Tik-61,181: Bioinformatics Kaski,Mannila,Nikkilä Exercises 1, Autumn 2000

In essay type answers try to answer briefly and concentrate on relevant issues. It is assumed that the assistant will need only reasonable amount of time when decoding the answers. If the opposite occurs, it may affect your grade.

The maximum length of an answer to one question is one page. If you make some proofs or simulations they can be included as appendixes. Every answer will be evaluated with the scale {0:failed, 3:accepted, 5:accepted with distinction}. In order to pass the course you need at least grade 3 for 60% of the exercises. In order to pass with distinction you need to return 95% of the exercises, and to get the grade 5 for most of them.

The deadline of the exercises is 31.1.2001.

a) Explain in detail how you would align the following sequences with pair HMM:s and with non-probabilistic methods: AAAG ACG (DEKM ch.2 and ch.4, S&M ch.3)

b) Analyze briefly the relation of the probabilistic approach and the non-probabilistic approach for sequence alignment. (DEKM ch.2 and ch.4, S&M ch.3)

c) Give an example of the possible uses of the MC-model and HMMs in bioinformatics. Outline briefly the main differences between the two models. (DEKM ch.3)

d) Relax. You are buying a drink from the notorious crazy coke machine while absentmindedly solving some exercises. The machine can be in either of two states: cola preferring state (CP) and mineral water (WP) preferring state. When you put in a coin, the output of the machine can be described with the following probability matrix:

cola mineral water lemonade
CP 0.6  0.1  0.3
WP 0.1  0.7  0.2

Draw the state model graph with transition probabilities P (CP → W P) = 0.3 and P (W P → CP) = 0.5 and calculate the probability of seeing the output sequence {cola,lemonade} if the machine always starts off in the WP state. What kind of behaviour would make this HMM to a (visible) Markov model? (for example DEKM ch.3)

e) Do the exercise 3.3 in DEKM and explain its result briefly in the bioinformatics framework. f) Compare briefly the FSAs and pairwise HMMs in searching.

(DEKM ch.4)

g) Analyze the relation of the profile HMMs, HMMs, and PSSMs.

h) Exercise 6.1 in DEKM.

i) Explain briefly the pros, cons, and the most useful applications of the different progressive alignment methods and profile HMMs in multiple alignment. (DEKM ch.6)

j) Explain the reasons why there are methods for fragment assembly and physical mapping. (S&M: ch.4 and ch.5)

k) Exercise 1 in ch.4 in S&M.

l) Exercise 5 in ch.5 in S&M.

m) Exercise 6 in ch.6 in S&M.

n) Exercise 8.2 in DEKM. Explain also the concept of multiplicativity here.

o) Exercise 8.7 in DEKM