Role of Electroosmosis in the Permeation of Neutral Molecules: CymA and Cyclodextrin as an Example

Abstract

To quantify the flow of small uncharged molecules into and across nanopores, one often uses ion currents. The respective ion-current fluctuations caused by the presence of the analyte make it possible to draw some conclusions about the direction and magnitude of the analyte flow. However, often this flow appears to be asymmetric with respect to the applied voltage. As a possible reason for this asymmetry, we identified the electroosmotic flow (EOF), which is the water transport associated with ions driven by the external transmembrane voltage. As an example, we quantify the contribution of the EOF through a nanopore by investigating the permeation of α-cyclodextrin through CymA, a cyclodextrin-specific channel from Klebsiella oxytoca. To understand the results from electrophysiology on a molecular level, all-atom molecular dynamics simulations are used to detail the effect of the EOF on substrate entry to and exit from a CymA channel in which the N-terminus has been deleted. The combined experimental and computational results strongly suggest that one needs to account for the significant contribution of the EOF when analyzing the penetration of cyclodextrins through the CymA pore. This example study at the same time points to the more general finding that the EOF needs to be considered in translocation studies of neutral molecules and, at least in many cases, should be able to help in discriminating between translocation and binding events.

Figure 1

(A) Cartoon representation of the wild-type CymA crystal structure (PDB: 4D51) including modeling of the missing residues (Glu10-Phe21). The first 15 N-terminus residues truncated in the ΔCymA mutant are highlighted in green. (B) View of the distribution of internal charged residues. In this side view of the channel, we highlighted the negatively charged residues aspartic/glutamic acids in red (upper left) and the positively charged residues arginine/lysine in blue (upper right). The top views of the pore (lower left and right) highlight again the charged residues (yellow, C atoms; blue, N atoms; red, O atoms). (C) One-dimensional free-energy profile of the ions (K⁺, Na⁺, Mg²⁺, and Cl⁻) along the channel axis determined using metadynamics simulations to illustrate the preference of cations over anions. The reaction coordinate distance is defined as the distance between the center of mass of the C_α atoms of the protein and the ion along the z axis. EC and PP denote the extracellular and periplasmic sides of the channel, respectively. To see this figure in color, go online.

Figure 2

IV curve for the ΔCymA mutant from electrophysiological experiments (A) and MD simulations (B) for three different salts: 1 M KCl (black line), 1 M NaCl (blue line), and 1 M MgCl₂ (red line). (C) Zero-current membrane potential, V_m, versus salt concentration ratio [c1/c2] in both chambers for the three different salt solutions. Insertions were obtained with 0.1 M salt solution in both chambers and the respective salt concentration gradient was established by adding equal amounts of 0.1 M and 1 M salt solutions to the trans and cis sides, respectively. The V_m values were measured on the diluted side (trans) for at least four independent measurements. (D) The I_cation/I_anion ratio calculated from the applied-field simulations. Both (C) and (D) illustrate the cation selectivity for the KCl and NaCl solutions and the anion selectivity for the MgCl₂ solution. To see this figure in color, go online.

Figure 3

(A) Typical ion-current recordings at positive voltage +100 mV (top row) and negative voltage −100 mV (bottom row) in the presence of 10 μM α-CD on the extracellular (trans) side for three buffers, i.e., 1 M KCl (black), 1 M NaCl (blue), and 1 M MgCl₂ (red). (B and C) Association rate, k_on (B), and residence time, τ (C), of the α-CD molecule as a function of applied voltage are shown corresponding to the current traces in (A). (D) The net flux of the cations K⁺, Na⁺, and Mg²⁺ and the anion Cl⁻ shown as a function of applied voltage. In addition, the net water flux is depicted. (E) The schematic representations illustrate the direction of the cations, anions, and water molecules at positive voltages through the ΔCymA pore (for negative voltages, all arrows need to change direction). To see this figure in color, go online.

Figure 4

Schematic representation of the EOF-mediated permeation of α-CD through ΔCymA. The direction of the EOF for three buffers, i.e., 1 M KCl (black), 1 M NaCl (blue), and 1 M MgCl₂, is shown at positive voltages (left) and negative voltages (right). The dashed arrows indicate the rare translocation events. EC and PP denote the extracellular and periplasmic sides of the channel, respectively. To see this figure in color, go online.

Figure 5

Unbiased and applied-field simulations at +1 V and −1 V were performed for the α-CD molecule bound at the entry site of ΔCymA in the absence of any ionic salt. Each MD trajectory is 50 ns long. The cocrystallized state of the α-CD molecule at the extracellular side of CymA (PDB: 4D5B) is shown together with the direction of the applied electric field. The distance indicates the distance of α-CD from the center of mass of the protein. In addition, the frequency of the molecule staying at a particular position for 0 V, +1 V, and −1 V is shown. To see this figure in color, go online.

Figure 6

(A) Unbiased simulation (0 V) and applied-field simulations using +1 V and −1 V were performed for the α-CD molecule bound at the entry site of ΔCymA in the presence of 1 M KCl (left) and 1 M MgCl₂ (right). In the absence of an external electric field (orange curve), α-CD shows a high stability, whereas the molecule leaves the binding site and starts to migrate toward the bulk when fields are applied (purple and green curves). Each frequency distribution curve is obtained from three simulations, each carried out for 50 ns. The direction of the electroosmotic flow is shown with respect to the polarity of the external field. (B) Constant-velocity SMD simulations were carried out to detach the α-CD molecule from the entry site in the presence of 1 M KCl (left) and 1 M MgCl₂ (right). The α-CD molecule was pulled toward the bulk along the pore axis with and without an external electric field. Each force profile is averaged over five simulations varying in length from 20 to 50 ns. To see this figure in color, go online.

Figure 7

(A and B) Association rate, k_on (A), and residence time, τ (B), as a function of applied voltage for α-CD, β-CD, and γ-CD (10 μM each) added on the extracellular side, in the presence of 1 M NaCl and 10 mM 2-(N-morpholino)ethanesulfonic acid at pH 6. (C) Schematic representation of the EOF-mediated permeation of all three CDs through ΔCymA. The direction of the EOF with respect to the applied voltages is shown. The dashed arrow indicates the rare translocation events. To see this figure in color, go online.