Final Exam Bioinformatics Spring 2004

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Final Exam Bioinformatics Spring 2004

BIO 7960, MAT 8790


1. Review ten talks given by your colleagues (not yourself) this semester. State at least
one new concept/idea/fact that you learned from each talk.


2. In class we showed with a very short seque
nce a simplified version of how BLAST
calculates the Y score, the unadjusted bit score, and the unadjusted E
-
value. Using your
first, middle and/or last name, create a string of at least 8 and no more than 1
4

legal
amino acid characters

(not J or O)
, run
a “short nearly exact sequence BLAST” on it, and
show how one could calculate the Y score, the unadjusted bit score, and unadjusted E
-
value.

Explicitly state which scoring matrix and gap penalties you used.


3. In class we mentioned that BLAST is reall
y a hypothesis test between two simple
hypotheses. What are the two hypotheses?


4. The calculation of q(i,j) and p_i and p’_j are presumed to be given on page 270 in
the
Ewens
-
Grant
text. The on
-
line BLAST explanation on the NCBI site,
The Statistics

of
Sequence Similarity
, by Altschul (recall the Karlin
-
Altschul sum statistic) describes how
BLAST actually estimates the lambda and K which in turn can be used to
estimate the

q

values
(see the
Ewens
-
Grant

text page

275)
.

(a.)
Read this on
-
line articl
e. Note the several formula boxes. Ewens and Grant give far
more detail; for each formula in Altschul, find the corresponding formula in our text.

(b.)
In several places but especially towards the end of his article, Altschul states several
ways that
BLAST uses heuristic or empirical ideas. List three examples of this.


5.
On the graph from the randomwalk excel file with c =
-
2, q = 0.65, d = +3, p = 0.35,
“three steps forward and two steps back”
, answer the following:

How many
ladder points

are sh
own?

How many zero excursion heights are there?

List the nonzero excursion heights (Y_j) (including the height of the last excursion even
though it probably runs off the end of the graph).

Among these excursion heights, what is the Y_max?


6.
“Gambler’s

Ruin”
:

We spent some pleasant time discussing
the
gambler’s ruin, and
some formulas that told us the probability of ruin. Assume the simplest case of bets of $1
only, so it is “simple random walk.” Let p be the probability that you win $1, and q be
the

probability that you lose $1. Let h be the initial amount of money you have, and
assume you will play till you are either broke (a=0) or until you win $100 (b=100).
Calculate the probability that you will win
the
$100 given:

Scenario 1: h = 2, p =
0.50
1,
q = 0.
499

Scenario 2: h = 2, p = 0.5
1
, q = 0.4
9

Scenario 3: h = 20
, p =
0.501,
q = 0.
499

Scenario 4: h = 20
, p = 0.5
1
, q = 0.4
9


7. Identify these matrices as yielding global, local, or fitted alignments.
Assume a matc
h

is +1
,
a mismatch is
-
1, and

a gap is
-
2.
List the best alignment that each is meant to tell
us.
Note that the minus signs seem to have gotten messed up in the copying, presumably
because the cell widths are not wide enough.





-

a

a

g

t

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a

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10



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2

0