Microarray Synthesis through Multiple-Use PCR Primer Design

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Microarray Synthesis through Multiple-Use PCR
Primer Design

• Research Proficiency Examination
• Rohan Fernandes

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Biology BackgroundPCR

• PCR animation (From the Dolan DNA Learning
  Center, CSHL)
• Applications of PCR include
• Genetic Fingerprinting.
• Medical Diagnostics.
• DNA Sequencing.

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What are Microarrays?
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What are Microarrays?

• A grid with different DNA probes in each
  location.
• Allows one to test a given sample for expression
  of multiple genes.
• Can compare gene expression by using different
  colored fluorescent markers in two samples.

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Genomic Data

• Sequences are known for more than 800 organisms!
• 100 free-living species have been sequenced
  already.
• But we know very little about most of these
  organisms biology.
• Exploiting full-genome sequence data, requires
  investigators to have inexpensive custom
  microarrays.

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Why Microarrays?

• Microarray technology has revolutionized our
  understanding of gene expression.
• Applications include
• Cell cycle analysis.
• Response of cells to environmental stress.
• Impact of gene knockouts.

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A Primer Design True Story!!

• Project for Futcher and Leatherwood to design PCR
  primers for microarray synthesis.
• Strict criteria for primer length, melting
  temperature, self-similarity were specified.
• Designed primers for 5827 and 5012 genes for
  Cerevisiae and Pombe.
• PCR done with sample set of primers designed for
  96 genes each of S. Pombe and S. Cerevisiae was
  100 successful.

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The 110,000 Dollar Problem

• Good primer design can be crucial in synthesizing
  microarray DNA.
• 110,000 out of a total budget of 220,000 for
  microarray synthesis was spent on PCR primers
  alone.
• We propose an alternative method of PCR primer
  design to reduce costs.

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Efficiency of PCR

• Usually, PCR primers are designed to occurs
  uniquely on the genome.
• However, efficiency of PCR falls exponentially as
  length of product increases.
• PCR becomes ineffective for product sizes beyond
  1200 bases.

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Exploiting PCR Efficiency Drop-off

• Amplification is significant only if primers
  hybridize near each other.
• We can reuse primers to amplify several genes,
  provided each primer pair is unique.
• We can save thousands of primers through reuse!

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Who can benefit?

• The total cost of PCR primers may dissuade
  investigators of less studied organisms from
  using microarrays.
• Our technique can reduce costs enough to make
  microarrays more attractive to less funded
  researchers.

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What is the potential win?

• Let (n,m) be the (number of genes, minimum number
  of primers required to amplify them).
• m primers can result in m(m1)/2 unique primer
  pairs.
• ?2n primers may be sufficient instead of 2n.
• Conventional primer design requires 12,000
  primers for 6,000 genes, but 110 might suffice.
• In practice this lower bound will be unreachable
  but there will still be a large win.

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Potential Win? (Example)

• Consider the cost of building a spotted
  microarray for a 20,000 gene organism.
• Conventional techniques will require us to use
  40,000 primers.
• Cost 160,000 at 4 a primer.
• If 3,000 primers suffice, cost is only 12,000.
• The best case is overoptimistic, but realistic
  wins are still impressive.

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Cost of Split Addressing

• What is the probability that two random strings
  will occur in a long random string in a certain
  order and with no more than a certain gap?

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Split Addressing (Contd)
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Split Addressing Conclusion

• Total length of primers required to ensure
  uniqueness of hybridization increases only very
  slowly with the length of the genome.
• The penalty for genome scale lengths and
  realistic PCR gap lengths amount to only
  additional 3-4 bases of primer over ungapped
  matching.
• These results support the potential of
  multiple-use primers.

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Minimum Primer Set Problem
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Budgeted Primer Set Problem
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Hardness of problems

• The Minimum Primer Set problem is NP-hard and
  hard to approximate to within a logarithmic
  factor.
• The Budgeted Primer Set problem is NP-hard and
  seems to be related to densest k-subgraph
  problem.
• Approximation bounds for densest k- subgraph
  problem are not encouraging.

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Reduction Gadget
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Reduction from Set Cover to Minimum Primer Set

• (S, X) is a set cover instance.
• S ??U, X ??W. Connect vertex in U to vertex in W
  iff corresponding set in S contains element from
  X.
• Label (color) each edge by the name of the
  element vertex at its end.
• MPS solution will include all element vertices
  and minimum number of set vertices which cover
  all sets. Q.E.D.

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A Heuristic to approximate MPS

• Based on greedy heuristic to find densest
  subgraph.
• Each edge is weighted with the value of (1/number
  of edges bearing that color).
• Vertex weight is set to sum of adjoining edge
  weights.
• Algorithm proceeds by removal of vertex with
  minimum weighted vertex without eliminating any
  color.
• Algorithm terminates when no more vertices can be
  eliminated.

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Example Run of Algorithm (1)

• Initially graph with vertex weights.

Color Edges Weight
Blue 2 1/2
Green 1 1/1
Red 3 1/3
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Example Run of Algorithm (2)

• After removing minimum weighted vertex.

Color Edges Weight
Blue 1 1/1
Green 1 1/1
Red 3 1/3
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Example Run of Algorithm (3)

• Final graph.

Color Edges Weight
Blue 1 1/1
Green 1 1/1
Red 1 1/1
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Performance of Heuristic

• O(V.(VEC)) time and O(VEC)
  space.
• This heuristic is too slow. It is quadratic in
  V hence very slow on large data sets.
• For our largest dataset this heuristic produced a
  solution in two days as opposed to 25 minutes for
  the next heuristic.

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A Linear-time Heuristic

• We select an edge of each color that has maximum
  colored adjacency to form our seed graph.
• We switch an edge for a color if that saves us
  any vertices in the seed graph
• If there are no savings but no additional
  vertices we switch edges with p1/2.
• Repeat above steps until no. of vertices is
  constant.
• Eliminate all colors whose edges are not
  isolated.
• Repeat above steps for remaining graph until no.
  of vertices is constant. Merge graph obtained.

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Selecting Seed Edges
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Replacing Seed Edges
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Retrying with Isolated Colored Edges
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Preparation of Experimental Data Sets

• Candidate primer sets for S. Cerevisiae and S.
  Pombe prepared using Primer3.
• Primer length range 8-12 bases.
• PCR product size range from 300-1200 bases.
• For each gene at most 10,000 pairs of primers
  were selected.
• Three melting temperature ranges for each of S.
  Cerevisiae and S. Pombe were selected.

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Degenerate Data Sets

• A degenerate primer is a mix of two or more
  primers usually differing in a small number of
  bases.
• Degenerate primers can make resulting colored
  graph more dense by merging primers.
• Created degenerate data sets by merging primers
  differing in at most one base.

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Summary of Results (Non-degenerate)
Yeast T_m Amplified Genes Lower Bound Cost (1) Cost (2) Savings (1) Savings (2)
Cerevisiae 47-57 3775 3065 5483 5511 2067 2039
Cerevisiae 42-52 2700 1344 3130 3232 2270 2168
Cerevisiae 40-50 5313 1241 4753 5157 5863 5469
Pombe 45-55 3583 2622 4987 5058 2179 2108
Pombe 43-53 4232 1988 4799 4951 3665 3513
Pombe 40-50 3400 1380 3651 3852 3149 2948
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Summary of Results (Degenerate)
Yeast T_m Amplified Genes Lower Bound Cost (1) Cost (2) Savings(1) Savings(2)
Cerevisiae 47-57 3775 1221 3638 3940 3912 3610
Cerevisiae 42-52 2700 475 2105 2481 3295 2919
Pombe 45-55 3583 1050 3283 3598 3883 3568
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Future Work

• Using longer primers would enable more efficient
  PCR.
• Increasing order of degeneracy would give a more
  dense colored graph and potentially greater
  savings.
• Combining the above two ideas is the focus of our
  current work.
• Consider the use of existing software
  architecture to solve other primer design
  problems.

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Acknowledgements

• Thanks to Steven Skiena, Bruce Futcher and Janet
  Leatherwood.
• Sponsored by NSF Grant CCR-9988112.