Problem SetsFall 19937.03 Problem Set 1due in class Friday, September 24All four problems will be graded. Some parts of these problems are quite difficult, ifyou get stuck try doing the other problems and come back to the hard parts later.1. Consider the following experiments designed to identify genes in yeast that arerequired for the synthesis of the amino acid arginine. Yeast mutants that are defectivein arginine synthesis and are therefore called Arg- can be identified because they cannot grow on medium that is not supplemented with arginine. Ten Arg- strains areisolated by screening mutagenized yeast colonies for those colonies that grow onminimal medium with arginine but will not grow on minimal medium without arginine.Five of the mutants are isolated in a haploid yeast strain of mating type cz (strains 1 - 5)and five of the mutants are isolated in a haploid strain of mating type a (strains 6 - 10).Remember that an a strain will only mate with an o_strain and that a will not mate witha and (z will not mate with o_. Pairwise matings are performed between differentstrains as indicated in the table below. When the resulting diploid can not grow onminimal medium without arginine a (-) is indicated at the intersection of the twoparental strains. When the resulting diploid can grow without arginine a (+) isindicated.strains of mating type o_1 2 3 4 5 wildtype6 + + -- + -- +7 + + + - -- +strains ofmatingtypea 8 + + -- + -- +9 + + + - -- +10 + + -- + -- +wildtype + + + + - +(a) Explain the unusual behavior of strain 5. Are any of the complementation testswith this mutant meaningful?(b) How many different genes or, more precisely, complementation groups arerepresented by these ten mutations. Indicate which mutations are in the samecomplementation group.(¢) In order to change its mating type, strain 1 is crossed to wild type, the diploid issporulated, and a haploid spore colony is isolated that is Arg- and mating type a.It is now possible to perform complementation tests between mutation 1 and themutations in the strains of mating type o_.Based on the results of these tests shownbelow, how many Arg- complementation groups do you now think that there are?mating type oc1 2 3 4 5mating type a 1 - -- + + -2. (a) In a large mouse breeding experiment, an unusual mouse with six digits onthe front paws is discovered in one of the litters. When this mouse is crossed to a wildtype mouse about half of the F1 are normal and half have six digits on the front paws.Describe in detail the crosses that you would perform in order to produce a truebreeding strain of mice with the six digit trait.(b) In a separate line of experiments in another lab, a true breeding strain has beendeveloped that exhibits six digits on the hind paws. Thinking that the two mutationsmight be related you decide to perform a cross between mice of the two strains. All ofthe F1 progeny of this cross have six digits on both the front and back paws. There aretwo reasonable explanations for this result. First the two mutant strains could havedominant alleles in two different genes. Alternatively the two different strains couldhave codominant alleles of the same gene. (If this second possibility does not makesense to you, try to relate these ideas to multiple alleles for the ABO blood antigens inhumans described on p. 89-90 of Suzuki. ) When the F1 mice are crossed, about halfof the F2 mice have six digits on both front and back paws, some have six digits in thefront, some have six digits on the back and a few are normal. Based on these resultswhich explanation best fits the data? Which phenotypic class of F2 mice is mostimportant in your decision and why?(¢) When you propagate the true breeding strains from parts (a) and (b) you noticethat although for the most part the traits appear to breed true, about 5% of the progenyappear to be wild type. When these apparently wild type mice are crossed to true wildtype mice most of the resulting progeny are mutant. These results can be explained asa result of incomplete penetrance. Propose a cross that would allow the twopossibilities outlined in part (b) to be distinguished even with 5% incompletepenetrance and give the outcomes that you would expect for the two cases. There area number of reasonable solutions to this problem.3. (a) You are a geneticist studying a rare human disorder that appears to beinherited. Presented with the following family where two sons (11-1 and 11-3) have thedisorder you propose that the trait is either X-linked recessive or autosomal recessive.Since you have been trained at MIT you decide to put these ideas to a quantitativetest. Using the chi-squared test, determine the probability that the inheritance patternexhibited by children I1-1 - 11-5 is significantly different from that expected forautosomal recessive inheritance. Can you draw a conclusion about the mode ofinheritance based on this family?I O =female1 2[--] = maleII _1 2 3 4 5HI1 2 3(b) Your plan is to perform a more significant test of the mode of inheritance bycollecting data from more families that exhibit the disorder. Before conducting thisstudy, it would be helpful to know how much additional data is needed to get asignificant answer. Assume that the disorder is due to an X-linked recessive allele.On average, how many children from families exhibiting the disorder would you needto look at in order to show a pattern of inheritance that differs significantly (ie p<.05)from the pattern expected for an autosomal recessive trait? (Assume equalfrequencies of males and females among the children in families exhibiting thedisorder.)4. Sickle cell anemia is one of the most prevalent genetic diseases debilitating about 1.8per 1000 U. S. blacks. The pathology of this disease stems from the circulating erythrocyteswhich have a sickled shape that obstructs capillaries and causes excessive erythrocytedestruction. The genetic basis of sickle cell disease was unraveled when it was discoveredthat within the U. S. population there was a milder and much more prevalent form of thedisease known as sicklemia. Sicklemic individuals are usually have no symptoms of anemiaand their blood cells in circulation are not sickled. However, blood removed from sicklemicindividuals will sickle under conditions of unusually low oxygen pressure. On testing ofrandom blood samples itturns out that about 8% of U. S. blacks are sicklemic. Incidentally,the sicklemic condition was first appreciated during World War II when many
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