A localized DNA finite-state machine with temporal resolution.

The identity and timing of environmental stimulus play a pivotal role in living organisms in programming their signaling networks and developing specific phenotypes. The ability to unveil history-dependent signals will advance our understanding of temporally regulated biological processes. Here, we have developed a two-input, five-state DNA finite-state machine (FSM) to sense and record the temporally ordered inputs. The spatial organization of the processing units on DNA origami enables facile modulation of the energy landscape of DNA strand displacement reactions, allowing precise control of the reactions along predefined paths for different input orders. The use of spatial constraints brings about a simple, modular design for the FSM with a minimum set of orthogonal components and confers minimized leaky reactions and fast kinetics. The FSM demonstrates the capability of sensing the temporal orders of two microRNAs, highlighting its potential for temporally resolved biosensing and smart therapeutics.

INTRODUCTION

State machine defines a history-dependent device that can be in one of many distinct states depending on its previous state and the present inputs (). Figure 1A depicts the concept of a two-input, five-state finite-state machine (FSM), in which, despite having the same combination of inputs, {A THEN B} and {B THEN A}, should be two distinct events, resulting in different final states. If we simply analyze the composition of the inputs without the temporally ordered information, then their variabilities would be regarded as random noises and treated equally as {A AND B}. When the number of inputs increases, such biases grow larger exponentially, leading to a great loss of information and misinterpretation of the underlying truth.

Fig. 1.

Construction of the two-input, five-state DNA FSM.

(A) The two-input, five-state FSM generates a unique state for each combination and ordering of inputs A and B. (B) The most prominent feature of the FSM, wherein the next state is determined not only by the added input but also by its current state, is implemented by the toehold-mediated DSD reactions. In particular, upon the addition of input A (a*-s*-x-s), the initiator (s-a) captures the input. The signal of the exposed segments (x-s) in the captured A is received by the transmitter hairpin probe (s-b-s*-x*). The probe is thus activated and exposes its sequestered segments (s-b) for the capture of the next input B (b*-s*-y-s). Yellow arrows indicate input A, and green arrows indicate input B. (C) Reaction trajectory of the DNA FSM for each event. In a free diffusion system, as some processing probes share the same toehold, there would be unintended reactions between them in the presence of the input, including cross-talks between P0 and P4 or P3, between input A–activated P1 and P2, and between P1 and input B–activated P2. When the spatial constraints of the DNA origami are introduced, these unintended reactions could be inhibited. (D) Illustration of spatial constraints in modulating the energy landscapes to achieve directional reaction path for each temporal input event. The relative energy levels of different states in the FSM illustrate the spontaneous transitions between states from higher levels to lower ones.

Such temporal signal is ubiquitous in natural systems. Living organisms encounter dynamic external environments with variable identities and orders of stimuli and respond through their internal temporally regulated networks with diversified outputs like behaviors or phenotypes (). For example, stem cells could differentiate into different types with specific functions by using same transcription factors but different temporal schedules (). Cells at different cell cycle would have distinct tolerance to the external salt stress: The cells that have just divided or about to divide are more likely to survive than those in the middle of the cell cycle (). Unveiling the underlying temporal information has broad practical applications in the biological field such as genetic engineering and tissue engineering. Hence, artificial state machines that sense and decipher the detailed temporal information in biological systems would be useful for discriminating the biases generated from the temporal-independent analysis and bringing new insights into the biological study. Moreover, better understanding of the dynamic temporal information may be beneficial for carcinogenesis research () and precise drug treatment ().

To address the challenge to decode temporally ordered information, researchers have developed FSMs with temporal resolution. One major direction is to record the time-dependent information into sequence. Escherichia coli cells have been harnessed to record the temporal order of external chemical inputs via synthetic biology (, ), where states are recorded in transcribed DNA sequences with state transition achieved by recombination events catalyzed by recombinases. Besides the protein-based designs, DNA provides a more programmable and versatile platform (–) for engineering FSMs that have memory to the dynamic information flow (–). However, current DNA-based FSMs rely exclusively on reaction diffusion systems wherein probes with high sequence specificity are allowed to freely diffuse and undergo orthogonal reactions, generating output products with different configurations or lengths. The stringent requirement of reaction orthogonality leads to compromised temporal resolution, high system complexity, and increasing demands for design skills. These free diffusion systems also suffer from relatively slow kinetics.

To respond with high accuracy and efficiency for the complex flux of molecular information, nature has evolved exquisite molecular structures to harness spatial constraints in controlling the paths of biochemical reactions. For example, cells spatially confine interactive molecular species within organelles and molecular templates, such as cytoskeletons and hub proteins, constructing an organized “highway transportation system” for complex cellular signaling (–). Artificially designed DNA origami structures (, ) provide a programmable molecular architecture to precisely manipulate molecule systems in a spatial manner with nanometer resolution (–). Previous theoretical work has proposed the framework to exploit DNA origami as a pegboard to control DNA strand displacement (DSD) reactions based on the spatial organization of the reactants, thus achieving scalable and parallel chemical reaction networks (–). Experimental works have shown less system leakage and faster reaction kinetics of the DNA origami–localized DSD reactions (–) and further demonstrated their capability to construct complex computing circuits (, ) and gene chips ().

Here, we have developed a new concept of localized two-input, five-state FSM, which deploys spatial constrained sequential DSD reactions along predefined paths on the DNA origami surface to sense and record the temporally ordered inputs. Spatial organization of the probes on the origami allows precise modulation of the energy barriers for reactive components, reducing cross-talk reactions and facilitating proximal hybridization. Hence, two temporally distinct events, {A THEN B} and {B THEN A}, which consist of highly homologous reactants, have been resolved successfully. In response to different temporally ordered inputs, a series of processing probes hybridized along distinct paths are autonomously encoded in the FSM without the aid of exogenous enzyme or fuel reagents. Enhanced temporal resolution, improved reaction kinetics, and a simplified design with a minimum set of orthogonal components have been achieved. Moreover, our FSM is demonstrated to have the ability in sensing the temporal orders of two microRNAs (miRs), highlighting its potential for temporal resolution of biological processes.

RESULTS

Framework for the design

To construct the two-input, five-state FSM shown in Fig. 1A, we exploit the design principle of a cascade DSD reaction, hybridization chain reaction (). The reaction provides a modular framework to simplify the design of signal propagation (note S2.1). We use two hairpin probes with orthogonal sequences in the loop and toehold regions to encode the identity of the inputs. The processing units are composed of an initiator probe and a set of transmitter hairpins (Fig. 1B). Upon the addition of an input, the initiator captures the input. The corresponding transmitter hairpin receives this upstream signal and is thus activated to expose its sequestered loop and stem regions for the capture of the next input. The distinct change of molecular configuration for the processing units thus encodes a transited state in the FSM (Fig. 1B). On the basis of the design principle, we design five processing units accordingly (probes P0 to P4) to implement the functionality of the two-input, five-state FSM. However, there would be cross-talk between the processing units, provided that no additional constraints are introduced in the design (Fig. 1C and fig. S1).

To reduce the leaky reactions, we explore to use the spatial constraints in the FSM. We envision that introducing the spatial constraints could eliminate unintentional cross-talk between the spatially inaccessible processing units while facilitating DSD reaction between the proximal units. To implement spatial constraints, we spatially address these processing units according to FSM reaction flow along two opposite paths onto a DNA origami (Fig. 1C). Once input A is introduced first to the FSM, it pairs with the initiator P0 and then hybridizes with the hairpin P1, mediating a state transition from S0 to S1 in the FSM. Subsequent introduction of input B allows hybridizing with the activated initiator in P1 followed by opening of the hairpin P3, inducing state transition from S1 to S3. Conversely, first introduction of input B results in state transition from S0 to S2, and subsequent input of A renders further transition from S2 to S4. As a result, a varied order of inputs A and B yields a distinct sequential reaction cascade on the DNA origami with a corresponding molecular configuration recorded for the processing probes. Note that in a free diffusion system, there are cross-talk reactions between probes P0 and P4 or P3, between input A–activated P1 and P2, and between P1 and input B–activated P2 (fig. S1). By contrast, in our spatial constrained system, these cross-talks are precluded because of the unreachable distance between the two reactive components (Fig. 1C). From the energy perspective, the increased physical distance between two spatially confined probes introduces a higher energy barrier into the reaction, which can be attributed to the dissociation of one of the two probes from the origami or the distortion of the origami to shorten their distance. Hence, the spatial constraints modulate the energy levels for different states and make the state transit preferentially toward a specific direction, guiding a distinct information flow on the DNA origami for each temporal input event (Fig. 1D). Therefore, by implementing the DSD reactions with precise spatial constraints on a DNA origami, we propose an elegant framework to construct a localized two-input, five-state FSM that enables simple design of the orthogonal components and minimal system leakage from the cross-talk reactions.

Spatial constrained DSD reaction

We next explore experimental implementation of the spatial constraint strategy to direct the desired reaction path and avoid cross-talk reactions. A basic module is first tested using two processing units immobilized on the DNA origami scaffold [10.44 base pairs (bp) per turn; figs. S2 and S3] with different interunit distances. We anticipate that shortening the distance between the two processing units could lower the energy barrier and facilitate the cascade DSD reactions, while a longer distance would increase the energy barrier and inhibit the reactions (Fig. 2, A and B). To deliver a detectable signal for the DSD-mediated configuration change for the processing probe, we conjugate a fluorophore/quencher pair to the processing unit (note S2.2).

Fig. 2.

Spatial constraint on reactions.

(A) Schematic diagrams show the modulation of the reaction energy state using spatial constraints. (B) Schematic representations of the detailed reactions under different spatial constraints. (C) Fluorescence responses. The reactants are positioned at different distances on the same DNA origami or on different origami planes. Reactions are carried out using 1 nM origami at 25°C and 100 nM input in 1× TAE/Mg2+ buffer. Input is added at 300 s.

When the two units are placed at a short distance (D1 ≈ 10.88 nm), the addition of the input triggers the DSD reactions at a very fast rate (t1/2 < 200 s) (Fig. 2C and fig. S3). When two units are positioned at an extended distance (D2 ≈ 22.42 nm), no substantial fluorescence activation is obtained (Fig. 2C). To ensure a high efficiency in the spatial constrained reaction, purification of excess processing probes that are not tethered to DNA origami is required (figs. S4 and S5). We also validate a very slow kinetics for the interorigami side reactions (Fig. 2C). Increasing the operating concentration of DNA origami does not appreciably speed up the undesired inter- and intraorigami reactions (fig. S6). In addition, this system has further demonstrated good parallelism (fig. S7). We test the spatial constrained DSD reactions using another DNA origami (10.67 bp per turn) (), which has a larger curvature (fig. S8), and observe substantial leakage for intraorigami reactions (fig. S9). Together, these results reveal that precise spatial constraints enable specific control of the desired DSD reactions and effective inhibition of the leakages.

To gain deep understanding of the spatial constrained DSD reaction, we perform theoretical calculations on the lengths for the DSD reaction products and the distances on the origami between related processing units based on DNA structural parameters and simulations using oxDNA (note S2.2) (–). The calculations validate that the extended distance precludes the undesired DSD reaction on the origami, and the short distance allows forming the DSD product.

Design of the first operating layer of FSM

Our DNA FSM is composed of two operating layers: One differentiates the first input A or B to obtain S1 or S2, while the other further responds to the second input to yield S3 or S4. The first layer of FSM is first constructed using an initiator unit and two processing units immobilized on the origami surface. The initiator unit is a concatenated initiator probe for both inputs A and B, and the two processing units are transmitter hairpin probes positioned at each side of the initiator unit separately, which allows specific DSD reactions with the corresponding input (Fig. 3A). As the initiator probe for input B is located at the outer segment of the initiator unit, the processing unit P2 for input B is placed at a farther distance to the initiator unit than P1 to ensure an effective spatial constraint. When input A is added, the first layer is activated on the right side with t1/2 <200 s, indicating a state transition from S0 to S1. We do not observe substantial fluorescence activation on the left side, suggesting no state transition to S2. Conversely, first input of B causes specific fluorescence activation signal for the state transition from S0 to S2 with no appreciable fluorescence response for state transition to S1 (Fig. 3A). It is of note that the rate-determining step of the fluorescence activation process is the capture of the input by the immobilized processing probe. Therefore, the higher reaction rate of input B (Fig. 3A) is dominantly determined by the preferential hybridization between probe P0 with input B to input A, which might be ascribed to the slightly higher GC (guanine-cytosine) content in the reactive toehold of input B than that of input A. Ideally, subsequent introduction of secondary input B should only react with P1 without inducing remarkable fluorescence increase on the left side, and there should not be leaky reactions between secondary input A and P1 either. However, we observe substantial leaky reactions for the secondary inputs (Fig. 3B). To avoid these leakages, we devise to incorporate successive processing blocks in the first operating layer (Fig. 3B and note S2.3). An extra processing unit P1′ is introduced on the right side to execute two successive DSD reactions in response to input A. Crucially, we find that subsequent introduction of input B does not induce remarkable fluorescence increase on the left side. Similarly, on the left side, the two successive processing units minimized the leaky reaction for the secondary input A with P1 (Fig. 3B), validating that spatial constraints can be exploited to avoid cross-talk reactions in the FSM.

Fig. 3.

Construction of the first operating layer.

(A) Input A or B is first differentiated to yield S1 or S2, respectively. The colored star below the node of the processing unit indicates that the unit is labeled with fluorophore-quencher pair. The related kinetics data are displayed in the same color as the star icon. (B) Strategy to avoid undesired reactions. Initially, there are unintended reactions between P1 and P2 when the secondary input was added. Processing units P1′ and P2′ are thus introduced by adjusting the distances to minimize the leaky reactions. (C) State transition from S1 to S3 occurs upon the addition of the secondary input B.

On the basis of the constructed first layer, we extend a processing unit P3 on the right side to testify whether the first layer could further process the secondary input B at P1 to undergo state transition from S1 to S3. We observe a fast-propagated signal from processing unit P0 to P1 in response to the first input A, and upon the addition of the secondary input B, an abrupt decrease for the fluorescence signal of P1 appears with a concomitant fluorescence activation for P3 (Fig. 3C). The signal drop at P1 indicates the deactivation of S1, while fluorescence activation at P3 suggests a state transition to S3. This result validates the ability for the first layer to propagate the response to the first input to the secondary one.

Design of the localized two-input, five-state DNA FSM

Then, it is possible to create the two-input, five-state DNA FSM by introducing the second layer (Fig. 4A and note S2.4). To verify the design (Fig. 4, B and C; fig. S2; and note S2.3), we perform atomic force microscopy (AFM) experiments to track the reactions on individual origami surfaces. One staple on the asymmetry loop of the origami is functionalized with biotin molecule, which has a strong binding affinity to the streptavidin protein, serving as a reference for the direction. The ends of input strands are also modified with biotin molecules to indicate their locations. The patterns shown in the zoom-in AFM images (Fig. 4D) are in accordance with the anticipated recorded configuration states (figs. S10 to S14). The statistical analysis evidences that majority of the origami sheets execute the reactions correctly (fig. S15).

Fig. 4.

Localized two-input, five-state DNA FSM.

(A) High-level abstraction of the workflow for the design of the two-input, five-state FSM. FI, fluorescence intensity. (B and C) Schematic representations of the FSM. (D) AFM images of individual FSMs under different temporal events. Scale bar, 50 nm. (E) Relative fluorescence intensity (RFI) of each processing unit under different temporal events. The results here are obtained by treating the initial signal of each processing probe as 0 and its highest intensity in the predefined state as 1. The results are plotted of three independent experiments. The first and second inputs are added at the 300 and 900 s, respectively.

We further evaluate the performance using fluorescence measurements. The initial state S0 is defined with no signal. States S1, S2, S3, and S4, which correspond to events A, B, A THEN B, and B THEN A, respectively, are defined by the activation of fluorescence signals for the corresponding processing units, P1, P2, P3, and P4 (fig. S16). To deactivate signals of the previous state, the processing units on the same side of P0 are labeled with the same quencher such that state transitions from S1 to S3 and S2 to S4 deliver quenched fluorescence for P1 and P2, respectively. As shown in the fluorescence emission data (Fig. 4D and fig. S17), for each temporal input event, the signals of these processing units match our expectation. Each fluorophore channel exhibits strong intensity only when it receives the predefined input event. We then explore the fluorescence activation kinetics for more details (fig. S18). Adding one input at a specific time, the scheduled processing unit exhibits a quick (t1/2 < 200 s) response. At the same time, the signal intensity of the preactivated upstream unit decreases at the same rate. Other processing units not involved in the reaction trajectory display much lower fluorescence changes. Control experiments confirm that our design effectively inhibits spurious leakages, including reactions skipping the intermediate processing unit (reactions between S0 and S3, and between S0 and S4), and cross-talk between irrelevant units (reactions between S1 and S2) (fig. S19). Together, these results verify the successful design of the two-input, five-state FSM.

FSM-based temporal detection of miR inputs

In the developed FSM model, the inputs are two orthogonal hairpin components with the same stem domains but different toehold domains. To interface the FSM with temporal signal in biological environment, the strand displacement () or catalytic cleavage reactions () can be exploited to transform biological signals into the orthogonal hairpin inputs for the FSM. As a proof of concept, we investigated the capability of the localized two-input, five-state DNA FSM for temporal detection of two miR inputs. miRs are known to play important regulatory roles in biology (). Here, we choose miR21 and miR122 as the case of study. miR21 is observed to be overexpressed in many human malignancies (), while miR122 is reported to be involved in liver function and development (). To convert miR inputs into the orthogonal hairpin inputs, we introduce two transducer probes bA and bB (Fig. 5A). bA and bB are designed as dumbbell structures that incorporate miR-specific extension regions at the toehold domain of the input hairpins. The extension domains have complementary sequences to the toehold domains, blocking the hybridization of the inputs with the FSM in the absence of miR triggers. When the miR triggers are introduced, the transducer probes hybridize with miRs and recover their active toeholds (a* and b*) for the FSM (Fig. 5B). On the basis of this design, we find that our FSM had the ability to differentiate the temporal order of two miR triggers. In the absence of miR triggers, the FSM shows little fluorescence changes after the addition of two transducer probes. When miR21 and miR122 are added at different orders, the FSM delivers activated fluorescence outputs in the predefined channel with lower fluorescence in the other channels (Fig. 5C and fig. S20). This result validates that the FSM enables temporally resolved detection of biological inputs.

Fig. 5.

miR detection.

(A) Abstraction for the design of the signal transducer motifs. (B) Operation principle for the signal transducer probes (bA and bB). (C) Fluorescence intensities of the FSM under different temporal events of miRs. a.u., arbitrary units.

DISCUSSION

The stochastic and heterogeneous nature of biological processes makes it pivotal to understand the information flows not only for the input identities but also for the temporal details. To achieve this goal, we have devised a DNA FSM machine by embedding spatial constrained sequential DSD reactions in a DNA origami to decode the temporal input information. The key design principle is to implement the DNA origami’s spatial constraints on the processing units to rationally modulate their energy states in response to different input orders. The spatial localized reaction minimizes the undesired leaky reactions and confers fast kinetics. In stark contrast to the state-of-the-art DNA origami-fabricated machines that lack the ability to differentiate temporal information (–, –), our FSM is the first effort to exploit spatial constraints within a localized DNA nanomachine to sense the temporal events.

Conceptually, the design principle of our two-input, five-state FSM could be extended to more complex temporally resolved system with multiple inputs, but two issues need to be addressed. First, there are leaky reactions because of insufficient stiffness of the origami and suboptimal orthogonality of hairpin probes. Further stiffness improvement could be achieved by using origami with multilayer architectures (). In addition, some effective design principles for leakless DSD reactions () might be integrated to optimize the design. Second, the origami used here is in relatively small size, limiting the number of hairpin probes immobilized on the origami. As our system has exhibited good parallelism (fig. S7), this limitation could be partially addressed by combining multiple origamis or using bigger origami (–). Through cooperation within multiple origamis with each origami used as a two-input, five-state FSM, the design could be further extended for FSM of multiple inputs. Another possible solution is to exploit bigger origami by using each separate area to construct the two-input, five-state FSM.

Although the inputs are designed as hairpin structures, we have demonstrated that transducer components could be introduced, allowing transformation of common biological signals such as miRs into the standard hairpin inputs. Besides miR inputs, the FSM has the potential to incorporate functional moieties on nucleic acids, such as aptamers (, , ), DNAzymes (), therapeutic oligos (), reactive chemicals (), metal nanoparticles (), and proteins (–, ) to achieve various formats of molecular inputs and outputs. For example, temporal information of biological molecules involved in diseases could be used to guide drug releases or program functional molecular devices. Overall, with attentions on historical contexts, our FSM opens new possibilities for temporally resolved biological sensing and smart therapeutics.

MATERIALS AND METHODS

Materials

The 7249-nucleotide DNA scaffold was purchased from Bayou Biolabs or Tilibit Nanosystems. The regular staples of DNA origami were purchased unpurified from Integrated DNA Technologies (IDT), USA. The processing probes, inputs, and staples with extensions were purchased unpurified from IDT and further purified by denaturing polyacrylamide gel electrophoresis (PAGE). Biotin-, fluorophore (ROX, FAM, Cy3, and Cy5)–, or quencher (BHQ1 and BHQ2)–conjugated strands and miR strands, and miR converting strands were purchased purified (high-performance liquid chromatography) from Shanghai Sangon Biotech, China. Detailed sequences are shown in table S3. Streptavidin was obtained from Pierce Biotechnology, USA.

Design and synthesis of DNA origamis

The 10.67–bp per turn rectangular DNA origami was the same with the published design in the year of 2006 (). The 10.44–bp per turn rectangular DNA origami was created on the basis of the published design (), with the big loop of the scaffold shifted from the middle to the edge (table S2).

DNA scaffold (40 nM) was mixed with 7.5 times excess of the regular staple strands and 15 times excess of the modified staple strands in 1× TAE/Mg2+ buffer [40 mM tris, 20 mM acetic acid, 2 mM EDTA, and 12.5 mM (CH3COO)2Mg·4H2O]. The annealing was processed with an automated polymerase chain reaction thermocycler (Mastercycler Pro, Eppendorf, Germany). The procedure was set as follows: The sample was first heated up to 90°C and incubated for 2 min, then slowly cooled to 71°C at 1°C every 1 min, from 70° to 60°C at 1°C every 10 min, from 59° to 30°C at 1°C every 15 min, and from 29° to 26°C at 1°C every 10 min, and incubated at 25 °C for 25 min, then held at 4°C.

After annealing, to purify the folded origami structures, gel filtration through hand-packed columns using Sephacryl S-300 HR (GE Healthcare, USA) was used. This procedure gave a small loss and less aggregation. Specifically, origami samples of up to 50 μl were purified two times, on columns of ~720-μl resin volume, by centrifugation at 1000g for 5 min. After size exclusion chromatography purifying, the DNA origami was incubated with approximately 2.5-fold excess of processing probes at 37°C for 30 min, slowly cooled to 15°C at 1°C every 2 min, and then held at 20°C. Of note, for probes in hairpin conformations, incubate them at 95°C for 5 min, then cool to 4°C rapidly, and hold for at least 30 min in 1× TAE/Mg2+ buffer before use. Samples were then purified eight times using 0.5-ml, 100-kDa spin filters (Amicon, Germany) each time for 7 min at 5000g. The concentration of the prepared DNA origami was lastly quantified by absorbance at 260 nm, assuming an extinction coefficient of ~123,735,380 M−1 cm−1.

AFM measurements

Samples for AFM imaging were first purified with 100-kDa Amicon spin filters and then incubated with 20-fold excess of streptavidin protein for 1 hour at room temperature. For AFM imaging, 10 μl of samples was deposited onto a freshly cleaved mica surface (Ted Pella, USA) for 1 min. The mica surface was then washed twice with 1× TAE/Mg2+ buffer using compressed air. After washing, 60 μl of 1× TAE/Mg2+ buffer and 2.5 μl of NiCl2 solution (0.2 M) were added. The samples were imaged in “ScanAsyst in Fluid” on the Dimension FastScan AFM with ScanAssyst Fluid+ probes (both from Bruker, USA). The 2-μm × 2-μm AFM images were scanned at a resolution of 1024 lines with 1024 pixels per line. We analyzed the patterns on around 200 origamis for the statistics of each temporal event.

Gel electrophoresis for purification characterization

To analyze the purification efficiency, 1% agarose gel was prepared by mixing 1 g of agarose (Thermo Fisher Scientific, USA) in 100 ml of 1× TAE/Mg2+ buffer. The solution was then heated in a microwave oven for 3 min and cooled to ~50°C before pouring it into the gel tray. After solidifying, the gel was placed in the gel tray in a container with ice. TAE/Mg2+ buffer (1×) was used as running buffer. The samples with 20× SYBR Green were loaded into agarose gels and subjected to gel electrophoresis at 80 V for 1 hour.

Fluorescence experiments

The fluorescence data were monitored with a Nanolog fluorometer (Horiba Jobin Yvon, Japan). Arbitrary fluorescence units (Sc/R values) were collected. Experiments were performed with 20 μl of reaction mixture in fluorescence cuvettes (Hellma, Germany) at 25°C in 1× TAE/Mg2+ buffer. The sample temperature was maintained by a water circulating bath connected to the cuvette holder. Before an experiment, the cuvettes were cleaned by washing five times with distilled water and three times with 70% ethanol. The excess residual ethanol was dried out of the cuvettes with airflow.

Excitation/emission slit widths and excitation wavelengths of the fluorophores used in spectrum detections were set as follows: FAM (5/5 nm, 485 nm), HEX (6/6 nm, 530 nm), ROX (6/6 nm, 575 nm), and Cy5 (7/7 nm, 640 nm). Excitation/emission slit widths and wavelengths of the fluorophores used in kinetics experiments were as follows: FAM (5/5 nm, 492/518 nm), HEX (7/7 nm, 530/559 nm), ROX (7/7 nm, 578/604 nm), and Cy5 (8/8 nm, 648/668 nm), and the integration time was 2 s.

The initial fluorescence signal for each sample was measured as baseline. The sample was then taken out for the addition of 100-fold excess of input strand and subsequent mixing by repetitive pipetting. The cuvette was then put back into the fluorometer. For the detection of miRs, 100-fold excess of the two transition probes, bA and bB, were first added and then miRs (20× bA and bB).

In general, for each batch of the synthesized origami modified with processing probes, we added initiator single-stranded DNA, which could hybridize with all the processing probes (fluorescence-quenched hairpin probes) immobilized on the origami, in 200-fold excess, and obtained a fluorescence signal (with background correction) for each fluorophore. The fluorescence signal was the maximum response for this batch of origami, indicating the total number of the corresponding fluorescence-quenched hairpin probes modified on the origami. Hence, we used it as positive control for normalization.

The raw data were first processed by subtracting the baseline values. The obtained signals were then normalized by dividing the maximum response (fig. S3).

Simulations

We used a coarse-grained model of DNA—oxDNA—to study the spatial control strategy. Molecular dynamics (MD) simulations were performed using the oxDNA model (oxDNA2 version with sequence-dependent parametrization) that had to be run on graphics processing units because of the large size of the origami. The simulations were run at 25°C with Andersen-like thermostat and integration time step of 0.005 in simulation units. During the simulations, the model treats each nucleotide as a single rigid body with interactions parameterized to reproduce basic thermodynamic, mechanical, and structural properties of single- and double-stranded DNA. We computed the distances between specified pairs of nucleotides as sampled in MD simulations to obtain their distribution. For the simulation on the lengths of the DSD reaction products, we simulated the distances between the last nucleotides of the two processing probes in DSD reaction products. For the distances between two processing units, we measured the distances between the last nucleotides of the selected staples using a pure DNA origami without any modifying probe (fig. S24).