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SimBio Virtual Labs®
EvoBeaker®: Sickle-Cell Alleles NOTE TO STUDENTS: This workbook accompanies the SimBio Virtual Labs® Sickle-Cell Alleles laboratory.
Only
ed subscribers are authorized to use this material. Laboratory subscriptions may not be shared or transferred.
Yama Sakha Student’s Name: _________________________________ Signature:
__________________________________
Date:
February 29th 2016 __________________________________
This and other SimBio Virtual Labs® are accessible through SimBio’s SimUText System®. .
.
SimBio Virtual Labs®: EvoBeaker®
Sickle-Cell Alleles Introduction Malaria is one of the world’s most serious diseases, infecting upwards of 300 million people and killing one and a half million people each year. It is most common in Africa but occurs in warmer climates worldwide. People are infected when bitten by mosquitoes carrying certain kinds of protozoa. The malarial protozoa are released as the mosquito’s mouth parts pierce the skin of the unlucky victim. The protozoa then swim through the victim’s blood until reaching the liver. There they reproduce and emerge to infect the host’s red blood cells, after which another mosquito can suck them back up and start the cycle over again. Just about anything that would protect people from malaria would be beneficial for those who live in the malaria-prone areas of the world. And indeed, some people carry an allele of a gene that provides just such a defense. Surprisingly, this anti-malaria allele was tracked down through studies of a seemingly completely unrelated disease: sickle-cell anemia. Sickle-cell anemia is every bit as nasty as malaria. Individuals with this disease have red blood cells that curve into a sickle shape instead of remaining in the circular doughnut shape of normal red blood cells. The sickle-shaped cells tend to get stuck in small blood vessels, blocking blood flow, and halting the supply of oxygen to downstream cells. Unlike malaria, sickle-cell anemia is a genetic disease. Individuals inherit alleles that cause the disease from their parents. Sickle-cell anemia is associated with a gene that encodes part of the hemoglobin molecule (called the Hb gene). Hemoglobin is the protein in red blood cells that carries oxygen. The allele for the normal hemoglobin protein is called HbA and the allele for sickle cell anemia is called HbS. People who inherit the HbS allele from both parents (i.e., have the “homozygous” genotype HbS/HbS) have a form of hemoglobin that makes their red blood cells highly prone to becoming sickle-shaped. People who inherit one sickle-cell and one normal hemoglobin allele (i.e., have the “heterozygous” genotype HbS/HbA) can experience health effects but often the effects are so minor that these people do not realize they carry the HbS allele. Although people with sickle-cell anemia typically die from the disease before they are old enough to reproduce, it is relatively common in some parts of the world. Why doesn’t natural selection
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SimBio Virtual Labs® | Sickle-Cell Alleles
eliminate the disease gene? The answer is that although the sickle-cell allele can cripple your red blood cells, it can also protect you against malaria. Having one copy of HbS (the sickle-cell allele) protects you from becoming sick from malaria. Heterozygous (HbS/HbA) red blood cells that become infected with the malaria protozoa will sickle. The body’s immune system recognizes that something is wrong with the sickled cells and disposes of them. So anyone who is heterozygous for the sickle-cell hemoglobin allele is protected from both malaria and sickle-cell anemia. In genetics lingo, this is an example of a case of “heterozygote advantage.”
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SimBio Virtual Labs® | Sickle-Cell Alleles
Some Important and Concepts Population Genetics The study of how the genes in populations change over time.
Genes, Loci, Alleles, and Gene Pools: A Quick Review of Genes are units of hereditary information composed of DNA (or sometimes RNA) sequences. Genes are found on chromosomes. The place along the chromosome where the gene is located is called the locus (plural=loci). Population geneticists often refer to genes as “loci”. Alleles are alternate versions of genes (they have different DNA sequences which may or may not code for different proteins). The total collection of genes in a population is called a gene pool. Population geneticists often focus on subsets of gene pools, such as all of the alleles at a particular locus.
The Hardy-Weinberg Equation In 1908 an English mathematician (G.H. Hardy) and a German physician (W. Weinberg) independently developed a formula that can be used for estimating allele frequencies from genotype frequencies or to estimate genotype frequencies from allele frequencies (for sexually-reproducing organisms). The formula: p2 + 2pq + q2 = 1 commonly referred to as the Hardy-Weinberg equation, applies when there are two alleles of a gene. The frequency of one allele is designated p and the other is designated q. The first part of the equation (p2) gives the frequency of homozygotes of the first allele, the middle part (2pq) gives the frequency of heterozygotes, and the third part (q2) gives the frequency of homozygotes of the second allele (note: sometimes these are referred to as “Hardy-Weinberg proportions”). If you know any one of the three parts, you can deduce the other two because p + q = 1 (and thus p=1-q and q=1-p). For example, if you know the frequency of homozygotes for the first allele in a population (perhaps because all homozygotes for that allele have a distinctive trait), then you know p2. By taking the square root of that, you get p and by subtracting that value from 1 you get q. Once you know p and q, you can then plug those numbers into the Hardy-Weinberg equation to figure out the expected frequency of heterozygotes (2pq) and homozygotes for the second allele (q2).
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SimBio Virtual Labs® | Sickle-Cell Alleles
The Hardy-Weinberg Theorem and Hardy-Weinberg Equilibrium The Hardy-Weinberg equation resulted from Hardy and Weinberg applying probability theory to basic Mendelian genetics. Theoreticians often apply certain “assumptions” in their models to simplify the underlying mathematics. Hardy and Weinberg assumed that populations are very large and that there is no immigration or emigration. They also assumed that individuals mate at random to produce the next generation. Given these conditions, and no mutations or selection, there will be no evolution, and populations will be at what is known as “Hardy-Weinberg equilibrium”. The frequency of any allele in a population will be the same as the frequency of that allele in the haploid gametes (the eggs and sperm) and all that will happen from one generation to the next is that the alleles will be randomly shuffled and sorted again into pairs. Given this scenario, the probability of the various combinations of alleles (genotypes) will depend entirely on the allele frequencies. One way to think about the Hardy-Weinberg theorem and Hardy-Weinberg equilibrium is to imagine a system in which alleles (e.g., A and a) are drawn in pairs from a pot. The pot contains the same allele frequencies as were present in the previous generation. This pot automatically replaces what is drawn from it so that the allele frequency composition remains constant. Applying probability theory, the chance of producing a genotype is the probability of drawing the first allele times the probability of drawing the second allele. If we substitute in p for the frequency of A and q for the frequency of a, the probability of A/A will be (p)(p) = p2. The probability of A/a will be (p)(q) and of a/A will be (q)(p) so the probability of a heterozygote (A/a or a/A) will be (p)(q)+ (q)(p) = 2pq. The probability of a/a will be (q)(q) = q2. The three probabilities must add up to 1 so p2 + 2pq + q2 = 1. This is how Hardy and Weinberg derived their famous equation.
Deviations From Hardy-Weinberg Equilibrium: Natural Selection and Genetic Drift As described in the previous section, the Hardy-Weinberg theorem applies to large, random-mating populations that do not experience mutation, migration, natural selection, or random genetic drift. Given that many populations in the real world probably don’t conform to those rules, you might wonder about the utility of the Hardy-Weinberg theorem. The power of the Hardy-Weinberg theorem is that it allows us to quantify our expectations of what would happen in populations if evolution were not occurring, which allows us to compare those expectations to what we see in real populations. For example, if we suspect natural selection is acting on a particular allele or genotype in a population, we can determine allele and/or genotype frequencies in the population in one generation and then see how well the frequencies conform with the expectations of Hardy-Weinberg equilibrium in future generations. If the frequencies are not very different than the expected Hardy-
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5
SimBio Virtual Labs® | Sickle-Cell Alleles
Weinberg proportions, that would be evidence that natural selection is not acting on that allele or that the selection pressure is too weak to detect with our data. Genetic drift: the changes in allele frequencies that are due to chance events. Genetic drift is another major factor that causes populations to evolve and thus deviate from Hardy-Weinberg equilibrium. While natural selection always has a positive effect by favoring the disproportionate propagation of beneficial alleles or genotypes, genetic drift can have a positive, neutral, or negative effect. Genetic drift is most pronounced when a population is small, because that is when chance events dominate. Going back to the “pot of alleles” example in the last section, imagine we need to create 1,000 populations of only 5 individuals each by drawing from the bottomless pot of alleles that was generated by the previous generation’s gametes. There will be a lot of variability in allele and genotype frequencies among those populations due to chance (like flipping a coin and getting 4 tails in a row). If any one of the small populations is used as the basis for a new bottomless pot of alleles, the next generation would likely be quite different than the previous one. (In population genetics this describes a special form of genetic drift called a “founder effect.”) However, if we lumped our 1,000 populations together and calculated the allele and genotype frequencies of the 5,000-individual population, the frequencies would likely be pretty close to those of the generation upon which the original pot of alleles was based.
© 2014, SimBio. All Rights Reserved.
6
SimBio Virtual Labs® | Sickle-Cell Alleles
The Sickle-Cell Alleles Model The first several exercises in this lab use a simulation model of individual people in a village. The simulated population hovers around 200 people, though that number rises and falls from year to year. Each year, each female in the population can have one offspring, which, for simplicity, becomes an adult in one year. (Realism suffers occasionally when making models.) Each offspring receives one allele of the Hb gene (described above) from each parent. The number of offspring in the population is limited by how close the population is to its carrying capacity of 200. Each year, each individual has a chance of dying that is independent of either disease, and this chance rises as the population size grows above its carrying capacity. The malaria and sickle-cell death rates also add to the chance of dying for homozygous HbA and HbS individuals, respectively. For simplicity, this model ignores any minor health effects associated with having a single copy of the HbS allele. The model is initialized with 100 individuals (50 male and 50 female) who are homozygous for HbA, and another 50 who are heterozygous (HbS/HbA).
© 2014, SimBio. All Rights Reserved.
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SimBio Virtual Labs® | Sickle-Cell Alleles
Exercise 1: Starting up [1]
Read the introductory sections of the workbook.
[2]
If you haven’t already, start SimUText® by double-clicking the program icon on your computer or by selecting it from the Start menu. When the program opens, enter your information and select the Sickle-Cell Alleles lab from your My Assignments window.
[3]
A village in Africa is depicted on the left side of the screen. Mosquitoes will hover in the blue sky above the village once you start the simulation. The graph entitled Allele Frequencies will plot the frequencies of the normal hemoglobin allele (HbA) and the sickle-cell allele (HbS) in the village over time.
[4]
[5]
–
The STATISTICS will track the number of deaths from malaria and sickle-cell anemia (every 5 years) as well as the frequency of sickle-cell anemia (which is the proportion of villagers that have sickle-cell anemia).
–
The PARAMETERS will allow you to experiment with the initial number of carriers of the sickle-cell allele that enter the village at time-step one, as well as the death rate of villagers afflicted with sickle-cell anemia.
–
The CONTROL buttons at the bottom of the screen run and stop the simulation. You’ll also see the current time-step of the simulation (the number of “years” that have ed) is displayed.
Advance the simulation one year by clicking on the STEP button (between the STOP and GO buttons). The “Time” should now be “1”. (Each time-step in the simulation represents one year in the village). Click the RESET button to reset the simulation to Time 0. Then try running the simulation by clicking on the GO button. You should see simulated people moving around in the village. Use the legend and the following table to determine how the different genotypes of villagers are represented in your simulation. SUSCEPTIBLE TO HAS SICKLE-CELL MALARIA? ANEMIA?
GENOTYPE
DESCRIPTION
HbA/HbA
homozygous for normal hemoglobin allele
yes
no
HbA/HbS
heterozygous
no
no
HbS/HbS
homozygous for sickle-cell allele
no
yes
Look at the Allele Frequencies graph and notice how the frequencies change over time. [ 5.1 ]
When the HbS allele goes up, what happens to the HbA allele?
[ 5.2 ]
What do the two allele frequencies add up to? [Hint: from the introduction, p+q= ?]
Once the HbS allele goes up the HbA allele decreases in frequency The two alleles add up to 0.5034 because q^2 = 0.21 square root of 0.21 = 0.45825 1-0.45825 = 0.54175 0.54175 = p 0.54175^2 = 0.2932 0.2934 = p^2 … p^2 + q^2 = 0.2934 + 0.21 = 0.5034
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SimBio Virtual Labs® | Sickle-Cell Alleles
[6]
The frequencies will always bounce around a bit, but eventually they will stabilize (i.e., the curve will level out and then stay within the same range). When they do, click on the STOP button in the Control to stop the model. [ 6.1 ]
What is the frequency of the sickle-cell allele?
[ 6.2 ]
What is the frequency of the normal hemoglobin allele?
0.19 [ 6.3 ]
How many malaria deaths were there in the past five years?
66 [ 6.4 ]
How many sickle-cell deaths were there in the past five years?
75 [7]
What would happen if you could eliminate malaria from the region of the village? You can simulate this experiment by selecting the “Dry/ No Mosquitoes” option next to the map of Africa. The map will highlight the dry regions of the continent. Then hit the GO button. [ 7.1 ]
What happened to the allele frequencies and number of deaths? Describe in the space below.
Since Malaria has been removed from the simulation the allele frequenceies have changed dramatically because the frequency of HbS/HbS individuals has dropped to 0 and the frequency of HbA/HbA has risen to 1 or 100 %. The death rate over time has decreased so much because there is no malaria there is no heterozygotes so sickle cell anemia is not present either so the death rate for both of these are zero.
[8]
Reset the model by clicking on the RESET button if you wish to repeat your experiment.
© 2014, SimBio. All Rights Reserved.
9
SimBio Virtual Labs® | Sickle-Cell Alleles
Exercise 2: How Many Carriers? Applying Hardy-Weinberg. In the simulated world on your computer screen you can keep track of the frequency of the sickle-cell allele (HbS) over time. In the real world, it is a little more challenging. Since HbS/HbS homozygotes have sickle-cell anemia, we can for their HbS alleles, but there are also sickle-cell carriers—the individuals that have only one copy of the HbS allele. Since they often don’t show any symptoms, is it possible to use the Hardy-Weinberg equation to estimate their frequency in the population?
[1]
Select Hardy-Weinberg from the Select an Exercise menu at the top of your screen. This will load the correct experiment. [ 1.1 ]
What is the Hardy-Weinberg equation? [If you don’t , consult the introductory pages of the workbook.]
The Hardy weinberg equation determines an estimate for allele frequencies from genotype frequencies or to estimate genotype frequencies from allele frequencies [2]
In the Hardy-Weinberg equation, p is the frequency of one of the two alleles and q is the frequency of the other. When you use the equation it doesn’t matter which allele you assign “p” and which you assign “q”. For the purpose of this exercise, if we assign p as the frequency of the normal hemoglobin allele (HbA), then... [ 2.1 ]
[ 2.2 ] [3]
What genotype would each part of the Hardy-Weinberg equation represent? p2 :
Homozygous HbA/HbA individual
q2 :
Homozygous HbS/HbS Individual
2pq :
Heterozygous HbA/HbS Individuals
HbS/HbS What is the genotype of villagers with sickle-cell anemia? _________
Select the “Wet/Some Mosquitoes” option next to the map of Africa. Then click the GO button, allow the model to run for approximately 100 time steps and then click the STOP button. [NOTE: you will use the data you just generated for the rest of the questions in this exercise, so DO NOT RESET!] [ 3.1 ]
Consulting the Statistics table, what is the proportion of villagers with sickle-cell anemia?
The proportion of villagers with sickle cell anemia is 11%
NOTE: The workbook introduction explained how to use the Hardy-Weinberg equation to estimate expected allele and genotype frequencies. YOU WILL PROBABLY FIND IT VERY HELPFUL TO REFER TO THAT SECTION!
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10
SimBio Virtual Labs® | Sickle-Cell Alleles
SHOW YOUR WORK WHEN ANSWERING THE FOLLOWING QUESTIONS: Using information in the Statistics table, according to the Hardy-Weinberg equation, what is the expected frequency of the HbS allele in the village? [Hint: There is a simple relationship between the proportion of villagers with sickle-cell anemia and q. You can click the calculator button at the bottom of the screen to launch your computer’s calculator.] Square root of 0.11 which is p^2 = 0.33 this is p 1- 0.33 = 0.67 and this is q So 2(p)(q) = 2(0.33)(0.44) = 0.2904 divide that by two because you only want one allele 0.2904/2= 0.1452 + 0.33 = 0.4752 The expeced frequency of HbS allele is 47.52% [ 3.3 ] According to the Hardy-Weinberg equation, what is the expected frequency of the HbA allele? [Hint: p+q=1] p+q=1 [ 3.2 ]
0.33 + q = 1 1-0.33 = q q = 0.67 [ 3.4 ]
What proportion of the population should be susceptible to malaria? [Hint: Which genotype is susceptible to malaria and what is the expected frequency of this genotype?]
The proportion immune to malaria should be around 44.89% [ 3.5 ]
[4]
According to the Hardy-Weinberg equation, what proportion of the population should be sickle-cell carriers? [Hint: Sickle-cell carriers are heterozygotes.]
2(0.33)(0.67) = 0.4422 =44.52%
Because you applied the Hardy-Weinberg equation to estimate the frequency of HbS in question [ 3.2 ], your estimate was based on an assumption the the factors that cause populations to deviate from Hardy-Weinberg equilibrium were not strongly impacting your data. In the next section, you will see that at least one assumption of the Hardy-Weinberg equation was almost certainly violated. However, if you check the allele frequencies displayed on your graph, you should see that your estimated frequencies of the HbA and HbS alleles were not too far from what you observed. [ 4.1 ]
What are the actual (observed) allele frequencies displayed on your graph?
For the HbA allele frequecny the observed is around 0,62 and for the HbS Allele frequency is around 0.43
Note: If your expected and observed frequencies were extremely different, you might want to recheck your calculations.
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SimBio Virtual Labs® | Sickle-Cell Alleles
Exercise 3: Where Should Sickle-Cell Anemia Occur? The probability of dying from malaria is greater in the regions of Africa with high annual precipitation because that’s where there are the most mosquitoes. In this simulation there is a 0.2 (20%) chance of dying from malaria per decade in the “very wet” regions of Africa. (The real world death rate may be even higher due to the under-reporting of infant mortality caused by malaria and the lack of centralized medical records in many sub-Saharan African nations.) In “dry” regions of Africa, on the other hand, there is no malaria, so there is no chance of dying from malaria. The simulation also includes two in-between zones with intermediate levels of death from malaria, as shown in the map on the bottom right of the screen. [Note: we have simplified this very complex disease for the purposes of the simulation.]
Next you will use the simulation to explore why sickle-cell anemia is more common in some areas than others. Specifically, you will investigate how the chance of death from malaria relates to the local frequency of sickle-cell alleles. You will run the simulation as you did in the Starting Up exercise (until the allele frequencies stabilize), but this time you will examine allele frequencies with different malaria death rates by activating different regions of the map of Africa. If you click on the buttons or the headings next to the different regions by the map of Africa (on the bottom right side of your screen), you should see that the Malaria Death Rate changes for each region.
© 2014, SimBio. All Rights Reserved.
12
SimBio Virtual Labs® | Sickle-Cell Alleles
[1]
Before you start doing experiments, first write down some predictions: [ 1.1 ]
When you run the simulation for each of the four regions (on the map and listed in the table on the previous page), where do you think you’ll find that the most villagers are dying from sickle-cell anemia? Justify your answer.
My estimate for the region with the highest death rate would be in the very wet area because that is where their is the highest density of mosquitos and the highest density of villagers with malaria. Thus giving arise to sickle cell anemia deaths. [ 1.2 ]
When you first start the model the frequency of the sickle-cell allele (HbS) will be 0.17. Do you think the sickle-cell allele will disappear (i.e., that the frequency will go to 0) in any of your runs for the different regions? Justify your answer.
My estimate is that in the runs that are dry with no mosquitos or few mosquitos the sickle cell allele will disappear because over time there wont be any human to that allele on to their offspring decreasing the density of that allele and eventually making it disappear. [2]
Select Regional Differences from the Select an Exercise menu. You will first simulate conditions in a village in the “Very Wet/ Many Mosquitoes” region of Africa. Click on GO to run the model until the allele frequencies level off (give it at least 150 years). [ 2.1 ]
Find and record the data for the first row in the table below. Reset and repeat the experiment for each of the other regions, filling in the following table with your data:
REGION
41
0.51
Wet
53
0.67
Dry
35 0
# OF SICKLE-CELL DEATHS IN LAST 5 YEARS (FROM STATISTICS)
APPROXIMATE FREQUENCY OF HBA (FROM GRAPH)
Very Wet
Slightly Wet
[ 2.2 ]
# OF MALARIA DEATHS IN LAST 5 YEARS (FROM STATISTICS)
57 29
0 0
0 0
What happened to the frequency of the sickle-cell allele (HbS) as you decreased the malaria death rate?
The frequency of the sickle cell anemia decreased drastically as we decreased the malaria death rate.
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13
SimBio Virtual Labs® | Sickle-Cell Alleles
[ 2.3 ]
Were your predictions in [ 1.1 ] and [ 1.2 ] correct? If not, explain how your data differed from your expectations and try to explain your unexpected results.
Yes my predictions were correct because as the wet weather became more dry this led to less mosquitos which meant less malaria and less sickle cell anemia frequencies arsing
[ 2.4 ]
As the malaria death rate decreased, what happened to the number of sickle-cell deaths?
As the malaria death rate decreased so did the number of sickle cell deaths.
[ 2.5 ]
As you decreased the malaria death rate, what do you think happened to the proportion of villagers with the HbA/HbA genotype? Explain your answer in of natural selection and the “heterozygote advantage”. [Note: the workbook introduction might be helpful here.]
As we decreased the malaria death rate, The proportion of villagers with the HbA/ HbA rose to 100%. This was because since we eliminated the allele that caused malaria eventually over time natural selection eliminated that allele from being in the genotypes of Humans. Since there was no need to be protected from malaria the heterozygote advantage for having one HbS allele and one HbA did not matter. So eventually the HbS allele was not needed to protect from malaria. So HbA started to dominate because there was normal hemoglobin proportions.
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14
SimBio Virtual Labs® | Sickle-Cell Alleles
Exercise 4: Establishment of New Alleles — Selection and Drift In this exercise you will explore what happens when a new allele enters a population, and you will investigate some of the factors that influence whether the new allele will become established. If you look at the Parameters , you should see that “Initial number of (sickle-cell) carriers” is set to 50. What this means is that at the beginning of each of your runs, there are 50 individuals that have the genotype HbA/HbS. All of the HbS alleles in the population start out in those 50 heterozygotes so that means there are 50 copies of the HbS allele at the beginning of each run.
[1]
Select Single Carrier from the Select an Exercise menu. To simulate a single allele entering a village where the allele is not already present, set the initial number of sickle-cell carriers to 1 and then click RESET. For the first set of runs, select the “Dry/No Mosquitoes” region (Malaria Death Rate = 0.0). [ 1.1 ]
Run the model for 100 years and indicate on the table below whether the HbS allele disappeared or became established. RESET and repeat this process nine more times to complete the table. [NOTE: You can tell when the allele has disappeared because the line on the graph will go completely flat.] MALARIA DEATH RATE=0.0 Trial
Did the HbS allele disappear?
1
Yes
2
Yes
3
Yes
4
Yes
5
Yes
6
Yes
7
Yes
8
Yes
9
Yes
10
Yes
No No Yes No Yes No No No Yes No yes No No No No No Yes No Yes No
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15
SimBio Virtual Labs® | Sickle-Cell Alleles
[2]
You probably noticed that the HbS allele disappeared right away in some runs, held out for a while and then disappeared in other runs, and became established at a low but seemingly stable frequency in at least one run. [ 2.1 ]
[3]
Why did the pattern vary from run to run?
It varied from run to run because it up to that single carrier to transmit the allele to others and their offspring.
Repeat the experiment with the malaria death rate set to 0.02 (Slightly Wet/Few Mosquitoes) and then to 0.2 (Very Wet/Many Mosquitoes). [Note: You can quit early if an allele disappears, which you can tell by the line on the graph going completely flat.] [ 3.1 ]
Record your results in the table below, and be certain to click RESET between each and every trial.
Trial
[4]
MALARIA DEATH RATE = 0.02
MALARIA DEATH RATE = 0.2
Did the HbS allele disappear?
Did the HbS allele disappear?
1
Yes
No No
Yes
No No
2
Yes
NoNo
Yes
Noyes
3
Yes
No
Yes
NoNo
4
Yes
Yes No No
Yes
No No
5
Yes
No
Yes
Yes
No No
6
Yes
No
Yes
Yes
NoNo
7
Yes
No
No
Yes
No No
8
Yes
No Yes
Yes
NoNo
9
Yes
No
Yes
Yes
NoNo
10
Yes
No
No
Yes
NoNo
The sickle-cell allele most likely originated when a mutation occurred in a normal hemoglobin allele. [ 4.1 ]
Nobody knows for sure where the sickle-cell allele first established, but based on your results do you think it was more likely in a very wet, wet, slightly wet, or dry climate? Explain.
Based on my results I can estimate that the HbS allele most likely first established in a Very wet climate because of the fact mosquitos are present and malaria is common because of the mosquitos therefore allowing natural selection and evolution to try and fight off malaria by introducing the heterozygote advantage by arising sickle cell and stoping malaria deaths.
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16
SimBio Virtual Labs® | Sickle-Cell Alleles
Exercise 5: Just Say “No” to Bugs! In this exercise we will provide free and 100% effective prevention and treatment to all Africans affected by malaria and/or sickle cell anemia. This will eliminate mortality from both causes—aren’t we amazing?! In our new set of disease-free African villages, natural selection will no longer be a factor in the maintenance or elimination of the HbS allele from populations. The fate of the HbS allele will be left completely to random genetic drift. We will explore what happens to the HbS allele using a module that will allow us to look at allele frequencies in villages of different sizes.
[1]
Select Genetic Drift from the Select an Exercise menu. The three graphs that appear will plot the frequency of the HbS allele over time in villages of different sizes. For simplicity, the HbA allele is not shown. You can easily figure out the frequency of HbA because there are only two alleles and their frequencies must add up to 1. The Parameters allows you to modify the initial frequency of the HbS allele in the three villages, as well as the size of each population.
[2]
Start the Multiple Villages model by hitting the GO button and letting it run until the frequency of the HbS allele in all 3 populations has stabilized. [ 2.1 ]
Record the allele frequencies in the table below. [Note: you need to do some arithmetic to get the HbA allele frequency.] VILLAGE SIZE
FREQUENCY OF HbS
SMALL
0
1
MEDIUM
0.62
0.37
0.50
0.50
LARGE
[3]
FREQUENCY OF HbA
RESET and rerun the model 5-10 more times. Looking at the allele frequencies graph, do you consistently see the allele frequencies you recorded in the table above? [ 3.1 ]
Which village has the most consistent allele frequencies from run to run?
[ 3.2 ]
Which village has the most variable allele frequencies?
Small village
Medium Village
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17
SimBio Virtual Labs® | Sickle-Cell Alleles
[4]
By now you have noticed that the HbS allele often stabilizes at either 0 or 1. (An allele is considered to have become “fixed” in the population when its frequency is 1— it will be present in every individual from that point on because the other allele has disappeared.) [ 4.1 ]
Do you think that decreasing the initial frequency of the HbS allele to 0.1 will increase the chance of that allele disappearing? Explain your prediction.
Yes I think that decreasing the Hbs allele to 0.1 will increase the chances for it to disappear because once the desnity of that allele is decreased it has a harder time being ed onto its offspring so less children have it eventually making it disappear.
[5]
Try the experiment. Change the initial HbS allele frequency to 0.1, click RESET, and run the model 5-10 times. [ 5.1 ]
Was your prediction in [ 4.1 ] correct?
[ 5.2 ]
Did the HbS allele consistently disappear from all of the villages?
[ 5.3 ]
What is genetic drift? [Note: see the introduction if you need a reminder.]
No
No
Genetic drift is the change in allele frequencies due to chance, it can be either negative, positive or neutral. [ 5.4 ]
Which village was influenced the least by genetic drift?
The Large village [ 5.5 ]
Which of the three villages would be the least likely to have allele frequencies at HardyWeinberg equilibrium? Explain.
The village least likely to have allele frequencies at Hardy-Weinberg Equilibrium is the small village. This is because in a small village Genetic drift is most likely to have an affect on its population. This prevents the allele frequency is the small village to be apart of hardy - weinberg equilibrium.
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18
SimBio Virtual Labs® | Sickle-Cell Alleles
Optional: More Things To Try You have probably noticed by now that there is a final experiment called On Your Own. This simulation lets you experiment with many of the same phenomena as the previous parts of the lab, but gives you more options. When you run this model, you can follow the frequency of one of two alleles in 5 identical populations (same number of people, same selection pressures, etc.) at the same time. These could be alleles of any gene, and so are called A and a. If you prefer, you can think of them as HbS and HbA. The frequency of the A allele in each population is shown on the graph in different colors for each population. Here are the different factors you can adjust in this model: PARAMETER
EXPLANATION
Fitness of AA
The fitness of the AA genotype relative to the other two genotypes. If this value is higher than the others, then this genotype is more fit.
Fitness of Aa
The fitness of the Aa genotype relative to the other two genotypes. To create a scenario with a heterozygote advantage, make this fitness higher than that of AA or aa.
Fitness of aa
The fitness of the aa genotype relative to the other two genotypes.
Initial Frequency of A
The initial frequency of the A allele. Must be between 0 and 1. The initial frequency of a is, of course, (1 — Initial Freq of A).
Immigration
The proportion of the population comprising immigrants each generation.
Frequency of the A allele in the immigrant population
The frequency of the A allele in immigrating populations.
Population Size
The size of the population. Population size is held fixed (every individual is exactly replaced every generation).
Mutation rate from A to a
The rate of mutation from A to a alleles per generation.
Mutation rate from a to A
The rate of mutation from a to A alleles per generation.
There are many different questions you could ask using this model. For instance, you could take a more systematic look at how population size influences drift. What happens if there is a small amount of selection with a large population size? How about a small amount of selection with just a small population size? How much migration do you need of one allele in order to counteract selection for the other allele? Do mutations substantially affect the frequencies of each allele? And so on. Use your imagination!
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SimBio Virtual Labs® | Sickle-Cell Alleles
Graded Questions [1]
Use the Select an Exercise menu to launch “Graded Questions”.
[2]
Enter your answers for each of the questions and click the SUBMIT ALL button. NOTE: You must answer all of the questions before you click the SUBMIT ALL button.
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20
SimBio Virtual Labs® | Sickle-Cell Alleles
Wrap Up In this lab, you saw that the environment can have a major effect on what traits you’ll see in a population. In this case, an environment with lots of mosquitoes and thus lots of malaria, selects for the sickle-cell allele, while a different environment without malaria selects for alleles of the hemoglobin gene that don’t sickle. The frequencies of the different hemoglobin alleles in a population depend on the prevalence of malaria and on the relative risk of having sickled red blood cells. The allele frequencies will change as the environment changes. For example, if the weather becomes drier there will be fewer mosquitoes, and the sickle-cell frequency will decrease. But, as you saw, even if malaria disappears, the sickle-cell allele might survive for quite a while as a rare allele. That might be quite important if malaria returned—that formerly rare allele could then rescue a population. This idea, that having many rare alleles around might protect populations from changes in the environment, is very important in conservation biology. In an endangered species whose population is getting very small, much of the diversity of alleles will disappear due to genetic drift. (You witnessed this happen again and again to the HbS allele in small villages in Exercise 5.) If the sickle-cell allele is relatively common in a population, there is a pretty good chance that two people who marry will both be heterozygous for the allele. Their offspring will have a one in four chance of getting sickle-cell anemia; each has a one in two chance of inheriting the sickle-cell allele from their mother and a one in two chance of inheriting it from their father. But, if the allele is fairly rare, it will also be rare that both parents will be heterozygous for the allele; therefore, only very occasionally will a child be born with sickle-cell anemia. However, that is only true if the parents are not related to each other. Let’s say a father with the sickle-cell allele has a daughter and a son. There is a pretty good chance that both of them inherited the sickle-cell allele from their father, but, since they would both be heterozygous, they wouldn’t get sick. However, if the daughter and son had children together, even if the sickle-cell allele is rare in the population, their offspring would have a one in four chance of being homozygous for sickle-cell. The chance of getting a genetic disease is much higher if your parents are part of the same family. That’s why most societies have a taboo against people marrying close relatives.
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21
EvoBeaker®: Sickle-Cell Alleles NOTE TO STUDENTS: This workbook accompanies the SimBio Virtual Labs® Sickle-Cell Alleles laboratory.
Only
ed subscribers are authorized to use this material. Laboratory subscriptions may not be shared or transferred.
Yama Sakha Student’s Name: _________________________________ Signature:
__________________________________
Date:
February 29th 2016 __________________________________
This and other SimBio Virtual Labs® are accessible through SimBio’s SimUText System®. .
.
SimBio Virtual Labs®: EvoBeaker®
Sickle-Cell Alleles Introduction Malaria is one of the world’s most serious diseases, infecting upwards of 300 million people and killing one and a half million people each year. It is most common in Africa but occurs in warmer climates worldwide. People are infected when bitten by mosquitoes carrying certain kinds of protozoa. The malarial protozoa are released as the mosquito’s mouth parts pierce the skin of the unlucky victim. The protozoa then swim through the victim’s blood until reaching the liver. There they reproduce and emerge to infect the host’s red blood cells, after which another mosquito can suck them back up and start the cycle over again. Just about anything that would protect people from malaria would be beneficial for those who live in the malaria-prone areas of the world. And indeed, some people carry an allele of a gene that provides just such a defense. Surprisingly, this anti-malaria allele was tracked down through studies of a seemingly completely unrelated disease: sickle-cell anemia. Sickle-cell anemia is every bit as nasty as malaria. Individuals with this disease have red blood cells that curve into a sickle shape instead of remaining in the circular doughnut shape of normal red blood cells. The sickle-shaped cells tend to get stuck in small blood vessels, blocking blood flow, and halting the supply of oxygen to downstream cells. Unlike malaria, sickle-cell anemia is a genetic disease. Individuals inherit alleles that cause the disease from their parents. Sickle-cell anemia is associated with a gene that encodes part of the hemoglobin molecule (called the Hb gene). Hemoglobin is the protein in red blood cells that carries oxygen. The allele for the normal hemoglobin protein is called HbA and the allele for sickle cell anemia is called HbS. People who inherit the HbS allele from both parents (i.e., have the “homozygous” genotype HbS/HbS) have a form of hemoglobin that makes their red blood cells highly prone to becoming sickle-shaped. People who inherit one sickle-cell and one normal hemoglobin allele (i.e., have the “heterozygous” genotype HbS/HbA) can experience health effects but often the effects are so minor that these people do not realize they carry the HbS allele. Although people with sickle-cell anemia typically die from the disease before they are old enough to reproduce, it is relatively common in some parts of the world. Why doesn’t natural selection
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SimBio Virtual Labs® | Sickle-Cell Alleles
eliminate the disease gene? The answer is that although the sickle-cell allele can cripple your red blood cells, it can also protect you against malaria. Having one copy of HbS (the sickle-cell allele) protects you from becoming sick from malaria. Heterozygous (HbS/HbA) red blood cells that become infected with the malaria protozoa will sickle. The body’s immune system recognizes that something is wrong with the sickled cells and disposes of them. So anyone who is heterozygous for the sickle-cell hemoglobin allele is protected from both malaria and sickle-cell anemia. In genetics lingo, this is an example of a case of “heterozygote advantage.”
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3
SimBio Virtual Labs® | Sickle-Cell Alleles
Some Important and Concepts Population Genetics The study of how the genes in populations change over time.
Genes, Loci, Alleles, and Gene Pools: A Quick Review of Genes are units of hereditary information composed of DNA (or sometimes RNA) sequences. Genes are found on chromosomes. The place along the chromosome where the gene is located is called the locus (plural=loci). Population geneticists often refer to genes as “loci”. Alleles are alternate versions of genes (they have different DNA sequences which may or may not code for different proteins). The total collection of genes in a population is called a gene pool. Population geneticists often focus on subsets of gene pools, such as all of the alleles at a particular locus.
The Hardy-Weinberg Equation In 1908 an English mathematician (G.H. Hardy) and a German physician (W. Weinberg) independently developed a formula that can be used for estimating allele frequencies from genotype frequencies or to estimate genotype frequencies from allele frequencies (for sexually-reproducing organisms). The formula: p2 + 2pq + q2 = 1 commonly referred to as the Hardy-Weinberg equation, applies when there are two alleles of a gene. The frequency of one allele is designated p and the other is designated q. The first part of the equation (p2) gives the frequency of homozygotes of the first allele, the middle part (2pq) gives the frequency of heterozygotes, and the third part (q2) gives the frequency of homozygotes of the second allele (note: sometimes these are referred to as “Hardy-Weinberg proportions”). If you know any one of the three parts, you can deduce the other two because p + q = 1 (and thus p=1-q and q=1-p). For example, if you know the frequency of homozygotes for the first allele in a population (perhaps because all homozygotes for that allele have a distinctive trait), then you know p2. By taking the square root of that, you get p and by subtracting that value from 1 you get q. Once you know p and q, you can then plug those numbers into the Hardy-Weinberg equation to figure out the expected frequency of heterozygotes (2pq) and homozygotes for the second allele (q2).
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4
SimBio Virtual Labs® | Sickle-Cell Alleles
The Hardy-Weinberg Theorem and Hardy-Weinberg Equilibrium The Hardy-Weinberg equation resulted from Hardy and Weinberg applying probability theory to basic Mendelian genetics. Theoreticians often apply certain “assumptions” in their models to simplify the underlying mathematics. Hardy and Weinberg assumed that populations are very large and that there is no immigration or emigration. They also assumed that individuals mate at random to produce the next generation. Given these conditions, and no mutations or selection, there will be no evolution, and populations will be at what is known as “Hardy-Weinberg equilibrium”. The frequency of any allele in a population will be the same as the frequency of that allele in the haploid gametes (the eggs and sperm) and all that will happen from one generation to the next is that the alleles will be randomly shuffled and sorted again into pairs. Given this scenario, the probability of the various combinations of alleles (genotypes) will depend entirely on the allele frequencies. One way to think about the Hardy-Weinberg theorem and Hardy-Weinberg equilibrium is to imagine a system in which alleles (e.g., A and a) are drawn in pairs from a pot. The pot contains the same allele frequencies as were present in the previous generation. This pot automatically replaces what is drawn from it so that the allele frequency composition remains constant. Applying probability theory, the chance of producing a genotype is the probability of drawing the first allele times the probability of drawing the second allele. If we substitute in p for the frequency of A and q for the frequency of a, the probability of A/A will be (p)(p) = p2. The probability of A/a will be (p)(q) and of a/A will be (q)(p) so the probability of a heterozygote (A/a or a/A) will be (p)(q)+ (q)(p) = 2pq. The probability of a/a will be (q)(q) = q2. The three probabilities must add up to 1 so p2 + 2pq + q2 = 1. This is how Hardy and Weinberg derived their famous equation.
Deviations From Hardy-Weinberg Equilibrium: Natural Selection and Genetic Drift As described in the previous section, the Hardy-Weinberg theorem applies to large, random-mating populations that do not experience mutation, migration, natural selection, or random genetic drift. Given that many populations in the real world probably don’t conform to those rules, you might wonder about the utility of the Hardy-Weinberg theorem. The power of the Hardy-Weinberg theorem is that it allows us to quantify our expectations of what would happen in populations if evolution were not occurring, which allows us to compare those expectations to what we see in real populations. For example, if we suspect natural selection is acting on a particular allele or genotype in a population, we can determine allele and/or genotype frequencies in the population in one generation and then see how well the frequencies conform with the expectations of Hardy-Weinberg equilibrium in future generations. If the frequencies are not very different than the expected Hardy-
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5
SimBio Virtual Labs® | Sickle-Cell Alleles
Weinberg proportions, that would be evidence that natural selection is not acting on that allele or that the selection pressure is too weak to detect with our data. Genetic drift: the changes in allele frequencies that are due to chance events. Genetic drift is another major factor that causes populations to evolve and thus deviate from Hardy-Weinberg equilibrium. While natural selection always has a positive effect by favoring the disproportionate propagation of beneficial alleles or genotypes, genetic drift can have a positive, neutral, or negative effect. Genetic drift is most pronounced when a population is small, because that is when chance events dominate. Going back to the “pot of alleles” example in the last section, imagine we need to create 1,000 populations of only 5 individuals each by drawing from the bottomless pot of alleles that was generated by the previous generation’s gametes. There will be a lot of variability in allele and genotype frequencies among those populations due to chance (like flipping a coin and getting 4 tails in a row). If any one of the small populations is used as the basis for a new bottomless pot of alleles, the next generation would likely be quite different than the previous one. (In population genetics this describes a special form of genetic drift called a “founder effect.”) However, if we lumped our 1,000 populations together and calculated the allele and genotype frequencies of the 5,000-individual population, the frequencies would likely be pretty close to those of the generation upon which the original pot of alleles was based.
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6
SimBio Virtual Labs® | Sickle-Cell Alleles
The Sickle-Cell Alleles Model The first several exercises in this lab use a simulation model of individual people in a village. The simulated population hovers around 200 people, though that number rises and falls from year to year. Each year, each female in the population can have one offspring, which, for simplicity, becomes an adult in one year. (Realism suffers occasionally when making models.) Each offspring receives one allele of the Hb gene (described above) from each parent. The number of offspring in the population is limited by how close the population is to its carrying capacity of 200. Each year, each individual has a chance of dying that is independent of either disease, and this chance rises as the population size grows above its carrying capacity. The malaria and sickle-cell death rates also add to the chance of dying for homozygous HbA and HbS individuals, respectively. For simplicity, this model ignores any minor health effects associated with having a single copy of the HbS allele. The model is initialized with 100 individuals (50 male and 50 female) who are homozygous for HbA, and another 50 who are heterozygous (HbS/HbA).
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7
SimBio Virtual Labs® | Sickle-Cell Alleles
Exercise 1: Starting up [1]
Read the introductory sections of the workbook.
[2]
If you haven’t already, start SimUText® by double-clicking the program icon on your computer or by selecting it from the Start menu. When the program opens, enter your information and select the Sickle-Cell Alleles lab from your My Assignments window.
[3]
A village in Africa is depicted on the left side of the screen. Mosquitoes will hover in the blue sky above the village once you start the simulation. The graph entitled Allele Frequencies will plot the frequencies of the normal hemoglobin allele (HbA) and the sickle-cell allele (HbS) in the village over time.
[4]
[5]
–
The STATISTICS will track the number of deaths from malaria and sickle-cell anemia (every 5 years) as well as the frequency of sickle-cell anemia (which is the proportion of villagers that have sickle-cell anemia).
–
The PARAMETERS will allow you to experiment with the initial number of carriers of the sickle-cell allele that enter the village at time-step one, as well as the death rate of villagers afflicted with sickle-cell anemia.
–
The CONTROL buttons at the bottom of the screen run and stop the simulation. You’ll also see the current time-step of the simulation (the number of “years” that have ed) is displayed.
Advance the simulation one year by clicking on the STEP button (between the STOP and GO buttons). The “Time” should now be “1”. (Each time-step in the simulation represents one year in the village). Click the RESET button to reset the simulation to Time 0. Then try running the simulation by clicking on the GO button. You should see simulated people moving around in the village. Use the legend and the following table to determine how the different genotypes of villagers are represented in your simulation. SUSCEPTIBLE TO HAS SICKLE-CELL MALARIA? ANEMIA?
GENOTYPE
DESCRIPTION
HbA/HbA
homozygous for normal hemoglobin allele
yes
no
HbA/HbS
heterozygous
no
no
HbS/HbS
homozygous for sickle-cell allele
no
yes
Look at the Allele Frequencies graph and notice how the frequencies change over time. [ 5.1 ]
When the HbS allele goes up, what happens to the HbA allele?
[ 5.2 ]
What do the two allele frequencies add up to? [Hint: from the introduction, p+q= ?]
Once the HbS allele goes up the HbA allele decreases in frequency The two alleles add up to 0.5034 because q^2 = 0.21 square root of 0.21 = 0.45825 1-0.45825 = 0.54175 0.54175 = p 0.54175^2 = 0.2932 0.2934 = p^2 … p^2 + q^2 = 0.2934 + 0.21 = 0.5034
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SimBio Virtual Labs® | Sickle-Cell Alleles
[6]
The frequencies will always bounce around a bit, but eventually they will stabilize (i.e., the curve will level out and then stay within the same range). When they do, click on the STOP button in the Control to stop the model. [ 6.1 ]
What is the frequency of the sickle-cell allele?
[ 6.2 ]
What is the frequency of the normal hemoglobin allele?
0.19 [ 6.3 ]
How many malaria deaths were there in the past five years?
66 [ 6.4 ]
How many sickle-cell deaths were there in the past five years?
75 [7]
What would happen if you could eliminate malaria from the region of the village? You can simulate this experiment by selecting the “Dry/ No Mosquitoes” option next to the map of Africa. The map will highlight the dry regions of the continent. Then hit the GO button. [ 7.1 ]
What happened to the allele frequencies and number of deaths? Describe in the space below.
Since Malaria has been removed from the simulation the allele frequenceies have changed dramatically because the frequency of HbS/HbS individuals has dropped to 0 and the frequency of HbA/HbA has risen to 1 or 100 %. The death rate over time has decreased so much because there is no malaria there is no heterozygotes so sickle cell anemia is not present either so the death rate for both of these are zero.
[8]
Reset the model by clicking on the RESET button if you wish to repeat your experiment.
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9
SimBio Virtual Labs® | Sickle-Cell Alleles
Exercise 2: How Many Carriers? Applying Hardy-Weinberg. In the simulated world on your computer screen you can keep track of the frequency of the sickle-cell allele (HbS) over time. In the real world, it is a little more challenging. Since HbS/HbS homozygotes have sickle-cell anemia, we can for their HbS alleles, but there are also sickle-cell carriers—the individuals that have only one copy of the HbS allele. Since they often don’t show any symptoms, is it possible to use the Hardy-Weinberg equation to estimate their frequency in the population?
[1]
Select Hardy-Weinberg from the Select an Exercise menu at the top of your screen. This will load the correct experiment. [ 1.1 ]
What is the Hardy-Weinberg equation? [If you don’t , consult the introductory pages of the workbook.]
The Hardy weinberg equation determines an estimate for allele frequencies from genotype frequencies or to estimate genotype frequencies from allele frequencies [2]
In the Hardy-Weinberg equation, p is the frequency of one of the two alleles and q is the frequency of the other. When you use the equation it doesn’t matter which allele you assign “p” and which you assign “q”. For the purpose of this exercise, if we assign p as the frequency of the normal hemoglobin allele (HbA), then... [ 2.1 ]
[ 2.2 ] [3]
What genotype would each part of the Hardy-Weinberg equation represent? p2 :
Homozygous HbA/HbA individual
q2 :
Homozygous HbS/HbS Individual
2pq :
Heterozygous HbA/HbS Individuals
HbS/HbS What is the genotype of villagers with sickle-cell anemia? _________
Select the “Wet/Some Mosquitoes” option next to the map of Africa. Then click the GO button, allow the model to run for approximately 100 time steps and then click the STOP button. [NOTE: you will use the data you just generated for the rest of the questions in this exercise, so DO NOT RESET!] [ 3.1 ]
Consulting the Statistics table, what is the proportion of villagers with sickle-cell anemia?
The proportion of villagers with sickle cell anemia is 11%
NOTE: The workbook introduction explained how to use the Hardy-Weinberg equation to estimate expected allele and genotype frequencies. YOU WILL PROBABLY FIND IT VERY HELPFUL TO REFER TO THAT SECTION!
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10
SimBio Virtual Labs® | Sickle-Cell Alleles
SHOW YOUR WORK WHEN ANSWERING THE FOLLOWING QUESTIONS: Using information in the Statistics table, according to the Hardy-Weinberg equation, what is the expected frequency of the HbS allele in the village? [Hint: There is a simple relationship between the proportion of villagers with sickle-cell anemia and q. You can click the calculator button at the bottom of the screen to launch your computer’s calculator.] Square root of 0.11 which is p^2 = 0.33 this is p 1- 0.33 = 0.67 and this is q So 2(p)(q) = 2(0.33)(0.44) = 0.2904 divide that by two because you only want one allele 0.2904/2= 0.1452 + 0.33 = 0.4752 The expeced frequency of HbS allele is 47.52% [ 3.3 ] According to the Hardy-Weinberg equation, what is the expected frequency of the HbA allele? [Hint: p+q=1] p+q=1 [ 3.2 ]
0.33 + q = 1 1-0.33 = q q = 0.67 [ 3.4 ]
What proportion of the population should be susceptible to malaria? [Hint: Which genotype is susceptible to malaria and what is the expected frequency of this genotype?]
The proportion immune to malaria should be around 44.89% [ 3.5 ]
[4]
According to the Hardy-Weinberg equation, what proportion of the population should be sickle-cell carriers? [Hint: Sickle-cell carriers are heterozygotes.]
2(0.33)(0.67) = 0.4422 =44.52%
Because you applied the Hardy-Weinberg equation to estimate the frequency of HbS in question [ 3.2 ], your estimate was based on an assumption the the factors that cause populations to deviate from Hardy-Weinberg equilibrium were not strongly impacting your data. In the next section, you will see that at least one assumption of the Hardy-Weinberg equation was almost certainly violated. However, if you check the allele frequencies displayed on your graph, you should see that your estimated frequencies of the HbA and HbS alleles were not too far from what you observed. [ 4.1 ]
What are the actual (observed) allele frequencies displayed on your graph?
For the HbA allele frequecny the observed is around 0,62 and for the HbS Allele frequency is around 0.43
Note: If your expected and observed frequencies were extremely different, you might want to recheck your calculations.
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11
SimBio Virtual Labs® | Sickle-Cell Alleles
Exercise 3: Where Should Sickle-Cell Anemia Occur? The probability of dying from malaria is greater in the regions of Africa with high annual precipitation because that’s where there are the most mosquitoes. In this simulation there is a 0.2 (20%) chance of dying from malaria per decade in the “very wet” regions of Africa. (The real world death rate may be even higher due to the under-reporting of infant mortality caused by malaria and the lack of centralized medical records in many sub-Saharan African nations.) In “dry” regions of Africa, on the other hand, there is no malaria, so there is no chance of dying from malaria. The simulation also includes two in-between zones with intermediate levels of death from malaria, as shown in the map on the bottom right of the screen. [Note: we have simplified this very complex disease for the purposes of the simulation.]
Next you will use the simulation to explore why sickle-cell anemia is more common in some areas than others. Specifically, you will investigate how the chance of death from malaria relates to the local frequency of sickle-cell alleles. You will run the simulation as you did in the Starting Up exercise (until the allele frequencies stabilize), but this time you will examine allele frequencies with different malaria death rates by activating different regions of the map of Africa. If you click on the buttons or the headings next to the different regions by the map of Africa (on the bottom right side of your screen), you should see that the Malaria Death Rate changes for each region.
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12
SimBio Virtual Labs® | Sickle-Cell Alleles
[1]
Before you start doing experiments, first write down some predictions: [ 1.1 ]
When you run the simulation for each of the four regions (on the map and listed in the table on the previous page), where do you think you’ll find that the most villagers are dying from sickle-cell anemia? Justify your answer.
My estimate for the region with the highest death rate would be in the very wet area because that is where their is the highest density of mosquitos and the highest density of villagers with malaria. Thus giving arise to sickle cell anemia deaths. [ 1.2 ]
When you first start the model the frequency of the sickle-cell allele (HbS) will be 0.17. Do you think the sickle-cell allele will disappear (i.e., that the frequency will go to 0) in any of your runs for the different regions? Justify your answer.
My estimate is that in the runs that are dry with no mosquitos or few mosquitos the sickle cell allele will disappear because over time there wont be any human to that allele on to their offspring decreasing the density of that allele and eventually making it disappear. [2]
Select Regional Differences from the Select an Exercise menu. You will first simulate conditions in a village in the “Very Wet/ Many Mosquitoes” region of Africa. Click on GO to run the model until the allele frequencies level off (give it at least 150 years). [ 2.1 ]
Find and record the data for the first row in the table below. Reset and repeat the experiment for each of the other regions, filling in the following table with your data:
REGION
41
0.51
Wet
53
0.67
Dry
35 0
# OF SICKLE-CELL DEATHS IN LAST 5 YEARS (FROM STATISTICS)
APPROXIMATE FREQUENCY OF HBA (FROM GRAPH)
Very Wet
Slightly Wet
[ 2.2 ]
# OF MALARIA DEATHS IN LAST 5 YEARS (FROM STATISTICS)
57 29
0 0
0 0
What happened to the frequency of the sickle-cell allele (HbS) as you decreased the malaria death rate?
The frequency of the sickle cell anemia decreased drastically as we decreased the malaria death rate.
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13
SimBio Virtual Labs® | Sickle-Cell Alleles
[ 2.3 ]
Were your predictions in [ 1.1 ] and [ 1.2 ] correct? If not, explain how your data differed from your expectations and try to explain your unexpected results.
Yes my predictions were correct because as the wet weather became more dry this led to less mosquitos which meant less malaria and less sickle cell anemia frequencies arsing
[ 2.4 ]
As the malaria death rate decreased, what happened to the number of sickle-cell deaths?
As the malaria death rate decreased so did the number of sickle cell deaths.
[ 2.5 ]
As you decreased the malaria death rate, what do you think happened to the proportion of villagers with the HbA/HbA genotype? Explain your answer in of natural selection and the “heterozygote advantage”. [Note: the workbook introduction might be helpful here.]
As we decreased the malaria death rate, The proportion of villagers with the HbA/ HbA rose to 100%. This was because since we eliminated the allele that caused malaria eventually over time natural selection eliminated that allele from being in the genotypes of Humans. Since there was no need to be protected from malaria the heterozygote advantage for having one HbS allele and one HbA did not matter. So eventually the HbS allele was not needed to protect from malaria. So HbA started to dominate because there was normal hemoglobin proportions.
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14
SimBio Virtual Labs® | Sickle-Cell Alleles
Exercise 4: Establishment of New Alleles — Selection and Drift In this exercise you will explore what happens when a new allele enters a population, and you will investigate some of the factors that influence whether the new allele will become established. If you look at the Parameters , you should see that “Initial number of (sickle-cell) carriers” is set to 50. What this means is that at the beginning of each of your runs, there are 50 individuals that have the genotype HbA/HbS. All of the HbS alleles in the population start out in those 50 heterozygotes so that means there are 50 copies of the HbS allele at the beginning of each run.
[1]
Select Single Carrier from the Select an Exercise menu. To simulate a single allele entering a village where the allele is not already present, set the initial number of sickle-cell carriers to 1 and then click RESET. For the first set of runs, select the “Dry/No Mosquitoes” region (Malaria Death Rate = 0.0). [ 1.1 ]
Run the model for 100 years and indicate on the table below whether the HbS allele disappeared or became established. RESET and repeat this process nine more times to complete the table. [NOTE: You can tell when the allele has disappeared because the line on the graph will go completely flat.] MALARIA DEATH RATE=0.0 Trial
Did the HbS allele disappear?
1
Yes
2
Yes
3
Yes
4
Yes
5
Yes
6
Yes
7
Yes
8
Yes
9
Yes
10
Yes
No No Yes No Yes No No No Yes No yes No No No No No Yes No Yes No
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15
SimBio Virtual Labs® | Sickle-Cell Alleles
[2]
You probably noticed that the HbS allele disappeared right away in some runs, held out for a while and then disappeared in other runs, and became established at a low but seemingly stable frequency in at least one run. [ 2.1 ]
[3]
Why did the pattern vary from run to run?
It varied from run to run because it up to that single carrier to transmit the allele to others and their offspring.
Repeat the experiment with the malaria death rate set to 0.02 (Slightly Wet/Few Mosquitoes) and then to 0.2 (Very Wet/Many Mosquitoes). [Note: You can quit early if an allele disappears, which you can tell by the line on the graph going completely flat.] [ 3.1 ]
Record your results in the table below, and be certain to click RESET between each and every trial.
Trial
[4]
MALARIA DEATH RATE = 0.02
MALARIA DEATH RATE = 0.2
Did the HbS allele disappear?
Did the HbS allele disappear?
1
Yes
No No
Yes
No No
2
Yes
NoNo
Yes
Noyes
3
Yes
No
Yes
NoNo
4
Yes
Yes No No
Yes
No No
5
Yes
No
Yes
Yes
No No
6
Yes
No
Yes
Yes
NoNo
7
Yes
No
No
Yes
No No
8
Yes
No Yes
Yes
NoNo
9
Yes
No
Yes
Yes
NoNo
10
Yes
No
No
Yes
NoNo
The sickle-cell allele most likely originated when a mutation occurred in a normal hemoglobin allele. [ 4.1 ]
Nobody knows for sure where the sickle-cell allele first established, but based on your results do you think it was more likely in a very wet, wet, slightly wet, or dry climate? Explain.
Based on my results I can estimate that the HbS allele most likely first established in a Very wet climate because of the fact mosquitos are present and malaria is common because of the mosquitos therefore allowing natural selection and evolution to try and fight off malaria by introducing the heterozygote advantage by arising sickle cell and stoping malaria deaths.
© 2014, SimBio. All Rights Reserved.
16
SimBio Virtual Labs® | Sickle-Cell Alleles
Exercise 5: Just Say “No” to Bugs! In this exercise we will provide free and 100% effective prevention and treatment to all Africans affected by malaria and/or sickle cell anemia. This will eliminate mortality from both causes—aren’t we amazing?! In our new set of disease-free African villages, natural selection will no longer be a factor in the maintenance or elimination of the HbS allele from populations. The fate of the HbS allele will be left completely to random genetic drift. We will explore what happens to the HbS allele using a module that will allow us to look at allele frequencies in villages of different sizes.
[1]
Select Genetic Drift from the Select an Exercise menu. The three graphs that appear will plot the frequency of the HbS allele over time in villages of different sizes. For simplicity, the HbA allele is not shown. You can easily figure out the frequency of HbA because there are only two alleles and their frequencies must add up to 1. The Parameters allows you to modify the initial frequency of the HbS allele in the three villages, as well as the size of each population.
[2]
Start the Multiple Villages model by hitting the GO button and letting it run until the frequency of the HbS allele in all 3 populations has stabilized. [ 2.1 ]
Record the allele frequencies in the table below. [Note: you need to do some arithmetic to get the HbA allele frequency.] VILLAGE SIZE
FREQUENCY OF HbS
SMALL
0
1
MEDIUM
0.62
0.37
0.50
0.50
LARGE
[3]
FREQUENCY OF HbA
RESET and rerun the model 5-10 more times. Looking at the allele frequencies graph, do you consistently see the allele frequencies you recorded in the table above? [ 3.1 ]
Which village has the most consistent allele frequencies from run to run?
[ 3.2 ]
Which village has the most variable allele frequencies?
Small village
Medium Village
© 2014, SimBio. All Rights Reserved.
17
SimBio Virtual Labs® | Sickle-Cell Alleles
[4]
By now you have noticed that the HbS allele often stabilizes at either 0 or 1. (An allele is considered to have become “fixed” in the population when its frequency is 1— it will be present in every individual from that point on because the other allele has disappeared.) [ 4.1 ]
Do you think that decreasing the initial frequency of the HbS allele to 0.1 will increase the chance of that allele disappearing? Explain your prediction.
Yes I think that decreasing the Hbs allele to 0.1 will increase the chances for it to disappear because once the desnity of that allele is decreased it has a harder time being ed onto its offspring so less children have it eventually making it disappear.
[5]
Try the experiment. Change the initial HbS allele frequency to 0.1, click RESET, and run the model 5-10 times. [ 5.1 ]
Was your prediction in [ 4.1 ] correct?
[ 5.2 ]
Did the HbS allele consistently disappear from all of the villages?
[ 5.3 ]
What is genetic drift? [Note: see the introduction if you need a reminder.]
No
No
Genetic drift is the change in allele frequencies due to chance, it can be either negative, positive or neutral. [ 5.4 ]
Which village was influenced the least by genetic drift?
The Large village [ 5.5 ]
Which of the three villages would be the least likely to have allele frequencies at HardyWeinberg equilibrium? Explain.
The village least likely to have allele frequencies at Hardy-Weinberg Equilibrium is the small village. This is because in a small village Genetic drift is most likely to have an affect on its population. This prevents the allele frequency is the small village to be apart of hardy - weinberg equilibrium.
© 2014, SimBio. All Rights Reserved.
18
SimBio Virtual Labs® | Sickle-Cell Alleles
Optional: More Things To Try You have probably noticed by now that there is a final experiment called On Your Own. This simulation lets you experiment with many of the same phenomena as the previous parts of the lab, but gives you more options. When you run this model, you can follow the frequency of one of two alleles in 5 identical populations (same number of people, same selection pressures, etc.) at the same time. These could be alleles of any gene, and so are called A and a. If you prefer, you can think of them as HbS and HbA. The frequency of the A allele in each population is shown on the graph in different colors for each population. Here are the different factors you can adjust in this model: PARAMETER
EXPLANATION
Fitness of AA
The fitness of the AA genotype relative to the other two genotypes. If this value is higher than the others, then this genotype is more fit.
Fitness of Aa
The fitness of the Aa genotype relative to the other two genotypes. To create a scenario with a heterozygote advantage, make this fitness higher than that of AA or aa.
Fitness of aa
The fitness of the aa genotype relative to the other two genotypes.
Initial Frequency of A
The initial frequency of the A allele. Must be between 0 and 1. The initial frequency of a is, of course, (1 — Initial Freq of A).
Immigration
The proportion of the population comprising immigrants each generation.
Frequency of the A allele in the immigrant population
The frequency of the A allele in immigrating populations.
Population Size
The size of the population. Population size is held fixed (every individual is exactly replaced every generation).
Mutation rate from A to a
The rate of mutation from A to a alleles per generation.
Mutation rate from a to A
The rate of mutation from a to A alleles per generation.
There are many different questions you could ask using this model. For instance, you could take a more systematic look at how population size influences drift. What happens if there is a small amount of selection with a large population size? How about a small amount of selection with just a small population size? How much migration do you need of one allele in order to counteract selection for the other allele? Do mutations substantially affect the frequencies of each allele? And so on. Use your imagination!
© 2014, SimBio. All Rights Reserved.
19
SimBio Virtual Labs® | Sickle-Cell Alleles
Graded Questions [1]
Use the Select an Exercise menu to launch “Graded Questions”.
[2]
Enter your answers for each of the questions and click the SUBMIT ALL button. NOTE: You must answer all of the questions before you click the SUBMIT ALL button.
© 2014, SimBio. All Rights Reserved.
20
SimBio Virtual Labs® | Sickle-Cell Alleles
Wrap Up In this lab, you saw that the environment can have a major effect on what traits you’ll see in a population. In this case, an environment with lots of mosquitoes and thus lots of malaria, selects for the sickle-cell allele, while a different environment without malaria selects for alleles of the hemoglobin gene that don’t sickle. The frequencies of the different hemoglobin alleles in a population depend on the prevalence of malaria and on the relative risk of having sickled red blood cells. The allele frequencies will change as the environment changes. For example, if the weather becomes drier there will be fewer mosquitoes, and the sickle-cell frequency will decrease. But, as you saw, even if malaria disappears, the sickle-cell allele might survive for quite a while as a rare allele. That might be quite important if malaria returned—that formerly rare allele could then rescue a population. This idea, that having many rare alleles around might protect populations from changes in the environment, is very important in conservation biology. In an endangered species whose population is getting very small, much of the diversity of alleles will disappear due to genetic drift. (You witnessed this happen again and again to the HbS allele in small villages in Exercise 5.) If the sickle-cell allele is relatively common in a population, there is a pretty good chance that two people who marry will both be heterozygous for the allele. Their offspring will have a one in four chance of getting sickle-cell anemia; each has a one in two chance of inheriting the sickle-cell allele from their mother and a one in two chance of inheriting it from their father. But, if the allele is fairly rare, it will also be rare that both parents will be heterozygous for the allele; therefore, only very occasionally will a child be born with sickle-cell anemia. However, that is only true if the parents are not related to each other. Let’s say a father with the sickle-cell allele has a daughter and a son. There is a pretty good chance that both of them inherited the sickle-cell allele from their father, but, since they would both be heterozygous, they wouldn’t get sick. However, if the daughter and son had children together, even if the sickle-cell allele is rare in the population, their offspring would have a one in four chance of being homozygous for sickle-cell. The chance of getting a genetic disease is much higher if your parents are part of the same family. That’s why most societies have a taboo against people marrying close relatives.
© 2014, SimBio. All Rights Reserved.
21
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