Digital immunoassay for biomarker concentration quantification using solid-state nanopores

Digital assay design

The quantification of specific protein concentrations from biological samples (e.g., serum) with solid-state nanopores requires precise, accurate, and robust electrical identification of these targets on a single-molecule (i.e., digital) basis from a complex background. To enable digital detection with solid-state nanopores for precise and consistent target concentration measurements, we designed a pair of double-stranded DNA (dsDNA) nanostructures in the shape of shooting stars that can be bound pairwise via a complementary single-stranded DNA (ssDNA) junction strand to form an easily distinguishable dumbbell-shaped nanostructure, as illustrated in Fig. 1. We refer to these shooting star-like DNA nanostructures as probes (P-1 and P-2) when they are unbound, and as dumbbells (DB) when they are linked by the junction strand.

P-1 and P-2 are composed of 12-arm dsDNA stars with 11 arms 25 bp in length, and a 12th arm consisting of either a 175 bp (P-1) or a 150 bp (P-2) linear dsDNA tail. At the end of this extended arm is a 25 nt ssDNA region that is complementary to half of the junction strand (Supplementary Fig. 1), which allows a P-1 and a P-2 probe to bind together to form a dumbbell-like structure (Fig. 1 and Supplementary Fig. 2). A description of probe assembly and purification can be found in Supplementary Notes 1 and 2.

Using the components identified above, our assay adapts a sandwich immunoassay scheme to enable digital detection with a nanopore, as depicted in Fig. 1. Briefly, we employed magnetic isolation to efficiently capture target proteins onto antibody-coated paramagnetic micron-sized beads⁴⁴ and to facilitate the necessary washes to remove background molecules and dissociate non-specifically bound complexes. Secondary detection antibodies bioconjugated with streptavidin, were then added to sandwich each target between the pair of high-affinity antibodies. After equilibration and washing, short pieces of 50 nt biotinylated ssDNA (the junction strand) were added, which bind to the detector antibody and label each target. These junction strands have a photocleavable linker inserted between the biotin and the oligonucleotide sequence. Following additional washing to remove the excess unbound junction strands, the full immunoassay mixture was exposed to UV light to cleave the junction strands from the beads and release them into the solution in proportion to the concentration of bound targets. The beads were magnetically immobilized, and the supernatant containing the cleaved junction strands was recovered. The recovered supernatant was incubated with known concentration of probes and then mixed with a high-concentration salt solution for nanopore sensing. A more detailed description of the assay steps and components is provided in the “Methods” section.

Following nanopore analysis, the translocations of unpaired probes were classified on a single-molecule basis as a “0”, while the translocations of dumbbells are classified as a “1”, thus converting the electrical nanopore signal into a digital count.

In this scheme, junction strands serve as proxies for the target proteins, and for a fixed probe concentration, the fraction of dumbbells formed can be calibrated to report on the original concentration of target proteins in a clinically relevant sample. As expected from controlled counting¹⁹, the use of relative counts of each population eliminates the error from varying intra- and inter-nanopore properties, allowing for highly reproducible assay performance between different nanopores.

Nanopore characterization of DNA nanostructures

In previous work, we showed that short, multi-arm dsDNA stars produce robust and easily identifiable signals^{53,54,55,56,57,58}. Here, we further modified the star nanostructures, extending one of the arms to form a linkage for the tail section of the probe, and added an internal carbon spacer in the middle of each star oligo’s sequence to relax the otherwise highly charged and sterically stressed core of the 12-arm star structure, to help facilitate translocation through nanopores. The resulting nanostructure provides a characteristic electrical signature when translocating a nanopore (Fig. 2). Differences in nanopore sensing profiles between the probes P-1 and P-2, due to 25 bp difference in the length of the tail, were not distinguishable.

Figure 2 shows the nanopore translocation characteristics of probes and dumbbells. As expected, Fig. 2b shows the most commonly observed nanopore signal of the probes, which involves a deep blockage level 6x deeper than dsDNA alone, corresponding to the body of the star⁵³. We normalized the nanopore current signal by the blockage produced by the unfolded translocation of 2 kbp linear dsDNA to remove the effects of any variations in pore geometry and operating conditions between experiments⁵³, thus facilitating comparison between experiments on different pores as detailed in Supplementary Note 3. These deep, 6x dsDNA, blockages are often (>90%) followed by a shallower 1x dsDNA blockage level corresponding to the tail, though bandwidth limitations sometimes (<10%) preclude resolving the tail part of the event. The mean translocation time was 27 (pm) 2 µs, though probe events do occasionally approach the 200 kHz bandwidth limit of the digital low-pass filter applied during the analysis. While this bandwidth limitation might in other contexts be problematic, the depth of the blockages ensures sufficient SNR to identify the event even if the signal is somewhat attenuated^59,60. In contrast, Fig. 2b shows that when the dumbbells translocate, they produce two deep blockages separated by a shallower blockage level indicative of the linear dsDNA section between the two 12-arm DNA stars, with a mean passage time of 70 (pm) 2 µs. We observed a slight shift in maximum blockage level (Fig. 2c, d) between the probes and the dumbbells since each dumbbell event produces two deep blockage levels and there is therefore a higher probability that at least one will be well-resolved, and the full blockage level correctly fitted. The presence or absence of this second, deep blockage level is confirmation of the presence of a junction strand in the sample.

In order to distinguish event types, we employed a simple threshold-crossing scheme detailed in Supplementary Note 3. Briefly, we counted the number of times the current trace in the event crossed a set of thresholds indicative of the transition between 1x dsDNA and 6x dsDNA blockage levels. With the threshold set to 2.5x dsDNA, a shooting star event registers 2 threshold-crossings, while a dumbbell event registers 4 threshold-crossings, as shown in Fig. 2b and Supplementary Fig. 4. The analysis of translocation events of the probes and dumbbells separately show that while the assembly into a dumbbell has only a mild effect on the passage time, the shape of the events are easily distinguishable. When using purified probes in the absence of junction strands we observed a false positive rate of <2%, primarily driven by either analysis artefacts or the binding of misassembled probe pairs (Supplementary Figs. 5 and 10). The latter is possible, for example, if both the probes P-1 and P-2 are missing the last two staple strands on the tip of their tails, in which case the probe pair overhang sequences are complementary and could form the dumbbell structure with a slightly shorter linkage in the absence of the junction strand. Future work will aim at resolving this by either having unique sequences for each staple in the entire tail on the respective probes, by increasing binding strength of the tail staples using longer sequences, and/or modifying the design of the DNA nanostructure labels.

Nanopore digital response characterization

To investigate and validate the dose response of our digital assay, we first characterized the response of the nanopore sensor as a function of different mixtures of known concentrations of junction strand and probes. For this, we fixed the concentration of both probes P-1 and P-2 at 20 nM and varied the concentration of the junction strand, from 0.2 nM (ratio of 0.01:1, junction strand-to-probe pair) to 400 nM (20:1). Figure 3a–c shows the scatter plots of the maximum blockage depth versus dwell time for all single-molecule events recorded for three junction strand-to-probe pair ratios (0.025:1, 1:1, and 10:1). The corresponding scatter plots for all concentrations are shown in Supplementary Fig. 9. As expected, with increasing junction strand concentration below the fixed probe pair concentration, we observed a linear increasing fraction of events attributed to the passage of dumbbell nanostructures, reaching a maximum at a ratio of 1, before the relative number of dumbbells linearly decreased again. This linear dose response is plotted in semi-log scale in Fig. 3d.

To understand this non-monotonic response, we developed a simple computational model that assumes irreversible first-order binding kinetics of junction strands to probes. This model predicts that the fraction of dumbbells formed at equilibrium will be in proportion to the ratio of junction strands-to-probe pairs when there are fewer junction strands than probe pairs, and the inverse ratio in the opposite case, that is,

where f_DB denotes the fraction of dumbbell events and x the ratio of junction strand (proxy for protein) concentration (({c}_{{{{{{{mathrm{Js}}}}}}}}))-to-each shooting star probe pair concentration (({c}_{{{{{{mathrm{P1}}}}}}}={c}_{{{{{{mathrm{P2}}}}}}}),) that is, (x=frac{{c}_{{{{{{{mathrm{Js}}}}}}}}}{{c}_{{{{{{mathrm{P1}}}}}}}}=frac{{c}_{{{{{{{mathrm{Js}}}}}}}}}{{c}_{{{{{{mathrm{P2}}}}}}}}).

This linear behavior can be understood readily by a simple intuitive argument. Assuming irreversible binding, if there are more probe pairs than junction strands ((x < 1)), every junction strand that binds one of the probes will eventually be able to find another of the matching pair with which to bind, leading to one dumbbell per junction strand (i.e.,({f}_{{{{{{{mathrm{DB}}}}}}}}=x)), depicted in Fig. 3d as the green section of the junction strand-to-probe ratio range. On the other hand, if there are more junction strands than probes ((x , > , 1)), probes will get capped and be unable to find a binding partner with a free binding site, with the probability of capping occurring before binding a partner being in proportion to the ratio of concentrations in the first-order approximation that diffusion times are not rate-limiting. This is in reasonably close agreement with our experimental results when (xne 1), as can be seen in Fig. 3d. In this regime, the model predicts a linear increase in probe capping or linear decrease in the dumbbell fraction as we increase the junction concentration (i.e.,({f}_{{{{{{{mathrm{DB}}}}}}}}={x}^{-1})). The experimental data suggest that there is a limit at which the dumbbell fraction still occurs, nearing 20%, even in the presence of overwhelming numbers of junction strands. Because of this limit the range of excess junction strands to probes should be avoided for quantification. While the expected peak at (x=1) is present in the experimental data, in contrast to the prediction of our computational model, the experimental data show that the dumbbell fraction only reaches a plateau of about 60%. During assembly of dumbbells, particularly as concentration ratios near parity, it was noted that as expected from hybridization kinetics⁶¹, the incubation times required to reach binding saturation are quite long due to progressive depletion of binding species as the reaction progresses. However, this underperformance of binding near the peak cannot be explained by short incubation times, since the reaction would have run past completion well before the experiments in Fig. 3d were conducted. To validate this dose response, we have also the same samples characterized by gel electrophoresis, which show good agreement with the nanopore results (see Supplementary Fig. 6).

The more likely explanation is that a fraction of the shooting star probes in our purified stocks were or became misassembled while stored, either prior to use or during manipulation ahead of nanopore sensing. This is a common issue with multi-component DNA nanostructures⁵³ which introduces potential false negatives in the analysis, as discussed in more detail in Supplementary Note 3. To support the hypothesis that our DNA nanostructure can incur partial disassembly post purification, we characterized samples of fully assembled dumbbells that were purified by gel band extraction. The data are shown in Supplementary Fig. 7 and reveal that up to 20% of the single-molecule events do not generate the electrical signature of four threshold crossings expected for the translocation of the dumbbell (Fig. 2b). While further investigation is required to better understand the stability of these DNA nanostructures and determine their shelf life and optimal storage conditions, the presence of misassembled nanostructures is controlled by performing a calibration curve and serum sample testing with a single batch of probes.

Proper performance of the digital assay also requires setting the junction strand-to-probe ratios between 0.01 and 0.5 to maintain the dumbbell assembly in the optimal range (linear dose response). For junction strand-to-probe ratios well below 1 ((x,le, 0.5)), the assay should perform as expected even in the presence of up to 20% of mis-assembly, but nearing ratios of 1 ((x , > , 0.5)) this issue becomes limiting and results in a reduced precision. It is therefore important, both from a timing and accuracy perspective, to ensure that the concentration of shooting star probes chosen be such that the ratio of junction strands-to-probes is below 0.5. This is also where the hybridization reaction is fastest⁶¹. The lower limit of ~0.01 is currently set by the presence of false positives at a rate of <2%, though we hope to push this limit down by improving the DNA nanostructure design. This 0.01–0.5 regime is highlighted in green in Fig. 3d and defines the dynamic range for a given probe concentration. We expect that the current ~50-fold dynamic range of this assay scheme can be extended to ~2–3-log by improving the DNA nanostructure labels, or to an arbitrarily wide range of clinically relevant biomarker concentrations by incubating the unknown concentration of junction strands (proxies for protein) with different fixed concentrations of probes in parallel. For example, splitting the sample volume and testing it against three different probe concentrations could, in principle, provide a 5-log dynamic range. Likewise, the sensitivity of this assay, currently limited by the lower bound of the concentration ratio of junction strand-to-probe, (x=frac{{c}_{{{{{{{mathrm{Js}}}}}}}}}{{c}_{{{{{{mathrm{P}}}}}}}}approx 0.01,) can be adjusted to accommodate any desired concentration range at the cost of linearly increasing the detection time of a single nanopore sensor as concentrations are reduced, though this increase in counting time can be offset through parallelization with an array of pores and other strategies that increase nanopore capture rate⁶². The limit of detection, while fixed by the parameters of a particular assay and the choice of probe concentration, can therefore be controlled by the counting time of the nanopore and for a fixed measurement time can be improved by speeding up the detection through parallelization, amplification, preconcentration, or capture rate enhancement schemes^{19,29,53,62,63,64,65,66,67,68}.

Nanopore digital immunoassay for TSH

To reliably quantify the concentration of TSH in human sera, our proof-of-concept protein target, we performed calibration curves using the full assay workflow presented in Fig. 1 and validated the reproducibility of the assay by testing the inter-pore variability. A five-point calibration curve was constructed using known concentrations of recombinant TSH (rTSH) (0.00, 0.15, 0.30, 0.60, and 1.2 nM) suspended in sample diluent (Fig. 4a). Note that after release of the junction strand (proxy for protein, Fig. 1f), a final concentration step was applied to the supernatant, increasing the concentration by ~17-fold before incubating for dumbbell assembly with a fixed 20 nM probe concentration (Fig. 1g). This particular probe concentration was selected in order to operate the assay in the optimal range of junction strand-to-probe ratio previously discussed for Fig. 3d, and to limit the single nanopore recording time to minutes to count a statistically significant number of single molecules.

Figure 4a presents the analyzed nanopore data, showing the fraction of dumbbell formed, f_DB, as a function of the initial spiked rTSH concentration in each of the calibrators. The calibrators were run on three different nanopores: a 10 nm (pore 1, magenta diamonds), an 11.5 nm (pore 2, blue triangles), and a 12 nm (pore 3, cyan circles). The calibration curve for the fraction of dumbbell events ranges on average from ~3% (blank) to ~40% (1.2 nM). The calibrators exhibit a linear trend as expected and overlap within their error bar for all three pores, highlighting the pore-to-pore reproducibility of our digital immunoassay scheme for pores sizes in this range. The straight line shown in Fig. 4a is a linear fit to the calibration points for pore 3. For the different pores tested, the blank sample shows a background level varying from 2.5% to 3.4%. We had previously observed a <2% false positive rate from dumbbells formed from purified probes in the absence of junction strand (see Supplementary Fig. 10), which we attributed to analysis artefacts and the agglomeration of misassembled probe pairs. We therefore assign this additional ~1% to the values of the blank due to non-specific binding during the immunoassay, most likely of the secondary antibody to the beads not removed during washes. Limits of detection (LoD) were determined for each calibration curve at 2.5 standard deviations (s.d.) above background (blank) as commonly done⁴². LoD determined from the three pore runs were averaged for an overall mean LoD of ~20 pM for these particular choice of assay workflow and parameters.

The gray squares in Fig. 4a represent the idealized values of the five rTSH calibrators for junction strand-to-probe ratios of 0:1, 0.125:1, 0.25:1, 0.5:1, and 1:1 as interpolated from Fig. 3d. These interpolated values of the ratios assume no losses due to disassociation of the components from the immunoassay during the wash steps, nor of reagents from sticking to tubes walls, and a 1:1 labeling of the detection antibodies with junction strands (i.e., a perfect translation of each protein target to exactly one junction strand). Since losses are to be expected throughout the assay⁶⁹, we empirically estimate these losses by comparing the interpolated values to our experimentally observed values. The difference in dumbbell fraction seen in Fig. 4a indicates that we are on average recovering half as many junction strands as there are target proteins present.

Next, we investigated the accuracy of the nanopore digital signal with clinically relevant biological samples and validated the reproducibility for protein concentration quantification in these conditions. To accomplish this, we spiked 0.48 nM of rTSH into a human serum sample, with a predetermined undetectable level of TSH (see “Methods” section) and measured it on the three different pores as above. Linear fits to the calibration points for each pore are used as calibration curves to convert the observed fraction of dumbbell into the concentration of TSH originally present in the human serum sample (i.e., ({C}_{{{{{{{mathrm{protein}}}}}}}}={{f}_{{{{{{{mathrm{DB}}}}}}}}/{{{{{rm{slope}}}}}}}_{{{{{{{mathrm{cal}}}}}}}.})). Figure 4b shows that the observed fraction of dumbbell formed are 19 (pm) 2%, 19(pm) 2%, and 19.2 (pm) 0.9% corresponding to 0.54 (pm 0.)04, 0.61 (pm)0.05, and 0.59 (pm)0.03 nM of rTSH, respectively. These triplicate measurements are in good agreement with one another. Interestingly, the quantified concentrations of TSH are systematically higher than the spiked concentration of 0.48 nM. The spike recovery analysis shows that we have a recovery of 121(pm)5%, which is close to the acceptable range of 80–120%⁷⁰. We attribute discrepancies here to non-specific binding and matrix effects in the presence of serum since the calibration curves were constructed from spiked rTSH in sample diluent. In future work, we anticipate that matrix effects can be normalized by running the calibration curve in TSH-depleted serum or could be reduced by further increasing the dilution factor of the sample from 4× to ≥10×⁷⁰. Additional data sets of calibration curves and serum measurements on two other pores using a different reagent batch yielded similar results as shown in Supplementary Fig. 11. Nanopore assay results were further validated by gel electrophoresis (see Supplementary Figs. 12 and 13), and five additional measurements of rTSH in human serum sample from 0.15 to 1.2 nM are shown in Supplementary Fig. 14.

To further improve the sensitivity of our digital immunoassay and lower the LoD for a fixed nanopore counting time of a few minutes, we implemented an amplification scheme to detect rTSH down to the high femtomolar range. To achieve a ~100× amplification, we replaced the biotinylated ssDNA junction strand with a detection complex composed of 30 nm gold nanoparticles decorated with detector antibodies and hundreds of junction strands following protocols by Mirkin & Co^45,71. This effectively translates one protein into hundreds of ssDNA junction strands instead of a single one as illustrated in Fig. 4c. Amplification experiments were carried out using the same assay workflow. This time, we measured concentrations of spiked rTSH in human serum samples at 0.8, 1.6, 3.2, 6.4, and 12.8 pM. Figure 4d shows the detected fraction of dumbbell formed of 7.5 (pm)0.9%, 12 (pm)1%, 16 (pm)2%, 24 (pm)2%, and 41 (pm)2%, with a blank serum measured at 2.9 (pm)0.6%. LoD for the particular parameters of this amplified digital assay is calculated to be 385 fM. Additionally, we performed a homebrew ELISA employing the same workflow and reagents as our nanopore digital assay to validate the performance of our assay components with an optical readout (see Supplementary Fig. 15).

Since the speed at which single molecules are counted is dictated by the capture rate of the nanopore (a Poisson process)¹⁹, the evolution of dumbbell fraction as a function of cumulative number of events offers insights into the assay time needed to accurately identify a particular concentration with a desired level of precision. Standard error propagation gives the mean and s.d. of the dumbbell fraction ({f}_{{{{{{{mathrm{DB}}}}}}}}pm {sigma }_{f}) as:

where ({N}_{{{{{{{mathrm{DB}}}}}}}}) is the number of “1” events (dumbbells) and ({N}_{{{{{{mathrm{P}}}}}}}) is the number of “0” events (probes), assuming Poisson error on both ({N}_{{{{{{{mathrm{DB}}}}}}}}) and ({N}_{{{{{{mathrm{P}}}}}}}), i.e. that the s.d. of each is equal to its square root. ({N}^{ast }) is the effective event count. Note the factor of 2 is included to pair probe events for the sake of comparison to the dumbbell fraction.

Like the standard error of a Poisson process or the s.d. of a capture rate, the uncertainty in the ratio of two Poisson processes scales inversely with the square root of the total event count. In the limit of f_DB approaching either extreme of 0 or 1, where one event type dominates the counting, the numerator of Eq. 3 approaches zero, and the uncertainty on f_DB is small and relatively insensitive to total event count as a result. Although intermediate values of f_DB show higher uncertainty for a given event count, ({sigma }_{f}) can be reduced greatly by recording more events.

The effective event count, ({N}^{ast }), required to determine the fraction of events which are counted as “1” (here dumbbells) accurately within a predetermined error of (pm {sigma }_{f}) depends on the value of the dumbbell fraction f_DB itself. Figure 4d shows the evolution of the multiple measured dumbbell fractions of pore 1, as a function of the effective event count with respective error bars plotted following Eq. 3. Figure 4d shows that at least 129, 173, 262, and 307 effective event counts are required to obtain an absolute uncertainty of ({sigma }_{f})= 0.025 (2.5%), for TSH concentrations of 0.15, 0.3, 0.6, and 1.2 nM, respectively. The minimal event count needed to distinguish two different concentrations also depends on the respective values of f_DB^72,73.

Our discussion has thus far pertained only to the number of single-molecule translocations (counts) instead of measurement time¹⁹. Under our experimental conditions and with the TSH concentration ranges presented, the DNA nanostructures have a capture rate of ~1 Hz nM⁻¹ on a single 10 nm nanopore, resulting in sensing times on the order of tens of minutes required for precisions of ({sigma }_{f}approx 0.01). Evidently, the time to response of the nanopore sensor can be reduced or the sensitivity and precision of the digital immunoassay increased by counting single molecules more rapidly in a fixed time. We have shown that the sensitivity of our digital nanopore assay can be significantly improved by amplification, yet in this configuration it is still limited by measurement time. As discussed previously, using a lower probe concentration can reduce the sensitivity by an equal factor at the cost of proportionally increasing the counting time unless the detection rate is accelerated by a combination of parallelization (array of pores), preconcentration, or capture rate enhancement schemes. See Supplementary Note 5 for an example of the latter strategy. In the idealized limit of rapid nanopore detection, the enhancement factor of the K_D by the antibody-coated magnetic bead and non-specific interactions would ultimately become the limiting factors.

We have shown that solid-state nanopores can be used as precise and specific digital sensors for magnetic bead-based sandwich immunoassays, using DNA nanostructures as proxies for the presence or absence of a specific target protein. We were able to accurately and most importantly consistently quantify the concentration of spiked protein in human serum in the high fM to the low nM range, overcoming several of the major challenges associated with using solid-state nanopores to quantify the concentrations of biomolecular targets in complex biological samples. This represents a ~1000× improvement in sensitivity compared to the previous nanopore studies quantifying protein concentration from serum^25,26,27. This digital scheme, based on the electrical counting of single-molecules, is an effective solution to the pore-to-pore consistency issue that has been slowing the development of bioassays on solid-state nanopores. The shooting star nanostructures used here give a high SNR of 20 (at 200 kHz), while using high recording bandwidth to better resolve translocation events. The advantages of the antibody-coated magnetic bead approach compared to DNA nanocarrier schemes is that the affinity (more precisely the on-rate, k_on) of the magnetic bead–antibody complex to capture protein targets is enhanced by a factor equal to the number of antibodies present on the bead surface, essentially turning each bead into a much more efficient antibody and enabling fM sensitivity⁷⁴. The selectivity is also increased by washing away background molecules and non-specifically bound objects, leaving only molecules of interest to translocate through the pore, thereby reducing false positives.

The next foci for performance optimization for our proposed assay are to increase the dynamic range and to further decrease the limit of detection while reducing the assay time to <1 h. Both dynamic range and limit of detection can, in principle, be arbitrarily extended by varying the probe concentration but are practically limited here by the measurement time. As discussed previously, the current optimal dynamic range spans a ratio of junction strand (proxy for protein)-to-probe of ~0.01 to ~0.5, and for probe concentrations below <10 nM the incubation time required to hybridize the junction strand to two nanostructured probes to assemble the dumbbells becomes much too long (days) to be of practical use⁶¹. To tackle this timescale problem, techniques to control and increase the rate of nucleic acid hybridization reactions, such as isotachophoresis⁷⁵, could be employed to extend the dynamic range from 10 nM down to the fM levels. Combined with the strategies for improving the rate of single-molecule counts by a nanopore already discussed (parallelization, amplification, preconcentration, and capture rate enhancement schemes), we expect the proposed solid-state nanopore-based digital immunoassays scheme to reach low fM levels with a ~3-log dynamic range to undertake relevant clinical applications.