Machine learning assisted single-molecule sensing of per- and polyfluoroalkyl carboxylic acids: Quantification without standards

Machine learning assisted single-molecule sensing of per- and polyfluoroalkyl carboxylic acids: Quantification without standards | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Machine learning assisted single-molecule sensing of per- and polyfluoroalkyl carboxylic acids: Quantification without standards Kaipei Qiu, Jiaqi Zuo, Hong-Shuang Li, Wen Tang, Xian Zhao, Meng-Yuan Cheng, and 5 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4603074/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 Mar, 2026 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Per- and polyfluoroalkyl carboxylic acids (PFCA) are of great concern due to their ubiquitous presence in the environment. Despite a severe shortage of authentic standards, compared to the rapid increase of possible structures identified, it remains difficult to quantify a mixture of PFCA without references. Herein, a standard-free single-molecule electrochemical sensing method was developed for the first time by establishing a linear correlation between current blockades and the volumes of PFCA simulated by molecular dynamics. A nearly 100% accuracy was realized for the simultaneous determination of 13 pristine or H- / Cl-substituted PFCA, using frequency-modulated multi-feature classification. Shortlisting the 21 high-priority features reduced the required number of training data by 7.6 folds, and almost 80% quantification reliability was maintained even with interference of 100 times concentration. Moreover, the detection limit of trifluoroacetic acid (an ultrashort-chain PFCA) went down to 57 ng·L -1 , comparable to the state-of-the-art performance. Earth and environmental sciences/Environmental sciences/Environmental chemistry/Environmental monitoring Physical sciences/Chemistry/Analytical chemistry/Sensors Physical sciences/Nanoscience and technology/Nanoscale devices/Nanopores Figures Figure 1 Figure 2 Figure 3 Introduction Per- and polyfluoroalkyl substances (PFAS) contamination has become a global concern due to their widespread environmental occurrenceand elevated human exposure 1 . It is a complex chemical class, covering almost all the compounds with at least a perfluorinated methyl (-CF 3 ) or methylene (-CF 2 -) functional group, according to the revised definition by the Organisation for Economic Cooperation and Development (OECD) 2 . Till now, over 14,000 chemicals have been registered in the U.S. EPA PFAS structure list 3 . Growing evidence indicates that the abundant tiny structural variation in PFAS can affect the respective partitioning 4 , transferring 5 , elimination 6 , transformation 7 , bioaccumulation 8 behaviours, and may pose distinct health risk 9 . Hence, it is imperative to determine the concentration of multiple structurally similar PFAS species in various environmental matrices simultaneously. The current analytical methods for PFAS, however, are hard to achieve precise quantification, high resolution and wide coverage concurrently. While great advances have been made over the past decades to enhance the resolution and detection limit of high-performance liquid chromatography-tandem mass spectrometry (HPLC-MS/MS) 10,11 , as well as gas chromatography-mass spectrometry (GC-MS) 12,13 , such quantitative analysis relied on the use of reference standard, of which the number of commercially available samples 14 were just over 120, less than 1% of the total PFAS. In contrast, progress in high-resolution mass spectrometry (HRMS) 15,16 opens the possibility to comprehensive, nontargeted screening of unknown PFAS, especially when coupled with ion mobility spectrometry (IMS) 17,18 . Nevertheless, the structure identified by HRMS is tentative 19 , and the concentration can, at best, be semi-quantified. So far, quantification of PFAS without standards remains challenging. Herein, a nanopore based single-molecule electrochemical sensor is proposed as an emerging technology to bridge the gap between the urgent demand for quantitative PFAS monitoring and the severe shortage of authentic standards. By measuring the change of ion movement through nanopore, single-molecule sensor (SMS) can identify and quantify a specific analyte with the characteristics and frequency of the resulting current blockade 20 . A linear correlation was established in this work between the magnitude of ionic current and the volume of PFAS simulated by molecular dynamics (MD), and thus the current response of unknown PFAS could be accurately predicted, avoiding the need for standards. Previous studies have demonstrated positive correlations between the magnitude of current blockade and the volume 21 or mass 22-26 of peptides 21-24 and proteins 25,26 using a variety of protein pores, e.g., α-hemolysin 22 , aerolysin 21 , FraC 23 , ClyA 25 , CytK 24 or YaxAB 26 , but a strict linear relationship ( R 2 = 0.9998) was realized for the first time, as far as the authors were aware, and the predicted blockade values were almost identical to experimental measurements. More importantly, a custom machine learning algorithm, based on the frequency-modulated multi-dimensional feature extraction, was developed to enhance the structural resolution of SMS, reaching an overall accuracy of 99.9% for a total of 13 per- and polyfluoroalkyl carboxylic acids (PFCA). Further optimisation of feature combination, reducing it from 43 to 21 dimensions, required only 13% of the training set for 99% accuracy. As a result, even under an interference of 100 times concentration, nanopore SMS was able to maintain 78% quantification reliability, over an order of magnitude better than ensemble analysis. Besides, a wide, interference-free linear-response range of 0.5 nM to 100 μM was achieved for trifluoroacetic acid, corresponding to the detection limit of 57 ng·L -1 , which was comparable to the state-of-the-art performance of UPLC-MS/MS 27 or GC 28 for this ultra-short PFCA. Establishment of a linear volume-current relationship using perfluoroalkyl carboxylic acids Building a structure-activity relationship was the prerequisite towards the development of standard-free quantification methods, and thus a linear correlation was established in the first place between the volume of PFCA molecules and the magnitude of current blockade measured by nanopore SMS. Despite many factors were proposed to influence the translocation induced current response, it was possible to compile them into two dominant factors, i.e., steric exclusion, counterion enhancement, or a combination of those two 29 . As for steric exclusion, the effective volume of nanopore for signal transduction could change dynamically, indicating that the residence position of analyte in nanopore was crucial when sensing small molecules 30 . Therefore, polycationic peptide probes were employed in this study to control the location of tethered PFCA in nanopore, while concentrated electrolytes were adopted to reduce the contribution of surface charge, so that the magnitude of current blockade was mainly determined by steric exclusion. More specifically, eight linear perfluoroalkyl carboxylic acids (C2 to C9) were chosen as typical PFCA to form the structure-current relation, Fig. 1a. They were connected to the N-terminal of an oligo-arginine leader (PFCA-R 6 ) and measured by the wild-type aerolysin (WT AeL) in 4 M KCl solution, Fig. 1b. It was found previously that WT AeL formed positive electrostatic barriers on both of its trans exit and cis entry under negative applied voltages 36 , and so the polycationic -R 6 probe might be able to drive the non-ionic PFCA targets to the identical position within the AeL nanopore. The typical current traces of C2-C9 PFCA-R 6 at -50 mV were shown in Fig. 1c, as well as the R 6 probe (C0). It was clear that both the magnitude of current blockade and dwell time increased with the length of PFCA. Histograms of the current blockade for C0 and C2 to C9 were given in Supplementary Fig. 1. The resulting magnitude of current blockade for C2-C9 PFCA-R 6 complexes exhibited a strong linear correlation ( R 2 = 0.9998) with their molecular volume (shown as shallow squares in Fig. 1d). The measured differences between the blockade of C2- and C9-R 6 was 11.8%, corresponding to an increase of 1.68% per -CF 2 - (ca. 73.5 Å 3 ) or a slope of 0.023%·Å -3 for this straight line. The effective transduction volume of 4.82 nm 3 , estimated at the blockade of 100%, was identical to the inner pore volume comprised between the A224 and S236 residues of WT AeL (4.82 nm 3 ), supporting the use of R 6 probe to direct the movement of PFCA targets. A total of 61 individual measurements (at least three for each sample) were conducted to reduce experimental errors, using perfluorohexanoic acid (C6) as an internal standard for calibration 31 . The average of error between different measurements was as low as 0.022%, one order of magnitude smaller than the overall standard deviation (0.198%) for the histogram of current blockade, confirming the reliability of our approach. The hydrodynamic volume of PFCA-R 6 was calculated via all-atom molecular dynamics simulations using GROMACS. More details of the simulation process were summarized in the “Methods” section, and the obtained raw data of volumes for C0 and C2 to C9 were given in Supplementary Figs. 2 and 3. Accurate prediction of current response of H- / Cl-substituted polyfluoroalkyl carboxylic acids Following the establishment of a linear correlation between the volume of perfluoroalkyl carboxylic acids and their magnitude of current blockade, the next step was to examine its prediction accuracy for other polyfluoroalkyl carboxylic acids. Among all the 622 carboxylic PFAS structures that were identified previously (CAS numbers available) 5 , 49% of them contained at least one C-H functional group while 5.7% had one or more C-Cl group. Therefore, five typical H- or Cl-substituted analytes, either terminal or internal, were examined in this study, including 3H-tetrafluoropropionic acid (3H), 5H-octafluoropentanoic acid (5H), 7H-dodecafluoroheptanoic acid (7H), 3Cl-tetrafluoropropionic acid (3Cl), and 3:3 fluorotelomer carboxylic acid (FTA), which were increasingly discovered in the wastewater from fluorochemical industry as well as the surrounding surface water 32-34 . Based on the MD simulated molecular volume, the predicted current blockades of H- or Cl-PFCA were in perfect accordance with experimental measurements, Fig. 1d and insert, with negligible deviation (0.022%) close to the observational errors, which clearly demonstrated the capability of using nanopore SMS for standard-free identification of PFAS. The current trace, histogram of blockade, and the simulated molecular volume of H- or Cl-PFCA were provide in Supplementary Figs. 4 and 5. Factors that affected the standard-free prediction and single-molecule identification of PFCA To further explore the origin of the observed linear correlation, different peptide structures (R 6 K-, R 5 K-, -R 7 and -R 6 ) were compared to analyse the role of probe length and orientation of connection. Perfluoropentanoic (C5), perfluorohexanoic (C6) and perfluoroheptanoic acid (C7) were linked to the lysine side chain of R 6 K- or R 5 K- probes, and to the N-terminals of -R 7 or -R 6 . Errors of the actual blockade from prediction was much smaller for C6-R 6 or -R 7 than R 6 K- or R 5 K-C6 (Fig. 1e), probably due to the narrow lumen of WT AeL (diameter between 1-1.4 nm) 35 . Meanwhile, the slope of the linear fit for -R 6 probe, i.e., signal sensitivity to the change of analyte volume, was 70% higher than -R 7 (Fig. 1e), suggesting the enlarged transduction volume of the latter. Although showing little improvement in linearity ( R 2 = 0.9995-0.9999 for the linear fit of C5-, C6- and C7-R 6 in 2-4 M KCl, (Supplementary Fig. 6), the elevated salt concentration reduced the standard deviation of blockade from 0.47% for 2 M to 0.165% for 4 M, Fig. 1f, which could triple the resolution of identification. One possible reason was the prolonged dwell time of PFCA in WT AeL, caused by the higher cis-to-trans driving force in 4 M KCl (or the lower trans-to-cis electroosmotic force) 20 . Nevertheless, it was noted that the sum of the three sigma of poly- and the adjacent per-fluoroalkyl carboxylic acids (highlighted as the error bar in Fig. 1d) were still greater than the difference between their blockade, indicating that the use of current blockade alone was unlikely to fully resolve the total 13 PFCA. Frequency-modulated multi-dimensional feature extraction for 100% classification accuracy An inherent advantage of SMS over ensemble methods was the ability to record multi-dimensional features of the signal generated by an individual molecule 36 . The use of five or more signal features was demonstrated recently as an effective approach to distinguish structurally similar compounds, e.g., achieving 92.4%-99.9% accuracy for the determination of saccharides 37 , riboses 38 , alditols 39 or benzenediols 40 . Herein, frequency modulation (using five low-pass filters of 2000, 800, 500, 200 or 100 Hz, as well as the wavelet transform) was applied to extend the eight common features of single-molecule signals, i.e., the magnitude (Δ I / I 0 ), duration ( τ on ), standard deviation ( I σ ), peak-to-peak ( I pp ) of current blockade, and the peak ( H peak ), full width at half maximum ( H FWHM ), skewness ( H skew ), kurtosis ( H kurt ) of the all-points histograms of current blockade, to a total number of 43 ( τ on remained constant at all frequencies), Fig. 2a. All the feature inputs were normalized by an internal standard (C6, C5 or C3) and averaged by at least three parallel measurements to minimize experimental errors. The resulting 43 features of 14 analytes were all fitted with a Gaussian distribution (Supplementary Figs. 7 to 20). Interestingly, despite the closely related physical meaning of Δ I / I 0 and H peak , or I σ , I pp and H FWHM , the resolving power of these features and their frequency dependent behaviours differed remarkably (Supplementary Figs. 21 to 29), implying the possibility to integrate multi-dimensional features for enhanced resolution. In fact, the combination of eight-dimensional feature (extracted from the raw data at 2000 Hz) increased the identification accuracy from 89.1% (using Δ I / I 0 only) to 96.7% for the 11 short-chain PFCA (excluding C8 or C9), and the further incorporation of frequency modulation (using the total 43 features) pushed it to 99.9%, Fig. 2b. A total of 2400 sets of data were collected for each analyte (2000 for training/validation and 400 for test). In total, 31 classifiers were evaluated, among which the Bagged trees model showed the highest identification accuracy, Supplementary Table 1. All the accuracies were calculated based on five or more repetitions of random holdout test sets, and a 10-fold cross-validation was applied for training. It was worth noting that the order of feature addition, from two to eight dimensions, for achieving the highest identification accuracy (left part of Fig. 2b), was distinct from the rank of their own one-dimensional accuracy (Supplementary Fig. 30), which suggested the significance of correlation and complementarity between features. The enhancement by feature addition reached a plateau when the number of dimensions exceeded four, meaning that certain features were less relevant or easier to replace in the classification of PFCA. Once frequency modulation was included, the identification accuracy quickly jumped over 99% (right part of Fig. 2b). The confusion matrix of all 13 PFCA plus the R 6 probe (also with an overall accuracy of 99.9%) showed that the biggest errors came from the misclassification of FTA with C5 and C6, Fig. 2c, and strikingly, small but non-negligible false identifications (0.01-0.04%) were constantly observed for the pairs of PFCA that could be resolved completely using blockade only (Supplementary Fig. 22). Such phenomena stressed the necessity to reduce model complexity or the number of features. Shortlisting high-priority features to minimise the size of training set for precise determination To optimise the combination of model input, the change of maximal validation accuracy against the number of features was examined, under various sizes of training set for C5, C6 and FTA, i.e., 2000, 200 or 20 signals for each PFCA. A similar trend was discovered in all three curves (Fig. 2d): when more features were included, the accuracy increased initially, then reached a plateau, and dropped slightly in the end, indicating that the optimal number of features should be neither too small (e.g., to avoid the deviation in training set) nor too large (e.g., to reduce the model complexity). The height, length and position of the plateau became lower, shorter, and left-shifted for smaller set, which decreased from 99.97% for 2000 signals with 28±10 features, to 98.40% for 20 signals with 21±5 features. In the meantime, the priority of features was also affected by training size: when only 20 signals were used, a general order of importance 2000 Hz < wavelet < 100 Hz < 200 Hz < 500 Hz < 800 Hz was followed; but in the case of 200 or 2000 signals, other features such as kurtosis at 200 and 500 Hz stood out, while all the filtered blockades (either wavelet or 100-800 Hz) were no longer critical, Supplementary Table 2-4. Taking into account of their rank in all three scenarios, a total of 21 features were shortlisted, Fig 2e, which was able to decrease the amount of data for training by 7.6 folds, compared to the full 43-feature model, and to increase the maximal identification accuracy from 99.58% to 99.92%. Maintaining nearly 80% quantification reliability with interference of 100 times concentration The aforementioned few-shot learning mode of nanopore SMS facilitated the accurate quantification of trace targets in the presence of structurally similar interferents with much higher concentrations, which was often difficult for ensemble measurements. For instance, with regard to the determination of FTA from more concentrated C5 and C6, the pre-developed 21-feature model was able to maintain over 78% accuracy with interference of 100 times concentration, Fig. 3a, and a substantial 44% was still detectable even under 1000 times. Such performance was at least one order of magnitude better than the multi-peak fit using the 2000 Hz blockade only, which was the best one-dimensional feature in this study to mimic ensemble analysis, showing an accuracy of 69% with 10 times interference and a rapid drop to zero at 20 times. In the meantime, the quantification reliability of the shortlisted 21-feature model was consistently higher than the full 43-feature counterpart as well, in accordance with the above analysis on the influence of feature number. Interference-free quantification of trifluoroacetic acid towards a detection limit of 57 ng · L -1 Trifluoroacetic acid (C2) was the simplest form of PFCA, with a much higher environmental level than other PFCA due to its more diverse sources 28 . Recent evidence suggested that the rising rate of C2 was considerable, and its potential adverse health effects could be higher than expected 41 . The quantitative analysis of C2, however, was arduous, and the limit of detection (LOD) was among 10-500 ng·L -1 , Supplementary Table 5 27,28,42-46 . Herein, linking the logarithm of C2 concentration and the logarithm of interval time measured at -50 mV and 20℃, a linear response range was established between 50 nM and 100 μM C2, insert of Fig. 3b. Interference such as C4, C5, C6 or tap water caused a tiny deviation less than 1%. Further adoption of an elevated voltage of -80 mV and a temperature of 30℃ pushed the LOD of C2 down to 0.5 nM or 57 ng·L -1 , Fig. 3b, comparable to the state-of-the-art 27,28 . Discussion This work realized for the first time standard-free quantification of PFCA through the combination of single-molecule sensing with multi-feature classification. The structure of polycationic probe was fine-tuned so that various PFCA analytes could be directed to the identical residence position within the WT AeL pore, enabling the establishment of a linear volume-blockade relationship. It was noted that difference between the current blockade of C2 and C8 was only 9.662%, but at least 452 PFCA 3 (with CAS available) had been identified in this range. Hence, to fully resolve all the PFCA above, the standard deviation of blockade has to be smaller than 0.00356% ( R = 1.5) 20 , which however was around 0.2% at best for WT AeL. It was thus essential to make the most of other features of single-molecule signals. Though the frequency modulated 43-feature model reached an overall accuracy of 99.58% for FTA/C5/C6, the hardest-to-distinguish combination of PFCAs in this study, when the size of training set was 2000 for each analyte, this value quickly dropped to 93.5% if only 20 signals were sampled. The shortlisted 21-feature model, according to the rank of importance, reduced the required amount of training data by 7.6 folds, enabling accurate quantification of trace targets at high-concentration interference. This was particularly crucial, indicating that a total of 20 signals recorded in 10-minute response time (or a capture rate of 1/30 Hz) was sufficient for precise PFCA determination. Future studies towards the measurements of all the 338 PFCA isomers by SMS would require the rationale engineering of nanopore interface in the context of multiple feature classification. Methods Reagents and chemicals. Potassium chloride (KCl, ≥99.9%), tris(hydroxymethyl)aminomethane (Tris, 99%), ethylenediaminetetraacetic acid (EDTA, ≥99.0%), and octane (≥99%) were purchased from Titan Scientific (Shanghai, China). The electrolyte adopted in this detection system was the aqueous solution of 4 M KCl, 10 mM Tris, and 1 mM EDTA. 1,2-diphytanoyl-sn-glycero-3-phosphocholine (DPhPC, powder, ≥99%) was purchased from Avanti Polar Lipids (Shanghai, China). DPhPC was dissolved in octane and sealed dryly at -20℃. Proaerolysin was purchased from GenScript Biotech (Nanjing, China), and trypsin agarose (25UN) was purchased from Sigma-Aldrich (Shanghai, China). Conjugates of perfluorocarboxylic acids and peptide leaders were produced by ChinaPeptides (Suzhou, China). Single-molecule sensing of perfluorocarboxylic acids. Proaerolysin was activated with immobilized trypsin at 4℃ for 10 hours to form monomeric aerolysin, which were involved in the oligomerization for aerolysin nanopores. After activation, proaerolysin was separated from trypsin at 10000 RPM and stored at -20℃ for further use. The above electrolyte was added into the detection chamber and the temperature was set as 20℃ constantly, except other stated. The DPhPC lipid bilayer membrane supporting the nanopore was formed across the 100 μm microcavities of MECA 4 Recording Chips (Nanion Technologies, Germany). Activated aerolysin was added into the cis chamber and formed a single nanopore on the DPhPC lipid bilayer membrane under the applied bias of +200 mV. The cis side of the detection chamber was seen as virtual ground whose potential was 0 mV and the voltage was applied on the trans side. If a single aerolysin nanopore was formed, open pore current would go to -100 pA as the applied voltage was set as -50 mV. PFCA-R 6 conjugates were added into the cis chamber and translocated to the trans side under negative voltages. Sampling rate and bandwidth were set as 20 and 10 kHz, respectively. Data acquisition and analysis. Electrical signals were recorded with a patch clamp amplifier (Orbit mini). Frequency-modulated signals were processed in MATLAB 2021b, via wavelet denoising or lowpass filter at 100, 200, 500 and 800 Hz. Machine learning models were trained, validated and predicted in MATLAB as well. Features of raw and frequency-modulated signals were extracted in Python 3.11, based on the pre-identified events from Clampfit 10.4. Feature normalization was done in Python. Graphs were drawn in OriginLab, MATLAB or Python. Molecular modelling and simulation. Three-dimensional structures of the R 6 probe and PFCA-R conjugates were generated in ChemBio3D. Energy minimization of these 3D structures were done with MM2 method and saved as pdb files. Structure topology files were generated with Ligand Reader & Modeler on CHARMM-GUI. Molecules were simulated and their volumes were calculated in an aqueous solution system. The aqueous solution system, including electrolyte, electric field, temperature and pressure, was modelled and stabilized in advance. A 7*7*7 nm 3 sized water box was built through Solution Builder on CHARMM-GUI, with a KCl concentration of 4 M and temperature at 293 K. To eliminate the redundant steric hindrance and minimize the energy of this water box, 5000 iterations were done with the steepest descent algorithm. A 125 ps long equilibrium simulation was carried out to maintain constant temperature and reasonable distribution of total compounds. Based on this finished product, a 5 ns long simulation with a time step of 2 fs was carried out using Nose-Hoover method for temperature control and Parrinello-Rahman method for pressure control. Electrostatic interaction was calculated with Particle mesh Ewald (PME) method. Cut-off radius referring to calculations of Coulomb interaction, electrostatic interaction and Van der Waals interaction was set as 12 Å. Calculations of hydrogen bonds were constrained with LINCS algorithm. The last frame of the simulation was adopted as the water box for later molecular dynamic simulations. Afterwards, each structure under simulated was inserted into this water box with gmx insert-molecule, replacing water molecules, potassium ions and chloride ions randomly. The whole system was controlled at 293 K with V-rescale method of temperature control. After 10000 iterations with the steepest descent algorithm, energy minimization of this system was achieved. As a final step, there was a 1 ns long NPT equilibrium. Molecular volumes of all kinds of conjugates were calculated in a 50 ns long simulation, with time step of 2 fs. In purpose of reducing the impact of R 6 leader and highlighting real volume differences between different types of PFCA, X-R conjugates (where X represented different types of targets) were designed and simulated at first, putting the volume of X at a dominant position while taking the junction between the target and the leader into consideration. The volume difference between C4-R and C4-R 6 was set as an internal standard to speculate all of the molecular volumes of X-R 6 . Declarations Data Availability Source data are provided with the paper. Other data are available upon request. Code Availability The custom MATLAB and Python scripts are available at https://github.com/DEWMEME. Acknowledgements This study was supported by the National Key R&D Program of China (2023YFC3008803), the National Natural Science Foundation of China (21972041 and 22006037), the Natural Science Foundation of Shanghai Municipality (23ZR1416300), and the Fundamental Research Funds for the Central Universities. Competing Interests The authors declare no competing interests. Additional Information Supplementary information. The online version contains supplementary material available at. References Evich, M. G. et al. Per- and polyfluoroalkyl substances in the environment. Science 375 , eabg9065 (2022). OECD. Reconciling terminology of the universe of per- and polyfluoroalkyl substances: Recommendations and practical guidance. Series on risk management No. 61 (2021). (accessed 14 th May 2024). https://one.oecd.org/document/ENV/CBC/MONO(2021)25/En/pdf. US EPA. PFAS structures in DSSTox (update August 2022). https://comptox.epa.gov/dashboard/chemical-lists/PFASSTRUCTV5. Liu, D. et al. 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Nanopore identification of alditol epimers and their application in rapid analysis of alditol-containing drinks and healthcare products. J. Am. Chem. Soc. 144 , 13717-13728 (2022). Hu, C. et al. Single-molecule sensing of acidic catecholamine metabolites using a programmable nanopore. Chem. Eur. J. 28 , e202201033 (2022). Scheringer, M., Cousins, I. T., & Goldenman, G. Is a seismic shift in the landscape of PFAS uses occurring? Environ. Sci. Technol. 58 , 6843-6845 (2024). Austin, C. et al. Hydrothermal destruction and defluorination of trifluoroacetic acid (TFA). Environ. Sci. Technol. 58 , 8076-8085 (2024). Zheng, G., Eick, S. M., & Salamova, A. Elevated levels of ultrashort-and short-chain perfluoroalkyl acids in US homes and people. Environ. Sci. Technol. 57 , 15782-15793 (2023). Sadia, M. et al. Occurrence, fate, and related health risks of PFAS in raw and produced drinking water. Environ. Sci. Technol. 57 , 3062-3074 (2023). Zhao, M. et al. Nontarget identification of novel per-and polyfluoroalkyl substances (PFAS) in soils from an oil refinery in southwestern China: a combined approach with TOP assay. Environ. Sci. Technol. 57 , 20194-20205 (2023). Cahill. T. M. Increases in trifluoroacetate concentrations in surface waters over two decades. Environ. Sci. Technol. 56 , 9428-9434 (2022). Additional Declarations There is NO Competing Interest. Supplementary Files MLreportingsummaryLHS.pdf Machine Learning Reporting Summary nrsoftwarepolicyLHS.pdf Software Policy Checklist SupplementaryInformation2024.06.28.pdf Cite Share Download PDF Status: Published Journal Publication published 13 Mar, 2026 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4603074","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":324524207,"identity":"dc08ef49-b915-478a-a9c6-68b32475e72b","order_by":0,"name":"Kaipei Qiu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYBACCQbGBgYGAwYeBnYgzWBgQYoWngMgLRLEaIGzElD5OIFk++G2Bx8KrGUMbj6/uuFHgQQDf3t3Al4t0jyJ7YYzDNJ5DG7nlN3sATpM4szZDXi1yDEktknzGBwGaUm7wQPUYiCRS0AL/8M26T8gLTfPpN38Q4wWaQmgLQwgLTfYj90myhbJGQ/bDXuAfpE8k8N2W8ZAgoegXyTOpz978OOPtT3f8ePPbr75YyPH396LXwsQsAExMxDzGIB4PISUI2thf0CM6lEwCkbBKBiBAABbK0UOe0/NAwAAAABJRU5ErkJggg==","orcid":"","institution":"East China University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Kaipei","middleName":"","lastName":"Qiu","suffix":""},{"id":324524208,"identity":"18293083-8058-4e65-ba07-026f4558ecd3","order_by":1,"name":"Jiaqi Zuo","email":"","orcid":"https://orcid.org/0000-0001-9170-9688","institution":"East China University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Jiaqi","middleName":"","lastName":"Zuo","suffix":""},{"id":324524209,"identity":"63342ec5-e1fd-4564-83d3-9f4695e9b8a0","order_by":2,"name":"Hong-Shuang Li","email":"","orcid":"https://orcid.org/0009-0001-6920-5106","institution":"East China University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Hong-Shuang","middleName":"","lastName":"Li","suffix":""},{"id":324524210,"identity":"c2778641-4ddd-451c-bd24-1d16385a32f9","order_by":3,"name":"Wen Tang","email":"","orcid":"","institution":"East China University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Wen","middleName":"","lastName":"Tang","suffix":""},{"id":324524211,"identity":"1c6f2e41-3599-4e52-ac56-1ad3d57c5596","order_by":4,"name":"Xian Zhao","email":"","orcid":"","institution":"East China University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Xian","middleName":"","lastName":"Zhao","suffix":""},{"id":324524212,"identity":"0d5cbc74-b546-4564-bc64-ed16e9b6f837","order_by":5,"name":"Meng-Yuan Cheng","email":"","orcid":"","institution":"East China University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Meng-Yuan","middleName":"","lastName":"Cheng","suffix":""},{"id":324524213,"identity":"8455949e-c257-4fa0-a074-11e0cf1f97a6","order_by":6,"name":"Zekai Yang","email":"","orcid":"","institution":"East China University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Zekai","middleName":"","lastName":"Yang","suffix":""},{"id":324524214,"identity":"2ee4257e-0b5d-4d17-9cb9-70567b0c70c3","order_by":7,"name":"Siyu Tian","email":"","orcid":"","institution":"East China University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Siyu","middleName":"","lastName":"Tian","suffix":""},{"id":324524215,"identity":"645095b0-bfe8-45d3-baa2-f506489e7408","order_by":8,"name":"Pufeng Li","email":"","orcid":"","institution":"East China University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Pufeng","middleName":"","lastName":"Li","suffix":""},{"id":324524216,"identity":"1cfed814-3598-49cb-a2b3-de733c785c44","order_by":9,"name":"Xueying Xie","email":"","orcid":"","institution":"East China University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Xueying","middleName":"","lastName":"Xie","suffix":""},{"id":324524217,"identity":"61f070d4-802d-4f64-96fa-cdc9fa3f64cf","order_by":10,"name":"Dan Luo","email":"","orcid":"","institution":"East China University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Dan","middleName":"","lastName":"Luo","suffix":""}],"badges":[],"createdAt":"2024-06-19 04:20:30","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4603074/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4603074/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-026-70718-3","type":"published","date":"2026-03-13T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":60278870,"identity":"2e305824-cf86-4235-a305-bf83d0d427f7","added_by":"auto","created_at":"2024-07-15 05:59:23","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":85507,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEstablishment and application of the linear volume-current relation for single-molecule sensing of PFCA.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e, The eight per-fluoroalkyl carboxylic acids used in this study to form the linear volume-current correlation (blue box on the left), and the five H- or Cl-substituted poly-fluoroalkyl carboxylic acids adopted to validate its correctness (brown box on the right). \u003cstrong\u003eb\u003c/strong\u003e, The PFCA molecules were tethered to four kinds of polycationic probes, -R\u003csub\u003e6\u003c/sub\u003e, -R\u003csub\u003e7\u003c/sub\u003e, R\u003csub\u003e5\u003c/sub\u003eK- and R\u003csub\u003e6\u003c/sub\u003eK-, and were measured by WT AeL nanopore at -50 mV in 4 M KCl. \u003cstrong\u003ec\u003c/strong\u003e, Typical current traces measured in the single-molecule sensing of C2- to C9-R\u003csub\u003e6\u003c/sub\u003e, as well as the R\u003csub\u003e6\u003c/sub\u003e probe (C0). \u003cstrong\u003ed\u003c/strong\u003e, The established linear relationship between the hydrodynamic volume of C0/C2-C9 PFCA-R\u003csub\u003e6\u003c/sub\u003e (blue squares and straight line) and the magnitude of their current blockade. The volume of PFCA was calculated via MD simulation using GROMACS (Supplementary Figs. 2 and 3). The experimentally measured current blockade of 3H, 5H, 7H, 3Cl, and FTA was shown as brown circles, which was almost identical with the prediction from volume-current correlation (insert in Fig. 1d). The error bars on blue squares and brown circles were the sum of three times standard deviations (NOT one) obtained from the histogram of their current blockade. \u003cstrong\u003ee\u003c/strong\u003e, Prediction errors for the current blockade of C6 using R\u003csub\u003e6\u003c/sub\u003eK-, R\u003csub\u003e5\u003c/sub\u003eK-, -R\u003csub\u003e7\u003c/sub\u003e, or -R\u003csub\u003e6\u003c/sub\u003e probe (blue bars), and the slope of their volume-current response (red bars). \u003cstrong\u003ef\u003c/strong\u003e, The average standard deviation for the histograms of current blockade of C5-C7 PFCA-R\u003csub\u003e6\u003c/sub\u003e measured in 2, 3, and 4 M KCl solutions.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4603074/v1/c1ced05751242ddda0a35cae.png"},{"id":60278865,"identity":"77962ad9-677f-468a-bb53-ed81cc7fb7bf","added_by":"auto","created_at":"2024-07-15 05:59:23","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":99591,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eIdentification performance for standard-free single-molecule sensing of PFCA. a\u003c/strong\u003e, The schematic illustration of frequency-modulated multi-feature extraction approach. The eight kinds of feature adopted were the magnitude (Δ\u003cem\u003eI\u003c/em\u003e/\u003cem\u003eI\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e), duration (\u003cem\u003eτ\u003c/em\u003e\u003csub\u003eon\u003c/sub\u003e), standard deviation (\u003cem\u003eI\u003c/em\u003e\u003csub\u003eσ\u003c/sub\u003e), peak-to-peak (\u003cem\u003eI\u003c/em\u003e\u003csub\u003epp\u003c/sub\u003e) of current blockade, and the peak (\u003cem\u003eH\u003c/em\u003e\u003csub\u003epeak\u003c/sub\u003e), full width at half maximum (\u003cem\u003eH\u003c/em\u003e\u003csub\u003eFWHM\u003c/sub\u003e), skewness (\u003cem\u003eH\u003c/em\u003e\u003csub\u003eskew\u003c/sub\u003e), kurtosis (\u003cem\u003eH\u003c/em\u003e\u003csub\u003ekurt\u003c/sub\u003e) of the all-points histograms of current blockade. Frequency modulation included the wavelet denoising and low-pass filters of 100, 200, 500 or 800 Hz, as well as the original 2000 Hz. \u003cstrong\u003eb\u003c/strong\u003e, Identification accuracy of 11 PFCA (C2-C7, 3H, 5H, 7H, 3Cl, and FTA) with various combination of feature. The order of feature addition was based on the rank of their important, i.e., to achieve the highest accuracy at any given dimension. The first eight dimension of feature referred to their values at 2000 Hz, while the subsequent addition was the groups of seven features (except \u003cem\u003eτ\u003c/em\u003e\u003csub\u003eon\u003c/sub\u003e) at different frequency. \u003cstrong\u003ec\u003c/strong\u003e, Confusion matrix for the identification of all 13 PFCA plus the R\u003csub\u003e6\u003c/sub\u003e probe using a bagged decision tree model. For each analyte, 2000 sets of features were used for training and 10-fold cross-validation, and another 400 signals were selected for test. The likelihood of misclassification for the group of FTA/C5/C6 was highlighted in red, and the misidentification that could have been resolved by blockade was labelled in grey. \u003cstrong\u003ed\u003c/strong\u003e, The relationship between the identification accuracy (validation) of FTA/C5/C6 and the number of features adopted, at the training data size of 20, 200 and 2000 for each analyte, respectively. \u003cstrong\u003ee\u003c/strong\u003e, The performance of identification accuracy (validation) of FTA/C5/C6 against the number of training data size using the full 43-feature and the shortlisted 21-feature model. The insert matrix showed the importance of each feature for the identification of FTA/C5/C6. Those ticked features were used in the shortlisted 21-feature model.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4603074/v1/f08e841cd16794ca5f35a8b5.png"},{"id":60278864,"identity":"81b28430-092c-4270-9d15-62c2f4bd87bf","added_by":"auto","created_at":"2024-07-15 05:59:23","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":42905,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eQuantification performance for standard-free single-molecule sensing of PFCA. a\u003c/strong\u003e, The quantification accuracy of FTA in presence of C5/C6 by ensemble analysis (mimicked by the multi-peak fitting using blockade only), the full 43-feature model, and the shortlisted 21-feature one. The concentration ratio of FTA to the C5/C6 interference ranged from 1:1 to 1:1000. \u003cstrong\u003eb\u003c/strong\u003e, The relationship between the logarithm of C2 concentration and the logarithm of its interval time, measured at 30℃ / -80 mV and 20℃ / -50 mV (insert), respectively. A broad linear response range was realized from 57 ng·L\u003csup\u003e-1\u003c/sup\u003e to 11.4 mg·L\u003csup\u003e-1\u003c/sup\u003e, which was almost inference-free in the presence of C4/C5/C6 or real water.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4603074/v1/bbe835347b1edc4c3e1f485d.png"},{"id":108171088,"identity":"c5ed203d-2184-48e7-aebf-ac4346c07694","added_by":"auto","created_at":"2026-04-30 07:07:20","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":530292,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4603074/v1/63d3b61b-ca83-43f3-83a1-b4d10b5db4eb.pdf"},{"id":60278866,"identity":"fe3cca54-bc68-4ff0-a228-764fc0d9b4b0","added_by":"auto","created_at":"2024-07-15 05:59:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":285234,"visible":true,"origin":"","legend":"\u003cp\u003eMachine Learning Reporting Summary\u003c/p\u003e","description":"","filename":"MLreportingsummaryLHS.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4603074/v1/6d3f9811d5fca0d2c87dab4c.pdf"},{"id":60278868,"identity":"31cf5ff5-0185-4a37-a0d0-46565384ce4e","added_by":"auto","created_at":"2024-07-15 05:59:23","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":1317046,"visible":true,"origin":"","legend":"\u003cp\u003eSoftware Policy Checklist\u003c/p\u003e","description":"","filename":"nrsoftwarepolicyLHS.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4603074/v1/1f94bac376e7a3fa2ab6e710.pdf"},{"id":60278867,"identity":"8d526880-4428-49f6-8493-f2ae9b4d06a6","added_by":"auto","created_at":"2024-07-15 05:59:23","extension":"pdf","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":7719064,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"SupplementaryInformation2024.06.28.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4603074/v1/78454d2f0288c4385c4c18eb.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Machine learning assisted single-molecule sensing of per- and polyfluoroalkyl carboxylic acids: Quantification without standards","fulltext":[{"header":"Introduction","content":"\u003cp\u003ePer- and polyfluoroalkyl substances (PFAS) contamination has become a global concern due to their widespread environmental occurrenceand elevated human exposure\u003csup\u003e1\u003c/sup\u003e. It is a complex chemical class, covering almost all the compounds with at least a perfluorinated methyl (-CF\u003csub\u003e3\u003c/sub\u003e) or methylene (-CF\u003csub\u003e2\u003c/sub\u003e-) functional group, according to the revised definition by the Organisation for Economic Cooperation and Development (OECD)\u003csup\u003e2\u003c/sup\u003e. Till now, over 14,000 chemicals have been registered in the U.S. EPA PFAS structure list\u003csup\u003e3\u003c/sup\u003e. Growing evidence indicates that the abundant tiny structural variation in PFAS\u003c/p\u003e\n\u003cp\u003ecan affect the respective partitioning\u003csup\u003e4\u003c/sup\u003e, transferring\u003csup\u003e5\u003c/sup\u003e, elimination\u003csup\u003e6\u003c/sup\u003e, transformation\u003csup\u003e7\u003c/sup\u003e, bioaccumulation\u003csup\u003e8\u003c/sup\u003e behaviours, and may pose distinct health risk\u003csup\u003e9\u003c/sup\u003e. Hence, it is imperative to determine the concentration of multiple structurally similar PFAS species in various environmental matrices simultaneously.\u003c/p\u003e\n\u003cp\u003eThe current analytical methods for PFAS, however, are hard to achieve precise quantification, high resolution and wide coverage concurrently. While great advances have been made over the past decades to enhance the resolution and detection limit of high-performance liquid chromatography-tandem mass spectrometry (HPLC-MS/MS)\u003csup\u003e10,11\u003c/sup\u003e, as well as gas chromatography-mass spectrometry (GC-MS)\u003csup\u003e12,13\u003c/sup\u003e, such quantitative analysis relied on the use of reference standard, of which the number of commercially available samples\u003csup\u003e14\u003c/sup\u003e were just over 120, less than 1% of the total PFAS. In contrast, progress in high-resolution mass spectrometry (HRMS)\u003csup\u003e15,16\u003c/sup\u003e opens the possibility to comprehensive, nontargeted screening of unknown PFAS, especially when coupled with ion mobility spectrometry (IMS)\u003csup\u003e17,18\u003c/sup\u003e. Nevertheless, the structure identified by HRMS is tentative\u003csup\u003e19\u003c/sup\u003e, and the concentration can, at best, be semi-quantified. So far, quantification of PFAS without standards remains challenging.\u003c/p\u003e\n\u003cp\u003eHerein, a nanopore based single-molecule electrochemical sensor is proposed as an emerging technology to bridge the gap between the urgent demand for quantitative PFAS monitoring and the severe shortage of authentic standards. By measuring the change of ion movement through nanopore, single-molecule sensor (SMS) can identify and quantify a specific analyte with the characteristics and frequency of the resulting current blockade\u003csup\u003e20\u003c/sup\u003e. A linear correlation was established in this work between the magnitude of ionic current and the volume of PFAS simulated by molecular dynamics (MD), and thus the current response of unknown PFAS could be accurately predicted, avoiding the need for standards. Previous studies have demonstrated positive correlations between the magnitude of current blockade and the volume\u003csup\u003e21\u0026nbsp;\u003c/sup\u003eor mass\u003csup\u003e22-26\u003c/sup\u003e of peptides\u003csup\u003e21-24\u003c/sup\u003e and proteins\u003csup\u003e25,26\u003c/sup\u003e using a variety of protein pores, e.g., α-hemolysin\u003csup\u003e22\u003c/sup\u003e, aerolysin\u003csup\u003e21\u003c/sup\u003e, FraC\u003csup\u003e23\u003c/sup\u003e, ClyA\u003csup\u003e25\u003c/sup\u003e, CytK\u003csup\u003e24\u003c/sup\u003e or YaxAB\u003csup\u003e26\u003c/sup\u003e, but a strict linear relationship (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e = 0.9998) was realized for the first time, as far as the authors were aware, and the predicted blockade values were almost identical to experimental measurements. More importantly, a custom machine learning algorithm, based on the frequency-modulated multi-dimensional feature extraction, was developed to enhance the structural resolution of SMS, reaching an overall accuracy of 99.9% for a total of 13 per- and polyfluoroalkyl carboxylic acids (PFCA). Further optimisation of feature combination, reducing it from 43 to 21 dimensions, required only 13% of the training set for 99% accuracy. As a result, even under an interference of 100 times concentration, nanopore SMS was able to maintain 78% quantification reliability, over an order of magnitude better than ensemble analysis. Besides, a wide, interference-free linear-response range of 0.5 nM to 100 μM was achieved for trifluoroacetic acid, corresponding to the detection limit of 57 ng·L\u003csup\u003e-1\u003c/sup\u003e, which was comparable to the state-of-the-art performance of UPLC-MS/MS\u003csup\u003e27\u003c/sup\u003e or GC\u003csup\u003e28\u003c/sup\u003e for this ultra-short PFCA.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEstablishment of a linear volume-current relationship using perfluoroalkyl carboxylic acids\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eBuilding a structure-activity relationship was the prerequisite towards the development of standard-free quantification methods, and thus a linear correlation was established in the first place between the volume of PFCA molecules and the magnitude of current blockade measured by nanopore SMS. Despite many factors were proposed to influence the translocation induced current response, it was possible to compile them into two dominant factors, i.e., steric exclusion, counterion enhancement, or a combination of those two\u003csup\u003e29\u003c/sup\u003e. As for steric exclusion, the effective volume of nanopore for signal transduction could change dynamically, indicating that the residence position of analyte in nanopore was crucial when sensing small molecules\u003csup\u003e30\u003c/sup\u003e. Therefore, polycationic peptide probes were employed in this study to control the location of tethered PFCA in nanopore, while concentrated electrolytes were adopted to reduce the contribution of surface charge, so that the magnitude of current blockade was mainly determined by steric exclusion. More specifically, eight linear perfluoroalkyl carboxylic acids (C2 to C9) were chosen as typical PFCA to form the structure-current relation, Fig. 1a. They were connected to the N-terminal of an oligo-arginine leader (PFCA-R\u003csub\u003e6\u003c/sub\u003e) and measured by the wild-type aerolysin (WT AeL) in 4 M KCl solution, Fig. 1b. \u0026nbsp;It was found previously that WT AeL formed positive electrostatic barriers on both of its\u003cem\u003e\u0026nbsp;trans\u003c/em\u003e exit and \u003cem\u003ecis\u003c/em\u003e entry under negative applied voltages\u003csup\u003e36\u003c/sup\u003e, and so the polycationic -R\u003csub\u003e6\u003c/sub\u003e probe might be able to drive the non-ionic PFCA targets to the identical position within the AeL nanopore. The typical current traces of C2-C9 PFCA-R\u003csub\u003e6\u003c/sub\u003e at -50 mV were shown in Fig. 1c, as well as the R\u003csub\u003e6\u003c/sub\u003e probe (C0). It was clear that both the magnitude of current blockade and dwell time increased with the length of PFCA. Histograms of the current blockade for C0 and C2 to C9 were given in Supplementary Fig. 1.\u003c/p\u003e\n\u003cp\u003eThe resulting magnitude of current blockade for C2-C9 PFCA-R\u003csub\u003e6\u003c/sub\u003e complexes exhibited a strong linear correlation (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e = 0.9998) with their molecular volume (shown as shallow squares in Fig. 1d). The measured differences between the blockade of C2- and C9-R\u003csub\u003e6\u003c/sub\u003e was 11.8%, corresponding to an increase of 1.68% per -CF\u003csub\u003e2\u003c/sub\u003e- (ca. 73.5 Å\u003csup\u003e3\u003c/sup\u003e) or a slope of 0.023%·Å\u003csup\u003e-3\u003c/sup\u003e for this straight line. The effective transduction volume of 4.82 nm\u003csup\u003e3\u003c/sup\u003e, estimated at the blockade of 100%, was identical to the inner pore volume comprised between the A224 and S236 residues of WT AeL (4.82 nm\u003csup\u003e3\u003c/sup\u003e), supporting the use of R\u003csub\u003e6\u003c/sub\u003e probe to direct the movement of PFCA targets. A total of 61 individual measurements (at least three for each sample) were conducted to reduce experimental errors, using perfluorohexanoic acid (C6) as an internal standard for calibration\u003csup\u003e31\u003c/sup\u003e. The average of error between different measurements was as low as 0.022%, one order of magnitude smaller than the overall standard deviation (0.198%) for the histogram of current blockade, confirming the reliability of our approach. The hydrodynamic volume of PFCA-R\u003csub\u003e6\u003c/sub\u003e was calculated via all-atom molecular dynamics simulations using GROMACS. More details of the simulation process were summarized in the “Methods” section, and the obtained raw data of volumes for C0 and C2 to C9 were given in Supplementary Figs. 2 and 3.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAccurate prediction of current response of H- / Cl-substituted polyfluoroalkyl carboxylic acids\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFollowing the establishment of a linear correlation between the volume of perfluoroalkyl carboxylic acids and their magnitude of current blockade, the next step was to examine its prediction accuracy for other polyfluoroalkyl carboxylic acids. Among all the 622 carboxylic PFAS structures that were identified previously (CAS numbers available)\u003csup\u003e5\u003c/sup\u003e, 49% of them contained at least one C-H functional group while 5.7% had one or more C-Cl group. Therefore, five typical H- or Cl-substituted analytes, either terminal or internal, were examined in this study, including 3H-tetrafluoropropionic acid (3H), 5H-octafluoropentanoic acid (5H), 7H-dodecafluoroheptanoic acid (7H), 3Cl-tetrafluoropropionic acid (3Cl), and 3:3 fluorotelomer carboxylic acid (FTA), which were increasingly discovered in the wastewater from fluorochemical industry as well as the surrounding surface water\u003csup\u003e32-34\u003c/sup\u003e. Based on the MD simulated molecular volume, the predicted current blockades of H- or Cl-PFCA were in perfect accordance with experimental measurements, Fig. 1d and insert, with negligible deviation (0.022%) close to the observational errors, which clearly demonstrated the capability of using nanopore SMS for standard-free identification of PFAS. The current trace, histogram of blockade, and the simulated molecular volume of H- or Cl-PFCA were provide in Supplementary Figs. 4 and 5.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFactors that affected the standard-free prediction and single-molecule identification of PFCA\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo further explore the origin of the observed linear correlation, different peptide structures (R\u003csub\u003e6\u003c/sub\u003eK-, R\u003csub\u003e5\u003c/sub\u003eK-, -R\u003csub\u003e7\u003c/sub\u003e and -R\u003csub\u003e6\u003c/sub\u003e) were compared to analyse the role of probe length and orientation of connection. Perfluoropentanoic (C5), perfluorohexanoic (C6) and perfluoroheptanoic acid (C7) were linked to the lysine side chain of R\u003csub\u003e6\u003c/sub\u003eK- or R\u003csub\u003e5\u003c/sub\u003eK- probes, and to the N-terminals of -R\u003csub\u003e7\u003c/sub\u003e or -R\u003csub\u003e6\u003c/sub\u003e. Errors of the actual blockade from prediction was much smaller for C6-R\u003csub\u003e6\u003c/sub\u003e or -R\u003csub\u003e7\u003c/sub\u003e than R\u003csub\u003e6\u003c/sub\u003eK- or R\u003csub\u003e5\u003c/sub\u003eK-C6 (Fig. 1e), probably due to the narrow lumen of WT AeL (diameter between 1-1.4 nm)\u003csup\u003e35\u003c/sup\u003e. Meanwhile, the slope of the linear fit for -R\u003csub\u003e6\u003c/sub\u003e probe, i.e., signal sensitivity to the change of analyte volume, was 70% higher than -R\u003csub\u003e7\u003c/sub\u003e (Fig. 1e), suggesting the enlarged transduction volume of the latter. Although showing little improvement in linearity (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e = 0.9995-0.9999 for the linear fit of C5-, C6- and C7-R\u003csub\u003e6\u003c/sub\u003e in 2-4 M KCl, (Supplementary Fig. 6), the elevated salt concentration reduced the standard deviation of blockade from 0.47% for 2 M to\u0026nbsp;0.165% for 4 M, Fig. 1f, which could triple the\u0026nbsp;resolution of identification. One possible reason was the prolonged dwell time of PFCA in WT AeL, caused by the higher cis-to-trans driving force in 4 M KCl (or the lower trans-to-cis electroosmotic force)\u003csup\u003e20\u003c/sup\u003e. Nevertheless, it was noted that the sum of the three sigma of poly- and the adjacent per-fluoroalkyl carboxylic acids (highlighted as the error bar in Fig. 1d) were still greater than the difference between their blockade, indicating that the use of current blockade alone was unlikely to fully resolve the total 13 PFCA. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFrequency-modulated multi-dimensional feature extraction for 100% classification accuracy\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAn inherent advantage of SMS over ensemble methods was the ability to record multi-dimensional features of the signal generated by an individual molecule\u003csup\u003e36\u003c/sup\u003e. The use of five or more signal features was demonstrated recently as an effective approach to distinguish structurally similar compounds, e.g., achieving 92.4%-99.9% accuracy for the determination of saccharides\u003csup\u003e37\u003c/sup\u003e, riboses\u003csup\u003e38\u003c/sup\u003e, alditols\u003csup\u003e39\u003c/sup\u003e or benzenediols\u003csup\u003e40\u003c/sup\u003e. Herein, frequency modulation (using five low-pass filters of 2000, 800, 500, 200 or 100 Hz, as well as the wavelet transform) was applied to extend the eight common features of single-molecule signals, i.e., the magnitude (Δ\u003cem\u003eI\u003c/em\u003e/\u003cem\u003eI\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e), duration (\u003cem\u003eτ\u003c/em\u003e\u003csub\u003eon\u003c/sub\u003e), standard deviation (\u003cem\u003eI\u003c/em\u003e\u003csub\u003eσ\u003c/sub\u003e), peak-to-peak (\u003cem\u003eI\u003c/em\u003e\u003csub\u003epp\u003c/sub\u003e) of current blockade, and the peak (\u003cem\u003eH\u003c/em\u003e\u003csub\u003epeak\u003c/sub\u003e), full width at half maximum (\u003cem\u003eH\u003c/em\u003e\u003csub\u003eFWHM\u003c/sub\u003e), skewness (\u003cem\u003eH\u003c/em\u003e\u003csub\u003eskew\u003c/sub\u003e), kurtosis (\u003cem\u003eH\u003c/em\u003e\u003csub\u003ekurt\u003c/sub\u003e) of the all-points histograms of current blockade, to a total number of 43 (\u003cem\u003eτ\u003c/em\u003e\u003csub\u003eon\u003c/sub\u003e remained constant at all frequencies), Fig. 2a. All the feature inputs were normalized by an internal standard (C6, C5 or C3) and averaged by at least three parallel measurements to minimize experimental errors. The resulting 43 features of 14 analytes were all fitted with a Gaussian distribution (Supplementary Figs. 7 to 20). Interestingly, despite the closely related physical meaning of Δ\u003cem\u003eI\u003c/em\u003e/\u003cem\u003eI\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e and \u003cem\u003eH\u003c/em\u003e\u003csub\u003epeak\u003c/sub\u003e, or \u003cem\u003eI\u003c/em\u003e\u003csub\u003eσ\u003c/sub\u003e, \u003cem\u003eI\u003c/em\u003e\u003csub\u003epp\u003c/sub\u003e and \u003cem\u003eH\u003c/em\u003e\u003csub\u003eFWHM\u003c/sub\u003e, the resolving power of these features and their frequency dependent behaviours differed remarkably (Supplementary Figs. 21 to 29), implying the possibility to integrate multi-dimensional features for enhanced resolution.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn fact, the combination of eight-dimensional feature (extracted from the raw data at 2000 Hz) increased the identification accuracy from 89.1% (using Δ\u003cem\u003eI\u003c/em\u003e/\u003cem\u003eI\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e only) to 96.7% for the 11 short-chain PFCA (excluding C8 or C9), and the further incorporation of frequency modulation (using the total 43 features) pushed it to 99.9%, Fig. 2b. A total of 2400 sets of data were collected for each analyte (2000 for training/validation and 400 for test). In total, 31 classifiers were evaluated, among which the Bagged trees model showed the highest identification accuracy, Supplementary Table 1. All the accuracies were calculated based on five or more repetitions of random holdout test sets, and a 10-fold cross-validation was applied for training. It was worth noting that the order of feature addition, from two to eight dimensions, for achieving the highest identification accuracy (left part of Fig. 2b), was distinct from the rank of their own one-dimensional accuracy (Supplementary Fig. 30), which suggested the significance of correlation and complementarity between features. The enhancement by feature addition reached a plateau when the number of dimensions exceeded four, meaning that certain features were less relevant or easier to replace in the classification of PFCA. Once frequency modulation was included, the identification accuracy quickly jumped over 99% (right part of Fig. 2b). The confusion matrix of all 13 PFCA plus the R\u003csub\u003e6\u003c/sub\u003e probe (also with an overall accuracy of 99.9%) showed that the biggest errors came from the misclassification of FTA with C5 and C6, Fig. 2c, and strikingly, small but non-negligible false identifications (0.01-0.04%) were constantly observed for the pairs of PFCA that could be resolved completely using blockade only (Supplementary Fig. 22). Such phenomena stressed the necessity to reduce model complexity or the number of features.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eShortlisting high-priority features to minimise the size of training set for precise determination\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo optimise the combination of model input, the change of maximal validation accuracy against the number of features was examined, under various sizes of training set for C5, C6 and FTA, i.e., 2000, 200 or 20 signals for each PFCA. A similar trend was discovered in all three curves (Fig. 2d): when more features were included, the accuracy increased initially, then reached a plateau, and dropped slightly in the end, indicating that the optimal number of features should be neither too small (e.g., to avoid the deviation in training set) nor too large (e.g., to reduce the model complexity). The height, length and position of the plateau became lower, shorter, and left-shifted for smaller set, which decreased from 99.97% for 2000 signals with 28±10 features, to 98.40%\u0026nbsp;for 20 signals with 21±5 features. In the meantime, the priority of features was also affected by training size: when only 20 signals were used, a general order of importance 2000 Hz \u0026lt; wavelet \u0026lt; 100 Hz \u0026lt; 200 Hz \u0026lt; 500 Hz \u0026lt; 800 Hz was followed; but in the case of 200 or 2000 signals, other features such as kurtosis\u0026nbsp;at 200 and 500 Hz stood out, while all the filtered blockades (either wavelet or 100-800 Hz) were no longer critical, Supplementary Table 2-4. Taking into account of their rank in all three scenarios, a total of 21 features were shortlisted, Fig 2e, which was able\u0026nbsp;to decrease the amount of data for training by 7.6 folds, compared to the full 43-feature model, and to increase the maximal identification accuracy from 99.58% to 99.92%.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMaintaining nearly 80% quantification reliability with interference of 100 times concentration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe aforementioned few-shot learning mode of nanopore SMS facilitated the accurate quantification of trace targets in the presence of structurally similar interferents with much higher concentrations, which was often difficult for ensemble measurements. For instance, with regard to the determination of FTA from more concentrated C5 and C6, the pre-developed 21-feature model was able to maintain over 78% accuracy with interference of 100 times concentration, Fig. 3a, and a substantial 44% was still detectable even under 1000 times. Such performance was at least one order of magnitude better than the multi-peak fit using the 2000 Hz blockade only, which was the best one-dimensional feature in this study to mimic ensemble analysis, showing an accuracy of 69% with 10 times interference and a rapid drop to zero at 20 times. In the meantime, the quantification reliability of the shortlisted 21-feature model was consistently higher than the full 43-feature counterpart as well, in accordance with the above analysis on the influence of feature number.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eInterference-free quantification of trifluoroacetic acid towards a detection limit of 57 ng\u003c/strong\u003e\u003cstrong\u003e·\u003c/strong\u003e\u003cstrong\u003eL\u003csup\u003e-1\u003c/sup\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTrifluoroacetic acid (C2) was the simplest form of PFCA, with a much higher environmental level than other PFCA due to its more diverse sources\u003csup\u003e28\u003c/sup\u003e. Recent evidence suggested that the rising rate of C2 was considerable, and its potential adverse health effects could be higher than expected\u003csup\u003e41\u003c/sup\u003e. The quantitative analysis of C2, however, was arduous, and the limit of detection (LOD) was among 10-500 ng·L\u003csup\u003e-1\u003c/sup\u003e, Supplementary Table 5\u003csup\u003e27,28,42-46\u003c/sup\u003e. Herein, linking the\u0026nbsp;logarithm of C2 concentration and the logarithm of interval time measured at -50 mV and 20℃, a linear response range was established between 50 nM and 100 μM C2, insert of Fig. 3b. Interference such as C4, C5, C6 or tap water caused a tiny deviation less than 1%. Further adoption of an elevated voltage of -80 mV and a temperature of 30℃ pushed the LOD of C2 down to 0.5 nM or 57 ng·L\u003csup\u003e-1\u003c/sup\u003e, Fig. 3b, comparable to the state-of-the-art\u003csup\u003e27,28\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis work realized for the first time standard-free quantification of PFCA through the combination of single-molecule sensing with multi-feature classification. The structure of polycationic probe was fine-tuned so that various PFCA analytes could be directed to the identical residence position within the WT AeL pore, enabling the establishment of a linear volume-blockade relationship. It was noted that difference between the current blockade of C2 and C8 was only 9.662%, but at least 452 PFCA\u003csup\u003e3\u003c/sup\u003e (with CAS available) had been identified in this range. Hence, to fully resolve all the PFCA above, the standard deviation of blockade has to be smaller than 0.00356% (\u003cem\u003eR\u003c/em\u003e = 1.5)\u003csup\u003e20\u003c/sup\u003e, which however was around 0.2% at best for WT AeL. It was thus essential to make the most of other features of single-molecule signals.\u003c/p\u003e\n\u003cp\u003eThough the frequency modulated 43-feature model reached an overall accuracy of 99.58% for FTA/C5/C6, the hardest-to-distinguish combination of PFCAs in this study, when the size of training set was 2000 for each analyte, this value quickly dropped to 93.5% if only 20 signals were sampled. The shortlisted 21-feature model, according to the rank of importance, reduced the required amount of training data by 7.6 folds, enabling accurate quantification of trace targets at high-concentration interference. This was particularly crucial, indicating that a total of 20 signals recorded in 10-minute response time (or a capture rate of 1/30 Hz) was sufficient for precise PFCA determination. Future studies towards the measurements of all the 338 PFCA isomers by SMS would require the rationale engineering of nanopore interface in the context of multiple feature classification.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cstrong\u003eReagents and chemicals.\u0026nbsp;\u003c/strong\u003ePotassium chloride (KCl,\u0026nbsp;≥99.9%), tris(hydroxymethyl)aminomethane (Tris, 99%), ethylenediaminetetraacetic acid (EDTA,\u0026nbsp;≥99.0%), and octane (≥99%) were purchased from Titan Scientific (Shanghai, China). The electrolyte adopted in this detection system was the aqueous solution of 4 M KCl, 10 mM Tris, and 1 mM EDTA. 1,2-diphytanoyl-sn-glycero-3-phosphocholine (DPhPC, powder,\u0026nbsp;≥99%) was purchased from Avanti Polar Lipids (Shanghai, China). DPhPC was dissolved in octane and sealed dryly at -20℃. Proaerolysin was purchased from GenScript Biotech (Nanjing, China), and trypsin agarose (25UN) was purchased from Sigma-Aldrich (Shanghai, China). Conjugates of perfluorocarboxylic acids and peptide leaders were produced by ChinaPeptides (Suzhou, China).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSingle-molecule sensing of perfluorocarboxylic acids.\u0026nbsp;\u003c/strong\u003eProaerolysin was activated with immobilized trypsin at 4℃ for 10 hours to form monomeric aerolysin, which were involved in the oligomerization for aerolysin nanopores. After activation, proaerolysin was separated from trypsin at 10000 RPM and stored at -20℃ for further use. The above electrolyte was added into the detection chamber and the temperature was set as 20℃ constantly, except other stated. The DPhPC lipid bilayer membrane supporting the nanopore was formed across the 100 μm microcavities of MECA 4 Recording Chips (Nanion Technologies, Germany). Activated aerolysin was added into the cis chamber and formed a single nanopore on the DPhPC lipid bilayer membrane under the applied bias of +200 mV. The cis side of the detection chamber was seen as virtual ground whose potential was 0 mV and the voltage was applied on the trans side. If a single aerolysin nanopore was formed, open pore current would go to -100 pA as the applied voltage was set as -50 mV. PFCA-R\u003csub\u003e6\u003c/sub\u003e conjugates were added into the cis chamber and translocated to the trans side under negative voltages. Sampling rate and bandwidth were set as 20 and 10 kHz, respectively.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData acquisition and analysis.\u0026nbsp;\u003c/strong\u003eElectrical signals were recorded with a patch clamp amplifier (Orbit mini).\u0026nbsp;Frequency-modulated signals were processed in MATLAB 2021b, via wavelet denoising or lowpass filter at 100, 200, 500 and 800 Hz. Machine learning models were trained, validated and predicted in MATLAB as well. Features of raw and frequency-modulated signals were extracted in Python 3.11, based on the pre-identified events from Clampfit 10.4. Feature normalization was done in Python. Graphs were drawn in OriginLab, MATLAB or Python.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMolecular modelling and simulation.\u0026nbsp;\u003c/strong\u003eThree-dimensional structures of the R\u003csub\u003e6\u003c/sub\u003e probe and PFCA-R conjugates were generated in ChemBio3D. Energy minimization of these 3D structures were done with MM2 method and saved as pdb files. Structure topology files were generated with Ligand Reader \u0026amp; Modeler on CHARMM-GUI.\u003c/p\u003e\n\u003cp\u003eMolecules were simulated and their volumes were calculated in an aqueous solution system. The aqueous solution system, including electrolyte, electric field, temperature and pressure, was modelled and stabilized in advance. A 7*7*7 nm\u003csup\u003e3\u003c/sup\u003e sized water box was built through Solution Builder on CHARMM-GUI, with a KCl concentration of 4 M and temperature at 293 K. To eliminate the redundant steric hindrance and minimize the energy of this water box, 5000 iterations were done with the steepest descent algorithm. A 125 ps long equilibrium simulation was carried out to maintain constant temperature and reasonable distribution of total compounds. Based on this finished product, a 5 ns long simulation with a time step of 2 fs was carried out using Nose-Hoover method for temperature control and Parrinello-Rahman method for pressure control. Electrostatic interaction was calculated with Particle mesh Ewald (PME) method. Cut-off radius referring to calculations of Coulomb interaction, electrostatic interaction and Van der Waals interaction was set as 12 Å. Calculations of hydrogen bonds were constrained with LINCS algorithm.\u003c/p\u003e\n\u003cp\u003eThe last frame of the simulation was adopted as the water box for later molecular dynamic simulations. Afterwards, each structure under simulated was inserted into this water box with gmx insert-molecule, replacing water molecules, potassium ions and chloride ions randomly. The whole system was controlled at 293 K with V-rescale method of temperature control. After 10000 iterations with the steepest descent algorithm, energy minimization of this system was achieved. As a final step, there was a 1 ns long NPT equilibrium. Molecular volumes of all kinds of conjugates were calculated in a 50 ns long simulation, with time step of 2 fs. In purpose of reducing the impact of R\u003csub\u003e6\u003c/sub\u003e leader and highlighting real volume differences between different types of PFCA, X-R conjugates (where X represented different types of targets) were designed and simulated at first, putting the volume of X at a dominant position while taking the junction between the target and the leader into consideration. The volume difference between C4-R and C4-R\u003csub\u003e6\u003c/sub\u003e was set as an internal standard to speculate all of the molecular volumes of X-R\u003csub\u003e6\u003c/sub\u003e.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSource data are provided with the paper. Other data are available upon request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCode Availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe custom MATLAB and Python scripts are available at https://github.com/DEWMEME.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was supported by the National Key R\u0026amp;D Program of China (2023YFC3008803), the National Natural Science Foundation of China (21972041 and 22006037), the Natural Science Foundation of Shanghai Municipality (23ZR1416300), and the Fundamental Research Funds for the Central Universities.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAdditional Information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSupplementary information. The online version contains supplementary material available at.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eEvich, M. G. et al. Per- and polyfluoroalkyl substances in the environment. \u003cem\u003eScience\u003c/em\u003e\u003cstrong\u003e375\u003c/strong\u003e, eabg9065 (2022).\u003c/li\u003e\n \u003cli\u003eOECD. Reconciling terminology of the universe of per- and polyfluoroalkyl substances: Recommendations and practical guidance. \u003cem\u003eSeries on risk management\u003c/em\u003e\u003cstrong\u003eNo. 61\u003c/strong\u003e (2021). (accessed 14\u003csup\u003eth\u003c/sup\u003e May 2024). https://one.oecd.org/document/ENV/CBC/MONO(2021)25/En/pdf.\u003c/li\u003e\n \u003cli\u003eUS EPA. PFAS structures in DSSTox (update August 2022). https://comptox.epa.gov/dashboard/chemical-lists/PFASSTRUCTV5.\u003c/li\u003e\n \u003cli\u003eLiu, D. et al. Distribution of per- and poly-fluoroalkyl substances and their precursors in human blood. \u003cem\u003eJ. 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Technol.\u003c/em\u003e\u003cstrong\u003e56\u003c/strong\u003e, 9428-9434 (2022).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4603074/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4603074/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePer- and polyfluoroalkyl carboxylic acids (PFCA) are of great concern due to their ubiquitous presence in the environment. Despite a severe shortage of authentic standards, compared to the rapid increase of possible structures identified, it remains difficult to quantify a mixture of PFCA without references. Herein, a standard-free single-molecule electrochemical sensing method was developed for the first time by establishing a linear correlation between current blockades and the volumes of PFCA simulated by molecular dynamics. A nearly 100% accuracy was realized for the simultaneous determination of 13 pristine or H- / Cl-substituted PFCA, using frequency-modulated multi-feature classification. Shortlisting the 21 high-priority features reduced the required number of training data by 7.6 folds, and almost 80% quantification reliability was maintained even with interference of 100 times concentration. Moreover, the detection limit of trifluoroacetic acid (an ultrashort-chain PFCA) went down to 57 ng·L\u003csup\u003e-1\u003c/sup\u003e, comparable to the state-of-the-art performance.\u003c/p\u003e","manuscriptTitle":"Machine learning assisted single-molecule sensing of per- and polyfluoroalkyl carboxylic acids: Quantification without standards","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-15 05:59:18","doi":"10.21203/rs.3.rs-4603074/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"8e34f4a3-0b08-4d95-91ce-95b6e75104c9","owner":[],"postedDate":"July 15th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":34323957,"name":"Earth and environmental sciences/Environmental sciences/Environmental chemistry/Environmental monitoring"},{"id":34323958,"name":"Physical sciences/Chemistry/Analytical chemistry/Sensors"},{"id":34323959,"name":"Physical sciences/Nanoscience and technology/Nanoscale devices/Nanopores"}],"tags":[],"updatedAt":"2026-04-30T07:07:16+00:00","versionOfRecord":{"articleIdentity":"rs-4603074","link":"https://doi.org/10.1038/s41467-026-70718-3","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2026-03-13 04:00:00","publishedOnDateReadable":"March 13th, 2026"},"versionCreatedAt":"2024-07-15 05:59:18","video":"","vorDoi":"10.1038/s41467-026-70718-3","vorDoiUrl":"https://doi.org/10.1038/s41467-026-70718-3","workflowStages":[]},"version":"v1","identity":"rs-4603074","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4603074","identity":"rs-4603074","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}