DOI: 10.1002/asia.201100664

Connectable DNA Logic Gates: OR and XOR Logics

Yulia V. Gerasimova and Dmitry M. Kolpashchikov*[a]

Introduction

Current microprocessor systems are based on semiconductorlogic gates that employ electronic input and output signalsand a power supply.[1] Data manipulation relies on thebinary digital nature of these signals, which protects againstnoise accumulated from serial operations and transmissionover distances. Each type of logic gate has a specific input–output signal correlation pattern, which is described by atruth table arising from George Boole�s classical ideas.[1,2]

Voltages can be simply high or low (above or below athreshold value), which corresponds to digital 1 or 0, respec-tively. A critical feature that contributes to the success ofelectronic circuits is input–output signal uniformity: thesame voltage value emerging as an output of one gate canbe admitted as an input of another gate. Such connectionsof logic units enable one to achieve desired functions ofvarying complexity. Very large scale integration is a crucialcomponent of modern silicon processors.[2] The developmentof more powerful processors depends on continued progressin miniaturizing their components. However, if currenttrends continue, conventional silicon chips will soon reachtheir physical limits.[3] By then, their transistors will be sosmall that current leakage will become an insurmountableproblem. It is believed that constructing computers in whichcomputations are performed by individual molecules is “theinevitable wave of the future”.[3] Although the potential ad-

vantage of nanometer-sized devices is not a novel concept,[4]

the implementation of concerted arrays of molecules re-mains challenging.

A number of research groups have created molecular en-sembles that perform logic operations.[2] Despite the factthat small scale connectivity of logic elements has been ach-ieved, there is still a lack of universal large-scale integration.One of the most important routes to the development of amolecular logic gate is believed to be “exploring new waysof serially integrating molecular logic gates”.[2c] This studycontributes to the development of molecular logic gates thatcan be uniformly connected to each other.

DNA has been considered as an excellent candidate for invitro computation,[5] as well as a convenient building blockfor molecular computational elements.[2] A number of DNAlogic gates have been designed in recent years.[6] However,the input/output homogeneity was not preserved in most ofthe designs. For example, in the deoxyribozyme gates devel-oped by Stojanovic et al. ,[7] the logic units were controlledby oligonucleotide inputs, while an enzymatic activity wasgenerated as an output. The logic gates were integrated insimple circuits by using a cascade of deoxyribozyme ligases,which communicated with a deoxyribozyme phosphodiester-ase.[7c] In this cascade, the oligonucleotide output synthe-sized by a DNA ligase served as an input for the down-stream phosphodiesterase YES gate. The rate of the inter-gate communication was limited by the ligation product re-lease. This process is slow because the oligonucleotide liga-tion product is longer and binds to ligase tighter than eachof the two substrates. The connectivity of logic gates wasachieved in a simple model reaction. However, there is adoubt that this approach will be useful for more complexnetworks.

At the same time, catalytic activity is not required for in-formation processing; hybridization-based DNA constructscan perform logic operations.[8] For example, entropy-driven

Abstract: Modern computer processorsare based on semiconductor logic gatesconnected to each other in complex cir-cuits. This study contributes to the de-velopment of a new class of connecta-ble logic gates made of DNA in whichthe transfer of oligonucleotide frag-ments as input/output signals occursupon hybridization of DNA sequences.The DNA strands responsible for a

logic function form associates contain-ing immobile DNA four-way junctionstructures when the signal is high anddissociate into separate strands whenthe signal is low. A basic set of logic

gates (NOT, AND, and OR) was de-signed. Two NOT gates, two ANDgates, and an OR gate were connectedin a network that corresponds to anXOR logic function. The design of thelogic gates presented here may contrib-ute to the development of the first bio-compatible molecular computer.

Keywords: DNA · logic gates ·molecular beacons · molecularcomputing · nanotechnology

[a] Dr. Y. V. Gerasimova, Dr. D. M. KolpashchikovChemistry DepartmentUniversity of Central Florida4000 Central Florida Blvd.Orlando, FL 32816-2366 (USA)Fax: (+1) 407-823-2252E-mail : Dmitry.Kolpashchikov@mail.ucf.edu

Supporting information for this article is available on the WWWunder http://dx.doi.org/10.1002/asia.201100664.

534 � 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Asian J. 2012, 7, 534 – 540

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catalytic gates developed by Seelig et al.[8a] use single-strand-ed nucleic acids as inputs and outputs. Again, the mecha-nism of gate communication relied on the strand displace-ment. The communication between the gates was achievedby cascading: an output oligonucleotide of one gate that hadbeen displaced from a DNA duplex by an input oligonucleo-tide served as an input for a downstream gate. A similar ap-proach for signal transfer in modular multilevel circuitsfrom solid-support-immobilized DNA-based logic gates wasreported.[8c,d] However, such systems operate slowly requir-ing hours to reach half-activation for multistep circuits.These low operation rates can be attributed to multiple rela-tively slow strand-displacement events that occur successive-ly during cascading.

We suggest an alternative scheme for inter-gate communi-cation of DNA logic gates. Recently, we have reported onthe design of a NOT and a two-input AND gate, and dem-onstrated the possibility to integrate the two gates in an IN-HIBIT logic (Figure 1).[9] Unlike previously suggested DNAgates,[6–8] the new design does not require strand-displace-ment hybridization or enzymatic catalysis for output release.Instead, signal transduction is mediated by the associationof several DNA strands. This may reduce the time for signaltransmission. Indeed, DNA hybridization requires only sec-onds to be completed.[10] The key features of this design arethe following: 1) short oligonucleotide fragments function asboth inputs and outputs; 2) cooperative action of two oligo-nucleotide fragments (signal-transmitting arms) is requiredto generate a high signal; and 3) transfer of the high signalis mediated by assembling the DNA strands in DNA-branched structures stabilized by DNA four-way junction(4J) elements.

In this study we demonstrate three-level integration of 4J-based DNA logic gates. First, we designed two NOT andtwo AND gates and incorporated them into two INHIBITgates. Second, we constructed an OR logic gate based onthe principles of 4J complex formation. Finally, the twoNOT gates, two AND gates, and OR gate were connectedin an exclusive OR (XOR) logic unit. The suggested ap-proach for inter-gate communication can be used in thedesign of more sophisticated nucleic acid based circuits.

Results and Discussion

The DNA logic gates described here take advantage ofDNA 4J structures to stabilize complex branched DNA as-sociates. The DNA 4J structure is a well-characterized struc-tural element, which is found in nature and known as Holli-day junction.[11] Immobile 4J structures have been widelyused in DNA nanotechnology for building 2D DNA latticesand other structures of desired shape.[12] We took advantageof the formation of 4J structures to build stable DNA associ-ates capable of transferring oligonucleotide output signals.As an option, the output can be conveniently detected inreal time by using a molecular beacon (MB) probe.[13] AMB probe is a DNA oligonucleotide that folds in a stem-loop structure (Figure 1 a). The oligonucleotide contains afluorophore at its 5’-end and a quencher at its 3’-end. Thequencher reduces the fluorophore�s fluorescence when theMB probe is folded in the stem-loop conformation. Bindingto a complementary oligonucleotide separates the fluoro-phore from the quencher, thus enabling an increase in fluo-rescence.

Below, we describe the design of NOT, AND, and ORgates, a basic set of logic gates that is sufficient to createany desired logic by connection of the gates to each other.[1]

We demonstrate how these gates can be connected to pro-duce INHIBIT and XOR logics.

Abstract in Russian:

Figure 1. Principle design of the connectable NOT, AND, and INHIBITDNA logic gates. a) NOT logic gate. b) AND gate. c) NOT gate connect-ed to the AND gate forms the INHIBIT logic. The input-recognition re-gions are gray. The signal-transmitting arms are shown in bold, and theTEG linkers are shown as dashed lines.

Chem. Asian J. 2012, 7, 534 – 540 � 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.chemasianj.org 535

NOT gates

The inverter, or NOT gate, switches from a high- to low-output signal when an input is applied (Figure 1 a). We de-signed two NOT gates, each of which was represented by asingle oligonucleotide strand containing two signal-transmit-ting arms and an input-recognizing region (Figure 1 a). Inthe absence of an input oligonucleotide, the NOT gateformed a folded dumbbell-like structure. In this structure,the signal-transmitting arms were brought together to hy-bridize to an MB probe, which fluorescently reported thehigh-output signal. The fluorescing associate was stabilizedby the 4J-like structure, which contained triethylene glycol(TEG) linkers at the point of strands crossing (dashed linesin Figure 1 and other figures). The introduction of TEGlinkers was important for maintaining the desirable confor-mation of the gates. It was shown that out of two possibleconformations of the DNA 4J structure,[11] TEG modifica-tion stabilizes the one that contains the MB probe in theelongated conformation, thus enabling high fluorescence ofthe DNA associate.[14] The 4J-containing complex betweenthe MB probe and the NOT gate can be reversibly decom-posed by the addition of an oligonucleotide input that iscomplementary to the NOT strand.[9] The thermodynamicbasis for the dissociation of the NOT gate from the complexwith the MB probe is the following: the hybridization of theinput oligonucleotide destroys the stabilizing 4J-like struc-ture. The two signal-transmitting arms are unable to effi-ciently open the MB probe without stabilization by 4J.

The design of a NOT gate used in the present study,NOT1, is shown in Figure 2. The NOT1 DNA strand is hy-bridized to MB-NOT1 (Figure 2 a, top). In this complex,MB-NOT1 was in an open, highly fluorescent conformation(Figure 2 b, curve 2 and bar 2). Addition of an input (I-NOT1) destroyed the 4J-like motif of the NOT1/MB-NOT1associate. As a result, the signal-transmitting arms could nolonger bind MB-NOT1, and MB-NOT1 was released fromthe complex (Figure 2 a, bottom). The free MB-NOT1 ac-quired the closed conformation, and the fluorescent signalwas low (Figure 2 b, curve 3 and bar 3). The fluorescence in-tensity of the NOT1 gate in the presence of I-NOT1 wasalmost equal to that of the control (MB-NOT1; Figure 2b,compare bars 1 and 3). Notably, the high- and low-fluores-cence outputs were observed immediately (in seconds) afteraddition of the input (data not shown). However, the datain Figure 2 b represents the fluorescent response of the gateafter 15 min, since within this incubation time the fluores-cent response of MB-NOT1 was stabilized. Similar princi-ples were used for the design of the NOT2 gate (see theSupporting Information). The behavior of the NOT2 gatecorresponded to the NOT logic, as predicted.

AND Gate

Two-input AND logic produces a high output only if bothinputs are introduced, according to the truth table shown inFigure 1 b. The gate consisted of the three DNA hairpins

AND-a, AND-b, and AND-c. The loop regions of the twohairpins (input-recognizing regions) were complementary tothe input oligonucleotides. The third hairpin AND-c wascomplementary to the remaining portions of AND-a andAND-b and was required for stabilization of the 4J complex.In the absence of inputs, all three hairpins coexisted in solu-tion in the dissociated form (Figure 1 b, left). Hybridizationof the two input oligonucleotides to the AND-a and AND-bhairpins resulted in the formation of the 4J-like DNA asso-ciate, which was detected by an MB probe (Figure 1 b,right). If one of the inputs was present, no fluorescent asso-ciate was formed, as partial associates with the gate�s strandsand either one of the two inputs are unstable. High signaloutput was detected only in the presence of both inputs si-multaneously. The design of AND1 gate was reported by usrecently.[9] The AND2 gate was designed using the sameprinciples (see the Supporting Information). The digital gateperformance of the gate was found to be excellent; it pro-

Figure 2. NOT gate. a) Secondary structure of the NOT1 gate in the ab-sence (top) or presence (bottom) of the oligonucleotide input I-NOT1.FAM and Q are fluorescein and dabcyl groups, respectively. The signal-transmitting arms are shown in bold. The input-recognizing fragment isshown in gray italic font. The TEG linkers are shown as dashed lines.b) Fluorescence emission spectra of the NOT gate in the absence (2) orpresence (3) of the input oligonucleotide; fluorescence background ofMB-NOT1 (1). Inset: fluorescent intensities at 517 nm after 15 min of in-cubation.

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FULL PAPERSY. V. Gerasimova and D. M. Kolpashchikov

duced a high signal only in the presence of the two input oli-gonucleotides.

INHIBIT Gates

INHIBIT logic generates a high output signal only in thepresence of one of the two inputs, while low output is pro-duced in the presence of another input or in the absence ofinputs (truth table in Figure 1 c). We have achieved thislogic by connecting NOT and AND gates, as shown by thescheme in Figure 1 c.

Figure 3 demonstrates how NOT2 and AND2 gates de-signed in this work can be connected to produce INHIBITlogic. The signal-transmitting arms of NOT2 were comple-mentary to the recognition region of AND2-a hairpin. Inthe absence of inputs, all DNA strands were in the closedhairpin conformations (Figure 3 a, top). The signal-transmit-ting arms of NOT2 could bind to the recognition region ofAND2-a and trigger the formation of partial associatesNOT2/AND2-a/AND-c, but even if formed, these associateswere unable to open up MB-AND2 and thereby produce ahigh fluorescent signal. When input I-NOT1 was added, it

hybridized to the input-recognition region of the AND2-bhairpin, thus opening AND2-b and enabling it to hybridizewith AND-c and MB-AND2. AND2-a was opened by hy-bridization with the signal-transmitting arms of the NOT2gate. Therefore, the components of the gate cooperativelyhybridize to each other to form the complex with two 4J-like structures. The AND–NOT associate contained the re-porter MB-AND2 in the elongated form (Figure 3 a,bottom). High fluorescence corresponded to the high-outputsignal (Figure 3 b, bar 2). Addition of a second oligonucleo-tide input (I-NOT2 in the Supporting Information) resultedin its hybridization to the recognition region of NOT2,which triggered the dissociation of NOT2 from the complex.The remaining associate was unstable; dissociation of NOT2triggered the dissociation of all the strands into solution;MB-AND2 was released from the complex as a hairpin,thereby leading to the low fluorescent signal (Figure 3 b,bar 4). The INHIBIT-1 gate was constructed according tothe same principles by connecting AND-1 to NOT-1 gates(see the Supporting Information). The logic behavior of theINHIBIT-1 gate corresponded to the truth table (Figure 1 c).

OR Gate

Any Boolean logic function can be achieved by connectingNOT, AND, and OR logic units in networks.[1] In this study,we have completed the design of the basic set of logic gatesby introducing a construct that performs an OR logic opera-tion.

A two-input OR gate produces a high-output signal in thepresence of each input separately or two inputs simultane-ously, according to the truth table (Figure 4 a). In ourdesign, a two-input DNA OR gate consisted of threestrands, OR-a, OR-b, and OR-c, and a fluorescent reporter,MB-OR. Strands OR-b and OR-c contained input-recogniz-ing regions in their loop portions (fragments in bold inFigure 4), which were complementary to I1-OR and I2-OR,respectively. In the absence of input oligonucleotides, allfour strands preferably acquired dissociated conformations,thus generating a low fluorescent output signal. I1-OR,when present, bound to OR-b and, together with OR-a andMB-OR, formed a fluorescent associate (Figure 4 b). A simi-lar associate was formed between OR-c, OR-a, and MB-ORin the presence of the second input, I2-OR. We observedthat the fluorescent response of the mixture of the hairpinsOR-a, OR-b, OR-c, and MB-OR corresponded to the pre-dicted logic behavior (Figure 4 c).

Using the principle for OR gate design, multi-input ORgates can be constructed: each additional channel requiresthe addition of one strand that contains a specific input-rec-ognition module. With the design of an OR gate, a set ofthe basic logic gates is completed. Using NOT, AND, andOR logic, any other logic units can be created simply byconnecting the three gates in complex circuits. Below, wedemonstrate how five logic gates developed in this study canbe connected to produce XOR logic.

Figure 3. The design and performance of the INHIBIT-2 gate. a) Predict-ed secondary structure of the INHIBIT gate in the presence of I-NOT1input (high signal output). The signal-transmitting arms are shown inbold. The input-recognition regions are shown in gray italic font. TheTEG linkers are shown as dashed lines. b) Fluorescent response of theINHIBIT gate in the presence of various input combinations.

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Connectable DNA Logic Gates

XOR Gate

The exclusive OR (XOR) gate is the key component ofhalf- and full-adders. On the molecular level, it is a hard-to-obtain logic.[2] A two-input XOR gate generates high outputin the presence of each of the two inputs separately, whereasin the presence of both inputs simultaneously the output be-comes low, according to the truth table (Figure 5 a). Thislogic can be obtained by connecting two NOT gates withtwo AND gates and an OR gate, according to the schemeshown in Figure 5 a.

In our design, outputs of NOT1 and NOT2 gates wererecognized as inputs by AND1 and AND2 gates, respective-ly. For this purpose, the signal-transmitting arms of NOT1and NOT2 were made complementary to the loop portionsof hairpins AND1-a and AND2-a, respectively, as it was forthe INHIBIT-1 and INHIBIT-2 gates (Figure 3 and in theSupporting Information). The input I-NOT1 was comple-mentary both to the input-recognition region of NOT1 andto the loop portion (input-recognition region) of the AND2-b hairpin. Correspondingly, I-NOT2 was complementary toNOT2 and AND1-b. To connect AND gates with an ORgate, the signal-transmitting arms of the AND1 and AND2gates were complementary to hairpins OR-b and OR-c, re-spectively. Thus, outputs of AND gates served as inputs forthe OR gate.

All of the DNA logic gates described above were mixedtogether in the presence of MB-OR as the only fluorescentreporter (Figure 5 b). Fluorescent associates I and II were

Figure 4. The structure and performance of the two-input OR gate.a) Gate symbol and the truth table. b) The structure of the OR gate inthe absence and in the presence of input oligonucleotides. The TEG link-ers are shown as dashed lines and arcs. The input-recognition regions areshown in bold. The signal-transmitting arms are in gray italic font.c) Fluorescence response of the gate in the presence of various inputcombinations.

Figure 5. XOR gate. a) The symbol; two NOT, two AND, and an ORgate connected in XOR logic, and the truth table. b) The structures of as-sociates I and II in the presence of one of the two inputs. The input-rec-ognition regions are in gray italic font. The signal-transmitting arms arein bold. The TEG linkers are shown as dashed lines. c) Fluorescence re-sponse of the gate in the presence of different input combinations.

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formed upon addition of inputs I-NOT2 and I-NOT1, re-spectively. In the presence of both inputs, both associateswere destroyed by hybridization of I-NOT1 to NOT1 and I-NOT2 to NOT2. Indeed, the high fluorescent signal was ob-served in the presence of only one of the two inputs but notin the absence or presence of both inputs (Figure 5 c), as itis implied by XOR logic. It should be noted that the signal-to-background ratio for the XOR gate was only about 2.This value is lower than that of individual gates, for which itwas at least 4. This relatively low turn-on response can beexplained by the relatively high background produced bythe imperfect digital behavior of the gates. It is likely thatpartial associates of DNA strands were formed even in theabsence of input oligonucleotides. Moreover, an extendedtime (about 30 min) was required to register the proper digi-tal response of the gates. These observations suggest thatlarger gate integration will soon bring us to the limit implicitby the present design. We realize that, in general, for the un-limited gate-to-gate signal transfer, an unlimited energyinput is required, as it is implemented in electronic devicesthat use power supplies. In our design of DNA logic gates,formation of the high-energy associates is triggered only bya limited energy source, that is, by the hybridization of a 16-nt input. Therefore, to make the connectivity of the DNAlogic gates universal and extendable to deeper integration,the problem of an energy source that would stabilize the for-mation of the DNA associates should be solved. On theother hand, we believe that a significantly more complexnetwork of integrated gates can be achieved by positioningthe gates in close proximity in a nano environment. In thiscase the gates will communicate only with the neighboringgates, thus reducing the crosstalk.

Conclusions

DNA logic gates presented in this work contribute to the so-lution of the problem of universal connectivity. The designof the gates is straightforward, and the response occurswithin the time of DNA hybridization. The gates have varia-ble domains, such as the stem-loop structures, which providethe signal transduction by switching from open to closedconformations, and vice versa. The modular structure of thegates makes it easy to further optimize input and output se-quences to improve the gates� digital performance. Howev-er, the pivotal elements for the design are the following:1) The input–output homogeneity is achieved by using oligo-nucleotides as inputs and outputs; 2) The gates� outputs aretwo-component, as the synergetic action of two parts of thesignal-transmitting arms is required for signal transfer; and3) The associates generating high output are stabilized byDNA 4J structures.

Despite the fact that the rate of the signal transduction isstill significantly lower than that of electronic devices,DNA-based logic elements have advantages such as biocom-patibility, which open a venue for biocybernetics. Anotherpossible advantage of the gates, which has not been ex-

plored in this work, is their apparent compatibility with 4J-containing structures developed by DNA nanotechnolo-gy.[2d,12] The ordering of DNA logic gates in arrays on a two-dimensional scaffold could be the next step in the develop-ment of DNA-based processors. One possibility to achievethis is to use 2D DNA lattices[15] made of double-crossover(DX) molecules or M13mp18 genomic DNA folded into a100 nm-sized DNA chip.[16]

Experimental Section

DNAse/RNAse-free water was purchased from Fisher Scientific Inc.(Pittsburgh, PA) and used for all buffers and for stock solutions of oligo-nucleotides. Oligonucleotides were custom-made by Integrated DNATechnologies, Inc. (Coralville, IA) and were purified by polyacrylamidegel electrophoresis (PAGE). The concentration of the oligonucleotides instock solutions was determined using the optical density at 260 nm, whichwas measured using an Ultrospec 3300 spectrophotometer (AmershamBiosciences, NJ, USA). Fluorescent spectra were recorded on a LS-55 lu-minescence spectrometer (Perkin–Elmer, San Jose, CA) equipped with aHamamatsu xenon lamp. Experiments were performed at the excitationwavelength of 485 nm and emission scan of 500–550 nm.

Logic Strands Design

The design of logic strands was accomplished using NUPACK web-basedsoftware.[17] The strands were designed to function at 22 8C in 50 mm

MgCl2. The concentrations and the design (stability of the stem loop) ofeach strand were optimized to maximize the fluorescent response in thecase of high output and minimize it in the case of low output.

Fluorescent Assays

Oligonucleotides were mixed in 10 mm Tris-HCl buffer (pH 7.4) contain-ing 50 mm MgCl2 at the following final concentrations: all MBs, 100 nm ;ANDc and ORb, 50 nm ; all other oligonucleotides, 100 nm. The mixtureswere split into separate tubes (120 mL in each) followed by the additionof indicated input oligonucleotides to a final concentration of 100 or1000 nm. The fluorescence of the samples was registered after 15–30 minof incubation at room temperature. Fluorescent intensities were mea-sured at 517 nm. Average values and standard deviations of four inde-pendent measurements are represented in Figures 2–5.

Acknowledgements

D.M.K. is grateful to Milan N. Stojanovic and Nadrian C. Seeman for dis-cussion and encouragement. The research work was supported by NSFCCF Division of Computer and Communication Foundations, AwardNumber 1117205 and by NHGRI R21HG004060.

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