diffusion-module-final-version-no-answers

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) Outline of concepts covered, module activities, and implementation…… …… 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: 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 ofmathematics 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 5,6 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 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 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 O 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 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 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 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 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 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 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 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 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 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 Using Fick’s first law, if the concentrations and distance are the same, but the diffusion coefficient doubles, what happens to the flux? Using Fick’s first law, if the concentrations and diffusion concentrations are the same, but the distance doubles, when what happens to the flux? 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) 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 diffusion across the respiratory membrane? How does this difference benefit the exercising person? The respiratory membrane in a bird lung is 0.1µm thick; yours is 0.4µm thick; a crocodile’s is 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) 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 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: 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) 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 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: 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 10 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 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 11