diffusion-module-final-version-no-answers

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

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

Alignment to HHMI Competencies for Entering Medical Students:

E1 Apply quantitative reasoning and

appropriate mathematics to describe or

explain phenomena in the natural world.

E1.1 Demonstrate quantitative numeracy and facility with the language ofmathematics 1,2 E1.2 Interpret data sets and communicate those

interpretations using visual and other appropriate tools.

3,4,5,6

E1.5 Make inferences about natural phenomena

E1.7 Quantify and interpret changes in dynamical systems.

5

E7: Explain how organisms sense and

control their internal environment

and how they respond to external change.

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.

1,4,5

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

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.)

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

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

glucose levels in the kidney filtrate cause not all of that glucose to be transported back into the bloodstream, as usual?

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 cm2/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

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?

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 O2 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 mm Do this now and bring with you to class.2

Suggested Assessment Questions:

E1 Apply quantitative reasoning and

appropriate mathematics to describe or

explain phenomena in the natural

world.

E1.1 Demonstrate quantitative numeracy and facility with the language of mathematics 2a - d.

E1.6 Apply algorithmic approaches and principles of

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