About this section: Gas exchange physiology will be covered in detail in lecture. There is also some good information in Campbell on this topic. However, I don't feel that Campbell provides enough background on the basic physics of gas exchange processes, so I made these pages on gas exchange physiology. We'll do a lab (more like a problem set) on gas exchange, and these pages should help you complete that. The information here should also help you on the midterm.
We couldn't live without gases. All eukaryotes (including plants!) must continually take in oxygen and eliminate carbon dioxide in order to live. In order to understand how gases influence biological processes (gas physiology), it's helpful to first review some basic gas physics.
Gas molecules in a closed container (animated gif). Image from Wikipedia article on the Kinetic Theory of Gases.
Gases consist of molecules that are widely spread out-- in other words, the distance between gas molecules is large compared to the size of the molecules themselves. The molecules fly around, occasionally colliding with each other or with solid objects (such as the walls of the container that holds the gas). The kinetic energy of the moving molecules is also called heat energy. The higher the temperature, the faster the molecules move.
According to the kinetic theory of gases, the collisions are elastic -- the molecules just collide and bounce off. Collisions with the walls of the container produce the pressure of the gas. Gas pressure is simply a measure of how often and how hard gas molecules collide with solid objects.
The chemical properties of the gas molecules aren't very important in determining the physical behavior of gases. Water vapor (H2O in gas form) behaves more or less like oxygen gas (O2), even though they are chemically very different.
Units of pressure
Pressure is defined as force/area. For a gas, the pressure comes from all those gas molecules colliding with a solid object. Pressure can be expressed in various units:
- Pascal (Pa): The SI unit of pressure is the Pascal (Pa; 1 Pa=N/m2), but Pascals are rarely used in physiology.
- Atmosphere (atm): a unit of pressure intended to represent the atmospheric air pressure on a typical day at sea level. Atmospheres are not widely used scientifically, but they're still conceptually useful for Bio 6A.
- Torr, or mm Hg: Pressure has traditionally been measured by the ability of a gas to push a column of mercury (Hg) upward into a tube; the greater the pressure, the higher the mercury is pushed upward. Blood pressure is typically measured in mm Hg, as are other physiologically relevant aspects of gas pressure. Technically, Torr and mm Hg aren't exactly the same; in practice, they are the same to about 7 significant figures.
- Conversion factors: 1 atmosphere = 760 torr = 760 mm Hg = 101,325 Pa
There are also other units of pressure; for an exhaustive list, see the Wikipedia article on Pressure.
Partial pressures
The total pressure of air in a particular container (or in the atmosphere) is the sum of the pressures of all the individual gases that make up the air. The pressure of each gas is called its partial pressure. Since N2 makes up about 78% of the molecules in air, it accounts for 78% of the pressure. If the total pressure of atmospheric air is 1 atm, the partial pressure of N2 (or PN2) is 0.78 atm. This principle is called Dalton's law.
Gases diffuse down their partial pressure gradients
Gas molecules move in random directions, depending on what they crash into. Any individual molecule of gas has an equal probability of moving in any direction. The net effect of the random movements of gas molecules is that the molecules end up being randomly dispersed throughout their container. This spreading out is called diffusion.
Suppose you have a closed container, and you carefully place some gas molecules (represented by purple dots) at one end, as shown here.
At first, there is a strong concentration gradient. Concentration gradient is defined as the difference in concentration between two locations, divided by the distance between the locations. A large difference in concentration over a short distance is a strong concentration gradient.
The gas molecules begin to move randomly due to heat energy. Each individual molecule is equally likely to move in any direction. Statistically, however, there is a very high probability of gas molecules moving away from an area of high concentration (the left side of the container) and toward an area of lower concentration (the right side). In other words, the gas molecules will tend to move down their concentration gradient. Since we're talking about molecules in the gas phase, the concentration gradient is exactly the same as the partial pressure gradient in this case (assuming that there is no temperature gradient).
After diffusion proceeds for a while, the molecules are randomly distributed; there is no more concentration gradient. The individual molecules still move just as fast, but there is no net movement in any direction.
Gas Laws
In general, we can assume that biologically important gases behave like ideal gases -- in other words, the individual molecules of the gas are spread out and don't interact with each other. (This isn't true for some non-biological situations, such as gases at very high pressures or with very large gas molecules, such as refrigerants).
Ideal gases obey the ideal gas law:
PV=nRT
Where
- P = pressure of the gas
- V = volume
- n = the number of gas molecules, usually given in moles
- R = the gas constant
- T = temperature
This is one of the best laws in physics -- simple and powerful. For the purposes of Bio 6A, you won't need to do any calculations with this, and the ideal gas law can be simplified in a couple of useful ways. For example, suppose the number of gas molecules (n) and the temperature (T) remain constant. Of course, the gas constant (R) also remains constant, so therefore,
PV = constant
Or, if you increase the pressure, you decrease the volume:
P1V1= P2V2
For a closed container of gas, if the pressure is doubled, the volume must be cut in half. This part of the ideal gas law is called Boyle's Law.
Similarly, if P, n, and R remain constant, there is an inverse relationship between temperature and volume:
V1/T1= V2/T2 or V1T2=V2T1
For a closed container of gas, if the absolute temperature (in Kelvin) is doubled, the volume must also be doubled. This part of the ideal gas law is called Charles's Law.
If you know the temperature and pressure, you could use the ideal gas law to calculate the number of moles of gas present in a given volume. This could be helpful, but in biology, gases such as O2 and CO2 aren't always in gas form. The most important properties of gases happen when they are dissolved in aqueous solutions. Therefore, we also need to consider solubility.
Dissolved gases and units of concentration
Suppose you have an open beaker of water. When a gas diffuses from the air into the water, the rate of diffusion depends on the concentration gradient between the air and the water. Individual molecules may move in any direction, but the net result will be that the concentration gradient gets weaker over time, until there is no more concentration gradient and no more net diffusion. The air and the water are at equilibrium. At that point, what will the concentration of the gas be? That depends on the partial pressure of the gas and its solubility.
This is an important point. Diffusion depends on the partial pressure gradient, but the dissolved gas concentration at equilibrium depends on both partial pressure and solubility. Therefore, in physiology we need to describe gases in terms of both partial pressure and concentration.
Partial pressure
In gas exchange physiology, we’re often looking at molecules that go from gas (in the air) to dissolved in liquid (in the blood). Since gases diffuse down their partial pressure gradients, gas concentration is usually expressed in terms of partial pressure units (mm Hg, Torr, or atm). If a liquid has a PO2 (oxygen partial pressure) of 100 mm Hg, it is in equilibrium with a gas having the same PO2. Even if there is no gas phase present (for example, in blood flowing through your veins), we can use PO2 to describe the gas pressure with which the blood would be in equilibrium.
Concentration
We need to use partial pressure units to describe which way gases will diffuse, but when the O2 is used within cells, the thing that ultimately matters is the number of O2 molecules available in a given volume (concentration). This depends on both the partial pressure and the solubility. In chemistry, the units of concentration are often moles/liter or molarity. Dissolved gases could be described in terms of molarity, but it's more common to use units such as ml O2/100 ml blood. For example, you could say that a liter of blood contains 200 ml O2. This means that if you could take all the dissolved O2 out of the blood and hold it in a container of pure O2 at standard temperature and pressure, you'd have 200 ml of O2 gas. As it turns out, a liter of air and a liter of oxygenated human blood would each contain about 200 ml of O2.
Diffusion and Fick's Law
In order for oxygen to be useful to you, it must be dissolved in the aqueous fluid in your cells. For an air-breathing animal, the O2 molecules must diffuse from the air in your lungs into the blood in your alveolar capillaries (the tiny blood vessels surrounding the small air sacs in your lungs). Likewise, CO2 is produced in your tissues, carried in your blood, and ultimately diffuses out of the blood into the air in the alveoli. Your blood carries these gases effectively, but the critical rate-limiting step is often the diffusion between the air and the blood.
The rate of diffusion depends on two things:
- The surface area of the lungs. More area means more chances for gas molecules to diffuse across.
- The rate of diffusion across each centimeter of surface area. This rate can be called the flux density.
The flux density itself depends on two factors:
- The concentration gradient of the gas. For example, the difference in O2 concentration between the air in the alveoli and the blood in the capillaries surrounding the alveoli. If there is a strong concentration gradient (high O2 concentration in the air and low O2 concentration in your blood), diffusion is fast.
- The "easiness" of movement of the gas between the air and the blood. In other words, how quickly the molecules can diffuse across the surface of the lungs at a given concentration gradient. The "easiness" is sometimes called diffusivity, and it can be expressed with a diffusion constant, described below.
Since there are only a few factors affecting the overall rate of gas diffusion into or out of an organism's body, it's possible to express the rate in a fairly simple equation, known as Fick's Law.
Fick's Law of Diffusion
The rate of diffusion of a gas across a permeable membrane can be described with Fick's law of diffusion. There are various forms of this equation, but this one has been adapted for use in physiology:
m/t= DS(ΔC/x)
- m/t: the amount of gas (m) diffusing from one place to another in a given time (t). For example, this might be the number of O2 molecules per second passing across the surface of your lungs. This is also called the oxygen flux.
- D: the diffusion constant, a measure of how easily a gas passes through a particular material (such as a cell membrane). There would be a specific D for O2 diffusing through water, a different D for O2 diffusing through air, and a different D for CO2 in water or air. In most biological situations, the diffusion constant is, in fact, constant, and we won't need to quantify it for this class. We'll be more concerned with the variables that change over time.
- S: the surface area for diffusion. In the case of an air-breathing mammal, this means the surface area of the alveoli in your lungs. For a fish, it would be the surface area of the gills. This surface area is a critical aspect of any animal's morphology, but it can't normally be changed quickly as a response to changing oxygen use.
- ΔC/x: the concentration gradient. The concentration gradient is the difference in concentration between two places ΔC, divided by the distance distance between those places (x). For example, ΔC could be the difference in O2 concentration between the air in your lungs and the blood in your alveolar capillaries. The short distance between air and blood (a couple of cells thick) would be x. For our purposes, it makes sense to express the O2 concentration in terms of partial pressure (PO2).
This equation says two important things about O2 uptake:
Oxygen flux is proportional to the O2 concentration gradient. Since the concentration gradient is the difference in concentration between air in the alveoli and blood in the alveolar capillaries, it can be changed by changing either of these quantities.
Oxygen flux is proportional to the surface area of the lungs or gills. This is important when comparing different animals, but it normally remains constant for a single individual (unless it's growing).
Fick's Law in Practice
You don't always consume oxygen at the same rate. If you exercise, your oxygen consumption rate (m/t) goes up. What changes on the other side of the equation? Not the diffusion constant (D); it remains constant. Not the surface area of your lungs (S); your lungs can't change that fast. (Breathing deeply might increase the volume of air in your lungs, but the surface area doesn't change much.) The only thing left to change is the concentration gradient, ΔC/x. The concentration gradient increases because the oxygen level in your blood decreases when you use the O2; therefore the the difference in concentration between air and blood is greater. Oxygen diffuses into your blood more quickly when you need it. Normally, any changes in your oxygen uptake rate can be explained by changes in the PO2 of blood, alveolar air, or both.
When you are comparing different animals (whether different species or different-sized individuals of the same species), the surface area for gas exchange (A) also becomes an important variable.
Fick's law applies whenever substances move by diffusion: CO2 moving out of a cell and into the bloodstream, water moving through the soil, etc. In all these cases, we are at the mercy of diffusion, and Fick's law tells us that the rate will depend on the surface area and the concentration gradient. Fick's law doesn't apply to oxygen being circulated in the blood, though; that's bulk flow, not diffusion.
To learn more:
Comparative Biomechanics: Life's Physical World (2003), by Steven Vogel, of Duke University. This book is the best overall source for learning about how organisms interact with the physical world, and I used it as a reference for these pages including the formulation of Fick's law. I also highly recommend Vogel's other books, such as Life in Moving Fluids, Life's Devices, or Glimpses of Creatures in Their Physical Worlds.
Blood Gas Calculator. This site lets you change specific physiological variables and see how other parameters will be changed.