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MIT 7 03 - Problem Set 1

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7.03 Problem Sets 20021 7.03 Problem Set 1Due before 5 PM on Thursday, September 19, 2002 Hand in answers in recitation section or in the box outside the class 1. You and your lab partner have isolated 20 new mutant yeast strains that are defective in synthesis of threonine, an amino acid. These Thr-mutants do not grow on minimal medium, but they do grow on minimal medium supplemented with threonine. Ten of your Thr-mutants (numbered 1 through 10) were isolated in a strain of mating type a (MAT a). The other 10 Thr-mutants (numbered 11 through 20) were isolated in a strain of mating type α (MAT α). You and your lab partner cross each of the MAT a strains to each of the MAT α strains, and you include crosses to the appropriate wild-type strains. Your experimental observations are shown in the table below, where (-) indicates diploids that did not grow on minimal medium and (+) indicates diploids that did grow on minimal medium. (a) Unfortunately, when all the data were collected and the plates discarded, your dog munched on your notebook, swallowing some data. From the data that remains, see if you can reconstruct the full table. strains of mating type α wild- 1 23 45 67 8910 type strains of mating type a wild-type + + + + + - + 11 - + + 12 + - + - -13 - + + + + 14 - - - - -15 - + - + 16 + - + - -17 + - + - -18 + + + - - + 19 + + -20 + - + + -2 (b) Which mutations are recessive? (c) Which mutations are dominant? (d) Which mutations do you know to be in the same gene? (e) Based on these experiments, what is the minimum number of genes required for threonine synthesis? (f) What is the maximum number of genes that these 20 mutants could represent? 2. Being a well-rounded geneticist, you also maintain a colony of chickens. In a cross between a female chicken from a true-breeding strain with three toes per foot and a male from a true-breeding strain with seven toes per foot, all of the F1 progeny have five toes per foot. (a) Based on the information that you have at this stage, is it possible that a single gene determines the differences in toe count among the two parental strains and progeny? If so, what toe counts should appear in the F2 generation and at what frequencies? (b) In fact, when F1 chickens are crossed among themselves, the following F2 progeny are produced: 46 chickens with five toes per foot, 30 chickens with four toes per foot, 28 chickens with six toes per foot, 8 chickens with seven toes per foot, and 7 chickens with three toes per foot. Propose a genetic model to account for the existence of the 5 phenotypic classes and their observed frequencies. In your answer, provide the genotypes of the parental chickens, the F1 chickens, and each class of F2 chickens. (c) Use the Chi-square test to show that the observed frequencies fit with the expected frequencies based on your model. For your answer, give the observed and expected phenotypic ratios, the degrees of freedom, your calculated value for . 2, and a rough estimate of the p value. 3. Your friends Ben and Jane are contemplating having children and seek your genetic counsel. Ben and Jane are unrelated, but both have younger brothers with the same, extremely rare genetic trait. (In fact, Ben and Jane met at a support group meeting for children and families of children with this rare disorder.) Ben’s parents and Jane’s parents are all unaffected.3 (a) Assume that the trait is autosomal recessive with complete penetrance. What is the probability that Ben and Jane’s first child will be affected with the trait? If not affected, what is the probability that the child is a carrier? (b) Assume that the trait is autosomal recessive with 80% penetrance. What is the probability that Ben and Jane’s first child will be affected? (c) Assume that the trait is X-linked recessive with complete penetrance. What is the probability that Ben and Jane’s first child will be affected? What is the probability that the first child will be a carrier? (d) Assume that the trait is autosomal dominant with 80% penetrance in heterozygotes and 100% penetrance in homozygotes. What is the probability that Ben and Jane’s first child will be affected? If not affected, what is the probability that the child is a carrier?1 Answers: 7.03 Problem Set 1 1. You and your lab partner have isolated 20 new mutant yeast strains that are defective in synthesis of threonine, an amino acid. These Thr-mutants do not grow on minimal medium, but they do grow on minimal medium supplemented with threonine. Ten of your Thr-mutants (numbered 1 through 10) were isolated in a strain of mating type a (MAT a). The other 10 Thr-mutants (numbered 11 through 20) were isolated in a strain of mating type α (MAT α). You and your lab partner cross each of the MAT a strains to each of the MAT α strains, and you include crosses to the appropriate wild-type strains. Your experimental observations are shown in the table below, where (-) indicates diploids that did not grow on minimal medium and (+) indicates diploids that did grow on minimal medium. (a) Unfortunately, when all the data were collected and the plates discarded, your dog munched on your notebook, swallowing some data. From the data that remains, see if you can reconstruct the full table. strains of mating type α strains of mating type a wild-type 1 2 3 4 5 6 7 8 9 10 wild-type + + + + + + + + + - + 11 + + - + + - + + + - + 12 + - + + + + - - + - + 13 + - + + + + - - + - + 14 - - - - - - - - - - -15 + + - + + - + + + - + 16 + + + - + + + + + - -17 + + + + - + + + - - + 18 + - + + + + - - + - + 19 + + + + - + + + - -+ 20 + + - + + - + + + - + Note: The table was filled in assuming that there are four complementation groups (see part d). (b) Which mutations are recessive? All except 9 and 14.2 (c) Which mutations are dominant? 9 and 14. (d) Which mutations do you know to be in the same gene? [1, 6, 7, 12, 13, 18] [2, 5, 11, 15, 20] [3, 10, 16] [4, 8, 17, 19] However, there are no data in the table that exclude the possibility that the third and fourth groups listed above actually form one large complementation group, i.e. [3, 10, 16, 4, 8, 17, 19]. Thus there are either three or four complementation groups. (e) …


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MIT 7 03 - Problem Set 1

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