Primer Selection Methods for Detection of Genomic Inversions and Deletions via PAMP

1. Primer Selection Methods for Detection of Genomic Inversionsand Deletions via PAMP Bhaskar DasGupta, University of Illinois at Chicago Jin Jun, and Ion Mandoiu University of Connecticut

2. Outline • Introduction • Anchored Deletion Detection • Inversion Detection • Conclusions

3. Genomic Structural Variation • Deletions • Inversions • Translocations, insertions, fissions, fussions…

4. Introduced by [Liu&Carson 2007] Experimental technique fordetecting large-scale cancer genome lesions such as inversions and deletions from heterogeneous samplescontaining a mixture of cancer and normal cells Can be used for Tracking how genetic breakpoints are generated during cancer development Monitoring the status of cancer progression with a highly sensitive assays Primer Approximation Multiplex PCR (PAMP)

5. PAMP details A. Large number of multiplexPCR primers selected s.t. • There is no PCR amplification in the absence of genomiclesions • A genomic lesion brings one or more pairs of primersin the proximity of each other with high probability, resulting in PCR amplification B. Amplificationproducts are hybridized to a microarray to identify thepair(s) of primers thatyield amplification Liu&Carson 2007

6. Outline • Introduction • Anchored Deletion Detection • Inversion Detection • Conclusions

7. Anchored Deletion Detection • Assume that the deletion spans a known genomic location (anchored deletions) • [Bashir et al. 2007] proposed ILP formulations and simulated annealing algorithms for PAMP primer selection for anchoreddeletions

8. Criteria for Primer Selection • Standard criteria for multiplex PCR primer selection • Melting temperature, Tm • Lack of hairpin secondary structure, and • No dimerization between pairs of primers • Single pair of dimerizing primers is sufficient to negate the amplification [Bashir et al. 2007]

9. Optimization Objective • Multiplex PCR primer set selection • Minimizenumber of primers and/or multiplex PCR reactions needed to amplify a given set of discreteamplification targets • PAMP primer set selection • Minimize the probabilitythat an unknown genomic lesion fails to be detected by the assay

10. PCR amplification success probability PCR amplification success probability 1 1 0 L L+1 Distance between two primers 0 Distance between two primers L PCR Amplification Efficiency Model • Exponential decay in amplification efficiency above a certain product length • 0-1 Step model (used in our simulations)

11. Probabilistic Models for Lesion Location • pl,r: probability of having a lesion with endpoints, l and r • where • Simple model: uniform distribution • pl,r=h if r-l>D, 0 otherwise • Function of distance • pl,r=f(r-l) • e.g. a peak at r-l=d • Function of hotspots • High probability aroundhotspots • e.g. two (pairs of) hotspots l h l r xmin xmax r-l=d D l r Hot- spots r Hotspots

12. PAMP Primer Selection Problem for Anchored Deletion Detection (PAMP-DEL) • Given: • Sets of forward and reverse candidate primers, {p1,p2,…,pm} and {q1,q2,…,qn} • Set E of primer pairs that form dimers • Maximum multiplexing degrees Nf and Nr, and amplification length upper-bound L • Find: Subset P’ of at most Nf forward and at most Nr reverse primers such that • P’ does not include any pair of primers in E • P’ minimizes the failure probability • where f(P’;l,r)=1 if P’ fails to yield a PCR product when the deletion with endpoints (l,r) is present in the sample, and f(P’;l,r)=0 otherwise.

13. l1 r1 f(P’;l,r)=1 r1 Failure (l1-1-xi’ )+(yj’ -r1-1) > L l1 ILP Formulation for PAMP-DEL r (l-1-xi’ )+(yj’ -r-1) = L Deletion anchor yj’ xi’ yj’ 5’ 3’ pi’ pi qj qj’ 3’ 5’ yj l xi’ xi

14. l2 r2 r2 f(P’;l,r)=0 (l2-1-xi’ )+(yj’ -r2-1) ≤L Success l2 ILP Formulation for PAMP-DEL • 0/1 variables • fi (ri) to indicate when pi (respectively qi) is selected in P’, • fi,j (ri,j) to indicate that pi and pj (respectively qi and qj) are consecutive primers in P’, • ei,i‘,j,j‘ to indicate that both (pi, pi’) and (qj, qj’) are pairs of are consecutive primers in P’ r (l-1-xi’ )+(yj’ -r-1) = L Deletion anchor yj’ xi’ yj’ 5’ 3’ pi’ pi qj qj’ 3’ 5’ yj l xi’ xi

15. Failure probability f0,i fi,j fj,k fi,m+1 . . . . . . Compatibility constraints pm+1 p0 pi pj pk : : : : Max. multiplex degree constraints No dimerization constraints Path connecting constraints ILP Formulation for PAMP-DEL (2)

16. PAMP-1SDEL • One-sided version of PAMP-DEL in which one of the deletion endpoints is known in advance • Introduced by [Bhasir et al. 2007] • Assume we know the left deletion endpoint • Let x1<x2<…<xn be the hybridization positions for the reverse candidate primers q1,…, qn • Ci,j: probability that a deletion whose right endpoint falls between xi and xj does not result in PCR amplification • ri, ri,j: 0/1 decision variables similar to those in PAMP-DEL ILP

17. PAMP-1SDEL ILP

18. Unconvered area 0 L 2L 2.5L 3L Forward primers + l1 L/2 Forward primers l1 l2 L/2 Forward primers + l2 dimerization Comparison to Bashir et al. Formulation • PAMP-DEL formulation in Bashir et al. • Each primer responsible for covering L/2 bases • Covered area by adjacent primers u, v: Failure prob. 1/2 0

19. PAMP-DEL Heuristics • ITERATIVE-1SDEL • Iteratively solve PAMP-1SDEL with fixed primers from previous PAMP-1SDEL • FixedNf (Nr) at each step • INCREMENTAL-1SDEL • ITERATIVE-1SDEL but with incremental multiplexing degrees • E.g. k/2k·Nf, (k+1)/2k·Nf, … , Nf • where k is the number of steps

20. Comparison of PAMP-DEL Heuristics • m=n=Nf=Nr=15, xmax-xmin=5Kb, L=2Kb, 5 random instances • PAMP-DEL ILP can handle only very small problem • Both ITERATED-1SDEL and INCREMENTAL-1SDEL solutions are very close to optimal for low dimerization rates • For larger dimerization rates INCREMENTAL-1SDEL detection probability is still close to optimal

21. INCREMENTAL-1SDEL Scalability • L=20Kb, 5 random instances

22. Outline • Introduction • Anchored Deletion Detection • Inversion Detection • Conclusions

23. Inversion Detection

24. PAMP Primer Selection Problem for Inversion Detection (PAMP-INV) • Given: • Set P of candidate primers • Set E of dimerizing candidate primer pairs • Maximum multiplexing degree Nand amplification length upper-bound L • Find: a subset P’ of P such that • |P’| ≤ N • P’ does not include any pair of primers in E • P’ minimizes the failure probability • where f(P’;l,r)=1 if P’ fails to yield a PCR product when the inversion with endpoints (l,r) is present in the sample, and f(P’;l,r)=0 otherwise.

25. f(P';l',r')=1 ILP Formulation for PAMP-INV • 0/1 variables • ei=1 iffpi is selected in P’, • ei,j=1 iff pi and pj are consecutive primers in P’, • ei,i‘,j,j‘=1iff (pi, pi’) and (pj, pj’) are pairs of are consecutive primers in P’ xj r r xi l 5’ 3’ pi’ pj’ pi pj xj’ 3’ 5’ r f(P';l,r)=0 xj 5’ 3’ (l-1-xi)+(r-xj) = L pj’ pi pj pi’ 3’ 5’ l (l-1-xi )+(r-xj) ≤L Success xi l xi’

26. ILP Formulation for PAMP-INV (2)

27. Detection Probability and Runtime for PAMP-INV ILP • PAMP-INV ILP can be solved to optimality within a few hours • Runtime is relatively robust to changes in dimerization rate, candidate primer density, and constraints on multiplexing degree. • xmax-xmin =100Kb • L=20Kb • 5 random instances

28. Effect of Inversion Length and Dimerization Rate • xmax-xmin=100Kb, L=20Kb, n=30, dimerization rate r between 0 and 20% and N=20 • Detection probability is relatively insensitive to Length of Inversion

29. Outline • Introduction • Anchored Deletion Detection • Inversion Detection • Conclusions

30. Summary • ILP formulations for PAMP primer selection • Anchored deletion detection (PAMP-DEL) • 1-sided anchored deletion detection (PAMP-1SDEL) • Inversion detection (PAMP-INV) • Practical runtime for mid-sized PAMP-INV ILP, highly scalable PAMP-1SDEL ILP • Heuristics for PAMP-DEL based on PAMP-1SDEL ILP • Near optimal solutions with highly scalable runtime

31. Questions?