Insights on the Permeability of Wide Protein Channels PDF

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View Article Online / Journal Homepage / Table of Contents for this issue Integrative Biology Dynamic Article Links Cite this: Integr. Biol., 2011, 3, 159–172 www.rsc.org/ibiology REVIEW ARTICLE Insights on the permeability of wide protein channels: measurement and interpretation of ion selectivity Vicente M. Aguilella,* Marı́a Queralt-Martı́n, Marcel Aguilella-Arzo and Antonio Alcaraz Received 31st May 2010, Accepted 12th October 2010 Published on 06 December 2010. Downloaded on 23/10/2014 00:19:59. DOI: 10.1039/c0ib00048e Ion channels are hollow proteins that have evolved to exhibit discrimination between charged solutes. This property, known as ion selectivity is critical for several biological functions. By using the bacterial porin OmpF as a model system of wide protein channels, we demonstrate that significant insights can be gained when selectivity measurements are combined with electrodiffusion continuum models and simulations based on the atomic structure. A correct interpretation of the mechanisms ruling the many sources of channel discrimination is a first, indispensable step for the understanding of the controlled movement of ions into or out of cells characteristic of many physiological processes. We conclude that the scattered information gathered from several independent approaches should be appropriately merged to provide a unified and coherent picture of the channel selectivity. 1. Introduction inherited cardiac arrhythmias to muscle disorders and forms of diabetes.4,5 The mechanisms by which ion channels regulate Ion channels are a large family of specialized pore-forming the transport of molecules and electric signal transduction proteins present in all living organisms that play a decisive role are often complex and even highly sophisticated. However, in the communications between and within cells. Proper the simplest picture of an ion channel may be a pore of nano- functioning of ion channels is crucial for neural transmission metre dimensions that acts either as a passive filter or as an as well as for key physiological processes that involve cardiac, externally activated valve within a biological membrane. Due pulmonary and muscle systems.1–3 Investigations of the function to the hydrophobicity and low polarizability of the lipid of biologically critical proteins bridge basic science with constituents of biological membranes, for ions and many clinical medicine. Such connections have been particularly metabolites the channel route is by far more energetically evident in the field of ion channels since the discovery of favourable than crossing the membrane.6 Thus, ion channels channelopathies: human diseases caused by the disturbed act as gatekeepers for charged solutes that enter or exit the function of ion channel subunits or the proteins that regulate cells and their organelles.1,2,7 The manipulation of biological them.4 As might be expected considering the variety of functions membranes and ion channels to take advantage of their performed by ion channels, channelopathies range from ‘sensing’ properties has been successful in a variety of biotechnological and analytical applications.8–10 Similar efforts Dept. Physics, Lab. Molecular Biophysics, Universitat Jaume I, have been directed to develop synthetic pores that mimic several 12080 Castellón, Spain. E-mail: [email protected] relevant functions of ion channels.11,12 Insight, innovation, integration Studying wide ion channels like bacterial porins, toxins measurements, in silico simulations and macroscopic and mitochondrial channels gives new insights into the electrodiffusion models to provide an original and attractive general problem of characterizing membrane permeabiliza- vision of protein channel function. Scattered, apparently tion by proteins and offers some innovative clues for the divergent, selectivity values found in the literature are exploration of antibiotic resistance in bacteria, toxin inhibi- harmonized in a single coherent picture after a careful tion and mitochondrial nucleotide exchange. This review analysis of the experimental conditions and assessment of shows that protein microscopic (atomic) information can the models used for the elucidation of membrane selective be successfully integrated with in vitro electrophysiological permeability. This journal is c The Royal Society of Chemistry 2011 Integr. Biol., 2011, 3, 159–172 159  View Article Online Electric signalling by way of ion channels is associated with rest of proteins, the lack of structural details is a breeding the movement of charges across a membrane.13 This task of ground of speculation about the folding path, the actual carrying electrical current is performed by the ions present in location of the residues and their ionization state and the all living systems (typically, but not exclusively, by Na+, K+, validity of the available theoretical approaches. Cl, Ca2+). Besides, a polarized interface is quite often The first structures (from the 1990s) of ion channels solved a requirement of some physiological function. Any electric at atomic resolution, i.e. below 3 Å, were those of the bacterial potential difference needs charge separation and this is porins, a family of homo-trimeric channel proteins. Therefore, accomplished in cells by keeping the concentration of positive one of them, the OmpF porin, a protein that forms wide and negative ions unbalanced between both sides of the channels just in the outer membrane of E. coli seems the ideal membrane. In the movement of ions through channels down candidate to become a ‘‘model system’’ revealing the fine their electrochemical gradients the net ionic transport reflects details of the structure/function correlation. The atomic the combined effect of the activity gradient and the electric structure of OmpF porin was first obtained from X-ray potential gradient. The vast majority of ion channels are analysis in 1992 with 2.4 Å resolution.19 Since then, subsequent able to display a preference for certain kind of ions and structures of OmpF have been reported in the presence of salts this property is generally known as ion selectivity.2 Such a of monovalent cations20 and divalent ones.21 Published on 06 December 2010. Downloaded on 23/10/2014 00:19:59. selection may be done simply by the ion charge (valence Most bacterial porins fall into the category of multiionic selectivity) or may be specific for particular ions or molecules. channels. Each subunit contains 16 to 18 transmembrane, On the one hand, the valence selectivity allows a broad anti-parallel b-strands forming a b-barrel structure. The classification of channels into cation selective and anion b-strands are amphipathic: they contain alternating polar selective, depending on whether cation or anion transport is and non-polar residues and the inter-strand interaction is fully favoured by the protein channel. On the other hand, the saturated with H-bonding. This creates a hydrophilic environ- specific selectivity serves very often to name the channel, e.g. ment providing a water filled channel weakly selective for chloride ion channel, potassium channel family, etc.14–17 small ions. The OmpF porin has an upper exclusion size limit Ion channels must discriminate efficiently between different corresponding to solute molecular weights ca. 600 Da. Because charged species, which is most easily achieved by a narrow most metabolites have molecular weights lower than 600 Da pore. However, ion channels should also transport ions as and have been shown to pass through porin channels, porins fast as possible, which is easier through a wider pore. The are called general diffusion pores.22,23 The study of their compromise between this two contrasting features configures selectivity is essential for many reasons, of which one of the the specific function of each channel. This review is focused on most important is the design of molecules with antibiotic the measurement and interpretation of ion selectivity in multi- properties and good permeability across the outer membrane ionic channels, collectively known as wide or mesoscopic of Gram-negative bacteria. As is known, porins provide a path channels because their pore dimensions: their size is too large through the outer membrane to small hydrophilic anti- to be specific but the channel walls still do have an influence on biotics.24 Other interesting protein channels that exhibit multi- the permeability. Understanding the mechanisms by which ionic transport are some bacterial toxins. The most widespread wide channels discriminate between different species of cations bacterial toxin found in the human organism is a-hemolysin and anions is a first, necessary step for an adequate interpreta- secreted by Staphylococcus aureus. This channel is a good tion of the specific selectivity in narrow channels.15 Besides, as example of how the interest of a particular toxin may go will be shown below, charge effects at the nanoscale are not beyond basic research up to novel biotechnology applications trivial at all and need to be correctly interpreted before like single molecule detection, chemical sensing, drug screening, attributing particular selective properties to a channel.18 RNA/DNA sequence readout, etc.8,10,25 We propose here to use the ion-channel analogue of the In the following sections we will first introduce the different well-known concept of ‘‘model system’’ in biology. Models are sources of selectivity in our OmpF model system. Then, those organisms with a wealth of biological data that make several ways of quantifying selectivity through experiments them attractive to study as examples for other species that are (in channels reconstituted on planar lipid bilayers) will be more difficult to analyze directly. One of the first model reviewed as well as the corresponding approaches to selectivity systems for molecular biology was the bacterium Escherichia used in MD and BD simulations. Finally, we will discuss what coli, present in the human digestive system. Several bacterial is needed for an adequate interpretation of those measure- viruses (bacteriophage) that infect E. coli have been also ments and calculations that may give a unitary view of channel very useful for the study of gene structure and gene regulation selectivity. (e.g. phages Lambda and T4). The search for a model system representative of wide channels must tackle a crucial issue. When the channel structure is known in detail, the combina- 2. The origin of ionic selectivity of multiionic tion of several approaches—molecular dynamics (MD), channels Brownian dynamics (BD) and continuum theories—provides 2.1 Narrow channels vs. multiionic wide channels a sound interpretation of certain function-related magnitudes (conductance, selectivity, etc.) measured in electrophysiology Channel selectivity is routinely measured in the laboratory experiments.17 But, unfortunately, such methodologies are as an element of the process of characterization of any only possible in the small group of channel-forming proteins transmembrane protein forming channels.2,26 One might whose structure has been solved at atomic resolution. In the think that a charged pore should allow passage of charged 160 Integr. Biol., 2011, 3, 159–172 This journal is c The Royal Society of Chemistry 2011  View Article Online solutes basically depending on their size and charge. Although narrow channels is often termed single-file because only one this is essentially true, the physicochemical mechanisms ion at a time can cross the selectivity filter. controlling ion selectivity are largely dependent on each Fig. 1 illustrates the different occupancy of selective narrow particular type of channel.16 For instance, such size and charge and large ion channels as well as the solvated or unsolvated controlled permeability would not be enough to understand state of the permeating ions. The wide channel on the left how aquaporins selectively conduct water molecules in represents a typical bacterial porin, whose slight cationic and out of the cell, while they are completely impermeable or anionic selectivity is low enough not to exclude cations to charged species, even to protons.27,28 Other factors like or anions. The narrow channel on the right represents a the characteristic aqueous solvation of each ionic species potassium channel specifically designed to let only bare K+ may be determinant in channel selectivity.29 In potassium ions in and out. The division into narrow and wide channels, channels, to mention another example, the coordination simple as it may appear, is very useful for the purpose of of the protein-channel carbonyl groups with the unsolvated analyzing channel selectivity. However, such categories are not permeating ion is essential to achieve a thousand-fold totally exclusive. In a large variety of channels the discrimina- K+/Na+ selectivity.30–32 tion between ions can be partially done in the short section Published on 06 December 2010. Downloaded on 23/10/2014 00:19:59. Leaving apart important channel features like their activa- called selectivity filter while other wider regions of the pore aid tion mechanism, their voltage-dependent function and the rapid diffusion.15 transition between states of different conductance, a broad classification of ion channels can be made between multiionic 2.2 The various sources of ion selectivity channels and ion-specific channels. The first ones are often known as mesoscopic channels and have pore dimensions that The discrimination between ions depends not only on the ion allow simultaneous passage of water molecules, positive and intrinsic properties (size, solvation, diffusivity in water, shielding negative ions of several types that may enter the pore without effects, etc.) but also on the particular interaction of permeating losing their hydration layer and even metabolites like ATP33 ions with the channel residues,2 as shown in Fig. 2. This or antibiotic molecules.34 The second type selects a particular general statement implies that ion selectivity is not an intrinsic ion so that permeability to other ions is usually very low property of the channel but necessarily includes both the (e.g. potassium channels have a permeability ratio for K+ over protein channel and the electrolyte flowing through it.36 When Na+ > 100 : 1 and calcium channels select for Ca2+ over Na+ this is particularized to the selectivity of large channels with a ratio > 1000 : 1). To achieve this high ion specificity, a towards small inorganic ions, the two leading contributions close interaction between the permeating ion and the protein to channel selectivity are the differences between cation and residues is needed.2 For this reason, channels displaying anion mobilities and the electrostatic exclusion due to the specific selectivity have pore dimensions comparable to the interaction between permeating ions and channel ionizable size of the permeating ion or at least there is a narrow region residues.26,37 Very often, a high selectivity is exclusively called selectivity filter—a term coined by Hille in 197135—that associated with the latter, thus overlooking not only diffusional discriminates between ionic species. Ion transport in such effects, but also additional factors such as entropic effects related to the preferential rejection of ions because of their size, short range non-electrostatic interactions and osmotic effects. In principle, diffusional effects can be identified and minimized. For instance, in salts where the cation and the anion have almost equal bulk diffusivities (e.g. KCl or CsCl), the diffusional contribution is negligible. This explains why so many measurements of channel selectivity have been per- formed in KCl solutions. Under such conditions, the channel selectivity can be correlated rather well with the net fixed Fig. 2 Several contributions to large channel selectivity under a salt concentration gradient. (a) A channel with net negative fixed charge Fig. 1 Cartoon illustrating the difference between single-file transport accumulates cations and partially excludes anions. (b) When cations and multiionic transport. Left: OmpF channel. Cations and anions and anions have different mobilities, there appears a net electric may enter the pore without losing their hydration layer. The channel current across the channel. (c) Short-range, non-Coulombic, inter- displays a slight preference for cations at neutral pH. Right: potassium actions between permeating ions and protein residues may alter and channel. Only unsolvated K+ ions are allowed to enter the pore. K+ even reverse the partitioning of cations and anions between solution transport takes place in a single-file fashion. and the channel pore and their respective mobilities. This journal is c The Royal Society of Chemistry 2011 Integr. Biol., 2011, 3, 159–172 161  View Article Online charge of the channel coming from the ionizable residues of constant and T is the absolute temperature. RP provides a the protein.36–38 This fact, combined with the technique of site joint measure of partition and diffusion.26 This means that directed mutagenesis, which allows altering the charge of the two different pieces of information are merged in a single channel by substituting charged residues with neutral ones, lies permeability ratio that cannot be easily connected to the on the basis of numerous studies of channel selectivity in physical structure of the channel. Quite the reverse, the OmpF39–41 and other wide channels like VDAC.42 However, limitations of the GHK theory (see section 3.4 below) are so it is not always reliable as will be explained later in the paper. important that this approach should be considered as a first The role of diffusion can be studied separately as well. In approximation.36,43 channels with very small net charge this is straightforward, A typical series of experiments consists of measuring since the accumulation of counterions and the exclusion of RP keeping a fixed salt concentration on one side of the coions are insignificant and do not contribute to channel channel and varying the concentration on the other side.36,44,45 discrimination between cations and anions. But in channels However, in many situations the reversal potential measured with non-negligible charge an alternative strategy may give depends not only on the concentration ratio but on the useful information on the actual relative mobilities of ions absolute value of concentrations, the pH of the solutions Published on 06 December 2010. Downloaded on 23/10/2014 00:19:59. inside the channel: the measurement of selectivity under and even the orientation of the channel with respect to the conditions where the partitioning of ions inside the channel salt gradient. The lipid composition of the membrane where reaches a limit (for instance, when bulk salt concentration is the channel is embedded may have also some influence since it much higher than the effective fixed charge concentration of can modulate the local ion concentrations near the channel the channel).38 openings.36 3. Measurement and modelling of channel 3.2 Bi-ionic potential selectivity The bi-ionic potential (BP) is the zero current potential measured in symmetric bi-ionic conditions: two different salts As commented before, the selectivity of large channels includes with a common ion on each side of the channel but both two components: partitioning, an equilibrium measure of the solutions with the same concentration. This approach is not channel preference for a particular ionic species, and diffusion, suitable to measure cation/anion selectivity but to measure a non-equilibrium average measure of the relative mobility of the relative selectivity of the channel to different cations ions in the channel.2,26,38 This fact becomes crucial when one (in salts of a common anion) or to different anions (in salts realizes that all the protocols used to estimate the ion channel of a common cation). The BP measurements, like the RP ones, selectivity are based on electrokinetic measurements that are also translated into permeability ratios. According to operate under non-equilibrium conditions (concentration GHK equation,46 for a pair of solutions of NaCl|KCl, we gradients of neutral and/or charged solutes, applied voltage, get the following relationship between BP and the ionic applied pressure, etc.). Thus, each particular way of quantify permeabilities Pi: selectivity will involve a different balance between ion partitioning and electrodiffusion, so that disparate outcomes   could be obtained even for the same channel.43 Here, we kT PNa cNa;cis þ PK cK;cis þ PCl cCl;trans summarize the most common approaches to measure channel BP ¼  ln ð2Þ e PNa cNa;trans þ PK cK;trans þ PCl cCl;cis selectivity in channels reconstituted on planar lipid bilayers. 3.1 Reversal potential As usual cis refers to the side of the protein addition and trans The reversal potential (RP) is defined as the applied trans- to the solution on the other side of the channel. To solve for membrane voltage that yields zero electric current when there the permeability ratio PNa/PK one must assume that channel is is an activity gradient across the channel. RP is the method of impermeable to chloride ions, i.e. PCl = 0. Then, in the choice to quantify selectivity for the sake of simplicity: the sign particular case that KCl is in the cis compartment and NaCl of the RP provides a quick estimation of the channel selectivity in the trans one, we get: and its preference for cations or anions. Furthermore, by using the Goldman–Hodgkin–Katz (GHK) equation the PNa/PK = eBP(e/kT) (3) measured RP can be converted into a single parameter for This equation is very useful in narrow channels with negligible each permeant ion: the permeability. Unfortunately, the GHK transport of coions.26 However, this is not the case in wide equation allows one to calculate permeability ratios, but channels, where the permeability ratios obtained using eqn (3) not absolute permeabilities.2 For a monovalent salt the are strongly dependent on salt concentration and have no cation/anion permeability ratio derived from the GHK trivial interpretation.43 As pointed out more than 40 years ago equation reads: by Sandblom and Eisenman,47 a constant permeability ratio Pþ 1  r eRPðe=kTÞ cannot be characteristic of all membrane systems but is ¼ RPðe=kTÞ ð1Þ restricted to certain physical situations, most notably those P e r in which a membrane is permeable only to species of one sign. Where r is the concentration ratio between the two salt This seems clearly incompatible with wide channels that are solutions, e is the elementary charge, k is Boltzmann’s weakly selective and allow a noticeable transport of coions.43 162 Integr. Biol., 2011, 3, 159–172 This journal is c The Royal Society of Chemistry 2011  View Article Online 3.3 Conductance ratio ion-ion interactions. Since the dynamics of the water molecules and the protein atoms are no longer included and time steps can Single channel I–V curves are measured by applying a voltage be longer, BD is many orders of magnitude faster and much less across the system in symmetric conditions (the same solution computationally costly than MD.69,70 in both baths). The current–voltage ratio G = I/V yields a At the next stage in the microscopic level of representation measurement of its conductance. A way of quantify the of protein atoms, solvent molecules and ions, lies a continuum relative preference of the channel by two different, say, cations electro-diffusion model in which the mobile ions are treated as is to measure the channel conductance in solutions of salts concentration profiles.71–73 Their distribution and motion are with a common anion. For instance, the ratio of the channel determined by random diffusion and by electrostatic forces conductances measured in two different experiments with (a mean field approximation). The atomic 3D structure of the NaCl and KCl salt solutions with the same concentration protein channel is used to get the spatial charge distribution. provides a measurement of the selectivity of the channel. In practice, Poisson equation of electrostatics and Thus, GNaCl/GKCl is regarded as a measure of the relative Nernst–Planck drift-diffusion equations are combined in a channel selectivity to Na+ and K+ cations. This is especially set of coupled partial differential equations. In the context of appropriate for highly selective narrow channels where the Published on 06 December 2010. Downloaded on 23/10/2014 00:19:59. ion permeation through channel proteins, this approach is whole electric current is carried almost exclusively by one ionic known as Poisson–Nernst–Planck (PNP-3D) theory.74–76 If species. However, measuring conductance in wide channels in the 3D channel structure is not available, the 3D concentration order to elucidate channel selectivity could lead to manifest function can be replaced by a 1D concentration (with the contradictions when compared to other protocols.45 As meaning of a cross-section averaged ion concentration) commented in the case of Bi-ionic Potential, the current flow and the whole problem becomes one-dimensional.77 Several across wide weakly selective channels involves a large amount numerical procedures have been developed in recent years to of correlated ions48,49 (both cations and anions) and cannot be solve the PNP system of equations as well as refinements of the understood under the assumption of the total exclusion of theory to get a more accurate representation of the protein- coions. solution boundary.75,78 For several decades, the macroscopic electrodiffusion model 3.4 Modelling channel selectivity based on 1D Nernst–Planck and Poisson equations has been There is no unique theoretical model that may account for all used to give a quantitative description of the ion transport the transport properties of such a complex structure like a properties of porous membranes, single microscopic or nano- biological ion channel.17 For this reason, several approaches scopic pores and biological ion channels.2 Since PNP have been used, each one addressed to a particular aspect. The equations are a system of coupled non-linear differential most powerful method to model channel selectivity consists in equations that cannot be solved in closed form (even in the a full all-atom non-equilibrium MD simulation whenever the simplest one-dimensional case), two main approximations atomic 3D structure of the channel is available.50–53 In large have been used to obtain analytical solutions for the RP. channels MD could be extremely challenging because it One of them is based on the assumption of charge neutrality involves the explicit consideration of protein atoms, water all over the pore and the other, initially proposed by Goldman molecules and ions and, most important, long enough simula- by assuming a constant electric field along the pore,79 led to tion runs to get statistically meaningful quantities. In such the well known GHK equation (eqn (2) in the text) widely cases, coarse grained models where the number of particles is used today to express channel relative selectivity in a single considerably reduced are a good alternative. In spite of this, parameter, the permeability ratio. The literature about the MD simulations have provided precious details about the conditions under which GHK equation can be safely used is permeation pathways of ions along a variety of channels54–58 abundant.2,26,47,80–83 To put it briefly, constant electric field and thanks to recent advances, it is now possible to compute and independence of ion fluxes are the basic requirements to explicitly channel conductance using all-atom MD simulations ensure GHK equation validity. Strictly speaking, those con- and analyze the behaviour of a single protein residue.52,59,60 In ditions are only rarely met. Nevertheless, there are exceptions addition to computing power, the accuracy of the various MD to the rule which show that constancy of the field must not methods relies on a good representation of the interaction necessarily be fulfilled.47,48 Indeed, even in wide channels like between the mobile ions themselves and the protein atoms. OmpF, VDAC or a-hemolysin displaying intricate amphoteric Different sets of parameters commonly referred to as force surfaces where the constant field assumption along the fields have been developed to this end.61,62 There is also a small channel seems totally unrealistic, there are situations where range of computing packages.63–65 GHK equation fails to describe properly the channel cationic There are other methods that avoid a full atomistic selectivity36,37 as well as cases where it works fine apparently.48 representation in exchange for computational efficiency. BD, Im & Roux have used the calculated free energy profile along dynamic lattice Monte Carlo and grand canonical Monte the OmpF channel as a paradigmatic example to discuss this Carlo BD have in common the implicit representation of matter. According to them, the number of free energy barriers the solvent and the membrane while ions are modelled and their relative position in the channel could explain the explicitly.48,66–68 The trajectory of each ion in the system can surprising validity of GHK equations in some specific cases.48 be obtained by solving a particular formulation of Newton’s In any case, it should be borne in mind that the real question second law: the so-called Langevin equation. A major advantage is whether the ionic permeabilities Pi involved in GHK of the BD approach is that it allows a direct simulation of equation are well-defined, physically-sound parameters for This journal is c The Royal Society of Chemistry 2011 Integr. Biol., 2011, 3, 159–172 163  View Article Online every ionic species in a given channel or whether they are This implies that the proton dissociation constant Ka of the empirically defined and allowed to be arbitrary functions of residue (or its equivalent in the logarithmic scale, the pKa) voltage and concentration. In the latter case, they become inside the protein may differ from that in free solution.85 ineffective to rationalize selectivity data in a wide range of Therefore, one needs to calculate the apparent pKa of each ionic species, salt concentrations and applied voltages.36,43 titratable residue inside the protein. The protocol followed to perform this calculation, based on the procedure described by 4. Structural insights from selectivity experiments Antosiewicz et al.,86,87 has been described elsewhere.36 A finite difference Poisson–Boltzmann solver can be used to compute and continuum models the apparent pKa from the 3D atomic crystal structure of The number of protein channels whose atomic structure has OmpF.88 been resolved by X-ray or NMR methods is still limited. The pKa calculations performed in a very acidic environ- Therefore, additional methods providing information about ment (pH = 2) in one of the three identical OmpF monomers channel tertiary structure are well received. Selectivity can be indicate that 41 residues are charged. 31 of them have positive helpful in this task because, under certain conditions, the charge whereas 10 have a negative one (Fig. 3a). This positive Published on 06 December 2010. Downloaded on 23/10/2014 00:19:59. amount of channel charged residues and their space distribu- net charge correlates qualitatively well with the reported tion can be probed by experiments. As mentioned in previous anionic selectivity of the channel under such conditions. sections, when diffusional effects can be reasonably excluded, At neutral pH (Fig. 3b), the balance between positive and channel selectivity correlates with the channel net charge.36 negative residues is inverted. There are 30 positives and Because channels accumulate ions with sign opposite to the net 41 negatives, yielding a net negative charge. However, the fixed charge of the ionizable residues, a channel with positive situation is quite different under basic conditions (pH = 12). net charge (i.e. more ionized basic residues than acidic According to the calculations 58 residues are charged, 14 of residues) will exhibit anionic selectivity. On the contrary, a them are positive and 44 are negative (Fig. 3c). This is channel with negative net charge will favour transport of consistent with the cation selectivity of the channel found in cations. This fact, combined with measurements over a wide experiments at pH 7 and 12. Therefore, considering all charged range of pH and a reasonable estimate of the pKa of the residues with their properly calculated pKa, the channel suspected ionizable residues may provide useful information. selectivity exhibits a good qualitative correlation with the total monomer charge. This conclusion does not hold if one 4.1 Selectivity measurements to explore residue titration assumes that the residues that face the channel lumen or are The elucidation of the structure/function correlation should in the vicinity of the aqueous pore are presumably most start on a proper understanding of the channel structure.16,36 relevant to the channel selectivity. Taking a reasonably The electrostatic interaction between the channel charges and cut-off distance of 3 Å to the pore solvent accessible surface, the permeating ions crucially regulates the transport through there are only 21 residues among the overall 102 ionizable the channel,26 so that the first issue to investigate is the charge residues of each monomer that match such condition. The state of the ionizable residues of the protein. This is not a result (for this region ‘‘accessible’’ to permeant ions) is trivial task because of the interplay of several factors. Each somewhat counterintuitive. At neutral pH, 13 residues are titratable residue of the channel is in an environment of low positively charged and 8 residues negatively charged. The net electric permittivity as is the protein. It interacts with the 5 positive charges per monomer are clearly irreconcilable with protein permanent fixed partial charges (due to the different the measured cationic selectivity of the channel at neutral pH. electronegativities of the atoms in the molecule) and with the Although the computed total net charge correlates quali- rest of titratable residues.84,77 In addition, these interactions tatively well with the reported ionic selectivity, this is not are influenced by the shielding effect of the ions in solution. the case quantitatively. Electric charges of such magnitude Fig. 3 Cartoon that illustrates the amount of charged OmpF residues in three environments at different pH. A ribbon representation of the tertiary structure of the OmpF porin is combined with colored balls representing the positively charged (yellow) and negatively charged (red) ionizable residues. (a) At pH 2 the positive residues exceed by 21 the negative ones, which is consistent with the anionic selectivity of the channel. (b) At pH 7 the net balance switches to negative (11). (c) At pH 12 negative residues are more than double the number of positive ones, what agrees with the large cationic selectivity measured at this pH. 164 Integr. Biol., 2011, 3, 159–172 This journal is c The Royal Society of Chemistry 2011  View Article Online obtained between the measured selectivity and the effective fixed charge of the channel.43,77 This effective charge is around 1–2 elementary charges, what originates realistic electric fields in the protein.77,89 Fig. 4 shows measurements of RP (dots) over a wide range of pH together with the calculated RP (solid line). These results show that average electrostatic properties obtained directly from the microscopic structure of the protein regulate the ionic transport under a variety of conditions. This conclusion holds also for some engineered OmpF mutants with very different electrostatic properties but similar atomic structure to that of wild type OmpF.37,90 The model outlined above constitutes a macroscopic electrodiffusion theory of the Fig. 4 Permeability ratio in OmpF channel as a function of pH. Dots ion transport across the pore, but it is based on microscopic Published on 06 December 2010. Downloaded on 23/10/2014 00:19:59. correspond to measurements in 1 M/0.1 M KCl solutions. Solid line structural information. One could wonder whether a rough 1D represents the calculated permeability ratio. Details of the experiments PNP approach using effective magnitudes can accurately are given elsewhere.36 describe the transport properties of a system in the nanoscale as is the OmpF porin. Recent studies in both synthetic and (B40 elementary charges) would create colossal electrical biological nanopores support this idea. One dimensional fields (1010–1011 V m1) around the protein that seem totally approaches based on Smoluchowski equation, Fick–Jacobs unfeasible.54,89 This indicates that understanding ion permeation approximation and Poisson–Nernst–Planck equations provide through the channel involves something else than counting interesting clues for planning more efficient synthetic biosensors, charges in the protein. The dielectric environment, the mutual nanopumps and nanodiodes.91–93 In addition, satisfactory interaction between residues and the distance from each comparisons between mean field theories and BD simulations particular residue to the permeation path of the ions becomes are found for wide biochannels.94 In fact, several PNP essential to explain possible screening effects. A detailed approaches describing satisfactorily the ion transport across theoretical model connecting the structural data to the experi- different biological ion channels have already been reported: mental observations seems mandatory. The acetylcholine receptor,95 the L-type calcium channel,71 the Despite their low resolution, mean field theories, such as calcium release channel,72 the gramicidin A channel,74 the PNP or the Teorell–Meyer–Sievers (TMS) theory, have been mitochondrial channel VDAC76,96,97 or the OmpF porin38,43,77 used to calculate electrodiffusion quantities in many ionic among others.76,75,36 systems like synthetic nanopores, ion exchange membranes, polyelectrolyte multilayers and ion channels. In their simplest 4.2 Role of the selectivity filter in wide channels versions, those approaches do not incorporate structural information but use effective parameters which are fitted to The traditional way to explore the channel distribution of the experimental data.36 A slightly different, more elaborated, ionizable residues is site directed mutagenesis. If the measured continuum approach consists in combining a 1D PNP model channel selectivity is not affected by the mutation, i.e. replace- with cross-section averaged structural information extracted ment of a given charged residue by a similar neutral one, this is from the 3D atomic structure of the channel. With a minimum regarded as a proof that such residue is not exposed to the ion computational effort, a good quantitative correlation is stream.39,42,98 This is based on the assumption that only the Fig. 5 (a) View of OmpF selectivity filter with two acidic residues (D113, E117) facing a cluster of three positive arginines (R42, R82, R132). (b) Permeability ratio of WT OmpF and D113C/E117C mutant as a function of solution pH (0.1 M KCl cis|1 M KCl trans). This journal is c The Royal Society of Chemistry 2011 Integr. Biol., 2011, 3, 159–172 165  View Article Online ionizable residues facing the aqueous pore or located at the selective to anions. This indicates that in the OmpF channel selectivity filter contribute to the channel selectivity. This may the selectivity filter plays an important role, but it is not the be true in channels like VDAC where practically there are no sole determinant of the measured selectivity. A large number residues buried99,100,101 but it seems inaccurate or even wrong of residues besides the five located in the selectivity filter seem in other channels like OmpF where there are ionizable residues to be involved.40,41,77,102 buried in a low polarizability environment that greatly In addition, the selectivity filter, being the narrowest region contribute to channel selectivity,84,36 as discussed in the above of the pore, is a key factor both regulating the channel section. Actually, the atomic structure of this channel shows conductance to small ions and limiting the size of the solutes that the overall net charge of ionizable residues facing the that cross the channel. Detailed MD and BD simulations aqueous pore is positive while the channel is cation selective. suggest that the charge asymmetry in the constriction zone, Obviously this means that the channel selectivity is the result clearly visible in Fig. 5a, originates a strong electric field of the concerted action of many residues, not simply of those transverse to the pore axis.54,103,98,48,49 This channel feature lining the pore or placed at the channel narrow constriction could be vital for the transport of dipolar molecules like some and it implies that the concept of selectivity filter,35 crucial in antibiotics34,104 and deserves a closer analysis. Published on 06 December 2010. Downloaded on 23/10/2014 00:19:59. highly selective (narrow) channels is less meaningful in wide Fig. 6 shows contour maps of the electric potential multiionic channels (see section 4.1). (in kT/e units) in the cross-sectional plane (at axial coordinate The OmpF channel has an hour-glass shape with a narrow z = 3.42 nm) of the central constriction of the WT-OmpF constriction located about half of the channel total channel (Fig. 6a) and the D113C/E117C mutant (Fig. 6b) length.19,21,20 Fig. 5a shows a schematic view of the constric- where the two carboxylates D113 and E117 have been replaced tion zone, showing two acidic residues (D113, E117) that face by neutral cysteines.41,102 In both panels the blue dot a cluster of three positive arginines (R42, R82, R132). At line separates the aqueous pore (enclosed region) and the neutral pH, all these five residues are ionized and the net surrounding protein domain, non accessible to solvent. charge at the channel constriction is +1e, what seems difficult Fig. 6a shows the strong negative electric potential due to to reconcile with the observed cationic selectivity of the the channel acid groups and also a region of positive potential channel under such conditions.77 The fact that channel located near the cluster of arginines. This is in good agreement selectivity is not only regulated by the channel constriction is with MD simulations reporting that cations and anions follow even more evident when site-directed mutations of the acidic well-separated permeation pathways along the OmpF porin in residues in the selectivity filter are performed. As can be screw-like way.48,49 Fig. 6b shows that the region of negative observed in Fig. 5b, the substitution of two carboxylates potential vanishes when two neutral residues replace the key D113 and E117 by neutral cysteines does not eliminate the acids D113 and E117. Such substitution clearly distorts the cation selectivity of the channel observed around neutral pH. subtle permeation mechanism described in Fig. 6a and hinders The qualitative trend in the D113C/E117C mutant seems the the transport of cations through the constriction. This con- same as that observed in the wild-type (WT) OmpF: the jecture is supported by the fact that in experiments performed channel preference for cations turns into a predilection for in 2 M KCl the conductance of the D113C/E117C mutant anions as pH decreases and acidic residues are successively (B2 nS) is less than one third of the conductance measured in protonated. WT OmpF (B7 nS).53 It is also true that some quantitative differences between In addition, for a proper interpretation of the role of WT OmpF and the D113C/E117C mutant are manifest. At selectivity filter in wide channels, it must be borne in mind pH = 4 the former is selective to cations and the latter is that any electrostatic interaction between ions and protein Fig. 6 Contour plot of the electric potential in a cross-sectional plane of the OmpF channel central constriction (at z = 3.42 nm). The coordinates x, y, z are those of the first OmpF atomic structure.19 Numbers denote the maximum value of the potential on each region in kT/e (B25.7 mV) units. The dot line depicts the limit between the aqueous pore (inner region) and the surrounding protein domain, non accessible to solvent. (a) Constriction of WT-OmpF. Even though the channel is cation selective, calculations show that there are two regions of positive and negative potential which may be the path for anions and cations when crossing the selectivity filter. This assumption has been confirmed by MD simulations.48,49 (b) Constriction of the D113C/E117C mutant. The region of negative potential is lost and cation permeation is hindered. 166 Integr. Biol., 2011, 3, 159–172 This journal is c The Royal Society of Chemistry 2011  View Article Online membrane is mostly unidirectional, as happens with the OmpF porin,36 this asymmetry can be probed by selectivity measurements.36,108 The RP measured in OmpF depends on the direction of the concentration gradient, i.e. the absolute value of RP for a given ratio Ccis/Ctrans = r and its inverse Ccis/Ctrans = 1/r is different. For a totally symmetric channel the two experiments should give the same RP, but opposite in sign.36,108 The difference between RP in the two cases may be used to probe channel orientation if the channel structure is known. Alternatively, it can be used to explore channel asymmetry when the channel orientation in experiments is known. Fig. 7 shows the results of RP measurements for a wide range of Fig. 7 Change of OmpF reversal potential (absolute value) with salt concentration ratio in KCl solutions at pH 6. The lower electrolyte concentration ratio values (For making easier the comparison, Published on 06 December 2010. Downloaded on 23/10/2014 00:19:59. concentration was kept at 0.1 M while the higher concentration was absolute values of RP are plotted). Model calculations can be changed to obtain the desired concentration ratio. Details of the used to rationalize the asymmetry of the channel selectivity in experiments are given elsewhere.36 terms of the distribution of channel ionizable residues in the axial direction. This asymmetrical channel charge distribution charges is enhanced in this region.89 Water in confined cannot be inferred from the usual current–voltage measure- geometries exhibits properties very different from those in ments unless its effect is high enough to produce current bulk. In such a small region and surrounded by charged rectification. As Fig. 8 shows, in OmpF almost no rectification residues, water molecules reduce their translational and is observed.109 Interestingly, charge asymmetry has been rotational mobility.105 The decreased polarizability of water reported in conical synthetic nanopores, showing that in such is reflected in a reduction of the dielectric constant known as system it is possible to use it as a basis to construct ionic dielectric saturation of water. Some studies addressed this nanofilters.93 problem by assigning to the effective dielectric constant of water in the channel a single value lower than the well known 4.4 Selectivity inversion by multivalent cations e B 80.106,107 For the specific case of OmpF, continuum electrostatic calculations combined with electric field dependent The close relationship between channel charge and selectivity dielectric constants have suggested that the water dielectric mentioned in previous sections is lost when another type of constant at the constriction may be reduced down to 50% of short-range interaction between permeant ions and protein its usual value in bulk water.89 This estimation changes groups outweighs the Coulombic attraction or repulsion.37,41 considerably the prediction of the free energy well that cations Any short-range interaction between ions and protein sites is encounter as they go through the channel eyelet. likely to take place in the narrow selectivity filter where the distances are much smaller. In this context, it becomes relevant 4.3 Selectivity measurements to explore channel asymmetry a recent publication of a 1.6 Å OmpF structure in 1 M MgCl2, The distribution of ionizable residues in many protein channels which showed that one Mg2+ ion is bound in the selectivity is not homogeneous but asymmetric. This means that the part filter between D113 and E117 of loop 3.21 This feature is of the channel facing the extracellular side may exclude/ probably behind the reported electrophysiological response of accumulate ions in a different way than the part of the channel the channel: the well-known moderate cationic selectivity of the that faces the cytosol or the intermembrane space.2 If the bacterial porin OmpF in salts of monovalent ions36,38,44,45,110 orientation of the channel when reconstituted in the lipid turns into anionic selectivity in salts of divalent40,41,37 and trivalent cations.102 Fig. 9a shows the permeability ratios obtained via GHK equation from RP measurements performed under a 10-fold concentration gradient of KCl and MgCl2. Also, sample current traces of the corresponding RP measure- ments are displayed in Fig. 9b and 9c. In the literature of ion channel biophysics, the selectivity experiments are customary interpreted in terms of an effective channel charge. This concept refers to the charge that gives rise to the electric field actually felt by the ions permeating through the channel.2,26 Following an intuitive reasoning one could speculate that the anion selectivity (P+/P E 0.2) found for MgCl2 around neutral pH could come from a ‘‘charge inversion’’ phenomenon, i.e. from an effective positive charge