Article pubs.acs.org/ac
Accurate Data Process for Nanopore Analysis Zhen Gu,†,‡ Yi-Lun Ying,† Chan Cao,† Pingang He,‡ and Yi-Tao Long*,† †
Key Laboratory for Advanced Materials and Department of Chemistry, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, People’s Republic of China ‡ Department of Chemistry, East China Normal University, 500 Dongchuan Road, Shanghai 200241, People’s Republic of China S Supporting Information *
ABSTRACT: Data analysis for nanopore experiments remains a fundamental and technological challenge because of the large data volume, the presence of unavoidable noise, and the filtering effect. Here, we present an accurate and robust data process that recognizes the current blockades and enables evaluation of the dwell time and current amplitude through a novel second-order-differential-based calibration method and an integration method, respectively. We applied the developed data process to analyze both generated blockages and experimental data. Compared to the results obtained using the conventional method, those obtained using the new method provided a significant increase in the accuracy of nanopore measurements.
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tion of the blockage shape is an impediment to accurate nanopore data analysis. Moreover, the low-pass filter suppresses only high-frequency noise. The low-frequency noise and noise from the analog−digital converter are still mixed in the recorded current trace. Therefore, the existing noise increases the difficulty of accurately locating and recovering individual blockages. The conventional method of detecting events in a data process is to assign a baseline that relates to the open-pore state by averaging the whole current trace. Hence, the blockages are regarded as clustered data points that deviate from the baseline by a threshold.12,30 The threshold is usually defined on the basis of the standard deviation of the current traces. The single-threshold method is fast and easily implemented in nanopore analysis software. However, the data points at the two edges of the blockages are missed because the assigned threshold should be sufficiently large to avoid the influence of the noise components. As an improvement, a two-threshold method could minimize the number of missed data points.34 For current traces with significant drifting due to the properties of the nanopore materials and the salt concentration,35,36 a constant baseline or threshold is neither sufficient to provide a flexible criterion for searching blockages nor able to measure the dwell time and the amplitude accurately because of the uncorrected recognition of the starting and stopping points of blockages. Hence, a localthreshold-based moving-window-averaging approach has been proposed.33,37 In other aspects, the slow frequency response in nanopore measurements induces deformed, short-lived blockages. To recover the blockages, current amplitudes were determined via monoexponential fitting according to the time constant of the amplifier.38 Recently, Baaken et al. demon-
anopores with unique volume and electrochemical properties have been demonstrated to be promising sensors for label-free, single-molecule detection, particularly for DNA sequencing.1−4 Such measurements are conducted by driving the analytes through a nanoscale channel. The transmembrane ionic flow is temporarily blocked because of the restriction of the available pore volume, which results in characteristic current blockages. The dwell time, amplitude, and frequency of the current blockages are important information used in most nanopore studies. These parameters have been used to investigate the biophysical, physicochemical, and chemical properties of analytes such as DNA,5−9 RNA,10−14 proteins,15−20 peptides,21−23 noble nanoparticles,24,25 and heavy-metal ions.26,27 For example, folding states of DNA were characterized by the shape of blockages,9,28 the kinetics of enzymatic degradation have been investigated via the dwell time of rapid translocations,29 conformations of a protein were distinguished through analysis of the dwell times and current amplitudes of bumping blockages,15,18,19 and the interactions between molecules have been investigated on the basis of statistical analysis of each blockage.12,30−32 Because of the random nature of single molecules, nanopore studies are always based on statistical analysis of numerous blockages, which requires the time-intensive recording of current traces. Furthermore, each individual blockage in the large volume of data must be identified. Inaccurate data processing can lead to unreliability and low repeatability in nanopore studies. Generally, manually assisted recognition of blockages not only is time-consuming but also introduces operator bias into the analysis. Hence, the development of automated methods for recognizing and measuring the blockages is important. However, the low-noise recording of nanopore data incorporates the usage of a low-pass filter, which results in the deformation of the blockage shape, particularly for rapid translocations and bumping blockages.33 The deforma© XXXX American Chemical Society
Received: August 1, 2014 Accepted: December 16, 2014
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KCl, 10 mM Tris−HCl, and 1 mM EDTA. Unless otherwise noted, all other chemicals were of analytical grade. Nanopore Experiments. As described previously,41−44 1,2diphytanoyl-sn-glycero-3-phosphocholine in decane (30 mg mL−1) was used to form a bilayer across a 150 μm orifice in a lipid bilayer chamber (Warner Instruments, Hamden, CT) filled with pH 8.0 buffer solution. The stability of the bilayer was evaluated by monitoring its resistance and capacitance. The solution of α-hemolysin was injected into the cis chamber proximal to the bilayer. Then seven monomers of α-hemolysin assembled to form a hydrophilic channel in the bilayer. The two compartments of the bilayer cell are termed cis and trans (shown in Figure 1). A pair of Ag/AgCl electrodes was inserted into the two compartments. After a single nanopore was formed on the bilayer, the analyte was injected into the cis chamber. The voltage was set to +100 mV during the experiments. A ChemClamp instrument (Dagan Corp., Minneapolis, MN) in the voltage clamp mode was used to amplify and measure the ionic current flowing through the nanopore. The amplified currents were filtered at 3 kHz and converted into digital signals by DigiData 1440A hardware (Axon Instruments, Forest City, CA) at a 100 kHz sampling rate. Nanopore data were recorded by the PClamp software (Axon Instruments). Generation of Ideal Blockades. A square-wave signal was generated by a DG1022U function generator (Beijing RIGOL Technology Co., Ltd., China). This signal was fed into a custom-designed circuit (Figure S1, Supporting Information) for input into the ChemClamp amplifier with a low-pass Bessel filter set at 3 kHz. The filtered signal was acquired by a DigiData 1440A at a 100 kHz sampling rate. Data Analysis. The data were processed using a MATLAB program called NANOPORE ANALYSIS. The detailed process for detection of the current blockages is described in the Supporting Information. This program is available from our laboratory Web site at people.bath.ac.uk/yl505, which also provides tools for data management, blockage preview, and statistical analysis. The conventional process is defined as using a local threshold method calibrated by a tracking-back routine.
strated a novel analysis method in which they modeled the nanopore system by measuring its impedance via a dynamic signal analyzer.39 These two methods require additional characterizations of the measurement system and lack calibration for the region of blockage. In previous studies, other automated programs such as OpenNanopore have been developed on the basis of a cumulative sums algorithm37 and QUB through Markov analysis.40 Here, we propose an automatic and accurate nanopore data process that includes blockage location and evaluation of both the dwell time and current amplitude. After the blockages were approximately located, a second-order-differential-based calibration (DBC) method was introduced to correct the region of the blockages and accurately measure the dwell time. We demonstrated that the DBC method improves the accuracy of the local threshold approach for the determination of the starting and stopping point of blockages without requiring extra instruments. Meanwhile, the current amplitude was evaluated by an integration method that provided advantages in recovering the accurate height of rapid blockages (Figure 1).
Figure 1. Schematic of the data process. A model illustrates the principle of the α-hemolysin nanopore sensor for the exemplar case of single-stranded DNA (ssDNA) analysis. An individual ssDNA enters the pore under an applied potential. The recorded experimental data contain rapid blockages, open-pore currents, and noise components. The starting and stopping points of a typical blockage (blue circles) were identified by the DBC method. The integration of blockage current was used to evaluate the current amplitude. The red curve represents the ideal shape of a typical blockage.
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RESULTS AND DISCUSSION Blockage Location. Achieving rapid data analysis requires that the processing time in the intervals between two blockages be decreased. Therefore, we approximately located the blockages as the first step in our data process. To minimize the influence of baseline drifting, a local baseline was estimated on the basis of moving-window averaging. The adjustable window width ω is related to the noise level. The local threshold (uj) is defined by subtracting a constant threshold (u0) from the local baseline:
The developed data process was further validated using generated blockages as well as experimental data for DNA and peptides. Our results showed that the developed methods significantly increased the accuracy of nanopore data analysis.
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EXPERIMENTAL SECTION Materials. α-Hemolysin and decane (≥99%) were purchased from Sigma-Aldrich (St. Louis, MO). 1,2-Diphytanoyl-sn-glycero-3-phosphocholine (chloroform, ≥99%) was purchased from Avanti Polar Lipids (Alabaster, AL). All of the oligonucleotides used in this study were synthesized by Invitrogen Life Technologies (Shanghai, China). β-Amyloid (Aβ42) with a purity of 98%, as determined by HPLC, was purchased from GL Biochem, Ltd. (Shanghai, China). βCyclodextrin (β-CD) was purchased from the Sinopharm Chemical Reagents Co., Ltd. (Shanghai, China). Before detection, Aβ42 was incubated with β-CD for 8.5 h at 4 °C in a refrigerator, as described in a previous study.15 Ultrapure water (resistivity of 18.2 MΩ·cm at 25 °C) was obtained from a Milli-Q system (EMD Millipore, Billerica, MA). The pH 8.0 buffer solution used in the experiments was composed of 1 M
uj =
1 ω
j
∑ k=j−ω
Ik − u0 (1)
where Ik is the value of the current at data point k. As an example, the gray and brown dashed lines in Figure 2A represent the local baseline and the local threshold, respectively. A program scans throughout the whole current trace to search and mark the data points where the current is lower than the corresponding local threshold (ignoring the boundary effect). The first and last points in a cluster of the marked points were set as starting (Ps1) and stopping (Pe1) points of blockages, respectively (red circles in Figure 2A). B
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Figure 2. (A) Region of blockage recognized by a local threshold. Gray and brown dashed lines represent the local baseline and local threshold, respectively. The recognized region of the blockage is marked between Ps1 and Pe1 (red circles). (B) A tracking-back routine is applied to reset the starting point and the stopping point as Ps2 and Pe2, respectively, which are indicated by green circles. (C) Correction of the blockage region by the DBC method. The blockage data are fitted by Fourier series and calculated by a second-order differential. The corrected region is between Ps3 and Pe3 (blue circles). Further calibration is carried out by resetting the stopping point from Pe3 to Pe4 (blue square), which is a local minimum of a blockage. (D) Second-order differential of both the generated blockage (blue) and the Fourier-series-fitted blockage (red). (E) Fourier series with order ranging from 1 to 5 for fitting blockages with a nominal dwell time (tnom) from 0.05 to 0.2 ms. Fitting results are shown as red curves. All presented data were generated by a function generator. The blockages were generated with a nominal current amplitude (Inom) of 100 pA.
Because of the noise effects, this initial location yields the missing data points on the two sides of the blockage. To recover the missing data points, a tracking-back routine is applied to reset the starting point (Ps2) and stopping point (Pe2) as the second step in determining the blockage location (Figure 2B). When the point is tracked from Ps1 back to the last blockage, Ps2 is the first point higher than its local baseline. Similarly, Pe2 is the first point higher than its local baseline when the point from Pe1 is tracked to the next blockage. Correcting the Dwell Time of Blockages. Although the missing data points at two edges of the blockages could be recovered by the tracking-back routine, this procedure will lead to the overcoverage of blockages in most cases. As a consequence, a positive error would be induced in measurements of the dwell time (td). Because the overcoverage contains mainly signal noise, the degree of error in the measurement of each blockage is arbitrary. Thus, the statistical distribution of dwell times would be strongly affected by an inaccurate location. To calibrate the region of blockages, we applied a second-order differential method named DBC to further determine the starting point and stopping point of blockages as the second step of our data process. The current drops in the real recorded blockage are unlike the shape of the Heaviside step function because a low-pass filter was used. Therefore, we introduced a modified criterion to identify the boundary of a blockage by finding the points of inflection at the two edges of the approximately located blockages. However, the trace of the second-order differential of the original data is overlapped by the noise, as shown in Figure 2D. Thus, direct determination of the points of inflection is difficult. To avoid the influence of noise, a smoothing method based on fitting the experimental
blockages to a Fourier series (Figure S4, Supporting Information) was applied prior to implementation of the DBC method: n
I (t ) = a 0 +
∑ (aj cos(jωt ) + βj sin(jωt )) j=1
(2)
where aj, βj, and ω are coefficients of the Fourier series and n is the order of the model. The Fourier series decomposes blockages into the sum of a set of simple oscillating functions (sines and cosines). Application of the Fourier smoothing routine allowed easy recognition of the minima of the secondorder differential, as shown in Figure 2D. As a result, the starting point and the stopping point of the blockage were calibrated from Ps2 and Pe2 to Ps3 and Pe3, respectively, by the DBC method (Figure 2C). Obviously, the order of the Fourierseries model could affect the performance of the fitting. Therefore, the performance of Fourier series with different orders was examined by fitting the generated blockages with nominal amplitude from 0.05 to 0.20 ms (Figure 2E). The R2 (regression performance) between the fitted and raw blockage indicated that the Fourier series with higher order performed better in fitting the blockages. Thus, a fourth-order model was implemented in the method as a compromise between performance and efficiency of the data process. To test the accuracy of the DBC method, pulses with dwell times ranging from 0.05 to 5 ms were generated. The recorded data were automatically processed using both the DBC method and the conventional method. The conventional method combined the local threshold method and the following tracking-back routine. The rise time of the filter induces the extension of the blockages. To avoid overestimation of the C
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approximately 0.22 ms. The low-pass filter removes the shortterm fluctuations such as flicker noise while deforming the blockage shape. Nevertheless, the area of a blockage is hardly affected by a low-pass filter.46 The integrated area is more suitable than the minimum (or plateau) for serving as the criterion for the measurement of the current amplitude, particularly in the case of blockages with dwell times of less than 2Tr. As inspired by the nature of the filter, a novel integration method was used as the next step in our data process to accurately evaluate the current amplitude. Because of the low-pass filter, the blockage current is seriously modified and slowly decreases without reaching the minimum of the square wave (Figure 4). We investigated the influence of the
dwell time, a modified method was used to reset the stopping point from Pe3 to Pe4 as the local minimum of the blockages.33 Hence, the region of the blockages that was finally determined was between Ps3 and Pe4. To ensure comparability between measurements, both the DBC method and the conventional method adopted this criterion when extracting the dwell times of the blockages. The test results for different nominal dwell times (tnom) are shown in Figure 3. The conventional method
Figure 4. Example of the measurement of the current amplitude of an individual blockage by an integration method. The blockage was generated with a tnom of 0.25 ms and an Inom of 40 pA. The recorded blockage and its ideal wave pulse are plotted as blue and black lines, respectively. Gray slashes represent the integrated area of the recorded blockage. The baseline is the gray dashed line. The cutoff frequency of the filter used to record the blockage was 3 kHz.
Figure 3. Relative errors of dwell time (tnom = 0.05, 0.10, 0.20, 0.50, 1.00, 2.00, and 5.00 ms) evaluated by the DBC method (blue line) and the conventional method (red line). Inset: dwell-time histograms of 300 generated blockages measured by the DBC method (blue bar) and the conventional method (red bar). The blockages were generated with an Inom of 100 pA.
cutoff frequency of the filter (1, 3, and 10 kHz) on the integrated currents of blockages. As shown in the Supporting Information, the integrations of filtered blockage currents are hardly affected by the low-pass filter (Figure S6, Supporting Information), which indicates that the integrated current exhibits the advantage of analyzing attenuated blockages. Therefore, the unmodified current amplitude (Ic) was calculated via eq 4. Because the recorded data point is discrete, eq 4 could be transformed into eq 5.
evidently produced a higher relative error (|td − tnom|/tnom) of approximately 140% for blockages with a nominal dwell time of 0.05 ms, whereas a lower relative error of approximately 41.8% was produced by the DBC method. For blockages with a nominal dwell time longer than 0.10 ms, the relative error of the DBC method was 60%). The statistical histograms of blockages with tnom of 0.05, 0.10, and 0.50 ms are presented in the inset of Figure 3. The values of td were obtained by fitting the distributions to an exponential function (see Figure S5 and Table S1, Supporting Information). The results showed that the distributions obtained by the DBC method are more concentrative than those obtained by the conventional method. The effect of random noise on the distribution of dwell times was largely eliminated by the DBC method. These results demonstrate the advantages of the DBC method for evaluating the dwell time, especially for processing rapid translocations or bumping blockages (tnom < 1 ms). Evaluating the Current Amplitude of Blockages. Conventionally, the amplitude of blockages (Ic) is evaluated by subtracting the minimum (or average of the plateau) from the baseline. However, the rise time (Tr) of the low-pass filter prevents the blockages from reaching their real minimum or plateau. Usually, blockages with a dwell time of less than 2Tr are seriously attenuated. The Tr of a filter can be estimated by Tr = 0.3321/fc
Ictd =
∫t
tend
(Ibase − I(t )) dt
start
Ictd =
1 fs
(4)
Pe2
∑ k = Ps2
(Ibase − Ik) (5)
where td is the dwell time of the square wave, fs is the sampling frequency of the analog-to-digital convertor, Ibase is the baseline current, and Ik is the current value at data point k. The integration method was subsequently compared with the conventional method by evaluating the amplitude of the generated blockages with dwell times ranging from 0.05 to 0.25 ms (Figure 5). The Gaussian function was used to fit the distributions of the current amplitudes. In comparison with the conventional method, the advantage of the integration method is obvious because the peak values are much closer to the nominal current amplitude (Inom = 100 pA) for all ranges of dwell times (Figure 5A). Although the decrease in the nominal dwell time (tnom) increases the uncertainty in the evaluation of the current amplitude, the integration method is still advanta-
(3)
where fc is the cutoff frequency of the filter. For the 3 kHz low-pass filter used in this work, the value of 2Tr is 45
D
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Figure 5. Evaluation of the generated current amplitude. (A) Histograms of 300 current amplitudes (Inom = 100 pA, tnom = 0.05, 0.10, 0.15, and 0.25 ms) evaluated by the integration method (blue bars and lines) and by the conventional method (red bars and lines). (B) Ic̅ of the integration method (blue line) and the conventional method (red line) vs tnom. The blockages were generated with an Inom of 100 pA. (C) Relative errors of the integration method (blue line) and the conventional method (red line) vs different Inom values. The blockages were generated with a tnom of 0.1 ms.
Figure 6. Analysis of the experimental data of poly(dA)60. The histograms of dwell time measured by the DBC method (A) and the conventional method (B) were fitted by exponential functions. The histograms of the current amplitudes were measured by the integration method (C) and the conventional method (D). Second-order Gaussian functions were used to fit the current histograms.
Ic = Inom erf(2.668f ceff tnom)
geous for recovering the blockages. The distance between the mean evaluated current amplitude (Ic̅ ) and Inom was reduced significantly when the nominal dwell time was less than 2Tr (∼0.22 ms for a 3 kHz low-pass filter), as shown in Figure 5B. The maximum distance between the Ic̅ and Inom in the case of the integration method was 25.4 pA at tnom = 0.05 ms, which is 36.4 pA less than the maximum distance between the Ic̅ and Inom in the case of the conventional method (61.8 pA). By analyzing blockages with different Inom values (Figure 5C), we noted that the relative error (Ic̅ − Inom)/Inom) was almost independent of the Inom. To estimate the performance of the integration method, we calculated the apparent cutoff frequencies (feff c ) using the theoretical model expressed by
(6)
where Ic is the evaluated current amplitude and erf(...) is the error function. The curves in Figure 5B were substituted into eff eq 6 to fit the feff c . As a result, the estimated fc of the integration method was 5.74 kHz, which was greater than the fc of the lowpass filter (3 kHz). In contrast, the feff c of the conventional method (2.78 kHz) was slightly lower than the fc of the filter (3 kHz). The feff c of the developed integration method was 2.06 times greater than that of the conventional method. These results indicate that our method can improve the accuracy of blockage analyses, even when the blockages are modified by a low-pass filter. E
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Applications to Experimental Data Analysis. We applied the developed data processing method, including blockage location as well as evaluation of both the dwell time and the current amplitude, for the analysis of α-hemolysin nanopore data. The current traces of poly(dA)60 were analyzed using both our method and the conventional method. The histograms of the dwell time were fitted by an exponential function, as shown in Figure 6A,B. The exponential decay of the conventional method gave a dwell time of 0.33 ms, which was much larger than the dwell time of the DBC method (0.13 ms). This significant difference in dwell times is ascribed primarily to blockage overcoverage resulting from use of the conventional method. The current histograms of poly(dA)60 were divided into two populations: PI and PII (Figure 6C,D, respectively). The assignments of the current populations have previously been reported as the translocation blockages (PII) of the ssDNA and the ssDNA collision with the vestibule (PI).41,47,48 The distributions acquired using the integration method resulted in PI at 33.4 pA and PII at 77.5 pA. Meanwhile, the conventional method led to the determination that the two populations peaked at 23.7 pA (PI) and 76.7 pA (PII). Our method showed that 31.5% of the blockages fall into the PI population, whereas the conventional method suggested that only 18.5% (PI) of poly(dA)60 translocated through αhemolysin. These two different probabilities of translocation demonstrate that the recovery of the attenuated blockages is vital for studying the single-molecule behavior of biomolecules via nanopore techniques. Furthermore, the presented method has been applied to analyze the nanopore data of β-amyloid 42 (Figure S7, Supporting Information). The results confirmed that our data process provided a more accurate and stable method for evaluating the dwell time and current amplitude from each blockage.
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ASSOCIATED CONTENT
S Supporting Information *
Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions
Z.G., Y.-L.Y., and Y.-T.L. designed the experiments, Z.G., Y.L.Y., and C.C. performed the experiments and analyzed the data, and Z.G., Y.-L.Y., P.H., and Y.-T.L. wrote the paper. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge funding from the National Natural Science Foundation of China (Grants 21327807 and 21421004). Y.T.L. is grateful for funds from the National Science Fund for Distinguished Young Scholars of China (Grant 21125522), Shanghai Science and Technology Committee (Grant 12JC1403500), and Eastern Scholar at Shanghai Institutions of Higher Learning.
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CONCLUSIONS We developed a robust data process that includes blockage location as well as evaluations of both the dwell time and the current amplitude to provide an accurate analysis of rapid blockages in nanopore experiments. First, a local threshold method and tracking-back routine were used to approximately detect blockages. Second, the dwell time was calibrated using the DBC method, which largely eliminates the effect of random noise. The relative error of the DBC method was 71% less than that of the conventional method for blockages with a nominal dwell time of 0.05 ms. To recover the current amplitudes of blockages, we developed a novel integration method that enhanced the feff c from 2.78 to 5.74 kHz for current amplitudes with dwell times of less than 2Tr. Because the integrated current was hardly affected by the cutoff frequency of the filter, the use of the integrated current for characterization of the nanopore blockages is a promising approach. The implementation of this data process requires only simple basic mathematical operations; thus, the data process could be popularized to a small dedicated microcomputer- or microprocessor-based realtime system. Combining our methods with classical methods such as the algorithm of the hidden Markov model (HMM)49 and support vector machines (SVMs),50 the developed data process could enhance understanding of experimental nanopore results and provide a clear picture of single-molecule behavior. F
DOI: 10.1021/ac5028758 Anal. Chem. XXXX, XXX, XXX−XXX
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DOI: 10.1021/ac5028758 Anal. Chem. XXXX, XXX, XXX−XXX
