Optically programming DNA computing in microﬂow reactorsBioSystems 59 (2001) 125–138 Optically programming DNA computing in microﬂow reactors John S. McCaskill * GMD-German National

BioSystems 59 (2001) 125–138

Optically programming DNA computing in microflowreactors

John S. McCaskill *GMD-German National Research Center for Information Technology, Schloss Birlingho6en, St. Augustin, D-53754 Bonn, Germany

Accepted 26 December 2000

Abstract

The programmability and the integration of biochemical processing protocols are addressed for DNA computingusing photochemical and microsystem techniques. A magnetically switchable selective transfer module (STM) ispresented which implements the basic sequence-specific DNA filtering operation under constant flow. Secondly, asingle steady flow system of STMs is presented which solves an arbitrary instance of the maximal clique problem ofgiven maximum size N. Values of N up to about 100 should be achievable with current lithographic techniques. Thespecific problem is encoded in an initial labeling pattern of each module with one of 2N DNA oligonucleotides,identical for all instances of maximal clique. Thirdly, a method for optically programming the DNA labeling processvia photochemical lithography is proposed, allowing different problem instances to be specified. No hydrodynamicswitching of flows is required during operation — the STMs are synchronously clocked by an external magnet. Anexperimental implementation of this architecture is under construction and will be reported elsewhere. © 2001Elsevier Science Ireland Ltd. All rights reserved.

Keywords: DNA computing; Combinatorial optimization; Selection; Microsystem; Photochemistry; Optical programming

www.elsevier.com/locate/biosystems

1. Introduction

DNA belongs to the class of informationalmacromolecules — it is both a chemical structureand a carrier of information. While all structurescan convey information, the linear sequence ofbases along a DNA molecule contains transmissibleinformation: the information can be read out andcopied. A single stranded DNA molecule displaysa chain of specific binding sites in which molecules

containing complementary matching bases can as-semble. This allows the discrimination betweenmatching and non-matching subsequences by hy-bridization. The use of DNA for computing asoriginally proposed (Adleman, 1994; Lipton, 1995)depends upon this property. Of course, manyscientists have investigated the natural informationprocessing exhibited by informational macro-molecules. The logical possibilities of the interplaybetween molecular construction and informationprocessing have also been investigated since vonNeumann’s seminal lecture (von Newmann, 1949).Adleman’s achievement was to establish a

* Tel: +49-2241-141527; fax: +49-2241-141511.E-mail address: [email protected] (J.S. McCaskill).

0303-2647/01/$ - see front matter © 2001 Elsevier Science Ireland Ltd. All rights reserved.

PII: S 0 3 0 3 - 2647 (01 )00099 -5

J.S. McCaskill / BioSystems 59 (2001) 125–138126

convincing case that molecular biotechnology hasreached the point where such systems can beprogrammed to solve complex mathematicalproblems.

DNA computing is potentially extremely pow-erful, not only because of the huge degree ofparallelism possible, but also because the basicoperations with DNA occur near to the thermalnoise limit with reasonable accuracy (Bennett,1982). It is also an attractive system for utilizinglogically reversible computation (Klein et al.,1999). The potential of DNA processing systemsto build new processors and new constructionhardware in the course of a computation distin-guishes them qualitatively from conventional andalternative computing paradigms (such as quan-tum computing), allowing investigations of evolv-ing computer hardware. We regard this interplayof construction and computation the primary longterm motivation for pursuing DNA computing.Actually, the original work on DNA computing(Adleman, 1994), further restricted reconstruc-tion, not even allowing for the construction ofnew potential solutions (data strings) during thecomputation. The microflow technology, to beoutlined below, already allows the incorporationof isothermal amplification and transformationmodules which allow the iterative construction ofnew potential sequence candidates during thecourse of a computation (for example allowingevolutionary algorithms (Back, 1996)).

First, however, we must sharpen the tools forprogramming massively parallel computationswith DNA and to do this we focus on a fixedarchitecture and a ‘conventional’ mathematicalproblem in this paper. We do not address alterna-tive strategies which reduce the amount of DNAneeded from Adleman (1994)’s exhaustive searchapproach, although improvements in pro-grammability obviously facilitate other endeavorsin this direction. The paper shows how, usingmicroflow reactors with an array of active ele-ments, the process of programming a DNA com-puter can be reduced to photochemical patterningvia photolithographic masks for a complete fam-ily of combinatorial problems. The initial se-quence setup is independent of the probleminstance and a single optical mask is sufficient to

program the particular problem instance in thefamily considered here. For other problems, asequence of optical masks will be required.

The well known NP-complete decision problemrelated to finding a maximum clique (Garey andJohnson, 1979) in a graph is used as a test exam-ple because of its relatively small input informa-tion (the edge list of the graph G, represented bya binary valued N×N matrix, where N is thenumber of vertices in the graph). An experimentalprocedure for solving very small instances of theclique problem with DNA was proposed and suc-cessfully implemented (Ouyang et al., 1997). Aclique is a fully edge-connected subset of vertices.Potential solutions are thus subsets represented asbinary strings, indicating the presence or absenceof graph vertices (in a predefined order). Since aclique is an independent set on the complemen-tary graph, the maximum clique problem is identi-cal to the problem of finding maximalindependent sets. This is also appealing as a self-referential problem to tackle with DNA, sincefinding maximal independent sets is one compo-nent in constructing good encodings for hy-bridization based DNA computing.

In the paper of Ouyang et al., the specificproblem graph was programmed in the sequenceof manual extraction and mixing steps. As usual,the way in which properties of the algorithm usedto solve a problem scale with N provides insightinto the tractability of an approach: O(N) forexample means a number proportional to N for Nlarge. The Ouyang procedure for maximum cliquewith DNA requires O(N2) manual extraction andmixing steps. It requires O(N) pre-synthesizedoligonucleotides, to assemble a population of 2N

different solution sequences, representing the pos-sible vertex subsets. Similarly, in Adleman (1994)the programming of the small instance of theHamiltonian path problem was divided betweenan instance graph specific synthesis of O(N2)oligonucleotide sequences (followed by paralleloverlap assembly of a solution space DNA li-brary) and a problem specific sequence of O(N)manual biochemical operations. While Ouyang’sprocedure required less synthesis at the start,more manipulations were necessary. For problemsof significant size (N=20–100), both procedures

J.S. McCaskill / BioSystems 59 (2001) 125–138 127

are prohibitive. A more recent DNA chip basedimplementation of 3-SAT (Liu et al., 2000) alsoscales poorly with problem size in terms of thenumber of different DNA syntheses and manualbiochemical processing steps.

Here, we restrict the oligonucleotide synthesisto be O(N) and independent of the problem in-stance (graph), we impart the graph informationvia a single optical mask (programmable via aconventional computer) and restrict biochemicalprocessing to a simple (graph independent) physi-cal alternation of magnetic field using novel mi-croflow technology. This results in our solutionscaling as N increases so as to retain a smallconstant number of manual biochemical manipu-lations (e.g. final readout).

The microreactors can be constructed by con-ventional photo-lithographic etching of siliconand glass wafers followed by multi-wafer anodicbonding to create sealed channel and chambernetworks. Such microreactors have already beenproduced for evolution research in our laboratory(McCaskill, 1997). As will be shown below, asingle microreactor design is sufficient to describeall possible graph instances up to a maximumsize. Which individual graph problem the DNAcomputer is to address is programmed by theconstruction of a photomask determining a pat-tern of locations at which DNA is to be immobi-lized photochemically onto beads in themicroreactor.

Microreactors allow complicated flow topolo-gies to be realized which can implement adataflow-like architecture for the processing ofDNA. One needs ‘only’ to find a way of program-ming such a device to select DNA moleculescontaining a desired sequence and transfer themto another channel for further pipeline processing.Transfer of specific DNA from one solution toanother can be achieved using magnetic beads, asa solid support. These have already been har-nessed for DNA computing, but only in connec-tion with sequential manual separation steps(Adleman, 1994; Ouyang et al., 1997). The releaseof DNA into the second solution can be achievedby so-called denaturants such as formamide orNaOH. The advantage of using an alkali solutionsuch as NaOH is that the denaturant may be

removed from the solution once without complexseparations by simply adding acid. Two solutionsin a microreactor can be placed in contact byremoving a section of the wall separating twoparallel flow channels without excessive mixing.This allows a magnet to transfer beads betweenconstantly flowing denaturing and non-denaturingsolutions to implement the basic clock step ofhybridization based DNA computing. If the selec-tion-transfer modules are arranged appropriately,a magnet can be used to synchronously clockmultiple modules.

This paper is structured as follows. The basicselection transfer modules (STMs) and their inter-connection are described in the following section.Section 3 describes the architecture for the com-plete selection of cliques, assuming an initial im-mobilization pattern of oligonucleotides to theSTMs. Section 4 describes a parallel optical pro-cedure for programming this starting pattern inwhich the specific graph is only encoded in anoptical mask. The paper concludes with a discus-sion of the significance and potential of thisapproach.

2. Selection transfer module

One key step in DNA processing is to extractall DNA strands with a specific subsequence froma complex population. While magnetic beadspresent an elegant means of doing this, the manip-ulations involved in extraction (separation, wash-ing and eluting the DNA in different buffersolutions) are considerable. In a microreactor, onecould imagine hydrodynamically switching differ-ent chemical solutions into a bead-retainingchamber to do this. However, scaling to largeproblem size, entailing simultaneous switching ofhundreds of flow processes appears unfeasible.Not only the size of the necessary switching units,but also the hydrodynamic stability of such achanging flow scheme seem questionable in a mi-croreactor. Consequently, in this section, we pro-pose a constant fluid flow module which resolvesthese difficulties.

A reversible titration system in continuous flowis employed to provide the necessary conditions


for sequence specific extraction and release ofDNA. DNA hybridization depends on many fac-tors: temperature, ionic strength of the solution,acidity and DNA binding of ligands, polyions andproteins (Manning, 1978). Once the selected DNAhas been separated, by sequence specific hy-bridization to complementary DNA on a solid-phase support, it is transferred to a fresh solutionin which conditions are not congenial to hy-bridization. The selected DNA can be dissociatedby choosing conditions such as high temperatureor high pH. The advantage of temperature issimple reversibility: the solution containing thereleased templates of DNA only needs to becooled again to allow the next separation processto be performed. Problems in controlling manytemperature jumps of 20°C or more on the scaleof 0.1 mm or less, however, make the denseintegration of this approach doubtful, despite therecent demonstration of chip-based PCR (Koppet al., 1998). In the case of chemical hybridizationcontrol, the other factors must be removed, either

physically or chemically, to allow the releasedDNA to rehybridize.

Perhaps the most straightforward case of re-versible chemical hybridization is acid-base titra-tion. The basic idea is to use a saturable neutralpH buffer as the hybridizing solution and a basicsolution (containing an excess of OH− ions) asthe denaturing solution. Stably hybridized (doublestranded) DNA can be dissociated at 37°C in 10mM NaOH solution (pH 12). A fresh buffer,added with a 1:2 dilution, is sufficient to returnthe solution containing released templates to neu-tral pH. This is the specific approach favored inthe current work, although it should be noted thatthe general principles can be applied to manyother separation techniques. The main advantageof the flow system is that, in contrast with a batchprocedure, the salt concentration does not accu-mulate in repeated separations when the flowmodules, to be introduced below, areconcatenated.

Fig. 1. Strand transfer module (STM). Left: symbols used for module designed to select DNA having a subsequence Si at positioni corresponding to the value xi=1 from a mixed population. Right: fluid flow realization of the selection module. Non-matchingDNA (dashed) flows straight through the left hand channel of the STM module. Matching DNA (solid) entering top left, is collectedon a complementary DNA labeled support and then synchronously clocked to the right hand chamber by a magnet where it isreleased into the outflow there. The bead support is then clocked back to the left hand channel, to complete the processing cycle.The solution containing the selected DNA must be neutralized (not shown) before pipelining to other STMs.


The concept of such a module is shown in Fig.1. The basic technique in implementing such amodule is to exploit the limited diffusive mixingof a fluid–fluid interface along the direction oflaminar flow. This has been tested in microreactorexperiments designed for the study of biochemicalreaction–diffusion systems (Bochman, 1997). Be-cause of the low Reynolds numbers in narrowchannels, the fluid flow in microreactors is lami-nar over the entire range of practical flow rates.The lateral diffusive mixing between two differentfluids develops with increasing contact length. Thediffusion constant D of Na+ ions in water is1.25×10−5 cm2 s−1 (Atkins, 1986), so that aseparation greater than the contact width, L=(Dt), is required to prevent the two parallelsolutions from mixing. For optimal operation, thetime t the two fluids are in contact is 10 s, as weshall derive below, and so L=100 mm and theproposed lateral spatial dimension of the STM (ca800 mm) satisfies this criterion. These relativelysharp fluid–fluid interfaces in a steady flow sys-tem allow magnetic beads to be transferred be-tween different proximal chemical solutionswithout switching flows. The use of parallel flowsin microreactors is now finding increasing accep-tance for a wider range of applications (Weigl andYager, 1999).

For DNA selection, super-paramagnetic beadsof ca 10–30 m diameter are restrained in a mi-croreactor flow chamber using a ledge shallowerthan the bead diameter. This concept has alreadyfound successful application in micro-mixing ap-plications (Schmidt and McCaskill, 1998). In thecurrent application on the surface of the beads,prior (photo)chemical treatment has immobilizedDNA sequences complementary to the desiredkey subsequence to be employed in the selection(see Section 4). The biochemical solution flowingon the left contains the population of differentDNA strands from which to select. MatchingDNA strands bind by complementary hybridiza-tion to the magnetic beads situated on this side ofthe module. The beads are then transferred to theright hand flow solution by means of a magnet,passing through the contact surface. Optionally,an additional DNA free buffer solution channelto wash away non-specifically bound DNA may

be interposed. The right hand solution contains adenaturing buffer which separates the hybridizedDNA from the beads, such as a NaOH solution.These then leave the right hand chamber acrossthe bead retaining ledge. The advantage of usingbasic denaturation is that the solution may bereadily converted back to neutral pH by a sepa-rate input channel containing fresh buffer, in or-der to allow selective binding of the DNA tosubsequent STM module beads (this is shown inFig. 2 below).

Note that laminar flow is expected even in thepresence of beads because of the extremely lowReynolds numbers at the low flow rates used insuch microreactors. The dimensions make waterflow like honey without eddy currents, turbulenceor other exotic mixing phenomena. Simple Taylorconvection due to parabolic velocity profiles willassist pure diffusive exchange in the vertical direc-tion, but otherwise material exchange is purelydiffusive.

Many such STM modules can be combined inseries or parallel to create complex selection pro-tocols, as required in DNA computing. Combina-tion of such modules in parallel involves splittingthe inputs A and B into two and combining theoutputs C and D from different modules: thesame bead clocking control can be used for bothchannels. Series combination requires alternatingmodules to be horizontally mirrored so that theDNA supports are in alternating solutions insuccessive modules, i.e. ready to collect the re-leased products of the previous module. Regard-ing subsequences Si as specific binary variables xi,logical functions of the variables can be imple-mented. The logical function (x1�x2)� (x3�x4)for example, describing those DNA sequenceswith either the subsequence x1 or x2 and thesubsequence x3 or x4, can be implemented withfour STMs arranged as shown in Fig. 2. Thecombination of several such STMs leads to thetopological problem of channel crossing in a sin-gle layer design. The microreactor design shownin Fig. 2 shows a two layer structure which can beimplemented using double-sided microstructuringof silicon and anodically bonded borosilicate glass(pyrex) wafers above and below to seal the reactor


Fig. 2. Combination of four STMs to implement (x1�x2)� (x3�x4) strand selection. This design involves two layers of fluid flowinterconnected only at the marked interlayer contacts. The individual modules were shown in more detail in Fig. 1, but here theadditional neutralizing buffer input B, supplied in parallel, is also shown. Each of the two horizontal pairs of modules implementsa logical OR by parallel selection, while the two pairs together implement a logical AND by serial selection. The second pair isinverted to ensure synchronous clocking of strands with a magnet from one module to the next.

(transparently). This technology has been success-fully employed in the production of spatially re-solved microflow reactors for biochemicalexperiments (McCaskill, 1997). Problems withsurface effects and silicon can be alleviatedthrough appropriate coatings and additives.

Although DNA–DNA hybridization in free so-lution is not diffusion-limited, the hybridizationto magnetic beads is, as the following calculationdemonstrates. The diffusion limited second orderrate coefficient of association (Schmolukowski ap-proximation) between two binding partners A and


B of contact radius R and diffusion coefficientsDA and DB is

k1=4p(DA+DB)R. (1)

This expression assumes that the reaction isinstantaneous when the partners reach the radiusR and is expressed in units of (molecules/cm3)−1s−1, which can be converted to M−1s−1

with the factor 10−3 N0, where N0 is Avogadro’snumber. For DNA up to 1 kb in length, diffusionconstants above 10−11 m2 s−1 give rise to diffu-sion limited values of k1\108 M−1 s−1 whereasmeasured hybridization rates kB108 (typicallyk=107) and hence are not diffusion limited. Aninterpolation formula

kfs(t)=eDk2t/R2k12

kErfc

×�kDt

Rk1

n+�

1−eDk2t

R2k12Erfc

�kDtRk1

n�k1 (2)

has been proposed (Noyes, 1961). On the otherhand, for magnetic beads as one of the partners,we calculate the first order rate constant for asso-ciation to a bead from volume V as

k1=4pDAR/V=4pR6 D6 /V6 [s−1] (3)

where the dimensionless parameters R6 , D6 and V6express R, D and V relative to typical dimensionsof 10 mm, 10−6cm2 s−1= (10 mm)2 s−1 and (10mm)3 respectively. With close packed beads on acubic lattice determining the volume, and typicalvalues of D6 =0.2, R6 =0.5 we obtain k1=2p/5$1.2 s−1. (Rates will be 30% larger in hexago-nal closest packed (hcp) configurations.) Thushybridization will be essentially complete after 1 s.At typical immobilization densities for oligoDNAof 40 pmol mg−1 beads, 10 mm beads have anequivalent concentration of c=20 mM in cubicpacked beads (and 28 mM for hcp). Such concen-trations, if homogeneously distributed, would giverise to a typical association rate kc=20×10−6×107=200 s−1. This is the initial rate, which isreduced to the diffusion limited value accordingto Eq. (2), on the time scale (k/k1)2 D/R2$10−3

s. In summary, after a short initial transient, therate becomes largely independent of the homoge-neous rate k and the only dependence on DNA tobe expected is via the diffusion coefficient. Thetime scale of hybridization is thus generically ca

1s for 10 mm beads for typical homogeneousassociation rates in the range 106 to 108 M−1s−1.The rate increases inversely with the square of theradius for smaller beads until the homogeneousrate is attained.

The flow rates appropriate are thus of the orderof 10 mm s−1. With interconnecting channels ofthe order of several bead diameters (50 mm), thisimplies a residence and fluid–fluid interface con-tact time of t=5 s. This is the value used aboveto estimate the lateral dimension necessary for thereactor. With a narrowing cross-section in theconnecting channels (a factor of 10), the ca 500mm separation between STMs can be overcome in5 s, giving a total transit time for the modules of10 s. With N=100 and N2 stages for a largeclique problem (see below), a calculation wouldtake one day.

The key problems with this concept for selectivetransfer of DNA are:1. Non-specific binding of DNA to the beads.

Surface coatings of beads and washing streamscan assist to limit non-specific binding. Anintermediate flow channel can be introduced inthe STM to wash beads as they are beingtransferred from one side to the other. Theproperties of this buffer can be separately ad-justed to provide optimal discrimination be-tween specific and non-specific binding. Thisand repeated selections may resolve some ofthe generic difficulties with specific strand ex-traction via hybridization (Amos et al., 1997).

2. Avoiding extensive dilution of the transferredDNA. The dissociation rate, flow rate andneutralization process determine the extent ofdilution necessary. We expect dissociationrates to be rapid in alkali solution (estimate)compared with the corresponding associationrates, so the specific DNA separated should infact be more concentrated than in the originalsolution after separation. The neutralizationprocess then requires a 1:2 dilution to returnthe strands to a neutral solution capable ofrehybridization.

3. Reliable magnetic transfer of the beads in theface of surface adhesion forces. Superpara-magnetic beads, typically with ca. 10% iron


compounds, can only be moved reliably withstrong magnets exhibiting also strong field gra-dients. Trials in microreactors with 50–100mmhave shown that beads of ]15 mm diametercan be moved reliably in microreactors.

4. Regulating the position of the two fluid con-tact surface. Here detailed hydrodynamic sim-ulation with different geometries can assist indetermining an optimal design. Commercialfluid dynamics simulation packages (e.g.Flumecad® from Microcosm) are available forthis purpose.

A practical implementation is under construc-tion to ascertain the limits posed by these andother potential problems and will be reportedelsewhere. Some basic experiments on hybridiza-tion to beads in microflow reactors have beenreported (Fan et al., 1999), indicating that DNAhybridization in flow can indeed be more rapidand efficient than in bulk solution.

3. Microflow reactor for maximal clique

The decision problem associated with findingmaximal cliques in a graph provides an exampleof an NP-hard problem with comparatively sim-ple input information. It is closely related to thecomplementary problem of finding maximal inde-pendent sets. The problem has already been ad-dressed experimentally for a small instance(Ouyang et al., 1997) and is somewhat simpler inencoding than the standard NP-complete problemN-sat, for which a general DNA computing pro-cedure has been proposed (Lipton, 1995). Theproblem may be divided into two stages: (i) selectfrom all node subsets, those corresponding tocliques in the graph; (ii) find the largest suchelement.

If, following Ouyang et al., (1997), we encodesubsets in such a way that subsets with morenodes correspond to longer sequences, then find-ing the longest molecular sequence is a straight-forward physical separation which may beperformed by gel electrophoresis. As we shallreturn to later, this step may also be performedwith a network of O(N2) STMs, so that in princi-ple a completely microreactor based solution is

possible. The difficult part of the procedure isselecting sequences corresponding to cliques. Ofcourse, such a population could be constructediteratively, as proposed in Head (1999), ratherthan adopting the Adleman and Lipton strategyof selecting from a large initial population. Thishas the great advantage of limiting the amount ofDNA which it is necessary to synthesize, althoughthis still increases exponentially with problem size.Iterative construction could also be performed inmicroreactors, following a similar procedure tothe one outlined here, but using ligase enzymes(Aoi et al., 1999). In this work, however, we wishto concentrate first on the problem of pro-grammable selection rather than synthesis.

Given a graph G, with nodes numbered 1 to Nand an edge set E with elements of the form (i, j )with N] i, j]1, we assume the same type ofencoding of node subsets adopted in Ouyang etal., (1997): for each node i, a distinct subsequences i

0 of length m0 is chosen to indicate the absenceof node i and a second distinct subsequence s i

1 oflength m1\m0 is chosen to indicate the presenceof node i. N such subsequences are ligated to-gether (separated by specific spacer sequences) toform sequences which correspond to vertex sub-sets of the graph G. Parallel overlap assembly(DNA shuffling) allows the construction of DNAlibraries containing all 2N possible subsets, formoderate values of N (Ouyang et al., 1997). Thebasic algorithm for selecting subsets correspond-ing to cliques is: for each node i (from 1 to N) inthe graph, retain only subsets either not contain-ing node i or having only other nodes j such thatthe edges (i, j ) are in the instance graph.

Fig. 3 shows how such a selection step i can beimplemented with individual selection modules. Nsuch steps must be performed in series to reducean initial subset population to cliques.

Two alternative strategies are available in ap-plying the STMs introduced in the previous sec-tion to implement the dataflow processing: eitherone can transfer wanted sequences (positive selec-tion) or unwanted sequences (negative selection).Both strategies are possible because the choice ata particular position (node i ) is binary. The for-mer strategy should be used for greater specificity:only positively recognized sequences are selected,rather than those left behind.


For the sake of simplicity we have presented theless specific, negative selection strategy in Fig. 3.If the microreactor is used iteratively, and strandcapture can be made relatively efficient in theflow, this may still be a good approach. Note thatat step j in the right hand channel, the sequencescontaining a 1 at node j should only be removedfrom the population (down the Y=yes channel) ifthe edge (i, j ) is not in the graph G (i.e. present inthe complementary graph G6 ). In implementingthis, the beads of the associated STM must onlybe loaded with immobilized oligonucleotides com-plementary to the ‘1’ subsequence at node j if theedge (i, j ) is in the complementary graph. Thisdistinction is achieved by photochemical immobi-lization (see the next section) during the setupphase.

A successive modification of the scheme in Fig.3, allows a transition to positive selection and asymmetric and finally modular scheme. Hydrody-namic control benefits from the symmetric and

modular scheme. The specificity should be im-proved with positive selection as shown.

A transition to only positive selection is shownin Fig. 4. To achieve positive selection, the ‘no’channels (labeled N) in the right hand lane of Fig.3 should be the selective transfer outputs ofSTMs. However, then the beads must be loadedboth with the complementary sequence to the ‘0’sequence at node j and if (i, j )�G also with the ‘1’sequence at node j. While this can in principle beaccomplished by a two stage immobilization pro-cess, it would require a switching between twodifferent oligonucleotides along the same channelwhich would complicate the setup phase. In thiscase, it may be better to employ two parallelSTMs, one positively selecting ‘0j’ sequences inde-pendently of the photochemistry and the otherconditionally selection ‘1j’ sequences. The twoparallel outputs should be combined as in the ORmodule described in the previous section. Thescheme shown in Fig. 4C should then be extendedto include three parallel STMs in each serial phaseof the processing (i, j ): (Si=0)�(Sj=0)�((Sj=1)�� (i, j )V(G)). The first two are independentof the photochemistry and may be combined in asingle STM where the beads are loaded with thecomplementary sequences to both (Si=0) and(Sj=0). However, this would increase the com-plexity of the bead loading phase channeling Thethird (graph dependent) condition will be pro-grammed by means of a photochemical mask (seebelow), which ensures that the oligonucleotidescomplementary to the (Sj=1) subsequence areonly then immobilized on the beads in the lastSTM when (i, j ) is an edge of the graph G.

Employing removal of unwanted strands, itwould be possible in principle to perform theentire chain of selection steps in the right handlane with a single separation, using a cocktail ofappropriate DNA oligonucleotides, depending onthe graph, but this would complicate the opticalprogramming of the device.

The selection of DNA sequences correspondingto subsets with a given number of vertices (neces-sary for the clique decision problem) can also beperformed in a network of STMs. This is closelyrelated to the synthesis procedure outlined inBach et al. (1998).

Fig. 3. Schematic of dataflow for selecting sequences fulfillingthe clique criterion at node i. Sequences encoding the presenceof node i follow the right hand outlet of the first (topmost)selection module. Sequences encoding the presence of node j inthe subset are selectively removed from the stream by righthand module j only if (i, j ) is not an edge in the problemgraph G (xij=1), i.e. the STM is oly loaded with the corre-sponding complementary DNA sequene if (i, j ) is an edge inthe complementary graph to E(G). The remaining sequencesare combined into a single output channel.


Fig. 4. Alternative forms of the data selection flow, having the same logical outcome, for stage i of the clique filtering scheme. (A)Identical scheme to Fig. 3, but with active selection of subsequences corresponding to binary 0 or 1 (rather than subtractiveselection). The logical variables xij are 0 or 1 depending on whether edge (i, j ) is in the graph or not. (B) As in (A) but balancedso that each pathway has the same number of STMs. (C) Modular scheme consisting of a series of identical small modules, obtainedby joining channels locally in (B).

4. Optically programming graph instances

As seen in the previous section, microflow net-works of STMs can be used to perform complexselections if the appropriate DNA oligonucle-otides are immobilized onto beads at specific loca-tions in the network. While it may be moreconvenient for medium scale problems to usebead dispensing systems to deliver the correctlylabeled bead (out of the 2N different ones) to theappropriate location in the microreactor, we see agreater scalability in delivering a single type of(unlabeled) bead to each of the STMs in paralleland then making yes–no labeling decisions via anoptical signal photochemically. The STMs arearranged in rows and columns such that all STMsin a row or column either have the same oligonu-cleotide label attached or are unlabeled. Duringthe setup (immobilization) phase then, only onetype of oligonucleotide sequence flows past anygiven bead. UV light, through a photolitho-graphic mask, then determines whether the se-quences are immobilized at each STM or not.

An overall flow scheme which can be used tosupport this immobilization procedure, compat-ibly with the above network for the clique prob-

lem, is shown in Fig. 5. In the initialization phase,the chemicals for photo-immobilization flow inparallel down the horizontal channels used laterfor the denaturation of hybridized DNA. All butone STM on the jth horizontal level have thesame oligonucleotide O6 j in the flow for light de-pendent immobilization: so that the horizontalimmobilization pattern is simply on or off for O6 j.A separate supply channel is provided for the oneSTM to be loaded with 16 j on each level, this STMis loaded independently of the particular graphinstance and does not require photochemicalmodulation. While this flow is sustained, the mi-croreactor is illuminated with UV light through amask which is opened above the relevant STMs.The mask pattern is a direct conversion of thebinary matrix representing the edges of the graphG to a pattern of opaque and transparent squares.Alternate serial STMs must be reflected to allowparallel magnetic synchronization. A balanced de-sign can be achieved by using N copies of thesame STM in both arms of each stage of theprocessing: this would also even up the hydrody-namic flow. N copies of the STM selecting subsetsnot containing node i (06 i) are placed in the lefthand branch, increasing the stringency of theselection, as in Fig. 4.


Hybridization of DNA immobilized onto solidsupports is a very common technique in molecularbiology for the isolation, identification, amplifica-tion, sequencing and genetic analysis of DNA.

What is required in the current work is a photo-chemically triggered, end-specific covalent attach-ment of DNA to bead surfaces which can beimplemented in situ for beads in flow chambers in

Fig. 5. Maximal clique: iterative solution in microflow reactor. Two of the N steps (from i−1 to i+1) of the full clique filteringprocess in microflow. Each step corresponds to the logical scheme shown in Fig. 4C, but the right hand STMs have been split intotwo (as discussed in Section 3) to allow a photo-programmable, completely positive selection solution. The 2N (N) blue labeledhorizontal (vertical) channels, are used to deliver one of 2N (N) oligonucleotide sequences for potential photo-immobilization on thebeads in each row (column) during the initial loading phase. The STMs in the third column of each stage are either illuminatedduring the parallel immobilization process or not, depending on a single photomask (non-illuminated STMs are covered by a graytranslucent screen in the diagram). After initialization, the blue channels carry uniformly the denaturation agent (NaOH). Everysecond sub-stage (horizontal level) has the STM connections inverted, so that the magnetic beads are in opposing buffer solutionsin alternating layers during operation. This enables the products released from level 1 (beads right) to be captured in level 2 andreleased synchronously to level 3 when the beads are transferred to the left hand side. The buffer solution is neutralized by anadditional channel (green) before the released DNA is delivered to the next stage. The horizontal channels in darker shades areconnected to the upper layer by vias (through connections) marked with a black square.


a microreactor. Commercially available DNAchips (Affymetrix) do not use a photo-immobi-lization procedure, but instead employ light di-rected DNA synthesis (Fodor et al., 1991). Thebinding of biotin labeled DNA to streptavidincoated surfaces achieves relatively high affinity inthe appropriate buffer solution at moderate load-ing densities. However, the stability of the com-plex is affected by different buffer solutions andlong periods of flow. Covalent photo-crosslinkingof DNA to solid supports has been developed(Kalachnikov et al., 1992), but the DNA is at-tached at random bonds along its length so thathybridization to this DNA is not reliable. Forthese reasons, a novel photoactivatable, covalentend-specific attachment of DNA to chemicallyfunctionalized magnetic beads has been developed(Penchovsky et al., 2000). The procedure requiresorganic solvents which are compatible with exist-ing microreactors (cf. Section 2) and has beendemonstrated to work in them (Penchovsky et al.,2000).

5. Conclusions

The above approach differs in the type of pro-gramming from previous experimental approachesto DNA computing in vitro (Adleman, 1994;Guarnieri et al., 1996; Sakamoto et al., 1999;Ouyang et al., 1997; Liu et al., 2000; Faulhammeret al., 2000) and in vivo (Khodor and Gifford,1999). Instead of programming by a manual seriesof biochemical pipetting operations, the entirefluid flow is held constant and a single lightpattern determines the program. Attention hasbeen paid to providing a scalable hands-off mi-crosystem technology for tackling large problems.Rather than making a catalog of possible, cur-rently in practice not yet truly integrable mi-crosystem modules, the current approach uses justone module, the STM, to perform calculations.This selection module will also have practicalutility in other areas of biomolecular processingsuch as evolutionary biotechnology. A furtherdevelopment involving dynamical photochemicalreconfiguration and evolution is planned.

As outlined in this paper, the approach onlythen provides a polynomial time (quadratic) solu-tion as the graph size increases, when the DNApopulation remains larger than the exponentiallygrowing solution space. Typical DNA popula-tions may be as large as 1017 molecules, withoutadopting a major biochemical scale-up, which al-ready allows maximum clique problems hard formodern computers to be tackled, but this windowof opportunity is small. It is clear that betteralgorithms, some of which have already beenproposed, will be necessary to give DNA comput-ing a valid computational niche. We have deliber-ately refrained from more complex algorithmshere, in order to focus on the basic scale upproblem. The construction of new solutions dur-ing the processing, necessary to overcome thelimitation of finite population size and exhaustivesearch, is possible both off-chip or using the sameSTM modules on-chip, with the DNA immobi-lized to the beads as primers for ligation or chem-ical PCR. Experiments in this direction are inprogress. More active MIMD processing is alsoachievable using the catalytic properties of DNA-and RNA-based enzymes. Because of the flow-setup, there is also no problem in introducingfeedback to the data-flow structure to allow itera-tive processing. If, instead of just transferringstrands, they are copied with variation, then anevolutionary algorithm may result from the itera-tive processing. This type of algorithm appears tohave a good match to the capabilities of DNAcomputing.

The microflow technology employed heredemonstrates that DNA processing can be pro-grammed dynamically without switching flows orusing a plurality of separate control devices. Ex-perience with currently functioning microreactorshave shown that it is wise at the current state ofdesign technology to keep components extremelysimple if a high scale-up is to be achieved. Thusthe current design presents a major step towards arealistic scale-up of DNA computing: hydrody-namic flows do not need to be switched; all mag-netic beads move in parallel under the control ofa single magnet; the problem instance is impartedsolely by an optical mask and only the same 2Noligonucleotides need to be synthesized for all


possible instances of a graph with up to N nodes.This is in contrast to speculation about the inte-gration of all manner of microfluidic componentsfor the implementation of microflow biomolecularcomputing (Gehani and Reif, 1999). It also differsfrom the surface (DNA chip) based approach(Frutos et al., 1997) and (Liu et al., 2000), whichentails large numbers of external processing stepsand DNA synthesis. The use of microflow reac-tors as described here was first proposed in talksby the author at two international workshops onDNA computing (Leiden, USA 1998; Princeton,USA 1999) and is now under construction in St.Augustin.

An assessment of errors associated with thebead based hybridization approach must beflanked by experimental evidence. Of course re-dundancy can be built into the array of STMs tocompensate for errors. It would be worthwhilehere simply to characterize the different factorsinfluencing fidelity. Two recent experimentalanalyses of errors in the hybridization processassociated with ligation have appeared (James etal., 1998; Cukras et al., 1999).

The technique is not restricted to the maximalclique problem. Indeed a solution scheme utilizingthe same architecture has been developed for 3-SAT. This will be reported in a separate paper.Although experimental work on implementingand linking up the STM modules has alreadyachieved significant success, this will be reportedin the relevant journals. The current work is adesign paper showing how principal problems inthe implementation of DNA computing can beresolved.

Acknowledgements

The author would like to thank R. Penchovskyand D. van Noort for a careful reading of themanuscript.

References

Adleman, L.M., 1994. Molecular computation of solutions tocombinatorial problems. Science 266, 1021–1024.

Amos, M., Gibbons, A., Dunne, P.E., 1997. The complexityand viability of DNA computations. In: Olsson, B.,Lundh, D., Narayanan, A. (Eds.), Biocomputing andEmergent Computations. World Scientific, London,Singapore.

Aoi, Y., et al., 1999. Ligation errors in DNA computing.Biosystems 22, 181–187.

Atkins, P.W., 1986. Physical Chemistry, 3rd. Oxford Univer-sity Press, Oxford.

Bach, E., Condon, A, Glaser, E., Tanguay, C., 1998. DNAmodels and algorithms for NP-complete problems. J.Comp. Sys. Sci. 57, 172–186.

Back, T., 1996. Evolutionary Algorithms in Theory and Prac-tice. Oxford University Press, New York.

Bennett, C.H., 1982. The thermodynamics of computation —a review. Int. J. Theoret. Phys. 21, 905–940.

Bochman, A., 1997. Experimentelle Untersuchungen an bio-chemischen Reaktionssystemen mittels fluorimetrischenMethoden. Dipl. Thesis, Physics and Astronomy Faculty,University of Jena, Germany.

Cukras, A.R., Faulhammer, D., Lipton, R.J., Landweber,L.F., 1999. Chess games: a model for RNA based compu-tation. Biosystems 52, 35–45.

Fan, Z.H., Mangru, S., Granzow, R., Heaney, P., Ho, W.,Dong, Q., et al., 1999. Dynamic DNA hybridization on achip using paramagnetic beads. Anal. Chem. 71, 4851–4859.

Faulhammer, D., Cukras, A.R., Lipton, R.J., Landweber, L.,2000. Molecular computation: RNA solutions to chessproblems. Proc. Natl. Acad. Sci. 97 (4), 1385–1389.

Fodor, S.P.A., Read, J.L., Pirrung, C., Stryer, L., Lu, A.T.,Solas, D., 1991. Light directed spatially addressable paral-lel chemical synthesis. Science 274, 767–773.

Frutos, A.G., et al., 1997. Demonstration of a word designstrategy for DNA computing on surfaces. Nucl. Acids Res.25, 4748–4757.

Garey, M.R., Johnson, D.S., 1979. Computers and Intractabil-ity. Freeman, New York.

Gehani, A., Reif, J., 1999. Microflow bio-molecular computa-tion. Biosystems 52, 197–216.

Guarnieri, F., Fliss, M., Bancroft, C., 1996. Making DNAadd. Science 273, 220–223.

Head, T., 1999. Maximal cliques and DNA. Preprint. LeidenCenter for Natural Computing, Leiden, Netherlands.

James, K.D., Boles, A.R, Henckel, D., Ellington, A.D., 1998.The fidelity of template-directed oligonucleotide ligationand its relevance to DNA computation. Nucl. Acids Res.26, 5203–5211.

Kalachnikov, S.M., Adarichev, V.A., Dymshits, G.M., 1992.Ultraviolet cross-linking of DNA to microporous mem-branes. Bioorg. Khim. 18, 52–62.

Khodor, J., Gifford, D.K., 1999. Design and implementationof computational systems based on programmed mutagen-esis. Biosystems 52, 93–97.

Klein, J.P., Leete, T.H., Rubin, H., 1999. A biomolecularimplementation of logically reversible computation withminimal energy dissipation. Biosystems 52, 15–23.


Kopp, M.U., de Mello, A.J., Manz, A., 1998. Chemical am-plification: continuous flow PCR on chip. Science 280,1046–1048.

Lipton, R., 1995. DNA solution of hard combinatorial prob-lems. Science 268, 542–545.

Liu, Q., Wang, L., Frutos, A.G., Condon, A.E., Corn, R.M.,Smith, L.M., 2000. DNA computing on surfaces. Nature403, 175–179.

Manning, G.R., 1978. The molecular theory of polyelectrolytesolutions with applications to electrolyte properties ofpolynucleotides. Quart. Rev. Biophys. 11, 179.

McCaskill, J.S., 1997. Spatially resolved in vitro molecularecology. Biophys. Chem. 66, 145–158.

von Neumann, J., 1949. In: Burks, A.J. (Ed.), Theory ofSelf-Reproducing Automata — 1966. University of IllinoisPress, Illinois.

Noyes, R.M., 1961. Effects of diffusion rates. Prog. React.Kinet. 1, 129–160.

Ouyang, Q., Kaplan, P.D., Liu, S., Libacher, A., 1997. DNAsolution to the maximal clique problem. Science 278, 446–449.

Penchovsky, R., Birch-Hirschfeld, E., McCaskill, J.S., 2000.End specific covalent photo-immobilization of syntheticDNA to paramagnetic beads. Nucl. Acids. Res 28 (22),e98, 1–6.

Sakamoto, K., et al., 1999. State transitions by molecules.Biosystems 52, 81–91.

Schmidt, K., McCaskill, J.S., 1998. Schaltbarer dynamischerMikromischer mit minimalen Totvolumen. InternationalPatent Application, PCT/EP98/03942.

Weigl, B., Yager, P., 1999. Microfluidic diffusion-based sepa-ration and detection. Science 283, 346–347.

.

Documents

Optically programming DNA computing in microﬂow reactorsBioSystems 59 (2001) 125–138 Optically programming DNA computing in microﬂow reactors John S. McCaskill * GMD-German National