Detection of Sub-fM DNA with Target Recycling and Self-Assembly Amplification on Graphene Field-Effect Biosensors.

All-electronic DNA biosensors based on graphene field-effect transistors (GFETs) offer the prospect of simple and cost-effective diagnostics. For GFET sensors based on complementary probe DNA, the sensitivity is limited by the binding affinity of the target oligonucleotide, in the nM range for 20 mer targets. We report a ∼20 000× improvement in sensitivity through the use of engineered hairpin probe DNA that allows for target recycling and hybridization chain reaction. This enables detection of 21 mer target DNA at sub-fM concentration and provides superior specificity against single-base mismatched oligomers. The work is based on a scalable fabrication process for biosensor arrays that is suitable for multiplexed detection. This approach overcomes the binding-affinity-dependent sensitivity of nucleic acid biosensors and offers a pathway toward multiplexed and label-free nucleic acid testing with high accuracy and selectivity.

Label-free and multiplexed nucleic acid testing is of interest for genetic screening and clinical diagnosis,[1,2] and nano-bio-electronics have shown great promise for this application.[3] Graphene field-effect transistors (GFETs) offer advantages of large surface-to-volume ratio, excellent biocompatibility, and high carrier mobility.[4] GFETs can be readily functionalized with single-stranded probe DNA for detection of specific target oligonucleotides with complementary sequences. By detecting the charge of target DNA hybridized with the probe, GFETs typically offer a limit of detection (LOD) ranging from 1 fM to 100 pM.[5−8] The broad range of sensitivities has been ascribed to the affinity-governed binding kinetics of target and probe DNA, which varies with the length of the complementary sequence:[5,9] higher target-probe binding affinity and lower LOD are achieved for longer probe and target DNA oligomers. For example, we reported[5] a LOD of ∼100 pM for 22 mer target DNA (as confirmed by others[8]) and 1 fM LOD for 60 mer target DNA due to the stronger target-probe affinity. Achieving a low LOD for oligonucleotides without the constraint of target sequence length, e.g., sub-fM for a ∼20 mer, is highly desired for the early diagnosis of various diseases by detecting biomarkers of oligonucleotides, such as cardiovascular disease[2] and cancer.[10]

Here we report an approach to overcome the length-dependent sensitivity of GFET nucleic acid sensors based on single-stranded probe DNA. The GFET sensor design was based on a scalable fabrication process.[5] In contrast to traditional GFET DNA biosensors based on a single-strand probe DNA,[5,6,8] our approach included a hairpin-structured probe DNA and a triggered self-assembly pathway to enable target recycling and a hybridization chain reaction to amplify the transduction signal and improve the LOD by a factor of 20 000 or more, depending on the incubation time. The results were in good agreement with a mass action kinetic model. Our tests showed that hairpin probe DNA offered enhanced specificity against noncomplementary DNA with a single-base mismatch compared to the traditional single-strand probe DNA, and we demonstrated multiplexed detection using the GFET arrays. The work creates the possibility for high-sensitivity nucleic acid testing independent of length constraints for the target DNA, which is significant for disease diagnosis in a realistic clinical setting.

Results and Discussion

Figure a is an optical image of a GFET array fabricated using a scalable photolithography process described in the Materials and Methods section. Briefly, large-area graphene (10 cm × 15 cm) was synthesized on Cu foil by low-pressure chemical vapor deposition and transferred onto a Si/SiO2 substrate with previously fabricated Cr/Au electrodes. GFET channels were defined using an optimized bilayer photolithographic process[4] and oxygen plasma etching. After processing, the GFET arrays were annealed in a H2/Ar atmosphere at 225 °C to remove resist residues. The GFETs were of high quality as assessed by Raman spectroscopy (Figure S1 of the Supporting Information). As shown in Figure S2, the current–gate voltage characteristics showed good device-to-device uniformity, a narrow distribution of the Dirac point (6.6 ± 1.3 V), and high carrier mobility (2700 ± 700 cm2/(V s)).

Figure 1

GFET biosensor arrays. (a) Optical image of a graphene field-effect transistor (GFET) array fabricated on 250 nm SiO2 chip. (b) Schematic of hairpin probe DNA bound to a back-gated GFET using a pyrene linker (purple). (c) Current–gate voltage curve evolution of GFET following different chemical treatment steps.

The GFETs were functionalized by incubation in a solution of 1-pyrenebutyric acid N-hydroxysuccinimide ester (PBASE) in N,N-dimethylformamide (DMF) (see Materials and Methods for details). The aromatic pyrenyl group of PBASE binds to the graphene basal plane by the π–π stacking interaction.[11,12] After functionalization, the GFETs were then incubated in an aqueous solution of aminated hairpin probe DNA (Figure b). The probe DNA layer images as a nearly uniform brush in AFM, suggesting a high density of probe DNA immobilized on the GFET surface (Figure S3 of the Supporting Information).[5] The I–Vg characteristics for a GFET array were measured after each functionalization step. Immobilization of probe DNA led to an increase in the Dirac voltage (ΔVD = 71.3 ± 6.0 V), which was explained quantitatively by assuming chemical gating of 56 elementary charges per probe oligomer, with a probe DNA density of ∼1.1 × 103 μm–2.

Figure illustrates the operating principle of detection based on target recycling and self-assembly signal amplification. The probe DNA sequence was designed to form a secondary hairpin structure after being annealed by gradually cooling from 95 °C to room temperature. The hairpin probe DNA was metastable and could be specifically opened by target DNA to trigger a self-assembly reaction. A detailed description and DNA designs can be found in the Materials and Methods section and Figure S6. The GFET sensor, functionalized with the hairpin probe DNA (H1), was exposed to a mixture of target DNA (T) and three helper DNAs (H2, H3, H4). The target triggered the nucleation between H1 and T via base-pairing, mediating a branch migration that opened hairpin H1 to form a complex H1·T. The protruding segment of H1·T bound to the toehold of hairpin H2 (segment 3*; see Figure ) to initiate the strand-displacement reaction to form the complex H1·H2 and release T. The dissociated T was recycled to trigger additional self-assembly cycles as described above. Meanwhile, the protruding segment of H1·H2 (segments 4 and 7) nucleated with hairpin H3 and triggered the hybridization chain reaction (HCR) with H4. The presence of T can be circularly used to trigger HCR, leading to long nicked double-stranded polymers for the amplification of DNA products that can be detected by GFET through chemical gating. The effectiveness of the self-assembly amplification was confirmed by electrophoresis analysis (see the Supporting Information, Figure S4), where a smear band was found due to the formation of H1·H2·H3·H4 complexes with higher molecular weights. The scheme described above is universal for the detection of short DNA or RNA by changing the sequences of segments 1, 2, 3, 1*, 2*, and 3*, and H1 and H2 can be correspondingly modified and used with universal H3 and H4 for the amplification. It is noted that our scheme is different from a typical competitive assay for detection of small analytes like small proteins and aptamers, where the labeled ligand is added to the sample to compete with analyte to bind an antibody.[13] In our approach, the label-free helper DNAs were added to displace target DNA from probe DNA and trigger target recycling hybridization chain reaction, offering the advantages of label-free, amplified signals as well as the capability of detecting short DNAs or RNAs.

Figure 2

Schematic showing the principle of the triggered self-assembly amplification for DNA detection on GFET. The GFET was functionalized by hairpin probe DNA H1 through the PBASE linker. The target DNA (T) opens the hairpin probe to form the complex H1·T. T is then displaced by helper DNA H2 through the toehold-mediated strand displacement reaction, leading to the formation of the H1·H2 complex and enabling target recycling. Hybridization chain reaction (HCR) was triggered by H1·H2 in the presence of two additional helper DNAs, H3 and H4. Amplified HCR products are then detected through a shift of the GFET Dirac voltage.

In sensing experiments, GFET biosensor arrays were tested against a mixture of a known concentration of the target DNA in the presence of three helper DNA, H2, H3, and H4, all at a concentration of 1 μM, in 5× saline-sodium citrate (SSC) hybridization buffer, and the I–Vg characteristics were measured in the dry state.[14] In all cases a positive shift of the Dirac voltage was observed (Figures c and 3a). The p-type doping effect of DNA binding is understood as chemical gating[15] of the GFET by DNA molecules that acquire a negative charge due to deprotonation of phosphate groups in residual water.[5] As done previously,[5] for a given target concentration, the sensor response is reported as ΔVDrel, the Dirac voltage shift relative to the shift measured upon exposure to the DNA mixtures without target. To minimize the hysteresis effect on sensing,[16,17] care was taken to keep the measurement protocol consistent through the entire study (back gate sweep rate, 0.2 V/s; sweep range, 0–100 V), and in all measurements, the forward sweeps were utilized for data analysis. Figure a shows the GFET response for 1 h incubation time. ΔVDrel varied systematically with the target concentration, which is ascribed to the additional chemical gating of the GFET channel by the negatively charged DNA products by hybridization. It is noted that direct comparison of Dirac voltage shifts between the probe DNA immobilization step (in deionized (DI) water) and the target DNA binding step (in 5× SSC buffer) is complicated by the very different salt contents of these two solutions. The LOD for the 21 mer target is ∼5 fM, which is 20 000× lower than earlier reports using single-strand probe DNA.[5,8]

Figure 3

Sensing results and kinetic model. (a) Sensor response as a function of target DNA concentrations. Error bars are standard deviation of the mean. The limit of detection is <10 fM. (b) Sensor response as a function of incubation time for different target concentrations. (c) Simulation results of H1·H2 complex examined for different concentrations of target DNA show good qualitative agreement with panel a. (d) Simulation results of H1·H2 concentrations as a function of time with different target concentrations, showing trends similar to panel b.

To elucidate the dynamics of the self-assembly amplification, we constructed a mathematical model that reflects key biochemical reactions that connect the target DNA oligomer to the initiation of the amplification response mediated by the hairpins H1 and H2. The kinetic model (detailed in the Materials and Methods section) is based on the assumption that the HCR reaction with H3 and H4 is nonreversible due to the high concentration of helper DNA species (1 μM), so the model does not consider reactions involving the helpers H3 and H4. Even in its simplicity, the model recapitulated the measured target DNA dose–response curve (Figure c). The model also predicted that the experimental dose–response curve is a function of incubation time: at low target concentration (fM range), the Dirac voltage shift was predicted to grow if the experiments were run for longer periods of time (>1 h) because the recycled target DNA would open additional H1 hairpins with time, increasing the number of H1·H2·H3·H4 complexes.

The model predictions were validated experimentally (Figure b). Three target DNA concentrations were used (100 pM, 100 fM, 100 aM) with the same experimental conditions except that incubation time was prolonged to 100 h instead of 1 h. Biosensor responses rapidly saturated in less than 1 h for a concentration of 100 pM. For lower concentrations (100 fM, 100 aM), the response increased more gradually over time. The model gave correct qualitative predictions for the temporal trajectories of the response to the target concentrations tested, although the kinetics of the model were accelerated compared to the experiment (compare the time axes in Figure b,d). This is most likely the result of not considering the polymerizing reactions involving H3 and H4. As shown in Figure b, the LOD for our approach is further decreased by 50× to 100 aM with a sensing time of ∼15 h. Here, the sensor responses for different incubation times are reported as the Dirac voltage shifts relative to the shifts measured upon exposure to the DNA mixtures without target, incubated for the appropriate sensing time. We observed very little Dirac voltage shift for DNA mixtures without target incubated for up to 3 h, with the Dirac voltage shift becoming significant (+6.1 V) for incubation times exceeding 24 h, presumably due to increased nonspecific binding of the helper DNAs. Going beyond the conventional HCR scheme for signal amplification used in other types of biosensors,[18,19] our approach includes target recycling for enhanced sensitivity, for all-electronic GFET based DNA detection with the prospect of simple, highly sensitive, and label-free diagnostics. Moreover, the reaction kinetics could be accelerated by optimizing the sensing parameters, e.g., H1, H2 concentration (see the Supporting Information, Figure S8) and incubation temperature,[20,21] which offers the opportunity to tune the sensing time as needed to enable point-of-care detection.

Figure 4

Biosensor response to positive and negative controls. (a) Relative Dirac voltage shifts for various positive control experiments based upon concentrations of 1 μM for the target DNA and the specified helper DNAs. (b) Relative Dirac voltage shifts for 10 nM target DNA and negative controls with base mismatches at the ends; detailed DNA sequences are listed in Table S1. Error bars are standard deviation of the mean. Helper DNAs were of 1 μM.

To validate the effectiveness of detection based on target recycling and self-assembly amplification, the GFET arrays were tested against several positive controls. As shown in Figure a, the mixture of target DNA (1 μM T) and helper DNAs (1 μM H2, 1 μM H3, 1 μM H4) gave the highest response of 9.5 ± 0.4 V. For the positive control with target recycling but no HCR (only mixture of T + H2), the signal dropped to 4.2 ± 0.9 V, consistent with the expectation that HCR leads to increased formation of DNA products, consistent with the electrophoresis test (Figure S4 of the Supporting Information). The sensor response further decreased to 3.1 ± 0.7 V by using a random sequenced H2 to suppress the target recycling reaction, which is similar to the response for the control sample with T only (1.9 ± 0.7 V).

The GFET arrays were also tested against various negative controls, all at a concentration of 10 nM, to confirm that the response reflected specific binding of the complementary target DNA. As seen from Figure a, this 10 nM test concentration corresponded to a fully saturated sensor response for the T strand. As shown in Figure b, the target DNA gives the largest signal (9.9 ± 0.7 V), while for target DNA with a single-base mismatch at the 3′ or 5′ end, the responses were significantly smaller, 3.1 ± 0.9 and 2.7 ± 1.0 V, respectively, which would correspond to a T concentration of 100 fM for the target DNA. This very strong rejection of binding for the single-base mismatch at the 3′ or 5′ end was greatly superior to our earlier report for GFET DNA sensors based upon single-stranded probe DNA.[5] The higher specificity is attributed to the stem-and-loop structure of the hairpin probe DNA.[22,23] The hybridization to the target DNA disrupts the hairpin structure of the probe DNA and is less thermodynamically favorable than the hybridization of target DNA to the single-stranded probe DNA.[23,24] The control oligomer with two mismatches at the 3′ and 5′ ends had a relative Dirac voltage shift of 0.6 ± 0.4 V, essentially identical to the Dirac voltage shift for buffer.

Finally, we demonstrated multiplexed detection of target DNAs T and T′ with a GFET sensor array, through the use of site-specific functionalization using two different hairpin probe DNAs. The second set of probe DNA (H1′) and helper DNA (H2′) was redesigned according to the base sequence of the second target DNA (T′) to trigger the self-assembly reaction in the presence of H3 and H4. As shown in Figure S5, exposure of the DNA mixture (100 nM T, 100 aM T′, 1 μM H2, 1 μM H3, and 1 μM H4 in 5× SSC buffer) leads to distinguishable response for the site-specifically functionalized GFET sensors (10.4 ± 1.9 V for H1 site, versus 0.6 ± 1.2 V for the H1′ site). The multiplexed sensor array is therefore capable of quantifying concentrations of T and T′ simultaneously in a single measurement, which is potentially valuable for use in a clinical setting.

Conclusions

We developed manufacturable GFET nucleic acid sensors based on hairpin probe DNA designed to enable signal amplification by target recycling and a hybridization chain reaction. Based upon a 1 h detection time, the limit of detection was ∼5 fM for a 21 mer, an improvement of 20 000× over earlier reports based on complementary probe DNA. The limit of detection could be lowered to below 1 fM by extending the time, in agreement with a simplified kinetic model we developed. The approach showed excellent specificity against single-base mismatches at the 3′ or 5′ end, as expected due to the design characteristics of the hairpin probe, and we also demonstrated simultaneous detection of multiple targets. Our approach offers a platform for DNA detection at a low concentration even for short DNA targets. The scalability and sensitivity of the GFET devices make them potentially applicable for disease diagnosis and label-free genetic diagnosis.

Materials and Methods

Graphene Synthesis

Graphene was synthesized in a low-pressure chemical vapor deposition system (OTF-1200X-4-C4-SL-UL, MTI Corp.). Cu foils (Alfa Aesar Item 46365) were cleaned with 5.4% HNO3 for 40 s and two DI water baths for 2 min, and then thoroughly blown dry using N2 gas. The reaction chamber was pumped to a base pressure of 50 mTorr. The Cu growth substrate was annealed at 1020 °C for 30 min with a gas flow of 500 sccm Ar and 80 sccm H2. Monolayer graphene was then grown using methane as a carbon source at a flow rate of 5 sccm for 5 min and then 10 sccm for 15 min with 80 sccm H2. The reactor was rapidly cooled to room temperature under a flow of 80 sccm H2 and 10 sccm CH4.

GFET Sensor Array Fabrication

Photolithographic processing was used to define an electrode array for 100 back-gated graphene FETs on a highly p-doped Si wafer with a 250 nm thermal oxide layer. The contact metallization was 5 nm Cr/40 nm Au, deposited by thermal evaporation. Graphene was then transferred onto the metallized SiO2/Si chip using the PMMA assisted “bubbling” transfer method.[4] Briefly, PMMA-coated graphene/Cu was slowly immersed into a 50 mM NaOH aqueous solution with a 20 V potential difference applied between the copper foil and the solution. PMMA-supported graphene was separated from the Cu foil by hydrogen gas bubbles formed at the Cu surface. After three deionized water baths (resistivity of 18.2 MΩ cm), the PMMA/graphene film was transferred onto the metallized SiO2/Si chip, followed by air drying and baking at 150 °C for 3 min. After removal of PMMA by immersion in acetone overnight, the chips were spin coated with a photoresist bilayer of PMGI (MicroChem Corp.) and S1813 (Shipley). Graphene channels were defined using photolithography and oxygen plasma etching (pressure, 1.25 Torr; power, 50 W; duration, 35 s). The photoresist residue on graphene channels was removed by a N-methylpyrrolidinone (NMP) based stripper (NANO Remover PG, MicroChem Corp.), acetone, and IPA to obtain the array of 100 FETs. Finally, the array was annealed in H2/Ar forming gas at 225 °C to reduce photoresist residues.

AFM Characterization

An atomic force microscope (AFM, Icon Bruker) equipped with a probe with a tip radius of <10 nm (TAP300Al-G, Budgetsensors) was used to evaluate the height increase for the PBASE functionalization and probe DNA immobilization.

1-Pyrenebutyric acid N-Hydroxysuccinimide Ester (PBASE) Functionalization with Hairpin Probe DNA Immobilization and Testing against Target or Control Solutions

GFET sensors were soaked in a 0.2 mM PBASE (Sigma-Aldrich) in DMF for 20 h and then washed thoroughly with DMF, IPA, and DI water for 3 min each. Care was taken to blow dry the GFET gently with N2 gas at a pressure of 10 psi for ∼1 min. The hairpin structure of the probe DNA was formed by heating the probe DNA at 95 °C for 5 min, allowed by gradual cooling to room temperature before use. GFET sensors were then incubated in 4 μM aqueous solution of hairpin probe DNA (sequence is listed in Table S1) in DI water for 3 h in a humid atmosphere to suppress the evaporation of the DNA solution. This was followed by washing with two DI water baths (2 min each) and drying with N2 gas gently with a pressure of 10 psi for ∼1 min. After I–Vg measurement, the probe DNA-immobilized GFET devices were immersed in 200 μL of DNA mixture with known concentrations of target and helper DNA (1 μM for H2, H3, and H4, respectively) for 1 h to allow for DNA hybridization. While incubating in the target DNA solution, GFET sensors were placed in a container with a hot water bath to create a humid atmosphere and suppress evaporation of the DNA solution. The hot water was replaced every few hours; no significant decrease in the volume of the DNA solution was observed. The devices were washed with two DI water baths (2 min each), followed by drying with N2 gas gently with a pressure of 10 psi for ∼1 min before measurement of the electrical properties.

The GFET I–Vg characteristics were measured after each functionalization step. Self-assembly of the PBASE layer led to an increased Dirac voltage (ΔVD = 18.8 ± 1.5 V), which is explained by assuming that NHS groups are hydrolyzed into carboxyl groups, which deprotonate and acquire a negative charge.[15,25] Functionalization with PBASE also led to decreased hole carrier mobility to μ = 1070 ± 200 cm2/(V s), Immobilization of probe DNA led to a further increase in the Dirac voltage (ΔVD = 71.3 ± 6.0 V), corresponding to a hole carrier density of ∼6 × 1012 cm–2 induced by the hairpin probe DNA. This is explained quantitatively by assuming chemical gating of 56 negative charges for each probe oligomer, so the observed Dirac voltage increase corresponds to a probe DNA density of ∼1.1 × 103 μm–2. This high density of immobilized probe DNA is consistent with the AFM images in Figure S3, where individual probe DNA molecules are not resolved.

Design of Hairpin Structures

The principle of kinetically trapped nucleic acid hairpin assembly and the mechanism of the hybridization chain reaction (HCR) were demonstrated by Pierce and co-workers.[24,26,27] We designed the target triggered self-assembly amplification circuit based on the ingenious combination of four-hairpin DNA. Figure S3 depicts the design of hairpin structures. The sequence of hairpin structures is described in terms of numbered domains, each of which represents a short fragment (5–15 nt) of DNA sequence. Numbered domains marked with * are complementary to the corresponding unmarked numbered domains. The lengths of toehold, stem, loop, and target regions were chosen based on kinetic and thermodynamic considerations. By using the UNAFold web server (http://unafold.rna.albany.edu/), we found this target triggered amplification is sensitive to short DNA with an optimum sequence length of 20–32 nt. We also set out to engineer hairpins that maximize the free energy benefit per polymerization step while retaining hairpin metastability in these conditions. Hairpin DNAs have identical secondary structures, with stems of length 15 bp, toehold of length 6–8 nt, and loop of length 8–15 nt. The four hairpin structures do not initially interact with each other.

Triggered Self-Assembly HCR Amplification

After immobilization of hairpin probe DNA H1 on GFETs, the target DNA with a known concentration (from 100 aM to 1 μM) and three helper DNAs (H2, H3, H4) at a concentration of 1 μM were introduced in an aqueous solution mixture with 5× SSC buffer. The four hairpin species, H1 (probe), H2 (helper), H3 (helper), and H4 (helper), coexist in metastable state in the absence of T (target). Exposure of target triggers the nucleation of H1 and T via base-pairing to the single-stranded toehold “1*” of T (Figure ), mediating a branch migration that opens the hairpin H1 to form a complex H1·T and release a single-stranded segment “3 and 4” (Figure ). H1·T complex then nucleates with hairpin H2 by means of base-pairing to toehold “3*”, mediating a branch migration that opens the hairpin to form the complex H1·T·H2, which is inherently unstable. T then dissociates from the complex H1·T·H2, leaving a stable H1·H2 duplex with a protruding segment “4 and 7”. The dissociated T is recycled into the DNA mixture, nucleates with a new H1 and triggers the same circuit as described above.

The protruding segment of H1·H2 nucleates with hairpin H3 via base-pairing to single-stranded toehold “4*”, mediating a branch migration that opens the hairpin H3 and forms a complex H1·H2·H3 releasing of single-stranded segment “8 and 7”. This complex nucleates with hairpin H4 by means of base-pairing to toehold “8*”, mediating a branch migration that opens the hairpin to form complex H1·H2·H3·H4 releasing of single-stranded segment “4 and 7”. Thus, the initiator sequence is regenerated, providing the basis for a hybridization chain reaction of alternating H3 and H4 polymerization steps. In this amplification system, target DNA can be circularly used to trigger HCR amplification, which results in the generation of numerous long nicked double-stranded amplification polymers. Due to the target recycling and self-assembly amplification nature, the presence of low concentration of target is expected to generate a large number of annealed H1·H2·H3·H4 complexes, which can potentially result in a significant change of Dirac voltage for GFET detection of trace amount of target DNAs and RNAs.

Electrical Measurement and Evaluation

Electrical measurements were performed under ambient conditions in a probe station equipped with a probe card that is capable of measuring the 100 devices simultaneously. Current–gate voltage (I–Vg) measurements were carried out using a Keithley 2400 sourcemeter, with a bias voltage of 0.1 V. The gate voltage was applied using a Keithley 6487 voltage source. In order to avoid the readout errors induced by extracting the Dirac voltage from the Dirac peak directly, the Dirac point voltage and hole carrier mobility were extracted by fitting the hole branch of the σ–Vg curve to following the equation:[28−30]where cg is the gate capacitance per unit area for the 250 nm thick SiO2 (11.5 nF/cm2), μ is the hole carrier mobility, VD is the Dirac voltage, and σs is the saturation conductivity as Vg → −∞.

Kinetic Model

We constructed a computational model that simulates the amplification response that enables the detection of a DNA oligomer. Specifically, the model reflects key biochemical reactions that connect the target DNA oligomer sequence to initiation of the amplification response mediated by the hairpin H1 and H2. The model is based on mass action kinetics and comprises 5 coupled ordinary differential equations (ODEs), each of which expresses the rate of change in the concentration of a biochemical species:

The model’s input is the target DNA oligomer concentration, and its output is the concentration time course (i.e., kinetic trajectory) for each biochemical species considered. The initial concentrations of the hairpin H1 and H2 are set to 4 and 1 μM, respectively. The model reactions and parameters representing the rates of different molecular and cellular processes, such as target DNA oligomer-helper association/dissociation, are defined in Table S2. All computational analyses were performed in the software suite MATLAB R2017a (MathWorks, Natick, MA), and the ODEs were solved using the ODE15S solver with an absolute tolerance of 10–15 μM and a relative tolerance of 10–12.

Agarose Gel Electrophoresis

The target triggered self-assembly amplification was confirmed on a step-by-step basis using agarose gel electrophoresis (Figure S1). Hairpin H1 reacts with target and leads to a band corresponding to the product of H1·T, which migrates slower than H1 in agarose gel. Complex of H1·T then reacts with hairpin H2 to produce a band that corresponds to the product of H1·H2, which migrates similarly as the H1·T in agarose gel. Displacement reaction between H2 and H1·T releases T which is recycled to react with another H1 to produce H1·T until the supply of H1 is exhausted. H1·H2 reacts with hairpin H3 and produces a band that correspond to products of H1·H2·H3, which migrates similarly with H1·H2 in agarose gel. In 2 h, a band of H3 remains, which does not react with H1·H2. H1·H2·H3 reacts with hairpin H4, which causes a chain reaction of alternating kinetic escapes by H3 and H4 species corresponding to polymerization into a nicked double helix. Amplification continues until the supplies of H3 and H4 are exhausted. As shown in Figure S1, H1·H2·H3·H4 complex with larger molecular weight exhibits a smear band.