Ions and Counterions in a Biological Channel: A Molecular Dynamics Simulation of OmpF Porin from Escherichia coli in an Explicit Membrane with 1 M KCl Aqueous Salt Solution

Abstract

A 5 ns all-atom molecular dynamics trajectory of Escherichia coli OmpF porin embedded in an explicit dimyristoyl-phosphatidylcholine (DMPC) bilayer bathed by a 1 M [KCl] aqueous salt solution is generated to explore the microscopic details of the mechanism of ion permeation. The atomic model includes the OmpF trimer, 124 DMPC, 13470 water molecules as well as 231 K⁺ and 201 Cl⁻, for a total of 70,693 atoms. The structural and dynamical results are in excellent agreement with the X-ray data. The global root-mean-square deviation of the backbone atoms relative to the X-ray structure is 1.4 Å. A cluster of three fully charged arginine (Arg42, Arg82, and Arg132) facing two acidic residues (Asp113 and Glu117) on L3 in the narrowest part of the aqueous pore is observed to be very stable in the crystallographic conformation. In this region of the pore, the water molecules are markedly oriented perpendicular to the channel axis due to the strong transversal electrostatic field arising from those residues. On average the size of the pore is smaller during the simulation than in the X-ray structure, undergoing small fluctuations. No large movements of loop L3 leading to a gating of the pore are observed. Remarkably, it is observed that K⁺ and Cl⁻ follow two well-separated average pathways spanning over nearly 40 Å along the axis of the pore. In the center of the monomer, the two screw-like pathways have a left-handed twist, undergoing a counter-clockwise rotation of 180° from the extracellular vestibule to the pore periplasmic side. In the pore, the dynamical diffusion constants of the ions are reduced by about 50% relative to their value in bulk solvent. Analysis of ion solvation across the channel reveals that the contributions from the water and the protein are complementary, keeping the total solvation number of both ions nearly constant. Unsurprisingly, K⁺ have a higher propensity to occupy the aqueous pore than Cl⁻, consistent with the cation selectivity of the channel. However, further analysis suggests that ion–ion pairs play an important role. In particular, it is observed that the passage of Cl⁻ occurs only in the presence of K⁺ counterions, and isolated K⁺ can move through the channel and permeate on their own. The presence of K⁺ in the pore screens the negative electrostatic potential arising from OmpF to help the translocation of Cl⁻ by formation of ion pairs.

Introduction

The outer membrane of Escherichia coli protects the cell against hostile agents and facilitates the uptake of nutrients. This activity is mediated by macromolecular structures called porins.1., 2., 3. These nonspecific porins, which allow the diffusion of hydrophilic molecules with molecular mass up to 600 Da, are not very selective and have only some specificity toward cations or anions. While the cation-selective matrixporin (OmpF), a major component of the outer membrane of E. coli, is produced under normal conditions, the anion-selective phosphoporin (PhoE) and the cation-selective osmoporin (OmpC) are expressed under phosphate limitations or under conditions of osmotic stress, respectively.

The three-dimensional structure of several porins has been determined to high resolution by X-ray crystallography.4., 5., 6., 7., 8., 9. For general reviews on porins the reader is referred to Schulz,¹⁰ Schirmer,¹¹ and Koebnik et al.¹² The porins have a high degree of sequence similarity, about 71% for OmpF, PhoE and OmpC. OmpK36 of Klebsiella pneumoniae is a closely related homologue of osmoporin (OmpC) of E. coli, with 81% identity. Most of the porins fold into similar homo-trimeric structures. Each monomer consists of a 16-stranded β-barrel with eight short turns (T1–T8) at the periplasmic side and eight relatively large loops (L1–L8) at the cell surface which confers a significant stability and rigidity to the structure. Each monomer possesses a wide aqueous pore narrowed by the loops on the outer entrance of the β-barrel. One of these loops (L3) is folded inside the β-barrel forming a narrow region of about 6 Å diameter within the wide aqueous channel at roughly half-way through the membrane. This narrowest region of the pore, called the “constriction zone”, is thought to be responsible for the charge specificity of the porins. For example, the structural basis for the difference in selectivity of OmpF for cations and PhoE for anions has been attributed to the presence of a lysine in PhoE in the constriction zone, substituting for a glycine in OmpF.⁵

The permeation properties of the bacterial porins are generally characterized with KCl or NaCl salt solutions over a wide range of concentration (from 5 mM to 3 M),1., 8., 13., 14., 15., 16. although it is very difficult to have stable experimental conditions under 50 mM salt solutions and those measurements have a higher uncertainty (N. Saint, personal communication). The single-channel conductance and the cation–anion permeability ratio P_c/P_a of OmpF, PhoE, and various OmpF mutants,14., 15., 16. Rhodobacter capsulatus porin,¹ and OmpK36 of K. pneumoniae (homologous to OmpC)⁸ have been measured mostly in NaCl solutions. The single-channel conductance in 1 M KCl salt solution is about 1.9 nS for OmpF, 1.8 nS for PhoE, and 1.5 for OmpC,¹³ although recent measurements indicate that the conductance of OmpF in 1 M KCl is around 1.45 nS¹⁷ or 1.34 nS (N. Saint, personal communication). The permeability ratio P_c/P_a was determined from the reversal potential with a tenfold KCl concentration gradient (10 mM and 100 mM); it is about 3.8 for OmpF, 0.30 for PhoE, and 26 for OmpC.¹³ The dependence of the single-channel conductance on salt concentration is normally attributed to variations in charge screening by the salt at the pore mouth.¹⁸ It should be noted that porins do not act simply as passive pores, but can also exhibit some complex voltage-dependent gating activity. The probability of opening and closing transitions of the pores, observed in single-channel experiments, depends on the applied transmembrane potential.¹⁹ The microscopic origin of this observed behavior is, however, poorly understood. Cross-linking experiments have shown that movements of L3, initially proposed to be responsible for closing of the pors,20., 21., 22. are not required for voltage-gating.19., 23. Atomic force microscopy (AFM) imaging has revealed the possibility of alternate structural conformation on the outer surface of the channel which could be responsible for the voltage-gating.24., 25.

Because they are well characterized, both structurally and functionally, the porins represent ideal systems for addressing questions about the fundamental principles underlying ion flow in molecular pores at the molecular level using theoretical models. There have been a number of theoretical studies of porins, focusing on different aspects of porin activity. Schirmer and co-workers have used the Poisson–Boltzmann (PB) equation to determine the ionization state of titratable residues and explore the nature of electrostatic fields in OmpF and PhoE.26., 27. In particular, it was noted that a cluster of three arginines (Arg42, Arg82, and Arg132) facing two acidic residues (Glu117 and Asp113) in the constriction zone created an unusually strong transverse electric field perpendicular to the pore axis. From those PB calculations, it was initially inferred that the cluster of three arginines should only carry a total charge of +2e, and would be otherwise unstable and inconsistent with the crystallographic structure. But this conclusion was later revised on the basis of further experimental data by Schirmer & Phale,¹⁵ illustrating some of the limitations of PB calculations in which the protein is generally rigidly fixed and not allowed to relax. The importance of protein flexibility is addressed more readily with molecular dynamics (MD) simulations.²⁸ MD trajectories have been generated to explore the fluctuations of porins.20., 21., 22., 29., 30. The influence of the solvent molecules was incorporated implicitly in the early studies,20., 21., 22. and they are inevitably limited for this reason. The later simulations of porins are much more realistic because they were carried out with explicit ions, solvent molecules²⁹ and also phospholipid bilayer membrane.³⁰ To explore the mechanism of ion conduction, Suenaga et al. simulated OmpF in the presence of an applied transmembrane potential.²⁹ The translocation of a single Na⁺ through the channel was observed in 1.3 ns under the influence of a potential of 500 mV. Tieleman & Berendsen generated a 1 ns MD simulation of an atomic model of OmpF trimer embedded into an explicit phospholipid bilayer membrane (for a total of 65,898 atoms).³⁰ This monumental simulation provided a wealth of information about the solvation of porin and its interaction with the surrounding lipids. However, only a few counterions were explicitly included (those needed to balance the total charge of OmpF), and therefore little insight could be gained about the ion permeation mechanism.

These previous studies illustrate well the general difficulties in studying ion channels based on all-atom MD simulations with explicit ions and solvent molecules. The calculations are computationally intensive, and yet, the time-scale of ion permeation is significantly longer than can be currently simulated. To avoid these limitations, a number of studies have used Brownian dynamics (BD) to explore the ion conduction mechanism.15., 16., 31., 32. In this approach, the channel and the ions are represented explicitly while the influence of the surrounding solvent molecules is incorporated implicitly via a stochastic random force, a friction coefficient damping the velocity, and some effective potential (generally calculated on the basis of a continuum electrostatic approximation). Schirmer and co-worker generated stochastic trajectories of isolated ions using the program UHBD33., 34. to examine the cation/anion specificity of OmpF, PhoE and OmpK36, as well as several OmpF mutants.15., 16. Only one ion was considered at a time in those simulations and finite-concentration effects were modeled implicitly via a PB approximation. A good correlation was achieved between calculated single-ion transmission probabilities and experimental ion selectivity. More recently, Im et al. generated BD trajectories of OmpF with explicit multiple ions using a Grand Canonical Monte Carlo (GCMC) and BD algorithm.31., 32. Assuming builk-like values for the diffusion constant of K⁺ and Cl⁻ in the pore the conductance of OmpF calculated from GCMC/BD simulations with a 200 mM KCl concentration was 420 pS,³² in relatively good agreement with the experimental estimate of 350 pS (N. Saint, personal communication).

Although much progress has been made to better understand the ion-conducting properties of porins, the current view has been developed, in large part, on the basis of BD simulations and continuum electrostatic PB calculations in which the solvent was represented implicitly. Such approximations are attractive because they are less computationally intensive than all-atom MD. However, their validity is still unknown in the context of molecular pores. For example, the orientational freedom of water molecules has been shown to be considerably affected in the pore³⁰ and it is unclear whether a structureless dielectric continuum is a valid representation. Furthermore, the channel structure is generally kept rigidly fixed during BD simulations and the coupling to protein fluctuations is ignored. In principle, detailed all-atom MD simulations with explicit ions, solvent and membrane lipids avoid such gross approximations and can provide information that can considerably enhance our understanding of the function of porins at the microscopic level. But as discussed above, the approach is facing significant challenges because it is difficult to obtain statistically meaningful results with finite length simulations due to the relatively small number of ions included explicitly in the simulations.29., 30.

Although the previous PB, BD, and MD studies provided many of the essential elements for understanding the function of outer membrane porins, several fundamental questions still need to be clearly and correctly answered at this point. What is the magnitude of protein fluctuations and what is their influence on the geometry and the size of the narrow pore? Is the charge specificity of OmpF arising only from the residues in the constriction zone, or are more residues being implicated? What are the dominant interactions governing ion translocation at the microscopic level? How is ion diffusion affected and what is the importance of cation–anion pairing in the wide aqueous pore? What are the properties of the water molecules in such confined environment? To address those questions, we have constructed an all-atom model of OmpF embedded in a fully solvated phospholipid bilayer membrane bathed by a 1 M KCl aqueous salt solution and generated a 5 ns MD trajectory. For comparison, a 1 M KCl bulk aqueous solution and a neat DMPC membrane bathed with the same salt solution were also simulated. From a computational point of view, the high salt concentration is advantageous. The large number of ions included explicitly in the simulations significantly helps to obtain statistically meaningful averages of the ion properties in the pore from a trajectory of finite length. A prohibitively long simulation time would be required to obtain convergence by simulating the corresponding atomic model with a low salt concentration. The previous MD simulations included only a small number of explicit ions. Suenaga et al. positioned counterions near every charged amino acid residues of OmpF for a total of 41 Na⁺ and 25 Cl⁻,²⁹ while Tieleman & Berendsen included only 27 Na⁺ to balance the total charge of OmpF.³⁰ Such treatments of the ions cannot simulate the influence of a finite salt concentration realistically. In comparison, the present simulation of OmpF includes 231 K⁺ and 201 Cl⁻. It should be stressed, however, that a 1 M KCl salt solution is not unrealistic. Similar salt concentrations are routinely used in experiments to measure ion fluxes13., 14., 15., 16. and in AFM imaging.³⁵ Interestingly, exposure of E. coli to such high salt concentration triggers the expression of OmpC, an outer membrane porin which is more strongly cation selective than OmpF.

The atomic model and the MD simulation protocol are described in the next section. Then, the main observations are described and discussed. Several properties are examined in detail such as the dynamics of the pore and the properties of water and ions inside the channel. A particular attention is given to the average of the ion properties for ion translocation across the aqueous pore. The paper is concluded with a brief summary of the main results.