03-511/711 Computational Genomics and Molecular Biology, Fall 2003 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 notallowed on this homework. Due Thursday, September 4th1. 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 fifth codon in the folloowing (very short) gene:ATGGCAAGAAGCGCAACAACGGCGTGTAAGAGTTAAWhat amino acid does it encode and what physico-chemical class does it belong to?(b) How many possible base changes can occur in this codon?(c) What is the probability that a single base change in this codon replaces the associatedamino acid for one in the same class?(d) What is the probability that a single base change in this codon leaves the amino acidunchanged?03-511/711 Computational Genomics and Molecular Biology, Fall 2003 22. Short questions:(a) What properties do viruses have in common with living organisms? In what way areviruses different from living organisms?(b) What is the relationship between the number of genes and the number of proteins in anorganism? Is your answer the same for bacteria and eukaryotes?(c) Does recombination (crossing over) typically occur in bacteria? Why or why not?(d) State two basic differences between protein synthesis in prokaryotes and eukaryotes.(e) What is the ribosome and what is its role in the cell?(f) What is the difference between tRNA and mRNA?03-511/711 Computational Genomics and Molecular Biology, Fall 2003 33. An X-linked dominant allele causes hypophosphatemia (low serum phosphorus) in humans.A man with hypophosphatemia marries a normal woman. What proportion of their sons willhave hypophosphatemia?4. An X-linked recessive allele Xcproduces a red-green colorblindness in humans. A normalwoman whose father was colorblind marries a colorblind man. The allele for normal vision isdenoted as XN.(a) What genotypes are possible for the mother of the colorblind man?(b) What are the chances that the first child from this marriage will be a colorblind boy?(Assume a 50-50 sex ratio at birth.)(c) Of the girls produced by these parents, what proportion can be expected to be colorblind?(d) What proportion of the children (sex unspecified) of these parents can be expected tohave normal color vision?03-511/711 Computational Genomics and Molecular Biology, Fall 2003 45. (a) What is the maximum number of leaves in a binary tree of depth d? How many edgesare in this tree?(b) What is the minimum number of leaves in binary a tree of depth d? How many edgesare in this tree?6. An Euler circuit in an undirected graph is a path that starts and ends at the same vertex anduses every edge exactly once. Show that a connected, undirected graph has an Euler circuitonly if each node has even degree.03-511/711 Computational Genomics and Molecular Biology, Fall 2003 57. Algorithms X and Y have worst case running times no greater than 150N log N and N2,respectively. Which algorithm has better asymptotic running time? For which values of Nwould you choose algorithm X over algorithm Y ? (You may give an algebraic or graphicalanswer.)8. Two fair coins are tossed and you are told that at least one coin came up heads. What is theprobability that both coins came up heads? The two “instinctive” answers 1/2 and 1/4 areincorrect. Use the formula for conditional probability and/or draw a Venn diagram of theevent space.Survey question (not graded): How familiar are you with the following topics? (1 = notfamiliar, 2 = understand concept, 3 = can use concept to solve problems).• Markov chains• Hidden Markov models• Dynamic programming• Computational complexity and big Oh notation• Sequence
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