New J. Phys. 19 (2017) 015006 doi:10.1088/1367-2630/aa53d0

PAPER

Design and analysis of linear cascade DNA hybridization chainreactions using DNA hairpins

HieuBui1, SudhanshuGarg1, VincentMiao2, Tianqi Song1, ReemMokhtar1 and JohnReif1,31 Department of Computer Science, DukeUniversityDurham,NC27708,USA2 Department of Biomedical Engineering, DukeUniversity Durham,NC27708,USA3 Author towhomany correspondence should be addressed.

E-mail: reif@cs.duke.edu

Keywords:DNA self-assembly, triggered self-assembly, DNAhairpins,metastableDNA, linear cascade reactions, strand displacement,DNAnanotechnology

Supplementarymaterial for this article is available online

AbstractDNA self-assembly has been employed non-conventionally to construct nanoscale structures anddynamic nanoscalemachines. The technique of hybridization chain reactions by triggered self-assembly has been shown to form various interesting nanoscale structures ranging from simple linearDNAoligomers to dendritic DNA structures. Inspired by earlier triggered self-assembly works, wepresent a system for controlled self-assembly of linear cascadeDNAhybridization chain reactionsusing nine distinctDNAhairpins. NUPACK is employed to assist in designingDNA sequences andMatlab has been used to simulateDNAhairpin interactions. Gel electrophoresis and ensemblefluorescence reaction kinetics data indicate strong evidence of linear cascadeDNAhybridization chainreactions. The half-time completion of the proposed linear cascade reactions indicates a lineardependency on the number of hairpins.

Introduction

Deoxyribonucleic acids (DNAs) are one of themajor building blocks of biological systems. Recently, researchershave been exploitingDNA self-assembly for constructing nanostructures aswell as programmingmoleculardevices [1–13]. Yurke et al first observed the phenomenon ofDNA strand displacement in their nanomachine[14]. Based onDNA strand displacement thermodynamics, the construction ofmolecular systems [15], logiccircuits [16, 17], sensors [18], amplifiers [19–21], molecularmachines [22–25], walkers [21, 22, 26–53], robots[27, 37, 38], chemical controllers [54], and neural networks [55]were realized. The use ofDNAhybridization asthe primary driving energy source has been the central theme inmanyDNA systems. An alternative energysource could also come frommetastableDNA [56]. For instance, Turberfield et al used unhybridizedDNAhairpin loops as the fuel source to operateDNAmotors [57]. In addition, energy fromDNAhairpins has beenused to assist with catalytic hybridization [58] and triggered self-assembly [21, 59]. Inspired by early work ontriggered self-assembly ofDNAnanostructures [21, 59–61], we present a system for the controlled self-assemblyof linear cascadeDNAhybridization chain reactions (LCR) usingDNAhairpins. Previous studies havedemonstrated the formation of linearDNAoligomers fromopen hairpins hybridized in a staggered two-repeatmonomer pattern [59, 61], with orwithout the assistance of a few auxiliary strands. Yin et al extended thetriggered self-assembly from linear growth oligomers to quadratic growth branched oligomers and exponentialgrowth dendritic oligomers [21]. Our system lies in the regime of linear growth oligomers with the followingadvantages: (i) our systemhas 9 distinct hairpins which can potentially form a longer chain, whereas prior works[59–62] used only two to four hairpins, (ii) our system allowsfluorescence detection at any given oligomerlength, (iii) our system enables quantification of chain reaction success rate for any given length, which can betailored to design larger systems as andwhen required, (iv) the original systembyDirks and Pierce [59] had to becarefully tailored to have a stemof 18 nt and a toehold/hairpin loop region of 6 nt. Our systemhowever,

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introduces clamp domains, removing this constraint, thus allowing us to design systemswith variable stem(>=12 nt) and toehold lengths, which considerably increases the sequence space and applicability of thesesystems and (v) because our systemhas 9 distinct hairpins (rather than the 2 hairpins ofDirks’s system [59]) itcan be extended to do localized reactions on a surface [63, 64]. Our experimental results indicate strong evidenceof linear cascade reaction responses based on gel electrophoretic analysis and reaction kinetics.

The assembly linear cascadeDNAhybridization chain reaction is shown infigure 1. Figure 1(A) shows thecomponents: nine hairpins (H1,H2,H3,H4,H5,H6,H7,H8,H9), and an initiator (I). Eachhairpin consists of astem, a loop, and a sticky end. The stemconsists of twodomains (Ci andR)which forma stable duplexwith 14 basepairs. The loop consists of two clampdomains (Ci−1 andCi+1), a spacer domain (L), and a sequestered domain(Si+1). The sticky end consists of an external toehold domain (Si)which is complementary to the loopdomain(Si−1)of hairpin (Hi−1).Hairpins are distinguishable by two single-stranded toeholddomains (Si and Si+1)—onetoehold is external (a single-stranded sticky end, readily available for hybridization) andone is sequesteredwithinthehairpin loop. The stem (R) and spacer (L)domains of all hairpins comprise the same sequences. The spacerdomain (L) is used to offset potential geometrical constraints. The clampdomain (C) is implemented tominimizethebreathing effect at the ends of theDNAduplex and to ensure that the cascade reactionproceeds in the forwarddirection [65].

Initially, all hairpin components aremixed together but do not hybridize. The cascade reaction is initiated bythe initiator (I)which interacts withH1 by hybridizing to the external toehold (S1) as illustrated infigure 1(B).The initiator displaces the stemofH1 by branchmigration, opening the loop and revealing its sequesteredtoehold domain (S2). The opened loop ofH1 can nowbind to the external toehold ofH2 and displace the stemofH2 by branchmigration, opening in turn the loop ofH2. This reaction cascades downstream as each additionalhairpin anneals to the growing structure (which displaces the stem and opens the loop,making the previouslysequestered toehold accessible for hybridization to initiate the next stage of chain growth). The designed productof the assembly is a linear chain formed by the staggered hybridization of nine hairpins. A reporter complexwasused to determine the rate of the chemical reaction.HairpinH9 triggered the opening of the reporter complex, asshown infigure 5(A).

Materials andmethods

Sequence designNUPACK [66] is open-source software with built-in functions for the design and optimization ofDNAsequences based on thermodynamic and kinetic criteria. To ensureminimal crosstalk among nine hairpins,

Figure 1. (A)Components of the linear cascadeDNAhybridization chain reaction system. (B)Autonomous reaction of controlledself-assembly. Hairpins 1–9 are stable in the absence of initiator I. The initiator binds at the sticky end ofH1 and undergoes anunbiased strand displacement interaction to open the hairpin. The newly exposed sequestered sticky end ofH1 binds to the externalsticky end ofH2 and opens the hairpin to expose a sequestered sticky end onH2. This cascade reaction continues until H9 is opened.The designed product is a linear chain formed by staggered hybridization of nine hairpins.

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multiple design techniqueswere implemented inNUPACK. (i)A3-letter codewas used on the stem region ofthe hairpin.One of the arms of the stem is ‘opened’upwhen an incoming strand displaces it. Note that the otherarm always stays double stranded pre- and post- (and during) branchmigration process. The arm that staysdouble strandedwas constrained to contain only A, G, andT. This ensures that the arm containing the ‘G’ isalways in double stranded form. This was so designed because guanine ismore promiscuous (binds to bothcytosine and thymine), and thus can create undesirable secondary structures when in single stranded state. (ii)Clampdomainswere introduced tominimize the breathing effect at both ends of the duplex. (iii)Negativedesignwas used tominimize off-target binding between hairpins during intermediate states and constrainedNUPACK to return sequences thatmaximize the probability of a sub-strand (the region of the hairpin that opensthe next hairpin) staying single-stranded in intermediate states. The lengths of toehold, stem, and loop domainswere optimized using prior reported systems [21, 59, 65]. NUPACKprovides the yield of the optimizedsequences and defects at equilibrium and in addition, the software avoids improper hybridization of hairpinsusingDirks and Pierce’s algorithm [67]. The yield of defect is updated after each optimization procedure(changing the sequence composition of stem, loop, toehold, and clamp) and the optimal set ofDNA sequences isselected based on the least amount of defect in the yield output. A detailed description of the sequence design isin SI S1.

Bimolecular reactionmodel of LCREachDNA sequence is treated as an individualmolecule. In the absence of the target initiatormolecule, the LCRsystem remains inactive. Onlywhen the target initiatormolecule is present is the LCR activated and the cascadechain reaction initiated, resulting in a linear duplex chain formation. The rate of the linear cascade chainreaction depends on the toehold-binding and branchmigration processes. To simulate the formation of variouslinear duplex lengths, previously reported rate constants were used [19, 68]. For instance, the rate constant fordisplacement of the reporter complexwas 1.3×106 M−1 s−1. The rate constant used for toehold-mediatedstrand displacement was 105 M−1 s−1. Because the toehold binding and branchmigration domains between apair of hairpins have the same length, the strand displacement rate constant is assumed to be equal across all 9hairpins. Other factors such as theG–Cbond having a higher binding energy than the A–Tbond, defects instrand synthesis, and non-functional hairpins were not taken into account during simulations. In addition, allhairpin–hairpin interactions were assumed to proceed forwardwith insignificant reverse reactions. Simulationresults of different linear cascade reactionswith 9, 6, 4, 2, and 1 hairpin(s) are shownfigure 2. As expected, thecompletion rate of the linear cascade reaction depends on the number of hairpins—less hairpins correspond to afaster completion rate. A description of simulation scripts is in the SI.

All DNA strandswere purchased lyophilized from IntegratedDNATechnologies and purified using PAGE.In brief, a denaturing PAGE gel was run for 90 min at 300 V constant voltage in 1×TBEbuffer. PurifiedDNAbandswere identified, excised, crushed and eluted in elution buffer (NaCl) overnight. The solution containingpurifiedDNAoligonucleotide was centrifuged and the liquidwas extractedwithout disturbing the crushed gelpieces. The solutionwaswashedwith butanol. DNAoligonucleotides were precipitated in pure ethanol and

Figure 2. Simulation results of various linear cascade reaction lengths. The length depends on the number of hairpins involved in eachreaction. Linear cascade reactionswhen the rate constant is 105 M−1 s−1 (A) versus 1.3×106 M−1 s−1 (B). Simulation is performedbased on the assumption that all hairpin–hairpin pairs follow the second order (bimolecular) chemical reaction. Simulationconditions are specified as the following: 5 nMconcentration of hairpins, 6.5 nMconcentration of reporter complex, 10 nMconcentration of initiator, and the rate constant of displacing the reporter complex is common across all simulation experiments.

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washedwith 70%/30% ethanol/water. Excess ethanol was removed and the remaining ethanol was removed byvacuumcentrifugation. PurifiedDNAwas then re-suspended in 1×TEbuffer pH 8.0. A list of all DNA strands isshown in table 1.Native PAGE analysis was used to identify the effects of the linear cascadeDNAhybridizationreactions. In brief, each native PAGEwas run for 3.5 h at a constant 170 V. Eachwell was loadedwith 5–10picomoles ofDNA sample. Ethidiumbromidewas used to stainDNA for visualizingDNAbands. Ensemblefluorescence spectroscopywas used tomonitor the linear cascade chain reaction kinetics ofDNAhybridizationin solution. A reporter complex consisting of afluorophore (Tetrachlorofluorescein TET) and a quenchermolecule (Iowablack FQ), was adopted fromZhang et al [19]. Only the last hairpin, when activated, binds to thereporter complex to trigger the fluorescence emission. An equimolar solution of hairpins was prepared. Thefluorophorewas excited at 524 nmand emissionwasmeasured at 541 nm. The excitation and emission slits wereset at 10 nmand 5 nm, respectively. For each experiment 80 μl of the sample (5 nMofDNAhairpins, 6.5 nMofreporter complexwith andwithout initiator)was combined in quartz cuvettes. In order to preventDNA loss inthe pipetting process (by adhesion to the pipette tips), a non-reactive 20 nt poly-T strandwas added to allfluorescence experiments at a concentration of 1 μM [19]. Allmeasurements were performed at 20 °C. Rapidmixingwas achieved by carefully but quickly pipetting thewhole volume up and down for 10 swithoutgeneration of air bubbles or loss ofmaterial. All experiments were performed in TAE/12.5 mMMg2+ buffersolution.

Experimental results and discussion

Analysis of the cascade reaction by polyacrylamide gel electrophoresis (PAGE) is shown infigure 3. Infigure 3(A), lane 1 contains a 20 bpDNA ladder. Lane 2 contains all hairpins but no initiator: products of highmolecular weight are almost completely absent, indicating a very low background rate of LCR. Lane 3 containsall hairpins but no initiator (the sample was incubated at room temperature overnight): some evidence ofassembly is visible, indicating leak of LCR (leak is defined as undesired reaction in the absence of the initiatorstrand). Lanes 4–8 contain all hairpins with different concentrations of initiator as indicated (samples wereincubated at room temperature overnight): strong evidence of assembly is visible, indicating that cascadereactions occurred, as designed. Presence of residual hairpins in those lanes could be due to (i) stoichiometricconcentration differences betweenDNA strands and (ii) erroneousDNA strands that did not take part in thereaction. By increasing the initiator concentration from1× to 2× excess (lanes 4 and 5), the products of highmolecular weight form two distinct bands, indicating that the assembly of 8 hairpins coexists with the assemblyof 9 hairpins (evidence in lanes 8 and 9 in figure 3(B)). Two distinct highmolecular weight products are visibleeven at higher excess initiator concentration (lanes 6–8). Infigure 3(B), lanes 1–9 contain different numbers ofhairpins as indicated: products of highermolecular weight are successively visible, indicating that each cascadereaction is achieved as designed. Residual hairpins are visible toward the lower end of the gel. Lane 10 contains a20 bpDNA ladder. Note that the difference between peaks 8 and 9 hairpin lanes infigure 3(B) appears smaller

Table 1.DNAoligomers for constructing linear cascadeDNAhybridization chain reactions. Note: toehold domains (colored green), stemdomains (colored blue), clamp domains (colored red), spacer domains (colored black). In hairpin sequences, stems are underlined. Forkinetic studies, RC complex is displaced via the highlighted domain on hairpinH9.

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than the difference between the two bands infigure 3(A). This discrepancy appears to be due to one or both ofthe following: (i) two different comb sizes were used to prepare the gels (i.e. a larger comb sizewas used infigure 3(A) thanfigure 3(B), (ii) each lane infigure 3(A)was loadedwith 10 pmoles whereas each lane infigure 3(B)was loadedwith 5 pmoles.

Control analysis of the linear cascade reactionwith different number of hairpins is shown infigure 4. In gelA, only hairpins 8 and 9 are characterizedwith andwithout the initiator (I8). Lane 2 contains amixture ofhairpins 8 and 9: products of highmolecular weight are almost absent. Lane 3 contains amixture of hairpins 8and 9 subjected to a quick 90 °Canneal for 10 min: products of highmolecular weight are visible butwith littleevidence that the cascade reaction occurred. Lane 4 contains hairpin 8with the initiator: products of highmolecule weight are visible, indicating that the hairpin and initiator formed as anticipated. Lane 5 contains bothhairpins 8 and 9with the initiator: products of highmolecular weight are visible, indicating that the linearcascade reaction occurred. Residual hairpins in lanes 4–5 indicate amismatch between hairpin concentrations.In gel B, only hairpins 6, 7, 8, and 9 are characterizedwith andwithout the initiator (I6). Lanes 2, 3, and 4 containamixture of twohairpins (H6–7), three hairpins (H6–8), and four hairpins (H6–9), respectively without theinitiator: products of highmolecular weight are slightly visible, indicating evidence of some leak. Lanes 5, 6, 7contain amixture ofH6–7, H6–8, andH6–9, respectively with the initiator: products of highmolecular weight arevisible, indicating strong evidence of linear cascade reactions. Amismatch of hairpin concentrations is alsovisible in lines 7 and 8. In gel C, only hairpins 4, 5, 6, 7, 8, and 9 are characterizedwith andwithout the initiator(I4). Lanes 2–6 contain amixture of two hairpins (H4–5), three hairpins (H4–6), four hairpins (H4–7),five hairpins(H4–8), and six hairpins (H4–9)without the initiator:most of hairpins stay asmonomers and little evidence ofcascade reaction is visible. Lanes 7–11 contain amixture ofH4–5, H4–6, H4–7, H4–8, andH4–9 with the initiator:products of highmolecular weight are visible, indicating that strong linear cascade reactions are initiated by theinitiator. Lanes 5, 8, and 11 in gels A, B, andC showhighmolecular weight of linear oligomer products formed,indicating strong evidence of linear cascadeDNAhybridization chain reactions as anticipated.

The kinetics of linear cascadeDNAhybridization chain reactions (LCR) can be explored using fluorescenceemissions. The reporter complex is initially quenched due to the close proximity of the fluorophore andquencher, which are constrained by duplex formation (figure 5(A)). Upon hybridization, the reporter complex isdisplaced by the open armof hairpin 9, resulting in an increase influorescence emission. Figure 5(B) shows real-time kinetic characterization of the linear cascadeDNAhybridization chain reaction of nine distinct hairpins.Allfluorescence emissionswere normalized to the concentration of the output of the last hairpin (H9); thenormalization techniquewas adopted fromprior studies [19]. In this case, each opened hairpin 9 is assumed tobind to the reporter complex. Infigure 5(B), nofluorescence emission is observedwhilemonitoring the kinetic

Figure 3.Native PAGE analysis of LCR: all samples were incubated at room temperature for at least 15 h. (A)Effect of initiatorconcentration on LCR. All samples were prepared at 500 nMand 20 μl of samplewas loaded into each lane. Lane 1: DNAmarkerwith20 bp increments (20–300 bp); Lane 2: 0 μMof initiator and 0.5 μMmixture ofH1–H9without overnight incubation. Lanes 3–8: sixdifferent concentrations of initiator (0, 0.5, 1, 2, 4, 8 μM) in a 0.5 μMmixture ofH1–H9. (B) Step-by-step of the assembly of cascadechain reaction. The initiator was added 1×. All samples were prepared at 100 nMand 50 μl of samplewas loaded into each lane.Subsequent higher gel bands correspond to longer linear duplexes being formed. The largest linear duplex is resulted from theassembly of linear cascadeDNAhybridization of 9 distinct hairpins. Lane 1:H1+targetDNA initiator; Lane 2:H1+H2+targetDNA initiator; Lane 3:H1+H2+H3+targetDNA initiator; Lane 4:H1+H2+H3+H4+targetDNA initiator; Lane 5:H1+H2+H3+H4+H5+target DNA initiator; Lane 6:H1+H2+H3+H4+H5+H6+targetDNA initiator; Lane 7:H1+H2+H3+H4+H5+H6+H7+targetDNA initiator; Lane 8:H1+H2+H3+H4+H5+H6+H7+H8+targetDNA initiator; Lane 9:H1+H2+H3+H4+H5+H6+H7+H8+H9+targetDNA initiator; Lane 10: DNAmarkerwith20 bp increments (20–300 bp).

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of LCR in the absence of initiator (black curve) formore than 10 h, indicating that the linear cascade chainreaction does not occur in the absence of the initiator (I). Addition of I to the hairpinmixture at 1×concentration leads to rapid fluorescence emission for up to 200 minwhich slowly increases as equilibrium isreached, provide strong evidence of the linear cascade chain reaction (red curve). In the presence of excessinitiator, the LCR system yieldsminimal difference influorescence signal compared to 1× concentration ofinitiator (green curve), demonstrating that the linear cascade chain reaction is sufficient at 1× concentration,although equilibrium gel analysis (figure 3(A) lane 5) indicatesminimal leftover hairpins in the presence of 2×initiator concentration. Figure 5(B) shows the effect of a leak (an undesired reaction) in the absence of theinitiator as a function of hairpin concentrations—a higher concentration causesmore leak. This result confirmsthe challenge of leakwhen constructingDNA systems to operate at high concentrations. Even thoughDNAstrandswere purified using a denaturing PAGEmethod, leaks are difficult to eliminate. At 5 nMconcentration,our LCR system leak occurs at a slower rate than the actual reaction as shown infigure 5(A). An alternativeapproach to conquer leak is (i) to tetherDNA systems on a surface ofDNAnanostructures [63, 64, 69–72], or (ii)to incorporate double or triple length domainmotifs [73]. Note that thefluorescence data for leaks at 50 nMindicates quite significant leaks as compared to the gel data for leaks at 500 nMof the same system at equilibriuminfigure 3(A) lane 3. This discrepancy appears to be due to any of the following: (i) thefluorescencemethodrelied on the signal readout from the reporter complexwhereas the gelmethod relied on the nanostructureformation directly due to just hairpins, (ii) improper synthesis of the last hairpin could cause interaction directlywith the reporter complex, and thus produce a false positive fluorescence signal in addition to the actualfluorescence leak resulting from triggering LCR in the absence of the initiator strand, or (iii) the gel images infigures 3(B) and 4 do show a detectable amount of leak, while the gel image in figure 3(A)does not showmanyintermediate bands as part of the leak, just DNAbands at the top of the lane. It is possible that at higherconcentration, the intermediate products shifted/aggregated to form larger products that can be seen as bands atthe top of lane 3.

Figure 4.Native PAGE gel of different linear cascade reactions involving 2 hairpins, 4 hairpins, and 6 hairpins with andwithoutaddition of target DNA initiator. (Gel A)Lane 1:DNAmarkerwith 10 bp increments (10–150 bp); Lane 2:mixture ofH8 andH9; Lane3: annealing ofH8 andH9; Lane 4:H8+targetDNA initiator; Lane 5:H8+H9+targetDNA initiator. (Gel B) Lane 1: DNAmarkerwith 20 bp increments (20–300 bp); Lane 2:mixture ofH6 andH7; Lane 3:mixture ofH6,H7, andH8; Lane 4:mixture ofH6,H7,H8,andH9; Lane 5:H6+targetDNA initiator; Lane 6:H6+H7+targetDNA initiator; Lane 7:H6+H7+H8+targetDNA initiator;Lane 8:H6+H7+H8+H9+targetDNA initiator. (Gel C) Lane 1: DNAmarkerwith 20 bp increments (20–300 bp); Lane 2:mixture ofH4 andH5; Lane 3:mixture ofH4,H5, andH6; Lane 4:mixture ofH4,H5, H6, andH7; Lane 5:mixture ofH4,H5,H6,H7,andH8; Lane 6:mixture ofH4,H5,H6,H7,H8, andH9; Lane 7:H4+targetDNA initiator; Lane 8:H4+H5+target DNA initiator;Lane 9:H4+H5+H6+H7+targetDNA initiator; Lane 10:H4+H5+H6+H7+H8+target DNA initiator; Lane 11:H4+H5+H6+H7+H8+H9+targetDNA initiator.

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The effect of the number of hairpins on the rate of the linear cascade reaction is shown infigure 6(A). Thedotted horizontal line indicates the half-life of the linear cascade reaction (i.e. the time required for the reactionto reach 50%completion). All experimental data was collected at 5 nMconcentration. Initiating the linearcascade chain reactionwith a single hairpin results in a rapid fluorescence emissionwhich slowly increases asequilibrium is reached (black curve). The linear cascade chain reaction reaches 50% completionwithin1.47 min. The linear cascade chain reaction involving nine hairpins (cyan curve) takes approximately 41.97 minto reach 50%completion, roughly 28 times slower than the reaction involving a single hairpin. To reach 50%completion, the linear cascade reactions involving two (red curve), four (green curve), and six (blue curve)hairpins weremeasured to be 8.84, 18.78, and 27.98 min, respectively. As expected from the simulation data infigure 2 and the experimental results infigure 6(A), a lower number of hairpins results in a faster linear cascadereaction and vice versa. Experimental results indicate that the half-time completion of our LCR system follows alinear behavior as shown infigure 6(B). Asmore hairpins are involved in the linear cascade reaction,more time isrequired to reach the half-time completion. The linear behavior provides an additional criterion for the designand scaling of newDNAcircuits. In addition, the experimental results in figure 6(A)were thenfitted using theleast squaresmethodwhichwas adopted fromZhang et al [74]. In particular, data from figure 6(A)were fitted to

Figure 5.Kinetic characterization of the linear cascadeDNAhybridization chain reactions. All samples were prepared at 5 nMofhairpin with 6.5 nMof reporter complex. (A) Schematic of LCR systembefore and after interactingwith the reporter complex. (B)Effect of initiator concentration on the rate of linear cascade reaction.Hairpins do not hybridize in the absence of initiator (9hairpins+0× I, black). The linear cascade reaction occurs in the presence of 1× initiator concentration (9 hairpins+1× I, red). Thelinear cascade reaction occurs at the same rate in the presence of excess initiator (9 hairpins+8× I, green). (C)Effect of hairpinconcentration on the rate of crosstalk and leak reactions: 5 nM (black curve), 25 nM (red curve), and 50 nM (green curve)without thepresence of initiator.

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the corresponding cascade simulations and the fitting results were detailed in SIfigure S3. The bimolecular rateconstant of the proposed systemwaswithin the same order ofmagnitude as of the prior studies [19, 74].

Although linear behavior has been observed in our systems, the yield of the cascade reaction is difficult toquantitatively obtain fromour gel data orfluorescence data. One possible approach to roughly estimate the yieldof the cascade reaction is to compare the rawfluorescence data among various linear cascade reaction chains(figure S2). Ideally, themaximumfluorescence intensity at thermal equilibriumof different numbers of hairpinsparticipating in the linear cascade reactionwould reach the same level. However, the actualfluorescence dataindicate that themaximum fluorescence intensity at thermal equilibriumof a linear cascade reaction consistingof a single hairpin is higher than that of a linear cascade reaction consisting of nine hairpins. Assuming that (i)themaximumfluorescence intensity at thermal equilibrium is correlatedwith the yield of hairpins participatingin the linear cascade reaction and (ii) the yield of a last hairpin participating in the linear cascade reaction is100%; then the yield of the cascade reaction consisting of 9 hairpins is approximated to be 79% (figure S2). Analternative approach to estimate the yield is to employ a quantitative calibratedDNA ladder via gelelectrophoresis or to directlymeasure the final linear structures via scanning probemicroscopy. To avoid non-completion reactions, stoichiometry amongDNA strandsmust be preserved and erroneousDNA strandsmustnot participate in the reaction. In addition to these proposed approaches, different versions of hairpins can betuned to determine the causes of additional peaks in the gel data.

Conclusion

Wehave demonstrated the design, simulation, and synthesis of linear cascadeDNAhybridization chainreactions by non-equilibrium assembly. Cascade reactions provide a potential strategy to reduce shortconventional step-by-step reactions in a highly efficient and elegant fashion. Cascade reactions have been showntowork inmany dynamicDNA systems.We have developed a linear cascadeDNAhybridization chain reactionconsisting of nine distinct DNAhairpins. Gel analysis and reaction kinetics indicate strong evidence of thedesigned assembly. For scaling upDNA circuits, empirical data show that half-time completion follows linearbehavior as the number of hairpins increases. Thismethod can be used for constructingmore complex linearcascade reactions on the surface ofDNAnanostructures aswell as for realizing nano-breadboardDNA circuits.

Acknowledgments

Thisworkwas supported byNSFGrants CCF-1217457 andCCF-1141847. The authors wish to thank BrianPetkovwho assisted in the proof-reading of themanuscript.

Figure 6. (A)Effect of the number of hairpins on the rate of linear cascade reaction: 1 hairpin (black curve), 2 hairpins (red curve), 4hairpins (green curve), 6 hairpins (blue curve), 9 hairpins (cyan curve). Note: the dotted horizontal line indicates the half-life of thelinear cascade reaction (the time required for the reaction to reach 50% completion). Inset shows the real-time kinetic of all linearcascade reactions at equilibrium. (B)Empirical projection of the half-time completion as a function of hairpins. Note: each circle is anexperimental result corresponding to the number of hairpins participating in the linear cascade reaction; a blue line is a fitted curvefrom those circles.

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