Overcharging below the nanoscale: multivalent cations reverse the ion selectivity of a biological channel

Electrophysiological dissection of the ion channel activity of the Pseudomonas aeruginosa ionophore protein toxin Tse5

We present an in-depth electrophysiological analysis of Tse5, a pore-forming toxin (PFT) delivered by the type VI secretion system (T6SS) of Pseudomonas aeruginosa. The T6SS is a sophisticated bacterial secretion system that injects toxic effector proteins into competing bacteria or host cells, providing a competitive advantage by disabling other microbes and modulating their environment. Our findings highlight the dependency of Tse5 insertion on membrane charge and electrolyte concentration, suggesting an in vivo effect from the periplasmic space. Conductance and selectivity experiments reveal a predominant and reproducible pore architecture of Tse5, characterized by a weak cation selectivity without chemical specificity. pH titration experiments suggest a proteolipidic pore structure influenced by both protein and lipid charges, a hypothesis further supported by experiments involving engineered mutants of Tse5 with altered glycine zippers. These results significantly advance our understanding of Tse5's molecular mechanism of toxicity, paving the way for potential applications in biosensing and macromolecular delivery.

Supralinear scaling behavior of ionic transport in membrane nanochannels regulated by outer-surface charges

The peculiarity of ion transport at the nanoscale is revealed through electrophysiological studies of two biological ion channels: the cation-selective bacterial porin-OmpF and the mitochondrial voltage-dependent anion channel (VDAC). We provide evidence of an unprecedented scaling behavior in the power-law relationship between conductivity and concentration G ∼ c α with α > 1 when functional groups attached to the pore inner wall have opposite charges to those located in the nanochannel's outer surface. Indeed, we find α ∼ 1.4 both for OmpF in positively charged membranes and for VDAC in negatively charged ones. The experiments are analyzed using different levels of theoretical models, starting with an equivalent circuit where total electrical current is described as the sum of ionic currents. Subsequently, we show that electrical circuits incorporating simplifying assumptions such as local electroneutrality and Donnan equilibrium consistently account for the measured G-c relationships yielding extremely similar results to the numerical results of structure-based Poisson-Nernst-Planck equations computed without these assumptions. We demonstrate that unexpected scaling exponents do not correspond to deviations from these classical equilibrium/electroneutrality assumptions, but rather to the structural features of the pore that are not included in oversimplified models in terms of shape and/or charge distribution. In contrast to the predictions of widely accepted models, we demonstrate both experimentally and theoretically that the conductance of ion-selective nanochannels can be drastically reduced in dilute solutions through a mechanism in which membrane charges and pore charges do not compensate for each other but act as interacting sites of opposite charge. Our insights into the critical role of external surface charges aim to open new conceptual avenues for developing nanofluidic devices with enhanced capabilities for energy conversion and sensing properties.

Biphasic concentration patterns in ionic transport under nanoconfinement revealed in steady-state and time-dependent properties

Ion permeation across nanoscopic structures differs considerably from microfluidics because of strong steric constraints, transformed solvent properties, and charge-regulation effects revealed mostly in diluted solutions. However, little is known about nanofluidics in moderately concentrated solutions, which are critically important for industrial applications and living systems. Here, we show that nanoconfinement triggers general biphasic concentration patterns in a myriad of ion transport properties by using two contrasting systems: a biological ion channel and a much larger synthetic nanopore. Our findings show a low-concentration regime ruled by classical Debye screening and another one where ion-ion correlations and enhanced ion-surface interactions contribute differently to each electrophysiological property. Thus, different quantities (e.g., conductance vs noise) measured under the same conditions may appear contradictory because they belong to different concentration regimes. In addition, non-linear effects that are barely visible in bulk conductivity only in extremely concentrated solutions become apparent in nanochannels around physiological conditions.

Dendritic polyelectrolytes with monovalent and divalent counterions: the charge regulation effect and counterion release

The charge regulation and the release of counterions are extremely important and substantial in determining the charge state of polyelectrolytes and the interaction between polyelectrolytes and proteins. Going beyond monovalent to multivalent cations, it is well-known that the effects of ions are qualitatively different. Therefore, the well-accepted descriptions of the charge regulation and the counterion release based on monovalent ions do not immediately apply to systems with multivalent ions. Here, we study the key structural and electrostatic features of charged dendrimers at hand of the pharmaceutically important dendritic polyglycerol sulfate (dPGS) macromolecule equilibrated with monovalent and divalent salts by molecular dynamics (MD) simulations. Following a simple but accurate scheme to determine its effective radius, the counterion condensed layer of the dPGS is determined with high accuracy and we observe the sequential replacement of condensed monovalent cations (MCs) to divalent cations (DCs) rendering a smaller dPGS effective charge versus the DC concentration. We resolve and track the release of counterions on the dPGS along its binding pathway with the plasma protein Human Serum Albumin (HSA). We find that the release of MCs remains favorable for the complexation leading to a considerable amount of release entropy as the driving force for complexation. The release of DCs only occurs above a certain DC concentration with a comparably smaller number of released ions than MCs. Its contribution to the binding free energy is small indicating a subtle cancellation between the entropy gain in releasing DCs and the enthalpy penalty from dissociating DCs from the dendrimer.

Specific adsorption of trivalent cations in biological nanopores determines conductance dynamics and reverses ionic selectivity

Adsorption processes are central to ionic transport in industrial and biological membrane systems. Multivalent cations modulate the conductive properties of nanofluidic devices through interactions with charged surfaces that depend principally on the ion charge number. Considering that ion channels are specialized valves that demand a sharp specificity in ion discrimination, we investigate the adsorption dynamics of trace amounts of different salts of trivalent cations in biological nanopores. We consider here OmpF from Escherichia coli, an archetypical protein nanopore, to probe the specificity of biological nanopores to multivalent cations. We systematically compare the effect of three trivalent electrolytes on OmpF current-voltage relationships and characterize the degree of rectification induced by each ion. We also analyze the open channel current noise to determine the existence of equilibrium/non-equilibrium mechanisms of ion adsorption and evaluate the extent of charge inversion through selectivity measurements. We show that the interaction of trivalent electrolytes with biological nanopores occurs via ion-specific adsorption yielding differential modulation of ion conduction and selectivity inversion. We also demonstrate the existence of non-equilibrium fluctuations likely related to ion-dependent trapping-detrapping processes. Our study provides fundamental information relevant to different biological and electrochemical systems where transport phenomena involve ion adsorption in charged surfaces under nanoscale confinement.

Rectification of bipolar nanopores in multivalent electrolytes: effect of charge inversion and strong ionic correlations

Bipolar nanopores have powerful rectification properties due to the asymmetry in the charge pattern on the wall of the nanopore. In particular, bipolar nanopores have positive and negative surface charges along the pore axis. Rectification is strong if the radius of the nanopore is small compared to the screening length of the electrolyte so that both cations and anions have depletion zones in the respective regions. The depths of these depletion zones is sensitive to sign of the external voltage. In this work, we are interested in the effect of the presence of strong ionic correlations (both between ions and between ions and surface charge) due to the presence of multivalent ions and large surface charges. We show that strong ionic correlations cause leakage of the coions, a phenomenon that is absent in mean field theories. In this modeling study, we use both the mean-field Poisson-Nernst-Planck (PNP) theory and a particle simulation method, Local Equilibrium Monte Carlo (LEMC), to show that phenomena such as overcharging and charge inversion cannot be reproduced with PNP, while LEMC is able to produce nonmonotonic dependence of currents and rectification as a function of surface charge strength.

Effect of Anion Species on Ion Current Rectification Properties of Positively Charged Nanochannels

Biological ion channels can realize delicate mass transport under complicated physiological conditions. Artificial nanochannels can achieve biomimetic ion current rectification (ICR), gating, and selectivity that are mostly performed in pure salt solutions. Synthetic nanochannels that can function under mixed ion systems are highly desirable, yet their performances are hard to be compared to those under pure systems. Seeking out the potential reasons by investigating the effect of mixed-system components on the ion-transport properties of the constructed nanochannels seems necessary and important. Herein, we report the effect of anions with different charges and sizes on the ICR properties of positively charged nanochannels. Among the investigated anions, the low-valent anions showed no impact on the ICR direction, while the high-valent component ferrocyanide [Fe(CN)₆^4-] caused significant ICR inversion. The ICR inversion mechanism is evidenced to result from the adsorption of Fe(CN)₆^4--induced surface charge reversal, which relates to solution concentration, pH conditions, and nanochannel sizes and applies to both aminated and quaternized nanochannels that are positively charged. Noticeably, Fe(CN)₆^4- is found to interfere with the transport of protein molecules in the nanochannel. This work points out that the ion species from mixed systems would potentially impact the intrinsic ICR properties of the nanochannels. Replacing highly charged counterions with organic components would be promising in building up future nanochannel-based mass transport systems running under mixed systems.

Inverse correlation between vascular endothelial growth factor back-filtration and capillary filtration pressures

Background

Vascular endothelial growth factor A (VEGF) is an essential growth factor during glomerular development and postnatal homeostasis. VEGF is secreted in high amounts by podocytes into the primary urine, back-filtered across the glomerular capillary wall to act on endothelial cells. So far it has been assumed that VEGF back-filtration is driven at a constant rate exclusively by diffusion.

Methods

In the present work, glomerular VEGF back-filtration was investigated in vivo using a novel extended model based on endothelial fenestrations as surrogate marker for local VEGF concentrations. Single nephron glomerular filtration rate (SNGFR) and/or local filtration flux were manipulated by partial renal mass ablation, tubular ablation, and in transgenic mouse models of systemic or podocytic VEGF overexpression or reduction.

Results

Our study shows positive correlations between VEGF back-filtration and SNGFR as well as effective filtration rate under physiological conditions along individual glomerular capillaries in rodents and humans.

Conclusion

Our results suggest that an additional force drives VEGF back-filtration, potentially regulated by SNGFR.

Properties of Ion Complexes and Their Impact on Charge Transport in Organic Solvent-Based Electrolyte Solutions for Lithium Batteries: Insights from a Theoretical Perspective

Electrolyte formulations in standard lithium ion and lithium metal batteries are complex mixtures of various components. In this article, we review molecular key principles of ion complexes in multicomponent electrolyte solutions in regards of their influence on charge transport mechanisms. We outline basic concepts for the description of ion–solvent and ion–ion interactions, which can be used to rationalize recent experimental and numerical findings concerning modern electrolyte formulations. Furthermore, we discuss benefits and drawbacks of empirical concepts in comparison to molecular theories of solution for a more refined understanding of ion behavior in organic solvents. The outcomes of our discussion provide a rational for beneficial properties of ions, solvent, co-solvent and additive molecules, and highlight possible routes for further improvement of novel electrolyte solutions.

On the physics of both surface overcharging and charge reversal at heterophase interfaces

A series of Monte Carlo simulations are employed to reveal the physics of both surface overcharging and charge reversal at a negatively charged dielectric interface exposed to a bulk solution containing a +2:−1 electrolyte in the absence and presence of a monovalent salt.

Scalable Graphene-Based Membranes for Ionic Sieving with Ultrahigh Charge Selectivity

Nanostructured graphene-oxide (GO) laminate membranes, exhibiting ultrahigh water flux, are excellent candidates for next generation nanofiltration and desalination membranes, provided the ionic rejection could be further increased without compromising the water flux. Using microscopic drift-diffusion experiments, we demonstrated the ultrahigh charge selectivity for GO membranes, with more than order of magnitude difference in the permeabilities of cationic and anionic species of equivalent hydration radii. Measuring diffusion of a wide range of ions of different size and charge, we were able to clearly disentangle different physical mechanisms contributing to the ionic sieving in GO membranes: electrostatic repulsion between ions and charged chemical groups; and the compression of the ionic hydration shell within the membrane's nanochannels, following the activated behavior. The charge-selectivity allows us to rationally design membranes with increased ionic rejection and opens up the field of ion exchange and electrodialysis to the GO membranes.

Progress and controversies in unraveling the glomerular filtration mechanism

PURPOSE OF REVIEW

At first sight, the glomerular filter appears like a problem that should be easily solved. The majority of researchers view the filter like an impermeable wall perforated by specialized and size-selective pores (pore model). However, the fact that this model is in conflict with many of the experimental findings suggests that it may not yet be complete.

RECENT FINDINGS

In the more recent electrokinetic model, we have proposed including electrical effects (streaming potentials). The present review investigates how this can provide a relatively simple mechanistic explanation for the great majority of the so far unexplained characteristics of the filter, for example why the filter never clogs.

SUMMARY

Understanding how the glomerular filter functions is a prerequisite to investigate the pathogenesis of proteinuric glomerular diseases and the link between glomerular proteinuria and cardiovascular disease.

Charge reversal at a planar boundary between two dielectrics

Despite the ubiquitous character and relevance of the electric double layer in the entire realm of interface and colloid science, very little is known of the effect that surface heterogeneity exerts on the underlying mechanisms of ion adsorption. Herein, computer simulations offer a perspective that, in sharp contrast to the homogeneously charged surface, discrete groups promote multivalent counterion binding, leading to charge reversal but possibly having not a sign change of the electrophoretic mobility. Counterintuitively, the introduction of dielectric images yields a significantly greater accumulation of counterions, which further facilitates the magnitude of charge reversal. The reported results are very sensitive to both the degree of ion hydration and the representation of surface charges. Our findings shed light on the mechanism for charge reversal over a broad range of coupling regimes operating the adsorption of counterions through surface group bridging attraction with their own images and provide opportunities for experimental studies and theoretical development.

A structural study of ion permeation in OmpF porin from anomalous X-ray diffraction and molecular dynamics simulations

OmpF, a multiionic porin from Escherichia coli, is a useful protypical model system for addressing general questions about electrostatic interactions in the confinement of an aqueous molecular pore. Here, favorable anion locations in the OmpF pore were mapped by anomalous X-ray scattering of Br(–) ions from four different crystal structures and compared with Mg(2+) sites and Rb(+) sites from a previous anomalous diffraction study to provide a complete picture of cation and anion transfer paths along the OmpF channel. By comparing structures with various crystallization conditions, we find that anions bind in discrete clusters along the entire length of the OmpF pore, whereas cations find conserved binding sites with the extracellular, surface-exposed loops. Results from molecular dynamics simulations are consistent with the experimental data and help highlight the critical residues that preferentially contact either cations or anions during permeation. Analysis of these results provides new insights into the molecular mechanisms that determine ion selectivity in OmpF porin.

How to reliably determine the complex refractive index (RI) of graphene by using two independent measurement constraints

Reliable determination of the complex refractive index (RI) of graphene inherently requires two independent measurement realizations for two independent unknowns of the real (n_G) and imaginary (k_G) components, i.e., RI = n_G + ik_G. Thus, any single set of measurement realization provides only one constraint that is insufficient to uniquely determine the complex RI of graphene. Tandem uses of two independent measurement techniques, namely the surface plasmon resonance (SPR) angle detection and the attenuated total reflection (ATR) intensity measurement, allow for the unique determination of the complex RI of CVD-synthesized graphene. The presently measured graphene RI is determined to be 2.65 + 1.27i for the E-field oscillating parallel to graphene at 634 nm wavelength, with variations for different numbers of L (1, 3 and 5) remaining within ±3%. Thus, our demonstration results for the specified wavelength serve as an impetus to suggest the need for two independent measurement techniques in determining both the real and imaginary RI values for graphene. Additional efforts have been made to characterize graphene layers using the density function theory (DFT): this calculation provides RI_G = 2.71 + 1.41i.

Rectification of Ion Current in Nanopores Depends on the Type of Monovalent Cations: Experiments and Modeling

Rectifying nanopores feature ion currents that are higher for voltages of one polarity compared to the currents recorded for corresponding voltages of the opposite polarity. Rectification of nanopores has been found to depend on the pore opening diameter and distribution of surface charges on the pore walls as well as pore geometry. Very little is known, however, on the dependence of ionic rectification on the type of transported ions of the same charge. We performed experiments with single conically shaped nanopores in a polymer film and recorded current-voltage curves in three electrolytes: LiCl, NaCl, and KCl. Rectification degrees of the pores, quantified as the ratio of currents recorded for voltages of opposite polarities, were the highest for KCl and the lowest for LiCl. The experimental observations could not be explained by a continuum modeling based on the Poisson-Nernst-Planck equations. All-atom molecular dynamics simulations revealed differential binding between Li⁺, Na⁺, and K⁺ ions and carboxyl groups on the pore walls, resulting in changes to both the effective surface charge of the nanopore and cation mobility within the pore.

Antibiotic uptake through membrane channels: role of Providencia stuartii OmpPst1 porin in carbapenem resistance

The role of major porin OmpPst1 of Providencia stuartii in antibiotic susceptibility for two carbapenems is investigated by combining high-resolution conductance measurements, liposome swelling, and microbiological assays. Reconstitution of a single OmpPst1 into a planar lipid bilayer and measuring the ion current, in the presence of imipenem, revealed a concentration-dependent decrease in conductance, whereas meropenem produced well-resolved short ion current blockages. Liposome swelling assays suggested a small flux of imipenem in contrast to a rapid permeation of meropenem. The lower antibiotic susceptibility of P. stuartii to imipenem compared to meropenem correlated well with the decreased level of permeation of the former through the OmpPst1 channel.

Divalent Metal Ion Transport across Large Biological Ion Channels and Their Effect on Conductance and Selectivity

Electrophysiological characterization of large protein channels, usually displaying multi-ionic transport and weak ion selectivity, is commonly performed at physiological conditions (moderate gradients of KCl solutions at decimolar concentrations buffered at neutral pH). We extend here the characterization of the OmpF porin, a wide channel of the outer membrane of E. coli, by studying the effect of salts of divalent cations on the transport properties of the channel. The regulation of divalent cations concentration is essential in cell metabolism and understanding their effects is of key importance, not only in the channels specifically designed to control their passage but also in other multiionic channels. In particular, in porin channels like OmpF, divalent cations modulate the efficiency of molecules having antimicrobial activity. Taking advantage of the fact that the OmpF channel atomic structure has been resolved both in water and in MgCl₂ aqueous solutions, we analyze the single channel conductance and the channel selectivity inversion aiming to separate the role of the electrolyte itself, and the counterion accumulation induced by the protein channel charges and other factors (binding, steric effects, etc.) that being of minor importance in salts of monovalent cations become crucial in the case of divalent cations.

Overcharging in biological systems: reversal of electrophoretic mobility of aqueous polyaspartate by multivalent cations

Charge reversal as an extreme case of charge compensation is directly observed by capillary electrophoresis for a negatively charged peptide in aqueous solutions of trivalent cations. Atomistic and coarse-grained simulations provide molecular interpretation of this effect showing that it is largely of electrostatic origin with a minor contribution of chemical specificity of the salt ions.

Asymmetric pore occupancy in crystal structure of OmpF porin from Salmonella typhi

OmpF is a major general diffusion porin of Salmonella typhi, a Gram-negative bacterium, which is an obligatory human pathogen causing typhoid. The structure of S. typhi Ty21a OmpF (PDB Id: 3NSG) determined at 2.8 Å resolution by X-ray crystallography shows a 16-stranded β-barrel with three β-barrel monomers associated to form a trimer. The packing observed in S. typhi Ty21a rfOmpF crystals has not been observed earlier in other porin structures. The variations seen in the loop regions provide a starting point for using the S. typhi OmpF for structure-based multi-valent vaccine design. Along one side of the S. typhi Ty21a OmpF pore there exists a staircase arrangement of basic residues (20R, 60R, 62K, 65R, 77R, 130R and 16K), which also contribute, to the electrostatic potential in the pore. This structure suggests the presence of asymmetric electrostatics in the porin oligomer. Moreover, antibiotic translocation, permeability and reduced uptake in the case of mutants can be understood based on the structure paving the way for designing new antibiotics.

Concentration dependent ion selectivity in VDAC: a molecular dynamics simulation study

The voltage-dependent anion channel (VDAC) forms the major pore in the outer mitochondrial membrane. Its high conducting open state features a moderate anion selectivity. There is some evidence indicating that the electrophysiological properties of VDAC vary with the salt concentration. Using a theoretical approach the molecular basis for this concentration dependence was investigated. Molecular dynamics simulations and continuum electrostatic calculations performed on the mouse VDAC1 isoform clearly demonstrate that the distribution of fixed charges in the channel creates an electric field, which determines the anion preference of VDAC at low salt concentration. Increasing the salt concentration in the bulk results in a higher concentration of ions in the VDAC wide pore. This event induces a large electrostatic screening of the charged residues promoting a less anion selective channel. Residues that are responsible for the electrostatic pattern of the channel were identified using the molecular dynamics trajectories. Some of these residues are found to be conserved suggesting that ion permeation between different VDAC species occurs through a common mechanism. This inference is buttressed by electrophysiological experiments performed on bean VDAC32 protein akin to mouse VDAC.

Rectification of the current in alpha-hemolysin pore depends on the cation type: the alkali series probed by MD simulations and experiments

A striking feature of the alpha-hemolysin channel-a prime candidate for biotechnological applications-is the dependence of its ionic conductance on the magnitude and direction of the applied bias. Through a combination of lipid bilayer single-channel recording and molecular dynamics (MD) simulations, we characterized the current-voltage relationship of alpha-hemolysin for all alkali chloride salts at neutral pH. The rectification of the ionic current was found to depend on the type of cations and increase from Li(+) to Cs(+). Analysis of the MD trajectories yielded a simple quantitative model that related the ionic current to the electrostatic potential, the concentration and effective mobility of ions in the channel. MD simulations reveal that the major contribution to the current asymmetry and rectification properties originates from the cationic contribution to the current that is significantly reduced in a cationic dependent way when the membrane polarity is reversed. The variation of chloride current was found to be less important. We report that the differential affinity of cations for the charged residues positioned at the channel's end modulates the number of ions inside the channel stem thus affecting the current properties. Through direct comparison of simulation and experiment, this study evaluates the accuracy of the MD method for prediction of the asymmetric, voltage dependent conductances of a membrane channel.

Insights on the permeability of wide protein channels: measurement and interpretation of ion selectivity

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.

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.

Critical assessment of OmpF channel selectivity: merging information from different experimental protocols

The ion selectivity of a channel can be quantified in several ways by using different experimental protocols. A wide, mesoscopic channel, the OmpF porin of the outer membrane of E. coli, serves as a case study for comparing and analysing several measures of the channel cation-anion permeability in chlorides of alkali metals (LiCl, NaCl, KCl, CsCl). We show how different insights can be gained and integrated to rationalize the global image of channel selectivity. To this end, reversal potential, channel conductance and bi-ionic potential (two different salts with a common anion on each side of the channel but with the same concentration) experiments are discussed in light of an electrodiffusion model based on the Poisson-Nernst-Planck formalism. Measurements and calculations based on the atomic crystal structure of the channel show that each protocol displays a particular balance between the different sources of selectivity.

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.