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338    Chapter 9    Digital Analysis of DNA


                16.  Suppose you are using a plasmid cloning vector that   fraction of the genome in a single recombinant clone.
                  has no EcoRI sites (5′ G^AATTC 3′) in its polylinker   (Note: ln is the natural log, sometimes written as log e .)
                  because the particular drug resistance gene your     b.  Calculate f for the genomic library described in part (a).
                  vector contains has an EcoRI site within it.         c.  How many different recombinant BAC clones
                  a.  How could you use the following two oligonucle-    would you need to have a 99% chance that a spe-
                    otides (and ligase enzyme) to ligate an insert       cific 100,000 bp region of the genome is repre-
                    that is an EcoRI fragment into the BamHI site        sented? How many clones for a 99.9% chance?
                    (5′ G^GATCC 3′) in the polylinker of your vector?
                                                                       d. How many genomic equivalents correspond to each
                                                                         of your answers in part (c)?
                               5' G A TC CG GGGG G GGG G  3'
                               5' A A TT CC CCCC C CCC G  3'           e.  Suppose that after you ligated the human DNA
                                                                         inserts with the BAC vectors and transformed
                  b. How many EcoRI sites will the recombinant DNA       E. coli with the mixture, you find that you have
                    contain? How many BamHI sites?                       only 30,000 drug-resistant colonies transformed
                  c.  In part (a), you used the two oligonucleotides to   with recombinant plasmids. What is the chance
                    make a so-called adapter. Adapters can also be       that any specific 100,000 bp region of the genome
                    used to ligate blunt-ended inserts into vectors cut   is represented in a recombinant plasmid?
                    with sticky-ended enzymes. Design an adapter that   f.  If you want to construct a complete human ge-
                    would allow you to ligate blunt-ended inserts into   nomic library that contains the smallest number of
                    the BamHI site of your vector’s polylinker.          independent recombinant clones possible, what is
                    (Note: Two blunt-ended DNA fragments can be li-      the key variable that you should adjust?
                    gated together, although the reaction is much less
                    efficient than sticky-end ligation.)           One difficulty in molecular cloning using plasmid vectors is
                17.  As a molecular biologist and horticulturist specializ-  that the restriction enzyme-digested vector can be resealed
                  ing in snapdragons, you have decided that you need to   by DNA ligase without an insert of genomic DNA. The next
                  make a genomic library to characterize the flower   two problems investigate methods to deal with this issue.
                  color genes of snapdragons.
                  a.  How many genomic equivalents would you like to    19.  The lacZ gene from E. coli encodes the enzyme
                                                                       β-galactosidase, which can catalyze the conversion of a
                    have represented in your library to be 95% confi-  colorless compound called X-gal into a blue product.
                    dent of having a clone containing each gene in     Molecular biologists have taken advantage of this prop-
                    your library?                                      erty by constructing plasmid vectors that contain the
                  b. How do you determine the number of independent    lacZ gene with an EcoRI site in its middle (see figure
                    clones that should be screened to guarantee this   that follows). After cutting this vector with the EcoRI
                    number of genomic equivalents?                     enzyme, scientists ligate it together with EcoRI-
                18.  Suppose you are constructing a human genomic li-  digested human genomic DNA, transform the resultant
                  brary in BAC vectors where the human DNA frag-       molecules into ampicillin-sensitive E. coli cells, and
                  ments are on average 100,000 bp.                     plate these cells on petri plates containing ampicillin
                  a.  What is the minimum number of different recom-   and X-gal. Some of the colonies growing on this plate
                    binant BACs you need to construct in order to have   are white in color, while others are blue. Why?
                    a greater than zero chance of having a complete
                      library—meaning one in which the entire genome
                    is represented?                                           lacZ gene
                  The simple statistical equation that follows allows you                     EcoRI       amp r
                  to determine the size that a genomic library needs to                       site
                  be (that is, the number of independent recombinant
                  clones you need to make) for a given likelihood that            Origin of
                                                                                  replication
                  the entire genome is represented in the library.
                                    ln (1 − P)                       20.  Your undergraduate research advisor has assigned
                                N =                                    you a task: Insert an EcoRI-digested fragment of
                                    ln (1 − f )
                                                                       frog DNA into the vector shown in Problem 19.
                  In the equation, N is the number of independent recom-  Your advisor suggests that after you digest your
                  binant clones; P is the probability that any particular part   plasmid with EcoRI, you should treat the plasmid
                  of the genome is represented at least one time; f  is the   with the enzyme alkaline phosphatase. This enzyme
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