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SimBio Virtual Labsreg

EvoBeakerreg Sickle-Cell Alleles

NOTE TO STUDENTS

This workbook accompanies the SimBio Virtual Labsreg Sickle-Cell Alleles laboratory Only

registered subscribers are authorized to use this material Laboratory subscriptions may not be

shared or transferred

Studentrsquos Name _________________________________

Signature __________________________________

Date __________________________________

This and other SimBio Virtual Labsreg are accessible through SimBiorsquos SimUText Systemreg

Yama Sakha

February 29th 2016



copy 2014 SimBio All Rights Reserved 2

SimBio Virtual Labsreg EvoBeakerreg

Sickle-Cell Alleles

Introduction

Malaria is one of the worldrsquos 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 mosquitorsquos mouth parts pierce the skin of the

unlucky victim The protozoa then swim through the victimrsquos blood until reaching the liver Therethey reproduce and emerge to infect the hostrsquos 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-shapedcells 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 (ie have

the ldquohomozygousrdquo genotype HbSHbS) have a form of hemoglobin that makes their red bloodcells highly prone to becoming sickle-shaped People who inherit one sickle-cell and one normal

hemoglobin allele (ie have the ldquoheterozygousrdquo genotype HbSHbA) 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 doesnrsquot natural selection



SimBio Virtual Labsreg | 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 (HbSHbA) red blood cells that

become infected with the malaria protozoa will sickle The bodyrsquos immune system recognizes thatsomething 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 ldquoheterozygote advantagerdquo





Some Important Terms 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 Terms

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 ldquolocirdquo 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 (GH 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 ldquoHardy-Weinberg proportionsrdquo) 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)





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 ldquoassumptionsrdquo in their models to

simplify the underlying mathematics Hardy and Weinberg assumed that populations are very largeand 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 ldquoHardy-Weinberg equilibriumrdquo 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 toimagine a system in which alleles (eg 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 AA will be (p)(p) = p2 The probability of Aa

will be (p)(q) and of aA will be (q)(p) so the probability of a heterozygote (Aa or aA) will be

(p)(q)+ (q)(p) = 2pq The probability of aa 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 donrsquot 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 ifevolution 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 andor 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-





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 ldquopot of allelesrdquo example in the last section imagine we need to

create 1000 populations of only 5 individuals each by drawing from the bottomless pot of alleles

that was generated by the previous generationrsquos 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 potof 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 ldquofounder effectrdquo) However if we

lumped our 1000 populations together and calculated the allele and genotype frequencies of the

5000-individual population the frequencies would likely be pretty close to those of the generation

upon which the original pot of alleles was based





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 yearto 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 (HbSHbA)





Exercise 1 Starting up

[ 1 ] Read the introductory sections of the workbook

[ 2 ] If you havenrsquot already start SimUTextreg by double-clicking the program icon on your computer or by

selecting it from the Start menu When the program opens enter your Log In 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

ndash The STATISTICS panel 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)

ndash The PARAMETERS panel 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

ndash The CONTROL PANEL buttons at the bottom of the screen run and stop the simulation Yoursquoll

also see the current time-step of the simulation (the number of ldquoyearsrdquo that have passed) is

displayed

[ 4 ] Advance the simulation one year by clicking on the STEP button (between the STOP and GO

buttons) The ldquoTimerdquo should now be ldquo1rdquo (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 villageUse the legend and the following table to determine how the different genotypes of villagers are

represented in your simulation

GENOTYPE DESCRIPTION

SUSCEPTIBLE TO

MALARIA

HAS SICKLE983085CELL

ANEMIA

HbAHbAhomozygous for normal

hemoglobin alleleyes no

HbAHbS heterozygous no no

HbSHbS homozygous forsickle-cell allele

no yes

[ 5 ] Look at the Allele Frequencies graph and notice how the frequencies change over time

[ 51 ] When the HbS allele goes up what happens to the HbA allele

[ 52 ] 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 05034 becauseq^2 = 021

square root of 021 = 0458251-045825 = 054175

054175 = p054175^2 = 0293202934 = p^2 hellip p^2 + q^2 = 02934 + 021 = 05034





[ 6 ] The frequencies will always bounce around a bit but eventually they will stabilize (ie the curve

will level out and then stay within the same range) When they do click on the STOP button in the

Control Panel to stop the model

[ 61 ] What is the frequency of the sickle-cell allele

[ 62 ] What is the frequency of the normal hemoglobin allele

[ 63 ] How many malaria deaths were there in the past five years

[ 64 ] How many sickle-cell deaths were there in the past five years

[ 7 ] What would happen if you could eliminate malaria from the region of the village You can simulate

this experiment by selecting the ldquoDry No Mosquitoesrdquo option next to the map of Africa The map will

highlight the dry regions of the continent Then hit the GO button

[ 71 ] What happened to the allele frequencies and number of deaths Describe in the space

below

[ 8 ] Reset the model by clicking on the RESET button if you wish to repeat your experiment

019

66

75

Since Malaria has been removed from the simulation the allele frequenceies have changed dramaticall

because the frequency of HbSHbS individuals has dropped to 0 and the frequency of HbAHbA has

risen to 1 or 100 The death rate over time has decreased so much because there is no malaria there is

heterozygotes so sickle cell anemia is not present either so the death rate for both of these are zero





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 account for their HbS alleles but there are also

sickle-cell carriersmdashthe individuals that have only one copy of the HbS allele Since they often donrsquot

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

[ 11 ] What is the Hardy-Weinberg equation [If you donrsquot remember consult the introductory

pages of the workbook]

[ 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 doesnrsquot matter which allele you assign ldquo prdquo and which you

assign ldquoqrdquo For the purpose of this exercise if we assign p as the frequency of the normal hemoglobin

allele (HbA) then

[ 21 ] What genotype would each part of the Hardy-Weinberg equation represent

p2

q2

2pq

[ 22 ] What is the genotype of villagers with sickle-cell anemia _________

[ 3 ] Select the ldquoWetSome Mosquitoesrdquo 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]

[ 31 ] Consulting the Statistics table what is the proportion of villagers with sickle-cell

anemia

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

The Hardy weinberg equation determines an estimate for allele frequencies from genotype frequencies or to

estimate genotype frequencies from allele frequencies

Homozygous HbAHbA individual

Homozygous HbSHbS Individual

Heterozygous HbAHbS Individuals

HbSHbS

The proportion of villagers with sickle cell anemia is 11





SHOW YOUR WORK WHEN ANSWERING THE FOLLOWING QUESTIONS

[ 32 ] 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 computerrsquos calculator]

[ 33 ] According to the Hardy-Weinberg equation what is the expected frequency of the

HbA allele [Hint p+q=1]

[ 34 ] What proportion of the population should be susceptible to malaria [Hint Whichgenotype is susceptible to malaria and what is the expected frequency of this genotype]

[ 35 ] According to the Hardy-Weinberg equation what proportion of the population

should be sickle-cell carriers [Hint Sickle-cell carriers are heterozygotes]

[ 4 ] Because you applied the Hardy-Weinberg equation to estimate the frequency of HbS in question[ 32 ] 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

[ 41 ] What are the actual (observed) allele frequencies displayed on your graph

Note If your expected and observed frequencies were extremely different you might want to

recheck your calculations

Square root of 011 which is p^2 = 033 this is p1- 033 = 067 and this is q

So 2(p)(q) = 2(033)(044) = 02904divide that by two because you only want one allele 029042= 01452 + 033 = 04752

The expeced frequency of HbS allele is 4752

p + q = 1

033 + q = 1

1-033 = q

q = 067

The proportion immune to malaria should be around 4489

2(033)(067)

= 04422

=4452

For the HbA allele frequecny the observed is around 062 and for the HbS Allele

frequency is around 043





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 thatrsquos where there are the most mosquitoes In this simulation there is a

02 (20) chance of dying from malaria per decade in the ldquovery wetrdquo 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 ldquodryrdquo 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





[ 1 ] Before you start doing experiments first write down some predictions

[ 11 ] 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 yoursquoll find that the most villagers are

dying from sickle-cell anemia Justify your answer

[ 12 ] When you first start the model the frequency of the sickle-cell allele (HbS) will be 017

Do you think the sickle-cell allele will disappear (ie that the frequency will go to 0) in

any of your runs for the different regions Justify your answer

[ 2 ] Select Regional Differences from the Select an Exercise menu You will first simulate conditions ina village in the ldquoVery Wet Many Mosquitoesrdquo region of Africa Click on GO to run the model until the

allele frequencies level off (give it at least 150 years)

[ 21 ] 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

OF MALARIA DEATHS

IN LAST 5 YEARS

983080FROM STATISTICS 983081

APPROXIMATE

FREQUENCY OF HBA

983080FROM GRAPH983081

OF SICKLE983085CELL

DEATHS IN LAST

5 YEARS

983080FROM STATISTICS983081

Very Wet

Wet

Slightly Wet

Dry

[ 22 ] What happened to the frequency of the sickle-cell allele (HbS) as you decreased the

malaria death rate

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 o

villagers with malaria Thus giving arise to sickle cell anemia deaths

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 pass that allele on to their offspring decreasing the d

of that allele and eventually making it disappear

41 051 57

53 067 29

35 0 0

0 0 0

The frequency of the sickle cell anemia decreased

drastically as we decreased the malaria death rate







Exercise 4 Establishment of New Alleles mdash

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 panel you should see that ldquoInitial number of (sickle-cell) carriersrdquo 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 HbAHbS 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 ldquoDryNo Mosquitoesrdquo region (Malaria Death Rate = 00)

[ 11 ] 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=00

Trial Did the HbS allele disappear

1 Yes No

2 Yes No

3 Yes No

4 Yes No

5 Yes No

6 Yes No

7 Yes No

8 Yes No

9 Yes No

10 Yes No

NoYes

Yes

No

Yes

es

No

No

Yes

Yes







Exercise 5 Just Say ldquoNordquo to Bugs

In this exercise we will provide free and 100 effective prevention and treatment to all Africans

affected by malaria andor sickle cell anemia This will eliminate mortality from both causesmdasharenrsquotwe 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 panel allows you to modify the initial frequency ofthe 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

[ 21 ] 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

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE

[ 3 ] 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

[ 31 ] Which village has the most consistent allele frequencies from run to run

[ 32 ] Which village has the most variable allele frequencies

0 1

062 037

050 050

Small village

Medium Village





[ 4 ] By now you have noticed that the HbS allele often stabilizes at either 0 or 1 (An allele is considered to

have become ldquofixedrdquo in the population when its frequency is 1mdash it will be present in every individual

from that point on because the other allele has disappeared)

[ 41 ] Do you think that decreasing the initial frequency of the HbS allele to 01 will increase

the chance of that allele disappearing Explain your prediction

[ 5 ] Try the experiment Change the initial HbS allele frequency to 01 click RESET and run the model

5-10 times

[ 51 ] Was your prediction in [ 41 ] correct

[ 52 ] Did the HbS allele consistently disappear from all of the villages

[ 53 ] What is genetic drift [Note see the introduction if you need a reminder]

[ 54 ] Which village was influenced the least by genetic drift

[ 55 ] Which of the three villages would be the least likely to have allele frequencies at Hardy-

Weinberg equilibrium Explain

Yes I think that decreasing the Hbs allele to 01 will

increase the chances for it to disappear because once the

desnity of that allele is decreased it has a harder time

being passed onto its offspring so less children have it

eventually making it disappear

No

No

Genetic drift is the change in allele frequencies

due to chance it can be either negative positive

or neutral

The Large village

The village least likely to have allele frequencies at Hardy-Weinberg Equilibrium is the sm

village This is because in a small village Genetic drift is most likely to have an affect on its pop

This prevents the allele frequency is the small village to be apart

of hardy - weinberg equilibrium





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 labbut 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 higherthan 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 mdash 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





Graded Questions

[ 1 ] Use the Select an Exercise menu to launch ldquoGraded Questionsrdquo

[ 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




Wrap Up

In this lab you saw that the environment can have a major effect on what traits yoursquoll see in a

population In this case an environment with lots of mosquitoes and thus lots of malaria selectsfor the sickle-cell allele while a different environment without malaria selects for alleles of the

hemoglobin gene that donrsquot 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 returnedmdashthat 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 Letrsquos 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 wouldnrsquot 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 Thatrsquos why most societies have a

taboo against people marrying close relatives




SimBio Virtual Labsreg EvoBeakerreg

Sickle-Cell Alleles

Introduction

Malaria is one of the worldrsquos 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 mosquitorsquos mouth parts pierce the skin of the

unlucky victim The protozoa then swim through the victimrsquos blood until reaching the liver Therethey reproduce and emerge to infect the hostrsquos 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-shapedcells 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 (ie have

the ldquohomozygousrdquo genotype HbSHbS) have a form of hemoglobin that makes their red bloodcells highly prone to becoming sickle-shaped People who inherit one sickle-cell and one normal

hemoglobin allele (ie have the ldquoheterozygousrdquo genotype HbSHbA) 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 doesnrsquot natural selection
















Population Genetics














p2 + 2pq + q2 = 1






































































































displayed







SUSCEPTIBLE TO

MALARIA


ANEMIA





no yes






square root of 021 = 0458251-045825 = 054175

054175 = p054175^2 = 0293202934 = p^2 hellip p^2 + q^2 = 02934 + 021 = 05034
















below


019

66

75
















in the population








allele (HbA) then


p2

q2

2pq






anemia









HbSHbS



























p + q = 1

033 + q = 1

1-033 = q

q = 067


2(033)(067)

= 04422

=4452







Exercise 3

































REGION

OF MALARIA DEATHS

IN LAST 5 YEARS


APPROXIMATE

FREQUENCY OF HBA


OF SICKLE983085CELL

DEATHS IN LAST

5 YEARS


Very Wet

Wet

Slightly Wet

Dry


malaria death rate







41 051 57

53 067 29

35 0 0

0 0 0










Selection and Drift
















1 Yes No

2 Yes No

3 Yes No

4 Yes No

5 Yes No

6 Yes No

7 Yes No

8 Yes No

9 Yes No

10 Yes No

NoYes

Yes

No

Yes

es

No

No

Yes

Yes





















VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up









































Population Genetics














p2 + 2pq + q2 = 1






































































































displayed







SUSCEPTIBLE TO

MALARIA


ANEMIA





no yes






square root of 021 = 0458251-045825 = 054175

054175 = p054175^2 = 0293202934 = p^2 hellip p^2 + q^2 = 02934 + 021 = 05034
















below


019

66

75
















in the population








allele (HbA) then


p2

q2

2pq






anemia









HbSHbS



























p + q = 1

033 + q = 1

1-033 = q

q = 067


2(033)(067)

= 04422

=4452







Exercise 3

































REGION

OF MALARIA DEATHS

IN LAST 5 YEARS


APPROXIMATE

FREQUENCY OF HBA


OF SICKLE983085CELL

DEATHS IN LAST

5 YEARS


Very Wet

Wet

Slightly Wet

Dry


malaria death rate







41 051 57

53 067 29

35 0 0

0 0 0










Selection and Drift
















1 Yes No

2 Yes No

3 Yes No

4 Yes No

5 Yes No

6 Yes No

7 Yes No

8 Yes No

9 Yes No

10 Yes No

NoYes

Yes

No

Yes

es

No

No

Yes

Yes





















VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up































Population Genetics














p2 + 2pq + q2 = 1






































































































displayed







SUSCEPTIBLE TO

MALARIA


ANEMIA





no yes






square root of 021 = 0458251-045825 = 054175

054175 = p054175^2 = 0293202934 = p^2 hellip p^2 + q^2 = 02934 + 021 = 05034
















below


019

66

75
















in the population








allele (HbA) then


p2

q2

2pq






anemia









HbSHbS



























p + q = 1

033 + q = 1

1-033 = q

q = 067


2(033)(067)

= 04422

=4452







Exercise 3

































REGION

OF MALARIA DEATHS

IN LAST 5 YEARS


APPROXIMATE

FREQUENCY OF HBA


OF SICKLE983085CELL

DEATHS IN LAST

5 YEARS


Very Wet

Wet

Slightly Wet

Dry


malaria death rate







41 051 57

53 067 29

35 0 0

0 0 0










Selection and Drift
















1 Yes No

2 Yes No

3 Yes No

4 Yes No

5 Yes No

6 Yes No

7 Yes No

8 Yes No

9 Yes No

10 Yes No

NoYes

Yes

No

Yes

es

No

No

Yes

Yes





















VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up




















































































































displayed







SUSCEPTIBLE TO

MALARIA


ANEMIA





no yes






square root of 021 = 0458251-045825 = 054175

054175 = p054175^2 = 0293202934 = p^2 hellip p^2 + q^2 = 02934 + 021 = 05034
















below


019

66

75
















in the population








allele (HbA) then


p2

q2

2pq






anemia









HbSHbS



























p + q = 1

033 + q = 1

1-033 = q

q = 067


2(033)(067)

= 04422

=4452







Exercise 3

































REGION

OF MALARIA DEATHS

IN LAST 5 YEARS


APPROXIMATE

FREQUENCY OF HBA


OF SICKLE983085CELL

DEATHS IN LAST

5 YEARS


Very Wet

Wet

Slightly Wet

Dry


malaria death rate







41 051 57

53 067 29

35 0 0

0 0 0










Selection and Drift
















1 Yes No

2 Yes No

3 Yes No

4 Yes No

5 Yes No

6 Yes No

7 Yes No

8 Yes No

9 Yes No

10 Yes No

NoYes

Yes

No

Yes

es

No

No

Yes

Yes





















VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up


















































































displayed







SUSCEPTIBLE TO

MALARIA


ANEMIA





no yes






square root of 021 = 0458251-045825 = 054175

054175 = p054175^2 = 0293202934 = p^2 hellip p^2 + q^2 = 02934 + 021 = 05034
















below


019

66

75
















in the population








allele (HbA) then


p2

q2

2pq






anemia









HbSHbS



























p + q = 1

033 + q = 1

1-033 = q

q = 067


2(033)(067)

= 04422

=4452







Exercise 3

































REGION

OF MALARIA DEATHS

IN LAST 5 YEARS


APPROXIMATE

FREQUENCY OF HBA


OF SICKLE983085CELL

DEATHS IN LAST

5 YEARS


Very Wet

Wet

Slightly Wet

Dry


malaria death rate







41 051 57

53 067 29

35 0 0

0 0 0










Selection and Drift
















1 Yes No

2 Yes No

3 Yes No

4 Yes No

5 Yes No

6 Yes No

7 Yes No

8 Yes No

9 Yes No

10 Yes No

NoYes

Yes

No

Yes

es

No

No

Yes

Yes





















VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up






























































displayed







SUSCEPTIBLE TO

MALARIA


ANEMIA





no yes






square root of 021 = 0458251-045825 = 054175

054175 = p054175^2 = 0293202934 = p^2 hellip p^2 + q^2 = 02934 + 021 = 05034
















below


019

66

75
















in the population








allele (HbA) then


p2

q2

2pq






anemia









HbSHbS



























p + q = 1

033 + q = 1

1-033 = q

q = 067


2(033)(067)

= 04422

=4452







Exercise 3

































REGION

OF MALARIA DEATHS

IN LAST 5 YEARS


APPROXIMATE

FREQUENCY OF HBA


OF SICKLE983085CELL

DEATHS IN LAST

5 YEARS


Very Wet

Wet

Slightly Wet

Dry


malaria death rate







41 051 57

53 067 29

35 0 0

0 0 0










Selection and Drift
















1 Yes No

2 Yes No

3 Yes No

4 Yes No

5 Yes No

6 Yes No

7 Yes No

8 Yes No

9 Yes No

10 Yes No

NoYes

Yes

No

Yes

es

No

No

Yes

Yes





















VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up














































displayed







SUSCEPTIBLE TO

MALARIA


ANEMIA





no yes






square root of 021 = 0458251-045825 = 054175

054175 = p054175^2 = 0293202934 = p^2 hellip p^2 + q^2 = 02934 + 021 = 05034
















below


019

66

75
















in the population








allele (HbA) then


p2

q2

2pq






anemia









HbSHbS



























p + q = 1

033 + q = 1

1-033 = q

q = 067


2(033)(067)

= 04422

=4452







Exercise 3

































REGION

OF MALARIA DEATHS

IN LAST 5 YEARS


APPROXIMATE

FREQUENCY OF HBA


OF SICKLE983085CELL

DEATHS IN LAST

5 YEARS


Very Wet

Wet

Slightly Wet

Dry


malaria death rate







41 051 57

53 067 29

35 0 0

0 0 0










Selection and Drift
















1 Yes No

2 Yes No

3 Yes No

4 Yes No

5 Yes No

6 Yes No

7 Yes No

8 Yes No

9 Yes No

10 Yes No

NoYes

Yes

No

Yes

es

No

No

Yes

Yes





















VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up









































below


019

66

75
















in the population








allele (HbA) then


p2

q2

2pq






anemia









HbSHbS



























p + q = 1

033 + q = 1

1-033 = q

q = 067


2(033)(067)

= 04422

=4452







Exercise 3

































REGION

OF MALARIA DEATHS

IN LAST 5 YEARS


APPROXIMATE

FREQUENCY OF HBA


OF SICKLE983085CELL

DEATHS IN LAST

5 YEARS


Very Wet

Wet

Slightly Wet

Dry


malaria death rate







41 051 57

53 067 29

35 0 0

0 0 0










Selection and Drift
















1 Yes No

2 Yes No

3 Yes No

4 Yes No

5 Yes No

6 Yes No

7 Yes No

8 Yes No

9 Yes No

10 Yes No

NoYes

Yes

No

Yes

es

No

No

Yes

Yes





















VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up





































in the population








allele (HbA) then


p2

q2

2pq






anemia









HbSHbS



























p + q = 1

033 + q = 1

1-033 = q

q = 067


2(033)(067)

= 04422

=4452







Exercise 3

































REGION

OF MALARIA DEATHS

IN LAST 5 YEARS


APPROXIMATE

FREQUENCY OF HBA


OF SICKLE983085CELL

DEATHS IN LAST

5 YEARS


Very Wet

Wet

Slightly Wet

Dry


malaria death rate







41 051 57

53 067 29

35 0 0

0 0 0










Selection and Drift
















1 Yes No

2 Yes No

3 Yes No

4 Yes No

5 Yes No

6 Yes No

7 Yes No

8 Yes No

9 Yes No

10 Yes No

NoYes

Yes

No

Yes

es

No

No

Yes

Yes





















VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up



















































p + q = 1

033 + q = 1

1-033 = q

q = 067


2(033)(067)

= 04422

=4452







Exercise 3

































REGION

OF MALARIA DEATHS

IN LAST 5 YEARS


APPROXIMATE

FREQUENCY OF HBA


OF SICKLE983085CELL

DEATHS IN LAST

5 YEARS


Very Wet

Wet

Slightly Wet

Dry


malaria death rate







41 051 57

53 067 29

35 0 0

0 0 0










Selection and Drift
















1 Yes No

2 Yes No

3 Yes No

4 Yes No

5 Yes No

6 Yes No

7 Yes No

8 Yes No

9 Yes No

10 Yes No

NoYes

Yes

No

Yes

es

No

No

Yes

Yes





















VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up






























Exercise 3

































REGION

OF MALARIA DEATHS

IN LAST 5 YEARS


APPROXIMATE

FREQUENCY OF HBA


OF SICKLE983085CELL

DEATHS IN LAST

5 YEARS


Very Wet

Wet

Slightly Wet

Dry


malaria death rate







41 051 57

53 067 29

35 0 0

0 0 0










Selection and Drift
















1 Yes No

2 Yes No

3 Yes No

4 Yes No

5 Yes No

6 Yes No

7 Yes No

8 Yes No

9 Yes No

10 Yes No

NoYes

Yes

No

Yes

es

No

No

Yes

Yes





















VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up









































REGION

OF MALARIA DEATHS

IN LAST 5 YEARS


APPROXIMATE

FREQUENCY OF HBA


OF SICKLE983085CELL

DEATHS IN LAST

5 YEARS


Very Wet

Wet

Slightly Wet

Dry


malaria death rate







41 051 57

53 067 29

35 0 0

0 0 0










Selection and Drift
















1 Yes No

2 Yes No

3 Yes No

4 Yes No

5 Yes No

6 Yes No

7 Yes No

8 Yes No

9 Yes No

10 Yes No

NoYes

Yes

No

Yes

es

No

No

Yes

Yes





















VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up

































Selection and Drift
















1 Yes No

2 Yes No

3 Yes No

4 Yes No

5 Yes No

6 Yes No

7 Yes No

8 Yes No

9 Yes No

10 Yes No

NoYes

Yes

No

Yes

es

No

No

Yes

Yes





















VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up































Selection and Drift
















1 Yes No

2 Yes No

3 Yes No

4 Yes No

5 Yes No

6 Yes No

7 Yes No

8 Yes No

9 Yes No

10 Yes No

NoYes

Yes

No

Yes

es

No

No

Yes

Yes





















VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up














































VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up












































VILLAGE

SIZE

FREQUENCY

OF HbS

FREQUENCY

OF HbA

SMALL

MEDIUM

LARGE





0 1

062 037

050 050

Small village

Medium Village











5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up




































5-10 times












No

No



or neutral

The Large village
















model

























Graded Questions







Wrap Up





































model

























Graded Questions







Wrap Up






























Graded Questions







Wrap Up





























Wrap Up


























Date post:	07-Aug-2018
Category:	Documents
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