Quantitative Framework for Stochastic Nanopore Sensors Using

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Quantitative Framework for Stochastic Nanopore Sensors Using Multiple Channels Robert Alexander Lazenby, Florika Caling Macazo, Richard F. Wormsbecher, and Ryan J. White Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b03845 • Publication Date (Web): 29 Nov 2017 Downloaded from http://pubs.acs.org on December 8, 2017

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Analytical Chemistry

Quantitative Framework for Stochastic Nanopore Sensors Using Multiple Channels Robert A. Lazenby,† Florika C. Macazo, ‡ Richard F. Wormsbecher, and Ryan J. White†,* Department of Chemistry and Biochemistry, University of Maryland Baltimore County, Baltimore, Maryland 21250.

* Corresponding author: email [email protected] †

Present address: Department of Chemistry, University of Cincinnati, Cincinnati, Ohio 45221.

‡

Present address: Department of Chemistry, University of Utah, Salt Lake City, Utah 84112.

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ABSTRACT:

Membrane protein channels employed as stochastic sensors offer large signal-to-noise ratios and high specificity in single molecule binding measurements. Stochastic events in a single ion channel system can be measured using current-time traces which are straightforward to analyze. Signals arising from measurement using multiple ion channels are more complicated to interpret. We show that multiple independent ion channels offer improved detection sensitivity compared to single channel measurements, and that increased signal complexity can be accounted for using binding event frequency. More specifically, the leading edge of binding events follows a Poisson point process, which means signals from multiple channels can be superimposed and the association times (between each binding event leading edge) allow for sensitive and quantitative measurements. We expand our calibration to high ligand concentrations and high numbers of ion channels to demonstrate that there is an upper limit of quantification, defined by the time resolution of the measurement. The upper limit is a combination of the instrumental time resolution and the dissociation time of a ligand and protein which limits the number of detectable events. This upper limit also allows us to predict, in general, the measurement requirements needed to observe any process as a Poisson point process. The nanoporebased sensing analysis has wide implications for stochastic sensing platforms that operate using multiple simultaneous superimposable signals.


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INTRODUCTION Stochastic nanopore sensing is a resistive pulse technique1 that measures current blockade events caused by single molecules reversibly binding to, or translocating through, a nanopore. This sensing method possesses high sensitivity, temporal resolution,1–4 and signal-to-noise, and has inherent signal amplification.1–3,5,6 As such, stochastic nanopore sensing has found significant use in sensing applications, including DNA sequencing,7,8 small molecule measurements,1–3,6,9–11 glio- or neurotransmitter detection12–14 and simultaneous topography15 and molecular flux imaging.16 The technique can also provide important kinetic information that is not readily attainable using current bulk macro- or microscale biosensing strategies, for example probing peptide cleavage17 and protease activity.18 Nanopore geometries are achieved through the use of artificial, solid-state nanopores, which can be engineered to promote specific binding or translocation of several analytes, or the use of biological nanopores in the form of transmembrane protein channels.2,3,9,10,14,19 Naturally occurring protein channels show promise as nanopore elements and have been the most widely used in stochastic sensing as a result of the reproducible nanometer-scaled pores that nature provides.2,3,6,9,20,21 Typically, these membrane proteins are incorporated into a lipid bilayer that separates two electrolyte solutions, with an electrode placed on either side of the bilayer. A potential bias is applied to induce an ionic current flow through the channel(s) which is altered as a molecule enters the channel. Alpha-hemolysin (αHL) is traditionally one of the more prolific protein channels for use as a biorecognition element in stochastic single-molecule detection3,4,20,21 and DNA sequencing,4,6–8,20,22 due to its efficient pore-forming capability, robust structure,2 and amenability to biomolecular engineering.3 In stochastic nanopore sensing, measurements employing single ion channel activity are the most widely and commonly used for quantitative analysis, owing to the ease of the signal analysis. The fraction of time that an ion channel is open during a recording is a facile way to analyze single channel data, and may be readily inferred from a histogram of measured current (Figure 1). Even non-stochastic and less ideal signals may be analyzed by simply integrating the charge flux.12 For stochastic processes, ACS Paragon Plus Environment

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kinetic information can be obtained using the idealization method of analysis, in which typically a threshold is set to define the open and closed states. The number of individual binding events occurring per unit time, or the frequency of translocation events, allows quantification of analyte concentration.3,9,10,13,14 The binding event dwell times (τoff) are used to identify individual analytes, in addition to the magnitude of the current blockade (Figure 1).23,24

Figure 1. Schematic of the types of analysis used for analyte quantification using a single channel. a) Non-stochastic signal analyzed by integrating the charge flux. b) Stochastic events analyzed by i) event frequency or ii) ratio of time spent in the closed channel to time spent in open channel state.

Most reports that quantify channel activity either use single channels or bulk measurements with numerous channels, in which stochastic ligand binding events or individual protein insertion events become lost in the noise of the large current signal and insufficient time resolution required to resolve individual event frequency. There are only a few reports on the intermediate regime of stochastic sensing using multiple channels, including the analysis of many channel systems when channels open infrequently,25 or looking at proportions of time spent at each current level.26,27 An advantage of


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multiple channel measurement, to which we elaborate here, is that the binding rate (read sensitivity) increases linearly with the number of channels in the lipid bilayer.28 Operating techniques using multiple ion channels is advantageous due to the increased sensitivity of the measurement, however obtaining a quantitative measurement is more difficult, especially when the number of identical ion channels capable of blockade events is not known. A more quantitative analysis of the flux of molecules detected at multiple ion channels is required. We aim to show that a single sensor with a complex signal arising from multiple incorporated channels can be quantitatively analyzed, without the need for a more intricate setup that may be required for individually accessible multichannel arrays.29,30 Here, we look at the well-studied αHL protein channel as a representative nanopore to detect the flux of negatively charged, sulfonated β-cyclodextrin (S7βCD), as a model target molecule. Using this system, we established a quantitative framework for analyzing stochastic signals from multiple independent nanopores, which will allow for highly sensitive and high signal-to-noise measurements, required for the detection of low concentration entities across a broad range of stochastic nanopore sensors.

EXPERIMENTAL Materials and Chemicals. Potassium chloride (KCl), sodium phosphate dibasic dihydrate (Na2HPO4·2H2O), sodium phosphate monobasic dihydrate (NaH2PO4·2H2O), and heptakis(6-O-sulfo)β-cyclodextrin heptasodium salt (S7βCD) were all purchased from Sigma (St. Louis, MO) and used as received. 10.0 mM phosphate buffer (pH = 7.4) was prepared by dissolving the appropriate amounts of the dibasic and monobasic phosphate salts using water purified (deionized) through a Millipore Milli-Q system (resistivity 18.2 MΩ cm at 25 °C). 1,2-diphytanoyl-sn-glycero-3-phosphocholine (DPhPC) in chloroform was obtained from Avanti Polar Lipids (Alabaster, AL), which was redissolved in n-decane (Sigma) and stored at -20 °C until use. Wild-type (WT) alpha hemolysin (αHL) from staphylococcus


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aureus was purchased as lyophilized powder from Sigma and used as received without further purification. Channel Formation and Ion Current Measurements. A lipid bilayer was formed across a 150 µm diameter pore in a delrin (polyoxymethylene) cup (Figure 2) in a bilayer chamber/cup setup (Warner Instruments, CT), using the previously described painting method.31 Briefly, the cup was primed, around the pore, with DPhPC in n-decane, which was allowed to evaporate. 3 ml of 10.0 mM phosphate buffer (pH = 7.4) containing 1 M KCl was added to each chamber. One side, denoted the cis side, had 5 nM αHL dissolved in it. The opposing side, denoted the trans side, had a series of concentrations of S7βCD, separated into a low range (0.01, 0.02, 0.03, 0.04 and 0.05 mM) and a high range (0.5, 1.0, 2.0 3.0 and 5.0 mM). The bilayer was formed by translating a 200 µl gel-loading tip across the pore. Current recordings were carried out at a temperature of 20 ± 1 °C. Data collected at the high concentration range were obtained using a slightly modified setup (Supporting Information, S1).

Figure 2. Schematic of the experimental setup for the bilayer cup, and a zoom-in of the micropore (150 µm diameter). A lipid bilayer covers the pore, into which αHL heptamers insert. Diagram is not to scale.


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Silver/silver chloride (Ag/AgCl) quasi-reference counter electrodes (QRCEs) were prepared by chemically chloriding (oxidizing) silver wire (0.5 mm diameter), by immersion in 6% sodium hypochlorite, NaOCl (Clorox, Oakland CA) for 30 minutes. A QRCE was placed into each chamber, and a potential of 100 mV was applied to the cis side, whilst trans side was held at ground (Figure 2). Ion channel current recordings were collected using a Dagan Chem-Clamp low-noise potentiostat (Minneapolis, MN) interfaced to a PC running custom LabVIEW code (LabVIEW 2014, National Instruments, Austin, TX). A headstage of N = 1 and 1 kHz low-pass Bessel filter were used with the potentiostat. and data points were collected every 3⅓ ms. All voltages reported herein are referenced to the Ag/AgCl electrode positioned at the trans side, thus we are applying a potential to the cis side with respect to the trans side. Recordings were made until a sufficient sample size was collected, in some cases from multiple measurements (typically over 50 events, Figure S-4, Supporting Information). The resulting current-time recordings were analyzed (vide supra) using code written in MATLAB version R2016a. This code could be easily modified to allow for different threshold values, which could distinguish different components for mixture solution analysis.

RESULTS AND DISCUSSION In this study, we present a quantitative framework for analyzing stochastic single-molecule measurements obtained using multiple identical nanopores. Our work and analysis is broadly applicable to nanopores in general, but as a proof of principle we studied the widely-used membrane protein ion channel αHL as a model system binding to the ligand S7βCD, a negatively charged derivative of βCD. The cyclodextrin reversibly binds to αHL, modeled by the following first-order reaction scheme: kon → αHL + S7βCD ← αHL:S7βCD koff

(1)

where kon (s-1 mM-1) is the association rate constant and koff (s-1) is the dissociation rate constant.23,28,32,33 The “on” state indicates a bound molecule, whereas in the “off” state the molecule is free, in this twostate Markovian model.34 ACS Paragon Plus Environment

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Single Ion Channel Measurements Using Association Dwell Time for Quantitative Analysis. To perform protein channel-ligand binding experiments, we employed a classic bilayer cup apparatus (Figure 2). Briefly, ion channels were reconstituted into a bilayer by spontaneous direct insertion, which allowed for the study of a series of numbers of ion channels (n = 1 – 5) in a single experiment (i.e. for each S7βCD concentration). The study of S7βCD binding to αHL provides exemplary data of stochastic single molecule detection using an individual nanopore. As S7βCD translocates into the protein channel, the current fluctuates in a well-defined manner.16,28 More specifically, the open channel current observed was 75 pA (noise 5 pA peak-to-peak), which corresponds to a channel conductance of 0.75 nS for the heptametric αHL subunits which has a most narrow constriction of 1.4 nm in diameter.35 Smaller channel conductances of about half the expected value (we observed insertions that gave a channel conductance of 0.34 nS) have previously been attributed to hexameric αHL subunits,28,36 which we ignored for all analysis because they did not exhibit S7βCD binding events. There could be other explanations for a lower than expected conductance state besides the formation of a hexamer, such as misfolding and incorrect formation37 or voltage gating.38 A notable advantage of using the direct insertion method for ion channel reconstitution in a bilayer, is that every protein insertion can be tracked and the total number of identical proteins unambiguously known, in contrast to the membrane patch method.39 The number of heptamer αHL protein channels inserted into the bilayer, that give the expected open channel current (or increase in current from previous channel state), can be unambiguously known by counting the step increases of expected current magnitude in the current-time trace. There are methods to estimate number of channels,40,41 the simplest being to use the maximum observed current as the maximum number of simultaneously open channels (knowing the current for one open channel), which works best for low numbers of channels (e.g. 4 or fewer).42 The analysis method presented herein provides a new way to determine the number


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of correctly formed ion channels, by performing binding event frequency in a standard solution of known concentration (binding) analyte. We observe distinct stochastic current blockades attributed to individual binding events between S7βCD and αHL. The residual current was 7 pA (i.e. when the channel is blocked by a S7βCD molecule), or ~10% that of the fully open channel. Some binding events were not as great in magnitude, and we attribute this to short timescale binding that is beyond our time resolution limit (data were recorded every 3⅓ ms) or blocking of the channel close to, but not at, the binding site. We set a binding event threshold to define a binding event, which was a current blockade of > 7 pA less than the open channel current (i.e. < 68 pA) just above the noise level (5 pA peak-to-peak) of our measurement. Using the 7 pA blockade threshold, the data were then binned to the nearest number of unblocked channels to give an idealized form of the current-time trace, which had the effect of digitizing the data (either 1 or 0 open channels) (Figure 3b).

Figure 3. a) Current-time trace for the ionic current through a single αHL ion channel, using an applied potential of 100 mV cis vs. trans, with 0.040 mM S7βCD in the trans side. b) Zoom-in of a) showing i) raw data and ii) idealized current data (i.e. assigned to whole number of unblocked ion channels).


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Association times are a quantitative metric for rate analysis. The time between two binding events is defined as the association time, τon (Figure 1b i). The residence time of the molecule, i.e. the time taken for a molecule to dissociate from the channel, is defined as the dissociation time, τoff. The association rate constant, kon, can be determined for species, S, using the inverse of the mean of τon to give an event frequency, f:

f=

1

τon

= kon[S]

(2)

Furthermore, the dissociation rate constant, koff, is given by:

koff =

1

τ off

(3)

The results of the analysis for single channel data using the frequency method are included with multiple channel results (vide infra). It has also been demonstrated that the method of using the ratio of open and closed channel occupancy achieves quantitative analysis for single channel data (Figures S-1, S-2 and S-3, Supporting Information), although this method cannot be used to determine binding rate constants.

Redefining τon for Quantitative Analysis using Multiple Channels. While the treatment of the data for a single channel can be achieved by simply collecting the τon (or τoff) times, and fitting an exponential to these values, this analysis fails when working with more than one channel. The reason for this breakdown results from the ambiguity in defining values for τon (and τoff) when multiple events occur simultaneously in multiple channels (Figure 4a). Conceptually, the ambiguity in τon and τoff arises because once more than one channel is occupied, experimentally you are unable to determine which channel opens first. A new definition of τon is required. While most reports use ⟨τon⟩ to determine a binding rate,23,32,33,43 it is necessary to use the event frequency for analysis of multichannel signals.28,44 A mean binding event time, ⟨τevent⟩, can be defined as the sum of the association time and the dissociation time, for single channel data: ACS Paragon Plus Environment

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τevent = τon +τoff

(4)

The mean binding event time can be used to calculate the binding event frequency, λ. When using ⟨τevent⟩ to determine event frequency λ, the binding event rate constant, kevent, is related in this way:

λ=

1

τevent

= kevent [S]

(5)

To redefine τevent when observing multiple channels, we use a Poisson process to describe the probability of observing a binding event at any channel. The probability event wait time distribution is given as follows:

P (τ event ) = λe−λτ event

(6)

The event frequency for n channels of parallel processes is: n

λ = nkevent [S] = ∑ kevent [S]

(7)

This expression essentially predicts the wait time distribution between the arrival of a cyclodextrin molecule, τevent, and is independent of the time the previous molecule spends in the channel (τoff). However, the measurement is not independent of τoff as described in detail below. To expand to multiple channels, we rely on the superposition properties of Poisson processes (as in equation 7). More specifically, for n independent Poisson processes, each with a given event frequency (λ in Equation 5), the combined process is also Poisson, with a rate that is the sum of the individual rates (nλ, if rates are equal). With this in mind, experimentally, only the leading edge of each binding event is needed in establishing the newly defined binding event time, denoted as τevent (Figure 4b). We took the mean event time to calculate binding event frequency, rather than fit an exponential to a histogram of the data (Figure S-4, Supporting Information). This analysis actually allows a more accurate estimate of the binding rate constant with fewer measurements.


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Figure 4. Schematic idealized current-time traces of a two-channel system showing a) previously defined τon, which shows ambiguity and b) the newly defined τevent, which allows for quantitative analysis. c) Schematics to show i) monitoring multiple channel insertions and ii) multi-component mixture analysis, in which τevent is shown for both βCD and S7βCD events.

Figure 4c shows how multi-component analysis can be achieved, provided that each component gives a unique characteristic blocking current magnitude. For example, in a two-component system of S7βCD and βCD, the magnitudes of the decrease in current (of the open channel current for one channel) during a blockade event are ~80-90% for S7βCD45 and ~60-80% for βCD.10 Data would need to be idealized using the change in current (binding event magnitude) to identify the molecule that caused the event, rather than using a series of thresholds to determine the number of events (as in Figures 3 and 5). This would allow the τevent of these distinguishable blockade events to be determined for each component


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independently. One component (S7βCD only) from the mixture, can be selected for exclusive binding event frequency (equation 7), using its binding event magnitude (Figure 4c), ignoring the other events that have a different blockade current magnitude. Alternatively, the total event frequency, λtotal, could be determined for N different types of event (two types of event are shown in Figure 4c) as follows: N

λtotal = n∑ kevent i [S]i

(8)

i

It should be noted that binding event residence times “toff” may also be used to distinguish events, but using just the event magnitude makes the analysis much simpler and is better suited for multiple channels, since residence time can only be ascertained unambiguously for a single ion channel. An instrumental set up with low noise levels and a good time resolution, to allow for complete blocking to be observed, would be favored in this scenario. Multiple channel data shows the same characteristic blockade events as single channel, with the added complexity resulting from multiple blockade events occurring simultaneously. The likelihood of multiple simultaneous blockade events is increased at higher channel number and S7βCD concentration. Multiple binding event thresholds are required for multiple channels, which requires explicit knowledge of the number of active (identical) ion channels in the membrane. For example, using two αHL ion channels, binding event thresholds were set for > 7 pA less than the open channel currents (i.e. < 140 pA and ≥ 68 pA for a single binding event and < 68 pA for two simultaneous binding events) (Figure 5a). As for the single channel data, current values were binned to the nearest number of unblocked channels, to give idealized data (to either 2, 1 or 0 open channels) (Figure 5b). Finally, the leading edges of these binding events allows for an event frequency to be calculated, using the newly defined value of τevent.


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Figure 5. a) Current-time trace for the ionic current through two αHL ion channels, using an applied potential of 100 mV cis vs. trans, with 0.040 mM S7βCD in the trans side. b) Zoom-in of highlighted region in a) showing i) raw data, ii) idealized current data (i.e. whole number of unblocked ion channels) and iii) event frequency.

Data obtained at low concentration (up to 0.05 mM S7βCD) and low number of ion channels (up to 5 channels) provided quantitative concentration information from the binding event frequency (Figure 6). The lines of best fit from the calibration plots (Figure 6a) were used to produce a three-dimensional (3D) surface (Figure 6b). Although non-integer values of the number of channels are not possible,


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plotting the data in this way is useful to show extrapolation to higher ligand concentrations and numbers of ion channels.

Figure 6. a) Calibration plot showing event frequency for 1 to 5 channels, using 0 – 0.05 mM S7βCD. The gradients of these lines provide the binding event rate constants, kevent, for 1 to 5 channels. Error bars are estimated from the central limit theorem for the wait time distribution. b) 3D plot of frequency vs. number of ion channels and concentration of S7βCD, using data obtained at low concentration (up to 0.05 mM) and up to 5 channels.

Extrapolated data from single channel binding predicts binding event frequencies for multiple channels and increased target concentration. In fact, a full 3D calibration surface can be obtained from a short series of concentrations at a single ion channel, using the principle of superposition of Poisson processes to deduce multiple channel responses. The gradients of the event frequency vs. concentration calibration plots obtained from the statistical analysis of data for 1 to 5 channels (Figure 6) give the binding event rate constants (using equation 5), which are a measure of the sensitivity of the sensor. The values of kevent are plotted against number of channels, which shows the sensitivity increasing linearly with increasing number of channels (Figure 7d). The gradient of this line is 47 s-1 mM-1 per channel, i.e.


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essentially the rate constant for a single channel (measured to be 48 s-1 mM-1). This clearly demonstrates the principle of superposition of a multiple Poisson point processes.

Figure 7. a) 3D plot of frequency vs. number of ion channels and concentration of S7βCD, using data obtained at low concentration (up to 0.05 mM) for one channel, extrapolated for multiple channels and higher concentration. b) 3D plot of frequency vs. number of ion channels and concentration of S7βCD, using extrapolation of data obtained at low concentration for one channel. c) Calibration plot showing event frequency for 1 to 4 channels, at high concentrations (using 0 – 5 mM) of S7βCD. d) The gradients of the lines of event frequency against S7βCD concentration (i.e. binding event rate constants, kevent) for ACS Paragon Plus Environment

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1 to 5 channels using data obtained at low concentration (up to 0.05 mM, black line) and high concentration (up to 5 mM, red line). Lines of fit are forced through the origin.

Providing a Threshold for Observing Poisson Process. Ion channel-based sensors will have an analytical working range for number of ion channels or ligand concentration that will be defined by the lower and upper limits of quantification (LLOQ and ULOQ). The ULOQ is related to the maximum frequency at which quantification is possible, and is governed by two dominant factors (Figure 8). Firstly, the time resolution of the measurement, limited by the data collection rate of the instrumentation (dead time).46 Secondly the dissociation time of the binding molecule, τoff, will limit the maximum concentration of analyte that can be quantified, since only one molecule can occupy one channel at a time. The time resolution limit means that, provided the concentration is low enough, many channels may constitute a quantitative sensor.

Figure 8. i) Schematic of how the 3D plots in Figure 7 can be used as a guide for data collection parameters. The horizontal transparent grey plane at a specific λ corresponds to the theoretical maximum obtainable rate, which defines the conditions for quantitative analysis (ULOQ), whilst the vertical transparent grey plane corresponds to the maximum quantifiable concentration. ii) Current-time ACS Paragon Plus Environment

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trace shows single channel data at 0.1 mM S7βCD. iii) Current-time trace in 100 mM S7βCD shows the channel(s) predominantly in the closed state, and seldom in a fully open state. This makes assigning the number of channels difficult. In this extreme case, where the channel does not adequately reach an unblocked state, events become merged and the number of events is grossly underestimated using the threshold analysis method.

It is more likely that current blockades are so closely separated (i.e. low τon) that events merge and the frequency of events is underreported due to a data collection rate that is too slow to distinguish individual events. This would also manifest itself in longer τoff times, although this information can be lost in multiple ion channel recordings with multiple simultaneous events. Dwell times, τoff, are independent of concentration and τoff does not affect τon. We therefore tested the system at a higher series of concentrations, that would be expected to give an underestimate of the binding rate, due to τon times that are sufficiently short that binding events merge and some stochastic information is lost. The results of the statistical analysis of data obtained for 1 to 5 channels at high S7βCD concentration (up to 5 mM) show much lower rates than predicted by extrapolation of low concentration data (Figure 7c). As previously, using equation 5, the gradients of these lines provide the binding event rate constants, kevent, which are all significantly less than expected (Figure 7d). The gradient of this line is 10 s-1 mM-1 per channel, when forced through the origin, which is around 5 times smaller than the expected gradient. This shows a failure of quantification and loss of the ability to use Poisson statistics, due to working above the ULOQ. Multiple ion channel measurements are advantageous over single channels, given that they maintain the high signal-to-noise ratio for small numbers of ion channels, and offer increased sensitivity. With very large numbers of ion channels, i.e. approaching bulk-type measurements, the signal-to-noise level will decrease and the importance of high time resolution becomes more apparent. Our work is intended to act as a guide to multiple ion channel or nanopore stochastic measurements, to optimize the number of channels to obtain high sensitivity, operating below the ULOQ. ACS Paragon Plus Environment

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For example, using an average value of τoff of 14 ms, determined for 1 channel, the maximum number of events at infinitely small τon is 70 s-1. Obtaining such a measurement would be unlikely, given that this would not constitute a stochastic process, and fully open channel occupancy may not be realized (Figure 8). At such high S7βCD concentration, and when high sensitivity is not required, a single channel calibration using the ratio of open and closed channel occupancy (Figure 1b i) will provide a more appropriate and easily accessible quantitative analysis (Figures S-1, S-2 and S-3, Supporting Information). Using multiple channels will be preferred at lower analyte concentration and when increased sensitivity is necessary. Ultimately, with an infinitely small time resolution, it would be possible to quantify the event frequency of any Poisson arrival process with very large numbers of channels, provided that the concentration is sufficiently low that extended τoff times, due to overlapping events, would not occur. However, this is also true for using this method of analysis for single channel measurements. In practice, the only limitations of using very large numbers of identical ion channels are simply the instrumental time resolution and signal-to-noise ratio, which are inherently linked. We presented data for up to 5 channels, well below the upper limit. There are two limiting factors that will govern the upper limit for the number of channels, for a given concentration; time resolution and signal-to-noise. Regarding signal-to-noise, the limit of detection of a single binding event is 3 standard deviations (SDs) of the noise of the open channel current. For 5 channels, we observed a binding event as a decrease in current of about 13 times the SD of the noise of the current associated with 5 open channels (which was also about the same difference for a single binding event at one open channel). The noise level will scale with number of channels, but so long as the binding event is 3 SDs of the noise (of the open channel current) and the time resolution is sufficient to distinguish events at a given concentration, then the measurement will be within the limit. Within the field of nanopore sensing, it is apparent that single nanopore measurements dominate the literature. Studies on large numbers of ion channels within a whole cell membrane, typically using patch clamp techniques, provide information on large changes to environment or concentration. Our paper addresses the intermediate regime; multiple nanopores in a single sensor. ACS Paragon Plus Environment

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CONCLUSIONS In this report, we introduced a framework to quantitatively measure the ion channel activity of multiple protein channels simultaneously embedded in an artificial lipid bilayer membrane for singlemolecule stochastic nanopore sensing. While we present a quantitation of the flux of S7βCD molecules detected by multiple αHL channels simultaneously, this quantitative framework is generalizable and can be used in the stochastic nanopore-based analysis of other target molecules. This is widely applicable to multiple nanopore and multiple ion channel measurements. This multiple channel analysis can be readily incorporated into existing data analysis software that works well for single channel analysis. Our analysis is presented for a single analyte species, although samples with multiple components capable of blocking could be achieved using defined thresholds based on their identity. We show that multiple ion channels lead to increased sensitivity and provide a quantitative framework for rate analysis that can be obtained from a concentration calibration of a single ion channel. We expand this by showing that there is a limit at high concentration and high number of channels that is due to the time resolution of the measurement based on the ligand dwell time in the channel and the instrumental time resolution. We believe that this analytical approach will provide a more quantitative understanding of the specific molecular flux measurements enabled by the recently developed bio-SICM technique,16 as well as other stochastic nanopore-based chemical and imaging studies.

ASSOCIATED CONTENT Supporting Information This material is available free of charge via the Internet at http://pubs.acs.org. Modified experimental setup for high concentration, single channel calibration using ratio of open and closed channel occupancy, and histograms of τevent. (PDF). AUTHOR INFORMATION ACS Paragon Plus Environment

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Corresponding Author * Corresponding author: email [email protected] Present Address †

Present address: Department of Chemistry, University of Cincinnati, Cincinnati, Ohio 45221.

‡

Present address: Department of Chemistry, University of Utah, Salt Lake City, Utah 84112.

Notes The authors declare no competing financial interest.

Acknowledgements The authors would like to thank the National Science Foundation (NSF) (grant number CHE1608679) for funding. In addition, this work was supported by the American Chemical Society (ACS) Division of Analytical Chemistry (DAC) Summer Fellowship, sponsored by the Society for Analytical Chemists of Pittsburgh (SACP) (F. C. Macazo – 2016 ACS DAC Fellow).

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Graphical Table of Contents


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Quantitative Framework for Stochastic Nanopore Sensors Using

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