Computational Questions

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Computational Questions

• Bioinformatics

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Where CS and Biology Meet

• Bioinformatics Applications of CS to the life
  sciences
• What are the computational issues?
• Storage and retrieval of genetic data, data
  mining, tools
• Analysis of genetic data similarities,
  differences, structure
• Processing experimental data

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Problem Solving inComputer Science

• Program Sequence of instructions that perform a
  particular task
• Task (problem) expressed as Given data (input),
  produce results (output)
• From problems to programs
• Formulate the problem
• Develop and verify an algorithm
• Write and test the program

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Algorithm Analysis

• Algorithm Conceptual/theoretical form of a
  program
• What is analyzed?
• Correctness does it solve the problem?
• Complexity how much resources (time and memory)
  does it consume?
• Tradeoffs sometimes, we need to sacrifice
  correctness for efficiency

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Example 1 Searching for an Element in a List

• Problem formulation
• Input sorted list L of n elements (e.g., names)
  and a target element x
• Output the position of the target element if it
  exists in the list
• Possible algorithms
• Linear search
• Binary search

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Linear Search

• Algorithm
• For each element in L (from the first to the last
  element), compare it with x and return the
  position if equal
• Time complexity
• Up to n comparisons performed
• On the average, n/2 comparisons
• Runs in linear time (proportional to the list
  size n)

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Binary Search

• Algorithm
• Compare middle element of the list with x, return
  the position if equal if not, reduce the list to
  either the lower half or the upper half of
  original list repeat the process
• Time complexity
• Up to log2n comparisons performed
• Runs in logarithmic time

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Linear vs Logarithmic Time
n n/2 log n
10 5 4
100 50 7
1000 500 10
1,000,000 500,000 20
2,000,000 1,000,000 21
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Comparing Running Times

• Exercise tabulate values of the following
  run-time functions for different values of n
• Functions
• log n (logarithmic)
• n (linear)
• n2 (quadratic)
• n3 (cubic)
• 2n (exponential)
• n!

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Example 2 Substring Search

• Problem formulation
• Input Strings s and t of characters
• Output If s is a substring of t, its position
  in t
• Example
• Input s ctct, t agtctcttctaac,
• Output 4
• Algorithm? Time Complexity?

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Example 3 Traveling Salesman

• Problem Formulation
• Input n cities, distances between cities
• Output shortest tour of all cities
• Algorithm
• Consider all permutations of the cities, compute
  total distances for each permutation, select the
  minimum among all total distances

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Exponential Algorithms and Intractable Problems

• The Traveling Salesman problem is an example of
  an intractable (NP-complete) problem
• Characterized by
• The existence of a correct exponential algorithm
• No known polynomial algorithm
• Exponential algorithm is impractical. Now what?

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Heuristics

• There are polynomial algorithms for intractable
  problems that do not always yield the correct
  answer
• Example Start with any city, go to the nearest
  unvisited city, repeat process
• Not always correct. Counterexample?
• Selection of nearest city is called a heuristic
• Compromise Can prove some statements on the
  (incorrect) algorithm and that may be enough in
  practice

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Back to Bioinformatics Some Objectives

• Formulate problems relevant to biology
• Devise/understand algorithms for these problems
• Computer scientists and biologists need to talk
  more
• Computer scientists have a tendency to make
  (often unreasonable) assumptions
• Biologists may place too much faith on results
  returned by automated systems

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Overview Selected Problems in Bioinformatics

• Sequence alignment
• Phylogeny
• Dealing with experimental results

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BLAST Search
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Blast Results
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DNA Sequence Databases

• Data representation, integrity, accuracy
• Search and scoring methods
• Meaning and reliability of results
• e.g., how does BLAST (Basic Local Alignment
  Search Tool) respond to random data?

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Sequence Alignment Problem

• Given two nucleotide sequence, obtain an optimal
  alignment between the sequences
• Example AT-C-TGAT -TGCAT-A-

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Dynamic Programming
T G C A T A
A
T
C
T
G
A
T
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Phylogeny

• Construction of phylogenetic trees based on
  genomic distance
• Problems to be solved
• Determining genomic distance
• Tree construction from the distances

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Determining Genomic Distance

• Given two genomes, determine the number of
  mutations necessary to obtain one from the other
• Common distance model (least number of mutations)
• Mutation on the genome level rearrangement
  (sorting!) operations on permutations

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(No Transcript)
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Sorting Permutations and a Graph Theoretic Model
0 3 5 6 7 2 1
4 8 9
0 1 2 7 6 5
3 4 8 9
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Phylogenetic Tree Reconstruction

• Given a set of species and genomic distances
  between the species, construct a phylogenetic
  tree that is (most) consistent with the distances
• Problem shown to be NP-complete
• This means we should try some heuristics

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Phylogenetic Tree
Mouse
Monkey
Human
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Experimental Results

• Image or data directly drawn from a device
• e.g., microarray, scanner
• Need to make objective, discrete conclusions
• e.g., pixel intensity vs. gene expression
• Need to handle errors and imperfections

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Microarray Image
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Image Analysis to Aid Microarray Experiments

• Automatically locating the grid of spots
• Use Fourier transforms to compute periods and
  offsets
• Extracting intensity
• Refine spot sample to collect significant,
  normalized data
• Make conclusions on genetic function

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Summary

• Bioinformatics a perfect opportunity for
  interdisciplinary research within the sciences
• Academics from the different backgrounds need to
  study, discuss, debate with each other