Download LS50B Problem Set #7

LS50B Problem Set #7
Due Friday, March 25, 2016 at 5 PM
Problem 1: Genetics warm up
Answer the following questions about core concepts that will appear in more detail on the rest of the Pset.
1. For a single locus, how many alleles can any one diploid individual have? Can there be more than this
number of alleles for this locus in the population as a whole? Why or why not?
2. Imagine a single locus with two alleles: A and a. A is dominant, but it is also homozygous lethal (AA
homozygotes die). What ratio of phenotypes and genotypes would you expect among the offspring of
an Aa x Aa cross?
3. Dont actually do the calculation, but describe the steps you would take to calculate the fraction of
the offspring of a cross between a fly with genotype AaBbCcDdEeFfGgHh and a fly with genotype
AABbccDdEeFfGGhh that have phenotype ABcDefGh (assume that capital letters denote dominant
alleles, and that the seven loci are known to assort independently).
4. How far apart, in centimorgans, are two loci that are located on different chromosomes?
5. What is the difference between a genetic screen and a genetic selection? Under what circumstances
would you perform a screen? A selection?
Problem 2: Genetic Mapping
A time machine takes you back to Thomas Hunt Morgans famous Fly Room. You have found three mutations
in your fruit fly colony, and you would like to know how close the three loci are to each other and how they
are ordered on the genome. Disclaimer: while the three phenotypes described here are real, their genetic
position in this problem set does not correspond to their genetic position in real flies.
First lets consider an arbitrary chromosome with three loci, A, B, and C, for which we know the order along
the chromosome (say its A, then B, then C). Lets say that α and a are the two alleles at locus A, β and b
are the two alleles at locus B, and β and c are the two alleles at locus C. Consider a heterozygous fly that
has alleles a, b, and c on one chromosome and α, β, and γ on the other.
1. With recombination events, how many different versions of this chromosome could this fly pass on to
its offspring?
2. Write down all of the possibilities, and rank them according to how likely they are to occur. Assume
that the genetic distance between A and B is larger than between B and C. Are any of the versions
equally likely? Justify your answers.
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3. Now lets consider your real data. The three phenotypes of interest to you are:
(a) Yellow body: The body of mutant flies is yellow, instead of tan for wild type flies. The yellow
body allele is recessive, so you decide to call the wild type allele B (for body) and the yellow allele
b.
(b) Curly wings: The wings of these flies curl upwards. The curly-winged allele, W, is dominant, and
the wild type allele, w, is recessive.
(c) Purple eyes: Wild type fruit flies have bright red eyes, but flies with this mutation have purple
eyes. The allele for purple eyes is recessive, so you call the wild type allele (for red eyes) R and
the recessive allele r.
Your goal for this problem is to create a genetic map of these three traits. You cross a fly that you
know is heterozygous at all three loci (parent 1) to a fly with the recessive phenotype for all three
traits (parent 2). You obtain the following progeny:
Eyes
purple
red
purple
red
purple
red
purple
red
Body Color
yellow
tan
tan
yellow
yellow
tan
tan
yellow
Phenotype
Wings
curly
wild type
curly
wild type
wild type
curly
wild type
curly
Progeny Number
435
430
68
75
183
205
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4. In your experiment, which alleles for each locus did each type of offspring receive from parent 2 (the
homozygous parent)? What is the phenotype of parent 2?
5. In your data, which two phenotypes are most common? Which two phenotypes are least common?
6. Based on this data, which alleles are present together on each chromosome in parent 1 (the heterozygous
parent)? (For example, one possibility is that all three dominant alleles are on one of the homologous
chromosomes and all three recessive alleles are on the other.) How do you know?
7. Which locus is in the middle? How do you know? Draw the three loci in order, without genetic
distances, and draw each of the two chromosomes present in parent 1.
8. Which offspring phenotypes represent a crossover event between the eye locus and the wing locus?
Between the wing locus and the body color locus? Between the eye locus and the body color locus?
(If you wish, you may mark these answers on the chart in this problem).
9. Use your answer to part 6 to calculate the recombination frequency between each pair of loci. Arrange
the three loci in a genetic map, showing both the order of the three loci along the chromosome and
the genetic distance between them in centimorgans.
10. Is it possible that your map underestimates any of the genetic distances? If so, what type of event
would cause this to occur? Given the genetic distances that you calculated, with what probability
would this event happen?
11. There was no PCR at the time of your experiment. How could you have known that parent 1 was
heterozygous for all three traits before setting up this cross? What was the phenotype of each of the
parents of the heterozygous fly (which we have been calling parent 1)? How did you select parent 1
from among its siblings to use for this cross? Could parent 1 and parent 2 be siblings?
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Problem 3: Real Life Graduate School
Your advisor has just been named an investigator of the Howard Hughes Medical Institute. He decides that
money is no object and based on some information of unusual provenance (see below), that you should begin
your PhD by identifying mutants that affect how yeast deals with lead in its environment. For simplicity,
assume that all mutations in the questions that follow are point mutations (i.e. each mutation changes a single
base pair) and that you have a way of controlling your mutagenesis so that you can produce any genome-wide
mutation rate you desire. Based on the calculations of his college room-mate, a former astrophysicist who
now plays chess for $5 a game in Harvard Square, and consultations at the Porter Square Psychic Studio
(1953 Mass. Ave. and now, alas, closed), your advisor has reached the following conclusions, of which he
reveals only the first two to you:
1. There are five genes that are required for yeast to convert lead chloride (soluble) into lead sulfide (an
insoluble black pigment).
2. Each gene has a mutational target size of 100 bp, meaning that any mutation in any one of these 100
bp will inactivate the gene.
3. Finding mutations that inactivate each of the five genes, and combining these mutations to produce
a quintuple mutant with all five genes inactivated will enable yeast to transmute lead into gold and
allow your advisor to become both richer and more reclusively strange than Hughes himself.
Equipped with such knowledge, you sit down at your lab bench and begin to grind away.
1. What mean number of mutants per gene in the predicted five-gene lead sulfide synthesis pathway do
you need to isolate in order to make 95% sure that you have found at least one mutation in all of the
five genes that your advisor predicts will exist?
2. Your advisor tells you that if you want to be as successful and respected as he, you should be prepared
to screen 20,000 colonies for their ability to produce lead sulfide. He asks you to calculate what
mutation rate (per bp) your mutagenesis will need to achieve if the 20,000 colonies are to reveal the
number of mutants per gene that you calculated in a). (Recall: each colony will grow from a single
cell in your culture). What is the required mutation rate per bp?
3. The yeast genome is 1.2 x 107 bp in size. At the mutation rate that you calculated in b), what is the
average number of mutations (base pair changes anywhere in the genome) that each mutagenized cell
will have? What is the variance in the number of mutations per cell?
Problem 4: Luria Delbruck
You plan to study the effect of various DNA repair mutants on mutation rate by determining the frequency of
mutations that confer resistance to a toxic compound, canavanine. Wild type cells that take up canavanine
from media will mistake canavanine for the amino acid arginine and incorporate it into proteins. Incorporation of canavanine disrupts the function of many important proteins, resulting in cell death. Mutant cells
that lose function in the arginine import machinery are not able to import canavanine into the cell and are
therefore able to grow on media containing canavanine.
Before you can begin your project, your advisor wisely suggests that you do a control experiment to look at
the spontaneous frequency of mutation to canavanine resistance. You inoculate 15 tubes of rich medium each
with a single haploid yeast cell, allow them to grow up to saturation (107 cells per tube), plate the contents
of each tube on canavanine- containing medium, and count the number of canavanine resistant colonies, with
the following results below:
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Tube
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
Can-resistant colonies
0
1
2
16
0
0
1
1
0
2
0
1
0
0
1
Make these assumptions in answering the following questions:
A The cells divide synchronously and are all arrested in G1 when the experiment is complete.
B There is no more than one mutation event in any tube.
C No cell death occurs in the duration of your experiment
1. What is the mean number of mutant cells per tube?
2. Fill in the following table:
Mutation Occured in
Never
Last cell division
Second to last division
Third to last division
Fourth to last division
Fifth to last division
Sixth to last division
Number of cultures (tubes)
3. Calculate the total number of cell division events that took place in each tube.
4. Using your answer above, calculate the frequency of mutation to canavanine resistance/cell/round of
DNA replication. Show your reasoning.
5. What experiment would you perform to determine how many different genes the canavanine resistance
mutations that you have isolated lie in? Be sure to state any assumptions you will need to make about
the effect of the mutations on their gene products.
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Problem 5: Tryptophan Biosynthesis
In this problem we’re going to consider one way in which molecular pathways are inferred from genetic
manipulations. To this end, consider the pathway for tryptophan biosynthesis below.
1. Which of these mutants can grow in the presence of indole? Complete the table below and explain
your answer. The two media contain all other 19 amino acids.
Mutant
Growth on medium
lacking tryptophan
Growth on medium
lacking tryptophan
but containing indole
trp1-1
trp2-1
trp3-1
trp4-1
trp5-1
leu2-1
2. Which of the diploids made by mating the indicated parents can grow on the indicated media? For
the parents, we only show the mutant genes. All other genes can be assumed to be wild type.
Mata
Matα
trp1-1
trp1-12
trp1-12
trp2-1
trp2-1
trp3-1
trp4-1
trp5-1
trp5-14
leu2-1
trp1-1
trp1-1
trp1-12
trp1-1
trp2-6
trp1-1
trp1-1
trp1-1
trp5-1
trp5-1
Growth on medium
lacking tryptophan
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Growth on medium
lacking tryptophan
but containing indole
3. Tryptophan is the largest amino acid, and, like other amino acids, both its amino and carboxyl groups
are ionized at physiological pH, whereas indole is smaller and uncharged. Can you think of a protein
that might be required for Trp- cells to grow with externally supplied tryptophan, but would not
be essential in cells that could make their own tryptophan? How could you screen for mutants that
inactivated this protein?
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