The ionization state of D37 in E. coli porin OmpF and the nature of conductance fluctuations in D37 mutants

Understanding the flow of ions through E. coli porin outer membrane protein F (OmpF) requires knowledge of the charge state of all titratable residues located along the permeation pathway. Earlier theoretical studies proved successful in the calculation of the pK values of most residues. The (apparent) pK of Asp37 (D37), on the other hand, appeared rather sensitive to the (unknown) protein dielectric used. We addressed the protonation state of D37 experimentally by replacing D37 with a (neutral) valine. This D37V mutant expressed reduced cation selectivity, in agreement with the view that D37 in wild-type (WT) OmpF is fully ionized, i.e., deprotonated. The introduction of a (positively charged) arginine at position 37 evoked current fluctuations. Similar behavior was observed in the D37K mutant and the cysteine mutants D37C-MTSEA and D37C-MTSET. Nontitratable [2-(trimethylammonium)ethyl]-methanethiosulfonate (MTSET) carries a permanent and pH-independent charge of 1e, implying that the fluctuations of the D37C-MTSET mutant do not represent (de)protonation reactions of MTSET. We therefore conclude that these fluctuations reflect transitions between conformational substates evoked by structural instabilities due to the positive charge at that particular position in the pore lumen. Based on the similarities between D37C-MTSET fluctuations and those seen in the other mutants, notably D37K, the underlying mechanism of these fluctuations may be (essentially) the same in all four mutants studied.     

Influence of membrane potentials upon reversible protonation of acidic residues from the OmpF eyelet

In this research we employed single-molecule electric recording techniques to investigate effects of the transmembrane and dipole potential on the reversible protonation of acidic residues from the constriction zone of the OmpF porin. Our results support the paradigm according to which the protonation state of aspartate 113 and glutamate 117 residues from the constriction region of OmpF is influenced by the electric potential profile, via an augmentation of the local concentration of protons near these residues mediated by increasing negative transmembrane potentials. We propose that at constant bulk pH, pK_a values for proton bindings at these residues increase as the applied transmembrane potential increases in its negative values. Our data demonstrate that the apparent pK_a for proton binding of the acidic aminoacids from the constriction region of OmpF is ionic strength-dependent, in the sense that a low ionic strength in the aqueous phase promotes the increase of the protonation reaction rate of such residues, at any given holding potential. Supplementary, we present evidence suggesting that lower values of the membrane dipole potential lead to an increase in the values of the ‘on’ rate of the eyelet acidic residues protonation, caused by an elevation of the local concentration of hydrogen ions. Altogether, these results come to support the paradigm according to which transmembrane and dipole potentials are critical parameters for the titration behavior of protein sites embedded lipid membranes.     

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.     

Porin channels in Escherichia coli: studies with liposomes reconstituted from purified proteins.

Rates of diffusion of uncharged and charged solute molecules through porin channels were determined by using liposomes reconstituted from egg phosphatidylcholine and purified Escherichia coli porins OmpF (protein 1a), OmpC (protein 1b), and PhoE (protein E). All three porin proteins appeared to produce channels of similar size, although the OmpF channel appeared to be 7 to 9% larger than the OmpC and PhoE channels in an equivalent radius. Hydrophobicity of the solute retarded the penetration through all three channels in a similar manner. The presence of one negative charge on the solute resulted in about a threefold reduction in penetration rates through OmpF and OmpC channels, whereas it produced two- to tenfold acceleration of diffusion through the PhoE channel. The addition of the second negatively charged group to the solutes decreased the diffusion rates through OmpF and OmpC channels further, whereas diffusion through the PhoE channel was not affected much. These results suggest that PhoE specializes in the uptake of negatively charged solutes. At the present level of resolution, no sign of true solute specificity was found in OmpF and OmpC channels; peptides, for example, diffused through both of these channels at rates expected from their molecular size, hydrophobicity, and charge. However, the OmpF porin channel allowed influx of more solute molecules per unit time than did the equivalent weight of the OmpC porin when the flux was driven by a concentration gradient of the same size. This apparent difference in "efficiency" became more pronounced with larger solutes, and it is likely to be the consequence of the difference in the sizes of OmpF and OmpC channels.     

Dielectric self-energy in Poisson-Boltzmann and Poisson-Nernst-Planck models of ion channels

We demonstrated previously that the two continuum theories widely used in modeling biological ion channels give unreliable results when the radius of the conduit is less than two Debye lengths. The reason for this failure is the neglect of surface charges on the protein wall induced by permeating ions. Here we attempt to improve the accuracy of the Poisson-Boltzmann and Poisson-Nernst-Planck theories, when applied to channel-like environments, by including a specific dielectric self-energy term to overcome spurious shielding effects inherent in these theories. By comparing results with Brownian dynamics simulations, we show that the inclusion of an additional term in the equations yields significant qualitative improvements. The modified theories perform well in very wide and very narrow channels, but are less successful at intermediate sizes. The situation is worse in multi-ion channels because of the inability of the continuum theories to handle the ion-to-ion interactions correctly. Thus, further work is required if these continuum theories are to be reliably salvaged for quantitative studies of biological ion channels in all situations.     

Tests of continuum theories as models of ion channels. I. Poisson-Boltzmann theory versus Brownian dynamics

Continuum theories of electrolytes are widely used to describe physical processes in various biological systems. Although these are well-established theories in macroscopic situations, it is not clear from the outset that they should work in small systems whose dimensions are comparable to or smaller than the Debye length. Here, we test the validity of the mean-field approximation in Poisson-Boltzmann theory by comparing its predictions with those of Brownian dynamics simulations. For this purpose we use spherical and cylindrical boundaries and a catenary shape similar to that of the acetylcholine receptor channel. The interior region filled with electrolyte is assumed to have a high dielectric constant, and the exterior region representing protein a low one. Comparisons of the force on a test ion obtained with the two methods show that the shielding effect due to counterions is overestimated in Poisson-Boltzmann theory when the ion is within a Debye length of the boundary. As the ion gets closer to the boundary, the discrepancy in force grows rapidly. The implication for membrane channels, whose radii are typically smaller than the Debye length, is that Poisson-Boltzmann theory cannot be used to obtain reliable estimates of the electrostatic potential energy and force on an ion in the channel environment.     

A fast and simple method to calculate protonation states in proteins.

A simple model for electrostatic interactions in proteins, based on a distance and position dependent screening of the electrostatic potential, is presented. It is applied in conjunction with a Monte Carlo algorithm to calculate pK(alpha) values of ionizable groups in proteins. The purpose is to furnish a simple, fast, and sufficiently accurate model to be incorporated into molecular dynamic simulations. This will allow for dynamic protonation calculations and for coupling between changes in structure and protonation state during the simulation. The best method of calculating protonation states available today is based on solving the linearized Poisson-Boltzmann equation on a finite difference grid. However, this model consumes far too much computer time to be a practical alternative. Tests are reported for fixed structures on bacteriorhodopsin, lysozyme, myoglobin, and calbindin. The studies include comparisons with Poisson-Boltzmann calculations with dielectric constants 4 and 20 inside the protein, a model with uniform dielectric constant 80 and distance-dependent dielectric models. The accuracy is comparable to that of Poisson-Boltzmann calculations with dielectric constant 20, and it is considerably better than that with epsilon = 4. The time to calculate the protonation at one pH value is at least 100 times less than that of a Poisson-Boltzmann calculation. Proteins 1999;36:474-483.     

pK(a) calculations for class C beta-lactamases: the role of Tyr-150

The Poisson-Boltzmann method was used to compute the pK(a) values of titratable residues in a set of class C beta-lactamases. In these calculations, the pK(a) of the phenolic group of residue Tyr150 is the only one to stand out with an abnormally low value of 8.3, more than one pK(a) unit lower than the measured reference value for tyrosine in solution. Other important residues of the catalytic pocket, such as the conserved Lys67, Lys315, His314, and Glu272 (hydrogen-bonded to the ammonium group of Lys315), display normal protonation states at neutral pH. pK(a) values were also computed in catalytically impaired beta-lactamase mutants. Comparisons between the relative k(cat) values and the Tyr150 pK(a) value in these mutants revealed a striking correlation. In active enzymes, this pK(a) value is always lower than the solution reference value while it is close to normal in inactive enzymes. These results thus support the hypothesis that the phenolate form of Tyr150 is responsible for the activation of the nucleophilic serine. The possible roles of Lys67 and Lys315 during catalysis are also discussed.     

Intrinsic pKas of ionizable residues in proteins: An explicit solvent calculation for lysozyme

Molecular dynamics simulations of triclinic hen egg white lysozyme in aqueous solution were performed to calculate the intrinsic pK_as of 14 ionizable residues. An all-atom model was used for both solvent and solute, and a single 180 ps simulation in conjunction with a Gaussian fluctuation analysis method was used. An advantage of the Gaussian fluctuation method is that it only requires a single simulation of the system in a reference state to calculate all the pK_as in the protein, in contrast to multiple simulations for the free energy perturbation method. pK_int shifts with respect to reference titratable residues were evaluated and compared to results obtained using a finite difference Poisson-Boltzmann (FDPB) method with a continuum solvent model; overall agreement with the direction of the shifts was generally observed, though the magnitude of the shifts was typically larger with the explicit solvent model. The contribution of the first solvation shell to the total charging free energies of the titratable groups was explicitly evaluated and found to be significant. Dielectric shielding between pairs of titratable groups was examined and found to be smaller than expected. The effect of the approximations used to treat the long-range interactions on the pK_int shifts is discussed. © 1994 Wiley-Liss, Inc.     

Brownian dynamics simulation of ion flow through porin channels

Bacterial porins, which allow the passage of solutes across the outer bacterial membrane, are structurally well characterized. They therefore lend themselves to detailed studies of the determinants of ion flow through transmembraneous channels. In a comparative study, we have performed Brownian dynamics simulations to obtain statistically significant transfer efficiencies for cations and anions through matrix porin OmpF, osmoporin OmpK36, phosphoporin PhoE and two OmpF charge mutants.The simulations show that the electrostatic potential at the highly charged channel constriction serves to enhance ion permeability of either cations or anions, dependent on the type of porin. At the same time translocation of counterions is not severely impeded. At the constriction, cations and anions follow distinct trajectories, due to the segregation of basic and acidic protein residues.Simulated ion selectivity and relative conductance agree well with experimental values, and are dependent crucially on the charge constellation at the pore constriction. The experimentally observed decrease in ion selectivity and single channel conductance with increasing ionic strength is well reproduced and can be attributed to electrostatic shielding of the pore lining.     

High Salt Concentrations Increase Permeability through OmpC Channels of Escherichia coli

OmpF and OmpC porin channels are responsible for the passage of small hydrophilic solutes across the outer membrane of Escherichia coli. Although these channels are two of the most extensively studied porin channels, what had yet remained elusive was the reason why OmpC shows markedly lower permeability than OmpF, despite having little difference in its channel size. The OmpC channel, however, is known to contain a larger number of ionizable residues than the OmpF channel. In this study, we examined the channel property of OmpF and OmpC using the intact cell of E. coli, and we found that the permeability of several β-lactams and lactose through OmpC became increased to the level comparable with OmpF with up to 0.3 m salt that may increase the Debye-Hückel shielding or with 2% ethanol or 0.3 m urea that may perturb the short range ordering of water molecules. Replacing 10 pore-lining residues that show different ionization behavior between OmpC and OmpF led to substantial conversion of channel property with respect to their permeability and response to external salt concentration. We thus propose that the overall configuration of ionizable residues in the channel that may orient water molecules and the electrostatic profile of the channel play a decisive role in defining the channel property of the OmpC porin rather than its channel size.     

The influence of amino acid protonation states on molecular dynamics simulations of the bacterial porin OmpF

Several groups, including our own, have found molecular dynamics (MD) calculations to result in the size of the pore of an outer membrane bacterial porin, OmpF, to be reduced relative to its size in the x-ray crystal structure. At the narrowest portion of its pore, loop L3 was found to move toward the opposite face of the pore, resulting in decreasing the cross-section area by a factor of approximately 2. In an earlier work, we computed the protonation states of titratable residues for this system and obtained values different from those that had been used in previous MD simulations. Here, we show that MD simulations carried out with these recently computed protonation states accurately reproduce the cross-sectional area profile of the channel lumen in agreement with the x-ray structure. Our calculations include the investigation of the effect of assigning different protonation states to the one residue, D(127), whose protonation state could not be modeled in our earlier calculation. We found that both assumptions of charge states for D(127) reproduced the lumen size profile of the x-ray structure. We also found that the charged state of D(127) had a higher degree of hydration and it induced greater mobility of polar side chains in its vicinity, indicating that the apparent polarizability of the D(127) microenvironment is a function of the D(127) protonation state.     

Prediction of titration properties of structures of a protein derived from molecular dynamics trajectories.

This paper explores the dependence of the molecular dynamics (MD) trajectory of a protein molecule on the titration state assigned to the molecule. Four 100-ps MD trajectories of bovine pancreatic trypsin inhibitor (BPTI) were generated, starting from two different structures, each of which was held in two different charge states. The two starting structures were the X-ray crystal structure and one of the solution structures determined by NMR, and the charge states differed only in the ionization state of N terminus. Although it is evident that the MD simulations were too short to sample fully the equilibrium distribution of structures in each case, standard Poisson-Boltzmann titration state analysis of the resulting configurations shows general agreement between the overall titration behavior of the protein and the charge state assumed during MD simulation: at pH 7, the total net charge of the protein resulting from the titration analysis is consistently lower for the protein with the N terminus assumed to be neutral than for the protein with the N terminus assumed to be charged. For most of the ionizable residues, the differences in the calculated pKaS among the four trajectories are statistically negligible and remain in good agreement with the data obtained by crystal structure titration and by experiment. The exceptions include the N terminus, which responds directly to the change of its imposed charge; the C terminus, which in the NMR structure interacts strongly with the former; and a few other residues (Arg 1, Glu 7, Tyr 35, and Arg 42) whose pKaS reflect the initial structure and the limited trajectory lengths. This study illustrates the importance of the careful assignment of protonation states at the start of MD simulations and points to the need for simulation methods that allow for the variation of the protonation state in the calculation of equilibrium properties.     

Assessing the acid-base and conformational properties of histidine residues in human prion protein (125-228) by means of pK(a) calculations and molecular dynamics simulations

A thorough study of the acid-base behavior of the four histidines and the other titratable residues of the structured domain of human prion protein (125-228) is presented. By using multi-tautomer electrostatic calculations, average titration curves have been built for all titratable residues, using the whole bundles of NMR structures determined at pH 4.5 and 7.0. According to our results, (1) only histidine residues are likely to be involved in the first steps of the pH-driven conformational transition of prion protein; (2) the pK(a)'s of His140 and His177 are approximately 7.0, whereas those of His155 and His187 are < 5.5. 10-ns long molecular dynamics simulations have been performed on five different models, corresponding to the most significant combinations of histidine protonation states. A critical comparison between the available NMR structures and our computational results (1) confirms that His155 and His187 are the residues whose protonation is involved in the conformational rearrangement of huPrP in mildly acidic condition, and (2) shows how their protonation leads to the destructuration of the C-terminal part of HB and to the loss of the last turn of HA that represent the crucial microscopic steps of the rearrangement.     

Linearity, saturation and blocking in a large multiionic channel: divalent cation modulation of the OmpF porin conductance

Measurement of unitary conductance is a fundamental step in the characterization of a protein ion channel permeabilizing a membrane. We study here the effect of salts of divalent cations on the OmpF channel conductance with a particular emphasis in dissecting the role of the electrolyte itself, the role of the counterion accumulation induced by the protein channel charges and other effects not found in salts of monovalent cations. We show that current saturation and blocking are not exclusive properties of narrow (single-file) ion channels but may be observed in large, multiionic channels like bacterial porins. Single-channel conductance measurements performed over a wide range of salt concentrations (up to 3 M) combined with continuum electrodiffusion calculations demonstrate that current saturation cannot be simply ascribed to ion interaction with protein channel residues.     

Altered pore properties and kinetic changes in mutants of the Vibrio cholerae porin OmpU

The electrophysiological technique of patch-clamp was used to characterize the pore properties of site-directed mutants in the Vibrio cholerae general diffusion porin OmpU. Changes in conductance and selectivity were observed, thus confirming the predicted pore location of these residues, based on homology with the Escherichia coli porins OmpF and OmpC. Some mutants acquire a weak selectivity for cations, which mirrors the properties of the homologous, deoxycholic acid sensitive, OmpT porin of V. cholerae. However, the mutants remain insensitive to deoxycholic acid, like wildtype OmpU. This result suggests that channel selectivity is not an important determinant in the sensitivity to this drug, and is in agreement with our finding that the neutral deoxycholic acid, and not deoxycholate, is the actual active form in channel block. Modifications in the kinetics of spontaneous closures were also noted, and are similar to those found for the E. coli channels. In addition, mutants at the D116 residue on the L3 loop display marked transitions to sub-conductance states. The results reported here are compared to a phenotypical characterization of the mutants in terms of permeability to maltodextrins and beta-lactam antibiotic sensitivity. No strict correlations are observed, suggesting that distinct, but somewhat overlapping, molecular determinants control electrophysiological properties and substrate permeability.     

Protonation of lysine residues inverts cation/anion selectivity in a model channel

A dimeric alamethicin analog with lysine at position 18 in the sequence (alm-K18) was previously shown to form stable anion-selective channels in membranes at pH 7.0 [Starostin, A. V., R. Butan, V. Borisenko, D. A. James, H. Wenschuh, M. S. Sansom, and G. A. Woolley. 1999. Biochemistry. 38:6144-6150]. To probe the charge state of the conducting channel and how this might influence cation versus anion selectivity, we performed a series of single-channel selectivity measurements at different pH values. At pH 7.0 and below, only anion-selective channels were found with P(K(+))/P(Cl(-)) = 0. 25. From pH 8-10, a mixture of anion-selective, non-selective, and cation-selective channels was found. At pH > 11 only cation-selective channels were found with P(K(+))/P(Cl(-)) = 4. In contrast, native alamethicin-Q18 channels (with Gln in place of Lys at position 18) were cation-selective (P(K(+))/P(Cl(-)) = 4) at all pH values. Continuum electrostatics calculations were then carried out using an octameric model of the alm-K18 channel embedded in a low dielectric slab to simulate a membrane. Although the calculations can account for the apparent pK(a) of the channel, they fail to correctly predict the degree of selectivity. Although a switch from cation- to anion-selectivity as the channel becomes protonated is indicated, the degree of anion-selectivity is severely overestimated, suggesting that the continuum approach does not adequately represent some aspect of the electrostatics of permeation in these channels. Side-chain conformational changes upon protonation, conformational changes, and deprotonation caused by permeating cations and counterion binding by lysine residues upon protonation are considered as possible sources of the overestimation.     

Energetics of a possible proton exit pathway for water oxidation in photosystem II

The crystal structure of photosystem II (PSII) at 3.0-A resolution suggests that titratable residues on the lumenal side of D1/D2 and PsbO form a polar channel, which might serve as a proton exit pathway associated with water oxidation on the Mn-cluster. With full account of protein environment, we calculated the pK(a) of these residues by solving the linearized Poisson-Boltzmann equation. Along the prospective proton channel, the calculated pK(a) of titratable residues (namely via D1-Asp61, D1-Glu65, D2-Glu312, D2-Lys317 D1-Asp59, D1-Arg64, PsbO-Arg152, and PsbO-Asp224) monotonically increase from the Mn-cluster to the lumenal bulk side. We suggest that these residues form the exit pathway guiding protons, which are released at the Mn-cluster as a product of water oxidation, in an exergonic process out of PSII. Upon the S2 to S3 transition, CP43-Arg357 showed a dramatic deprotonation of ca. one H(+), suggesting that this residue is coupled to the redox states of the Mn-cluster and the tyrosine Y(Z). The calculated pK(a) values of 4.2-4.4 for D2-Glu312 and those of approximately 8-10.9 for D1-Asp59 and D1-Arg64 are indicative of the experimentally determined pK(a) values for inhibition of S-state transitions. Upon removal of the atomic coordinates of PsbO, the pK(a) of these residues are dramatically affected, indicating a significant role of PsbO in tuning the pK(a) of those residues in the proton exit pathway.     

Altered pore properties and kinetic changes in mutants of the Vibrio cholerae Porin OmpU

The electrophysiological technique of patch-clamp was used to characterize the pore properties of site-directed mutants in the Vibrio cholerae general diffusion porin OmpU. Changes in conductance and selectivity were observed, thus confirming the predicted pore location of these residues, based on homology with the Escherichia coli porins OmpF and OmpC. Some mutants acquire a weak selectivity for cations, which mirrors the properties of the homologous, deoxycholic acid sensitive, OmpT porin of V. cholerae. However, the mutants remain insensitive to deoxycholic acid, like wildtype OmpU. This result suggests that channel selectivity is not an important determinant in the sensitivity to this drug, and is in agreement with our finding that the neutral deoxycholic acid, and not deoxycholate, is the actual active form in channel block. Modifications in the kinetics of spontaneous closures were also noted, and are similar to those found for the E. coli channels. In addition, mutants at the D116 residue on the L3 loop display marked transitions to sub-conductance states. The results reported here are compared to a phenotypical characterization of the mutants in terms of permeability to maltodextrins and β-lactam antibiotic sensitivity. No strict correlations are observed, suggesting that distinct, but somewhat overlapping, molecular determinants control electrophysiological properties and substrate permeability.     

The pH-induced release of iron from transferrin investigated with a continuum electrostatic model.

A reduction in pH induces the release of iron from transferrin in a process that involves a conformational change in the protein from a closed to an open form. Experimental evidence suggests that there must be changes in the protonation states of certain, as yet not clearly identified, residues in the protein accompanying this conformational change. Such changes in protonation states of residues and the consequent changes in electrostatic interactions are assumed to play a large part in the mechanism of release of iron from transferrin. Using the x-ray crystal structures of human ferri- and apo-lactoferrin, we calculated the pKa values of the titratable residues in both the closed (iron-loaded) and open (iron-free) conformations with a continuum electrostatic model. With the knowledge of a residue's pKa value, its most probable protonation state at any specified pH may be determined. The preliminary results presented here are in good agreement with the experimental observation that the binding of ferric iron and the synergistic anion bicarbonate/carbonate results in the release of approximately three H+ ions. It is suggested that the release of these three H+ ions may be accounted for, in most part, by the deprotonation of the bicarbonate and residues Tyr-92, Lys-243, Lys-282, and Lys-285 together with the protonation of residues Asp-217 and Lys-277.