Microarray Synthesis through Multiple-Use PCR Primer Design

1. Microarray Synthesis through Multiple-Use PCR Primer Design Research Proficiency Examination Rohan Fernandes

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

3. What are Microarrays?

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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!

11. 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.

12. 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(m+1)/2 unique primer pairs. • 2n primers may be sufficient instead of 2n. • Conventional primer design requires 12,000 primers for 6,000 genes, but 110might suffice. • In practice this lower bound will be unreachable but there will still be a large win.

13. 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.

14. 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?

15. Split Addressing (Contd)

16. 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.

17. Minimum Primer Set Problem

18. Budgeted Primer Set Problem

19. 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.

20. Reduction Gadget

21. 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.

22. 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.

23. Example Run of Algorithm (1) • Initially graph with vertex weights.

24. After removing minimum weighted vertex. Example Run of Algorithm (2)

25. Example Run of Algorithm (3) • Final graph.

26. Performance of Heuristic • O(|V|.(|V|+|E|+|C|)) time and O(|V|+|E|+|C|) 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.

27. 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 p=1/2. • 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.

28. Selecting Seed Edges

29. Replacing Seed Edges

30. Retrying with Isolated Colored Edges

31. 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.

32. 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.

33. Summary of Results (Non-degenerate)

34. Summary of Results (Degenerate)

35. 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.

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