Protein Ligand-Induced Amplification in the 1/f Noise of a Protein-Selective Nanopore

Abstract

Previous studies of transmembrane protein channels have employed noise analysis to examine their statistical current fluctuations. In general, these explorations determined a substrate-induced amplification in the Gaussian white noise of these systems at a low-frequency regime. This outcome means a lack of slowly appearing fluctuations in the number and local mobility of diffusing charges in the presence of channel substrates. Such parameters are among the key factors in generating a low-frequency 1/f noise. Here, we show that a protein-selective biological nanopore exhibits a substrate-induced amplification in the 1/f noise. The modular composition of this biological nanopore includes a hydrophilic transmembrane protein pore fused to a water-soluble binding protein on its extramembranous side. In addition, this protein nanopore shows an open substate populated by a high-frequency current noise due to the flickering of an engineered polypeptide adaptor at the tip of the pore. Yet, the physical association of the protein ligand with the binding domain reversibly switches the protein nanopore from a high-frequency noise substate into a quiet substate. In the absence of the protein ligand, our nanopore shows a low-frequency white noise. Remarkably, in the presence of the protein ligand, an amplified low-frequency 1/f noise was detected in a ligand concentration-dependent fashion. This finding suggests slowly occurring equilibrium fluctuations in the density and local mobility of charge carriers under these conditions. Furthermore, we report that the excess in 1/f noise is generated by reversible switches between the noisy ligand-released substate and quiet ligand-captured substate. Finally, quantitative aspects of the low-frequency 1/f noise are in accord with theoretical predictions of the current noise analysis of protein channel-ligand interactions.

Graphical Abstract

INTRODUCTION

β-barrel protein pores, porins, and channels represent key permeation mechanisms across outer membranes of Gram-negative bacteria, mitochondria, and chloroplasts.^{1, 2} In addition, toxins secreted by various pathogens form β-barrel pores that induce cell lysis once inserted into a target membrane.^{3, 4} Standard single-channel analysis of the time domain in the form of time-resolved events identified that these proteins exhibit current transitions among various substates, spanning a broad range of durations. Yet, using the analysis of the frequency domain through a fast Fourier transformation (FFT) approach, the power spectral density (PSD) of these proteins revealed the amplitude distribution of the statistical current fluctuations measured at various frequencies. Wohnsland and Benz (1997)⁵ have previously documented that the open state of many bacterial β-barrel porins exhibits 1/f noise in the low-frequency regime (0 – 100 Hz), or the so-called flicker noise.^{6, 7} 1/f noise is generated by slowly occurring equilibrium fluctuations in the number and local diffusion of charge carriers.^{7, 8} Previous studies have demonstrated that 1/f flicker noise is ubiquitous in protein pores,^{9, 10} porins,^11-14, and channels,^{15, 16} as well as in other ion-conduction synthetic systems, such as solid-state nanopores.^{10, 17-26} However, some β-barrel proteins^27-30 showed a frequency-independent Gaussian white noise in a broader frequency range, including the low-frequency regime. The absence of the frequency-dependent 1/f noise at low frequencies indicates the lack of significant equilibrium fluctuations in the density and local mobility of charge carriers across these β barrels. Very recently, Dekker and coworkers (2020) have reviewed the comparisons and contrasts of different aspects of current noise in biological and synthetic nanopores.¹⁰

In general, two distinct protein systems have been previously observed with respect to substrate-induced modulation of the excess spectral noise. First, there are protein pores, porins, and channels, such as staphylococcal α-hemolysin (αHL)^27-30 and outer membrane protein F (OmpF)^{31, 32} of E. coli, which exhibited a flat “white noise” in the low-frequency regime in the absence of any chemical agent. Yet, the presence of a small-molecule ligand at concentrations near half of the equilibrium dissociation constant, K_d, produced an excess in the white noise of these protein systems. Second, there are other protein systems, such as protective antigen (PA₆₃) channel of anthrax toxin^{33, 34} and maltoporins,^{11-14, 35-37} which showed a 1/f flicker noise in the low-frequency domain. However, the addition of a small-molecule ligand or a channel blocker ignited an excess in the white noise in this low-frequency range.^{11-14, 33-37} Therefore, these prior studies indicated that the small-molecule ligands significantly increase the white noise in the low-frequency domain.

In this paper, we provide compelling experimental evidence that a protein-selective β-barrel protein nanopore shows a protein ligand-induced amplification in the frequency-dependent 1/f noise. The functional architecture and modular composition of this protein nanopore are inspired by the structure-function properties of outer membrane proteins of Gram-negative bacteria. Specifically, its transmembrane stem is the β barrel of ferric hydroxamate uptake component A (FhuA)^{38, 39} of Escherichia coli. This is a 455-residue single-polypeptide protein, also called t-FhuA (Fig. 1a).⁴⁰ The binding domain of the nanopore is a 110-residue, water-soluble RNAse barnase (Bn),⁴¹ which cannot fit within the hydrophilic pore interior. Therefore, Bn was tethered outside the t-FhuA pore, at its N terminus, through a flexible Gly/Ser-based hexapeptide. This was the basis for generating a synthetic Bn-t-FhuA nanopore (Experimental Section).⁴⁰ Barstar (Bs),⁴² the high-affinity 89-residue inhibitor for Bn, was employed as a protein ligand.⁴³ Previously, the Bn-Bs complex formation has been readily observed at single-recognition event precision in homogeneous solutions⁴⁰ and in heterogeneous biological fluids.⁴⁴ These explorations were facilitated by the presence of a dodecapeptide adaptor (O), which was engineered at the N terminus of Bn.

Figure 1: The composition of Bn-t-FhuA, a protein-selective protein nanopore.

(a) This single-polypeptide protein nanopore comprises a heavily truncated ferric hydroxamate uptake protein A of E. coli (t-FhuA), which is marked in blue.⁴⁸ This truncated β-barrel outer membrane protein pore, which serves as the transmembrane permeation pathway of ions, was fused, at its N terminus, to a barnase (Bn, marked in green) protein via a flexible Gly/Ser-based hexapeptide tether (marked in magenta).⁴⁰ An unstructured dodecapeptide adaptor (O, marked in orange), at the N terminus of Bn, flickered at the tip of the pore opening. (b) A snapshot of a single-channel electrical trace of Bn-t-FhuA when barstar (Bs, marked in red) was added to the cis side of the chamber. Bs produced stochastic conductance switches between high-frequency current noise-generated substates and high-frequency current noise-quenched substates.

Here, we analyze these Bn-Bs interactions at a very broad bandwidth and show that Bn-t-FhuA exhibits an open substate of high-frequency current noise in the absence of Bs. This high-frequency current noise is likely due to frequent and short-lived moieties of the adaptor, O, at the tip of the t-FhuA pore (Fig. 1b). In contrast, our protein-selective biological nanopore lies in a quiet substate when Bs is transiently captured by the Bn binding domain. In the latter case, the O adaptor is likely detached from the pore opening. Reversible Bn-Bs complex formations within the extramembranous side of t-FhuA can be observed through stochastic alternations of the quiet substates and high-frequency noise events. Furthermore, when Bs was not present in solution, a uniform and voltage-dependent current noise of Bn-t-FhuA, which is reminiscent of a flat (“white”) noise, was noted in the low-frequency regime.

In this article, we provide experimental substantiation that the reversible switches of the Bs-captured and Bs-released substates produce a significant amplification in the frequency-dependent 1/f flicker noise.⁵ The maximum of the low-frequency 1/f noise amplification is reached at a Bs concentration near K_d/2, where K_d is the equilibrium dissociation constant. This experimental outcome is in accordance with theoretical predictions of the current noise analysis of ligand-gated ion channels. Remarkably, the presence of Bs at concentrations much greater than the K_d value abolished the amplification in the 1/f noise and reverted the signature of current noise of Bn-t-FhuA to a white-noise pattern in the low-frequency domain.

EXPERIMENTAL SECTION

Cloning and mutagenesis of the protein nanopore and protein ligand.

Conventional and assembly PCR techniques were employed to create all genes used in this work. Cloning was conducted using the pPR-IBA1 expression vector. The primary gene, obn(ggs)₂t-fhua, encoded the Bn-t-FhuA nanopore, which included the dodecapeptide adaptor (MGDRGPEFELGT), fused at the N-terminus of barnase (Bn), a flexible glycine/serine-rich hexapeptide arm (GGSGGS), as well as an extensively truncated ferric hydroxamate uptake protein A (t-FhuA) and KpnI sites at both ends.^{40, 44} This gene was developed using genes of individual Bn and t-FhuA proteins, bn and t-fhua, respectively, and assembly PCR reactions. An H102A mutant of Bn was used, because this suppressed RNase activity, so that Bn-t-FhuA is not toxic to the expression host.^{41, 45} In addition, the bs gene of the barstar (Bs) included a double-alanine mutant, C40A/C82A.⁴⁶

Protein expression, purification, and refolding.

Protocols for protein expression and purification of the Bn-t-FhuA nanopore were previously reported.^{47, 48} Lyophilized Bn-t-FhuA samples were solubilized in 200 mM KCl, 8 M urea, 50 mM Tris-HCl, pH 8 to a concentration of ~15 μM, then placed at room temperature for several hours. Refolding of the denatured Bn-t-FhuA samples was accomplished by adding n-dodecyl-β-D-maltopyranoside (DDM) to a final concertation of 1.5% (w/v).^{49, 50} Then, a slow dialysis of protein samples was conducted against 200 mM KCl, 20 mM Tris-HCl, pH 8, at 4 °C for at least 3 days. Bn-t-FhuA samples for single-channel electrical recordings were obtained by 20-fold dilution in 200 mM KCl, 20 mM Tris-HCl, pH 8, 0.5% DDM. For the Bs protein, transformed cells were grown in Luria-Bertani (LB) medium at 37°C until OD₆₀₀ was ~0.5. Then, the temperature was reduced to 20°C and induction was performed in the presence of IPTG.⁴⁰ The cells were further cultured for a period of ~18 hours using the same temperature. Cultured cells were centrifuged at 3,700×g at 4°C for 30 min, then resuspended in 150 mM KCl, 50 mM Tris-HCl, 5 mM EDTA, pH 8. This step was followed by cell lysis using a Model 110L microfluidizer (Microfluidics, Newton, MA). The supernatant and insoluble pellet were separated by centrifuging the lysates at 108,500 × g at 4°C for 30 min. Then, the supernatant, which was processed through ammonium sulfate precipitation, was dialyzed overnight at 4°C against 20 mM Tris-HCl, pH 8 and purified on a Q-Sepharose column (Bio-Rad, Hercules, CA). A further purification step was performed using size-exclusion chromatography via a Superdex-75 size-exclusion column (SEC; GE Healthcare Life Sciences, Pittsburg, PA).

Current noise and single-channel electrical recordings using planar lipid bilayers.

Standard protocols for single-channel electrical recordings were employed using planar lipid membranes.^{51, 52} The Bn-t-FhuA nanopore was added to the cis side of the chamber (Fig. 1a) at a final concentration in the range of 0.3-1 ng/μl. The cis side was grounded, meaning that an applied positive potential corresponds to the translocation of positive ions from the trans to cis side of the chamber. The electrolyte solution contained 300 mM KCl, 10 mM Tris-HCl, pH 8. All recordings were collected at room temperature (23 ± 1°C). Single-channel electrical currents were acquired using an Axopatch 200B patch-clamp amplifier (Axon Instruments, Foster City, CA). Electrical signals were digitized using a low-noise acquisition system, Model Axon 1440A (Axon Instruments), sampled at a frequency of 50 kHz, and filtered at a filter frequency of 10 kHz using a low-pass eight-pole Butterworth filter, Model 900B (Frequency Devices, Ottawa, IL), unless otherwise stated. Single-channel electrical data acquisition and analysis were executed using pClamp 10.5 software package (Axon) and Origin 8.5 (OriginLab, Northampton, MA).

The power spectral density (PSD) was generated in ClampFit (pClamp, Axon) by using a built-in power spectrum function applied to single-channel electrical traces. In this way, a fast Fourier transformation (FFT) method was digitally employed. The low-frequency limit of PSD, S(0), was determined from the lowest experimental frequency of the PSD of current noise. For the relationship S(0) ∝ (ΔI)², where ΔI is the absolute difference in the single-channel electrical currents between the Bs-released and Bs-captured substates, average values of these currents were determined from Gaussian fits of all-point histograms of these two open substates. Fits of 1/f^c flicker noise in the low-frequency domain of the PSD were conducted in a log-log representation and in the frequency range of (f_min, f_cut), where f_min and f_cut are the minimum experimental frequency in the PSD and the cut-off frequency, respectively. Here, f_cut is the experimental frequency that corresponds to the onset of the low-frequency 1/f flicker noise. Fits of white noise in the low-frequency domain of the PSD were conducted using a Lorentzian function,

$$S(f)=\frac{S(0)}{1+(\frac{f}{f_c}{)}^{{}^2}}$$ (1)

where f_c is the corner frequency. Filter frequencies of either 100 Hz or 1 kHz were also used for data analysis of the low-frequency domain (f_min – 100 Hz), as they do not affect the PSD of this spectrum range. In general, 15 individual 10 second-duration single-channel electrical traces, which were filtered at a frequency of 10 kHz using a low-pass eight-pole Butterworth filter, were used to obtain average values of low-frequency noise parameters S(0) and f_c,^{34, 53} unless otherwise stated. Shorter-duration electrical traces were also employed to analyze individual Bs-released or Bs-captured substates.

RESULTS AND DISCUSSION

Single-channel electrical signature of a protein-selective protein nanopore.

Our single-polypeptide chain protein nanopore, Bn-t-FhuA, consists of the t-FhuA pore,⁴⁰ an extensive truncation of the outer membrane protein FhuA^{38, 39} of E. coli, which was fused to Bn, a small RNase barnase (Fig. 1a).⁴¹ The fusion of both proteins was conducted at the N terminus of t-FhuA via a flexible Gly-Ser hexapeptide tether. This construct also included the O adaptor, a dodecapeptide extension fused at the untethered terminus of Bn (Experimental Section). This dodecapeptide is slightly negatively charged and unstructured in solution.⁵⁴ The O adaptor should cover the distance between the entrance of t-FhuA and the untethered terminus of Bn. A representative single-channel signature of our protein-selective nanopore, Bn-t-FhuA, is shown in Fig. 2a. At a transmembrane potential of −40 mV and in 300 mM KCl, 10 mM Tris-HCl, pH 8.0, this signature corresponds to an open-channel conductance, g_open, of 1.26 ± 0.02 nS (n = 3). g_open was determined using the average current corresponding to the peak maximum resulting from an all-points current amplitude histogram (Fig. 2a). This open substate (O_on) was populated by highly frequent and short-lived current spikes. Many current spikes were not time resolvable, so that they lacked well-defined current levels. Remarkably, the addition of 25.25 nM barstar (Bs)⁴² to the cis side of the chamber produced reversible switches between substates containing current spikes and substates free of current spikes (Fig. 2b, Supporting Information, Fig. S1). In the absence of the O adaptor, these Bn-Bs binding events were not noted in the current recordings, because these interactions occurred outside the t-FhuA nanopore.⁴⁰ Thus, the O adaptor produced distinctive current levels of the high frequency noise-generated open substate (O_on) and the high frequency noise-quenched open substate (O_off). For example, this resulted in shifting the high frequency noise-generated open substate (O_on) to the high frequency noise-quenched open substate (O_off), whose conductance, g*_open, was increased to 1.52 ± 0.02 nS (g*_open > g_open, n = 3) (Fig. 2b). g*_open was also calculated using the average current of the corresponding peak maximum, which resulted from an all-points current amplitude histogram.

Figure 2: High-bandwidth single-channel data acquisitions of Bn-t-FhuA in the presence of Bs.

Single-channel electrical traces, which were filtered at 1 kHz using a low-pass 8-pole Butterworth filter, are provided for Bs concentrations of 0 nM (a), 25.25 nM (b), 50.6 nM (c), and 100.9 nM (d) added to the cis side of the chamber. The O_on and O_off levels represent the Bs-released and Bs-captured substates. The applied transmembrane potential was −40 mV. The insert in (d) is an example of the Bs-released substate event. For the sake of clarity, this single-channel electrical trace was also filtered at 1 kHz using a low-pass 8-pole Butterworth filter. Corresponding all-point current amplitude histograms are displayed on the right side. Maxima of the peaks of the current amplitude represent substate “off” (Bs-captured event, O_off, left) and open substate “on” (Bs-released event, O_on, right). The following values are provided as mean ± s.e.m. (a) O_on was −49.4 ± 0.1 pA. (b) O_on and O_off were −50.6 ± 0.1 pA and −60.1 ± 0.1 pA, respectively. (c) O_on and O_off were −49.5 ± 0.1 pA and −59.4 ± 0.1 pA. respectively. (d) O_on and O_off were −50.6 ± 0.1 pA and −60.7 ± 0.1 pA, respectively. All-point current amplitude histograms were developed using 20-second duration single-channel electrical traces. The bin size of these histograms is 1 pA. These single-channel electrical traces are representative over a subset of at least n = 3 distinct experiments.

The frequency of the high frequency noise-quenched open substate events (O_off) was elevated at increased Bs concentrations (Fig. 2cd; Supporting Information, Fig. S1), leading to reduced durations of the high-frequency noise-generated substate events (O_on). Here, let us denote by τ_on and τ_off the average durations of the high frequency noise-generated open substate (O_on) and the high frequency noise-quenched open substate (O_off), respectively. Previously, we demonstrated that a change in 1/τ_on scaled in a ratio 1:1 with a change in the Bs concentration, whereas τ_off was independent on the Bs concentration.^{40, 44} This result was obtained at a highly increased signal filtering, so that these events were unambiguously determined through their current amplitudes, as the occurrence and suppression of the short-lived current spikes coincide with the current levels of the O_on and O_off events, respectively. Therefore, the O_on (corresponding to g_open) and O_off (corresponding to g*_open) substates represent the Bs-released and Bs-captured events. In this way, k_on = 1/([Bs]τ_on) and k_off = 1/τ_off are the association and dissociation rate constants, respectively, where [Bs] is the Bs concentration. In other words, the Bs-captured and Bs-released events occurred as bimolecular association and unimolecular dissociation processes, respectively. Interestingly, the unitary conductance of the quiet open substate of Bn-t-FhuA (O_off) was closely similar to those values recorded with an O adaptor-free Bn-t-FhuA pore or with a t-FhuA pore (g_t-FhuA = 1.6 ± 0.1 pS),⁴⁰ suggesting that Bn was indeed exclusively located on the extramembranous side of the nanopore.

What is the role played by the O adaptor?

To produce a detectable signal of the Bs-capture and Bs-release events, additional development of this protein sensor was necessary. The dodecapeptide O adaptor, which was engineered at the N terminus of the Bn binding domain, signals the physical associations and dissociations of Bs with Bn in real time. Without the O adaptor, Bn-t-FhuA exhibits a larger-conductance open substate (~1.52 nS) that is relatively quiet.⁴⁰ However, with the engineered O adaptor, Bn-t-FhuA shows a lower-conductance open substate (~1.26 nS) that is very noisy. Thus, the O adaptor not only produced a slightly lower conductance of the Bn-t-FhuA nanopore with respect to that of t-FhuA, but also created highly frequent and short-lived current spikes. Here, we tentatively interpret that a reduced transmembrane current and short-lived current spikes of the O_on substate result from the interactions of the slightly negatively charged O adaptor with the positively charged groups located on the nanopore entrance. The Bs-captured event, which was identified by the O_off substate, is accompanied by the detachment of the O peptide from the pore opening, thus increasing and quieting the transmembrane current. A comprehensive understanding of these conformational changes as well as their coordination with the single-channel current fluctuations might be accomplished by full-atomistic molecular dynamics (MD) simulations of the entire biomolecular system⁵⁵ and under similar experimental conditions. Insightful information from these MD simulations might prove instrumental for the extension of this approach to other protein ligand-protein receptor pair interactions.

The Bs-amplified 1/f noise of the Bn-t-FhuA nanopore.

Throughout this article, experimental values of the low-frequency limit, S(0), are the current noise amplitudes that correspond to the lowest measured frequency in the PSD. In the absence of Bs and at a zero transmembrane potential, we observed a flat (“white”) noise of Bn-t-FhuA with S(0) in the range of (2 – 6)×10⁻²⁹ A²/Hz (Fig. 3a; Supporting Information, Figs. S2-S7). These values were near the sum of the Johnson-Nyquest thermal noise^{12, 25, 56-60} of 2.06×10⁻²⁹ A²/Hz and shot noise^{12, 25, 58-60} of 1.61×10⁻²⁹ A²/Hz (Supporting Information, Supporting Methods):^{25, 61}

$$S_{\text{white}}=S_{\text{thermal}}+S_{\text{shot}}$$ (2)

Figure 3: Excess spectral density of current noise of the Bn-t-FhuA nanopore as a function of the Bs ligand concentration and at a negative transmembrane potential.

S(f) was obtained from a 10 second-duration single-channel electrical trace. Each trace included both the Bs-released and Bs-captured substates. Single-channel electrical traces were filtered at 10 kHz using a low-pass eight-pole Butterworth filter. (a) Representative PSD of current noise of the Bn-t-FhuA nanopore in a log-log representation. The PSD was averaged over n = 15 different PDSs obtained from distinct single-channel electrical traces. Data were recorded at 0 mV without Bs (black), at −40 mV without Bs (red), and at −40 mV in the presence of 25.25 nM Bs (navy). (b) A linear-scale plot that shows the comparison of model-dependent S(0) with experimental S(0), which was recorded from the PSD of current noise, versus the Bs concentration. The low-frequency limit of the excess spectral density, S(0), was obtained as average over 15 distinct 10 second-duration single-channel electrical traces recorded from n = 3 distinct experiments at a transmembrane potential of −40 mV. Data points represent mean ± s.d. obtained from n = 3 distinct experiments.

These values were obtained using the single-channel conductance of ~1.26 nS for Bn-t-FhuA (Fig. 2a). This white-noise signature was also noted at both negative and positive transmembrane potentials (Supporting Information, Figs. S4-S7, Table S1). The Bs-free and Bs-amplified S(0) were proportional to either the square of transmembrane potential or to the square of transmembrane current (Supporting Information, Figs. S8-S9, Table S2). Therefore, S(0) corresponds to a quadratic function that depends on the applied transmembrane potential, a situation also found with other porins¹⁴ or other solid-state systems.^{6, 62}

Remarkably, at a transmembrane potential of −40 mV, the presence of 25.25 nM Bs drastically enhanced the low-frequency limit of the PSD of current noise, S(0), almost four orders of magnitude with respect to the background current noise in the absence of Bs (Fig. 3a). Moreover, the profile of the Bs-amplified current noise is reminiscent of low-frequency 1/f flicker noise, which had an onset at a cut-off frequency, f_cut, of ~40 Hz. However, Bs-dependent S(0) followed a biphasic dependence on the Bs concentration (Fig. 3b; Supporting Information, Figs. S10-S15). For example, S(0) increased from (12.2 ± 0.6)×10⁻²⁷ A²/Hz in a Bs-free solution (Supporting Information, Table S2) to (42.9 ± 5.6)×10⁻²⁴ A²/Hz and (71.1 ± 9.7)×10⁻²⁴ A²/Hz at Bs concentrations of 12.63 and 25.25 nM, respectively (Supporting Information, Table S3). Then, S(0) gradually decreased at Bs concentrations greater than 25.25 nM. The biphasic pattern of S(0) with respect to the substrate concentration was also discovered when small-molecule analytes interacted with binding sites within protein pores.^{27, 28, 36, 63} In this work, the maximum of the low-frequency limit of excess 1/f noise was reached at a Bs concentration near half of the K_d. This outcome agrees well with previous theoretical estimates of the dependence of S(0) on the substrate concentration.^{27, 64}

The current dependence of S(0) is given by the following formula:⁶⁴

$$S(0)=4(\Delta I{)}^2{\tau }_{\text{off}}\frac{\frac{[L]}{K_{\mathrm{d}}}}{{\left(1+\frac{[L]}{K_{\mathrm{d}}}\right)}^3}$$ (3)

where, ΔI is the absolute difference in the transmembrane current between the Bs-captured and Bs-released substates. Here, [L] and K_d denote the Bs concentration and the equilibrium dissociation constant, respectively. τ_off is the binding duration, which is the reciprocal of the dissociation rate constant, k_off. Eq. (3) exhibits a maximum value at a Bs concentration equal to one half of the K_d:

$$S(0)\to S(0{)}_{max}when[L]=\frac{K_d}{2}$$ (4)

In this case,

$$S(0{)}_{max}=\frac{16}{27}(\Delta I{)}^2{\tau }_{off}$$ (5)

Therefore, S(0)_max depends on the current difference between the two substates and the binding duration. Using the time-resolved analysis of current events with an absolute current difference between the Bs-captured and Bs-released substates, ΔI = 10 pA, the equilibrium dissociation constant, K_d = 64 nM, and the rate constant of dissociation, k_off = 0.86 s⁻¹,⁴⁰ we obtain a model-dependent S(0)_max = 68.9×10⁻²⁴A²/Hz, a value that is closely similar to that experimentally determined at a Bs concentration of 25.25 nM. Indeed, this Bs concentration is close to K_d/2, which is in accord to Eq. (4) (Fig. 3b). This experimental finding is in good agreement with theoretical predictions of the low-frequency limit of the PSD (Supporting Information, Figs. S16-S17, Tables S3-S4).^{27, 64}

What is the source of the low-frequency 1/f flicker noise?

We then asked whether the dependence of S(0) on the Bs concentration is reflected by the PSD of either the Bs-captured events or Bs-released events. A detailed analysis of these events illuminated that S(0) of the Bs-released events was amplified by the presence of Bs in a biphasic signature (Supporting Information, Figs. S18-S19). This pattern was qualitatively similar to that noted in Fig. 3b (Supporting Information, Figs. S16-S17). On the contrary, S(0) of the Bs-captured events was reduced, yet independently of the Bs concentration in the range of 12.63 nM – 627.3 nM (Supporting Information, Figs. S20-S22). Therefore, the presence of the Bs has an opposite effect on the substates of the Bn-t-FhuA nanopore, increasing S(0) of the Bs-released events, but decreasing S(0) of the Bs-captured events. Enhancing the Bs concentration shortens the total duration of the Bs-released substate and lengthens the total duration of the Bs-captured substate. Hence, we postulate that the Bs concentrations in excess would normally lead to a significant reduction in the current noise (see below). Furthermore, the Bs-released substate and the Bs-captured substate are virtually 1/f noise-free in the low-frequency domain (Supporting Information, Figs. S20-S21). This outcome suggests that the discrete current switches between the Bs-captured and Bs-released substates (Figs. 1-2) contribute at least in part to the generation of low-frequency 1/f flicker noise.¹²

Is the low-frequency limit of the 1/f noise biphasic at a positive potential as well?

We then asked whether the Bs-amplified 1/f current noise, which was noted in a biphasic pattern with respect to the Bs concentration, can also be acquired at a positive potential. If so, are the experimental S(0) values in accordance with theoretical predictions of the current noise analysis? Therefore, we examined the spectral noise, both quantitatively and qualitatively, at a positive transmembrane potential. Single-channel electrical recordings in the presence of low-nanomolar Bs concentrations at a transmembrane potential of +15 mV are illustrated in Fig. 4. In the absence of Bs, the unitary conductance, g_open, of Bn-t-FhuA was 1.42 ± 0.01 nS (O_on; Bs-released substate; Fig. 4a). Yet, in the presence of Bs, transient openings of Bn-t-FhuA to an O_off substate of conductance, g*_open, of 1.48 ± 0.02 nS (g*_open > g_open, n = 3, Bs-captured substate; Fig. 4b) occurred in a concentration-dependent fashion (Figs. 4bcd; Supporting Information, Fig. S23). Interestingly, under similar experimental conditions, the absolute current difference between the O_on and O_off substates, ΔI, was ~1.2 pA at +15 mV, a significantly lower value than that acquired at −40 mV (~10 pA). These current difference values correspond to conductance difference values, Δg, of ~0.08 nS and 0.25 nS, respectively.

Figure 4: High-bandwidth single-channel electrical recordings of Bn-t-FhuA in the presence of Bs at a positive potential.

Single-channel electrical traces, which were filtered at 100 Hz using a low-pass 8-pole Butterworth filter, are provided for Bs ligand concentrations of 0 nM (a), 25.25 nM (b), 50.6 nM (c), and 100.9 nM (d) added to the cis side of the chamber. The Oon and Ooff levels represent the Bs ligand-released and Bs ligand-captured open substates. The applied transmembrane potential was +15 mV. The following values are provided as mean ± s.e.m. (a) O_on was 21.0 ± 0.1 pA. (b) O_on and O_off were 21.1 ± 0.1 pA and 22.4 ± 0.1 pA, respectively. (c) O_on and O_off were 20.9 ± 0.1 pA and O_off is 22.4 ± 0.1 pA, respectively. (d) O_on and O_off were 21.1 ± 0.1 pA and 22.4 ± 0.1 pA, respectively. Corresponding all-point current amplitude histograms are displayed on the right side. Multiple-peak Gaussian fittings were used. Maxima of the peaks of the current amplitude represent substates “off’ (O_off, right) and “on” (O_on, left). The all-point current amplitude histograms were developed using 20 s-duration single-channel electrical traces. The bin size of these histograms is 0.2 pA. These single-channel electrical traces are representative from a subset of at least n = 3 distinct experiments.

Remarkably, the low-frequency domain also showed a 1/f-type noise signature (Fig. 5a). Moreover, the Bs-induced excess in 1/f current noise depended on the Bs concentration in a biphasic fashion (Fig. 5b), which is reminiscent of the outcomes resulted at a transmembrane potential of −40 mV. Here, S(0) can also be calculated using Eq. (3), along with parameters derived from time-resolved analysis of discrete events. Using ΔI = 1.2 pA, K_d = 60 nM, and k_off = 0.95 s⁻¹,⁴⁴ we obtain model-dependent S(0) values, which are closely similar to experimentally-determined S(0) values (Fig. 5b; Supporting Information, Fig. S24, Table S5). The biphasic signature of S(0) resulted, at least in part, from the alteration in the slope of 1/f current noise with respect to the Bs concentration. Hooge’s phenomenological formula of the low-frequency 1/f current noise is:^{5, 65-67}

$$S(f)=\frac{\alpha I_0^2}{N{f}^c}$$ (6)

where I₀ is the open-state single-channel current. N and f denote the number of channels in the membrane and frequency, respectively. c is a constant. Here, α is Hooge’s phenomenological parameter of current noise. We obtained values of α in the range of 0.001 - 0.002 at low-nanomolar Bs concentrations and at a transmembrane potential of −40 mV (Supporting Information, Table S3). Yet, these values were significantly lower, in the range of 0.0003 – 0.0005, at a transmembrane potential of +15 mV (Supporting Information, Table S5). Our Hooge’s parameters are in accordance with those previously determined by other groups using various protein pore systems.^{5, 12}

Figure 5: Excess spectral density of current noise of the Bn-t-FhuA nanopore as a function of the Bs ligand concentration and at a positive transmembrane potential.

The low-frequency limit of the excess spectral density, S(0), was obtained as a mean from 15 distinct 5 second-duration single-channel electrical trace intervals recorded at a transmembrane potential of +15 mV. Each trace included both the Bs-released and Bs-captured substates. Single-channel electrical traces were further low-pass filtered at 100 Hz using an eight-pole Butterworth filter. (a) Representative PSDs of current noise recorded at various Bs ligand concentrations. PSDs illustrated in this panel were averaged over n = 15 different PDSs obtained from n = 15 distinct single-channel electrical traces. (b) Comparison of model-dependent S(0) with experimental S(0) recorded from PSD from (a). Data points represent mean ± s.d. obtained from n = 3 distinct experiments.

The low-frequency 1/f-type noise signature is abolished at a high occupancy of Bn.

Next, we wanted to explore whether the Bs-induced 1/f noise is yet present at Bs concentrations much greater than the K_d, under conditions of high occupancy of Bn-t-FhuA by Bs (Supporting Information, Figs. S25-S28, Table S6). Thus, Bn-t-FhuA was exposed to low-micromolar Bs concentrations, which were in the range between a 20- and 80-fold increase with respect to the K_d. In accordance with our expectation, S(0) was drastically reduced in this range of the Bs concentration (Supporting Information, Fig. S29). In addition, the very low-frequency regime (0.2 Hz < f < 30 Hz) of the PSD showed a rather white-noise signature (Supporting Information, Figs. S30-S31). This finding suggested that the Bs-amplified 1/f noise signature was nearly eliminated at Bs concentrations approaching the saturation of the Bn binding site. We observed that S(0) recorded at Bs concentrations in excess gradually decreased by increasing the Bs concentration (Supporting Information, Table S7). For example, excess of Bs at a concentration of 4.8 μM, which is about ~150-fold of the K_d/2, produced a significant, 530-fold reduction in the 1/f flicker noise with respect to its maximum value, S(0)_max. Yet, S(0) was about one order of magnitude greater at 4.8 μM Bs than the value recorded in the absence of Bs under similar experimental conditions. This is a significantly reduced S(0) value with respect to that acquired at 25.25 nM Bs (Fig. 3a). Finally, the onset of the white-noise plateau, in the form of a corner frequency, f_c,¹⁴ increased at greater Bs concentrations (Supporting Information, Fig. S32, Table S8).

Voltage dependence of the low-frequency 1/f flicker noise.

We also asked whether the 1/f flicker noise can be revealed at other transmembrane potentials than those presented above. Therefore, we have extensively explored the low-frequency domain at transmembrane potentials in the range of −50 mV through +50 mV (Supporting Information, Figs. S33-S37). Fig. 6a shows representative examples of the PSD of Bn-t-FhuA recorded at transmembrane potentials of ±5 mV and ±40 mV and in the presence of 12.63 nM Bs. These examples demonstrate that the low-frequency limit of the PSD increases by decreasing the frequency. In a log-log plot, linear fits of data for the low-frequency domain show a 1/f^c signature, where c is the power constant that was always greater than unity (Fig. 6b, Supporting Information, Table S9). We also noted that the frequency onset of the 1/f^c signature of the PSD, f_cut, was voltage dependent and slightly increased by enhancing the applied transmembrane potential in a U-shape fashion with respect to the voltage bias. Therefore, the 1/f noise signature is a conserved property regardless of the applied transmembrane potential. However, a greater transmembrane potential expands the range of the low-frequency domain that is subjected to this 1/f noise signature.

Figure 6: Low-frequency domain of the excess spectral density of current noise of the Bn-t-FhuA nanopore at various transmembrane potentials.

S(0) was obtained as mean ± s.d. from 15 distinct 5 second-duration traces recorded at 12.63 nM Bs. Each trace included both the Bs-released and Bs-captured substates. Single-channel electrical traces were further filtered at 100 Hz using a low-pass eight-pole Butterworth filter. (a) Representative averaged PSD of single-channel current noise recoded at various transmembrane potentials. PSDs illustrated in this panel were averaged over n = 15 different PDSs obtained from n = 15 distinct single-channel electrical traces. (b) Linear fits of the PSD data from (a) shown in a log-log representation.

The lower S(0) values at positive potentials with respect to negative voltage biases can be explained in terms of the lower absolute current difference, ΔI, between the Bs-captured and Bs-released substates. We employed Hooge’s phenomenological formula (Eq. 6) for examining the characteristics of the Bs-amplified 1/f noise of the nanopore. However, we found that α, Hooge’s phenomenological constant, was slightly greater at negative potentials (> 0.001) than at positive potentials (< 0.001) (Supporting Information, Table S9), suggesting an asymmetry of the 1/f flicker noise with respect to the voltage bias. Therefore, 1/f flicker noise of the Bn-t-FhuA nanopore is characterized by a voltage asymmetry. This finding is not surprising, given that t-FhuA shows a permeability ratio P_K/P_Cl of 5.5 ± 1.7 in the asymmetric condition of 20 mM KCl/200 mM KCl.⁶⁸ Therefore, t-FhuA is a non-ohmic transmembrane protein pore. The asymmetry of 1/f noise with respect to the voltage bias was also discovered in other non-ohmic nanopores.²² Interestingly, the slope of the function S(f) in a log-log representation was c with values between 1 and 2. In general, maltoporins and other bacterial outer membrane proteins showed an ideal 1/f flicker noise function with c ≅ 1.0.^{5, 12} However, deviations from the ideality of 1/f flicker noise have been determined in other cases.^{15, 18, 69} It is not clear what the physical meaning of the departure of c from this ideality is. One possibility is that the low-frequency domain of the PSD is populated by a hybrid mixture of a 1/f noise factor and two or more Lorentzian distributions of white noise with different corner frequencies.^{70, 71} Here, this hypothesis is supported by the complex combination of a number of factors, such as the lack of 1/f noise from either Bs-released or from Bs-captured substates, the dependence of S(0) of the Bs-released substate on the Bs concentration, and the dependence of the frequency onset (f_cut) of the 1/f noise on the transmembrane potential.

CONCLUSIONS

In this paper, we provide experimental evidence for the Bs-amplified 1/f noise of a protein-selective protein nanopore. Amplification in the low-frequency limit of current noise, S(0), has been previously observed for ion channels permeating small-molecule analytes, such as protons,^{27, 28, 31} sugars^{14, 36}, nucleotides,^{64, 72} and antibiotics.⁷³ Bn-t-FhuA also serves for explorations of reversible protein-protein interactions in real time and protein detection in aqueous phase at single-molecule precision. Related protein nanopores have been previously developed by other groups using a diverse range of recognition elements, such as small molecules,^74-77 DNA aptamers,⁷⁸ and peptides.^{30, 79} The fundamental distinction of Bn-t-FhuA from other highly specific nanopores for protein detection is the relatively large size of the recognition element, in this case a 110-residue Bn protein.

In summary, we show significant qualitative and quantitative alterations in the low-frequency current noise regime of a protein-selective biological nanopore when a protein ligand is reversibly captured by its recognition element. This Bs-amplified 1/f noise is asymmetric with respect to the voltage bias and can be reverted back to a white-noise signature at Bs concentrations in excess. The reversible Bs-induced conductance switches appear to generate, at least in part, the 1/f noise in a Bs concentration-dependent fashion, because the Bs-captured and Bs-released substates are virtually 1/f noise-free. It should be noted that these Bs-Bn binding interactions occur near the opening of the t-FhuA pore, so that we conclude that the low-frequency 1/f flicker noise results from subtle Bs-induced alterations in the pore dynamics at the tip of the pore. Finally, this Bs-amplified low-frequency 1/f noise is likely generated by equilibrium conductance fluctuations, because the low-frequency limit of the current noise, S(0), is proportional to the square of applied transmembrane potential.^{7, 12, 72}