Coil–Globule versus Field-Driven Coil–Blob Transitions of PEG under Nanopore Confinement

Abstract

Poly­(ethylene glycol) (PEG) undergoes a coil–globule transition above its lower critical solution temperature (LCST) as hydration weakens. While this behavior is commonly tuned using chemical modification or cosolutes, nanoscale confinement provides an alternative physical means by which to influence polymer properties. Here, we use nanopore-based size discrimination as an indicator of full polymer confinement to track driven conformational transitions at the single-polymer level by examining the temperature-dependent transport of polydisperse PEGs (1500, 2000, and 3400 g·mol^–1) through two β-barrel protein nanopores with distinct geometries and surface properties: α-hemolysin (α-HL) and aerolysin (Ael), over the temperature range 5–45 °C. While temperature does not affect nanopore structure, it strongly modulates PEG–nanopore interaction kinetics. In α-HL, blockade durations for larger PEGs increase strongly with temperature, enabling size discrimination of PEG 2000 above 25 °C and PEG 3400 at 45 °C, consistent with a confinement-induced coil–globule transition and a reduced apparent LCST. In contrast, in Ael, blockade durations decrease with temperature for all PEG sizes, restricting size discrimination to low temperatures under high applied voltages. This behavior, although our observations are inferred from transport dynamics rather than direct structural measurements, indicates a field-driven, blob-like polymer confinement, in which the chain is forced into the nanopore by the electric field rather than stabilized by thermodynamics. These contrasting regimes are rationalized by using scaling arguments and a unified free-energy framework for polymer confinement.

Introduction

Poly­(ethylene glycol) (PEG) has long served as a model polymer in nanopore studies owing to its chemical simplicity, tunable molecular weight, and well-characterized solution properties. In bulk aqueous solution, PEG exhibits thermoresponsive behavior characterized by a lower critical solution temperature (LCST), above which weakening polymer–water interactions lead to a coil–globule transition. − Traditionally, tuning this transition relies on chemical modification, copolymerization, or the addition of cosolutes, approaches that increase system complexity and often compromise sustainability. , An alternative and largely unexplored route is to regulate polymer phase behavior through nanoscale confinement, where the geometry and interfacial interactions provide a purely physical means of control.

From a fundamental perspective, conformational transitions also govern protein folding and unfolding and are strongly influenced by the temperature and spatial confinement. In proteins, increasing temperature generally promotes unfolding by destabilizing intramolecular interactions, whereas in thermoresponsive polymers, such as PEG, temperature can induce chain collapse via an LCST. Despite these opposite thermal responses, unfolded proteins and flexible polymers share a common physical description under confinement. In both cases, restricted geometries drive coil-to-blob–like conformational transitions. , This correspondence identifies nanoconfinement as a universal control parameter for conformational transitions and establishes a physical framework for controlling molecular capture, translocation dynamics, and signal resolution in nanopore-based sensing and protein sequencing technologies.

Historically, in nanoscale confinement, PEG was first employed as a molecular probe to estimate nanopore dimensions by comparing bulk electrolyte conductivity with changes in pore conductance upon addition of polydisperse PEG solutions. This approach relied on steric exclusion of PEG from the pore, leading to a mismatch between bulk and pore conductance, and successfully yielded an estimate of the α-hemolysin (α-HL) pore radius (∼1.3 nm). Subsequent studies revealed pore asymmetry, in agreement with the α-HL crystal structure. These early analyses assumed negligible specific interactions between PEG and the pore, an assumption later challenged by extensive studies demonstrating size-dependent PEG partitioning and diffusion within protein nanopores, including alamethicin. −

PEG subsequently emerged as a powerful system for exploring the fundamental physics of polymer partitioning under nanoscale confinement, particularly at relatively high salt concentrations. − At near-saturating KCl concentrations (4 M), PEG−α-HL interactions produce well-defined ionic current blockades. Both blockade depth and dwell time increase with polymer size over an intermediate molecular weight range, whereas blockade amplitudes saturate and dwell times decrease for larger PEGs. Remarkably, blockade amplitudes can be used to construct single-molecule “mass spectra” with monomer-level resolution, enabling the identification of individual PEG species within polydisperse mixtures. For each species, dwell times follow monoexponential distributions with characteristic values that increase with polymer size, consistent with a first-order binding process. Together, these findings established nanopore-based size discrimination as a robust single-molecule analytical framework.

Under these high-salt conditions, α-HL has been shown to resolve up to 25 distinct PEG oligomers within a polydisperse sample averaging 34 repeat units (∼1500 g·mol^–1), spanning PEG 24 to PEG 48 at modest applied voltages. Achieving monomeric resolution requires full-chain entry into the pore and sufficient ionic current sensitivity for each monomer to contribute independently to the blockade signal. This strategy has since been used to water-soluble polymers, − although broad applicability remains challenging due to variations in molecular architecture, size, chemistry, and binding affinity.

Significant efforts have therefore focused on extending nanopore-based size discrimination to other analytes, including metallic clusters, short DNA fragments, homopeptides, heteropetides, − and glycosaminoglycan, , and on expanding the accessible size range for nonionic polymers. One approach employed Ael, an alternative β-barrel protein nanopore, which, at high salt concentration, enables discrimination of smaller PEG oligomers than α-HL and extends monomeric resolution to a broader size range under high trans-negative voltages. Other strategies, such as DNA hairpin conjugation, have enabled the detection of very small PEGs (∼140 g·mol^–1), though not in the context of size discrimination. Conversely, extension toward larger PEGs was achieved in α-HL by increasing temperature. At elevated temperatures, size discrimination becomes possible for PEGs that cannot be resolved at room temperature, a phenomenon attributed to reduced PEG solubility and temperature-induced polymer compaction that facilitates pore entry and confinement.

Here, we introduce nanopore-based size discrimination spectra as a sensitive and quantitative indicator of full polymer confinement, an approach that, to our knowledge, has not been previously exploited to track driven conformational transitions at the single-polymer level. We examine how temperature and driving forces under nanoscale confinement jointly regulate the coil–globule versus field-driven coil–blob transitions of nonionic poly­(ethylene glycol) (PEG) in protein nanopores. In particular, we address whether this temperature-induced enhancement of PEG size discrimination reflects an intrinsic property of PEG under confinement or instead depends on the nanopore architecture and interaction landscape. By directly contrasting these two nanopores, which differ markedly in geometry and electrostatics, we show that PEG transport through nanopores can occur in two distinct regimes depending on pore architecture: a thermodynamically stabilized coil–globule transition associated with full-chain confinement and a field-driven coil–blob regime in which confinement is dominated by the applied electric field. We rationalized these mechanisms, using a unified free-energy framework for polymer confinement and scaling arguments, including an analogy between polymer random walks and quantum particle trajectories, which qualitatively captures the measured confinement free energies across different polymers and nanopores.

Results and Discussion

Temperature Effect on the Structural Integrity and Effective Dimensions of the Pores

Before investigating the effect of temperature on the size discrimination of nonionic polymers (PEGs) transport through α-HL and Ael nanopores, we first examined whether temperature variations influence the structural integrity and effective dimensions of the pores themselves (Figure ) as well as the ion transport through α-HL and Ael (Figures SI 1 and SI 2, Table SI 1). To this end, conductance–temperature measurements were performed for both nanopores in 3 M KCl over a temperature range from 5 to 45 °C. Figure shows the conductance of Ael and α-HL nanopores as a function of the temperature. In both cases, the open-pore current increases by approximately a factor of 2.5 when the temperature is raised from 5 to 45 °C, in excellent agreement with bulk conductivity. The bulk conductivity of 3 M KCl is approximately σ­(5 °C) ≈ 165 mS/cm and σ­(45 °C) ≈ 385 mS/cm, yielding a ratio of ∼2.3, which is very close to the measured factor through nanopore measurements. Interestingly, this trend can be rationalized using a simple scaling argument. The conductivity σ is proportional to the ionic mobility μ (σ ∝ μ), which is inversely proportional to the solvent viscosity η. Therefore, σ­(T) ∝ 1/ η­(T), and the ratio of conductivities at two temperatures T ₁ and T ₂ can be expressed as

$$\frac{{\sigma (T}_2)}{{\sigma (T}_1)}\approx \frac{{\eta (T}_1)}{{\eta (T}_2)}$$

1.

Integrity of the nanopores and measurement of the effective energy barrier for ion transport. (a) Conductance of α-HL (circles) and Ael (triangles) nanopores as a function of temperature. (b) Natural logarithm of α-HL naopore conductance ln (G) as a function of inverse temperature. (c) Natural logarithm of AeL naopore conductance ln (G) as a function of inverse temperature. Solid lines correspond to linear fits of the form y = bx + a . For α-HL b = −1994 ± 28.6, a = 7.7047 ± 0.0961; For AeLb = −2198 ± 55.7, a = 7.9538 ± 0.191. Open-pore conductance measurements were repeated three times. Error bars represent the standard deviation of three independent experiments. The error bars are smaller than the symbols used; they are not clearly visible.

Using the known viscosities of water, η­(5 °C) ≈ 1.5 mPa·s and η­(45 °C) ≈ 0.6 mPa·s, one obtains

$$\frac{\sigma (45{}^{°}\mathrm{C})}{\sigma (5{}^{°}\mathrm{C})}\approx \frac{\eta (5{}^{°}\mathrm{C})}{\eta (45{}^{°}\mathrm{C})}\approx \frac{1.5}{0.6}\approx 2.5$$

which is in excellent agreement with the measured value through nanopore measurements.

The conductance exhibits a slightly nonlinear dependence on temperature, with an average increase of ∼2% per °C for α-HL and ∼2–3% per °C for Ael. This behavior closely follows the temperature dependence of the bulk electrolyte conductivity, strongly suggesting that the temperature does not alter the pore structure or dimensions within this range.

To further quantify the temperature dependence, the experimental data in Figure were fitted by using an Arrhenius model

$$G\sim G_0\exp (-\frac{\Delta E}{k_{\mathrm{B}}T})$$

(Figure b,c) yielding an effective energy barrier ΔE for ion entry into the nanopores of approximately ΔE = 6.7 ± 0.1 k _B T for α-HL and ΔE = 7.4 ± 0.2 k _B T for Ael. Using a simple scaling argument in which the pore length l and radius r are considered the dominant geometric parameters, the energy barrier can be estimated as

$$\Delta E\approx k_{\mathrm{B}}T\frac{l}{r}$$

Although this simplified expression neglects electrostatic interactions and the electrical potential landscape experienced by ions at the pore entrance, it predicts an energy barrier on the order of 5–8 k _B T. This estimate is in good agreement with the value extracted from the Arrhenius fits. Energy barriers of similar magnitude have been reported previously for ion entry into other nanopores, including ΔE ≈ 6 k _B T for the mitochondrial TOM channel in 1 M KCl at 40 mV, and ΔE ≈ 5 k _B T for the aerolysin nanopore at an applied voltage of 120 mV, further supporting the validity of our analysis.

Metric for Identifying and Quantifying Size Discrimination of Different Species in Polydisperse PEGs

Schematics of the experimental setup used to probe the interaction of PEGs of different molar masses with the α-HL and Ael nanopores are shown in Figure a. A typical recorded current trace induced by PEG interacting with a nanopore is shown in Figure b. The metric used to identify and quantify size discrimination of the polydisperse PEGs studied here is based on the shape of the scatter plots and their corresponding histograms (Figure c) obtained from a statistical analysis of PEG-induced current blockade events (Figure b). The mean open-pore current value I ₀ = 138.36 ± 3.26 and its standard deviation σ₀ are obtained by a Gaussian fit of the open-pore current trace. The detection of current blockades is based on a two-threshold method: , a possible current blockade event starts when the nanopore current value becomes smaller than a first current threshold Th ₁ = I ₀ – 4σ₀, and ends when the nanopore current returns to a value greater than Th ₁. If the mean current value during the event is greater than a second current threshold Th ₂ = I ₀ – 5σ₀, the event is not considered as a PEG-induced current blockade and is rejected. Each point in the scatter plot corresponds to an individual current blockade produced by the interaction of a single polymer chain with the nanopore.

2.

Metric used to identify and quantify different PEG species present in polydisperse PEG. (a) Schematics of the experimental setup used to probe the interaction of PEGs of different molar masses with the α-hemolysin (left) and aerolysin (right) nanopores. (b) Typical current trace versus time recording through α-hemolysin nanopore in the presence of polydisperse PEG 1500 g·mol-1 (34 monomers) in KCl 3 M Tris 25 mM pH = 7 at +50 mV and at 25 °C. The left axis indicates the current I values, and the right axis indicates the relative current I/I0 values. An enlargement of the current trace shows typical current blockades of different amplitudes and durations. (down) Illustration of a typical current blockade event. The interaction of a PEG with the nanopore is detected as a partial and temporary blockade of the electrical current flowing through the nanopore from its open-pore current value I ₀ to the blockade current value I _b. The current blockade duration Δt corresponds to the duration of the PEG/nanopore interaction. (c) (top) Histogram (black line) of the relative blockade current I _b/I ₀ values corresponding to the current trace and (bottom) superimposed scatter plot of current blockades (red dots) plotted versus relative current. The histogram reveals the existence of at least 18 distinct populations corresponding to preferred relative blockade current values, allowing to quantify different PEG species present in polydisperse PEG, ranging from PEG (24) to PEG (41). The green line is a Gaussian fit of the reference population (PEG 28). Arrows serve as guides to the eye to distinguish the different populations. The typical histogram of relative mean residual current I _b/I ₀ is constructed with a bin width of 0.002. (d) I _b/I ₀ values as a function of monomer units (mu) in the case of Ael (empty circle) and α-HL (black circle).

Size discrimination is achieved when the scatter plot exhibits distinct, well-separated clusters of points (Figure c). Each cluster corresponds to a specific PEG species and is characterized by a nominal relative current value, I _b/I ₀, where I _b is the mean residual current during the blockade and I ₀ is the open-pore current (Figure d and Table SI 2).

To identify the different PEG species present in the polydisperse sample, we used the relative current value I _b/I ₀ of a monodisperse polymer, composed of 28 monomers, PEG 28 (1251 g·mol^–1) as reference, following previous works. ,, Because the position of PEG 28 in the scatter plot is precisely known, it serves as a calibration point to assign the positions of all PEG species with single-monomer resolution. The location of the PEG 28 population is indicated by a green arrow in the scatter plots, and the locations of other species are indicated by a black arrow (Figure c).

The I _b/I ₀ values of PEG species are extracted from the relative current histogram by fitting each population with Gaussian fits (Figure ). For α-hemolysin, the reference corresponds to I _b/I ₀ = 0.2607 ± 0.0003, in agreement with ref , whereas for aerolysin, it corresponds to I _b/I ₀ = 0.4370 ± 0.0003.

Using this reference, all PEG species present in the polydisperse sample can be identified and quantified with single-monomer resolution (Figure and Table SI 2). Conversely, when no distinct clusters (broad distributions) are observed, size discrimination is not achieved. Moreover, nanopores are capable of resolving polymers of identical mass with sub-Dalton precision.

Temperature-Dependent Size Discrimination of PEGs of Varying Molecular Mass

It has been shown that both pores formed by α-HL or by AeL enable, under high salt concentration, the size discrimination of short 1500 g·mol^–1 polydisperse poly­(ethylene glycol) (PEG) molecules that differ by one monomer unit (1 mu). , Specifically, at 4 M KCl, Ael nanopore enabled 31 species of PEG present in a solution of short polydispers PEG 34 mu (1500 g·mol^–1), ranging from PEG 17 mu (748 g·mol^–1) to PEG 47 mu (2068 g·mol^–1), at optimal trans-negative applied voltage −120 mV. While at the same salt concentration (4 M KCl), α-HL nanopore enabled to resolve only 25 species of PEG present in a solution of short polydispers PEG 34 mu (1500 g·mol^–1), ranging from PEG 24 mu (1056 g·mol^–1) to PEG 48 mu (2112 g·mol^–1) at optimal trans-positive applied voltage +40 mV. Interestingly, the range of size discrimination of large PEG molecules at high salt concentration was extended up to PEG 77 mu (3400 g·mol^–1) by increasing temperature through α-HL nanopore. In order to check whether the effect of temperature is intrinsic to the PEG/α-HL system or whether it is more universal, we decided here to conduct a comparative study of the effect of the temperature on the size discrimination of polydisperse PEG mixtures of different average molar masses (PEG 1500 g·mol^–1, PEG 2000 g·mol^–1, and PEG 3400 g·mol^–1) at 3 M salt concentration through α-HL and Ael nanopores and under constant applied voltages optimized for each nanopore: a trans-positive voltage of +50 mV for α-HL and trans-negative voltages of −100 or −140 mV for Ael, unless otherwise stated. All measurements were carried out using electrophysiology experiments (see Figures a and SI 1 for the experimental configuration).

Thermal Dependence of PEG 1500 Interactions with α-Hemolysin and Aerolysin Nanopores

PEG−α-HL interactions were probed by adding PEG molecules to the trans-compartment, whereas PEG/Ael interactions were investigated by adding PEG to the cis-compartment (Figure a). Under our experimental conditions, no significant current blockades were observed when PEGs were added to the trans-compartment in the case of Ael, in agreement with previous reports. , The choice of high salt concentration (3 M KCl), polymer addition side, and applied voltages (+50 mV for α-HL and −100 mV or −140 mV for Ael) was made to promote strong PEG–nanopore interactions and to allow direct comparison with earlier studies. ,, Representative current traces corresponding to the interaction of PEG 1500 g·mol^–1 with α-HL, recorded at three different temperatures in 3 M KCl, are shown in Figure a. The corresponding scatter plots of blockade duration versus relative residual current (I _b/I ₀) are presented in Figures b and SI 3. The temperature dependence of both the blockade frequency and blockade duration for PEG 1500 g·mol^–1 interacting with α-HL and Ael is summarized in Figure c. As evidenced by the recorded current traces, PEG molecules interact with both nanopores over the entire temperature range investigated. Well-resolved current blockades were observed for both pores at all temperatures. However, for Ael at −100 mV, the scatter plots of blockade duration versus I _b/I ₀ do not exhibit clearly discernible populations (Figure SI 3b). In contrast, distinct populations emerge at −140 mV (Figure SI 3c). For α-HL, well-defined populations are observed at all of the applied temperatures investigated. These populations correspond to the different molecular species present within the polydisperse PEG 1500 g·mol^–1 sample. For both nanopores, the blockade frequency increases exponentially with temperature (thermal agitation dominates), while the mean blockade duration decreases exponentially. Increasing the temperature might reduce cation binding, leading to weaker polymer–pore interactions in agreement with Reiner et al.’s previous work.

3.

Effect of temperature on the size discrimination of PEG 1500 g·mol-1 through α-HL and Ael nanopores: (a) Typical single-channel current traces of PEG 1500 g·mol^–1 through α-HL and Ael nanopores. (b) Scatter plots of blockade duration versus the relative residual current I _b/I ₀ of PEG 1500 g·mol^–1 through α-HL and Ael nanopores. (c) Blockade duration and blockade frequency induced by PEG 1500 g·mol^–1 through α-HL (circles) and Ael, at −100 and −140 mV (respectively white and black triangles), nanopores as a function of temperature. All recordings were performed in 3 M KCl solution buffered with 25 mM Tris at pH = 7. PEG 1500 g·mol^–1 was added to the trans side of α-Hl and applied voltage ΔV = +50 mV, whereas PEG 1500 g·mol^–1 was added to cis side of Ael and applied voltage ΔV = −140 mV. Error bars represent the standard deviation of three independent experiments. The recorded events vary from 1000 to 20,000 events.

For all experiments, we verified that the variation of pore conductance with temperature followed the calibration curve presented in Figure , Table SI 1. This ensures that any effects resulting from the buffer evaporation are avoided.

Specifically, the blockade frequency increases by approximately a factor of 20 over a 40 °C temperature interval for α-HL, compared to a factor of about 6 for Ael. Conversely, the mean blockade duration decreases by approximately a factor of 14 over the same temperature range for Ael, whereas only a 2-fold decrease is observed for α-HL. Thus, PEG-induced blockades through α-HL shorten gradually with increasing temperature, while they decrease substantially quicker in the case of Ael.

As a consequence, the resolution of PEG-induced populations in the scatter plots is progressively degraded for Ael as the temperature increases. For α-HL, although the populations move closer together as the temperature rises from 5 to 45 °C, distinct populations remain resolvable even at the highest temperature investigated. In contrast, for Ael, the strong temperature-induced shortening of blockade durations results in a substantial loss of resolution. Finally, although at low temperature (5 °C), the mean blockade durations induced by PEG 1500 g·mol^–1 through Ael at −100 mV are comparable to those observed through α-HL, discernible populations are not resolved in the corresponding scatter plots for Ael at −100 mV (Figure SI 3b). Interestingly, increasing the applied voltage to −140 mV restores population resolution (Figure b), highlighting the critical role of the electric field in enhancing size discrimination in the Ael nanopore.

Thermal Dependence of PEG 2000 and 3400 Interactions with α-Hemolysin and Aerolysin Nanopores

It has been demonstrated that increasing the temperature in experiments using the α-HL nanopore at high salt concentrations (3 M KCl) enables the discrimination of individual molecular species within polydisperse PEG 3400 g·mol^–1 solutions. At room temperature, such discrimination was not achievable, primarily because the polymer chains could not be fully accommodated within the nanopore. The emergence of size discrimination at elevated temperatures was attributed to a decrease in PEG solubility and a temperature-induced collapse of PEG chains, leading to more compact conformations capable of entering the pore. To determine whether this temperature-induced enhancement of size discrimination is intrinsic to the PEG−α-HL system or represents a more general, nanopore-independent phenomenon, we performed a comparative study of the temperature dependence of size discrimination for PEG 2000 g·mol^–1 and PEG 3400 g·mol^–1 using both α-HL and AeL nanopores.

Representative current traces of PEG 2000 g·mol^–1 and PEG 3400 g·mol^–1 interacting with α-HL at a trans-positive voltage of +50 mV and with Ael at a trans-negative voltage of −140 mV, recorded at three different temperatures in 3 M KCl, are shown in Figures a and a, respectively. The corresponding scatter plots of blockade duration versus relative residual current (I _b/I ₀) are presented in Figure b (PEG 2000 g·mol^–1) and Figure b (PEG 3400 g·mol^–1). The temperature dependence of blockade frequency and blockade duration is summarized in Figures c and c. For both PEG sizes and both nanopores, the event frequency increases with the temperature, consistent with the behavior observed previously for PEG 1500 g·mol^–1 (Figure ). For α-HL, increasing temperature markedly enhances the resolution of PEG-induced current blockades. Size discrimination of individual PEG species within the polydisperse PEG 2000 g·mol^–1 sample emerges above 25 °C, whereas discrimination within PEG 3400 g·mol^–1 is observed only at 45 °C (Figures b and b). In contrast, no size discrimination of PEG 2000 g·mol^–1 or PEG 3400 g·mol^–1 is detected using the Ael nanopore over this temperature range at −100 mV (Figures SI 4 and SI 5). Instead, in Ael, size discrimination is observed only below 25 °C, with optimal discrimination occurring at the lowest investigated temperature (5 °C) under high voltage ΔV = −140 mV (Figures b and b).

4.

Effect of temperature on the size discrimination of PEG 2000 g·mol^–1 through α-HL and Ael nanopores: (a) Typical single-channel current traces of PEG 2000 g·mol^–1 through α-HL and Ael nanopores. (b) Scatter plots of blockade duration versus the relative residual current I _b/I ₀ of PEG 2000 g·mol^–1 through α-HL and Ael nanopores. (c) Blockade duration and blockade frequency induced by PEG 2000 g·mol^–1 through α-HL (circles) and Ael, at −100 and −140 mV (respectively white and black triangles), nanopores as a function of temperature. All recordings were performed in 3 M KCl solution buffered with 25 mM Tris at pH = 7. PEG 2000 g·mol^–1 was added to the trans side of α-Hl and applied voltage ΔV = +50 mV, whereas PEG 2000 g·mol^–1 was added to the cis side of Ael and applied voltage ΔV = −140 mV. Error bars represent the standard deviation of three independent experiments. The recorded events vary from 1000 to 20,000 events.

5.

Effect of temperature on the size discrimination of PEG 3400 g·mol^–1 through α-HL and Ael nanopores: (a) Typical single-channel current traces of PEG 3400 g·mol^–1 through α-HL and Ael nanopores. (b) Scatter plots of blockade duration versus the relative residual current I _b/I ₀ of PEG 3400 g·mol^–1 through α-HL and Ael nanopores. (c) Blockade duration and blockade frequency induced by PEG 3400 g·mol^–1 through α-HL (circles) and Ael, at −100 and −140 mV (respectively white and black triangles), nanopores as a function of temperature. All recordings were performed in 3 M KCl solution buffered with 25 mM Tris at pH = 7. PEG 3400 g·mol^–1 was added to the trans side of α-Hl and applied voltage ΔV = +50 mV, whereas PEG 3400 g·mol^–1 was added to the cis side of Ael and applied voltage ΔV = −140 mV. Error bars represent the standard deviation of three independent experiments. The recorded events vary from 1000 to 20,000 events.

Quantitatively, the temperature dependence of the blockade frequency differs substantially between the two nanopores and depends strongly on the PEG size. For Ael, the blockade frequency increases by approximately a factor of 6 over a 40 °C interval for PEG 1500 g·mol^–1 (Figure c), by a factor of 16 for PEG 2000 g·mol^–1 (Figure c), and by a factor of 43 for PEG 3400 g·mol^–1 (Figure c). For α-HL, the corresponding increases are approximately 20-fold for PEG 1500 g·mol^–1, 9-fold for PEG 2000 g·mol^–1, and 30-fold for PEG 3400 g·mol^–1. The temperature dependence of the blockade duration also reveals pronounced differences between nanopores and polymer sizes. For Ael, blockade durations decrease with increasing temperature for all PEGs, with a 14-fold decrease over 40 °C for PEG 1500 g·mol^–1, a 7-fold decrease for PEG 2000 g·mol^–1, and an almost temperature-independent behavior for PEG 3400 g·mol^–1 (Figures c, c,, and c). In contrast, while the PEG 1500 g·mol^–1 blockade durations decrease with temperature in α-HL, the blockade durations induced by larger PEGs increase with temperature. Specifically, blockade durations increase by approximately 1.6-fold over 40 °C for PEG 2000 g·mol^–1 and by nearly 2 orders of magnitude (≈86-fold) for PEG 3400 g·mol^–1 (Figures c and c).

These contrasting trends reveal fundamental differences in the mechanisms governing PEG–nanopore interactions in α-HL and Ael. In α-HL, elevated temperatures promote polymer compaction and increased residence times, which are essential for the size discrimination of large PEGs. In contrast, in Ael, size discrimination of large PEGs is achieved only at low temperatures and high applied voltages, where electric forcing overcomes the entropic barrier associated with partial insertion, enabling full-chain confinement and prolonged residence times. This behavior indicates that PEG confinement in α-HL is thermodynamically stabilized, whereas in Ael it is enforced by field-induced forcing (Figure ).

6.

Schematic illustration of PEG–nanopore interaction pathways inferred from transport dynamics in α-HL and Ael.

The strong dependence on nanopore architecture highlights the critical role of pore geometry and the electrostatic landscape in controlling polymer statics and dynamics under otherwise identical conditions. Notably, the voltage dependence of dwell times differs markedly between the two nanopores. In α-HL, dwell times exhibit a nonmonotonic dependence on voltage, reaching a maximum near 40 mV before decreasing, consistent with previous reports. In contrast, in Ael, we observe a similar nonmonotonic behavior, but with the maximum shifted to much higher voltages (∼−180 mV) (Figures SI 6 and SI 7). In both nanopores, the absence of size discrimination for large PEGs originates from incomplete confinement, where a portion of the polymer remains outside the pore and acts as an entropic spring, opposing further entry (Figure top).

It is well established that PEG, especially at high salt concentrations, can complex cations through coordination with its ether oxygen atoms, typically involving multiple oxygens along the polymer backbone. ,,,,,− Thus, PEG behaves as a weakly charged and flexible polymer, and the applied electric field facilitates its entry by overcoming the entropic restoring force. For an ideal chain of N monomers of size a, the coil size scales as

$$R=a{N}^{1/2}$$

For PEG 3400 g·mol^–1 (N = 77), this yields R ≈ 3 nm, which exceeds the aerolysin pore diameter (D ≈1.7 nm). This indicates that thermal fluctuations alone are insufficient to fully confine the polymer within the pore (see SI Sections 6 and 10). Under a sufficiently strong electric field, however, the polymer can overcome the associated free-energy barrier and occupy the entire pore volume. Assuming that the confined polymer adopts a “pearl necklace” conformation, i.e., a one-dimensional sequence of blobs of diameter comparable to the pore diameter (Figure SI 8), the number of monomers per blob is

$$g={\left(\frac{D}{a}\right)}^2\cong 26$$

yielding an axial extension

$$R_{\parallel }=\left(\frac{N}{g}\right)D\cong 5\mathrm{nm}$$

shorter than the pore length (L ≈ 8 nm) (Figure bottom). This demonstrates that the entire PEG 3400 chain can be accommodated within aerolysin, under field-induced confinement, provided that R _∥ < L, critical for size discrimination.

If we assume that PEG chains behave as excluded-volume coils, the number of monomers per blob becomes

$$g={\left(\frac{D}{a}\right)}^{5/3}\cong 15$$

leading to an axial extension R _∥ ≅ 9 nm, which is slightly longer than the pore. This scenario is likely, as it accounts well for our experimental observations. Specifically, scatter plots for polydisperse PEG 3400 in Ael show populations at high I _b/I ₀ values corresponding to lower-mass species, suggesting that larger mass species remain excluded. Additional evidence supports this interpretation. The high I _b/I ₀ populations disappear at elevated voltages ΔV = −200 mV (Figure SI 7), as their dwell times decrease, whereas the dwell times of larger-mass PEG species continue to increase up to approximately ≈ −180 mV. However, no clear size discrimination is observed in this regime due to blockade saturation. Altogether, these observations indicate that polymer confinement in Ael is driven primarily by the applied electric field rather than by a coil–globule collapse transition, as size discrimination is restored at room temperature or below. By contrast, experiments performed with α-HL at 45 °C exhibit well-defined populations at low I _b/I ₀ values, consistent with collapsed conformations of larger PEG 3400 species within the pore.

Note that the choice between an ideal-chain model and an excluded-volume coil description can, in principle, be informed by evaluating the Flory exponent γ from the diffusion-limited capture rate k ₀ (i.e., the capture rate in the absence of an applied voltage). By measuring k ₀ for PEGs of different molecular weights and plotting the capture rate as a function of chain length N, one expects a scaling relation

$$k_0\sim D_{\mathrm{diffusion}}\sim N^{-\gamma }$$

However, within the range of molecular weights investigated here, the precision of the fit is not sufficient to unambiguously determine the exponent. In previous work, using several PEG sizes, the data were fitted using γ = 3/5.

The coil–blob transition suggested here is expected, given the physical characteristics of the system. These include the ratio between polymer size and pore diameter R/D _pore, the high polymer flexibility reflected by a persistence length comparable to the monomer size l _p ≅ a, the long contour length of the aerolysin pore, the ratio D _pore/l_p , and the weakly charged nature of the polymer. Together, these properties are similar to those of unfolded proteins, which have been reported to adopt blob-like conformations during nanopore interaction. , Such conformations prevent strict single-file transport, thereby complicating amino-acid sequence readout in proteins or information recovery when polymers such as PEG are used as molecular storage supports.

Achieving a single-file configuration for a flexible polymer requires both geometric and energetic constraints: the pore diameter must approach the polymer persistence length, and a strong external driving force must be applied to stretch the chain. This driving force may originate from electrophoretic transport (as in the present work), electro-osmotic flow, critical solvent fluxes J _c on the order of $J_{\mathrm{c}}\approx \frac{k_{\mathrm{B}}T}{\eta }$ (η denotes the solvent viscosity), or osmotic pressure Π in semidilute polymer solutions, where $\mathrm{\Pi }\approx \frac{k_{\mathrm{B}}T}{{\xi }^3}$ , where ξ denotes the mesh size of the polymer network. Critical solvent fluxes or osmotic pressure-driven translocation are more applicable to solid-state nanopores, as it involves large pressures that can force polymer entry into narrow pores. In the latter case, polymer penetration is expected when the mesh size satisfies ξ ≤ D _pore. For ξ ≅ D _pore ≅ 1 nm, the estimated pressure Π ≈ 40 bar is too large to be supported by a lipid membrane when the polymer solution is present on only one side.

Treating the confined polymer as an entropic spring (see the entropic spring model in Supporting Information Section S7), and by assuming the extension R̃ under a confinement force f follows the linear-response relation

$$\mathrm{R̃}(f)=\left(\frac{N{a}^2}{3k_{\mathrm{B}}T}\right)f$$

here, k _B is the Boltzmann constant, and T is the absolute temperature. The relative extension reads

$$\frac{\delta R}{R}=\frac{\mathrm{R̃}}{N^{1/2}a}=\frac{N^{1/2}a}{3k_{\mathrm{B}}T}f\approx 0.6$$

We estimate

$$f\cong 1.8\frac{k_{\mathrm{B}}T}{N^{1/2}a}\cong 2{10}^{-12}\mathrm{N}$$

(which is on the order of a few piconewtons), consistent with the forces typically involved in single-molecule experiments. Interestingly, a simple scaling argument leads to the same estimate: taking the relevant energy scale as k _B T and the relevant length scale as the pore diameter D _pore, which sets the degree of confinement of the chain between the pore walls, one obtains

$$f\cong \frac{k_{\mathrm{B}}T}{D_{\mathrm{pore}}}\cong 2{10}^{-12}\mathrm{N}$$

in excellent agreement with the above calculation.

Thermodynamic parameters associated with PEG–nanopore interactions were extracted from the temperature dependence of the dissociation constant k _off(s ^–1) = 1/τ_off.

The Eyring transition-state formalism reads

$$k_{\mathrm{off}}=\frac{k_{\mathrm{B}}T}{h}\exp (-\frac{\Delta G}{\mathrm{R̅}T})$$

As ΔG = ΔH – TΔS,

$$k_{\mathrm{off}}=\frac{k_{\mathrm{B}}T}{h}\exp (\frac{T\Delta S}{\mathrm{R̅}T}-\frac{\Delta H}{\mathrm{R̅}T})$$

Thus,

$$\ln \left(\frac{k_{\mathrm{off}}}{T}\right)=-\frac{\Delta \mathrm{H}}{\mathrm{R̅}}\frac{1}{T}+\ln \left(\frac{k_{\mathrm{B}}}{h}\right)+\frac{\Delta S}{\mathrm{R̅}}$$

Here, R̅ is the universal gas constant, and h is the Planck constant, see Supporting Information Figures SI 9–11.

Specifically, plots of $\ln \mathrm{}\left(\frac{k_{\mathrm{off}}}{T}\right)$ versus $\frac{1}{T}$ allows the dissociation enthalpy (ΔH), entropy (ΔS), and the dissociation free energy (ΔG) to be determined. In this framework, ΔH reflects the dissociation enthalpy within the confined nanopore environment, including desolvation and polymer–pore interactions, whereas ΔS quantifies the loss of conformational freedom associated with polymer confinement. Table SI 3 shows that the dissociation enthalpy ΔH decreases systematically with increasing PEG molecular weight for both nanopores, indicating enhanced stabilization of longer polymers under confinement and consistent with increased dwell times. Although larger polymers are expected to experience a greater entropic penalty upon confinement, this effect is compensated by stronger enthalpic contributions. In particular, longer PEG chains provide more ether oxygen sites for cation coordination ,,,,,− and increased interactions with the pore, leading to cooperative stabilization. As a result, polymer–ion–pore interactions dominate, consistent with the observed increase in dwell times.

In α-HL, ΔH becomes negative and ΔS strongly negative, revealing entropy-limited dissociation and a confinement-induced apparent LCST lowering. In contrast, aerolysin exhibits predominantly positive ΔH, consistent with field-stabilized rather than thermodynamically driven confinement.

The association activation free energy ΔG is extracted from the slope α of the association constant rate k _on by plotting ln k _on versus $\frac{1}{T}$ , assuming an Arrhenius behavior (see Figures SI 12–14)­

$$k_{\mathrm{on}}\sim \exp (-\frac{\Delta G}{k_{\mathrm{B}}T})$$

Or

$$\ln k_{\mathrm{on}}\sim -\frac{\mathrm{\Delta }G}{k_{\mathrm{B}}}\times \frac{1}{T}$$

Thus,

$$\Delta G\cong \alpha k_{\mathrm{B}}$$

For instance, for the largest PEG (3400), ΔG ≅ 27 k _B T in α-HL and 9 k _B T in AeL. See Table SI 4 for other sizes.

The confinement energy ΔG _conf (see Section S10 in the Supporting Information) can be evaluated by using a simple scaling argument by considering that the activation free energy grows linearly with chain length

$$\Delta G_{\mathrm{conf}}(N)\sim N=\chi N$$

Thus, ΔG _conf can be directly extracted from the slope of the residence time by plotting ln τ versus N, assuming an Arrhenius behavior

$$\tau \sim \exp \left(\frac{\Delta G}{k_{\mathrm{B}}T}\right)$$

The slope of ln τ versus N yields the coefficient χ (Figure SI 15, Table SI 5). In the case of α-HL, this analysis gives

$$\frac{\Delta G}{k_{\mathrm{B}}T}=0.08N$$

and in the case of Ael,

$$\frac{\Delta G}{k_{\mathrm{B}}T}=0.05N$$

For PEG 3400, N = 77 yields ΔG ≅ 6.2 k _B T in α-HL and 3.8 k _B T in AeL.

Interestingly, simple scaling arguments based on the analogy between a random walk and a quantum particle trajectory qualitatively capture the measured confinement free energy of different polymers and pores. The confinement free energy of an ideal chain of N monomers of size a inside a pore of diameter D scales as

$$E_{\mathrm{conf}}\sim k_{\mathrm{B}}T\frac{N{a}^2}{D^2}$$

This scaling arises from the 1/D ² dependence of the confinement energy imposed by Heisenberg’s uncertainty principle and from the fact that an ideal chain contains $\frac{N{a}^2}{D^2}$ blobs of size D confined in the nanopore. Typically, if an ideal flexible chain of PEG contains 77 monomers of monomer size a = 0.35 nm confined in a pore of diameter D = 1.7 nm, it yields E _conf ≅ 4 k _B T in excellent agreement with confinement free energies of PEG 3400 measured here.

To further evaluate the roles of pore geometry and electrostatics, we investigated PEG transport when the polymer was introduced from the cis side (vestibule side) of the α-HL nanopore (Figure ). Under these conditions, no distinct blockade populations were observed at the elevated temperatures. Although the PEG blockade duration increased with temperature, this effect was markedly weaker than when PEG was added from the trans side, not sufficiently stabilizing collapsed conformations even if hydration weakens with temperature. These observations indicate that the entry sideassociated with different degrees of confinement (high through the trans side and low through the cis vestibule) and distinct electrostatic environments (surface charge distribution)is a critical determinant of size discrimination for large PEGs.

7.

Geometry and electrostatic effect on size discrimination of large PEGs: (a) Blockade duration as a function of temperature through α-HL for PEG 3400 g·mol^–1 in cis side (white circles) and trans side (black circles). Error bars represent the standard deviation of three independent experiments. (b, c) Scatter plots of blockade duration versus the relative residual current I _b/I ₀ of PEG 3400 g·mol^–1 through α-HL at 25 °C (b) and et 45 °C (c). Red dots correspond to PEG added to the trans side, and black dots to PEG added to the cis side. The experiments were performed in 3 M KCl, 25 mM TRIS, pH = 7, −50 mV (cis side) or +50 mV (trans sides).

The contrasting temperature and voltage dependence of PEG confinement in α-hemolysin and aerolysin can thus be understood within a unified free-energy framework for polymer confinement,

$$\Delta G={\Delta H}_{\mathrm{hydration}}-T\Delta S+{\Delta G}_{\mathrm{confinement}}+{\Delta G}_{\mathrm{surface}}$$

In α-hemolysin, the narrow β-barrel geometry imposes a substantial entropic penalty on coil conformations, ΔG _confinement > 0, while favorable polymer–pore interactions provide a stabilizing surface contribution ΔG _surface < 0. As the temperature increases, weakening of PEG hydration reduces the favorable hydration enthalpy ΔH _hydration, allowing confinement and surface terms to dominate the free-energy balance and shift the minimum toward compact, globular conformations. This confinement-induced lowering of the apparent LCST promotes full-chain occupancy of the pore, manifested experimentally as sharply increased blockade durations and consequently enhanced size discrimination for large PEGs at elevated temperatures. In contrast, in aerolysin, the balance of confinement free-energy terms differs: although geometric confinement remains significant, polymer–pore interactions do not sufficiently stabilize collapsed conformations as hydration weakens with temperature. Consequently, blockade durations decrease with increasing temperature for all PEG sizes, reflecting faster polymer dynamics rather than thermodynamic stabilization. Full-chain confinement in aerolysin is therefore achieved predominantly under high applied voltages at low temperatures, where strong electric fields mechanically force the polymer into the pore and overcome the unfavorable free-energy balance. Together, these results reveal two distinct confinement regimesthermodynamically driven confinement in α-hemolysin and field-forced confinement in aerolysindemonstrating that temperature-induced coil-to-globule behavior and enhanced size discrimination are nanopore-specific rather than universal (Figure SI 16).

Future studies exploring different nanopore types, including biological nanopores and solid-state nanopores, and varying salt species across the Hofmeister series, over wide concentration and temperature ranges, may enable precise tuning of polymer solubility and confinement. Such investigations would improve our understanding of LCST reduction under confinement.

Conclusions

In this work, we investigated how temperature, driving forces, and nanoscale confinement jointly regulate the transport and size discrimination of nonionic poly­(ethylene glycol) (PEG) in protein nanopores. By comparing PEGs of different molar masses (1500, 2000, and 3400 g·mol^–1) interaction with two β-barrel nanopores with distinct geometries and surface chargesα-hemolysin and aerolysinover a wide temperature range, we demonstrate that temperature modulates PEG behavior in a strongly nanopore-specific manner.

We showed that increasing temperature does not alter the nanopore structure but profoundly affects PEG–nanopore interaction kinetics. In α-hemolysin, elevated temperatures markedly increase blockade durations for larger PEGs, enabling effective size discrimination of PEG 2000 above 25 °C and PEG 3400 at 45 °C. This behavior, although our observations are inferred from transport dynamics rather than direct LCST measurements, is consistent with a confinement-induced lowering of the apparent LCST, where weakened PEG hydration at higher temperatures allows confinement and surface interaction terms to dominate the free-energy balance, favoring compact conformations and full-chain pore occupancy. In contrast, aerolysin exhibits the opposite temperature dependence: blockade durations decrease with an increase in temperature for all PEG sizes, indicating faster polymer dynamics rather than thermodynamic stabilization. In this case, full-chain confinement is achieved only at low temperatures and under high applied voltages, where strong electric fields mechanically force the polymer into the pore, inducing a coil-blob transition.

These contrasting behaviors can be rationalized within a unified free-energy framework that balances the hydration, entropy, confinement, and surface interaction contributions. Our results revealed two distinct confinement regimes: a thermodynamically driven confinement in α-hemolysin and a field-induced confinement in aerolysin. Importantly, we find no evidence for a classical bulk-like coil-to-globule transition occurring during pore entry from the cis side in α-hemolysin. Instead, under highly confined and high-salt conditions, temperature-dependent local dehydration and nanopore-specific interaction landscapes govern PEG residence times and transport dynamics.

Experimental Section

Polymers Used

Polydisperse poly­(ethylene glycol) (PEG) of average molar masses of 1500, 2000, and 3400 g·mol^–1 were used in this study. The final PEG concentrations were kept below 100 μM to ensure experiments in the dilute regime, well below the polymer overlap concentration. Assuming water to be a good solvent for PEG, the overlap concentration was estimated using the scaling relation

$$c^{*}\left(\frac{g}{\mathrm{c}{\mathrm{m}}^3}\right)=\frac{M\left(\frac{g}{\mathrm{mol}}\right)}{\frac{4}{3}\pi R_{\mathrm{g}}^3(\mathrm{c}{\mathrm{m}}^3)N_{\mathrm{A}}(\mathrm{mo}{\mathrm{l}}^{-1})}=\frac{m\left(\frac{g}{\mathrm{mol}}\right)N}{\frac{4}{3}\pi {(\frac{a}{\sqrt{6}}·N^{0.6})}^3(\mathrm{c}{\mathrm{m}}^3)N_{\mathrm{A}}(\mathrm{mo}{\mathrm{l}}^{-1})}\approx 6N^{-0.8}$$

while the radius of gyration was calculated as

$$R_{\mathrm{g}}(\mathrm{nm})=0.146N^{0.6}$$

where N _A(mol^–1) = 6,02 × 10^–23 is the Avogadro number, N is the number of monomers, and $m\left(\frac{g}{\mathrm{mol}}\right)=44$ is the molar mass of the PEG monomer unit, and the monomer size was taken as a = 0.35 nm. The PEG molar masses used, corresponding polymer dimensions, experimental concentrations, and estimated overlap concentrations are summarized in Table .

1. Summary of Experimental Data .

PEG	N	R g (nm)	C* (w/v) (%)	C PEG (α-Hl) (%)	C PEG (Ael) (%)
1500	34	1.18	35	0.75 × 10–2	3 × 10–4
2000	45	1.40	28	10–2	4 × 10–4–2 × 10–3
3400	77	1.93	18	4 × 10–2	6.8 × 10–4

^a N denotes the number of repeat units, R _g the radius of gyration of the polymer in aqueous solution, and C* the polymer overlap concentration. CPEG (α-HL) is the final polymer concentration used in experiments with the α-HL nanopore, while CPEG (Ael) is the final polymer concentration used with the AeL nanopore. The molar mass of a single PEG repeat unit is 44 g·mol^–1.

Different PEG sizes were used. N denotes the number of repeat units, R _g denotes the radius of gyration of the polymer in aqueous solution, and C* denotes the polymer overlap concentration. C _PEG (α-HL) is the final polymer concentration used in experiments with the aHL nanopore, while C _PEG (Ael) is the final polymer concentration used with the AeL nanopore. The molar mass of a single PEG repeat unit is 44 g·mol^–1.

Aerolysin Production

AeL is a pore-forming toxin from Aeromonas hydrophila produced as a precursor protein, proaerolysin (ProAeL), which forms soluble dimers. Recombinant wild-type ProAeL was produced in Escherichia coli BL21 using the pET22b-PA vector. ProAeL is produced after IPTG induction and localizes into the bacteria periplasm. The periplasmic fraction containing soluble ProAeL dimers was extracted by using an osmotic shock. Because the recombinant protein is C-terminal His-tagged, ProAeL was further purified by affinity chromatography using Ni-Sepharose MiniSpin columns, and elution was made by adding imidazole. The recombinant ProAeL purity (about 99%) was determined by SDS-polyacrylamide gel electrophoresis and Coomassie blue staining. The ProAeL concentration was estimated by the optical absorbance at 280 nm. ProAeL (3 μg) was activated by 0.25 units of trypsin–agarose in 25 mM HEPES at pH 7.5 for 30 min at 25 °C, as previously reported.

Nanopore Recording

A vertical lipid bilayer electrophysiology setup (Warner Instruments, Hamden, CT, USA) was used for all of the experiments (α-HL or AeL). The lipid bilayer was formed by painting and spontaneous thinning a film of diphytanoyl-phosphocholine, DPhPC (Avanti Polar Lipids, Alabaster, AL, USA), in decane (Merck, Darmstadt, Germany) at 10 mg/mL over a 150 μm diameter aperture on a Teflon support separating the cis- and trans-compartments. The aqueous solutions on both sides of the membrane contained 1 mL of 3 M KCl, buffered in 25 mM TRIS at pH 7 (Merck, Darmstadt, Germany). Two matched Ag/AgCl electrodes (Alfa Aesar, Ward Hill, MA, USA) were used to apply a voltage of millivolts across the membrane and measure the ionic current. The cis-compartment is defined as the virtual ground. After forming the lipid bilayer, either α-HL or activated aerolysin was added to the cis-compartment at ≈50 ng/mL final concentration. Once a single nanopore formed, a PEG solution was added either to the trans-compartment (PEG - α-HL) or to the cis-compartment (PEG - AeL).

Single-channel current recordings were performed using an Axopatch 200B patch-clamp amplifier (Molecular Devices, Sunnyvale, CA, USA) in whole-cell mode with a CV-203BU headstage. The signal was filtered using the internal 4-pole Bessel filter at a cutoff frequency of 10 kHz. The data were digitized at 100 kHz using a DigiData 1440 A/D-converter (Molecular Devices) controlled by Clampex 10.2 software (Molecular Devices). The solution temperature was controlled with a Peltier device controlled by a bipolar temperature controller (CL-100, Warner Instruments) coupled to a liquid cooling system (LCS-1, Warner Instruments).

Data Analysis

Data analysis was performed using Igor Pro 6.12A software (WaveMetrics, OR, USA) with in-house routines (Figure SI 17). The approach relies on a statistical analysis of the properties of the polydisperse PEGs-induced current blockades, involving at least several hundred (more typically thousands) events. The detection of each individual current blockade in a nanopore current vs time recording is based on a single current threshold (Th) method. A blockade event is detected when the current magnitude becomes smaller than Th, until it returns to a value greater than Th. The beginning of the blockade is defined as the first point of current increase after having monotonically decreased below Th, and its end is defined as the last point of current decrease before monotonically increasing above Th. This defines the range of points used to compute the characteristic quantities of the blockade, such as dwell time t _b, mean residual current value I _b, and standard deviation σ_b of the residual current. Here, Th = I ₀ – 5 σ₀, where I ₀ and σ₀ are the mean value and standard deviation of a Gaussian fit of the open-pore current distribution, respectively.

The mean blockade duration is determined by fitting the distribution of the blockade duration with a single-exponential function. The mean blockade frequency is determined by fitting the distribution of the duration between successive events with a single-exponential function (see Figures and SI 17).

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsmeasuresciau.6c00050.

• Ion transport in protein nanopores: α-hemolysin versus aerolysin, Figures SI 1–2; nanopore conductance, Tables SI 1–2; scatter plots, Figures SI 3–5; voltage dependence of dwell times for Ael, Figure SI 6; scatter plot PEG 3400 at −150 mV, −180 mV, −200 mV, Figure SI 7; flexible chain in free geometry vs confined geometry, Figure SI 8; polymer as an entropic spring; thermodynamic parameters: dissociation energy values, Figures SI 9–11, Table SI 3; thermodynamic parameters: association energy values, Figures SI 12–14, Table SI 4; confinement energy, Figures SI 15–16, Table SI 5; and data analysis, Figure SI 17 (PDF)

∥.

A.A., C.D., and F.P. contributed equally to this work. A.A, C.D, and F.P. performed nanopore experiments and analyzed the data. M.P.G. produced the aerolysin nanopore, N.L.G. was involved in the discussion, A.O. conceived the project, wrote the manuscript, and developed the physical model and scaling arguments. All authors have approved the final version of the manuscript.

This work was financially supported by the French National Research Agency (ANR) under grant ANR-17-CE09–0032–01. A.A. and A.O. acknowledge financial support from CY Advanced Studies (CY Cergy Paris Université). A.A. acknowledges UEFISCDI Romania, PN-IV-PCE-2023–0678. A.O. and N.L.G acknowledge the financial support from CY Initiative.

The authors declare no competing financial interest.