Discriminating single-bacterial shape using low-aspect-ratio pores

Conventional concepts of resistive pulse analysis is to discriminate particles in liquid by the difference in their size through comparing the amount of ionic current blockage. In sharp contrast, we herein report a proof-of-concept demonstration of the shape sensing capability of solid-state pore sensors by leveraging the synergy between nanopore technology and machine learning. We found ionic current spikes of similar patterns for two bacteria reflecting the closely resembled morphology and size in an ultra-low thickness-to-diameter aspect-ratio pore. We examined the feasibility of a machine learning strategy to pattern-analyse the sub-nanoampere corrugations in each ionic current waveform and identify characteristic electrical signatures signifying nanoscopic differences in the microbial shape, thereby demonstrating discrimination of single-bacterial cells with accuracy up to 90%. This data-analytics-driven microporescopy capability opens new applications of resistive pulse analyses for screening viruses and bacteria by their unique morphologies at a single-particle level.

. Schematic illustration of a micropore set up. A micropore chip consisting of a microscale hole sculpted in a SiN membrane on a Si substrate is sealed by two polydimethylsiloxane (PDMS) blocks. Two holes in each block serve as inlet and outlet for injecting liquid into the pore. Ag/AgCl electrodes are inserted into another hole for measuring the cross-pore ionic current. Figure S2. Ionic current spike height Ip versus width td scatter plots for Escherichia coli and Bacillus subtilis. a-d, Data obtained using micropores having diameter and thickness of (a) diameter dpore = 3.0 μm and length Lpore = 40 nm; (b) diameter dpore = 3.0 μm and Lpore = 240 nm; (c) diameter dpore = 3.0 μm and Lpore = 490 nm; and (d) diameter dpore = 3.0 μm and Lpore = 990 nm. Red and blue plots correspond to E. coli and B. subtilis, respectively.  Straightforward analysis assigns the ionic spikes with Ip larger than Ith as derived from translocation of B. subtilis through the micropore whereas those smaller than the threshold to that of E. coli. The discriminability deduced from the number of correct reads (summation of the sky-blue and pink area) divided by the whole number of spikes is 69 %. Figure S5. Effects of peak regions on sensor accuracy. a, Bluntness of resistive pulses βapex is given as the deviation of time stamps whereat Iion crosses the current level at YthIp/100, where Ip is the ionic spike height. Here, Yth in per cent unit defines the amount of peak region used to extract βapex. b, Yth dependence of the discriminability P of E. coli and B. subtilis by statistical analysis of βapex and Ip distributions. Results for 3 μm-sized pores with Lpore = 40 nm (red) and 990 nm(blue) are shown. P changes little with Yth due presumably to the fact that the volume exclusion effect is reflected in almost entire region of the resistive pulses. On the other hand, only limited portions of the ionic current drops are brought by ion exclusion in the low-aspect-ratio pore; in other words, most of the current decrease occurs during the pre-translocation processes where the bioparticles obstruct the ion transport at pore exterior and give rise to appreciable change in the access resistance. This gives rise to the optimal P at Yth = 30 % where the particle shape effectively affects Iion. On contrary, as the particle size and shape would matter little on the ionic current blockade outside the pore, the sensor performance is degraded as Yth is increased above 30 %. Figure S6. Ionic current spikes obtained for Escherichia coli and Bacillus subtilis under the applied voltage of 0.05 V using micropore sensors having different geometries. a-b, Two dimensional histograms of resistive pulses obtained with ultrathin micropores of diameter dpore = 3.0 μm and length Lpore = 40 nm; c-d, dpore = 3.0 μm and Lpore = 240 nm; e-f, dpore = 3.0 μm and Lpore = 490 nm; g-h, dpore = 3.0 μm and Lpore = 990 nm. Left and right panels correspond to the data for Escherichia coli and Bacillus subtilis, respectively. Each graph was constructed with data of more than 200 ionic spikes. Base current is offset to zero. The spikes are extracted from the whole traces by finding the resistive pulses and taking out the 20 ms regions before and after the Iion minima. Figure S7. βapex distributions of Escherichia coli and Bacillus subtilis. a-d, βapex histograms constructed with the ionic current spikes obtained with 3 μm-sized pores with depth Lpore = 40 nm (a,b) and 990 nm(c,d). e, Gaussian fits to the βapex distributions. Red and blue lines correspond to the histograms of E. coli and B. subtilis, respectively. Figure S8. Low-aspect-ratio pore analysis to investigate a role of bacterial motility on the ionic spike line-shapes. More than 500 resistive pulses were obtained for flagellated (wild-type) and non-flagellated (fliC inactivated mutant) E. coli in 1/10 diluted PBS buffer under the applied electrophoretic voltage of 0.05 V using 3 μm-sized SiN pore sculpted in a 40 nm thick membrane. The ionic spikes recorded had very similar waveforms as marked by the completely overlapped plots of the pulse height Ip with respect to the width td and the corresponding histograms. Figure S9. Ionic current spike height Ip versus width td scatter plots for Streptococcus salivarius obtained using micropores having diameter and thickness of (purple) diameter dpore = 1.4 μm and length Lpore = 40 nm and (green) dpore = 3.0 μm and length Lpore = 40 nm. The small signals with variable td are ascribable to flying-by events of the bacteria skimming through the pore orifice [S1-3]. Figure S11. Ionic current spike wave patterns acquired for Streptococcus salivarius with a micropore of dpore = 1.4 μm and thickness Lpore = 40 nm showing two-bump feature indicative of translocation of the bacteria having a two-bead chain form. a, An example of the corrugated ionic spike. b, Magnified views of the peak feature indicated by the square in (a), which display characteristic corrugations reflecting the double-bead shape of the bacteria. Red broken lines are guide to the eyes for the positions of the two minima. The difference in the waveforms are attributed to a variation in the bacterial shape and size and/or the translocation dynamics.

Figure S12.
Statistical occurrence of the corrugated ionic spikes of Streptococcus salivarius in the microsensor with dpore = 1.4 μm and thickness Lpore = 40 nm. a, Five distinct types of the ionic spike wave patterns: A peak with single (1, blue), double (2, red), triple (3, green), or quadruple (4, purple) bump feature; and significantly weak pulses (black). b, The number of each type of spikes detected. Figure S13. Dependence of the ionic current spike line-shapes of Streptococcus salivarius on the pore diameter. a, Micropores of different diameter dpore ranging from 2.0 μm to 1.2 μm and the same length of Lpore = 40 nm were used to record resistive pulses during translocation of single S. salivarius in 1/10 diluted PBS buffer under the applied dc voltage Vb of 0.05 V. b-h, Two dimensional histograms of resistive pulses obtained with the ultrathin micropores of (b) dpore = 2.0 μm, (c) 1.8 μm (d) 1.6 μm, (e) 1.5 μm, (f) 1.4 μm, (g) 1.3 μm, and (h) 1.2 μm. Only single-peak pulses were obtained for pores of larger than 1.6 μm. On the other hand, the characteristic corrugations in ionic spikes reflecting the bead-chain structure of S. salivarius were observed in pores smaller than 1.5 μm.

Statistical estimations of the respective numbers of E. coli and B. subtilis
Statistical estimations of the respective numbers of E. coli and B. subtilis were conducted by applying non-parametric probability density estimation of each bacteria in feature spaces where every feature space is formed by a pairwise combination of distinct features of the ionic current waveforms. Specifically, we chose the pulse height Ip and width td (Fig. S14a), the bluntness βapex of the apex (Fig. S14b), the onset angle θ (Fig.  S12a), the area A (Fig. S15b) and its ratio rm before and after the spike maxima (Fig. S15c), and the momenta with respect to the longitudinal (Im; Fig. S15d) and transverse axes (Iw; Fig. S15e). Once the distribution of the pairs of the pulses in the feature space is given, the distribution is approximated by a weighted combination of the non-parametric probability densities learnt beforehand for the two bacteria species. The weights which provide optimal approximation are proportional to the respective numbers of the two bacteria species.
Figure S14. Peak features: pulse height, width, and bluntness. a, A resistive pulse was extracted by using 5σ as a threshold to find a pulse onset. The time whereat the fluctuations of the ionic current Iion decreases below 5σ was also identified (red lines). Furthermore, the peak regions were expanded by 0.256 ms at both sides (blue lines) whereby defining the regions of ionic current spikes. In the figure, ts and te denote the onset and the end position of the resistive pulse, respectively. The pulse width td = tets and the pulse height Ip are the feature parameters used for pattern analysis. b, The bluntness of resistive pulse apex βapex was extracted by first normalizing the spike height by the height Ip as Inorm = Iion / Ip and width by te and ts as tnorm = (tts) /(tets). Then, βapex was deduced as βapex where ti is the time stamps whereat Iion curves intersect the Iion level Yth % from the peak maxima. In the description, tave and m denote the arithmetic mean of ti-ts and the number of intersecting time points, respectively. Figure S15. Peak features: onset angle, pulse area and its ratio, and longitudinal and transverse momenta. a, The onset angle θ defined by the slope 1/r from Inorm at tnorm = 0 to r, where r is the peak position. b, The area A is calculated by dividing a pulse into n regions (dotted lines) and taking summation of the average Inorm, hi, at each section. c, The ratio rm between the area at the peak onset (purple) and that after the peak maximum (yellow). d-e, The inertia Im (d) and Iw (e) calculated with respect to longitudinal and transverse axes, respectively.

Single-bacteria discriminations
Single-bacteria discriminations were performed by pattern-analyze individual ionic current spikes using classification algorithms of machine learning. For this, we also used the aforementioned distinct features of the ionic current pulse waveforms. In addition to these parameters, the line shapes of resistive pulses were characterized in more general sense by the vectors in the current ( We created 60 different feature vectors by combining the above mentioned parameters as follows: Pattern analysis of ionic current spikes of E. coli or B. subtilis was exhibited on basis of the thus acquired dataset using The Waikato Environment for Knowledge Analysis (Weka) machine learning workbench with 67 Rotation Forest ensembles where each applies a distinct base classifier such as naïve Bayes models. In this supervised learning, 161 pulses of each bacteria, either E. coli or B. subtilis, (in total 322 vectors) was used as teacher data to judge the other 18 spikes (While up to 500 pulses were obtained in some measurements (see Tab. S1), we randomly selected 179 pulse data from the larger pools to keep the number of pulses the same for the machine learning analysis). The output was further evaluated to deduce F-Measure score FMeas = 2PprePRec/(PPre + PRec), where PPre and PRec are the precision and recall calculated through TP/(TP + FP) and TP/(TP + FN), respectively, with TP, FP, FN denoting respectively the number of true-positive, falsepositive, false-negative cases.

Statistical variability of the estimation
We used the ten-fold cross validation which is standard in statistics and machine learning for evaluating the accuracy of the classifiers. In this scheme, the experimentally obtained data set consisting of the spikes and their types such as E. coli and B. subtilis is partitioned into ten blocks containing an equal number of spikes. Then, in a fold stage, the spike data with the bacteria types in the nine blocks among the ten are used for the classifier learning, and the accuracy of the classifier is evaluated by matching the estimated types and the experimentally known types of the individual spikes in the rest test block which have not been seen by the classifier yet. This fold stage is repeated ten times by interchangeably changing the nine learning blocks and the rest test block, and the total accuracy of the classifier is provided by the average accuracy of the ten tests.
The idea behind this 10-fold cross validation scheme is to properly evaluate the accuracy of the classification method for unseen spikes while ensuring less experimental variability of the data and better efficiency to use the limited amount of the data.
In our experiment, the variability of the classification accuracy over the ten tests remains 4-8% in terms of the standard deviation (Fig. S17). Since the identifications of the individual spikes by the classifiers should be mutually independent and have an identical error risk when the experimental condition was well maintained, this resultant accuracy should follow a binominal distribution of true and false identifications. Thus, the standard deviation of the accuracy is expected to be √ (1 − )/N ≅ √0.8(1 − 0.8)/36 = 6.7% where N is the number of the spikes in the test data. Accordingly, the variability of the accuracy demonstrated in our experiment is very reasonable to conclude that the experiment was statistically well controlled during the data acquisition. Figure S17. The maximum F-measures and their standard errors for 5 thicknesses of the pores. The maximum F-measures achieved by the forty base classifiers with the Rotation Forest meta-classifier are depicted for the pores having the 5 thicknesses. The F-measure and its error bar for each thickness are the average F-measure and its standard deviation across the ten-fold cross validation on the pore. Table S1. The number of resistive pulses recorded.

Physical model for finite element analysis.
To simulate the electric current density j at a steady state, we use the convergence condition expressed as 0  j . The ionic current through a nanopore is given by Here, Vc, σw and F are the electric potential, the electrical conductivity of water (5.5×10 −6 S/m) and the Faraday constant (9.649×10 4 C/mol), respectively, while zi, ui, and ci denote the charge, the electrical mobility and the concentration for ion species of i. In this study, as we used 10 times diluted phosphate buffered saline (0.1×PBS) as the electrolyte, we approximated it by NaCl 13.7 mmol/L in this simulation. We used zi = 1, ui, = 5. Meanwhile, not only current flow but also static charge plays a role in the electric current in nanopore devices, because it describes the spatial distribution of ions (ci) in the electric double layer on solid-electrolyte interfaces. The distribution of ions at the equilibrium state is given by Boltzmann statics ci = ci 0 exp(-zieVs/kBT), where ci 0 , e, and Vs denote the ion concentration for i ion at the zero potential, the elementary charge, and electrostatic potential. Hence, the Poisson-Boltzmann equation is described by Here, ρ and εw are effective static charge by ions and the permittivity of water (εw = 7.083×10 −10 F/m). Also, Eq. 2 was simultaneously solved with Nernst-Plank equation where, Ji is the ion flux for i ion. The first, second, and third terms denote diffusion, electrical migration, and convention, respectively.
The velocity of electrolyte solution U in Eq. 1 and 3 was calculated by incompressible Navier-Stokes equation expressed as where p and μ are pressure and dynamic viscosity of water (1.009×10 −3 Ns/m 2 ). f is the body force applied to electrolyte solution, and we defined it as by assuming the electric dragging force for electrolyte solution. All calculations were performed by COMOL Multiphysics 5.0.

Structural model and boundary condition for finite element method (FEM).
We used the model of two-dimensional space together with a rotational symmetry to simulate the straight translocation of bacteria via naopore, which possess a cylindrical configuration. The structure of S. salivarius was modeled in reference to the scanning electron microscope image (Fig. S18), and four type models, in which each S. salivarius possess 1-4 cocci, were created to simulate experimentally-observed current peak signatures.  The model for two cocci S. salivarius is depicted in Fig. S19, where a case at z position of 5 μm is provided. The model for the nanopore device was constructed as follows. The radius and height for cis-and trans-chambers were 4 μm and 7.1 μm, respectively. A 40 nm thick SiN membrane (a conductivity of 1.0×10 −14 S/m and a permittivity of 1.851×10 −11 F/m were used for SiN) with a 0.7 μm radius pore is placed between the cis-and trans-chambers as seen in Fig. S20a. The simulation for the translocation of S. salivarius via the nanopore was conducted by sweeping the center position of S. salivarius from z = 5 μm to z = −5 μm.
Subsequently, we set up boundary conditions for solving the differential equations 1-4. Figure S19b a, b, Vs+Vc, c, cNa, d, cCl and e, U for the model illustrated in Fig. S19. As the constructed model has rotational axis at r = 0, the practical 3D view is given by the revolution, seen in the relation between a and b. Insets in c and d are the enlarged view at the interface between the surface of SiN for the pore and electrolyte.
The prepared models were meshed by extremely fine condition and the corners and layer boundaries of those were refined enough to simulate the physics within Debye-length , where NA is Avogadro constant of 6.02×10 −23 mol −1 . On the condition in this study, λD ≈ 3.5 nm is evaluated. As an example of the simulated results, the independent variables of Vs + Vc, cNa, cCl, and U are depicted in Fig. S20, of which model corresponds to that of Fig. S19. Vs and Vc respectively represent the electric potential solved by Eq. (1) and (2), that is, Vs + Vc illustrates the total electric potential in the given model as seen in Fig. S20a. Because of the presence of the rotational symmetry, the physical properties for the pore devices are eventually given by the revolution of the prepared models as shown in a cylindrical shape of Fig. S20b. Figs. S20c and d indicates the distribution of cNa and cCl, and also each inset figure is for that of the interface between the inner wall of the pore and electrolyte liquid. Due to the negative surface charge on the SiN wall, Na + cation and Cl − anion is respectively accumulated and depleted at the interface. As a result, electric double layer is formed, and electroosmotic flow is yielded by being coupled with the applied electric field (Fig. S20d). The simulated current trace profiles during the translocation of S. salivarius were given, including the above-mentioned phenomena such as electricity, ion transport, and electro-osmosis. Figure S21. Simulated ionic current spikes for S. salivarius consisting of three cocci. Models of micropores of different diameter dpore ranging from 3.0 μm to 1.2 μm and the same length of Lpore = 40 nm were used to calculate the ionic current blockage during axial translocation of individual S. salivarius in 0.1 x PBS buffer under the applied voltage of 0.05 V. Each cocci was sized 0.8 μm and 0.3 μm diameter at the thickest and the thinnest parts, respectively. While the bacterial shape induced corrugation is evident in pores smaller than 1.6 μm, the spikes become increasingly featureless as dpore becomes lager than 1.8 μm due to increasing effects of the access resistance that significantly blurs the ion exclusion effects inside the pore.

Structural model for E. coli and B. subtilis for FEM.
Figures S22a and b are the SEM images for E. coli and B. subtilis. As contrasted with E. coli of which appearance is a spheroid-like shape, B. subtilis shows a cylinder-like one.
To elucidate the shape effect for the measured ionic current trace originating from this shape difference, we constructed the model as follows. Figure S22. SEM images for a, E. coli and b, B. subtilis. Depicted scale bars correspond to 2 μm. c, Schematic illustrations for a part of the constructed model for elucidating the difference of shape effect between E. coli and B. subtilis. Although the size of the modeled cis-and trans-chambers are 12 (= 4×3) μm radius and 12.12 (= 7×3 1/2 ) μm height, the aria around the pore is illustrated. The center position of the object was swept from z = 10 μm to z = − 10 μm, and the case of z = 0 μm is shown.
We used a two-dimensional space with a rotational axis in the same manner as the above-described, and kept the height and radius of the target objects as 2.6 μm and 0.4 μm (Fig. S22c). By filleting the two corner of a rectangle (2.6 μm height and 0.4 μm width) at 1-400 nm radius, we constructed cylinder-like objects which are referred to as R = 1 to R = 400 as shown in Fig. S18c. Regarding the case of R ≥ 400, we placed the quadrant of the ellipse, of which major-and minor-axis is respectively R nm and 400 nm, at both side of a small rectangle. The height of this small rectangle was adjusted to 2.6 μm − 2R μm and the width of that was 0.4 μm. There structures are referred to as R = 400 to R = 1100 in Fig. S18c. Both procedures give the same structure at R = 400.
As the pore radius used in the experiment is 1.5 μm, which is larger than that of the pore for S. salivarius, we prepared cis-and trans-chambers as 12 (= 4×3) μm radius and 12.12 (= 7×3 1/2 ) μm height. In the simulation, we set a of −15mC/m 2 at the objects surface, and performed the calculation in the same methodology. By sweeping the center position of the objects from z = 10 μm to z = −10 μm, we obtain the ionic current traces during passing through the objects via the pore. The physical description for the FEM simulations is used in the same manner. Figure S23. Particle shape-dependence of the ionic spike waveforms. a, Ionic spikes obtained through COMSOL simulations of single-rod-shaped object through a micropore of diameter 3 μm and depth 40 nm. The object has different roundness defined by R. Axis-translocation is assumed. Curves for R = 10 nm (Black: sharpedged cylinder) and R = 1100 nm (Dark yellow: rounded cylinder) are emphasized for the sake of clarity. b, The ionic current curves normalized by the pulse height. Color coding is the same as that in (a). Figure S24. Adsorption radius of bacteria. The electrophoretic velocity of E. coli around a micropore of diameter 3 μm and thickness 40 nm under the voltage of 0.05 V. Solid curve illustrates the adsorption radius. The bacteria tend to be drawn into the pore electrophoretically once crossing the boundary.

Electrophoresis of bacteria
It is important to clarify whether E. coli and B. subtilis are allowed to pass through the micropore under the conditions tested. S4 To elucidate the electrophoretic motion of bacteria, we performed the FEM simulations on the nanopore model of which pore diameter and depth were 3 μm and 40 nm, and also the cell radius and height for chambers of 20 μm were set to prepare enough space in simulating the movement induced by electrophoretic drag force. We simplified the bacterial structure to a sphere of which radius was 0.62 μm, because the volume of E. coli and B. subtilis was ~1 μm 3 . At a steady state, the drag force to an rs radius sphere on an electrophoretic velocity of vep is given by 6πμrsvep, where μ is a dynamic viscosity of fluid. When the spherical particle possesses a charge of q and is placed on an electric field of E, an electrostatic force of qE, which balances with the drag force, is yielded. By substituting q with 4πrs 2 σs, here σs is the surface charge of the particle, the electrophoretic velocity is expressed as Figure S25 shows the results of velocity (color map) and velocity field (magenta arrows) of the simulated electrophoresis by using σs = −15 mC/m 2 . Along with the electric field, the electrophoresis is yielded between the ground (top side) and the bias voltage terminal (bottom side) via the pore, especially the electrophoretic motion is enhanced around pore.
Another factor regarding the motion of particle dispersed in a fluid is Brownian motion.
For the detection of particles, the target particles must be translocated through a pore in finite measurement time by overcoming the Brownian motion. The mean verbosity of Brownian motion vBM is given by Here, m is the mass of a particle. Assuming the m is the mass of ~1 μm 3 water, vBM = ~2 mm/s is obtained. The green circle in Fig. S25 illustrates the isosurface of vep = vBM, thus the particles are translocated immediately in entering the inside area of the black sphere that extends over 5 μm from the orifice.