Ion permeation and selectivity of OmpF porin: a theoretical study based on molecular dynamics,Brownian dynamics,and continuum electrodiffusion theory

Three different theoretical approaches are used and compared to refine our understanding of ion permeation through the channel formed by OmpF porin from Escherichia coli. Those approaches are all-atom molecular dynamics (MD) in which ions, solvent, and lipids are represented explicitly, Brownian dynamics (BD) in which ions are represented explicitly, while solvent and lipids are represented as featureless dielectrics, and Poisson-Nernst-Planck (PNP) electrodiffusion theory in which both solvent and local ion concentrations are represented as a continuum. First, the ability of the different theoretical approaches in reproducing the equilibrium average ion density distribution in OmpF porin bathed by a 1M KCl symmetric salt solution is examined. Under those conditions the PNP theory is equivalent to the non-linear Poisson-Boltzmann (PB) theory. Analysis shows that all the three approaches are able to capture the important electrostatic interactions between ions and the charge distribution of the channel that govern ion permeation and selectivity in OmpF. The K(+) and Cl(-) density distributions obtained from the three approaches are very consistent with one another, which suggests that a treatment on the basis of a rigid protein and continuum dielectric solvent is valid in the case of OmpF. Interestingly, both BD and continuum electrostatics reproduce the distinct left-handed twisted ion pathways for K(+) and Cl(-) extending over the length of the pore which were observed previously in MD. Equilibrium BD simulations in the grand canonical ensemble indicate that the channel is very attractive for cations, particularly at low salt concentration. On an average there is 1.55 K(+) inside the pore in 10mM KCl. Remarkably, there is still 0.17 K(+) on average inside the pore even at a concentration as low as 1microM KCl. Secondly, non-equilibrium ion flow through OmpF is calculated using BD and PNP and compared with experimental data. The channel conductance in 0.2M and 1M KCl calculated using BD is in excellent accord with the experimental data. The calculations reproduce the experimentally well-known conductance-concentration relation and also reveal an asymmetry in the channel conductance (a larger conductance is observed under a positive transmembrane potential). Calculations of the channel conductance for three mutants (R168A, R132A, and K16A) in 1M KCl suggest that the asymmetry in the channel conductance arises mostly from the permanent charge distribution of the channel rather than the shape of the pore itself. Lastly, the calculated reversal potential in a tenfold salt gradient (0.1:1M KCl) is 27.4(+/-1.3)mV (BD) and 22.1(+/-0.6)mV (PNP), in excellent accord with the experimental value of 24.3mV. Although most of the results from PNP are qualitatively reasonable, the calculated channel conductance is about 50% higher than that calculated from BD probably because of a lack of some dynamical ion-ion correlations.     

Rectification properties and pH-dependent selectivity of meningococcal class 1 porin

We studied the current rectification properties and selectivity of class 1 porin (PorA) from Neisseria meningitidis (strain H44/76 Δ3Δ4) reconstituted in planar lipid membranes varying salt concentrations and pH. PorA channel shows voltage gating with a characteristic time remarkably longer than other porins. Its current-voltage asymmetry, evaluated as the current rectification ratio, changes nonmonotonically with salt concentration. Interestingly, it reaches its maximum value at physiological concentration. Porin selectivity, quantified by reversal potential measurements, is also significantly asymmetric. Depending on the direction of the salt gradient, the channel becomes more or less selective (10:1 vs. 5:1 Na⁺/Cl⁻). Besides, the reversal potential measurements suggest that porin inserts directionally following the concentration gradient. Measurements over a wide range of pH show that although PorA is strongly cation selective at pH >6, its selectivity gradually changes to anionic in an acidic medium (pH < 4). We show that a continuum electrodiffusion model quantitatively accounts for conductance and reversal potential measurements at positive and negative applied voltages.     

Chemical modification of the bacterial porin OmpF: gain of selectivity by volume reduction

OmpF is an essentially nonselective porin isolated from the outer membrane of Escherichia coli. Here we report on the manipulation of the ion selectivity of OmpF by chemical modification with MTS reagents (MTSET, MTSEA, and MTSES) and the (rather bulky) tripeptide glutathione, all cysteine specific. When recorded in a gradient of 0.1//1 M CaCl2 or 0.1//1 M NaCl, pH 7.4 solutions, measured reversal potentials of the most cation-selective modified mutants were (virtually) identical to the Nernst potential of Ca2+ or Na+. Compared to this full cation selectivity, the anion-selective modified mutants performed somewhat less but nevertheless showed high anion selectivity. We conclude that a low permanent charge in combination with a narrow pore can render the same selectivity as a highly charged but wider pore. These results favor the view that both the electrostatic potential arising form the fixed charge in the pore and the space available at the selectivity filter contribute to the charge selection (i.e., cation versus anion selectivity) of a biological ion channel.     

Residue ionization and ion transport through OmpF channels

Single trimeric channels of the general bacterial porin, OmpF, were reconstituted into planar lipid membranes and their conductance, selectivity, and open-channel noise were studied over a wide range of proton concentrations. From pH 1 to pH 12, channel transport properties displayed three characteristic regimes. First, in acidic solutions, channel conductance is a strong function of pH; it increases by approximately threefold as the proton concentration decreases from pH 1 to pH 5. This rise in conductance is accompanied by a sharp increase in cation transport number and by pronounced open-channel low-frequency current noise with a peak at ~pH 2.5. Random stepwise transients with amplitudes at ~1/5 of the monomer conductance are major contributors to this noise. Second, over the middle range (pH 5 ÷ pH 9), channel conductance and selectivity stay virtually constant; open channel noise is at its minimum. Third, over the basic range (pH 9 ÷ pH 12), channel conductance and cation selectivity start to grow again with an onset of a higher frequency open-channel noise. We attribute these effects to the reversible protonation of channel residues whose pH-dependent charge influences transport by direct interactions with ions passing through the channel.     

Polymer Partitioning and Ion Selectivity Suggest Asymmetrical Shape for the Membrane Pore Formed by Epsilon Toxin

Using poly-(ethylene glycol)s of different molecular weights, we probe the channels formed in planar lipid bilayers by epsilon toxin secreted by the anaerobic bacterium Clostridium perfringens. We find that the pore is highly asymmetric. The cutoff size of polymers entering the pore through its opening from the cis side, the side of toxin addition, is ∼500 Da, whereas the cutoff size for the polymers entering from the trans side is ∼2300 Da. Comparing these characteristic molecular weights with those reported earlier for OmpF porin and the α-Hemolysin channel, we estimate the radii of cis and trans openings as 0.4 nm and 1.0 nm, respectively. The simplest geometry corresponding to these findings is that of a truncated cone. The asymmetry of the pore is also confirmed by measurements of the reversal potential at oppositely directed salt gradients. The moderate anionic selectivity of the channel is salted-out more efficiently when the salt concentration is higher at the trans side of the pore.     

Ion transport through channels formed in lipid bilayers by Staphylococcus aureus alpha-toxin

Staphylotoxin channel appears to be predominantly anion-selective with non-linear and asymmetric current-voltage characteristics (CVC) at neutral pH. Increased salt concentrations induce linearity and asymmetry of CVC and loss of selectivity. At lower pH both the channel conductivity and anion selectivity increase. Higher temperatures raise the channel conductivity in parallel with the changes in electrical conductivity of the salt solution, but do not change selectivity. Experimental dependences are described obtained by approximation of electrical diffusion and considering the interactions of penetrating ions with fixed charges at the entrances and the channel energy profile.     

Ionic partition and transport in multi-ionic channels: a molecular dynamics simulation study of the OmpF bacterial porin

We performed all-atom molecular dynamics simulations studying the partition of ions and the ionic current through the bacterial porin OmpF and two selected mutants. The study is motivated by new, interesting experimental findings concerning their selectivity and conductance behavior at neutral pH. The mutations considered here are designed to study the effect of removal of negative charges present in the constriction zone of the wild-type OmpF channel (which contains, on one side, a cluster with three positive residues, and on the other side, two negatively charged residues). Our results show that these mutations induce an exclusion of cations from the constriction zone of the channel, substantially reducing the flow of cations. In fact, the partition of ions inside the mutant channels is strongly inhomogeneous, with regions containing an excess of cations and regions containing an excess of anions. Interestingly, the overall number of cations inside the channel is larger than the number of anions, this excess being different for each protein channel. We found that the differences in ionic charge inside these channels are justified by the differences in electric charge between the wild-type OmpF and the mutants, following an electroneutral balance.     

Charge selectivity of the designed uncharged peptide ion channel Ac-(LSSLLSL)3-CONH2.

Charge selectivity in ion channel proteins is not fully understood. We have studied charge selectivity in a simple model system without charged groups, in which an amphiphilic helical peptide, Ac-(Leu-Ser-Ser-Leu-Leu-Ser-Leu)3-CONH2, forms ion channels across an uncharged phospholipid membrane. We find these channels to conduct both K+ and Cl-, with a permeability ratio (based on reversal potentials) that depends on the direction of the KCl concentration gradient across the membrane. The channel shows high selectivity for K+ when [KCl] is lowered on the side of the membrane that is held at a positive potential (the putative C-terminal side), but only modest K+ selectivity when [KCl] is lowered on the opposite side (the putative N-terminal side). Neither a simple Nernst-Planck electrodiffusion model including screening of the helix dipole potential, nor a multi-ion, state transition model allowing simultaneous cation and anion occupancy of the channel can satisfactorily fit the current-voltage curves over the full range of experimental conditions. However, the C-side/N-side dilution asymmetry in reversal potentials can be simulated with either type of model.     

Electrical properties and molecular architecture of the channel formed by Escherichia coli hemolysin in planar lipid membranes

A 107 kDa hemolysin from Escherichia coli is able to open pores in lipid membranes. By studying its interaction with planar phospholipid bilayers we have derived some structural information on the organization of the pore. We measured the current-voltage characteristic and the ion selectivity of the channel both in neutral membranes, made of egg phosphatidylcholine (PC) and in negatively charged membranes, made of a 1:1 mixture of PC with phosphatidylserine (PS). Experiments were performed varying both the pH and the salt concentration of the bathing KCl solution. In neutral membranes the pore is ohmic and its conductance increases almost linearly with the salt concentration. The channel is cation-selective at high pH but nearly unselective at low pH. We interpret these results in terms of a minimal model based on classical electro-diffusional theories assuming that the pore is wide and bears a negative charge at its entrances. In membranes containing the acidic lipid the current-voltage curve is non-linear in such a way to suggest that the trans (but not the cis) entrance of the pore is affected by the surface potential of the membrane. Applying our model we find that the trans and cis entrances are located, respectively, about 0.5 nm and more than 5 nm apart from the plane of the membrane. We confirmed the asymmetric disposition of the channel by enzymatic digestion of preformed pores. This was effective only when the enzyme was applied on the cis side.     

Diffusion, Exclusion, and Specific Binding in a Large Channel: A Study of OmpF Selectivity Inversion

We find that moderate cationic selectivity of the general bacterial porin OmpF in sodium and potassium chloride solutions is inversed to anionic selectivity in concentrated solutions of barium, calcium, nickel, and magnesium chlorides. To understand the origin of this phenomenon, we consider several factors, which include the binding of divalent cations, electrostatic and steric exclusion of differently charged and differently sized ions, size-dependent hydrodynamic hindrance, electrokinetic effects, and significant “anionic” diffusion potential for bulk solutions of chlorides of divalent cations. Though all these factors contribute to the measured selectivity of this large channel, the observed selectivity inversion is mostly due to the following two. First, binding divalent cations compensates, or even slightly overcompensates, for the negative charge of the OmpF protein, which is known to be the main cause of cationic selectivity in sodium and potassium chloride solutions. Second, the higher anionic (versus cationic) transport rate expected for bulk solutions of chloride salts of divalent cations is the leading cause of the measured anionic selectivity of the channel. Interestingly, at high concentrations the binding of cations does not show any pronounced specificity within the divalent series because the reversal potentials measured in the series correlate well with the corresponding bulk diffusion potentials. Thus our study shows that, in contrast to the highly selective channels of neurophysiology that employ mostly the exclusion mechanism, quite different factors account for the selectivity of large channels. The elucidation of these factors is essential for understanding large channel selectivity and its regulation in vivo.     

Alamethicin channel conductance modified by lipid charge

The membrane surface charge modifies the conductance of ion channels by changing the electric potential and redistributing the ionic composition in their vicinity. We have studied the effects of lipid charge on the conductance of a multi-state channel formed in planar lipid bilayers by the peptide antibiotic alamethicin. The channel conductance was measured in two lipids: in a neutral dioleoylphosphatidylethanolamine (DOPE) and a negatively charged dioleoylphosphatidylserine (DOPS). The charge state of DOPS was manipulated by the pH of the membrane-bathing solution. We find that at high salt concentrations (e.g., 2 M NaCl) the effect of the lipid charge is below the accuracy of our measurements. However, when the salt concentration in the membrane-bathing solution is decreased, the surface charge manifests itself as an increase in the conductance of the first two channel levels that correspond to the smallest conductive alamethicin aggregates. Our analysis shows that both the salt and pH dependence of the surface charge effect can be rationalized within the nonlinear Poisson-Boltzmann approach. Given channel conductance in neutral lipids, we use different procedures to account for the surface charge (e.g., introduce averaging over the channel aperture and take into account Na+ adsorption to DOPS heads), but only one adjustable parameter: an effective distance from the nearest lipid charge to the channel mouth center. We show that this distance varies by 0.3-0.4 nm upon channel transition from the minimal conducting aggregate (level L0) to the next larger one (level L1). This conclusion is in accord with a simple geometrical model of alamethicin aggregation.     

Interaction of zwitterionic penicillins with the OmpF channel facilitates their translocation

To study translocation of beta-lactam antibiotics of different size and charge across the outer bacterial membrane, we combine an analysis of ion currents through single trimeric outer membrane protein F (OmpF) porins in planar lipid bilayers with molecular dynamics simulations. Because the size of penicillin molecules is close to the size of the narrowest part of the OmpF pore, penicillins occlude the pore during their translocation. Favorably interacting penicillins cause time-resolvable transient blockages of the small-ion current through the channel and thereby provide information about their dynamics within the pore. Analyzing these random fluctuations, we find that ampicillin and amoxicillin have a relatively high affinity for OmpF. In contrast, no or only a weak interaction is detected for carbenicillin, azlocillin, and piperacillin. Molecular dynamics simulations suggest a possible pathway of these drugs through the OmpF channel and rationalize our experimental findings. For zwitterionic ampicillin and amoxicillin, we identify a region of binding sites near the narrowest part of the channel pore. Interactions with these sites partially compensate for the entropic cost of drug confinement by the channel. Whereas azlocillin and piperacillin are clearly too big to pass through the channel constriction, dianionic carbenicillin does not find an efficient binding region in the constriction zone. Carbenicillin's favorable interactions are limited to the extracellular vestibule. These observations confirm our earlier suggestion that a set of high-affinity sites at the narrowest part of the OmpF channel improves a drug's ability to cross the membrane via the pore.     

Probing tubulin-blocked state of VDAC by varying membrane surface charge

Reversible blockage of the voltage-dependent anion channel (VDAC) of the mitochondrial outer membrane by dimeric tubulin is being recognized as a potent regulator of mitochondrial respiration. The tubulin-blocked state of VDAC is impermeant for ATP but only partially closed for small ions. This residual conductance allows studying the nature of the tubulin-blocked state in single-channel reconstitution experiments. Here we probe this state by changing lipid bilayer charge from positive to neutral to negative. We find that voltage sensitivity of the tubulin-VDAC blockage practically does not depend on the lipid charge and salt concentration with the effective gating charge staying within the range of 10-14 elementary charges. At physiologically relevant low salt concentrations, the conductance of the tubulin-blocked state is decreased by positive and increased by negative charge of the lipids, whereas the conductance of the open channel is much less sensitive to this parameter. Such a behavior supports the model in which tubulin's negatively charged tail enters the VDAC pore, inverting its anionic selectivity to cationic and increasing proximity of ion pathways to the nearest lipid charges as compared with the open state of the channel.     

Ion permeation through the alpha-hemolysin channel: theoretical studies based on Brownian dynamics and Poisson-Nernst-Plank electrodiffusion theory

Identification of the molecular interaction governing ion conduction through biological pores is one of the most important goals of modern electrophysiology. Grand canonical Monte Carlo Brownian dynamics (GCMC/BD) and three-dimensional Poisson-Nernst-Plank (3d-PNP) electrodiffusion algorithms offer powerful and general approaches to study of ion permeation through wide molecular pores. A detailed analysis of ion flows through the staphylococcal alpha-hemolysin channel based on series of simulations at different concentrations and transmembrane potentials is presented. The position-dependent diffusion coefficient is approximated on the basis of a hydrodynamic model. The channel conductance calculated by GCMC/BD is approximately 10% higher than (electrophysiologically measured) experimental values, whereas results from 3d-PNP are always 30-50% larger. Both methods are able to capture all important electrostatic interactions in equilibrium conditions. The asymmetric conductance upon the polarity of the transmembrane potential observed experimentally is reproduced by GCMC/BD and 3d-PNP. The separation of geometrical and energetic influence of the channel on ion conduction reveals that such asymmetries arise from the permanent charge distribution inside the pore. The major determinant of the asymmetry is unbalanced charge in the triad of polar residues D127, D128, and K131. The GCMC/BD or 3d-PNP calculations reproduce also experimental reversal potentials and permeability rations in asymmetric ionic solutions. The weak anionic selectivity of the channel results from the presence of the salt bridge between E111 and K147 in the constriction zone. The calculations also reproduce the experimentally derived dependence of the reversible potential to the direction of the salt gradient. The origin of such effect arises from the asymmetrical distribution of energetic barriers along the channel axis, which modulates the preferential ion passage in different directions.     

Permeation properties of an engineered bacterial OmpF porin containing the EEEE-locus of Ca2+ channels

The selectivity filter of the bacterial porin OmpF carries a small net charge close to -1 e and is therefore only slightly cation-selective. Calcium channels, on the other hand, contain four negatively charged glutamates, the EEEE-locus, and are among the most selective cation channels known. We aimed to turn the essentially nonselective OmpF into a Ca2+-selective channel. To that end, two additional glutamates (R42E and R132E) were introduced in the OmpF constriction zone that already contains D113 and E117. Mutant OmpF containing this DEEE-locus has a high Ca2+ over Cl- selectivity and a Na+ current with a strongly increased sensitivity to 1 mM Ca2+. The charge/space competition model, initially applied to the L-type Ca2+ channel, identifies the fixed charge and filter volume as key determinants of ion selectivity, with the precise atomic arrangement having only second-order effects. By implication, the reproduction of fixed charge and filter volume should transform two channels into channels of similar selectivity, even if the two belong to entirely different ion channel families, as is the case for OmpF and the L-type Ca2+ channel. The results presented here fit quite well in the framework of charge/space competition theory.     

Understanding pH-dependent selectivity of alamethicin K18 channels by computer simulation

Alamethicin K18 is a covalently linked alamethicin dimer in which the glutamine residue at position 18 in each helix has been replaced by a lysine residue. As described in previous work, channels formed by this peptide show pH-dependent selectivity. The maximum anion selectivity of the putative octameric conducting state is obtained at pH 7 or lower. Inasmuch as no change in selectivity is seen between pH 7 and pH 3, and because protons are expected to be in equilibrium with the open state of the channel during a selectivity measurement, the channel is believed to be fully charged (i.e., all eight lysines protonated) at pH 7. In an effort to understand how such a highly charged channel structure is stable in membranes and why it is not more selective for anions, we have performed a number of computer simulations of the system. Molecular dynamics simulations of 10 ns each of the octameric bundle in a lipid bilayer environment are presented, with either zero, four, or eight lysines charged in the absence of salt, and with eight lysines charged in the presence of 0.5 M and 1 M KCl. When no salt is present and all lysines are charged, on average 1.9 Cl(-) ions are inside the channel and the channel significantly deforms. With 0.5 M KCl present, 2.9 Cl(-) ions are inside the channel. With 1 M KCl present, four Cl(-) ions are present and the channel maintains a regular structure. Poisson-Boltzmann calculations on models of the octameric channel also predict an average of 2-4 Cl(-) ions near the lysine residues as a function of ionic strength. These counterions lower the apparent charge of the channel, which may underlie the decrease in selectivity observed experimentally with increasing salt concentrations. We suggest that to increase the selectivity of Alm K18 channels, positive charges could be engineered in a narrower part of the channel.     

Membrane surface-charge titration probed by gramicidin A channel conductance.

We manipulate lipid bilayer surface charge and gauge its influence on gramicidin A channel conductance by two strategies: titration of the lipid charge through bulk solution pH and dilution of a charged lipid by neutral. Using diphytanoyl phosphatidylserine (PS) bilayers with CsCl aqueous solutions, we show that the effects of lipid charge titration on channel conductance are masked 1) by conductance saturation with Cs+ ions in the neutral pH range and 2) by increased proton concentration when the bathing solution pH is less than 3. A smeared charge model permits us to separate different contributions to the channel conductance and to introduce a new method for "bilayer pKa" determination. We use the Gouy-Chapman expression for the charged surface potential to obtain equilibria of protons and cations with lipid charges. To calculate cation concentration at the channel mouth, we compare different models for the ion distribution, exact and linearized forms of the planar Poisson-Boltzmann equation, as well as the construction of a "Gibbs dividing surface" between salt bath and charged membrane. All approximations yield the intrinsic pKain of PS lipid in 0.1 M CsCl to be in the range 2.5-3.0. By diluting PS surface charge at a fixed pH with admixed neutral diphytanoyl phosphatidylcholine (PC), we obtain a conductance decrease in magnitude greater than expected from the electrostatic model. This observation is in accord with the different conductance saturation values for PS and PC lipids reported earlier (, Biochim. Biophys. Acta. 552:369-378) and verified in the present work for solvent-free membranes. In addition to electrostatic effects of surface charge, gramicidin A channel conductance is also influenced by lipid-dependent structural factors.     

Dependence of ion flow through the hemocyanin channel on a fixed charge at the pore mouth: effects of H + and Ca2+ ions

Incorporation of Megatura crenulata hemocyanin into planar phospholipid bilayers results in the formation of ionic channels whose conductance can be directly measured. We have studied the effects of the pH on the electrical properties of these channels in the presence both of a K₂SO₄ solution, at high and low concentration, and of a KCl one. We have found that the conductance of the channel depends on the proton concentration following a positive titration curve, i.e., increasing sigmoidally with the pH at all the concentrations used; at any given pH, it additionally increases sublinearly with the concentration of the salt. The sublinear conductance-concentration dependence can be reverted to an almost linear one by the addition of suitable amounts of an indifferent cation such a tetramethylammonium to keep the ionic strength constant. The current-voltage curve of the channel, which is strongly voltage-dependent, is shifted along the voltage axis towards negative values by an increase in the proton concentration. Calcium ions have similar effects. The selectivity of the channel for cations over anions is strongly pH-dependent in the case of a KCl solution, being lost at pH 4.5, but is almost invariant in a K₂SO₄ solution. All experimental results are interpreted assuming the existence of a mechanism of voltage gating of the channel and of discrete negative charge fixed near its mouth. This charge can be neutralized by specific binding either of H⁺ or of Ca²⁺ ions. The dissociation constants from the channel found for these two ions are consistent with those given in the literature for the hemocyanin protein and indicate that carboxyl groups and/or histidines are involved in forming the negative charge of the pore.     

Increased salt concentration promotes competitive block of OmpF channel by protons

Porins are channel-forming proteins that are located in the outer membranes (OM) of Gram-negative bacteria and allow the influx of hydrophilic nutrients and the extrusion of waste products. The fine regulation of the ion transport through these wide channels could play an important role in the survival of the bacteria in acidic media. We investigate here the mechanism responsible for the pH sensitivity of the trimeric porin OmpF, of Escherichia coli. Planar lipid bilayer electrophysiology and site-directed mutagenesis were used to study the effect of pH on the ion conductive properties of the OmpF channel in its fully open, "nongated" conformation. At low pH we observe a large drop in the OmpF open channel conductance that is accompanied by a substantial increase of the current noise. These channel features are strongly dependent on the salt concentration and we propose that they are originated by competitive binding of cations and protons occurring in the narrow central constriction of the channel. This subtle mechanism reveals to be capital for the channel function because it not only drives the channel sensitivity to pH but is also indispensable for the particularly efficient permeation mechanism of the channel at physiological conditions (~neutral pH).     

Ionization states of residues in OmpF and mutants: effects of dielectric constant and interactions between residues

To understand ion permeation, one must assign correct ionization states to titratable amino acid residues in protein channels. We report on the effects of physical and methodological assumptions in calculating the protonation states at neutral bulk pH of titratable residues lining the lumen of the native Escherichia coli OmpF channel, and five mutants. We systematically considered a wide range of assumed protein dielectric constants and all plausible combinations of protonation states for electrostatically interacting side chains, and three different levels of accounting for solute shielding: 1), full nonlinear Poisson-Boltzmann; 2), linearized Poisson-Boltzmann; and 3), neglect of solute shielding. For this system we found it acceptable to neglect solute shielding, a result we postulate to be generalizable to narrow lumens of other protein channels. For the large majority of residues, the protonation state at neutral bulk pH was found to be independent of the assumed dielectric constant of the protein, and unambiguously determined by the calculation; for native OmpF only Asp-127 has a protonation state that is sensitive to the assumed protein dielectric constant. Our results are significant for understanding two published experimental observations: the structure of the narrow part of the channel, and the ionic selectivity of OmpF mutants.