03-511/711 Computational Genomics and Molecular Biology, Fall 2009 1Problem Set 0This homework is intended to be a self-administered placement quiz, to help you (and me) determineif you have the background for the course or need to read additional material.Collaboration is not allowed on this homework. You may consult only with me and theTA. You may refer to textbooks and other written materials, but not to solution sets from previousyears.Due September 1st1. This question asks you to compare properties of typical animal, plant and bacterial cells.It is not necessary to consider unusual spec ies with properties that differ from the cellularorganization of commonly studied organisms.(a) Animal cells: The left most column in the table below gives a list of cellular features,i.e. a molecule, molecular complex or cellular process. The top row lists various cellularcompartments. In each row, put an ‘X’ under each compartment in which the corre-sponding cellular feature occurs in animal cells. For any given row, zero, one, or morethan one ‘X’ may be required.Chloroplast Cytoplasm Mitochondrion NucleusChromosomal crossoverCircular chromsomesDiploid chromosomesDNAmRNARibosomesSplicingTranscriptionTranslationtRNA03-511/711 Computational Genomics and Molecular Biology, Fall 2009 2(b) Bacterial cells: The left most column in the table below gives a list of cellular features,i.e. a molecule, complex or process. The top row lists various c ellular compartments.In each r ow, put an ‘X’ under each compartment in which the corresponding cellularfeature occurs in bacterial cells. For any given row, zero, one, or more than one ‘X’ maybe required.Chloroplast Cytoplasm Mitochondrion NucleusChromosomal crossoverCircular chromsomesDiploid chromosomesDNAmRNARibosomesSplicingTranscriptionTranslationtRNA03-511/711 Computational Genomics and Molecular Biology, Fall 2009 3(c) Plant cells: The left most column in the table below gives a list of cellular features,i.e. a molecule, complex or process. The top row lists various c ellular compartments.In each r ow, put an ‘X’ under each compartment in which the corresponding cellularfeature occurs in plant cells. For any given row, zero, one, or more than one ‘X’ may berequired.Chloroplast Cytoplasm Mitochondrion NucleusChromosomal crossoverCircular chromsomesDiploid chromosomesDNAmRNARibosomesSplicingTranscriptionTranslationtRNA2. An X-linked dominant allele causes vitamin D resistant rickets, a form of rickets due to lowserum phosphorus in humans. A man with vitamin D resistant rickets marri es a normalwoman. What proportion of their sons will have rickets? What proportion of their daughterswill have rickets? (Use the symbol XRfor the mutant and X for the normal or wild typeallele. )03-511/711 Computational Genomics and Molecular Biology, Fall 2009 43. To solve this problem, you will need a table of the genetic code and the following table givingthe physico-chemical properties of the 20 amino acids:small hydrophobic polar basic acidicGly Val Phe Asn Asp LysAla Cys Tyr Gln Glu ArgSer Ile Met HisThr Leu TrpPro(a) Consider the tenth codon in the folloowing (very short) gene:ATG GCA AGA AGC GCA ACA ACG GCG TGT AAG AGA TAAWhat amino acid does it encode and what physico-chemical class does it belong to?(b) Write down all codons that can result from a single base-pair replacement in the tenthcodon.(c) What is the probability that a single base change in this codon results in a substitutionof the associated amino acid for one in the same class?(d) What is the probability that a single base change in this codon leaves the amino acidunchanged?(e) What will be the impact on the protein sequence if the first adenine in the codon isreplaced by a thymine?03-511/711 Computational Genomics and Molecular Biology, Fall 2009 54. Phenylketonuria (PKU) is a recessive disease caused by mutations in the phenylalanine hy-droxylase gene on chromosome 12 in humans. In PKU, phenylalanine, which is toxic to thebrain, is not broken down and accumulates in the blood. Untreated individuals with PKUshow progressive developmental delay in the first year of life, mental retardation, seizures,autistic-like behavior and a peculiar body odor. Approximately 1 individual in 50 is a carr ier.(a) A phenotypically normal man whose father had PKU marries a phenotypically normalwoman from outside the family, and the couple consider having a child.What are the possible genotypes of the husband? Of the husband’s father? Of the wife?(Use the symbol “a” for the mutant and “A” for the normal or wild type allele. )(b) Given this information and the frequency of carriers in the population, what is the chancethat the couple’s first child will have PKU?(c) If the first child does have PKU, what is the probability that the second child will benormal?(d) The incidence of PKU is roughly 1 in 16,000 individuals worldwide. Diagnostic tests ininfants have a 90% false positive rate. The probability of a false negative approacheszero by the third day of life. Assuming that the false negative rate is zero, what is theprobability that a randomly selected infant who tests positive, actually has the disease?(Hint: use Bayes’ theorem)03-511/711 Computational Genomics and Molecular Biology, Fall 2009 65. A clique is an undirected graph G = (V, E) in which every pair of vertices is connected by anedge. Suppose |V | = n.(a) Give the number of edges in G in terms of n.(b) What is the degree of each vertex, v?(c) Let Tbbe the spanning tree obtained from a breadth first search of G. Give the numberof edges in Tbin terms of n.(d) The diameter of a tree is defined to be maxu,v∈V{the shortest path from u to v}. Whatis the diameter of Tb?(e) Let Tdbe the spanning tree obtained from a depth first search of G. Give the numberof edges in Tdin terms of n.(f) What is the diameter of Td?03-511/711 Computational Genomics and Molecular Biology, Fall 2009 76. Assume that the trees in all of the following problems are rooted. A complete binary tree is atree in which every node has either zero or two children. Let T be a complete, rooted binarytree with L leaves.(a) Give the number of edges in T in terms of L.(b) Give the number of nodes in T in terms of L.(c) What is the maximum possible depth of a complete, rooted binary tree with L leaves?What is the minimum possible depth of a complete, rooted binary tree with L leaves?Give your answer in terms of L.(d) Which of the following data structures would
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