BioSystems 52 (1999) 25–33

Progress toward demonstration of a surface based DNAcomputation: a one word approach to solve a model

satisfiability problem

Qinghua Liu a, Anthony G. Frutos a, Liman Wang a, Andrew J. Thiel a,Susan D. Gillmor b, C. Todd Strother a, Anne E. Condon c, Robert M. Corn a,

Max G. Lagally b, Lloyd M. Smith a,*a Department of Chemistry, Uni6ersity of Wisconsin-Madison, Madison, WI 53706, USA

b Department of Materials Science and Engineering, Uni6ersity of Wisconsin-Madison, Madison, WI 53706, USAc Department of Computer Sciences, Uni6ersity of Wisconsin-Madison, Madison, WI 53706, USA

Abstract

A multi-base encoding strategy is used in a one word approach to surface-based DNA computation. In thisdesigned DNA model system, a set of 16 oligonucleotides, each a 16mer, is used with the format 5%-FFF-FvvvvvvvvFFFF-3% in which 4–8 bits of data are stored in eight central variable (‘v’) base locations, and theremaining fixed (‘F’) base locations are used as a word label. The detailed implementations are reported here. In orderto achieve perfect discrimination between each oligonucleotide, the efficiency and specificity of hybridizationdiscrimination of the set of 16 oligonucleotides were examined by carrying out the hybridization of each individualfluorescently tagged complement to an array of 16 addressed immobilized oligonucleotides. A series of preliminaryhybridization experiments are presented and further studies about hybridization, enzymatic destruction, read out anddemonstrations of a SAT problem are forthcoming. © 1999 Elsevier Science Ireland Ltd. All rights reserved.

Keywords: Surface-based; Hybridization; Multi-base encoding; Satisfiability (SAT); DNA computing

www.elsevier.com/locate/biosystems

1. Introduction

Computer scientists rank computational prob-lems in three classes: easy, hard, and uncom-putable (Ouyang et al., 1997). One of the majorachievements of computer science in the last two

decades is the understanding that many importantcomputational search problems are NP-completeand thus are unlikely to have efficient algorithmsthat solve the problem exactly (Garey and John-son, 1979).

Algorithms that solve optimization versions ofsuch problems exactly are suitable only for small-size instances in the worst case. ‘Heuristic’ al-gorithms such as simulated annealing(Kirkpatrick et al., 1983) often work well in prac-

* Corresponding author. Tel.: +1-608-263-2594; fax: +1-608-265-6780.

E-mail address: smith@chem.wisc.edu (L.M. Smith)

0303-2647/99/$ - see front matter © 1999 Elsevier Science Ireland Ltd. All rights reserved.

PII: S 0303 -2647 (99 )00029 -5

Q. Liu et al. / BioSystems 52 (1999) 25–3326

tice, but offer no guarantee of obtaining an opti-mal solution. ‘Approximation algorithms’ guaran-tee a solution within some percentage of optimal,for example there are known efficient approxima-tion algorithms for the Satisfiability (SAT) prob-lem that output a truth assignment satisfying anumber of clauses that is at least 75% of thenumber of clauses satisfied by the best possibletruth assignment.

Recently Adleman (1994) showed that DNAcan be used to solve a computationally hardproblem, the Directed Hamiltonian Path problem(DHPP), and demonstrated the potential power ofparallel, high-density computation by moleculesin solution. This parallelism allows DNA comput-ers to solve larger hard problems such as NP-complete problems in linearly increasing time, incontrast to the exponentially increasing time re-quired by a Turing machine (Ouyang et al., 1997).

After Adleman initiated the field of DNA com-puting in 1994, Lipton (1995) proposed DNAexperiments to solve the SAT problem. In 1997,Ouyang et al. (1997) presented a molecular biol-ogy-based experimental solution to the ‘maximalclique’ problem. This problem is in the same class(NP-complete) as the DHPP. The paper is signifi-cant because it shows a functional demonstrationof improved design principles for DNA comput-ing, and the use of living organisms (Escherichiacoli ) to read the answer of a computation bycloning.

All three works (Adleman 1994; Lipton 1995;Ouyang et al., 1997) use the tools of molecularbiology (in this case, DNA as an informationcarrier, ligation, PCR, gel electrophoresis, mag-netic bead separation, enzymatic digestion, etc. asoperations), and all demonstrate the feasibility ofcarrying out computations at the molecular level.However, since they are all solution-based meth-ods, they share the common problems of scale-upof this test tube-based approach for a number ofreasons, including poor efficiencies in the purifica-tion and separation steps.

In contrast with the solution-based experimentsof Adleman (1994), Lipton (1995), and Ouyang etal. (1997), surface-based DNA computations ma-nipulate DNA strands that are immobilized on asurface using chemical linkers (Cai et al., 1997;

Frutos et al., 1997; Liu et al., 1998; Smith et al.,1998; Liu et al., 1999). This means that a keyoperation used in solution-based DNA computa-tions, that of selectively separating strands intoseparate test tubes, cannot be performed. Also thenumber of DNA strands involved in the computa-tion is limited since the strands are restricted totwo rather than three dimensions (Cai et al.,1997). (The number of strands that can fit on a 1cm2 planar surface is roughly 1012.) Nevertheless,it is our premise that surface-based chemistry willbe important to advances in DNA computation.Detailed discussions about the strategy for a sur-face-based approach to DNA computation arereported in Smith et al. (1998).

In this paper a one-word DNA experimentusing a surface-based approach is designed and inprogress as a demonstration of a small-scale pro-totype DNA computer with several ‘operations’that could perform simple calculations such as theSAT problem (Garey and Johnson, 1979).

2. Operations on surfaces

A simple version of surface-based DNA com-puting uses three basic operations MARK, UN-MARK, and DESTROY (Smith et al., 1998). Inthe MARK operation a less complex combinato-rial mixture of DNA corresponding to the querywould be added to the surface; the complemen-tary strands would bind to form a duplex; thusMARKED strands would be duplexed, and UN-MARKED strands would be single-stranded. Thisoperation has been demonstrated with both sin-gle-base and multiple-base encoding strategies(Frutos et al., 1997; Liu et al., 1998; Smith et al.,1998).

The DESTROY operation consists of addingan exonuclease specific for single-stranded DNA.Every unmarked strand is destroyed, leaving onthe surface only the MARKED DNA molecules.This operation has been demonstrated with threecycles of selective enzymatic destruction of un-marked (single-stranded) DNA words in the pres-ence of marked (hybridized) oligonucleotidesusing 3% � 5% single-strand-specific E. coli Exonu-clease I (Frutos et al., 1997; Smith et al., 1998)).

Q. Liu et al. / BioSystems 52 (1999) 25–33 27

The UNMARK operation consists of subject-ing the surface to conditions under which hybridsdissociate into single strands. This is performedthrough a combination of increased temperatureand addition of denaturants such as urea. Subse-quent washing with a suitable buffer removes thefree strands in solution and regenerates the DNA-modified surface (Smith et al., 1998).

After each cycle of MARK, DESTROY, andUNMARK, fewer molecules remain on the sur-face. Repeated queries constitute the DNA com-putation process, permitting subsets of the initialcombinatorial space to be eliminated, leaving thedesired solutions to the problem of interest.

The end result of a DNA computation is asurface on which DNA molecules exist, whosesequence encodes the solution to a combinatorialproblem of interest. It is thus necessary to deter-mine the sequence(s) of these surface-bound DNAmolecules in order to ascertain the solution to thecomputational problem in question (this opera-tion is called READOUT). Both conventionalelectrophoresis-based DNA sequencing and hy-bridization to word-specific addressed arrays havebeen studied (Gillmor et al., 1998; Wang et al.,1998).

3. One word SAT problem model system

A model system for demonstration of a oneword SAT problem was designed, using the multi-ple base encoding strategy with 16mers attachedto a chemically modified gold surface.

The exhaustive search algorithm for the SATproblem is as follows (Liu et al., 1999):

for each clause C dofor each unnegated variable xi in C do

mark (i, 1)for each negated variable xi in C do

mark (i, 0)comment: all remaining solutions that set Cto ‘true’ are markedDESTROY-unmarked (using single-strandexonuclease)

test-if-emptyHere, the initial set of strands represent all 2n

possible truth assignments to the variables

x1,…, xn of the input formula. Mark (i, 1) meansthat all strands in which variable i is set to trueare marked.

The DNA model system is a set of 16, 16-baseoligonucleotides, which are attached to chemicallymodified gold surfaces as described previously(Frutos et al., 1997). The 16mers have the follow-ing design sequence 5%-FFFFvvvvvvvvFFFF-3% inwhich the fixed sequences are 5%-HS-(T)15-GCTTvvvvvvvvTTCG-3%. The variable sequenceschosen are from the set of 108 8-mers previouslyidentified (Frutos et al., 1997). Each member ofthis set differs from every other member of the setin at least 4 base locations. Table 1 shows thevariable sequence regions (from 5% to 3%) for the 16oligonucleotides in the model system. Each panelof Table 1 contains the same sequences as theother panels, but each panel is different in that itshows the number of matches and mismatchesand their distributions when each oligonucleotidein the set is hybridized with a particular comple-ment. Blue letters represent perfect matches to thespecific complements being tested, red representsmismatches, and black represents a partial match.For example, in panel 1 in the upper left corner,the complement considered will be 3%-CGAAgttgggttAAGC-5%, which is perfectlymatched with the first sequence in blue, and is twobase matched (two bases in black) with the secondDNA molecule (AACCTGGT) and eight basemismatched (all in red) with the third DNAstrand (ACCAAACC), and so on. When the com-plement 3%-CGAAttggaccaAAGC-5% is considered,the perfectly matched oligonucleotide will be thesecond one in panel 2 at the upper left corner(blue in second sequence), and the DNA strandwith the first sequence in that box will be twobase matched (two are in black) with the comple-ment, and so on.

The set of 16 oligonucleotides is used to encodefour bits (four binary variables, 24=16) of infor-mation. One of the possible encoding schemes isshown below. In this encoding scheme, the vari-able DNA sequences encode 4 binary variablesx1, x2, x3 and x4.

We have proposed to solve the following spe-cific SAT problem using the set of 16 oligonucle-otides:

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Liu

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BioS

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25–

3328Table 1

Variable sequence regions for the 16 oligonucleotides

Q. Liu et al. / BioSystems 52 (1999) 25–33 29

(x1� x2% � x4) � (x3) � (x2% ) � (x4� x1% )

This particular problem was chosen arbitrarily;many other problems would be equally good asmodel SAT demonstration problems (example inSmith et al. (1998)). Note that the problem in-volves all four variables, and has four clauses. Theproblem can be solved easily by checking each ofthe 16 strands. However, successfully solving thisproblem would be the first demonstration of aSAT calculation by DNA computation using asurface-based approach. Solving the problem byDNA computation requires four cycles ofMARK, DESTROY, and UNMARK (since thereare four clauses), followed by READOUT.

DNA Variable sequences x1x2x3x4

(probe No.)

S0 (4) CAACCCAA 00000001AACCTGGTS1 (85)

ACCAAACCS2 (2) 00100011AGAGTCTCS3 (29)

ATATCGCGS4 (24) 0100CCAAGTTGS5 (87) 0101

0110GGTTCAACS6 (81)0111S7 (94) GTTGGGTT1000TATAGCGCS8 (18)

TCTCAGAGS9 (11) 1001TGGTTTGGS10 (92) 1010

1011TTGGACCAS11 (79)ACTGGTCAS12 (108) 1100

1101CAGTTGACS13 (107)ATGCAGGAS14 (73) 1110

1111S15 (19) ATCGAGCT

In preparation for the DNA computation, com-binatorial mixture of strands S0–S15 would first beimmobilized on a gold surface. In the first compu-tational cycle, all strands which do not satisfy thefirst clause are destroyed, namely those twostrands in which both x1 and x4 are set to ‘false’and x2 is set to ‘true’ (S4 [0100] and S6 [0110]).Specifically, this would be accomplished in thefollowing manner: first, hybridize the sur face-bound S0…S15 to a mixture of complements C0,C1, C2, C3, C5, C7, C8, C9, C10, C11, C12, C13,C14, C15 (complements of S0 to S15 are denoted as

C0 to C15), at room temperature in 2×SSPE/0.2%SDS buffer for 30 min., leaving S4 and S6 unhy-bridized. The surface is then subjected to E. coliExonuclease I digestion for 3 h to selectivelydestroy surface-bound unmarked strands S4 andS6. Finally, the surface is re-generated by theUNMARK operation using 8.3 M urea (the 14different hybridized duplexes would be denaturedin this step to return the surface to single-strandedform without S4 and S6).

In the second computational cycle, the remain-ing seven strands (S0 [0000], S1 [0001], S5 [0101],S8 [1000], S9 [1001], S12 [1100], and S13 [1101])which do not satisfy the second clause are de-stroyed, namely those left on the surface in whichx3 is set to ‘false’. Again, this would be accom-plished as follows: first, hybridization of the 14strands left on the surface from the first cycle to amixture of the complements C2, C3, C7, C10, C11,C14, and C15, followed by E. coli Exonuclease Idigestion to selectively destroy surface-bound un-marked strands S0, S1, S5, S8, S9, S12, and S13.Finally, the surface is re-generated by the UN-MARK operation to return the surface-boundoligonucleotides S2, S3, S7, S10, S11, S14 and S15 totheir single-stranded form.

In the third computational cycle, the remainingthree strands (S7 [0111], S14 [1110], and S15 [1111])which do not satisfy the third clause are de-stroyed, namely those left on the surface in whichx2 is set to ‘true’. The implementation is quitesimilar to the two cycles described above, but withhybridization to the mixture of complementsC2, C3, C10, and C11. The Exonuclease I digestiondestroys unmarked strands S7, S14 and S15, andthe final UNMARK operation leaves S2, S3, S10

and S11 single-stranded on the surface.In the last cycle, the one strand (S10 [1010])

which does not satisfy the fourth clause is de-stroyed, namely the strand left on the surface inwhich x4 is set to ‘false’ and x1 is set to ‘true’. Thistime, the remaining surface-bound strands arehybridized to complement C2, C3 and C11; S10

which is unmarked is destroyed by Exonuclease I,followed by re-generation of the surface, leavingthe three satisfying assignments, S2 [0010], S3

[0011], and S11 [1011] on the surface.

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The final operation is READOUT. As men-tioned previously, two approaches have been in-vestigated: cycle sequencing (Blakesley, 1993), andPCR amplification (Mullis and Faloona, 1987;Erlich et al., 1991)) followed by hybridization toaddressed arrays.

Before going into detail about the ‘READOUT’operation, several details of the computationalcycles should be addressed. In the four successivecycles of MARK, DESTROY, and UNMARKoperations, both fluorescein-labeled and unlabeledcomplements are employed. Sometimes hybridiza-tion, destruction, and/or denaturation needs to bemonitored, therefore fluorescently tagged comple-ments need to be utilized. When no monitoring isneeded, unlabeled complements are used. In addi-tion, since cycle sequencing or PCR amplificationis needed, appropriate flanking PCR-primer se-quences should be designed into the set of com-plements for the final READOUT. If the materialis cycle-sequenced, a suitable primer sequence,which can be the same as one of those employedfor PCR amplification, should be included in theset of complements to permit eventual enzymaticsequence analysis.

If an addressed array of 16 spots is employedfor READOUT, two primer sequences need to beincorporated into the set of complements for PCRamplification before the READOUT hybridiza-tion. Therefore, for a complement design suitablefor both cycle sequencing and PCR amplification,two 20mer sequences should be added to the16mer complements as shown below. The lowercase sequences are the two primers, the upper casesequences are fixed word labels, and v is thecomplement region shown in Table 1:

5%-tatttttgagcagtggctccCGAAvvvvvvvvAAGCtag-ctatctacaagattcag-3%

For cycle sequencing READOUT, the primer islabeled either with one dye (FAM) or with fourdyes (Fam-C, Joe-A, Tamra-G, and Rox-T). Inthe first case, each reaction (dideoxy C, dideoxyA, dideoxy G and dideoxy T) must be performedin a separate container and the products loaded infour separate lanes on the electrophoresis gel; inthe latter case, the reactions are performed in fourseparate containers, but the products are pooled

and analyzed in a single lane on the electrophore-sis gel. 6% denaturing polyacrylamide gels can beused on an ABI DNA sequencer. The sequence ofthe primer is complementary to the 3% end of thesequence shown above:

5%-dye-ctgaatcttgtagatagcta-3%

For PCR amplification and addressed arrayhybridization READOUT, the amplified materi-als should be fluorescently tagged and be comple-mentary to one or more of the surface-boundDNA molecules. Therefore, the PCR primersmust be designed accordingly. One primer shouldbe biotinylated to permit strand separation afterPCR amplification, as explained later. The otherprimer should be fluorescently tagged as shownbelow:

5%-biotin-ctgaatcttgtagatagcta-3%

5%-FAM-tatttttgagcagtggctcc-3%

After PCR amplification, the products are double-stranded 56mers with one strand biotinylated, andthe other strand fluorescein labeled. Prior to ad-dressed array readout, double-stranded PCRproducts are strand-separated using DynabeadsM-280 streptavidin (Dynal Prod.). The superna-tant (containing FAM labeled strands) is desaltedand concentrated on a Microcon 10 concentrator(Amicon, Beverly, MA). The concentratedfluorescently tagged single-stranded PCR prod-ucts are to be applied to a 16-spot addressed arrayfor READOUT.

4. Progress toward demonstration of one wordSAT problem

All oligonucleotides designed above were syn-thesized by the University of Wisconsin Biotech-nology Center on an ABI 308B or 391 DNAsynthesizer. Glen Research 5%-thiol-modifier C6and ABI 6-FAM were used for 5%-thiol modifiedand 5%-fluorescein-modified oligonucleotides, re-spectively. Prior to purification, thiol-modifiedoligonucleotides were deprotected as specified byGlen Research Corporation (1990). Before use,each oligonucleotide was purified by reverse-phase

Q. Liu et al. / BioSystems 52 (1999) 25–33 31

Fig. 1. Results obtained when a combinatorial mixture of 16fluorescently tagged DNA targets is hybridized to an array oftheir 16 complements immobilized on a gold surface. Panel Ashows the eight nucleotide variable regions and their probenumbers. Panel B shows the hybridization pattern obtainedafter washing at room temperature.

the many different DNA strands spotted onto thehydrophilic portions of the slide. Detailed surfaceattachment reactions, hybridizations, and denatu-rations were carried out as described previously(Frutos et al., 1997).

The efficiency and specificity of hybridizationdiscrimination of the set of 16 oligonucleotideswere examined. Fig. 1 shows the results obtainedwhen a combinatorial mixture of 16 fluorescentlytagged DNA complements is hybridized to anarray of the 16 surface-bound DNA molecules.The sequence of the eight nucleotide (nt) variableregions, along with their probe numbers withinthe set of 108 oligonucleotides, are shown in panelA, and the pattern of fluorescence binding atroom temperature in panel B. Under the condi-tions employed, all members of the array showsignificant fluorescence binding, demonstratingthe accessibility of the surface-bound oligonucle-otides to hybridization.

An exhaustive study was conducted in whicheach individual fluorescently tagged complement(a total of 16) was hybridized to this array of 16immobilized oligonucleotides to verify that onlyone spot is hybridized per complement, and atwhat stringency conditions perfect discriminationcan be achieved.

Fig. 2 shows the results obtained when thesurface-immobilized arrays are sequentially hy-bridized to each single fluorescently taggedoligonucleotide complement (CF). Sixteen succes-sive hybridizations to CFs were performed. Forexample, ‘4CF’ is the fluorescently tagged comple-ment of probe 4 (3%-CGAAgttgggttAAGC-FAM5%). For each hybridization step, all 16 perfectlymatched pairs were observed. Nine of the 16perfect matches (85-85CF, 24-24CF, 87-87CF, 81-81CF, 11-11CF, 79-79CF, 108-108CF, 73-73CF,and 19-19CF) in the set were perfectly discrimi-nated after washing the surface in a 37°C buffersolution for 20 min. Also shown in the Figure isthe fluorescence image obtained at room tempera-ture (22°C) prior to washing at 37°C; at roomtemperature 85-85CF, 87-87CF and 73-73CF arethe three perfectly matched pairs observed inwhich no mismatch hybridization was detected. Inother words, perfect discrimination can beachieved at room temperature for the three pairs,

high performance liquid chromatography. Theconcentrations of the oligonucleotides were deter-mined by UV spectrophotometry at 260 nm(Smith et al., 1987). All thiol oligonucleotidesshould be used immediately after purification.Gold substrates were prepared with self-assem-bled monolayers of 11-mercaptoundecanoic acid(MUA) and poly-L-lysine (PL) using the methoddescribed elsewhere (Liu et al., 1998). With theMUA and PL monolayers attached to the surface,the sample was irradiated with a 200 W mercuryarc lamp for 3 h with a patterned mask (Jordanand Corn, 1997). The sample was then immersedin 1 mM n-octadecylmercaptan to create hydro-phobic and hydrophilic regions on the surface(Gillmor et al., 1998). The hydrophobic surfacebarrier prevents any cross-contamination between

Q. Liu et al. / BioSystems 52 (1999) 25–3332

Fig. 2. Results obtained when an array of 16 oligonucleotides immobilized on a gold surface is successively hybridized to each singlefluorescently tagged oligonucleotide complement (CF), perfectly complementary to each surface-bound probe. Two hybridizationpatterns obtained after washing at room temperature and 37°C are shown for each hybridization test.

and it can be obtained at 37°C for the other sixpairs. Complete hybridization discrimination be-tween 4-4CF, 2-2CF, 29-29CF, 94-94CF, 18-18CF, 92-92CF, and 107-107CF could not beachieved at 37°C. The sequences between the mis-matched pair were compared (e.g. for mismatchedpair 29-4CF, variable sequence region of the com-plement of 4: 3%-gttgggtt-5% and that of immobi-lized oligonucleotide 29: 5%-agagtctc-3% arecompared and only partial matches are foundwhich are shown in the bolded regions). In thecase of 94-94CF, 94CF is totally mismatched withprobe 92 immobilized on the surface, but 92-94CFis observed (second column, last block). By exam-ining the variable sequences between 94CF (3%-caacccaa-5%) and probe 92 (5%-tggtttgg-3%), there aretwo pairs of g-a’s in a row which is claimed as thestable mismatches (Li et al., 1991). Several mis-matched pairs have multiple Gs which are knownto form stable mismatches (Aboul-ela et al., 1985;Werntges et al., 1986; Ikuta et al., 1987). However,the reasons that the mismatched pairs are ob-served even at 40°C washing are not clear yet andfurther studies such as solution melting tempera-ture measurements are underway now to deter-mine if oligonucleotides other than the ones in the

set of 16 are needed to achieve perfect discrimina-tion.

5. Summary

A small-scale prototype of a DNA computer,with oligonucleotides immobilized on gold sur-faces, is designed, and progress is being madetoward testing this DNA computer with a one-word four-variable SAT problem. The experi-ments presented here have tested the hybridizationdiscrimination and efficiency in the MARK opera-tion. Other work is underway to test ExonucleaseI destruction, PCR amplification and cycle se-quencing conditions for readout. The long termbenefit of this work will be a real-world demon-stration of a surface-based DNA SAT calculation,as well as providing a foundation of ready-to-useoperations for more complex DNA computationsin the future.

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