Effect of single nanoparticle-nanopore interaction strength on ionic current modulation

Abstract

Solid-state nanopores are rapidly emerging as promising platforms for developing various single molecule sensing applications. The modulation of ionic current through the pore due to translocation of the target molecule has been the dominant measurement modality in nanopore sensors. Here, we focus on the dwell time, which is the duration taken by the target molecule or particle to traverse the pore and study its dependence on the strength of interaction of the target with the pore using single gold nanoparticles (NPs) as targets interacting with a silicon nitride (SiN) nanopore. The strength of interaction, which in our case is electrostatic in nature, can be controlled by coating the nanoparticles with charged polymers. We report on an operating regime of this nanopore sensor, characterized by attractive interactions between the nanoparticle and the pore, where the dwell time is exponentially sensitive to the target-pore interaction. We used negatively and positively charged gold nanoparticles to control the strength of their interaction with the Silicon Nitride pore which is negatively charged. Our experiments revealed how this modulation of the electrostatic force greatly affects the dwell time. Positively charged NPs with strong attractive interactions with the pore resulted in increase of dwell times by 2–3 orders of magnitude, from 0.4 ms to 75.3 ms. This extreme sensitivity of the dwell time on the strength of interaction between a target and nanopore can be exploited in emerging nanopore sensor applications.

1. Introduction

The nanopore measurement technique has gained prominence due to its potential in label-free high-throughput single-molecule detection [1–7]. The concept is simple; a single nanometer sized pore forms the only means of passage through an otherwise impermeable membrane between the two chambers of a fluidic cell. On applying an electrical potential difference between the two chambers, the molecule or target analyte of interest is driven through the pore and subsequently modulates the ionic current based on its conformation and charge distribution. Nanopores with a comparable dimension as that of the analyte gives a detectable current signature every time there is a passage of the molecule [8–10]. Recent advances in fabrication methods have made solid-state nanopores a popular choice. The solid-state nanopores are mechanically robust compared to biological nanopores [11] and have the added advantage of scalable manufacturing based on conventional silicon chip fabrication methods [12–16].

Nanopore detection technique, as opposed to bulk detection techniques such as sample conductance measurement, does not involve ensemble averaging. Nanopore devices enable us to detect analytes at the single molecule resolution which has produced many new physical insights. As the molecule passes through the nanopore it produces a characteristic current profile. These current signatures generally contain two kinds of information. First, the amplitude of current modulation due to a translocation event and second, the duration of the current modulation, which in this article we refer to as the dwell time of the target analyte through the nanopore. By using 5 nm and 10 nm diameter gold nanoparticles (NP) and by modifying their surfaces to enable strong, attractive electrostatic interactions with the nanopore walls, we investigate how the difference in their size, surface charge (and consequently NP-nanopore interaction) affect these two types of information in the ionic current traces. In particular, the exponential dependence of escape rate from an attractive trap [19,20], leads to large differences in dwell time depending on the strength of interaction, which controls the trap depth. In other words, the dwell time of the target inside the nanopore is exponentially dependent on the strength of the interaction between the target and the nanopore. This means that minor difference in the interaction strength, for example single base mismatches between single stranded DNA immobilized on translocating NP and the nanopore, can result in measurable differences in the dwell time. In this manner highly sensitive dwell time based nanopore sensors could be developed for various applications.

Although intuitively we imagine that the translocation of an NP through the nanopore would cause a reduction in current from its baseline, due to the blocking of the pore by the NP, under certain conditions it is known that an enhancement of current from the baseline value can also arise [21–23]. This enhancement is due to the enhanced Debye layer interactions in low ionic strength solutions. As a result, the NP carries a large charge cloud along with it which will counteract the pore blockade and result in a higher local charge density when the NP is inside the pore leading to current enhancement due to NP translocation [21,24]. We expect that the magnitude of this current enhancement effect will be directly related to the rate at which the charges are transported across the nanopore. Hence faster transport of the same magnitude of charges will result in a greater current enhancement and conversely, slower transport of charges, associated with larger dwell time values, will lead to a suppression of this enhancement effect. Indeed, we show here that the current modulation observed in our experiments can switch from an enhancement-dominated mode to a blockage-dominated mode by increasing the attractive interaction between the AuNP and the nanopore resulting in long dwell times. Thus, the dwell time and its effect on the current modulation can be used as a sensitive probe for the strength of interaction between the target analyte and the nanopore. In the subsequent sections, we present our experimental system and discuss the results in detail.

2. Materials and methods

2.1. Nanopore fabrication

The nanopore devices were fabricated using e-beam lithography (EBL) and reactive ion etching (RIE). The process is briefly described here. Chips containing 30 um square SiN membranes of thickness 100 nm were first fabricated using low pressure chemical vapour deposition (LPCVD) of low-stress SiN followed by selective Si etch using potassium hydroxide (KOH) solution. Then an approximately 80 nm thick e-beam resist poly(methyl methacrylate) (PMMA) C3 950 K was spin-coated on top of the membrane. Pixel exposure method was used in the e-beam writer with 20 KeV electron energy and doses of 2–8 fC/shot with 10 um aperture. After developing the resist in 1: 3 methyl isobutyl ketone: isopropyl alcohol (MIBK : IPA) solution for one minute, the pattern was transferred onto the SiN layer by RIE with SF₆ (15 s, 50 W, 45 sscu). Finally, the remaining resist was stripped off using acetone. Depending on the e-beam dose, pores with a range of sizes (15 nm–50 nm) can be fabricated using this method (see Supplementary Information Fig. SI-1.2).

2.2. Nanopore characterization methods

In order to characterize the nanopore fabrication process, we did scans using Scanning Electron (SEM) Atomic Force (AFM) microscopies and current-voltage (I–V) characteristics. Arrays of pores were fabricated and using the SEM we checked the repeatability and consistency of the pore diameter [see Supplementary Information Fig. SI-1.2]. AFM Imaging was performed using Peak Force Quantitative Nanomechanical Mapping (PFQNM) mode [25] in Bruker Dimension Icon AFM. A Bruker Scanasyst-AIR probe (nominal tip radius = 2−12 nm, spring constant = 0.2− 0.8 N/m) [26] was used to scan the specimen. As the radius of nanopores and tip radius are within the same orders of magnitude, even a little damage to the tip may affect the lateral resolution of scan significantly. So, a peak force setpoint of 3 nN was used so as to minimize the damage to the tip while scanning the hard SiN surface. The tip being small ∼2 nm, it allowed us to scan well within the pore structures which clearly showed the conical profile of the pores. I–V characteristics revealed the actual diameter of the pore. The chip was mounted in the flowcell and after flushing with 1 M potassium chloride (KCl) solution voltage sweeps were done (−200 mV to 200 mV in steps of 20 mV) and the corresponding current was recorded.

2.3. Nanopore current measurement setup

Prior to experiment, the chips containing single nanopores were piranha cleaned for 10 min. After mounting in a custom-made polytetrafluoroethylene (PTFE) holder cell, voltage conditioning with 8 V pulses in 1 M KCl was done to ensure a low rms noise [27] [see Supplementary Information Fig. SI-1.2]. The thickness of our in-house silicon nitride membranes being in the ranges of 50 nm, significant improvement was detected at this comparatively higher voltage. Following this a salt solution of 100 mM KCl, 0.1 mM ethylenediaminetetraacetic acid (EDTA) buffered to pH 8 with 1 mM tris-hydrochloride (Tris−HCl) was injected into the cell. Prior to injecting the NP into the nanopore device, UV spectroscopy was performed to ensure that aggregation of the NP did not occur [see SI-2]. Current measurements were carried out with a patch clamp amplifier (Axopatch 200B, Molecular Devices) via silver/silver chloride (Ag/AgCl) electrodes. Nanopore current data were digitally acquired at a sampling rate of 50–100 KHz with Digidata 1440B and low-pass filtered at 5 KHz or 10 KHz for an improved signal-to-noise ratio. The data was processed using a customized Matlab code.

2.4. Nanoparticle translocation experiments

Citrate stabilized 5 nm and 10 nm diameter spherical gold nanoparticles (Sigma Aldrich, USA) were used as the model analyte in our experiments. The particles were diluted 1000 fold from the stock concentration of ∼5.5E + 13 particles/mL, in the degassed and filtered measurement buffer. 400 u L of this solution was then introduced into the cis side chamber of our flow cell and on the trans side chamber we injected only the buffer solution. Next, we immersed the Ag/AgCl electrodes from the top into the electrolyte compartments and bias voltages were applied to the trans side electrode. Application of this bias caused the NPs to pass from the cis side to the trans side through the nanopore and the resulting ionic current traces were acquired and analyzed as mentioned before. A schematic of the nanopore experiment technique is illustrated in Supplementary Information Fig. SI-1.3. First set of experiments were done with 5 nm and 10 nm NPs introduced separately in the nanopore setup. Next we made a mixture of 5 nm and 10 nm NPs at a ratio of 2:1, which was then used as the analyte. Another set of experiments were done by changing the surface charge on the NPs with polyelectrolytes multilayers coating [28,29].

2.5. Poly-electrolyte coating

The polyelectrolyte solutions were prepared as previously mentioned by our group [30,31]. Cationic polyelectrolyte poly(allylamine hydrochloride) (PAH, Mw ∼15,000 Da) and anionic poly(acrylic acid)(PAA, Mw ∼200,000 Da) were purchased from Sigma Aldrich, USA. Polyelectrolyte solutions of 0.01 M (based on the repeat unit molecular weight) were made from deionized (DI) water with ionic strength of 0.1 M sodium chloride (NaCl) and pH adjusted to 5.5 with 0.1 M hydrochloric acid (HCl) and 0.1 M sodium hydroxide (NaOH). The gold nanoparticles were coated with polyelectrolytes by alternatively sonicating the NPs in cationic PAH and anionic PAA, for 1 min then filtering out the supernatant to create polyelectrolyte multilayer (PEM) stacks. The process also included a DI water sonication-filtration step after each polyelectrolyte (PE) layer to remove any loosely bound PE molecules. The process was repeated thrice to create a 1.5 bilayer stack on the NP, with a final layer of cationic PAH and zeta potential of around 25 mV on the PEM coated NP.

2.6. Numerical simulations

Transport through nanopores is well-described by the coupled Poisson–Nernst–Planck–Stokes equations (PNPS) [32,33]. The ion distribution J and potential profile ϕ(r) in the system are modeled by the Nernst–Planck–Poisson equations as below:

$${\mathbf{J}}_i=-D_i\nabla c_i(\mathbf{r})-\frac{D_i{z}_{i}e}{k_{B}T}{c}_i(\mathbf{r})\nabla \varphi (\mathbf{r})+c_i(\mathbf{r})\mathbf{u}(\mathbf{r})$$ (1)

$${\nabla }^2\varphi (\mathbf{r})=-\frac{{\rho }_e(\mathbf{r})}{{\epsilon }_0{\epsilon }_r}$$ (2)

J_i, D_i , c_i(r), z_i are the ionic flux, diffusion coefficient, concentration and valency of species i in solution, respectively. For KCl, zi = ±1, DK+ = 1.95 × 10 − 9 m2/s and DCl− = 2.03 × 10 − 9 m2/s [34]. e = 1.6 × 10 − 19 C is the elementary charge, kB ∼ 1.38 × 10 − 23 J/K is the Boltzmann constant, T =300 K the absolute temperature, and u(r) the fluid velocity field. ε_r is the relative dielectric constant of water ∼ 80 with ε₀ = 8.85 × 10 − 12 F/m being the permittivity of free space. ρ_e(r) in denotes charge distribution.

The fluid velocity is obtained using the Stokes equation:

$$\mu {\nabla }^2\mathbf{u}=\nabla p+{\rho }_e(\mathbf{r})\nabla \varphi (\mathbf{r})$$ (3)

where μ is the dynamic viscosity and p the pressure inside the fluid.

The ionic current I is calculated using the integral

$$\mathbf{I}=N_{A}e\underset{S}{{\displaystyle \int }}\left({\mathbf{J}}_{K^{+}}-{\mathbf{J}}_{C{l}^{-}}\right)d\mathbf{S}$$ (4)

where S is the surface area of the cross-section of the pore. We have taken S halfway through the pore [35] [see Fig. 2(a)]. N_A ∼ 6.023 × 10²³ / mol is the Avogadro’s constant. The set of PNPS equations were solved numerically using the commercial finite-element solver COMSOL Multiphysics 5.2.

Fig. 2.

Normalized current traces of translocation events where the open pore current of 20.3 nA was subtracted so that the baseline is brought down to 0 nA in all the cases. (a) a typical current trace obtained using negatively charged AuNP (mention zeta potential) (b) the waveform of a single translocation event and (c) PNPS simulation of a single AuNP using parameters described in Table 1, reveals that current enhancement events are related to translocation of single NPs.

The parameters used are in our simulation are given in Table 1. Following the AFM scans of our nanopore structures (Fig. 1(b)), two sets of pore geometries were considered with base (tip) diameters D_P (d_P) of 30(20) nm and 15(6) nm, length of the pore in both cases was L = 50 nm. A 2D-axisymmetric geometry was used which was revolved about the axis to produce the full 3D structure. The reservoirs on both sides had dimensions of 4 L, large enough to account for the access resistance factor. The nanoparticle was modelled as a sphere with diameter d_NP = 5 nm, and 10 nm) with a surface charge density of −20mC/m², based on experimentally measured zeta potentials [see Supplementary Information section SI-2]. We took the SiN membrane surface charge density to be −23 mC/m² [21]. Changes in SiN surface charge mainly modifies the current baseline, the overall shape remains roughly the same [see Supplementary Information section SI-3].

Table 1.

PNPS simulation parameters.

Salt Molarity [mM]	Diffusion co-efficient [m2/s]		Pore and particle dimension [nm]		Surface charge density [mC/ m2]
100	K+	1.95 × 10− 9	Pore Diameter DP(dP)	30(20), 15(6)	Pore	− 23
			Pore Length L	50
	Cl-	2.03 × 10− 9	Particle Diameter dNP	5, 10	Particle	− 20

PNPS simulation parameters.

Fig. 1.

Nanopore fabrication and characterization: (a) Schematic of the fabrication process: (i) LPCVD nitride deposition, (ii-iv) Optical lithography followed by RIE, (v) SiN membrane release by backside KOH etch, (vi-vii) E-beam Lithography with pixel exposure (viii) Nanopore formation by subsequent RIE; (b) AFM scan showing the conical shape of the pore; (c) SEM image of arrays of nanopores and a zoomed in pore of 30 nm diameter and (d) I-V characteristics showing good agreement of experimental data with theoretical estimates and numerical simulation based on conical pore geometry obtained from AFM.

3. Results and discussion

3.1. Nanopore characterization

Combined analysis based on SEM, AFM and I–V characteristics revealed that the fabricated nanopores had diameters ranging from 26 nm to 32 nm [see Supplementary Information Fig. SI-1.2] and most importantly, they had a conical profile. The conical profile was evident from the AFM scans shown in Fig. 1(b) which shows conical pores with a base diameter of around 30 nm tapering down to 15− 20 nm. I–V characteristics have been used to determine the diameter of nanopores. This is based on comparison of experimentally obtained conductance from the I–V curves with the theoretical formula involving the pore geometric parameters. We estimated the I–V characteristics using the conical profile parameters obtained from AFM scans and substituting it in the theoretical conical pore conductance expression [36].

$${\mathbf{G}}_{cone}=\frac{\pi \sigma d_P{\mathbf{D}}_P}{4\left(\mathbf{L}+0.8\left(d_P+{\mathbf{D}}_P\right)\right)}$$ (5)

where σ is the conductivity of the buffer solution, d_P, D_P and L are the pore diameters at the tip, base and pore length, respectively, which are obtained from AFM data. The theoretically calculated I–V curves using the conical pore geometry matched the experimental data closely as seen in Fig. 1(d). Additionally, we simulated the I–V characteristics numerically using the PNPS equations as described in the preceding section using a conical pore of 30 nm base diameter tapering down to 20 nm. The results of the direct numerical simulation also agree quite well with the experimental data.

Shiu Liu et al. [37], investigated the pore geometry fabricated by conventional ion-beam drilling with subsequent shrinking and its effect in nanoparticle detection. This revealed many important aspects of detection capability of different types of nanopores [37,38], however, there are very few studies investigating e-beam lithography fabricated pores of sub-30 nm diameter [39]. The process flow of our fabrication method is schematically illustrated in Fig. 1(a). The conical pores obtained in this study may be a result of using a thin layer of resist used to achieve the small dimensions. The resist starts getting etched during the RIE process and combined with asymmetric resist profile due to e-beam scattering the pores become conical [see Supplementary Information section SI.1]. Sensors based on conical pores are beneficial in the study of protein complexes, nanoparticles, etc. [40–45]. Since the pore has a dimension of below 30 nm along a considerable length, biomolecules can be trapped [46,47] inside and their interactions can be examined with the sensitive conical tip obtained using our fabrication method.

3.2. Current trace of single translocation events

We performed translocation experiments using 5 nm and 10 nm spherical gold nanoparticles as described in the methods section. A typical translocation experiment using negatively charged NPs with zeta potential of − 12 mV produces a stream of ionic current spikes as shown in Fig. 2(a). A single spike, as shown in Fig. 2(b) corresponds to the translocation of a single nanoparticle. We observed that the spikes observed in the current trace have the characteristic shape depicted in Fig. 2 (b) consisting of an increase in ionic current from the baseline followed by a slight reduction below the baseline before finally returning to the baseline after the passage of the NP. Relative to the baseline, an increase in the ionic current due to the presence of an NP in the nanopore (referred henceforth as an enhancement event) may appear counter-intuitive as one may naturally expect a reduction in ionic current due to pore blockage by the NP (referred henceforth as a blockade event). However, enhancement events in current traces are well documented and understood to arise in low ionic strength solutions where the significantly larger Debye layers of the NP and nanopore interact resulting in a net increase of charge density in the nanopore during the translocation event [21,24]. This effect counteracts the blockage effect and results in a net increase of the ionic current relative to the baseline.

However, the dip below baseline as the NP exits the pore has not been documented in previous studies [19,21]. In order to verify that the observed current enhancement events are indeed arising from the passage of a single NP and to understand the characteristic shape of the ionic trace of single translocation events, we performed numerical simulation of the PNPS equations as described before. Close agreement between the shape of the ionic current trace obtained from experimental data [see Fig. 2(b)] and the numerical simulation shown in Fig. 2(c) supports the fact that single translocation events are indeed being measured. The simulation correctly estimates the enhancement observed in experiments and also reveals that the dip below baseline in the ionic trace arises due to the conical pore geometry where the pore diameter is non-uniform. At the exit of the nanopore the diameter becomes larger than the Debye layer thickness and the enhancement effect no longer counteracts the blockade effect leading to a decrease in ionic current relative to the baseline as observed. Therefore, the characteristic shape of the current trace we observe is a result of the conical profile of our nanopores.

In our simulations, the particle position was varied along the z-axis by Δz = 2 nm and the current was measured. So, the resultant current profile is position specific and independent of the bias direction. Even when the particle flow direction is reversed, we got the dip near the wider part followed by the enhancement at the tip. Additional simulations were done to study the different effects of the experimental conditions on the resultant current. These are detailed in the Supplementary Information sections SI-3 to SI-6.

3.3. Differentiating translocation signals based on NP size

The translocation signal of a single NP shown in Fig. 2(b) has two independent features, namely, the sign and magnitude of the ionic current change relative to the baseline and the duration of the translocation event, referred henceforth as the dwell time. Samples containing only 5 nm or 10 nm NPs were run to characterize the magnitude of current change and the dwell time. As shown in Fig. 3(a), translocation of larger 10 nm diameter NPs resulted in higher current change (0.13 nA) compared to the 5 nm diameter NP (0.05 nA). This is not surprising as we would expect increased interaction between the Debye layers of the NP and pore-wall for larger NPs. Similarly, the 10 nm NPs take longer to pass across the pore likely due to increased probability of collisions with the pore wall. The scatterplot of the 5 nm and 10 nm NP translocation signals reveal an interesting feature of the data. While the majority of the data from the two species of NP is well separated, there is a section of the 5 nm NPs which overlaps with the 10 nm NP events. Interestingly, the mean current change and dwell time of the overlapping section of the 5 nm NPs lie close to that of the 10 nm NP population. It is important to note that there is no such bleed-through of the data from the 10 nm population into the region of the current-dwell time graph occupied by the 5 nm population. We believe that in addition to the slight variations in size this is mainly due to the possibility of two or up to three 5 nm NPs simultaneously passing through the nanopore whose constriction is around 15−20 nm. The clustering leads to a fraction of the 5 nm NPs producing larger current change and longer dwell time, comparable to that of the 10 nm NPs.

Fig. 3.

(a) Current change and dwell time distributions for separate experiments with 5 nm and 10 nm AuNPs showing a detectable increase in the 10 nm case. (b) Experiment conducted with a mixture of 5 nm and 10 nm particles at a ratio of 2:1. (i) Normalized current trace showing translocation events of the mixture solution, with two detectable levels of current change. Open pore current was 20.8 nA at an applied potential of 400 mV. (ii) The parameters obtained from mixture matches that of the separate cases. The mixture model shows 5 nm particles have lower current change and dwell time values (blue traces), 10 nm particles have a larger current change and dwell time values (red traces). This is consistent with the fact smaller the particle lesser will be the charge carried by it and faster will it move and our nanopore setup is capable of differentiating this change. Pores used in all the experiments have a diameter of 20 ±2 nm.

After characterizing the translocation data of individual NPs we mixed the 5 nm and 10 nm populations in a ratio of 2:1 respectively and analyzed the translocation events produced by this mixture. We fitted the distribution of current changes and dwell times to a sum of two gaussians representing the two populations. The mean current change for the two populations based on the best fit to experimental data was 0.04 nA and 0.08 nA, close to the values obtained for the 5 nm and 10 nm NPs, namely, 0.05 nA and 0.13 nA respectively. Similarly, the mean dwell time for the two populations based on the best fit to experimental data was 5 ms and 20 ms, close to the values obtained for the 5 nm and 10 nm NPs, namely, 5 ms and 15 ms respectively.

3.4. Differentiating translocation signals based on NP surface charge

As described in the methods section, the as procured 5 nm and 10 nm diameter NPs are negatively charged with a zeta potential of − 12 mV. By coating with polyelectrolyte multilayers, we switched the sign of the surface charge on the NP yielding a zeta potential of 25 mV. Based on AFM scans of PEM stacks [30], the (PAH/PAA)_1.5 coated NPs have diameters of 11 nm and 16 nm. We then compared the effect of the surface charge on the translocation signals. As shown in Fig. 4(a), the uncoated negatively charged NPs, produce an ionic current enhancement relative to the baseline as described in the previous section.

Fig. 4.

Normalized current traces of translocation events with (a) uncoated negatively charged NPs showing mostly enhancements (b) poly-electrolyte coated positively charged NPs showing mostly blockages. The open pore current in both figures (a) and (b) was approximately 67 nA at 800 mV. (c)Interaction between the positively charged AuNP with the negatively charge SiN membrane causes a change from the enhancement regime to the blockage regime and a significant increase in dwell time. Also notable is positive Au NP at lower potential (500 mV) has a larger dwell time than the higher potential (800 mV), which is not prominent in the negative AuNP cases.

However, we found that translocation of positively charged NPs result in a reduction of ionic current with respect to baseline, corresponding to a blockade dominated regime. Most remarkably, when we compare the dwell times of positively charged NPs, we see that the dwell times have increased by nearly two orders of magnitude illustrating the dramatic influence of surface charge on the dwell time. In order to further understand this observation better we studied the current change and dwell time distributions for two different drive voltages, namely, 500 mV and 800 mV. From Fig. 4. we see that there was only a slight difference of about 20 % in the mean current change and dwell time for the negatively charged particle with increasing drive voltage, while there was a nearly 10x decrease in the dwell time with increased drive voltage. Such an enormous difference in the behavior of translocation signals depending on surface charge has not been reported in previous studies and naturally leads to the question of its origin.

In order to understand the effect of surface charge on translocation signal, firstly we note that the probability of attractive surface interactions is significantly higher with positively charged NP and negatively charge nanopore due to electrostatic attractive forces. We might therefore qualitatively understand the translocation process of NPs as a Kramer’s escape problem from a potential well [48–50], where increased attractive interactions increase the depth of the well while the drive voltage, provides the energy to escape from the well. The effective potential barrier U_eff, experienced by the particle can be written as U_eff = U_NP− _pore + qV_drive, where U_NP−pore represents the interaction between the NP and the pore-wall, q is the charge carried by the NP and V_drive is the applied potential. It is well known from the solution of the Kramer’s problem that the rate of escape from such a potential barrier is proportional to a factor which has exponential dependence on the barrier strength, i.e. the rate of escape is proportional to $\exp \left(U_{cff}/kT\right)$ [48–50]. Strong electrostatic attraction between the NP and pore results in a strongly negative value of U_NP−pore. Applying a drive voltage to enable the translocation of NPs counteracts U_NP−pore. However, for small enough values the sign of U_eff remains negative signifying a potential-well. The exponential dependence of the rate of escape from the well on U_NP−pore implies that the dwell time, which is related to the inverse of the rate will also be exponentially dependent on the NP-pore interaction. This qualitative picture explains why changing the drive voltage from 500 mV to 800 mV resulted in a nearly 10x decrease in dwell time of positively charged NPs (having strong attractive electrostatic interaction with the pore) due to the reduction of the effective barrier U_eff with increasing drive voltage. However, for negatively charged NPs changing the drive voltage by the same amount had relatively negligible effect because for weak attractive interactions or even repulsive interactions there is no effective barrier (i.e.,U_eff≳0) and escape rates would only have a weak dependence on V_drive.

As seen in Fig. 4(c) the sign of current change becomes negative (blockage dominated) in the case of positively charged NPs while it is positive (enhancement dominated) for negatively charged NPs. To understand why this reversal occurs, firstly, as mentioned before, there are two counteracting charge transport phenomena underlying the translocation events. On the one hand the presence of NPs block the pore leading to a decrease in current flow (blockage effect). On the other hand, under certain situation, Debye layer interactions can lead to a greater charge density and consequently a greater charge transport rate during translocation leading to an increase in ionic current from the baseline (enhancement effect). This mechanism has been elucidated clearly in several previous studies [21–23]. In order to get a net enhancement in ionic current, as experimentally observed for negatively charged NPs, the enhanced charge transport rate must overcome the blockage effect.

However, in the case of positively charged NPs with strong attractive interactions with the pore, the dwell times increase by 2–3 orders of magnitude resulting in a drastic reduction of enhanced charge transport rate which is then not able to counteract the blockage effect. In this case, the net current change would be negative (relative to baseline) as observed in experiments. Though the analysis presented here is only from a qualitative point of view, the general trends in the data appear consistent with this picture. A rigorous quantitative analysis of this phenomenon by modeling NP translocation as a Kramer’s escape problem will be communicated in detail in a subsequent article. The exponential dependence of dwell time on the NP-pore interaction strength paves the way for developing highly sensitive sensing techniques based on dwell time of NPs through nanopores. For instance, one could functionalize the nanopore with a single stranded DNA sequence, including aptamers, with the objective of sensing complementary single stranded sequences or proteins attached to NPs. Due to the exponential dependence of the dwell time on the strength of interaction, minor variations in the interaction strength, for example due to single base mismatches or non-specific protein binding would lead to large differences in dwell time. Thus dwell time based nanopore sensing methodologies may have significant advantages over other methodologies such as ionic current based ones which do not possess the exponentially sensitive regime.

4. Conclusions

To summarize, Debye layer interactions combined with non-uniform pore diameter results in a bi-directional current profile, a unique feature of conical nanopore which, to the best of our knowledge has not been reported before. Utilizing the sensitivity of the conical pore we were able to differentiate two populations in a mixture of 5 nm and 10 nm nanoparticles. Moreover, we have used a method of poly-electrolyte functionalization of gold nanoparticles to modify the electrostatic force of interaction between the NP and the nanopore. We have demonstrated extreme sensitivity of the dwell time of NPs through nanopores on these interactions. In addition to the ionic current change, dwell time can serve as an important piece of information about the translocating particles. Under suitable conditions, the sign of current modulation will depend on the strength of NP-pore interactions as we showed in this article. We believe that the exponential dependence of dwell time on the NP-pore interaction strength will lead to novel high-sensitivity sensing techniques based on dwell time of NP through nanopores.

Biography

Sohini Pal joined the Centre for Nano Science and Engineering Department, IISc in 2015 for Ph.D. under Prof. Manoj Varma. She completed B.Tech in 2014 on Electronics and Communication Engineering (ECE) from West Bengal University of Technology, Kolkata. Her PhD research area is on Nanopore based single molecule detection.

Ramkumar B. obtained his B.Tech in Electrical engineering from Government College of Technology, Coimbatore, under Anna University, Chennai. He joined Dr. Varma’s group in July 2015. His current research interests are focused on nanopore based DNA sequencing and Atomistic modelling & simulation of DNA origami.

Sanket Jugade completed his B.Tech in Mechanical Engineering from National Institute of Technology, Surathkal in 2018. He joined the Prof. Naik’s group as a Project Assistant. He is currently working on indentation experiments on suspended 2D materials using Atomic Force Microscopy.

Dr. Anjana Rao A member of the National Academy of Sciences, Dr. Rao received her undergraduate and master’s degrees from Osmania University in India and her Ph.D. from Harvard University. After many years as a faculty member at the Harvard Medical School and the Immune Disease Institute in Boston, she joined the La Jolla Institute in 2010. She has worked on signaling and gene transcription for many years, is a member of numerous advisory panels, and has received several major awards.

Dr. Akshay Naik received his Ph.D. in Electrical Engineering from University of Maryland, College Park, in 2006. He then worked at Caltech first as Postdoctoral Associate from 2006 to 2008 and then as Research Engineer from 2008 to 2011. In Dec 2011, he joined the Indian Institute of Science, Bangalore where he is currently an Associate Professor at the Centre for Nano Science and Engineering. His research interests are physics and application of Nano-mechanical systems.

Dr. Banani Chakraborty received her Bachelors’ in Science degree from Presidency College, Kolkata, India in 2000 and Masters’ degree from Indian Institute of Tech- nology, Kanpur, India in 2002 in Chemistry. She has received her Doctorate (PhD in Bio-molecular Chemistry) from New York University, New York, USA in 2008 on DNA Nanotechnology. She did post-doctoral research in two stretches, first one focused on DNA aptamer-based biosensors in Simon Fraser University, British Columbia, Canada and second one as an Alexander Von Humboldt post-doctoral fellow in RWTH Aachen University, Germany where she started to functionalize DNA origami with enzymes. In 2015she joined as a Ramalingaswami Fellow (DBT) in Department of Chemical Engineering, Indian Institute of Science, Bangalore, India. Her current research focuses on functional aspect of DNA origami combining DNA aptamer-based biosensors.

Dr. Manoj Varma received the B. tech degree from Indian Institute of Technology Madras, India, in 1999, and the Ph.D. degree from Purdue University, West Lafayette, IN, USA, in 2005. He was the Director of engineering from Quadraspec Inc., Purdue Research Foundation, from 2005 to 2007. He is currently an Associate Professor with the Centre for Nano Science and Engineering, Indian Institute of Science, Bangalore, India. His current research interests include developing technologies for biological applications. Examples include optical techniques for biomolecular sensing, tools for cell micropatterning, integrated Lab-on-Chip devices.