Learning Scenario - Cystic Fibrosis (Excel)

Basic Model:

Description

This is a system model demonstrating two parents passing on a recessive or dominant allele to their offspring. This model attempts to demonstrate a real world scenario by providing two parents with randomly selected traits and genetically calculating the verdict of whether the parents should have children. Cystic Fibrosis is one example of such a recessive trait, and the model helps to simulate the processes that parents must go through in order to decide whether they can have kids without passing on such a disorder. There are no variables to manipulate, but the simulation may be run multiple times and studied for patterns.

Background Information

Dominant genes are always expressed in humans, since they trump the recessive allele if it is present. If both genes are recessive, the person expresses the recessive allele, since it does not have any other instructions with how to display that trait. Therefore, if someone inherits a recessive genetic disorder from both parents, he or she will express that disorder. Cystic Fibrosis (CF) is a rare, genetic disorder that can affect those who inherit two recessive alleles from their parents. About 30,000 children and adults have cystic fibrosis and about one in thirty one Americans are carriers for the CF gene. CF is a disorder where mucus will build up in organs of the body and prevent necessary processes from working. This model attempts to demonstrate the possibilities for passing on the disease.

Science/Math

The fundamental principle behind this model is HAVE = HAD + CHANGE. For each fun of the simulation, the following things happen:

1. Each parent in columns A and B have their dominance or recessiveness calculated by a random variable (<0.5, recessive; else, dominant)
2. Column C is calculated to alert the parents that they can either have more kids or stop having kids to prevent passing on the recessive trait. This is based off of whether both parents pass on the recessive allele or not

The CHANGE includes both the random number generation and the simple observations done to determine the offspring's inherited traits. While the random numbers represent two random people's alleles, it is not directly applicable to the CF studies that are done in real life. On the other hand, the method of studying the genotypes in would-be-parents is what scientists use to test for those carrying the CF gene.

Teaching Strategies

An effective way of introducing this model is to relate the topic to a manifestation that the students are already familiar with. Ask students to count the number of people who have brown hair and study the class percentage of people who do not. The number of people who do not have brown hair should be less than those who do. Have the students answer these questions in order to start with a better idea of genetic inheritance:

1. What do you think will happen if a kid inherits two dominant alleles from his or her parents? One dominant, one recessive? Two recessive? Explain.
2. If a kid inherits one dominant and one recessive allele, what happens to the recessive allele? Is it still there?
3. What does the ratio of those who express the recessive trait to those who do not represent?
4. One dominant trait is having brown hair. How many people in the classroom have brown hair? What percent of the class does not have brown hair? Is this larger or smaller than the expected ratio?

Have students write down their hypotheses for each of these questions so that they can be tested when using the model.

Implementation:

How to use the model

While there are no parameters that can be changed, this model allows the user to refresh the random variables and thereby come up with new dominant or recessive traits in parents. In order to do both of these, simply press [Ctrl]+ [=]. Immediately, new random variables will be calculated and affect the dominant or recessive traits in parents, which will in turn determine the verdict for the parents' offspring inheritance. **Note: Make sure that under Excel > preferences > calculation: be sure to select calculate sheets "Manually", to check the box marked "Limit Iteration" and set "Maximum Iterations" = 1. For more information on Excel, reference the Excel tutorial at: http://shodor.org/tutorials/excel/IntroToExcel.

Learning Objectives

1. Understand the idea of genotypes and phenotypes in relation to dominant and recessive inheritance
2. Understand the probabilities involved in passing on a recessive genetic disorder

Objective 1

This objective encompasses the overall concept that the model attempts to teach the user. When two parents contribute dominant or recessive alleles to their offspring, the recessive trait will always be "hidden" by the dominant trait. When two parents both have the recessive trait, it is possible for their kids to get the disease. If only one has the trait, the dominant allele from the other parent will overpower the recessive allele, thus having kids without the disease is possible. Ask the following questions to guide their discovery:

1. Study the verdict in column C of the model. When does the model suggest that the parents stop having kids? What are the similarities the parents share that should stop having kids?
2. Does the model suggest that all parents with a recessive trait stop having kids? Why or why not?
3. Assuming the parents do not have the disease themselves, what do you think would happen if parents who both have recessive alleles have a kid? Are there multiple possibilities? Explain.
4. If a child were to inherit one recessive allele and one dominant allele, could that child's offspring possibly contract the disease? How?

Objective 2

Scientists use Punnett squares to predict the hypothetical offspring of two parents. These squares can be used to also predict the probability of a child inheriting CF. Since the genetic disease is an autosomal recessive trait, the probability of inheriting the disease from two carrier parents is .25. Provide and explain the Punnett square to students. Use the Punnett square to calculate the predicted amount of parents who would be recommended to stop having kids. Compare this to the calculations in the model (.5 chance of one parent being dominant or recessive). Ask the following questions:

1. Calculate the number of couples who are advised to stop. Run the simulation multiple times, paying attention to the number of people who are advised to stop having kids. About what is the average percentage of people who are advised to stop? Do you know why this is?
2. Double click on one of the cells in the parent column. Find the chance that someone would have a recessive gene. Calculate the percentage that any random couple (who don't have the disease themselves) would pass on the disease. Is this number close to the percentage that you calculated in Question 1? Why or why not?
3. Your teacher will introduce a Punnett square to you. Use the Punnett square to calculate the predicted percentages of parents with different genotypes who have a chance of passing on the disease. Are these numbers similar to the number calculated in Question 4? Explain.
4. How could the predicted percentages be changed? What factors would change this?
5. How could someone use this method in real life screening for Cystic Fibrosis, an autosomal recessive disorder?

Extensions:

1. Explore the mathematical equations for populations at Hardy Weinberg equilibrium
2. Extend the idea of alleles to chromosomes and karyotypes with an activity
3. Understand the application of random numbers to the real world

Extension 1

The RATIO column in the model calculated the percentage of people who expressed the recessive phenotype in a population (the populations of kids). At Hardy Weinberg Equilibrium, populations have set relationships for the frequency of each allele. The equations p2+2pq+q2=1 and p+q=1 governs these relationships with p being the frequency of the dominant allele and q being the frequency of the recessive allele. Have students research the (hypothetical) requirements for Hardy Weinberg Equilibrium and calculate the frequency of the dominant allele after running the simulation once.

1. What are the five requirements for Hardy Weinberg Equilibrium? What does it mean to say that a population is in equilibrium?
2. What variable does the probability calculated in Objective 2 question 2 represent in the equation p2+2pq+q2=1? How would you use this equation and p+q=1 to find the ratio of kids who have both the recessive and dominant alleles?
3. What does it mean to be homozygous? To be heterozygous? Does the ratio display the percentage of individuals who are homozygous dominant, homozygous recessive, or heterozygous?

Extension 2

The Cystic Fibrosis model deals with genes that specifically code for a certain trait. The following activity should help in teaching students the overall importance of genes as well as understanding the process by which genetic disorders are found. When someone has their genes karyotyped, their chromosomes are set out in size order. If there is an abnormality in one of the 43 human chromosomes (23 in haploid cells) or there is the wrong number of chromosomes, scientists can detect genetic disorders. The following activity simulates that process:

1. Prepare and cut out 23 chromosomes, simulating the chromosomes in a human gamete
2. Make a mutation on one or more of the chromosomes, such as a deletion, duplication, etc.
3. Have the students order the chromosomes in size order, from largest to smallest
4. Ask the students to find the chromosome with the mutation and explain what happened in relation to cell reproduction (meiosis in this case)
5. Make sure students understand the connection between this activity and the genes that were calculated in the Cystic Fibrosis model. Ask the following questions after completion of the activity:
   • Where are the genes located on each chromosome? Are there any mutations to any of the genes? Explain.
   • What is the difference between a gene and allele? How are these related to chromosomes?
   • How can karyotyping be used to find genetic disorders?

Extension 3

This extension deals with the random number aspect of the Cystic Fibrosis model. Since random numbers from a random number generator are traditionally not random, the resulting ratio obtained could be affected by bias in the computer program that is generating numbers. Give students the following links to research this idea and supply the HotBits Genuine Random number generator for comparison. Ask the following questions:

1. What is a pseudorandom number? Would you say that pseudorandom numbers determine the genes of the Mom and Dad in the Cystic Fibrosis model?
2. Why can a computer not output truly random numbers? Explain.
3. Compare the random number generator below to the HotBits number generator. What is the difference between the two? Are the HotBits numbers truly random?

Supplemental Materials:

1. Fourmilab Hotbits
2. Random Number Generator

Related Models

• Dominant Recessive Sampling
  

  The Dominant Recessive Sampling model is a similar model to Cystic Fibrosis, but it includes more topics as well. The model calculates the parents and offspring similar to the Cystic Fibrosis model, but it extends the list of data points in order to explore the Law of Large numbers. When more samples are factored into the calculations, the actual percent of people with the recessive trait grows much closer to the predicted number. While the purpose of the Cystic Fibrosis model is to simulate parental screening, this model analyzes the parents' offspring, and the traits passed on do not have to be tied to a deadly disease that prevents parents from having children.

• Pseudo Random Numbers
  

  The random numbers in the Monte Carlo Integrals model used x-values that were randomly generated by Excel. The Pseudo Random Numbers Model explains the flaws in generating random numbers on a computer and how the numbers generated were not truly random. This model will be a good complement to Extension 3 and will allow students to better understand the flaws in the model.

• DNA Sequence Analysis
  

  This model allows students to explore genes more in depth by studying the different nucleotide sequences on DNA strands. Users are given strands of DNA sequences and the model calculates the number of the specified nucleotide (C, G, A, T). The process moves in a step-by-step fashion, just as many biological processes do to inspect the strand for errors. The Cystic Fibrosis model focused only on the traits that come from genes, but this one will expand that into the actual sequences that make up and code for each individual allele.