Model the Chances of Getting an Autoimmune Disease
Summary

Overview
Can genetic or environmental factors affect our chances of getting a certain disease? In this activity, your students will model how an existing predisposition can impact the probability of developing an autoimmune disease using dice and M&M's® candy!Learning Objectives
- Understand the factors that contribute to getting an autoimmune disease
- Explain why, in a given population, some people have an autoimmune disease, and some do not
- Apply the concepts of probability to model the likelihood of getting an autoimmune disease based on an existing predisposition
NGSS Alignment
This lesson helps students prepare for these Next Generation Science Standards Performance Expectations:- HS-LS3-3. Apply concepts of statistics and probability to explain the variation and distribution of expressed traits in a population.
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Science & Engineering Practices
Developing and Using Models.
Develop and/or use a model (including mathematical and computational) to generate data to support explanations, predict phenomena, analyze systems, and/or solve problems.
Analyzing and Interpreting Data. Apply concepts of statistics and probability (including determining function fits to data, slope, intercept, and correlation coefficient for linear fits) to scientific and engineering questions and problems, using digital tools when feasible. Engaging in Argument from Evidence. Construct, use, and/or present an oral and written argument or counter-arguments based on data and evidence. |
Disciplinary Core Ideas
LS3.B: Variation of Traits. Environmental factors also affect expression of traits, and hence affect the probability of occurrences of traits in a population. Thus, the variation and distribution of traits observed depends on both genetic and environmental factors.
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Crosscutting Concepts
Scale, Proportion, and Quantity.
Algebraic thinking is used to examine scientific data and predict the effect of a change in one variable on another (e.g., linear growth vs. exponential growth).
Systems and System Models. Models can be used to predict the behavior of a system, but these predictions have limited precision and reliability due to the assumptions and approximations inherent in models. |
Materials

Materials per class:
- Four desks
- Enough room to fit the whole class on each end of the desks (see Figure 2)
- Bowls or cups (8)
- M&M's candies (24 of each color: red, green, yellow, blue)
- Six-sided dice (6)
- Pencil or pen for each student
- Clear tape
Background Information for Teachers
This section contains a quick review for teachers of the science and concepts covered in this lesson.Our immune systems are made up of different cells and organs that normally defend us against pathogens (harmful microorganisms that can make us sick). The immune system goes through a process called the immune response to fight off a pathogen. Most of the work is done by white blood cells. There are several different types of white blood cells, including B cells and T cells; collectively, the different types of white blood cells are also called leukocytes. White blood cells must find the pathogen in the body, tell it apart from the body's regular cells, then make antibodies, which are tiny particles specifically designed to only attach, or bind, to the pathogen. Once bound to the pathogen, antibodies get help from white blood cells to destroy the pathogen.

An immune cell on the left and right compared when attached to both a self and non-self cell. Non-self cells will connect to non-self receptors, and self cells will connect to self receptors. However, self cells also have self antigens which attach to self antibodies.
Figure 1. Simplified diagram of the self/non-self recognition mechanism. In an autoimmune response, autoantibodies produced by immune cells bind to healthy body cells (self cells).
The process by which the immune system tells pathogens apart from own body cells is called self/nonself-recognition (Figure 1). If it fails, it can cause autoimmune disease or an infection. When the immune cells accidentally make an antibody that binds to its own body cells, it is called autoimmunity, or an autoimmune response, while the antibody is called an autoantibody. Autoimmunity is common and usually not serious, but if it is not stopped by the body, it can turn into an autoimmune disease, which is when the immune system chronically attacks healthy cells in the body. A person's genetics can make them predisposed, or more likely, to get an autoimmune disease. For example, some mutations within specific genes can cause an autoimmune disease. Environmental factors, such as where a person lives, what a person eats, and things that a person is exposed to, can also affect whether a person gets an autoimmune disease.
There are three checkpoints that the immune system follows in order to stop an autoimmune response from becoming an autoimmune disease (note that these steps are simplified).
- Checkpoint 1: Sometimes, white blood cells (specifically B cells, which are made in the bone marrow, or T cells, which are made in the thymus) are made that have autoimmunity, meaning their antibodies bind to healthy body cells. The body must destroy them before they escape from the bone marrow or thymus, or they can cause an autoimmune disease.
- Checkpoint 2: Right before an immune response is triggered to fight a pathogen, white blood cells (called regulatory T cells) make sure that other white blood cells are not accidentally attacking the body's own cells. They need to do their job correctly to prevent an autoimmune disease.
- Checkpoint 3: After a pathogen is destroyed in the body, white blood cells (specifically activated T cells and B cells) must destroy themselves (through a process called apoptosis) to stop the immune response, or it could lead to an autoimmune disease.
One common autoimmune disease that you could discuss with your students is diabetes mellitus type 1, more commonly known as type 1 diabetes. Type 1 diabetes is caused when the immune system attacks and destroys beta cells in the pancreas that normally make insulin. Before the effects of type 1 diabetes become visible, autoantibodies can be detected. Even if a person has autoantibodies, they are not guaranteed to get type 1 diabetes, but they do have an increased likelihood of developing diabetes over their lifetime. The more types of autoantibodies that are present, the greater the risk.
The incidence varies from about 0.013% of people in Northern Europe and the United States, to a high of 0.035% of people in Scandinavia and a low of 0.001% of people in Japan and China. There is a genetic component to this condition, but it is not completely genetic—environmental factors also matter. If it were completely genetic, then if one identical twin had diabetes, the other twin would also get it; however, medical records show that if one identical twin has diabetes, the other twin is only 30–50% likely to also get it. This, among other medical evidence, shows that both genetics and environment matter.
In this activity, students will use M&M's candies and a die to model the immune system and find out how a person's predisposition (genetics and other factors) affect whether they get an autoimmune disease or not.
Additional Background Links
- How does the immune system work?, PubMed Health
- FAQ on Autoimmune Diseases, Autoimmune Disease Research Center, Johns Hopkins Medicine, Pathology
- Autoimmunity Genetic Factors, News Medical Life Sciences
Prep Work (20 minutes)
- In your classroom, set up one station (desk) for each of the three immune system checkpoints and an additional setup desk as shown in Figure 2.

Four tables lined up to be used as a starting point and three checkpoints in the autoimmune disease activity. Students will travel from the starting table to each subsequent checkpoint until they reach the end and are health, or they develop an autoimmune disease and must stand in a separate group from those that remain healthy.
Figure 2. Classroom setup to model the likelihood of getting an autoimmune disease.
- Designate a "start" area for all students in front of the setup desk and assign two separate areas after Checkpoint 3: one for students who did get an autoimmune disease and one for students who did not get an autoimmune disease, as shown in Figure 2.
- For each station, print out one or two instruction sheets and tape them to the respective desk.
- On each desk/station put two bowls with three M&M's of each color (red, green, yellow, blue)—one on each side of the desk. Add two six-sided dice to each of the checkpoint desks.
- Print out a student worksheet and autoimmune disease handout for each student.
Teacher Tool Box
Engage (15 minutes)
- Introduce and discuss the immune system and autoimmune diseases.
Does anybody know a person who has an autoimmune disease? What types of autoimmune diseases do you know?Some common autoimmune diseases include lupus, Graves' disease, Hashimoto's disease, rheumatoid arthritis, diabetes type 1, and celiac disease. Note: If your students do not know anybody with an autoimmune disease you can give examples of celebrities who have been diagnosed with an autoimmune disease. Depending on your students' interest, you can elaborate on specific conditions if you have time.
- Collectively write a list of all mentioned autoimmune diseases on the blackboard. Then, ask what is an autoimmune disease? Explain to your students that to answer this question, they have to understand how our immune system works. Then start a discussion about the immune system using the questions below.
Alternatively, you can show your students this video that explains the immune system and autoimmunity. Note: Stop the video at 2:18, as after that the video will give away the answers to some of the student's upcoming tasks!
How does our body fight pathogens (microorganisms that make us sick) when we get sick?Once a pathogen invades our body, our immune system triggers an immune response. This means it recruits many immune cells in our body, mainly white blood cells, to fight the invaders. Several types of white blood cells (e.g. B-cells and T-cells) work together to eliminate the pathogen, but they first have to find the pathogen in the body, tell it apart from your own body cells, and then make antibodies. These are tiny particles that attach, or bind to, the pathogen. Once the antibodies have bound to the pathogen, other white blood cells take over and destroy it.What prevents antibodies from binding to non-pathogenic microorganisms or healthy cells in our body?Antibodies are specifically designed to only match one type of pathogen. Antibody binding works similarly to a key lock system. If the binding region of the antibody matches with the marker on the invading cell, it successfully binds to the pathogen. If the binding region does not match, the cell is ignored. This means that our immune system has to make different antibodies for each type of pathogen or disease.What happens if our immune system fails and the white blood cells cannot distinguish between "good" and "bad" cells anymore?If the process by which the immune system tells pathogens apart from our own body cells fails, it can cause autoimmune diseases (or an infection). When our immune system accidentally makes an antibody that binds to our regular cells (autoantibodies), it is called autoimmunity, or an autoimmune response. Autoimmunity is common and usually not serious, but if it is not stopped by the body, it can turn into an autoimmune disease, which is when the immune system chronically attacks healthy cells in the body.Now that you know what an autoimmune disease is, we will investigate how autoimmunity can get triggered. What factors increase the risk of getting an autoimmune disease?Collect answers and then tell your students that they will look at some autoimmune disease data to find the answer to this question.
Explore (60 minutes)
- Split your class into groups of 3-4 students. Distribute one autoimmune disease handout to each group and explain that this handout provides information on the variation and distribution of autoimmune diseases worldwide. Then ask your students to analyze the data and graphs carefully and give them 15 minutes to discuss the questions listed on the handout within their groups. At the end of their discussion they should have filled out the included claim-evidence-reasoning (CER) tables.
- Collect all claims from each group and make a list of all the factors that contribute to a higher risk of getting an autoimmune disease on the blackboard. Make sure that genetic and environmental factors are mentioned. Additional factors could be diet, age, gender, exposure to chemicals or pollution, location, etc. Let students think about why these are relevant factors. State that this is an active field of research and that scientists are still trying to find out why some of these factors increase the risk of getting an autoimmune disease.
Now that you know what factors can contribute to getting an autoimmune disease, why do you think some people get the disease and others do not? Where does this variation in our population come from?
- To answer this question, you will do an experiment to model how the likelihood of getting an autoimmune disease changes with the presence or absence of factors known to cause autoimmune diseases such as genetic or environmental factors. To do this, you will model an actual (but simplified) autoimmune response in your classroom.
- Explain to your students that our immune system has developed different mechanisms to stop an autoimmune response from becoming an autoimmune disease. Introduce the three "checkpoints" that our immune system has. The slideshow includes a diagram of all these steps, which might be helpful to show to your students while explaining the process.
- Checkpoint 1: Check if immune cells develop autoimmunity (meaning their antibodies bind to healthy body cells) before they leave the organs where they are produced. The body must destroy them before they can cause an autoimmune disease.
- Checkpoint 2: Check if immune cells can stop an autoimmune response (meaning that white blood cells are accidentally attacking the body's own cells) during an infection. Immune cells need to do their job correctly to prevent an autoimmune disease.
- Checkpoint 3: Check if immune cells destroy themselves to stop the immune response after an infection. Failure to destroy themselves could lead to an autoimmune disease.
- Explain to your students that, depending on genetic or environmental factors, each checkpoint has a certain probability to fail, which would lead to an increased risk of developing an autoimmune disease.
Tell them that they will model the immune system response to autoimmune white blood cells, going through all three checkpoints described above.
At each point, there is a chance that the immune system fails, and the result will be an autoimmune disease.
How can we model the probability of an event, or simulating a chance that success or failure will happen at each of the checkpoints?A good method would be flipping a coin or rolling a die and assigning each number on the die to a certain outcome (failure or success). As it is usually unlikely to get an autoimmune disease, numbers 1, 2, 3, 4 and 5 could be assigned to passing the checkpoint, whereas rolling a 6 would mean failing the checkpoint.What would be the probability in this case to fail the checkpoint?The probability to fail the checkpoint in this case would be one out of six, or about 17%.How could you reflect the presence or absence of genetic or environmental factors that increase the probability of getting an autoimmune disease in this model?If you have a predisposition (for example, if one of your first-degree relatives has an autoimmune disease), you are more likely to develop an autoimmune disease. This could be reflected by increasing the amount of numbers on the die that are assigned to failure at a certain checkpoint. For example, for people with an existing predisposition, checkpoint failure (which is more likely) could be assigned to numbers 5 and 6 or in the extreme case to all numbers from 2–6, whereas passing the checkpoint would only be assigned to numbers 1–4 or in the extreme case to only 1.How would the probability to fail the checkpoint change based on an existing predisposition?Based on which numbers you assign to checkpoint failure due to an existing predisposition, the likelihood of checkpoint failure would increase from 17% (one out of six) to about 33% (if two numbers on the die [5 and 6] are assigned to failure) or in the extreme case (where five numbers out of six [2–6] are assigned to failure) to 83%.
- Tell your students that they will apply the concept of probability to model the chances of getting an autoimmune disease with and without a predisposition. The slideshow contains a slide that demonstrates how the concept of probability applies to the model you will use. Students will do two classroom simulations. The first one will represent people with a normal probability for getting an autoimmune disease. The second simulation will represent people that have an increased likelihood of developing an autoimmune disease due to a predisposition.
- Walk the students through the experimental procedure described below. (The slideshow includes instructions to guide your students through the experiment before doing it.)
Simulation without Predisposition
In this simulation, each student represents a person with no predisposition to an autoimmune disease, meaning that this person has normal chances of developing an autoimmune disease.
- Make sure each student has a simulation log sheet which is included in their student worksheet. Then ask all students to move to the designated start area. They should build a line in front of the setup station/desk. Students can pass on each side of the desk.
- Each student needs to follow the instructions displayed at each station/desk. At the setup station, they need to close their eyes, mix the M&M's with their hand, and then randomly pick an M&M candy from the bowl (see Figure 3). The color of the selected M&M will be the body's label for its own cells. They have to record this color on their log sheet and remember it throughout the checkpoints! Make sure they return the M&M to the bowl before they move on to the next desk (Checkpoint 1).

The setup for the game requires each student to blindly pick an M&M candy and record the color of the candy they get. That color will be used to determine their "self" color.
Figure 3. Start your model by picking a random M&M's candy from the bowl.
- Students move to the next desk to simulate Checkpoint 1, following the steps described in Figure 4. Make sure that they close their eyes while picking an M&M and that they return the M&M to the bowl before moving on. Students should record all their results on their log sheet.

Checkpoint 1 begins by a student randomly choosing another M&M, if the color does not match their original "self" color then they are safe and can proceed to the next checkpoint. If the color does match, then they must roll a six sided die. Rolling any number besides 6 will result in the student being safe and proceeding to the next checkpoint. If a 6 is rolled the student develops an autoimmune disease and must stand in the disease group.
Figure 4. Steps for simulating Checkpoint 1. Dark grey boxes indicate what each step in the model represents.
- Depending on the outcome of Checkpoint 1, students either continue to Checkpoint 2 or go to the designated autoimmune disease area. At Checkpoint 2 they follow the steps described in Figure 5. Again, make sure that they close their eyes while picking an M&M and that they return the M&M to the bowl before moving on. Students should record all their results on their log sheet.

Checkpoint 2 begins by randomly choosing another M&M, if the color does not match their original "self" color then they are safe and can proceed to the next checkpoint. If the color does match, then they must roll a six sided die. Rolling any number besides 6 will result in the student being safe and proceeding to the next checkpoint. If a 6 is rolled the student develops an autoimmune disease and must stand in the disease group. If the "pre-disposed" varient is being played, than rolling numbers one through five will result in developing an autoimmune disease, while rolling a six will result in safe passage to the next checkpoint.
Figure 5. Steps for simulating Checkpoint 2. Dark grey boxes indicate what each step in the model represents.
- Depending on the outcome of Checkpoint 2, students either continue to Checkpoint 3 or go to the designated autoimmune disease area. At Checkpoint 3 they follow the steps described in Figure 6. Again, make sure that they close their eyes while picking an M&M and that they return the M&M to the bowl before moving on. Students should record all their results on their log sheet.

Checkpoint 3 begins by randomly choosing another M&M, if the color does not match their original "self" color then they are safe and can proceed to the "safe" group. If the color does match, then they must roll a six sided die. Rolling any number besides 6 will result in the student being safe and proceeding to the next checkpoint. If a 6 is rolled the student develops an autoimmune disease and must stand in the disease group. If the "pre-disposed" varient is being played, then rolling numbers one through five will result in developing an autoimmune disease, while rolling a six will result in safe passage to the next checkpoint.
Figure 6. Steps for simulating Checkpoint 3. Dark grey boxes indicate what each step in the model represents.
- Once all students completed all checkpoints, collectively count how many students got an autoimmune disease (stand in the designated autoimmune disease area). Then count all the students that did not get an autoimmune disease. Write the results on the blackboard for everyone to see.
Simulation with Predisposition
In this simulation, each student represents a person with an existing predisposition to an autoimmune disease, meaning that this person has an increased chance of developing an autoimmune disease.
- Gather all students again in the designated start area in front of the setup desk.
- Ask them to repeat the previous simulation (steps 2–6) but tell them that this time for Checkpoint 2 and 3 the predisposed rules (light grey boxes) apply for rolling the die, which means that this time a Checkpoint 2 and 3 failure occurs when a 2, 3, 4, 5, or 6 is rolled.
- Once all students completed Checkpoint 1–3, again collectively count how many students got an autoimmune disease (stand in the designated autoimmune disease area). Then count all the students that did not get an autoimmune disease. Write the results on the blackboard for everyone to see.
Reflect (30 minutes)
- Once students have finished both simulations, start a discussion with your class about their results. Some questions that you could ask are listed below.
Did all predisposed people with a higher risk of getting an autoimmune disease actually get one, or were there any who did not?How many of you had an autoimmune response (matching M&M color) that did not turn into an autoimmune disease (the die roll was not high enough to cause an autoimmune disease)? Note: Students have to check their simulation log sheets to answer this question.
- Based on the collected results on the blackboard, have students calculate the percentage of people who got an autoimmune disease for the predisposed versus non-predisposed simulation.
- Optionally, you can ask them to visualize their data by making a bar graph comparing both percentages.
In which group—normal risk, or higher risk—did you observe more people with an autoimmune disease? Can you explain why?In each group, the chances of matching the M&M's candy color and triggering an autoimmune response is the same (1 out of 4, since there are four M&M's candy colors). However, the group with a genetic predisposition should have had a higher occurrence of autoimmune diseases because Checkpoints 2 and 3 had greater odds of having an autoimmune response turn into an autoimmune disease (5 out of 6 compared to 1 out of 6, based on the die roll).
- Optional: If your students have learned about probability trees and probability calculations, let them calculate the probability for a person to develop an autoimmune disease in each simulation. If not, continue with step 8.
- To do the probability calculations, they first have to determine the probability to get to an autoimmune disease for each of the steps within a checkpoint (see Table 1).
| Probability of: | Checkpoint 1 | Checkpoint 2 | Checkpoint 3 | |
|---|---|---|---|---|
| Without Predisposition | Picking matching color | 1/4* | 1/4* | 1/4* |
| Rolling high number | 1/6** | 1/6** | 1/6** | |
| With Predisposition | Picking matching color | 1/4* | 1/4* | 1/4* |
| Rolling high number | 1/6** | 5/6*** | 5/6*** |
**as an autoimmune disease occurs when one number (6) is rolled and there are six numbers on the die
***as an autoimmune disease occurs when five numbers (2, 3, 4, 5, 6) are rolled and there are six numbers on the die
Table 1. Probabilities for each step at each checkpoint within the simulation.
- Once they have determined the probability for each step, they can draw
a probability tree
(see Figure 7) for going through all the checkpoints, including the probabilities for each step in both simulations. If your students have difficulties drawing a probability tree, you can show them a sample probability tree, which is shown on the last slide in the slideshow.
Image Credit: Svenja Lohner, Science Buddies / Science Buddies
Figure 7. Probability tree for the autoimmune disease simulation going through all the checkpoints.
- Once they have drawn the probability tree, ask students to
calculate the final probabilities
of getting an autoimmune disease in each scenario. To do this, they have to multiply all probabilities along one single path that leads to an autoimmune disease. Then, they need to add up all the individual probabilities that lead to an autoimmune disease to determine the final probability of getting an autoimmune disease for one simulation. Remind the students to change the probabilities for rolling the die at Checkpoints 2 and 3 in the simulation with an existing predisposition. An example calculation for the orange probability path in Figure 7 is shown below for both simulations:
Without predisposition:
With predisposition:
How much higher is the probability to develop an autoimmune disease in the predisposed group compared to the non-predisposed group?According to your calculations, a person without a predisposition has a likelihood of about 12% to get an autoimmune disease. This number more than triples to about 40% for people with an existing predisposition.Did your calculated percentages match the ones that you actually observed in your simulations?If there is a 12% likelihood to get an autoimmune disease in your simulation, then you should have seen about 1 in 10 people get an autoimmune disease. With predisposition, you should have observed about 3–4 times as many people get an autoimmune disease. However, remember that these are just calculated probabilities. Due to the random nature of picking one color out of four or rolling a specific number with a die, there is no guarantee that you will see the theoretical probabilities in reality. - Come back to your original question and discuss reasons for the variation and distribution of autoimmune diseases in a given population.
Based on your results and evidence from your data, present arguments for why in a given population only a few people have an autoimmune disease (or other diseases).Each person has a different predisposition to autoimmune diseases. Some might have an autoimmune disease that runs in their family, some might be exposed to toxic chemicals, or others have a genetic mutation, etc. This means that the chances of actually getting a specific disease are not equally distributed within a population. Depending on their genetic or environmental predisposition to a certain disease, some are more likely to develop the disease than others, which is why not everybody, but just a few people, actually develop the disease.Can you think of means to decrease your risk of getting an autoimmune disease?If you are genetically predisposed to a certain disease, you cannot change your genes to decrease your risk of develop the disease. However, often your genes only increase the likelihood of getting the disease, which means you can decrease your risks by minimizing, for example, environmental influences that can cause a certain disease.
Assess
You can use this quiz to assess student learning after the activity:
- Online quiz, assignable in any LMS
- Quiz (pdf) and answer key (PDF)
Make Career Connections
Discussing or reading about these careers can help students make important connections between the in-class lesson and STEM job opportunities in the real world.
Lesson Plan Variations
This science activity can be expanded or modified in a number of ways. Here are a few options:
- Have students repeat this activity, but pick different checkpoints to be at higher risk, such as only one checkpoint, two different checkpoints, or all three checkpoints. How do their results change as the number of checkpoints at higher risk increases? How do the probabilities of developing an autoimmune disease change?
- Let students add more factors that can change the probability of developing an autoimmune disease to their model. Students could introduce different checkpoints or add more steps at each checkpoint to vary the model. One possibility could also be to roll the die twice at each checkpoint: once to check for failure and success due to genetic factors, and once for the environmental factors. You could also vary the number assignments for the die, e.g. which numbers result in failure or success at each checkpoint.
- Have students pick a specific autoimmune disease and do some research on it. They can try to find out what is known about the causes of the autoimmune disease, how often a person gets it, and how it is treated. See if students can model the cause of the disease using or changing the original model. Tip: One autoimmune disease that is fairly well understood is celiac disease.
- Go into more details about our immune system and find out how antibodies work in the Fighting Infections with Your Immune System lesson plan.


















