) does not change with altitude — only the total barometric pressure decreases.

---

Slide 38

Applied example: Cabin decompression at altitude

At 35,000 ft cruising altitude:

\[P_IO_2 = (178 - 47) \times 0.21 = 27 \text{ mmHg}\]

• This is only 18% of sea-level P_IO₂ (149 mmHg) — lower than typical venous blood oxygen levels.
• At this P_O₂, the brain is rapidly starved of oxygen.

Time of useful consciousness after decompression

Altitude (ft)	Consciousness time
45,000	9–15 seconds
40,000	15–20 seconds
35,000	30–60 seconds
30,000	1–2 minutes
25,000	3–5 minutes
20,000	30+ minutes

• This is why emergency oxygen masks are essential in aircraft — consciousness can be lost in under a minute at cruising altitude.

---

Slide 39

• Over the next several lectures, the course will march through each step of the oxygen supply cascade.
• For each step, the relevant physical principles governing oxygen uptake and the factors that limit oxygen delivery will be examined.
• Background reading on the oxygen supply cascade (Deranged Physiology) provides additional preparation.

---

Slide 40

Lecture 2 — Key takeaways

1. All tetrapods inherited a mechanical conflict between running and breathing from their aquatic ancestor. Mammals and birds independently evolved solutions to this constraint.
2. Oxygen delivery follows a cascade of alternating convection and diffusion steps, with P_O₂ decreasing at each stage from ~150 mmHg in inspired air to ~10–20 mmHg at the mitochondria.
3. The gas laws (Boyle’s, Charles’, Gay-Lussac’s) are all derivable from the ideal gas law ($PV = nRT$).
4. Calculating inspired P_O₂ requires correcting for water vapor pressure: $P_IO_2 = (P_B - 47) \times 0.21$.
5. Barometric pressure decreases with altitude, dramatically reducing oxygen availability — at Mt. Everest, inspired P_O₂ is only one-third of sea level.

---

Key Equations

Equation	Name	Description
$PV = nRT$	Ideal Gas Law	Relates pressure, volume, temperature, and number of gas molecules via the gas constant R
$P_1V_1 = P_2V_2$	Boyle’s Law	At constant T and n, pressure is inversely proportional to volume
$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	Charles’ Law	At constant P and n, volume is directly proportional to temperature
$\frac{P_1}{T_1} = \frac{P_2}{T_2}$	Gay-Lussac’s Law	At constant V and n, pressure is directly proportional to temperature
$\frac{P_1V_1}{n_1T_1} = \frac{P_2V_2}{n_2T_2}$	Combined Gas Law	General form from which individual gas laws are derived by holding variables constant
$P_{\text{air}} = P_{O_2} + P_{CO_2} + P_{N_2}$	Dalton’s Law	Total pressure of a gas mixture equals the sum of individual partial pressures
$P_{O_2} = P_B \times F_{O_2}$	Partial pressure	Partial pressure of a gas equals barometric pressure multiplied by its fractional concentration
$P_IO_2 = (P_B - P_{H_2O}) \times F_{O_2}$	Inspired PO₂	Partial pressure of inspired O2, corrected for water vapor pressure (47 mmHg at 37°C)

---

Glossary of Key Terms

Term	Definition
Barometric pressure (PB)	The pressure exerted by the atmosphere at a given point, equal to the weight of the air column above that point. Standard sea-level value: 760 mmHg.
Partial pressure	The pressure exerted by a single gas within a mixture, calculated as the total pressure multiplied by the fractional concentration of that gas.
Oxygen cascade	The progressive decrease in the partial pressure of oxygen at each step from ambient air to the cellular mitochondria.
Convection	Bulk flow of a fluid (air or blood) that transports gases over large distances; the mechanism of ventilation and circulatory transport.
Diffusion	The passive movement of gas molecules from regions of high partial pressure to low partial pressure across a membrane or barrier.
Water vapor pressure (PH₂O)	The partial pressure exerted by water vapor in a gas mixture. At body temperature (37°C), saturated water vapor pressure is 47 mmHg.
Inspired PO₂ (PIO2)	The partial pressure of oxygen in air after it has been warmed to body temperature and saturated with water vapor in the airways.
Tidal volume	The volume of air inhaled or exhaled in a single breath during normal breathing.
Aerobic scope	The difference between resting and maximal aerobic metabolic rate; a measure of capacity for sustained physical activity.
Chronic mountain sickness	A condition affecting long-term residents at high altitude, caused by chronic hypoxia, characterized by excessive red blood cell production and cardiovascular complications.
Torr	A unit of pressure equal to 1 mmHg. 760 Torr = 1 atmosphere.
Ideal gas law	The equation PV = nRT relating pressure, volume, number of gas molecules, and temperature through the universal gas constant R.
Dalton’s Law	The principle that the total pressure of a gas mixture equals the sum of the partial pressures of each component gas.
Burst locomotion	A locomotor strategy characterized by short, high-intensity sprints rather than sustained aerobic activity; typical of lizards and other sprawling tetrapods.