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\noindent 
{\bf 18.417 - Introduction to Computational Molecular Biology}
\hfill{\bf PS 2}\\
{\bf Bonnie Berger and Manolis Kamvysselis} \hfill October 2, 2001\\
\noindent

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{\Large \bf Problem Set 2}\\
{\large \bf Due Date: Tuesday, October 16}\\
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\begin{enumerate}
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\item{ {\bf{Using BLAST:}} Open up a web browser and go to\\
\mbox{http://www.ncbi.nlm.nih.gov/cgi-bin/BLAST/nph-psi\_blast}\\
Using the NR database (NR stands for Non-Redundant - this is the
default), enter the amino acid sequence GLSPETRRLVRQRQ. Note that if you
just type in those 14 letter in upper case, the sequence will be in
FASTA format. How many database sequences are returned? Click on the first
14-mer to find out more about it. What is the accession ID? Now do a
BLAST search (from the same page as before) on this accession ID. What
family have you found? Family is not meant here as a technical term -
just explain what biological function all the most closely aligned
proteins share.}

\item{ {\bf{Understanding FASTA:}} 

(a) In class we said that FASTA does not
compute an exact alignment. In this problem we will investigate one
way in which FASTA can fail. Take the sequences

$\begin{array}{l}
ACCGTAGAAGAA\\
ACCTACAACAAC\\
\end{array} $

and consider the effect of running FASTA to align the two sequences using
only 3-mers. What is the only offset value at which we have a non-zero
score? Now consider the alignment depicted below.

$\begin{array}{l}
ACCGTAGAAGAA{\bf-}\\
{\bf-}ACCTACAACAAC\\
\end{array} $

Using the scoring metric that matches receive a +1, mismatches a -1, and
gaps a -2, what is the score of the alignment produced by FASTA? What is
the score of the alignment depicted in the second picture? What does
this show about FASTA? 

(b) Compute the optimal FASTA alignments of ACTGTACGTA and ACTGCGTACG
using a window of length 3 and a band of width 2 on either side of the
diagonal. Only consider the single optimal offset produced by FASTA.
Turn in your scoring matrix.} 

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\item{
%
{\bf The Gibbs Sampling algorithm.}
%
Choose a set of orthologous sequences from
%
{\tt ftp://ncbi.nlm.nih.gov/pub/COG/COGs/},
%
and apply the code in {\tt /mit/18.417/share/problem\_code/gibbs.py} to
find a motif in it.  You may find the code in
%
{\tt .../problem\_code/tests/test\_gibbs.py}
%
has helpful examples of how to use it.  Don't forget to mention which
group of proteins you ran the code on!

Which residues have the greatest frequency at each position?  Does this
seem like a genuine motif?

The code in {\tt gibbs.py} does not take into account the
%
{\em background frequency} of the residues.  Find a way to fix this.
(Hint: personally, I found the description of Gibbs Sampling at

{\tt http://bayesweb.wadsworth.org/gibbs/content.html} very helpful.)

}

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\item{{\bf{Physical Mapping: }} Suppose you are studying a new plasmid (with circular DNA) that
is 2500 bases long, whose restriction map you wish to construct. You
treat the plasmid DNA with a set of restriction endonucleases and
measure the size of the resulting fragments by gel electrophoresis to
obtain the following results. 

\begin{tabular}{lcl}
EcoRI & {\bf --} & 2500\\
HindIII & {\bf --} & 2500\\
PstI & {\bf --} & 2500 \\
MboI & {\bf --} & 1300, 800, 400\\
MboI  &$+$& EcoRI  -- 1300, 600, 400, 200\\
MboI & $+$& HindIII -- 1300, 800, 300, 100\\
MboI &$+$& PstI -- 1000, 800, 400, 300\\
EcoRI & $+$ & HindIII -- 2000, 500\\
EcoRI & $+$ & PstI -- 1600, 900\\
HindIII & $+$ & PstI -- 2100, 400
\end{tabular}

Construct a restriction map based on this information. To break the
circularity, place base pair 1 at the HindIII cleavage site.}

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\item{{\bf{Genetic mapping:}} The family described below has been
genotyped for three linked markers, A, B, and C.  The pair of alleles
found (each represented by a digit) is listed below for each marker and
each person in the family. All the alleles come from genes located on a
single chromosome.

\begin{tabular}{ll}
{\bf Father:} & I--1\\
{\bf Mother:} & I--2\\
{\bf Offspring:} & II--1 through II--10
\end{tabular}

\begin{tabular}{lccc}
& & {\bf marker} & \\
{\bf Person} & {\bf A} & {\bf B} & {\bf C}\\ \hline
I--1 & 1,5 & 2,3 & 6,8 \\
I--2 & 1,9 & 4,7 & 3,6 \\
II--1 & 1,5 & 2,7 & 6,6 \\
II--2 & 1,9 & 3,4 & 3,8 \\
II--3 & 1,5 & 2,7 & 6,8 \\
II--4 & 5,9 & 3,4 & 3,6 \\
II--5 & 1,9 & 3,7 & 3,8 \\
II--6 & 5,9 & 2,4 & 6,6 \\
II--7 & 1,1 & 3,4 & 6,8 \\
II--8 & 1,5 & 2,7 & 6,6 \\
II--9 & 5,9 & 2,4 & 3,6 \\
II--10 & 1,9 & 3,4 & 6,8 
\end{tabular}

a.  For each of the offspring, list which alleles were inherited from the mother and which from the father.

b.  Count the frequency of each  parternally- and maternally-derived haplotype.  What are the parents' haplotypes most likely to be?

c.  For each pair of markers, count the total number (both maternal and paternal ) of crossovers that occurred between just those markers.  (I.e., for markers A and C, ignoring the data for marker B entirely, how many crossovers do you see?) Use this information to build a map of the markers.

d.  Verify your map by determining the haplotypes corresponding to double crossovers.  How often do they occur?}

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