High-Throughput Assay Design. Microarrays. Applications. Overview. Algorithms Universal DNA Tag Array Design and Optimization

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1 Algorithms for Universal DNA Tag Array Design and Optimization Watson- Crick C o m p l e m e n t a r i t y Four nucleotide types: A,C,T,G A s paired with T s (2 hydrogen bonds) C s paired with G s (3 hydrogen bonds) Ion Mandoiu Computer Science & Engineering Department University of Connecticut High-Throughput Assay Design Fast growing number of applications, with more stringent constraints on sensitivity, reproducibility, cost, etc. Source of challenging combinatorial problems Multiplex PCR primer set selection Probe selection Fidelity probes Mask design This talk: design and optimization of universal tag arrays Labeled DNA/RNA mixture flushed over array of probes DNA Microarrays Laser activation of fluorescent labels Optical scanning used to identify probes with complements in the mixture Images courtesy of Affymetrix. Overview Applications Gene expression (transcription analysis) Genomic-based microorganism identification Single Nucleotide Polymorphism (SNP) genotyping 1

2 Gene Expression Robotic cdna Arrayers Cells express different subsets of genes under different environments Pin Technology Quill Pen Technology Ink jet Technology Pin Ring Technology Translation Transcription Protein mrna Gene Two-Color Technique Sample labeled RED Control labeled GREEN YELLOW probes hybridize to both sample and control BLACK probes hybridize to neither VLSIPS Array Synthesis cell type 1 RNA 1 target 1 Cy3Cy3Cy3 target 2 Cy5Cy5Cy5 RNA 2 cell type 2 Images courtesy of Affymetrix. Microarray Technologies Arrays of cdnas Obtained by reverse transcription from Expressed Sequence Tags (ESTs) Oligonucleotide arrays Short (20-60bp) synthetic DNA strands Oligonucleotide Arrays Pros Highly versatile Very high integration (VLSIPS ~106 probes/cm2) Cons Higher cost Application specific, non-reusable designs 2

3 Overview Universal Array Advantages Cost effectiveness Array does not change economies of scale Customization Fast, only need to synthesize new set of reporter probes Reliability Solution phase hybridization better understood than hybridization on solid support Universal Arrays Brenner 97, Morris et al. 98 Key idea Array consisting of application independent t a g s T w o-part reporter probes: aplication s p e c i f i c primers ligated to a n t i t a g s Detection carried by a sequence of reactions separately involving the primer and the antitag p a r t of reporter probes Overview Universal Array Experiment + Tag Set Requirements Hybridization constraints ( H 1 ) Antitags hybridize strongly to complementary tags (H2) No antitag hybridezes to a non - complementary tag ( H 3 ) Antitags do not cross-hybridize to each other Two conflicting goals Maximize number of tags Ensure hybridization constraints 3

4 Hybridization Model Melting temperature Tm: temperature at which 50% of duplexes are in hybridized state 2-4 rule Tm = 2 #(As and Ts) + 4 #(Cs and Gs) More accurate models exist, e.g., the nearneighbor model, however, 2-4 rule reasonably accurate for short oligos c-h code problem [Ben -Dor et al. 00] give a constructive upperbound on largest c-h code size and a nearoptimal algorithm based on DeBruijn sequences [MT05] c-h code problem can be formulated as a maximum integer flow problem with capacity constraints on (disjoint) sets of vertices Solvable in practical time for small values of c Tag Set Design Problem Token Content of a Tag [Ben -Dor et al. 00] Conservative formalization of (H1)+(H2) based on nucleation complex theory and 2-4 rule (C1) Every tag must have total weight h (C2) No 2 tags share a common substring of weight c Where w(a)=w(t)=1, w(c)=w(g)=2 c, h are given constant (Affymetrix uses l+h in C1) c = 4 CCAGATT CC CCA CAG AGA GAT GATT c-h codes c -token: left-minimal DNA string of weight c, i.e., w ( x ) c w ( x ) < c for every proper suffix of x Layered c-token graph, length-l tags c 1 c/2 (c/2)+1 l-1 l [Ben-Dor et al. 00] A set of tags is called c -h code if (C1) Every tag has weight h (C2*) Every c -token is used at most once s t c -h code problem: given c and h, find largest c -h code c N 4

5 token s-t path in layer graph ILP Results c=4, l=7 tag = CCAGATT L a y e r s CC CCA CAG AGA GAT GATT t Integer Program Formulation Periodic Tags If multiple c -token copies are not allowed in a tag (uniqueness property), every tag uses roughly one c - token per letter (except for first up to c -1 letters) A tag t is periodic if it is the prefix of (α) for some string α t periodic with period α t uses at most α c -tokens O ( hn ) constraints and variables, where N = #c-tokens Lemma: there is always an optimum solution consisting exclusively of periodic tags and tags with uniqueness property Number of c-tokens Portion of successor c-token graph, c=4 Let G n = #strings of weight n G 1 = 2; G 2 = 6; G n = 2 G n G n -1 W=A or T, S=C or G Token type Num tokens CC <c-2 > S 2 G c -2 AAG AAC S<c-3 > S 4 G c -3 AAAA <c-1>w 2 G c -1 AAAT S<c-2>W 4 G c -2 5

6 Tag Set Design Algorithm 1. Construct successor graph G over c-tokens 2. T {} 3. For all cycles C defining periodic tags, in increasing order of cycle length, do If C has no c-tokens in common with T, then A d d a t a g d e f i n e d b y C t o T Remove C from G 4. Perform a pruned alphabetic tree search and add to T tags with no c -tokens in common with T 5. Return T Antitag-to-Antitag Hybridization Additional practical constraint: antitags do not cross-hybridize (including self) Ignored by Ben-Dor e t a l Formalization in c-token hybridization model: (C3) No two (anti)tags contain complementary substrings of weight c Cycle packing and tree search extend easily Vertex-disjoint Cycle Packing Problem Results w/ Extended Constraints Given directed graph G, find maximum number of vertex disjoint directed cycles in G [ M T 0 5 ] A P X -hard even for regular directed graphs with in-degree and out-degree 2 h -c/2+1 approximation factor for tag set design problem [Salavatipour and Verstraete 0 5 ] Quasi-N P -hard to approximate within Ω (log 1 -ε n ) O ( n 1/2 ) approximation algorithm Experimental Results Overview 6

7 More Possible Mis-Hybridizations MAPS Problem Maximum Assignable Primer Set (MAPS) Problem: given primer set P and tag set T, find maximum size assignable subset of P Degrees of freedom: partition of primers on multiple arrays, tag assignment within an array (may be forced to leave tags unassign e d ) Here we focus on avoiding case (a), primer- t o- tag hybridization [Ben-Dor 04] Greedy deletion heuristic: repeatedly delete primer of maximum weight from P until it becomes assignable, where Potential of tag t is 2 - P ( t ) Potential of primer p is sum of potentials of conflicting tags Assignable Primers Set P of primers is assignable to set T of tags if, for every tags t,t and primers p,p with t hybridizing to primer p, at most one of the assignments (p,t), (p,t ), (p,t) can be made t t p p Universal Array Multiplexing Problem Multiplexing Problem: given primer set P and tag set T, find partition of P into minimum number of assignable sets [Ben-Dor 04] Repeatedly find approximate MAP using greedy deletion Characterization of Assignable Sets [Ben-Dor 04] Set P is assignable to T iff X + Y P, where, in the conflict graph induced by P+T X = number of primers incident to a degree 1 tag Y = number of degree 0 tags Integration with Probe Selection In practice, several primer candidates with equivalent functionality In SNP genotyping, can pick primer from either forward and reverse strand X=1 Y=2 In gene expression/identification applications, many primers have desired length, Tm, etc. 7

8 Pooled Array Multiplexing Problem Results: GenFlex T a g s, c = 7 [ M P T 0 5 ] Given set of primer pools P and tag set T, find a primer from each pool and a partition of selected primers into minimum number of assignable sets X+Y Characterization no Longer Holds Results: GenFlex T a g s, c = 8 Pooled Multiplexing Algorithms GenFlex vs. PerTags, c=8 ( T =213) 1. Primer -Del = greedy deletion for pools similar to [Ben-Dor et al 04] 2. Primer -Del+ = same but never delete last primer from pool unless no other choice 3. Min-Pot = select primer with min potential from each pool, then run Primer -D e l 4. Min-Deg = select primer with min conflict degree, then run Primer -D e l 8

9 Overview Open Problems Settle approximation complexity of (vertex) disjoint cycle packing ([Salavatipour and Verstraete 0 5 ] s h o w approximation preserving reductions between edge and vertex disjoint versions) Establish better approximation bound for special instances arising in tag set design Improved approximation algorithms for maximum assignable tag set and the tag assignment problems Conclusions New techniques for tag set design and tag assignment lead to significantly improved multiplexing Enforcing antitag-t o -antitag hybridization constraints make universal arrays more reliable Other applications of universal tags: Lab - on -c h i p, D N A-driven assembly (e.g., carbon nanotubes), DNA computing [Brenneman&Condon 02] Other applications of assignment techniques: Genotyping by mass-spectroscopy [ A u m a n n et al 05] Genotyping using l-m e r arrays Acknowledgments Claudia Prajescu and Dragos Trinca UCONN Research Foundation Ongoing Work Special type of universal arrays: l- mer arrays Initially introduced for sequencing by hybridization, but proved impractical Currently investigated for use in resequencing by hybridization More promising application: SNP genotyping Isothermal prefix sets instead of l-m e r arrays? Deeper integration between tag assignment and probe selection, e.g., in string barcoding Extend algorithms to more accurate near-neighbor hybridization model monotonic Tm c-tokens successor graph 9