TOPIC: Diffusion: Delivering O2 And Glucose As Fast As Possible!
TUTOR GUIDE
MODULE CONTENT: This module contains simple exercises for biology
majors taking an introductory course in biology. The major goals of the module
are for students to: a) gain a conceptual and quantitative understanding of
diffusion; b) practice with both linear and exponential relationships in
mathematical models; and c) recognize the importance of speedy diffusion of
oxygen and carbon dioxide into and out of organisms, especially large or
endothermic organisms. The module includes an introduction to the biological
and mathematical principles of diffusion and practice with manipulating, and
understanding the effects of changes in, variables that affect the rate of diffusion,
using real biological examples.
The module is designed for implementation in a 60-minute classroom
session with a preparatory assignment for students to complete and turn in at the
beginning of the session. Diffusion is a critical concept in higher-level biology
courses, especially physiology courses; understanding the physical and
mathematical basis of diffusion in an introductory course will lay the foundation
for later increases in conceptual understanding. The module is also an
opportunity for students to extend the linear and exponential modeling skills they
have used in other modules or contexts.
TABLE OF CONTENTS
Alignment to HHMI Competencies for Entering Medical Students (Learning
Objectives).............................................................................................................2
Outline of concepts covered, module activities, and implementation……..……....2
Module: Worksheet for completion in class........................................................3-6
Pre-laboratory Exercises (mandatory)................................................................7-9
Suggested Questions for Assessment……………........................................... 9-10
Guidelines for Implementation……………………………...............…...................10
Contact Information for Module Developers........................................................11
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Alignment to HHMI Competencies for Entering Medical Students:
Competency
E1. Apply quantitative reasoning and
appropriate mathematics to describe or
explain phenomena in the natural world.
E7: Explain how organisms sense and
control their internal environment
and how they respond to external change.
Learning Objective
E1.1 Demonstrate quantitative numeracy and
facility with the language of
mathematics
Activity
1,2
E1.2. Interpret data sets and communicate those
interpretations using visual and other appropriate
tools.
E1.5. Make inferences about natural phenomena
using mathematical models
E1.7 Quantify and interpret changes in dynamical
systems.
E.7.1 Explain maintenance of homeostasis in living
organisms by using principles of mass transport,
heat transfer, energy balance, and feedback and
control systems.
3,4,5,6
Mathematical Concepts covered:
- Power functions
- Linear models
- Unit conversions
Components of module:
- Preparatory assignment to complete and turn in as homework before class
- In-class worksheet
- Suggested assessment questions
- Guidelines for implementation
Estimated time to complete in class worksheet:
- 60 minutes
Targeted students:
- First year-biology majors in introductory biology course
Quantitative Skills Required:
- Basic arithmetic
- Logical reasoning
- Understanding of unit conversion
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5,6
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1,4,5
MODULE WORKSHEET
TOPIC: Diffusion: Delivering Glucose And Oxygen as Fast as Possible
As you read in the pre-lab, animal cells must constantly produce ATP to power
their activities and maintain homeostasis. Nearly all animal cells do this using
oxygen and sugar to produce ATP in a process called cellular respiration.
Specifically, to make ATP, the chemical equation is:
C6H12O6 (glucose) + 6O2  6CO2 + 6H2O + ~36 ATP
Animal cells must transport both glucose and oxygen across their cell
membranes by diffusion as quickly as possible in order to provide sufficient
energy to power cellular activities, like muscle contraction.
As you learned in the pre-lab, the concentration gradient of the molecule
across the cell membrane is one critical variable determining speed of diffusion;
the higher the concentration gradient, the faster the diffusion. Additionally, the
permeability of the membrane to that molecule greatly affects its rate of
diffusion.
I. Fick’s First Law
As you learned in the pre-lab, the diffusion “flux” (net movement of molecules)
across a membrane is called J, and depends on D (diffusion coefficient), the
concentration gradient (C1-C2) and X (the distance over which diffusion occurs):
J=D (C1-C2)/X
In the pre-lab, you used Fick’s first law to assess changes in movement of
oxygen across respiratory membranes of terrestrial (land-living) animals. Now,
consider the effect of living in water, as follows.
Question 1. Oxygen is much more soluble in air than in water; because of this,
oxygen’s permeability in water is very poor-- the diffusion coefficient D for O2 in
air is 0.1 cm2/second, but in water it’s 1.8 x 10-5 cm2/second. How much lower is
O2 diffusion (all other things being equal) across a fish’s respiratory membrane,
versus a lizard’s? Why don’t endothermic animals such as marine mammals like
dolphins, breathe water? (Hint: mammals have very high metabolic rates, or
rates of O2 use, that come as the cost of maintaining steady body temperature.)
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II. The effect of distance: Fick’s Second Law
In the pre-lab, after working with Fick’s First Law, you moved on to consider how
long it takes something to diffuse; with the consideration of time, the distance
over which the molecule diffuses becomes critical—and its relationship to
diffusion isn’t linear. Specifically, the time it takes a molecule to cover a given
distance increases exponentially with increasing distance. This is called Fick’s
Second Law:
T (time to diffuse)= X2/2D
Again, X= distance and D= the diffusion coefficient.
In the pre-lab, you used Fick’s second law to consider the effect of the thickness
of the respiratory membrane on oxygen diffusion in different animals. Here,
continue to consider how diffusion of oxygen is different for different animals.
Question 2. Some animals don’t have lungs at all. To understand why you have
lungs but jellyfish don’t, consider the fact that the body of a jellyfish is two cells
thick— thus the thickness of the epithelial membrane (from the “bell” body to the
inside of the animal) is about 50µm.
2 cells!
Using a diffusion coefficient of 1.8 x 10-5 cm2/second (since nearly all the
distance covered is inside an animal, which is a bunch of bags of water—cells—it
makes sense to use the value of the diffusion coefficient for oxygen in water):
a) How long would it take for oxygen to diffuse into the middle of this jellyfish
body? Recall from the prelab that you converted 1.8 x 10-5 cm2
to µm2. This number will be helpful in this problem.
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b) This (answer to part a) still seems like a long time. Why doesn't this lead to an
oxygen deficit in this organism?
c) How long would it take for oxygen to diffuse from the outside to the middle of a
mouse if its body has a 1 cm radius?
d) How about a rhino whose body has a radius of 75 cm?
Now you can see why rhinos, and even mice, really need lungs!
III. Facilitated Diffusion: glucose
The examples above all involved a process called simple diffusion; because
oxygen is small and uncharged, it can diffuse across the cell membrane directly.
But the other thing cells need to make ATP—glucose—is too big to cross the cell
membrane that way. It needs a carrier, a protein that spans the cell membrane
and transports glucose, one molecule at a time, down its concentration gradient
across the cell membrane. This is still diffusion—it’s down the concentration
gradient of glucose, and requires no ATP—but as you saw in the pre-lab,
saturation can occur: if the carriers get “full,” no further increase in the rate of
glucose transport can occur. This type of diffusion is called facilitated diffusion.
One place glucose is transported by facilitated diffusion is across the lining of
your small intestine, from the lumen of the small intestine (where you put it, by
eating!) to the bloodstream. The diffusion coefficient D for glucose in solution in
humans= 600µm2/sec.
Question 3. By what factor (how much) will drinking a can of soda increase the
diffusion of glucose across the intestinal lining into the blood if it increases
glucose concentration in the epithelial cell from 200 to 500mM, and capillary
glucose is 50 mM throughout? Use Fick’s first law, ignoring variables that are the
same between the two conditions.
Question 4. In the disease diabetes mellitus, glucose levels in the blood are
higher than normal. Normally, glucose in the kidney filtrate (the fluid in the kidney
that is “on its way” to becoming urine) is completely transported back into the
blood. In individuals with diabetes mellitus, though, not all glucose is reabsorbed;
some remains in the filtrate and exits the body in the urine. Why would high
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glucose levels in the kidney filtrate cause not all of that glucose to be transported
back into the bloodstream, as usual?
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Pre-Lab Exercises
In this pre-lab worksheet you will learn about the concept of diffusion, in which
chemicals move along their concentration gradients. In particular, you will be
introduced to Fick’s first and second laws, which explain the relationships
among the variables that affect diffusion. Please read carefully because you will
be asked to use these answers and concepts on your lab worksheet.
Animal cells must constantly produce ATP to power their activities and maintain
homeostasis. Nearly all animal cells’ preferred method of producing ATP is
cellular respiration, or oxidative phosphorylation. To do this, cells need two
things: oxygen and sugar (glucose).
Specifically, to make ATP, the chemical equation is:
C6H12O6 (glucose) + 6O2  6CO2 + 6H2O + ~36 ATP
Oxygen and glucose must, then, be delivered to cells as quickly as possible.
Both oxygen and glucose are capable of transport down their concentration
gradients across cell membranes, which is called diffusion. Organisms use
diffusion as the preferred method of transmembrane transport of molecules
because it does not require cellular energy, or ATP. For molecules that are
needed in great quantity, such as oxygen and glucose, organisms evolve to
maximize the rate of diffusion of these molecules. Essentially, an organism’s
ability to do work is limited by the rate at which it can produce ATP, and the rate
at which a cell can make ATP is itself limited by the rate at which oxygen and
glucose can be delivered to cells. Thus, maximizing the rate of diffusion of these
molecules is of critical importance for living things!
The rate of diffusion is a function of several other variables. Thus, if organisms
“control” those variables, they can control the rate of diffusion. The
concentration gradient of the molecule across the cell membrane is one critical
variable; the higher the concentration gradient, the faster the diffusion.
Along with concentration gradient, two other major factors influence how fast a
molecule can diffuse across a cell membrane. The first major factor is
permeability, or simply how easy it is for the molecule to move across the
particular membrane. Size, charge and polarity are the major factors affecting
permeability in living systems; large, charged, and polar molecules all have more
difficulty crossing membranes—lower permeability. Along with temperature,
permeability is included in a “diffusion coefficient” that is particular to the
substance that is diffusing and the local conditions. For example, the diffusion
coefficient for oxygen diffusing in air at 20 degrees Celsius is 0.153 cm 2/sec. The
second major factor is distance. Because we will first look at the “J” or “flux”—a
snapshot of molecule movement over one moment in time—we can treat
distance as having a simple inverse relationship to diffusion; that is, the larger the
distance something has to diffuse, the lower the “flux.” Shortly, we will see that
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when we look at diffusion rates—diffusion over time—the relationship with
distance is exponential.
I. Fick’s First Law
Because concentration gradient (the difference in concentration on either side of
the cell membrane, or C1-C2) and permeability (as noted above, included in the
diffusion coefficient D) are both directly related to diffusion—the higher they are,
the more diffusion there will be—and distance (we’ll call it X) is inversely related
to diffusion rate—the higher it is, the less diffusion there will be—we can write for
a diffusion “flux” (net movement of molecules), which for some reason we call J:
J=D (C1-C2)/X
This is called Fick’s First Law and was a model first put together by the clever
Adolf Fick in 1955. Fick’s law applies perfectly to oxygen diffusion. In animals,
oxygen diffuses into the blood from the local medium—air or water—at the
animal’s lung or gill, which is made up of a series of folded, super-thin
membranes collectively called the respiratory membrane.
II. The effect of distance: Fick’s Second Law
To assess the effect of distance on diffusion, we have to start thinking about the
effect of distance on how long it takes something to diffuse across that distance.
And when we do that, we find out that the effect of distance isn’t linear.
Remember, molecules don’t “know where they’re going”; a molecule may take
“one step” in the “right” direction, then randomly move back in the initial, or in an
orthogonal, direction. Because of this, as the distance the molecule needs to
diffuse gets larger, the likelihood of the molecule covering that distance in a given
period of time goes way down. Specifically, we can say that the time it takes a
molecule to cover a given distance increases exponentially with increasing
distance. This is called Fick’s Second Law:
T (time to diffuse)= X2/2D
Again, X= distance and D= the diffusion coefficient.
Almost all animals need oxygen to make ATP, but some animals need it much
faster than others—endotherms, which heat their bodies using metabolic energy.
This means they must modify their lungs to deliver oxygen more quickly.
Now that you have carefully read about Fick’s first and second laws, please
answer the following questions.
1. Using Fick’s first law, if the concentrations and distance are the same, but the
diffusion coefficient doubles, what happens to the flux?
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2. Using Fick’s first law, if the concentrations and diffusion concentrations are the
same, but the distance doubles, when what happens to the flux?
3. At sea level, O2 partial pressure in air is 159 mmHg; in blood it is normally 40
mm Hg. On top of Mt. Everest, O2 partial pressure is 54mm Hg. How much
greater is O2 diffusion across the respiratory membrane into your bloodstream
from the air at sea level, than on Mt. Everest? (You can ignore any variables that
are the same at sea level and Mt. Everest when calculating).
4. When you exercise, your O2 partial pressure drops in your blood, since cells
are using it up more quickly than before. How does this change affect O 2
diffusion across the respiratory membrane? How does this difference benefit the
exercising person?
5. The respiratory membrane in a bird lung is 0.1µm thick; yours is 0.4µm thick; a
crocodile’s is 2 µm thick. How much faster will diffusion of gases occur in a bird
than in you, and in a bird than in a crocodile? (Don’t worry about units here, just
the effect of the change in distance).
6. During the worksheet you will need to convert 1.8 x 10-5 cm2
to µM by first converting to mm2. Do this now and bring with you to class.
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Suggested Assessment Questions:
Competency
E1. Apply quantitative reasoning and
appropriate mathematics to describe or
explain phenomena in the natural
world.
Learning Objective
E1.1. Demonstrate quantitative numeracy and facility
with the language of mathematics
Activity
2a. - d.
E1.6. Apply algorithmic approaches and principles of
logic to problem solving
2a. - d.
Potential topics of additional, summative assessment questions:
1. Provide students with a saturation curve depicting the relationship between
(for example) glucose concentration (X axis) and glucose transport (Y axis). The
curve flattens at a high glucose concentration, with transport levels not continuing
to increase. Ask students why not (the transporters are full).
2. Hummingbirds have huge numbers of glucose carriers in their small intestine
lining, due to their incredibly high metabolic rates. You could have students
calculate the effect of increased carriers. First, they should think about where in
the equation this shows up (it’s the diffusion coefficient), then ask them how
much faster diffusion of glucose will occur of the number of carriers is doubled or
quadrupled.
3. As I put a tea bag in my hot water, caffeine diffuses out of the tea bag into the
water. Using the diffusion equation(s)!, explain how the following will affect the
rate of diffusion of caffeine into the water:
a) the thickness of the tea bag (not including the tea leaf particles, just the bag
itself),
b) the temperature of the water, and
c) the size of my mug (amount of water in mug)
Instructions for Implementation by TAs:
Collect homework (pre-lab exercises). Have students break up into groups,
ideally of 4-5 students each. From here you can proceed on one of two ways:
1. Give each student group a simple dry-erase board (available for about $3
apiece at office-supply stores), mini-chalkboard, or large piece of paper, and a
marker. Ask each question in the module, one at a time, by projecting the slide
with the question or writing it on the board.
Give the students a few minutes with each question or sub-question—not a long
time, no more than 3-4 minutes per question-- and some questions need only a
minute, such as the first two questions. The shorter the interval, the higher the
level of energy and interest in the room. As the students work, circulate and
assist them (without giving them the answer, of course). At the end of the time
period for the question, announce that there are 10 seconds remaining, then ring
a bell or use some other pre-agreed signal, and at the signal, all student groups
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hold up their white boards with their answers. Use the boards as a basis for
discussion if answers differ. If most student groups have the right answer, move
on quickly to the next question.
2. Alternatively, the questions can all be given together to each student group as
a worksheet. This sounds like less work and stress for the TAs/instructors, but
the one-at-a-time-method (method #1) keeps everyone on track, energized and
having fun. Try it!
Module Developers:
Please contact us if you have comments/suggestions/corrections
Kathleen Hoffman
Department of Mathematics and Statistics
University of Maryland Baltimore County
khoffman@math.umbc.edu
Jeff Leips
Department of Biological Sciences
University of Maryland Baltimore County
leips@umbc.edu
Sarah Leupen
Department of Biological Sciences
University of Maryland Baltimore County
leupen@umbc.edu
Acknowledgments:
This module was developed as part of the National Experiment in Undergraduate
Science Education (NEXUS) through Grant No. 52007126 to the University of
Maryland, Baltimore County (UMBC) from the Howard Hughes Medical Institute.
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