Effect of screening on the transport of polyelectrolytes through ... - lambe

May 7, 2008 - ionic strength is that one lowers the electrical conductivity ... iments, where the elution properties of polyelectrolytes ... Materials and methods. –.
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Effect of screening on the transport of polyelectrolytes through nanopores ´, J. Pelta and L. Auvray G. Oukhaled, L. Bacri, J. Mathe EPL, 82 (2008) 48003

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May 2008 EPL, 82 (2008) 48003 doi: 10.1209/0295-5075/82/48003

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Effect of screening on the transport of polyelectrolytes through nanopores ´1 , J. Pelta2 and L. Auvray1(a) G. Oukhaled1 , L. Bacri1 , J. Mathe 1

Institut de Chimie des Mat´eriaux Paris-Est, ´equipe Mat´eriaux Polym`eres aux Interfaces, CNRS-UMR 7182, ´ ´ Universit´e d’Evry - Bd F. Mitterrand, 91025 Evry, France, EU 2 Groupe Micro-environnement et Comportements Cellulaires, Universit´ e de Cergy-Pontoise - 2. av. A. Chauvin, 95302 Cergy-Pontoise Cedex, France, EU received 3 July 2007; accepted in final form 26 March 2008 published online 7 May 2008 PACS PACS

82.37.-j – Single molecule kinetics 82.35.Rs – Polyelectrolytes

Abstract – We study the transport of dextran sulfate molecules (Mw = 8000 Da) through a bacterial α-hemolysin channel inserted into a bilayer lipid membrane submitted to an external electric field. We detect the current blockades induced by the molecules threading through one pore and vary the ionic strength in an unexplored range starting at 10−3 M. In the conditions of the experiment, the polyelectrolyte molecules enter the pore only if the Debye screening length is smaller than the pore radius in agreement with theory. We also observe that large potentials favour the passage of the molecules. The distribution of blockade durations suggests that a complex process governs the kinetics of the molecules. The dwelling time increases sharply as the Debye length increases and approaches the pore radius. c EPLA, 2008 Copyright 

Introduction. – As shown for the first time in 1996 on the case of single-strand RNA and DNA [1], one detects directly by a simple electrical method the passage of a single water-soluble macromolecule through a protein nanopore inserted in a bilayer lipid membrane. A very convenient protein is α-hemolysin from Staphylococcus aureus [2]. It forms an heptameric transmembranar passive pore about 10 nm long and 2 nm wide. If the membrane is submitted to an electrical tension of order 100 mV (corresponding to an electric field of 2 × 107 V/m), one chain passing in the pore induces during a fraction of millisecond or longer a variation of electrical current of order 100 pA, depending on the chain length and ionic strength. Several teams in the world explore theoretically [3–5] and experimentally [1,6–10] (for a review see ref. [10]) the wide possibilities of this technique concerning the development of nano-sensors [6], the fast sequencing of nucleic acids [1,7], the manipulation of biological macromolecules [9–11] and the fundamental properties of confined polymer chains [8]. Most of the experiments in this last field have been performed on neutral polymers such as poly(ethylene glycol) (PEG) in dilute solutions [8] or (a) E-mail:

[email protected]

with natural or synthetic polyelectrolytes at high ionic strength, with salt concentrations equal to or larger than 1 M [12]. In this regime, the only particularity of polyelectrolytes with respect to neutral polymers is that they are driven in the pore by the applied electric field. The influence of the electric field and the effect of the chain length have been studied on single-strand DNA [13,14], double-strand DNA (with artificial nanopores) [15] and more recently on poly(styrenesulfonate), a classical model polyelectrolyte [16]. Only one experiment [17] explored the low-salt regime, where the electrostatic effects are the strongest [18]. One experimental difficulty in lowering the ionic strength is that one lowers the electrical conductivity and the observed electrical currents. The behaviour of polyelectrolytes confined in pores has not been much studied in the past. The first observations were performed in gel permeation chromatography experiments, where the elution properties of polyelectrolytes were studied as a function of the ionic strength [19]. The elution curves show that the polyelectrolyte chains are excluded from the smallest pores of the gel at low ionic strength. In the absence of surface charges, two effects, discussed in ref. [20], prevent a polyelectrolyte chain from entering a long narrow pore: the reluctance of ions to enter a medium of low dielectric constant and the necessity

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Materials and methods. – Planar bilayer experiments. The lipid used is 1,2diphytanoyl-sn-glycerophosphocholine from Aventi Polar Lipid and α-hemolysin is from Sigma. The lipid and protein are used without further purification. Bilayer lipid membranes are deposited on a 150 µm wide hole separating two (cis and trans) compartments (Warner) from a lipid solution in decane by using the original painting method of Rudin and Mueller [26]. By definition the cis compartment corresponds to the one of the reference electrode. After thinning of the decane film and formation of a planar bilayer, the channels are formed by adding 0.15 nanomole of monomeric α-hemolysin from a mother solution in the 1 ml cis compartment. Single-channel currents are recorded by an Axopatch 200B patch-clamp amplifier (Axon Instruments) in the whole-cell mode with a CV-203BU headstage. Data are acquired at 10 µs intervals (100 kHz) with the DigiData 1322A digitizer coupled to the Clampex software (Axon instruments). The data are filtered using an 8-pole Bessel filter (the internal filter of the Axopatch 200B) at a cut-off frequency of 10 kHz except for the experiments made with 0.05 M KCl and below, which are filtered at 2 kHz in order to improve the signal over noise ratio. Buffer solution. A series of buffer solutions of 1, 6.25, 12.5, 25, 50, 75, 100, 200, 500, and 1000 mM KCl, 5 mM HEPES, pH = 7.5 were prepared in order to get media of increasing conductivity and decreasing Debye length. Dextran sulfate. The dextran sulfate sodium salt is purchased from Sigma and is used without purification. Its average molar mass is 8000 Da. Dextran sulfate is a strongly charged polymer with 2 sulfate groups per

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of compressing the counterions cloud of the chains to locally insure electroneutrality. The dielectric effect has been discussed theoretically by Parsegian [21] and more recently by Shklovskii [22] in the case of small ions. The case of infinitely thin polyelectrolytes is studied in ref. [23] while the more realistic case of chains with a finite diameter is discussed in comparison with experiments in ref. [17] and detailed in ref. [24]. The second effect comes into play when the Debye screening length κ−1 is larger than the pore radius [23]. It was checked directly in one neutron scattering experiment probing the structure of polystyrene sulfonate chains confined in Vycor glass that polyelectrolytes chains indeed enter pores smaller than the chain size if κ−1 is smaller than the pore size [25]. This effect has, however, not been observed directly at the single pore and single-molecule level and it was interesting to use the technique of nanopore recording to study it. This is the aim of the experiments reported in this article. We tried several polyelectrolytes, polystyrene sulfonate (PSSNa), polyacrylic acid (PAA) and dextran sulfate. PSSNa and PAA interact with the lipid membrane, this makes the experiments very difficult. We report here our work on dextran sulfate.

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Time (s) Fig. 1: Current trace of dextran sulfate at 75 mM KCl (κ−1 = 1.1 nm) (data filtered at 10 kHz) and its histogram showing the definition of the different current thresholds.

monomer. Due to Manning’s condensation, its effective charge density is one elementary charge −e per Bjerrum length lB , defined as lB = e2 /(4πε0 εw kB T ), e is the elementary charge, ε0 the vacuum dielectric constant, εw the dielectric constant of water, kB the Boltzmann constant and T the temperature. At ambient temperature, lB = 0.7 nm. All experiments are made under the same conditions. The applied potential V is fixed at 100 mV unless stated otherwise. The necessary amount of dextran sulfate is added on the cis side of the membrane from a mother solution to reach the final concentration of 0.5% (w/v). The KCl concentration of the solution in the presence of a polymer is varied from 0.0125 M (κ−1 = 2.7 nm) to 1 M (κ−1 = 0.3 nm). Statistical analysis of the data. An example of the measured current trace in the presence of dextran sulfate is shown in fig. 1. One distinguishes the baseline, which corresponds to the noisy ionic current through one “empty” channel and the pulses caused by the dextran sulfate molecules dwelling in the pore. The main issue of the data analysis is to separate the pulses of electric current from the noise. This is done by imposing that a pulse height must be larger than a given threshold in order to be considered as significant. A first threshold I1 is defined by the relation I1 = I0 − 2σ, where I0 is the average baseline current and σ is the standard deviation from the baseline current in the empty channel. But this first choice is not selective enough. Molecules approaching the pore entry and partially blocking it without going in might contribute significantly to the blockades statistics. For this reason, we decided to impose a second, more severe, discrimination. The second discrimination threshold I2 is determined from the histogram of the digitized values of the electric current (fig. 1). One observes two populations separated by one gap located at M . The largest population is associated to the fluctuating baseline current. The second population is associated to the blockades. If the two peaks are well separated, it is natural to choose I2 = M . If this is not the case, we choose I2 = I0 − 3σ. In each case the width of the pulses Tt is measured at the first cut-off I1 .

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Results and discussions. – The first experiment we performed aimed at finding the lowest limit of the ionic strength where the insertion of channels and the current measurements were still possible. Our observations show that hemolysin insertions in the lipid bilayer are still possible and observable at a KCl concentration of 1 mM. The current jump corresponding to one insertion is then 0.3 pA (fig. 2). We measured the pore conductance as a function of the ionic strength in the range 1 mM–1 M at a fixed applied potential V = 100 mV. The statistical analysis of current levels as several channels are inserting successively into the lipid bilayer enables us to define precisely the mean unitary current of one open pore (fig. 2a). The pore conductance depends linearly on the salt concentration except at very low salt where a small deviation from the linear behaviour is perceptible. This could be due to a very weak contribution of the counterions of the surface charges of the pore to the pore conductivity [28]. Let us now consider the results in presence of dextran sulfate. Typical current records obtained for three different KCl concentrations, 50, 100, et 1000 mM, are reported in figs. 3a, b, c. For V = 100 mV, the values of the mean electric current through one channel are, respectively 5, 10 and 100 pA. In each case, current blockades due to the presence of dextran sulfate molecules in the pore are

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The average frequency of blockades is deduced from the distribution of the time intervals Ti between two successive blockades. In all practical cases this distribution is described with a very good approximation by a single exponential y = A exp(−t/τ ) as expected for independent events [27]; τ is the average time interval between successive blockades and is the reciprocal of the average frequency of blockades. The distribution of the pulses width or blockades duration Tt is also of interest. The statistical analysis of the data is performed with the software Igor from Wavemetrics, Inc.

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Fig. 2: a) Conductance jumps measured as several α-hemolysin channels insert themselves progressively into a lipid bilayer, [KCl] = 6.25 mM, V = 100 mV. The inset is the corresponding histogram of the electric current. b) Plot of the α-hemolysin conductance vs. KCl concentration. The inset shows the jump of the current due to the insertion of one channel at the lowest KCl concentration studied, 1 mM.

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Fig. 3: Left: single channel records in the presence of dextran sulfate, V = 100 mV. a) [KCl] = 1 M (κ−1 = 0.3 nm), b) [KCl] = 0.1 M (κ−1 = 0.95 nm), c) [KCl] = 0.05 M (κ−1 = 1.35 nm). d) Distribution of the time intervals Ti between two successive blockades in semi-logarithmic coordinates. The solid line is an exponential fit. e) Measured frequency of blockades vs. Debye length between [KCl] = 1 M and [KCl] = 0.05 M. No blockades are observed below 0.05 M. The solid line is a linear interpolation of the data.

observed. The horizontal time axes of the three traces are plotted on the same scale and one clearly observes that the frequency of the blockades increases as the ionic strength increases. The statistical analysis yields values of blockades frequency varying from 1 Hz at [KCl] = 0.05 M to 22 Hz [KCl] = 1 M. No blockades are observed below 50 mM when V = 100 mV. The frequency of blockades is plotted as a function of the Debye screening length of the solutions in fig. 3e. No blockades are observed at [KCl] = 25 and 12.5 mM, corresponding to Debye lengths of 1.9 and 2.7 nm. The simplest possible (linear) extrapolation of the data shows the frequency of blockades is cut off above κ−1 = 1.4 nm corresponding to [KCl] = 45 mM. This threshold is close to the value of the channel radius in the stem, 1.3 nm [2], in agreement with the simple theoretical prediction for long pores. In our case, a compression of the counterions cloud over the finite length of the channel appears sufficient to hinder the passage of the dextran sulfate chains. If the electrical force is sufficiently strong, it should be possible to force the passage of the chains through the hemolysin, even if the Debye length is larger than the pore radius. We could not observe all the regimes because of the difficulty of the experiments. In particular, in the low-salt regime where no passage was initially observed, we could not force the passage of the chains by increasing the potential without breaking the lipid membrane. But we could observe the reverse effect: a decrease of potential

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Fig. 4: Average frequency of current blockades vs. applied voltage in semi-log representation, [KCl] = 50 mM (κ−1 = 1.35 nm). The continuous line is a best fit to a van ’t Hoff-Arrhenius law. No blockades are observed below 70 mV.

leading to the disappearance of the passage of the chains. This is shown in fig. 4, where we plot the average frequency of the blockades measured as the function of the applied voltage when [KCl] = 50 mM. No blockades are observed when the electric potential is smaller than 70 mV. Our interpretation is that at this point the electric driving force does not overcome anymore the confinement force. If this force is due to the confinement of counterions, its order of magnitude is (omitting logarithmic terms) kB T , b where b is the average distance between effective charges on the chain. Because of the counterions condensation, b is equal to the Bjerrum length lB . The electric force is qE = zeV /L, q = ze is the electrical charge of the chain submitted to the electric field E = V /L in the pore, L is the length of the pore. If we equal the two forces at the threshold we estimate the number z of dextran sulfate effective electric charges in the pore F∼

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With kB T /e = 25 mV, we deduce z = 5 with L = 10 nm. This value is smaller than the one, L/lB (= 14 for L = 10 nm), deduced from a direct calculation assuming one effective charge per Bjerrum length. At this point, one can raise the question of the influence of the electrical charge of the hemolysin, which is certainly important in the absence of screening. In the pH range of our study, the hemolysin heptamer has 7 positive charges, mainly localized inside the stem [29]. If we assume that the effect of the 7 charges of hemolysin is in first approximation to neutralize 7 charges of the polyion and that the counterions of hemolysin have escaped in the bulk for entropic reasons, we deduce that the number of effective charges of the polyion submitted to the electric field is only 14 − 7 = 7, which is quite close our observed value of 5.

The effect of the applied voltage on the translocation frequency of DNA single-strand molecules through hemolysin in 1 M KCl has been studied in ref. [13]. The blockade frequency f is well described by a van ’t HoffArrhenius law f = pν exp[−(U ∗ − δU )]/kB T , where p is a probability factor, ν a frequency factor, U ∗ an activation energy and δU = zeV , the energy difference due to the transmembrane potential V . In a vanishing potential the blockade frequency is f0 = pν exp − U ∗ /kB T . f is then written as f = f0 exp(zeV /kB T ). This equation describes approximately our data as shown in fig. 4 (continuous line). A best fit yields experimentally f = 5 × 10−3 exp 0.05V (with V in mV). This would correspond to an effective charge z = 1.25 and to a zero voltage frequency f0 = 5 × 10−3 s−1 . The value of the charge is still smaller as the one evaluated above by a simple argument. It is also of the same order as the one measured on ssDNA and other polyelectrolytes such as PSSNa (unpublished data). According to a recent theory [24], such a low effective value could traduce an increased condensation of the counterions due to the confinement of the charges in a medium of low dielectric constant. This is a very interesting effect, which has to be further studied. To obtain an estimation of the activation energy, we assume p = 1 and evaluate the frequency factor ν by a barrier penetration calculation [13], which gives ν ≈ Cb Ddif f A/l, where Cb is the bulk concentration of the polymer chains, Ddif f the chains diffusion coefficient, A the area of the channel section and l the width of the barrier. In our case Cb = 625 µM corresponding to 3.75 × 1017 chains per cm3 , A = 3 × 10−14 cm2 and we take l ≈ 10 nm. Assuming as an order of magnitude Ddif f ≈ 10−6 cm2 s−1 , we obtain U ∗ ≈ 14.6 kB T , a very high value, larger than the one observed at 1 M KCl (which is of order 8 kB T for ssDNA and PSSNa). This expresses the strength of the electrostatic effects when the Debye length becomes larger than the pore radius. We also analyzed the duration of the current blockades, which yields information on the dynamics of entrance or passage of the chains in the hemolysin channel. We plot in fig. 5a one example of the statistical distribution of the blockades duration, noted Tt . In the simplest cases, this distribution is exponential. This is what we observed at long times. In fact, the observed time distribution is best fitted by a sum of two exponentials, yielding two characteristic times, a short and a long one. These times remain in the same ratio as we vary the ionic strength at constant voltage. Their variation as a function of the Debye screening length is reported in fig. 5b. The uncertainty on the data at low salt is large because the experiments are difficult. The trend of the variation is best represented by a sigmoidal curve. The measured times are constant at large salt concentrations, when κ−1 is smaller than 0.5 nm and increases rapidly as the Debye screening length approaches the pore radius, 1 nm, and then remain constant within the uncertainty of the

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Fig. 5: a) Distribution of the duration of the blockades or “dwell time”. The solid line is a fit by a sum of two exponentials, [KCl] = 75 mM. b) Plot of the variation of the short and long characteristic times with the Debye length showing the slowingdown of dynamics of the confined dextran sulfate chains as the Debye length increases.

experiments at larger κ−1 . At this stage we cannot explain the shape of the distribution of the blockades duration. The value of the mean dwelling time of the dextran sulfate at large salt is of order 0.1 ms. This is the same order of magnitude as the transit time of short neutral polymer chains of equivalent length. Our data show clearly that the kinetics of polyelectrolyte confined in a channel is strongly slowed down (in our case by almost two orders of magnitude) when the Debye screening length becomes equal to the size of the pore. This is not shocking but remains to be explained in detail. Part of the effect might be explained by the electrostatic stretching of the polyelectrolyte chains, which increases the viscous friction, as this is the case in the bulk when the ionic strength is lowered. But this does not account for the large observed variation. It would be interesting to probe the effect of the applied potential. This will be done in future experiments. Conclusion. – We have directly evidenced the difficulty of confining electrically charged polymer chains in small pores when the Debye screening length is larger than the pore radius and when the pore and the chains are sufficiently long. This possibility of playing with “field effects” to control the transport of macromolecules may be useful in future nanotechnological devices. More systematic studies are needed. It will be of interest to vary the length of the molecule, the pore parameters, length, radius and surface charges and to proceed with the experiments on the effects of the voltage in order to attempt to force the passage of polyelectrolyte chains through very small pores at very low ionic strength. ∗∗∗ ´gan, M. PastorizaWe thank R. Daniel, P. Gue Gallego and L. Brun for useful discussions. REFERENCES [1] Kasianowicz J. J., Brandin E., Branton D. and Deamer D. W., Proc. Natl. Acad. Sci. U.S.A., 93 (1996) 13770.

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