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Held: Thursday, 8 October 2009
Summary:
We continue our exploration of how DNA sequence databases are created.
Related Pages:
Notes:
- Upcoming work: Read Chapter 6 for Tuesday, read Kellis et al. 2003 for Thursday.
- Things that depress Sam: So few students at George Drake's history of the two Grinnells.
- Bio and CS talks at noon tomorrow!
- Class will end early today (2:25).
- Interestingly, one of today's topic (P vs. NP) was a subject of an article in yesterday's New York Times.
Overview:
- Sequencing DNA, Continued
- CS Detour: TSP and NP-Completeness
- Reassembling Shotgun Sequences
- Testing Assembly Algorithms
- Problem: How do you use a technique for sequencing short
segments and turn it into a technique for sequencing long segments?
- Solutions may require both biology and computer science
- Approach one (primarily biological): Sequential sequencing:
- Since you can use a primer to determine where sequencing starts
(or so we hope), you sequence a little, make a primer, sequence
a little more, make a primer, and so on and so forth.
- Should be very accurate (unless, of course, your primer is wrong
or binds at the wrong place)
- Takes a lot of time to do
- Approach two (primarily computational): Shotgun sequencing
- Blast your sequence into lots and lots of small sequences.
- Sequence each of those small sequences
- Use cool algorithms to glue them back together.
- Why choose one over the other?
- The book mentions that alignment is similar in difficulty to the
Traveling Salescritter Problem (TSP).
- Computer scientists like to analyze the efficiency by which problems
can be solved.
- We often look at how much work an algorithm we develop requires. For
example, the N-W algorithm requires some constant times NxM steps,
where N is the length of one sequence and M is the length of the
other.
- We also like to provide bounds on the solution time of
algorithms. For example, it would be impossible to write an algorithm
that aligns the two sequences that takes less than N+M steps, since we
presumably have to look at each element of each sequence at least once.
- TSP is a relatively straightforward problem:
- You have a list of cities and distances between them
- You want to find the shortest path that visits every city
(and doesn't visit any city twice)
- There's an obvious solution:
- List every possible order of visiting the cities
- For each order, find the distance
- Choose the smallest
- Unfortunately, there are a lot of ways to order
N different cities (N factorial, to be precise).
- Suppose there are 20 different cities
- 20! = 2,432,902,008,176,640,000
- Suppose we could do a trillion operations a second (a lot more than
most current computers).
- We'd still have about 2 million seconds worth of operations to do.
- About 33,000 minutes
- About 555 hours
- You can do the rest
- Interestingly, there is no known algorithm that is significantly better.
- And we've been working on TSP for more than thirty years.
- There are known fast algorithms that approximate the best solution.
- A number of years ago, some computer scientists looked at a group of
problems like TSP and developed a useful theory.
- There are some problems we know that have relatively efficient algorithms.
Approximate string alignment is one of these. We call this set of problems
'P' (for 'solvable in polynomial time')
- There are some problems in which we can check a potential solution of
a problem quickly. We call these 'NP'.
- A variant of TSP is in this form: 'Is there a path through the cities
of distance less than D?'
- The 'NP' problems are 'nondeterministic polynomial'.
- There are a subset of problems in NP that are provably as hard as
any other problem in NP. We call these 'NP Complete'.
- There are problems that we know to be at least as hard as the problems
in NP. We call these NP hard.
- Many problems in NP are also in P. (That is, we can check an answer
quickly and we can find an answer quickly.)
- But there are many problems for which we have yet to find a
fast algorithm, even if we can check solutions quickly.
- Open question: Are there problems in NP for which we can never find
a fast solution? (Most computer scientists say 'Yes.')
- When we say a problem is 'NP complete' or 'NP hard' we mean:
- There's no known fast (or even reasonably fast) solution.
- We can prove that this problem is as difficult as many other problems
for which there is no known solution.
- We therefore think it's unlikely that there will every be a fast
exact solution.
- All in all, it's bad news.
- Expected Problems
- A lot of data: Computationally expensive
- The algorithm the book gives appears exponential in the number
of sequences
- Don't know which strand each sequence comes from
- Doesn't do well with long sections of repeats (but, then, neither
does the previous method)
- Since there is no clear biological basis to the assembly, how do we
know that the result is accurate?
- Note: The task of taking a group of strings and finding a string that
contains all of them is called the
shortest superstring problem
- It is known to be NP complete
[Maier and Storer, 1977, cited in Gary and Johnson 1979]
- No provenly good approximation is known either
- Gap between CS and Bio: Whether or not the shortest superstring
problem or an approximation was solved, these techniques may not
give the correct sequence.
- But, hey let's try
- Basic operation: Finding the best alignment of two segments (contigs)
- Slightly different metric for
best
than we've used
previously, since it's okay for ends to stick out (these would normally
be considered insertions and deletions).
- How would you upate our algorithms to handle this issue?
- Once we can align two sequences (or know the value of their best alignment),
what do we do next?
- The greedy algorithm:
- As long as contigs with high-value alignments remain
- Find the value of the alignment of all pairs of contigs.
- Choose the one with the greatest value.
- Merge those two contigs into a single contig
- How do we know whether an assembly algorithm works? We test it.
- Computational approach: Start with a known sequence, simulate breaking
it up into pieces, assemble, see if you get the the original sequence.
- Another computational approach: Think hard about kinds of sequences in
which the algorithm will have difficulty, and then do the same thing.
- A possible biological approach: Sequence using another technique,
break up using the shotgun approach, and see if the result is the
known sequence.
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