# Suppose you are constructing a human genomic library in BAC vectors where the human DNA fragments are on average 100,000 bp. a. What is the minimum number of different recombinant BACs you need to construct in order to havea greater than zero chance of having a completelibrary—meaning one in which the entire genomeis represented?The simple statistical equation that follows allows youto determine the size that a genomic library needs tobe (that is, the number of independent recombinantclones you need to make) for a given likelihood thatthe entire genome is represented in the library.N = ln (1 − P)ln (1 − f )In the equation, N is the number of independent recombinant clones; P is the probability that any particular partof the genome is represented at least one time; f is thefraction of the genome in a single recombinant clone.(Note: ln is the natural log, sometimes written as loge.)b. Calculate f for the genomic library described in part (a).c. How many different recombinant BAC cloneswould you need to have a 99% chance that a specific 100,000 bp region of the genome is represented? How many clones for a 99.9% chance?d. How many genomic equivalents correspond to eachof your answers in part (c)?e. Suppose that after you ligated the human DNAinserts with the BAC vectors and transformedE. coli with the mixture, you find that you haveonly 30,000 drug-resistant colonies transformedwith recombinant plasmids. What is the chancethat any specific 100,000 bp region of the genomeis represented in a recombinant plasmid?f. If you want to construct a complete human genomic library that contains the smallest number ofindependent recombinant clones possible, what isthe key variable that you should adjust?One difficulty in molecular cloning using plasmid vectors isthat the restriction enzyme-digested vector can be resealedby DNA ligase without an insert of genomic DNA. The nexttwo problems investigate methods to deal with this issue.

Question

Suppose you are constructing a human genomic library in BAC vectors where the human DNA fragments are on average 100,000 bp.
a. What is the minimum number of different recombinant BACs you need to construct in order to have
a greater than zero chance of having a complete
library—meaning one in which the entire genome
is represented?
The simple statistical equation that follows allows you
to determine the size that a genomic library needs to
be (that is, the number of independent recombinant
clones you need to make) for a given likelihood that
the entire genome is represented in the library.
N = ln (1 − P)
ln (1 − f )
In the equation, N is the number of independent recombinant clones; P is the probability that any particular part
of the genome is represented at least one time; f is thefraction of the genome in a single recombinant clone.
(Note: ln is the natural log, sometimes written as loge.)
b. Calculate f for the genomic library described in part (a).
c. How many different recombinant BAC clones
would you need to have a 99% chance that a specific 100,000 bp region of the genome is represented? How many clones for a 99.9% chance?
d. How many genomic equivalents correspond to each
of your answers in part (c)?
e. Suppose that after you ligated the human DNA
inserts with the BAC vectors and transformed
E. coli with the mixture, you find that you have
only 30,000 drug-resistant colonies transformed
with recombinant plasmids. What is the chance
that any specific 100,000 bp region of the genome
is represented in a recombinant plasmid?
f. If you want to construct a complete human genomic library that contains the smallest number of
independent recombinant clones possible, what is
the key variable that you should adjust?
One difficulty in molecular cloning using plasmid vectors is
that the restriction enzyme-digested vector can be resealed
by DNA ligase without an insert of genomic DNA. The next
two problems investigate methods to deal with this issue.

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