Multiple Word DNA Computing on Surfaces Liman Wang,† Qinghua Liu,†,§ Robert M. Corn,† Anne E. Condon,‡,# and Lloyd M. Smith†,* Contribution from the Department of Chemistry, Department of Computer Science, UniVersity of Wisconsin-Madison, 1101 UniVersity AVenue, Madison, Wisconsin 53706 ReceiVed March 22, 2000 Abstract: The enzymatic manipulation of DNA molecules immobilized on a surface that each contain linked, multiple “DNA words” is demonstrated, with applications to DNA computing. A new DESTROY operation to selectively remove unmarked DNA strands from surfaces, consisting of polymerase extension followed by restriction enzyme cleavage, has been developed for multiple-word DNA computing. DNA polymerase is used to extend DNA primers hybridized to DNA strands that are covalently attached to a chemically modified gold thin film. The efficiency of this surface polymerase extension reaction is >90%, as determined by removal of the extended DNA molecules from the surface followed by gel electrophoretic analysis. Complete extension of the DNA strands creates a Dpn II restriction enzyme site in the duplex DNA; these molecules may then be cleaved from the surface by addition of Dpn II, with an efficiency exceeding 90%. DNA molecules may be protected from such destruction by hybridization of a peptide nucleic acid (PNA) oligomer to one of the words. The hybridized PNA blocks polymerase extension, thereby preventing formation of the restriction site and consequent strand cleavage. The utility of these operations for DNA computing is demonstrated by solving a small (2-bit) Satisfiability problem in which information was encoded in two tandem words. I. Introduction on surfaces, which utilizes 16-base oligonucleotides, or DNA “words”, to encode information. The 16mer DNA words contain The field of DNA computing was initiated in 1994 by 8 fixed word label bases and 8 variable bases which encode Adleman,1 who proposed that the tools of molecular biology the information in each word. In the multiple-word strategy,4,6 could be used to solve instances of difficult mathematical the word label sequence is the same for every 16mer in a given problems known as NP-complete problems.2 We have adapted these ideas to combinatorial mixtures of DNA molecules word set; additional word sets are generated by varying the word attached to surfaces in an unaddressed format and have label sequence. By linking different word sets together to form performed logical manipulations of sets of data by the hybrid- multiple-word DNA strands, large combinatorial mixtures can ization and enzymatic manipulation of the attached oligonucle- be created to encode the set of possible solutions to large 6 otides. In a recent paper,3 we solved a 4-variable 3-Satisfiability computational problems. We have shown previously that the (SAT) problem using a brute-force search algorithm applied to enzyme T4 DNA ligase can be utilized to create and manipulate a mixture of 16 distinct DNA strands attached to chemically such linked multiple-word DNA strands. However, the DE- modified gold thin films. Three “primitive” operations were STROY operation developed previously for single-word DNA employed: “MARK”, in which subsets of the DNA strands are computing is not suitable for use in multiple-word DNA tagged (marked) by the hybridization of complementary strands; computing. In this paper we describe the development of a new “DESTROY”, in which DNA strands that are not marked are DESTROY operation suitable for use in multiple-word DNA removed from the surface; and “UNMARK”, in which marked computing, and demonstrate how to use this operation to solve molecules are untagged by removing hybridized complements.4 a small Satisfiability problem with multiple words. To scale-up this approach to solve larger problems, a larger The DESTROY operation for single-word DNA computing combinatorial set of DNA molecules is required, encoding more consists of adding an exonuclease specific for single-stranded possible solutions to the computational problem. A previous DNA.3,5 After the MARK operation, each unmarked strand is study5 has described a word design strategy for DNA computing in a single-stranded form. It is then destroyed by single-strand specific enzyme E. coli exonuclease I, leaving on the surface * Corresponding author. E-mail: [email protected]. † Department of Chemistry, University of Wisconsin-Madison. only the marked double-stranded DNA molecules. In the § Present Address: 10210 Genetic Center Drive, Mail Stop #6, Gen- multiple-word strategy, the words are “linked” together when Probe, Inc., San Diego, CA 92121. synthesized, and the resultant multiple-word DNA strands are ‡ Department of Computer Science, University of Wisconsin-Madison. # Present Address: The Department of Computer Science, University attached to the surface; thus, a single surface-bound oligonucle- of British Columbia, 201-2366 Main Mall, Vancouver, BC V6T1Z4. otide might be comprised of several consecutive words from (1) Adleman, L. M. Science 1994, 266, 1021-1024. different word sets. In this case, the MARK operation may target (2) Garey, M. R.; Johnson, D. S. Computers and Intractability: A guide to the Theory of NP-Completeness; W. H. Freeman and Company: New a single word within the multiple-word oligonucleotide, resulting York, 1979. (3) Liu, Q.; Wang, L.; Frutos, A. G.; Condon, A. E.; Corn, R. M.; Smith, (5) Frutos, A. G.; Liu Q.; Thiel A. J.; Sanner, A. M. W.; Condon, A. E.; L. M. Nature 2000, 403, 175-179. Smith, L. M.; Corn, L. M. Nucleic Acids Res. 1997, 25, 4748-4757. (4) Smith, L. M.; Corn, R. M.; Condon, A. E.; Lagally, M. G.; Frutos, (6) Frutos, A. G.; Smith, L. M.; Corn, R. M. J. Am. Chem. Soc. 1998, A. G.; Liu Q.; Thiel, A. J. J. Comput. Biol. 1998, 5, 255-267. 120, 10277-10282. 10.1021/ja0010195 CCC: $19.00 © xxxx American Chemical Society Published on Web 00/00/0000 PAGE EST: 5.6 B J. Am. Chem. Soc. Wang et al. unmodified oligonucleotide, to avoid their displacement by the polymerase enzyme during the strand extension reaction. These operations for multiple-word DNA computing were developed and tested upon a small example of the Satisfiability (SAT) problem.2 The SAT problem is one of the first NP- complete search problems described. The simple example of the SAT problem we examined in the present work is (x ∨ yj) ∧ (xj ∨ y). (Note that this small example is a 2-SAT problem (two variables or fewer per clause), which is not NP-complete; however, as we have shown previously,3 these methods are readily applied as well to 3-SAT problems, which are NP- complete.) The variables x and y are Boolean logic variables which can hold only one of two possible values, 0 (false) and 1 (true). This example consists of two clauses separated by the logical AND operation (denoted by “∧”; x ∧ y )1 if and only if x ) y )1); within each clause, Boolean variables are separated by the logical OR operation (denoted by “∨”; x ∨ y ) 0, if and Figure 1. Overview of the DESTROY operation for multiple-word only if x ) y ) 0). The problem is to find whether there are DNA computing. The figure shows three four-word DNA strands on values for the variables that simultaneously satisfy each clause the surface. Strands S1 and S2 are marked by complements at word 3 in a given instance of the problem. xj denotes the “negation” of and word 1, respectively, whereas strand S3 is not marked by any x (xj)0 if and only if x ) 1, and xj)1 if and only if x ) 0). complements. Therefore, the DNA polymerase extends the primer annealed to strand S to form a double-stranded restriction enzyme Each of the two variables can be either true or false and thus 3 there are a total of 22 or 4 candidate solutions. cleavage site near the spacer region. Strand S3 is thus cleaved by the restriction enzyme, whereas the polymerase extensions are blocked on It may be noted that although the primary emphasis of this 3,10-12 both strands S1 and S2 by marked complements. Peptide nucleic acid paper is in the area of surface-based DNA computing, (PNA) oligonucleotide analogues were used in the MARK operation the chemical and biochemical procedures being developed are rather than standard unmodified oligonucleotides to avoid their likely to find substantial applicability in other areas as well. displacement by the polymerase enzyme during the strand extension There is presently widespread interest and activity in the reaction. development and use of large arrays of proteins and nucleic acids on surfaces, permitting highly parallel analyses of RNA, in a short double-stranded region (the word which was marked) protein, and small molecule binding and other activities in flanked by single-stranded DNA (the words that have not been biological systems.13-22 The ability to enzymatically manipulate marked). Treatment of such a structure with the single-strand surface-bound biomolecules substantially extends the power and specific E. coli exonuclease I will result in destruction of single- versatility of such array-based methodologies. stranded DNA from the 3′ terminus, an unwanted result if an internal word was marked. II. Experimental Section Accordingly, an alternative strategy for the DESTROY A. Materials. The chemicals 11-mercaptoundecanoic acid (MUA) operation for multiple-word DNA computing has been devel- (Aldrich), poly(L-lysine)hydrobromide (PL) (Sigma), sulfosuccinimidyl oped here, consisting of polymerase extension followed by 4-(N-maleimidomethyl)cyclohexane-1-carboxylate (SSMCC) (Pierce), restriction enzyme cleavage (Figure 1). Each surface im- urea (United States Biochemical), and triethanolamine hydrochloride mobilized DNA strand has a common primer site at the 3′ (TEA) (Sigma) were all used as received. Gold substrates were terminus and a specific restriction site near its spacer region manufactured by Evaporated Metal Films (Ithaca, NY).