Improving the Performance of DNA Strand Displacement Circuits by

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Improving the Performance of DNA Strand Displacement Circuits by Shadow Cancellation Tianqi Song, Nikhil Gopalkrishnan, Abeer Eshra, Sudhanshu Garg, Reem Mokhtar, Hieu Bui, Harish Chandran, and John Reif ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b07394 • Publication Date (Web): 29 Oct 2018 Downloaded from http://pubs.acs.org on October 29, 2018

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Improving the Performance of DNA Strand Displacement Circuits by Shadow Cancellation Tianqi Song,† Nikhil Gopalkrishnan,‡ Abeer Eshra,†,¶ Sudhanshu Garg,† Reem Mokhtar,† Hieu Bui,§ Harish Chandran,k and John Reif∗,†,⊥ †Department of Computer Science, Duke University, Durham, North Carolina 27708, United States ‡Wyss Institute, Harvard University, Boston, Massachusetts 02115, United States ¶Department of Computer Science and Engineering, Faculty of Electronic Eng., Menoufia University, Menouf, Menoufia 32831, Egypt §National Research Council, 500 Fifth Street NW, Keck 576, Washington, DC 20001, United States kDeepMind, Mountain View, California 94043, United States ⊥Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, United States E-mail: [email protected] Abstract DNA strand displacement circuits are powerful tools that can be rationally engineered to implement molecular computing tasks because they are programmable, cheap, robust and predictable. A key feature of these circuits is the use of catalytic gates to amplify signal. Catalytic gates tend to leak, that is, they generate output signal even in the absence of intended input. Leaks are harmful to the performance and correct operation of DNA strand displacement circuits. Here, we present “shadow

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cancellation”, a general-purpose technique to mitigate leak in catalytic DNA strand displacement circuits. Shadow cancellation involves constructing a parallel shadow circuit that mimics the primary circuit and has the same leak characteristics. It is situated in the same test tube as the primary circuit and produces “anti-background” DNA strands that cancel “background” DNA strands produced by leak. We demonstrate the feasibility and strength of the shadow leak cancellation approach through a challenging test case, a cross-catalytic feedback DNA amplifier circuit that leaks prodigiously. Shadow cancellation dramatically reduced the leak of this circuit and improved the signal-to-background difference by several folds. Unlike existing techniques, it makes no modifications to the underlying amplifier circuit and is agnostic to its leak mechanism. Shadow cancellation also showed good robustness to concentration errors in multiple scenarios. This work introduces a direction in leak reduction techniques for DNA strand displacement amplifier circuits, and can potentially be extended to other molecular amplifiers.

Keywords DNA nanotechnology, DNA strand displacement circuits, leak reduction, detection, molecular programming

DNA strand displacement circuits 1,2 have been used for several purposes such as specific detection of molecular targets, 3–5 amplification of nucleic acid signals 6–8 and Boolean, analog and neural network computation, 9–17 etc. 18–25 Using catalytic gates to amplify signal is a main property of these circuits. A catalytic gate generates multiple output molecules from a single input molecule, with the aid of fuel molecules. The input molecule catalyzes the conversion of a fuel signal to an output signal. Clearly, catalytic gates are indispensable for

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the tasks of detection and amplification. Perhaps surprisingly, they are also critical to the robust operation of Boolean and neural network circuits, since circuits with catalytic gates operate asymptotically faster than circuits without any catalytic gates. 26 Thus, catalytic gates are essential components of almost all DNA strand displacement circuits. The performance of catalytic circuits is often limited by the effectiveness of their catalytic reaction machinery. Catalytic reactions tend to leak, that is, the reactions have a propensity to occur even in the absence of a catalyst. This releases output molecules even in the absence of input, albeit at a reduced rate. Leaks harm the performance and correct operation of DNA strand displacement circuits in a variety of ways. We will summarize them briefly. The most apparent effect of leak is to reduce the sensitivity of detection circuits by generating background. They also cause the incorrect operation of Boolean and neural network circuits by producing background above tolerable thresholds. Leaks increase with the concentration of the interacting DNA complexes. Thus, the concentration of the circuit components (DNA complexes and DNA strands), and consequently the speed of circuit operation, is limited. Leaks also accumulate over time. This proves problematic for circuits of greater depth (i.e. having many layers), since the DNA complexes at deeper circuit layers wait longer for signal and accumulate more leak products, ultimately failing. Thus, leak also limits the depth of circuits that we can implement. Leaks are especially problematic for circuits with feedback loops, causing instability. An output molecule generated by leak can feed back and trigger the operation of the circuit along an intended pathway, releasing even more output molecules. Thus, leak is amplified in feedback circuits, resulting in unstable circuits that have a tendency to leak prodigiously. A mitigation of the leak problem has the potential to affect the performance of almost all catalytic DNA strand displacement circuits, by improving their sensitivity, increasing speed of operation, allowing for the implementation of larger circuits and significantly improving the stability of feedback circuits. Several techniques have been developed to reduce leak such as the use of clamp domains, 7,27–29 base-pair mismatches, 30–32 and ultra-pure DNA strands, 4 etc. 33,34 All of these

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techniques attempt to reduce leak by attacking a particular leak mechanism. This requires both knowledge of the underlying leak mechanism and an ability to modify the DNA circuit. The predominant leak mechanisms are not always discernible, and also vary from one DNA circuit to another. The ability to modify the DNA circuit is also not always within one’s means. For instance, the DNA circuit could be interacting with other systems and any modifications could cause cascading deleterious effects. Thus, there exists a need for leak mitigation techniques that are agnostic to the leak mechanism and also do not require any modifications to the target DNA circuit.

Figure 1: Strategy of shadow cancellation. The shadow circuit mimics the primary circuit and has the same leak profile. The two leaks cancel each other by designated reactions to stop the leak from propagating in the primary circuit.

Here, we present a leak reduction technique termed “shadow cancellation” which mitigates leak in DNA circuits irrespective of the underlying leak mechanism. The target (or primary) DNA circuit is not modified in any way. Instead, as shown in Figure 1, a “shadow circuit” is created to sequester the products of leak. Specifically, the shadow circuit is designed to have the same architecture as the primary circuit, and as a consequence has a leak profile that is near-identical to it. The products of the leaks of the primary and shadow circuits cancel each other through rationally designed leak cancellation reactions. It is important that the leak profile of the shadow circuit be near-identical to that of the primary circuit. A faster shadow leak rate will damp the output signal from the primary circuit, while a slower shadow leak rate will fail to cancel leak products in a timely manner. Note 4


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that the leak is actively suppressed in a cancel-as-you-go manner. This is critical since catalytic circuits have feedback machinery that amplifies any leak signal that is not canceled in a timely manner. To demonstrate our technique, we chose a previously described 35,36 DNA strand displacement powered cross-catalytic amplifier which leaks prodigiously. Shadow cancellation dramatically reduces the leak of this circuit and improves the signal-to-background difference. As shown in Figure 2 (top), the cross-catalytic amplifier is composed of two catalytic seesaw amplifiers 10 each catalyzing the other. One seesaw gate is composed of a gate complex GA1 and a fuel strand FA1, and the other seesaw gate is composed of a gate complex GA2 and a fuel strand FA2. Strand OA1, initially sequestered as part of the gate complex GA1, is the output of the first seesaw gate and serves as input to the second gate. Strand OA2, initially sequestered as part of the gate complex GA2, is the output of the second seesaw gate and feeds back as input to the first seesaw gate. We use strand OA2 to trigger the cross-catalytic amplifier. Strand OA1 is used to trigger the downstream reporter complex RC. We monitor the circuit operation through the fluorescence generated by triggering the reporter complex RC. The cross-catalytic amplifier can be modeled as a chemical reaction network, described in reactions (1a) to (1d). Reactions (1a) and (1b) encapsulate the catalytic cycle of each seesaw gate. In (1a), the catalyst strand OA2 triggers the release of the output OA1, driven by the consumption of the fuel strand FA1 which is sequestered in the waste complex WA1. Similarly, in (1b), the catalyst strand OA1 triggers the release of the output OA2, driven by the consumption of the fuel strand FA2 which is sequestered in the waste complex WA2. Reactions (1c) and (1d) model the leak (the products of unintended uncatalyzed reactions), where outputs OA1 and OA2 are produced even in the absence of the catalyzing strands OA2 and OA1, respectively. Note that the rates of the leak reactions (1c) and (1d) could be much slower than the catalyzed reactions (1a) and (1b) but still produce disproportionately large leak, since the outputs of the leak reactions feed into the catalyzed pathway, setting off a chain reaction. In particular, any leak will be exponentially amplified. The detailed DNA

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strand displacement mechanisms that implement these reactions are shown in Figures 3.

Figure 2: The architecture of a cross-catalytic DNA amplifier and its shadow circuit. Top: The cross-catalytic seesaw amplifier consists of two DNA seesaw gate complexes GA1 and GA2 and two DNA fuel strands FA1 and FA2. Strands OA1 and OA2 are the outputs of gates GA1 and GA2, respectively. The output of a gate feeds into the other gate and acts as a catalyst. Reporter complex RC is used to monitor the performance of the amplifier and is triggered by one of the output strands, OA1. Bottom: The shadow circuit has an identical architecture to the primary amplifier and consists of two DNA seesaw gate complexes GB1 and GB2 and two DNA fuel strands FB1 and FB2. Middle: The DNA complexes C1 and C2 are cooperative hybridization gates that implement the leak cancellation reactions. C1 sequesters strands OA1 and OB1, and C2 sequesters strands OA2 and OB2. The sequences of the domains can be found in Table 1.

OA2 + GA1 + FA1 −−→ OA2 + OA1 + WA1

(1a)

OA1 + GA2 + FA2 −−→ OA1 + OA2 + WA2

(1b)

GA1 + FA1 −−→ OA1 + WA1

(1c)

GA2 + FA2 −−→ OA2 + WA2

(1d)

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Figure 3: DNA strand displacement reactions of the cross-catalytic amplifier. (a) The intended reactions: DNA reactions 1 and 2 implement reaction (1a). DNA reactions 3 and 4 implement reaction (1b). The reactants of a reaction are indicated by triangular solid arrows if the reaction is reversible, and the products of a reaction are indicated by regular plain arrows. (b) The leak reactions: DNA reaction 5 implements reaction (1c). DNA reaction 6 implements reaction (1d). The detailed mechanism of these leak reactions is discussed by Qian et al. 27 (c) The reactions between OA1 and RC to generate fluorescence: The red triangle represents fluorophore (6-FAM) and the black circle represents quencher (Iowa Black). After the reactions, the fluorophore leaves the quencher and emits fluorescence.

The shadow circuit, shown in Figure 2 (bottom), has the same architecture (except it lacks the bm domain for fluorescence reporting) as the primary cross-catalytic amplifier. The difference is in the sequences of the displacement domains (R1, R2, R3 and R4 instead of S1, S2, S3 and S4). This is meant to ensure that the shadow circuit operates independently and in parallel to the primary circuit, but with near-identical kinetics. Note that the toehold sequences are the same for both the primary and shadow circuits. The shadow circuit operation is described by chemical reactions (2a) to (2d), which is the same, except for the 7


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identity of the molecules, as the reactions for the primary cross-catalytic amplifier.

OB2 + GB1 + FB1 −−→ OB2 + OB1 + WB1

(2a)

OB1 + GB2 + FB2 −−→ OB1 + OB2 + WB2

(2b)

GB1 + FB1 −−→ OB1 + WB1

(2c)

GB2 + FB2 −−→ OB2 + WB2

(2d)

The primary and shadow circuits are coupled through the DNA co-operative hybridization complexes 37 C1 and C2, shown in Figure 2 (middle). Co-operative hybridization complexes are AND gates; they sequester a pair of signal molecules if and only if both are encountered almost simultaneously. There is no dependency between the sequences of the sequestered molecules. Thus, they are ideal for leak cancellation purposes. C1 sequesters the pair of output signals OA1 (from the primary circuit) and OB1 (from the shadow circuit), and C2 sequesters outputs OA2 (from the primary circuit) and OB2 (from the shadow circuit). The cancellation process is described by chemical reactions (3a) and (3b). The DNA strand displacement mechanism that implements reaction (3a) is shown in Figure 4. The mechanism for reaction (3b) is analogous, and is not sketched here.

OA1 + OB1 + C1 −−→ ∅

(3a)

OA2 + OB2 + C2 −−→ ∅

(3b)

In the absence of any input to the primary circuit, its leak profile will (ideally) match that of the shadow circuit. In particular, the signals OA1 and OA2 produced in the primary circuit because of leak will be exactly matched by the signals OB1 and OB2 produced in the shadow circuit. These signals will stoichiometrically cancel via the co-operative hybridization complexes C1 and C2. Note that not all the leak can be suppressed in this manner. Some

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Figure 4: The cancellation reaction between OA1 and OA2 via C1. The reaction is based on cooperative hybridization. 37 There are two possible cancellation paths as in (a) and (b): reaction 7 → reaction 8 and reaction 9 → reaction 10. Both paths produce the same set of waste products.

of the signal will be involved in the cross-catalytic reactions ((1a), (1b), (2a) and (2b)), resulting in further leak. However, by tuning the rates of the cross-catalytic reactions ((1a), (1b), (2a) and (2b)) versus the cancellation reactions ((3a) and (3b)) we can trade-off leak suppression versus responsiveness to input. A cancellation reaction that is too slow will lead to more leak, as more signal escapes cancellation. A cancellation reaction that is too fast will slow down the response of the amplifier, as even genuine signal (not attributable to leak) will be temporarily sequestered in the cancellation complex. This effect, analogous to impedance in electrical circuits, is commonly referred to as “retroactivity”.

Results and Discussion The cross-catalytic amplifier was first tested without shadow cancellation. As shown in Figure 5 (a), the “Signal” curve shows the fluorescence output of the amplifier when 5 nM 9


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of target strand OA2 was added. The “Leak” curve shows the fluorescence output of the amplifier even in the absence of external target strand OA2. Fluorescence intensity was normalized as described in Section ”Materials and Methods”. The concentrations of the amplifier components were [GA1] = [GA2] = 100 nM and [FA1] = [FA2] = 200 nM. In the cross-catalytic amplifier with no shadow cancellation, even 5 nM of OA2 was barely distinguishable from the leak. To quantify the difference between “Signal” and “Leak”, we use the signal-to-background difference (SBD) as the benchmark which is defined to be the difference between “Signal” and “Leak” at time t80% (Equation 4), where t80% is the time when “Signal” has reached 80% of its maximum fluorescence intensity. The experiment was repeated three times and the average SBD termed SBDave from three repeats was 0.076 as shown in Figure 5 (d). In this paper, all SBDave values are calculated from three repeats.

SBD = Signal(t80% ) − Leak(t80% )

(4)

The amplifier was then tested in the presence of the two cancellation complexes C1 and C2, but no shadow circuit. This experiment helps us understand the retroactive effects of adding cancellation complexes. The cancellation complexes should not irreversibly react with the signal strands (OA1 and OA2). However, there is a reversible reaction between the cancellation complexes and the signal strands that causes them to be temporarily sequestered. This is expected to slow down the operation of the cross-catalytic amplifier. The concentrations of the cancellation complexes were as follows: [C1] = [C2] = 75 nM. Figure 5 (b) shows that the performance was not much different from the case of the amplifier alone, and the SBDave was 0.084. However, as expected the retroactive effects of the cancellation complexes increases t80% . We then tested the full system, consisting of the primary and shadow cross-catalytic amplifiers with respective cancellation complexes. The concentrations of the shadow amplifier components were set to match the concentrations of the corresponding components of the primary amplifier. In particular, we set [GB1] = [GB2] = 100 nM and [FB1] = [FB2] 10


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(a) The amplifier

(b) The amplifier with cancellation complexes

(c) The amplifier with shadow cancellation

(d) SBDs from three repeats.

Figure 5: Performance of shadow cancellation. The amplifier was tested alone, with cancellation complexes, and with shadow cancellation, and the SBDave s were 0.076, 0.084 and 0.631, respectively. In each subfigure, the “Signal” curve represents the case that 5 nM of target strand OA2 was added, and the “Leak” curve represents the case that no OA2 was added. Each experiment was repeated for three times.

= 200 nM. The concentrations of the cancellation complexes were the same as described in the previous paragraph. As shown in Figure 5 (c), the shadow cancellation scheme significantly improves the signal to background difference of the amplifier. The SBDave was 0.631, which works out to a

0.631−0.076 0.076

= 730% improvement over the case of the cross-catalytic

amplifier lacking shadow cancellation. A more sophisticated statistical analysis is included in Supporting Information. The shadow leak cancellation scheme presumably delivers the best results when the

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(a) 90% shadow

(b) 100% shadow (same as Figure 5c)

(c) 110% shadow


Figure 6: The utility of shadow cancellation with shadow circuit that was 10% lower, the same, and 10% higher in concentration than the amplifier. When the shadow circuit had a lower concentration than the amplifier, the SBDave was smaller than when the two circuits were balanced. When the shadow circuit had a higher concentration than the amplifier, the SBDave was comparable to when the two circuits were balanced. For α% shadow, [GB1] = [GB2] = 100 × α% nM, [FB1] = [FB2] = 200 × α% nM. The cancellation complexes are at 75 nM in all three scenarios.

shadow amplifier exactly mimics the leak characteristics of the primary amplifier. Any deviance from this ideal should result in worse amplifier performance. We evaluated the sensitivity of the amplifier to deviations of the shadow amplifier from exact mimicry by introducing a mismatch in the putative concentrations of the shadow and primary amplifier components. This is an easy way to achieve less than exact mimicry since the leak rate of the primary and shadow cross-catalytic amplifier as well as the cancellation reactions are concentration dependent. A mismatch in their concentrations results in less than ideal leak

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cancellation. If the shadow circuit is at a higher concentration than the primary circuit, it will leak faster and damp legitimate signal. On the other hand, if the shadow circuit is at a lower concentration than the primary circuit, it will fail to cancel leak in a timely manner, resulting in runaway leak due to cross-catalytic feedback. In practice, we found that the amplifier was robust to shadow circuit component concentration variations of ±10%. As shown in Figure 6, in response to putative concentration mismatches of −10% and 10%, the SBDave did not deviates much. Even in this scenarios, it performs better than in the absence of any shadow leak cancellation. There is an asymmetry in the response to putative excess versus putative lesser shadow component concentrations. Putative excess concentration does not significantly change the performance, while putative lesser concentration causes noticeable adverse effects. We also studied the effects of varying the concentrations of the cancellation complexes C1 and C2 on the performance of the amplifier. As noted earlier, the cancellation complexes compete with the cross-catalytic reaction machinery to sequester signal strands. All of these reaction rates are concentration dependent. Increasing the concentration of the cancellation complexes, relative to the concentration of the seesaw gates, will increase the fraction of signal strands that participate in leak cancellation reactions as opposed to the cross-catalytic seesaw reactions. Hence, we have the ability to respond to varying leak rates by simply appropriately tuning the concentrations of the cancellation complexes. We tested three different concentrations for the cancellation complexes, [C1] = [C2] = 65 nM, 75 nM and 85 nM. As shown in Figure 7, when [C1] = [C2] = 65 nM, the leak cancellation is inadequate and significant background is generated. However, as the concentrations were increased to 75 nM and 85 nM, the leak cancellation significantly improves the performance of the amplifier.

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(a) 65 nM of cancellation complexes

(b) 75 nM of cancellation complexes (same as Figure 5c)

(c) 85 nM of cancellation complexes


Figure 7: The utility of shadow cancellation with different concentrations of cancellation complexes. The performance was compromised in (a) because cancellation reactions could not suppress the leak well in the amplifier due to low concentration of cancellation complexes. The shadow amplifier is 100% in all three scenarios.

Conclusions DNA strand displacement circuits have already found many applications, for example, in nucleic acid detection, 3–6 cell membrane probing, 38,39 and molecular biological computing. 9–11,13 Leaks decrease the performance, and hence limit the usefulness, of DNA strand displacement circuits. In this work, we introduce shadow leak cancellation as a strategy for mitigating leak. In contrast to previous efforts to mitigate leak, shadow cancellation is agnostic to the

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mechanism of leak. In addition, it does not require us to modify the target DNA strand displacement circuit. Instead, additionally strand displacement machinery is introduced to cancel the leak in a timely (cancel-as-you-go) manner. It also has the added advantage that it works in conjunction with existing leak mitigation strategies like using clamp domains, 7,27,28 introducing base-pair mismatches 30,32 and using ultra-pure DNA strands 4 and others. 33,34 We demonstrated the efficacy of shadow leak cancellation by applying it to a challenging test case, a cross-catalytic seesaw DNA amplifier that leaks prodigiously. The performance of the cross-catalytic amplifier improved dramatically in the presence of leak cancellation. We also showed that we can tune how aggressively we suppress leak by simply varying the concentration of the leak cancellation complexes. We also showed that shadow leak cancellation is robust to inexact mimicry and the resulting performance loss is often insubstantial. A main aspect of shadow cancellation is that it can slow down a primary circuit, and this will be a problem if the utility of the circuit is more about “detection sensitivity” rather than “reaction speed”. This issue can potentially be mitigated by reducing retroactivity and achieving a better match between the reaction rates of the primary and shadow circuits by better sequence design. In addition to signal amplification, shadow cancellation could be used in DNA strand displacement circuits that perform computation or produce dynamical signals, because a lower leak will give these circuits a better performance. We believe that the shadow leak cancellation paradigm is likely to find use beyond just DNA strand displacement circuits. We believe that RNA-based gene circuits, enzyme-abetted DNA circuits (like PCR) and even protein signaling pathways can benefit from this strategy. The key to achieving a successful shadow leak cancellation is to construct a shadow circuit that can mimic the primary circuit, but remains orthogonal to it, only interacting with it for the purposes of canceling leak. To demonstrate the universality of shadow cancellation, we have also studied its effect on abstract chemical reaction networks as shown in Supporting Information, and the simulation results are very positive.

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Methods Design of DNA Sequences. DNA sequences of the domains were mainly adopted from a prior paper by Qian et al. 27 All the DNA strands and DNA complexes were examined by NUPACK 40 to make sure that there were no significant unwanted secondary structures or unwanted intermolecular interactions. Table 1: Sequence design of the domains in the system shown in Figure 2. Some domain sequences were adopted from a prior paper by Qian et al. 27

Domain Sequence (5’ to 3’) c CA ∗ c TG t TCT ∗ t AGA S1b TTCCACT S1b∗ AGTGGAA S1 TCCATTCCACT S1∗ AGTGGAATGGA S2 CCACCAAACTT ∗ S2 AAGTTTGGTGG S3 CAACTCATTAC S4 CATAACAAAAC bm ATACAAATCCACACCG ∗ bm CGGTGTGGATTTGTAT R1 CTCATCCTTTA ∗ R1 TAAAGGATGAG R2 AACACTCTATT ∗ R2 AATAGAGTGTT R3 TTCCTACATTT R4 TACCCTTTTCT

Length (nt) 2 2 3 3 7 7 11 11 11 11 11 11 16 16 11 11 11 11 11 11

Buffer Conditions. The DNA strands were stored in 1× TE buffer at 4◦ C for short term, and at -20◦ C for long term. DNA complexes were stored in 1× TAE/Mg2+ buffer (Mg2+ was at 12.5 mM) at 4◦ C for short term, and at -20◦ C for long term. All the fluorescence experiments and annealing were conducted in 1× TAE/Mg2+ buffer. DNA Strands Purification. The DNA strands were ordered from Integrated DNA Technologies after desalting but without additional purification. We then purified the strands by 16


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10% denaturing PAGE (polyacrylamide gel electrophoresis). The electrophoresis was run at 300 V for 90 mins in 1× TBE buffer. The gel pieces corresponding to the full-length product were excised and then eluted in 300 mM sodium chloride solution to obtain purified DNA strands. DNA Complexes Preparation. Seesaw gate complexes and cooperative hybridization complexes were annealed and subsequently purified, to mitigate leak resulting from imperfectly annealed complexes, by native polyacrylamide gel electrophoresis (12% PAGE, 1× TBE buffer). The electrophoresis was run at 150 V for 6 hours. The gel pieces corresponding to the complexes were excised and soaked in 1× TAE/Mg2+ buffer for 24 hours to obtain the purified DNA complexes. Fluorescence Experiments. The fluorescence experiments were performed on a Varian Cary Eclipse Fluorescence Spectrophotometer at 20◦ C. The excitation wavelength for 6-FAM was 495 nm and the emission wavelength was 520 nm. Before each experiment, the cuvettes were washed several times with DI water and 70% ethanol and then dried with nitrogen gas. Fluorescence Data Normalization. For each curve, the data is usually normalized using the minimum fluorescence intensity as “0”, and the maximum fluorescence intensity (average of the last three data points) as “1”. However, for the “Leak” curves in Figures 6 and 7, because they do not reach full signal during the experiments, we normalized them against the maximum fluorescence intensity of their corresponding “Signal” curves.

Supporting Information Available This material is available for download from http://pubs.acs.org: Three repeats for each scenario, and simulation results for the universality of shadow cancellation (PDF); LBS code for the simulation (ZIP).

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Competing Interests The authors do not have competing interests.

Acknowledgements This work is supported by NSF Grants CCF-1320360, CCF- 1217457, CCF-1617791 and CCF-1813805.

References 1. Yurke, B.; Mills, A. P. Using DNA to Power Nanostructures. Genet Program Evol M 2003, 4, 111–122. 2. Zhang, D. Y.; Winfree, E. Control of DNA Strand Displacement Kinetics Using Toehold Exchange. J. Am. Chem. Soc. 2009, 131, 17303–17314. 3. Li, B.; Ellington, A. D.; Chen, X. Rational, Modular Adaptation of Enzyme-Free DNA Circuits to Multiple Detection Methods. Nucleic Acids Res. 2011, 39, e110–e110. 4. Chen, X.; Briggs, N.; McLain, J. R.; Ellington, A. D. Stacking Nonenzymatic Circuits for High Signal Gain. Proc. Natl. Acad. Sci. U. S. A. 2013, 110, 5386–5391. 5. Li, B.; Chen, X.; Ellington, A. D. Adapting Enzyme-Free DNA Circuits to The Detection of Loop-Mediated Isothermal Amplification Reactions. Anal. Chem. 2012, 84, 8371– 8377. 6. Dirks, R. M.; Pierce, N. A. Triggered Amplification by Hybridization Chain Reaction. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 15275–15278. 7. Yin, P.; Choi, H. M.; Calvert, C. R.; Pierce, N. A. Programming Biomolecular SelfAssembly Pathways. Nature 2008, 451, 318–322. 18


Page 18 of 23

Page 19 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

8. Zhang, D. Y.; Turberfield, A. J.; Yurke, B.; Winfree, E. Engineering Entropy-Driven Reactions and Networks Catalyzed by DNA. Science 2007, 318, 1121–1125. 9. Seelig, G.; Soloveichik, D.; Zhang, D. Y.; Winfree, E. Enzyme-Free Nucleic Acid Logic Circuits. Science 2006, 314, 1585–1588. 10. Qian, L.; Winfree, E. A Simple DNA Gate Motif for Synthesizing Large-Scale Circuits. J. R. Soc. Interface 2011, 8, 1281–1297. 11. Qian, L.; Winfree, E.; Bruck, J. Neural Network Computation with DNA Strand Displacement Cascades. Nature 2011, 475, 368–372. 12. Cherry, K. M.; Qian, L. Scaling Up Molecular Pattern Recognition with DNA-Based Winner-Take-All Neural Networks. Nature 2018, 559, 370. 13. Song, T.; Garg, S.; Mokhtar, R.; Bui, H.; Reif, J. Analog Computation by DNA Strand Displacement Circuits. ACS Synth. Biol. 2016, 5, 898–912. 14. Song, T.; Garg, S.; Mokhtar, R.; Bui, H.; Reif, J. Design and Analysis of Compact DNA Strand Displacement Circuits for Analog Computation Using Autocatalytic Amplifiers. ACS Synth. Biol. 2018, 7, 46–53. 15. Garg, S.; Shah, S.; Bui, H.; Song, T.; Mokhtar, R.; Reif, J. Renewable Time-Responsive DNA Circuits. Small 2018, 14, 1801470. 16. Zhang, D. Y.; Seelig, G. DNA-Based fixed Gain Amplifiers and Linear Classifier Circuits. DNA Computing and Molecular Programming. Berlin, Heidelberg, 2010; pp 176–186. 17. Thubagere, A. J.; Thachuk, C.; Berleant, J.; Johnson, R. F.; Ardelean, D. A.; Cherry, K. M.; Qian, L. Compiler-Aided Systematic Construction of Large-Scale DNA Strand Displacement Circuits Using Unpurified Components. Nat. Commun. 2017, 8, 14373.

19


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

18. Fern, J.; Scalise, D.; Cangialosi, A.; Howie, D.; Potters, L.; Schulman, R. DNA StrandDisplacement Timer Circuits. ACS Synth. Biol. 2017, 6, 190–193. 19. Bui, H.; Shah, S.; Mokhtar, R.; Song, T.; Garg, S.; Reif, J. Localized DNA Hybridization Chain Reactions on DNA Origami. ACS Nano 2018, 12, 1146–1155. 20. Bui, H.; Miao, V.; Garg, S.; Mokhtar, R.; Song, T.; Reif, J. Design and Analysis of Localized DNA Hybridization Chain Reactions. Small 2017, 13, 1602983. 21. Wilhelm, D.; Bruck, J.; Qian, L. Probabilistic Switching Circuits in DNA. Proc. Natl. Acad. Sci. U. S. A. 2018, 201715926. 22. Thubagere, A. J.; Li, W.; Johnson, R. F.; Chen, Z.; Doroudi, S.; Lee, Y. L.; Izatt, G.; Wittman, S.; Srinivas, N.; Woods, D.; Winfree, E.; Qian, L., A Cargo-Sorting DNA Robot. Science 2017, 357, eaan6558. 23. Chatterjee, G.; Dalchau, N.; Muscat, R. A.; Phillips, A.; Seelig, G. A Spatially Localized Architecture for Fast and Modular DNA Computing. Nat. Nanotechnol. 2017, 12, 920. 24. Yordanov, B.; Kim, J.; Petersen, R. L.; Shudy, A.; Kulkarni, V. V.; Phillips, A. Computational Design of Nucleic Acid Feedback Control Circuits. ACS Synth. Biol. 2014, 3, 600–616. 25. Sadowski, J. P.; Calvert, C. R.; Zhang, D. Y.; Pierce, N. A.; Yin, P. Developmental Self-Assembly of A DNA Tetrahedron. ACS Nano 2014, 8, 3251–3259. 26. Seelig, G.; Soloveichik, D. Time-Complexity of Multilayered DNA Strand Displacement Circuits. DNA Computing and Molecular Programming. Berlin, Heidelberg, 2009; pp 144–153. 27. Qian, L.; Winfree, E. Scaling Up Digital Circuit Computation with DNA Strand Displacement Cascades. Science 2011, 332, 1196–1201.

20


Page 20 of 23

Page 21 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

28. Seelig, G.; Yurke, B.; Winfree, E. Catalyzed Relaxation of A Metastable DNA Fuel. J. Am. Chem. Soc. 2006, 128, 12211–12220. 29. Srinivas, N.; Parkin, J.; Seelig, G.; Winfree, E.; Soloveichik, D. Enzyme-Free Nucleic Acid Dynamical Systems. Science 2017, 358, eaal2052. 30. Jiang, Y. S.; Bhadra, S.; Li, B.; Ellington, A. D. Mismatches Improve the Performance of Strand-Displacement Nucleic Acid Circuits. Angew. Chem., Int. Ed. 2014, 53, 1845– 1848. 31. Machinek, R. R.; Ouldridge, T. E.; Haley, N. E.; Bath, J.; Turberfield, A. J. Programmable Energy Landscapes for Kinetic Control of DNA Strand Displacement. Nat. Commun. 2014, 5, 5324. 32. Olson, X.; Kotani, S.; Padilla, J. E.; Hallstrom, N.; Goltry, S.; Lee, J.; Yurke, B.; Hughes, W. L.; Graugnard, E. Availability: A Metric for Nucleic Acid Strand Displacement Systems. ACS Synth. Biol. 2016, 33. Kotani, S.; Hughes, W. L. Multi-Arm Junctions for Dynamic DNA Nanotechnology. J. Am. Chem. Soc. 2017, 139, 6363–6368. 34. Thachuk, C.; Winfree, E.; Soloveichik, D. Leakless DNA Strand Displacement Systems. DNA Computing and Molecular Programming. Berlin, Heidelberg, 2015; pp 133–153. 35. Qian, L.; Winfree, E. A Simple DNA Gate Motif for Synthesizing Large-Scale Circuits. DNA Computing and Molecular Programming. Berlin, Heidelberg, 2009; pp 70–89. 36. Gopalkrishnan, N. Engineering Exquisite Nanoscale Behavior with DNA. Ph.D. thesis, Duke University, 2012. 37. Zhang, D. Y. Cooperative Hybridization of Oligonucleotides. J. Am. Chem. Soc. 2010, 133, 1077–1086.

21


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

38. You, M.; Lyu, Y.; Han, D.; Qiu, L.; Liu, Q.; Chen, T.; Wu, C. S.; Peng, L.; Zhang, L.; Bao, G.; Tan, W., DNA Probes for Monitoring Dynamic and Transient Molecular Encounters on Live Cell Membranes. Nat. Nanotechnol. 2017, 12, 453. 39. Rudchenko, M.; Taylor, S.; Pallavi, P.; Dechkovskaia, A.; Khan, S.; Butler Jr, V. P.; Rudchenko, S.; Stojanovic, M. N. Autonomous Molecular Cascades for Evaluation of Cell Surfaces. Nat. Nanotechnol. 2013, 8, 580–586. 40. Dirks, R. M.; Bois, J. S.; Schaeffer, J. M.; Winfree, E.; Pierce, N. A. Thermodynamic Analysis of Interacting Nucleic Acid Strands. SIAM Rev. 2007, 49, 65–88.

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Improving the Performance of DNA Strand Displacement Circuits by

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