Interactions of membrane active peptides with planar supported bilayers: an impedance spectroscopy study

Impedance sensing of antibiotic interactions with a pathogenic E. coli outer membrane supported bilayer

Antibiotic resistance is a growing global health concern due to the decreasing number of antibiotics available for therapeutic use as more drug-resistant bacteria develop. Changes in the membrane properties of Gram-negative bacteria can influence their response to antibiotics and give rise to resistance. Thus, understanding the interactions between the bacterial membrane and antibiotics is important for elucidating microbial membrane properties to use for designing novel antimicrobial drugs. To study bacterial membrane-antibiotic interactions, we created a surface-supported planar bacterial outer membrane model on an optically-transparent, conducting polymer surface (poly (3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS)). This model enables membrane characterization using fluorescence microscopy and electrochemical impedance spectroscopy (EIS). The membrane platform is fabricated using outer membrane vesicles (OMVs) isolated from clinically relevant Gram-negative bacteria, enterohemorrhagic Escherichia coli. This approach enables us to mimic the native components of the bacterial membrane by incorporating native lipids, membrane proteins, and lipopolysaccharides. Using EIS, we determined membrane impedance and captured membrane-antibiotic interactions using the antibiotics polymyxin B, bacitracin, and meropenem. This sensor platform incorporates aspects of the biological complexity found in bacterial outer membranes and, by doing so, offers a powerful, biomimetic approach to the study of antimicrobial drug interactions.

Polydiacetylene vesicles acting as colorimetric sensor for the detection of plantaricin LD1

The interaction of antimicrobial peptides with membrane lipids plays a major role in numerous physiological processes. In this study, polydiacetylene (PDA) vesicles were synthesized using 10, 12-tricosadiynoic acid (TRCDA) and 1, 2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). These vesicles were applied as artificial membrane biosensor for the detection of plantaricin LD1 purified from Lactobacillus plantarum LD1. Plantaricin LD1 (200 μg/mL) was able to interact with PDA vesicles by changing the color from blue to red with colorimetric response 30.26 ± 0.59. Nisin (200 μg/mL), used as control, also changed the color of the vesicles with CR% 50.56 ± 0.98 validating the assay. The vesicles treated with nisin and plantaricin LD1 showed increased infrared absorbance at 1411.46 and 1000-1150 cm^-1 indicated the interaction of bacteriocins with phospholipids and fatty acids, respectively suggesting membrane-acting nature of these bacteriocins. Further, microscopic observation of bacteriocin-treated vesicles showed several damages indicating the interaction of bacteriocins. These findings suggest that the PDA vesicles may be used as bio-mimetic sensor for the detection of bacteriocins produced by several probiotics in food and therapeutic applications.

Hydropathicity-based prediction of pain-causing NaV1.7 variants

Background

Mutation-induced variations in the functional architecture of the NaV1.7 channel protein are causally related to a broad spectrum of human pain disorders. Predicting in silico the phenotype of NaV1.7 variant is of major clinical importance; it can aid in reducing costs of in vitro pathophysiological characterization of NaV1.7 variants, as well as, in the design of drug agents for counteracting pain-disease symptoms.

Results

In this work, we utilize spatial complexity of hydropathic effects toward predicting which NaV1.7 variants cause pain (and which are neutral) based on the location of corresponding mutation sites within the NaV1.7 structure. For that, we analyze topological and scaling hydropathic characteristics of the atomic environment around NaV1.7’s pore and probe their spatial correlation with mutation sites. We show that pain-related mutation sites occupy structural locations in proximity to a hydrophobic patch lining the pore while clustering at a critical hydropathic-interactions distance from the selectivity filter (SF). Taken together, these observations can differentiate pain-related NaV1.7 variants from neutral ones, i.e., NaV1.7 variants not causing pain disease, with 80.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}% sensitivity and 93.7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}% specificity [area under the receiver operating characteristics curve = 0.872].

Conclusions

Our findings suggest that maintaining hydrophobic NaV1.7 interior intact, as well as, a finely-tuned (dictated by hydropathic interactions) distance from the SF might be necessary molecular conditions for physiological NaV1.7 functioning. The main advantage for using the presented predictive scheme is its negligible computational cost, as well as, hydropathicity-based biophysical rationalization.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04119-2.

Microcavity-Supported Lipid Bilayers; Evaluation of Drug-Lipid Membrane Interactions by Electrochemical Impedance and Fluorescence Correlation Spectroscopy

Many drugs have intracellular or membrane-associated targets, thus understanding their interaction with the cell membrane is of value in drug development. Cell-free tools used to predict membrane interactions should replicate the molecular organization of the membrane. Microcavity array-supported lipid bilayer (MSLB) platforms are versatile biophysical models of the cell membrane that combine liposome-like membrane fluidity with stability and addressability. We used an MSLB herein to interrogate drug-membrane interactions across seven drugs from different classes, including nonsteroidal anti-inflammatories: ibuprofen (Ibu) and diclofenac (Dic); antibiotics: rifampicin (Rif), levofloxacin (Levo), and pefloxacin (Pef); and bisphosphonates: alendronate (Ale) and clodronate (Clo). Fluorescence lifetime correlation spectroscopy (FLCS) and electrochemical impedance spectroscopy (EIS) were used to evaluate the impact of drug on 1,2-dioleyl- sn-glycerophosphocholine and binary bilayers over physiologically relevant drug concentrations. Although FLCS data revealed Ibu, Levo, Pef, Ale, and Clo had no impact on lipid lateral mobility, EIS, which is more sensitive to membrane structural change, indicated modest but significant decreases to membrane resistivity consistent with adsorption but weak penetration of drugs at the membrane. Ale and Clo, evaluated at pH 5.25, did not impact the impedance of the membrane except at concentrations exceeding 4 mM. Conversely, Dic and Rif dramatically altered bilayer fluidity, suggesting their translocation through the bilayer, and EIS data showed that resistivity of the membrane decreased substantially with increasing drug concentration. Capacitance changes to the bilayer in most cases were insignificant. Using a Langmuir-Freundlich model to fit the EIS data, we propose R_sat as an empirical value that reflects permeation. Overall, the data indicate that Ibu, Levo, and Pef adsorb at the interface of the lipid membrane but Dic and Rif interact strongly, permeating the membrane core modifying the water/ion permeability of the bilayer structure. These observations are discussed in the context of previously reported data on drug permeability and log P.

Mechanistic Landscape of Membrane-Permeabilizing Peptides

Membrane permeabilizing peptides (MPPs) are as ubiquitous as the lipid bilayer membranes they act upon. Produced by all forms of life, most membrane permeabilizing peptides are used offensively or defensively against the membranes of other organisms. Just as nature has found many uses for them, translational scientists have worked for decades to design or optimize membrane permeabilizing peptides for applications in the laboratory and in the clinic ranging from antibacterial and antiviral therapy and prophylaxis to anticancer therapeutics and drug delivery. Here, we review the field of membrane permeabilizing peptides. We discuss the diversity of their sources and structures, the systems and methods used to measure their activities, and the behaviors that are observed. We discuss the fact that "mechanism" is not a discrete or a static entity for an MPP but rather the result of a heterogeneous and dynamic ensemble of structural states that vary in response to many different experimental conditions. This has led to an almost complete lack of discrete three-dimensional active structures among the thousands of known MPPs and a lack of useful or predictive sequence-structure-function relationship rules. Ultimately, we discuss how it may be more useful to think of membrane permeabilizing peptides mechanisms as broad regions of a mechanistic landscape rather than discrete molecular processes.

Properties of Omp2a-Based Supported Lipid Bilayers: Comparison with Polymeric Bioinspired Membranes

Omp2a β-barrel outer membrane protein has been reconstituted into supported lipid bilayers (SLBs) to compare the nanomechanical properties (elastic modulus, adhesion forces, and deformation) and functionality of the resulting bioinspired system with those of Omp2a-based polymeric nanomembranes (NMs). Protein reconstitution into lipid bilayers has been performed using different strategies, the most successful one consisting of a detergent-mediated process into preformed liposomes. The elastic modulus obtained for the lipid bilayer and Omp2a are ∼19 and 10.5 ± 1.7 MPa, respectively. Accordingly, the protein is softer than the lipid bilayer, whereas the latter exhibits less mechanical strength than polymeric NMs. Besides, the function of Omp2a in the SLB is similar to that observed for Omp2a-based polymeric NMs. Results open the door to hybrid bioinspired substrates based on the integration of Omp2a-proteoliposomes and nanoperforated polymeric freestanding NMs.

Antimicrobial peptides: biochemical determinants of activity and biophysical techniques of elucidating their functionality

Antimicrobial peptides (AMPs) have been established over millennia as powerful components of the innate immune system of many organisms. Due to their broad spectrum of activity and the development of host resistance against them being unlikely, AMPs are strong candidates for controlling drug-resistant pathogenic microbial pathogens. AMPs cause cell death through several independent or cooperative mechanisms involving membrane lysis, non-lytic activity, and/or intracellular mechanisms. Biochemical determinants such as peptide length, primary sequence, charge, secondary structure, hydrophobicity, amphipathicity and host cell membrane composition together influence the biological activities of peptides. A number of biophysical techniques have been used in recent years to study the mechanisms of action of AMPs. This work appraises the molecular parameters that determine the biocidal activity of AMPs and overviews their mechanisms of actions and the diverse biochemical, biophysical and microscopy techniques utilised to elucidate these.

Dynamic studies of the interaction of a pH responsive, amphiphilic polymer with a DOPC lipid membrane

Deeper understanding of the molecular interactions between polymeric materials and the lipid membrane is important across a range of applications from permeation for drug delivery to encapsulation for immuno-evasion. Using highly fluidic microcavity supported lipid bilayers, we studied the interactions between amphiphilic polymer PP50 and a DOPC lipid bilayer. As the PP50 polymer is pH responsive the studies were carried out at pH 6.5, 7.05 and 7.5, corresponding to fully, partly protonated (pH = pK_a = 7.05) and fully ionized states of the polymer, respectively. Fluorescence correlation spectroscopy (FCS) using both labelled lipid and polymer revealed the PP50 associates with the bilayer interface across all pHs where its diffusion along the interface is impeded. Both FCS and electrochemical impedance spectroscopy (EIS) data indicate that the PP50 does not penetrate fully into the bilayer core but rather forms a layer at the bilayer aqueous interface reflected in increased resistance and decreased capacitance of the bilayer on PP50 binding. The extent of these effects and the dynamics of binding are influenced by pH, increasing with decreasing pH. These experimental trends concurred with coarse grained Monte Carlo simulations of polymer-bilayer interactions wherein a model hydrophilic polymer backbone grafted with side chains of varying hydrophobicity, to mimic the effect of varying pH, was simulated based on the bond fluctuation model with explicit solvent. Simulation results showed that with increasing hydrophobicity, the polymer penetrated deeper into the contacting bilayer leaflet of the membrane suppressing, consistent with EIS data, solvent permeation and that a full insertion of the polymer into the bilayer core is not necessary for suppression of permeability.

On Chip Bioelectric Impedance Spectroscopy Reveals the Effect of P-Glycoprotein Efflux Pumps on the Paracellular Impedance of Tight Junctions at the Blood-Brain Barrier

Bioelectric impedance spectroscopy was used to elucidate the influence of P-gp efflux pumps on the kinetics of tight junction down-regulation in confluent monolayers of Madine Darby Canine Kidney Epithelial Cells (MDCK) following administration of phenylarsine oxide (PAO), a molecule that inhibits protein tyrosine phosphatases (PTP) and induces matrix metalloproteinase activity. Matrix metalloproteinases (MMPs) and phosphatase inhibitors induce modification of occludin tight junction proteins critical for the proper function of the blood-brain barrier. The addition of PAO to MDCKII cell lines resulted in a dramatic decrease in monolayer resistance. In contrast, MDCKII-MDR1 cells transfected with the MDR1 gene treated with PAO showed an initial decrease in monolayer resistance followed by a partial recovery and subsequent decrease. This resistance decay reversal was suppressed with the addition of the P-glycoprotein (P-gp) pump inhibitor elacridar, and is attributed to PAO efflux. These results illustrate impedance spectroscopy can be used to characterize the competing kinetics of efflux and down-regulation of tight junctions. In addition, the resistance decay reversal effect can be used to evaluate P-gp pump inhibitor efficacy.

The Hydrophobic Effect Contributes to the Closed State of a Simplified Ion Channel through a Conserved Hydrophobic Patch at the Pore-Helix Crossing

Ion selectivity-filter structures are strikingly similar throughout the large family of K⁺⁺ channels and other p-loop-like receptors (i.e., glutamate receptors). At the same time, the triggers for opening these channels, or gating, are diverse. Two questions that remain unanswered regarding these channels are: (1) what force(s) stabilize the closed non-conducting channel-pore conformation? And (2) what is the free energy associated with transitioning from a closed (non-conducting) to an open (conducting) channel-pore conformation? The effects of charge and hydrophobicity on the conformational states of a model tetrameric biological ion channel are shown utilizing the amino acid sequence from the K⁺ channel KcsA as the model “channel”. Its widely conserved hydrophobic bundle crossing located adjacent to the lipid head-groups at the intracellular side of the membrane was calculated to have a 5 kcal/mol free energy difference between modeled open and closed conformations. Simulated mutants of amino acids within the hydrophobic region significantly contribute to the size of this difference. Specifically for KcsA, these residues are part of the pH sensor important for channel gating and our results are in agreement with published electrophysiology data. Our simulations support the idea that the hydrophobic effect contributes significantly to the stability of the closed conformation in tetrameric ion channels with a hydrophobic bundle crossing positioned in proximity to the lipid head groups of the biological membrane.

Spontaneous membrane-translocating peptides: influence of peptide self-aggregation and cargo polarity

Peptides that translocate spontaneously across cell membranes could transform the field of drug delivery by enabling the transport of otherwise membrane-impermeant molecules into cells. In this regard, a 9-aminoacid-long motif (representative sequence: PLIYLRLLR, hereafter Translocating Motif 9, TM9) that spontaneously translocates across membranes while carrying a polar dye was recently identified by high-throughput screening. Here we investigate its transport properties by a combination of in cuvette physico-chemical assays, rational mutagenesis, live-cell confocal imaging and fluorescence correlation spectroscopy measurements. We unveil TM9 ability to self-aggregate in a concentration-dependent manner and demonstrate that peptide self-aggregation is a necessary –yet not sufficient– step for effective membrane translocation. Furthermore we show that membrane crossing can occur with apolar payloads while it is completely inhibited by polar ones. These findings are discussed and compared to previous reports. The present results impose a careful rethinking of this class of sequences as direct-translocation vectors suitable for delivery purposes.

Photosynthetic Proteins in Supported Lipid Bilayers: Towards a Biokleptic Approach for Energy Capture

In nature, plants and some bacteria have evolved an ability to convert solar energy into chemical energy usable by the organism. This process involves several proteins and the creation of a chemical gradient across the cell membrane. To transfer this process to a laboratory environment, several conditions have to be met: i) proteins need to be reconstituted into a lipid membrane, ii) the proteins need to be correctly oriented and functional and, finally, iii) the lipid membrane should be capable of maintaining chemical and electrical gradients. Investigating the processes of photosynthesis and energy generation in vivo is a difficult task due to the complexity of the membrane and its associated proteins. Solid, supported lipid bilayers provide a good model system for the systematic investigation of the different components involved in the photosynthetic pathway. In this review, the progress made to date in the development of supported lipid bilayer systems suitable for the investigation of membrane proteins is described; in particular, there is a focus on those used for the reconstitution of proteins involved in light capture.

Polypyrrole-supported membrane proteins for bio-inspired ion channels

Biomedical platforms constructed by immobilizing membrane proteins in matrixes made of synthetic organic polymers is a challenge because the structure and function of these proteins are affected by environmental conditions. In this work, an operative composite that regulates the diffusion of alkali ions has been prepared by functionalizing a supporting matrix made of poly(N-methylpyrrole) (PNMPy) with a β-barrel membrane protein (Omp2a) that forms channels and pores. The protein has been unequivocally identified in the composite, and its structure has been shown to remain unaltered. The PNMPy-Omp2a platform fulfills properties typically associated with functional bio-interfaces with biomedical applications (e.g., biocompatibility, biodegrabadility, and hydrophilicity). The functionality of the immobilized protein has been examined by studying the passive ion transport response in the presence of electrolytic solutions with Na(+) and K(+) concentrations close to those found in blood. Although the behavior of PNMPy and PNMPy-Omp2a is very similar for solutions with very low concentration, the resistance of the latter decreases drastically when the concentration of ions increases to ∼100 mM. This reduction reflects an enhanced ion exchange between the biocomposite and the electrolytic medium, which is not observed in PNMPy, evidencing that PNMPy-Omp2a is particularly well suited to prepare bioinspired channels and smart biosensors.

Structural and Thermodynamic Insight into Spontaneous Membrane-Translocating Peptides Across Model PC/PG Lipid Bilayers

We present results of Martini coarse-grained force field simulations to estimate the potentials of mean force for a series of recently screened spontaneous membrane-translocating peptides, SMTPs. We consider model bilayer composed of POPC and POPG, the latter providing the anionic component as used in experimental studies. We observe a significant barrier for translocation in the case of the canonical cationic cell-penetrating peptide nona-arginine, ARG9. In the case of the TP1, TP2, and TP3 peptides, potentials of mean force are systematically lower relative to the ARG9 case. Though the barriers predicted by the simulations, on the order of 20 kcal/mol, are still rather large to recapitulate the experimental kinetics of internalization, we emphasize that the qualitative trend of reduction of barrier heights is a significant result. Decomposition of the PMFs indicates that though there is a substantial entropic stability when the peptides reside at bilayer center, barriers as predicted from these force field-based studies are largely determined by enthalpic (potential energy) interactions. We note that the binding of the SMTPs is critically dependent on the mix of hydrophilic and hydrophobic residues that constitute the amino acid motif/sequence of these peptides. For the cationic ARG9 which only contains hydrophilic residues, there is no tight binding observed. The specific motif [Formula: see text] (where [Formula: see text] is a general residue) is a potential sequence in drug/peptide design. The SMTPs with this motif are able to translocate into membrane at a significantly lower free energy cost, compared to the negative control peptides. Finally, we compare the different membrane perturbations induced by the presence of the different peptides in the bilayer center. In some cases, hydrophilic pores are observed to form, thus conferring stability to the internalized state. In other cases, SMTPs are associated only with membrane defects such as induced membrane curvature. These latter observations suggest some influence of membrane rigidity as embodied in the full range of membrane undulatory modes in defining pore-forming propensities in bilayers.

Highly efficient macromolecule-sized poration of lipid bilayers by a synthetically evolved peptide

Peptides that self-assemble, at low concentration, into bilayer-spanning pores which allow the passage of macromolecules would be beneficial in multiple areas of biotechnology. However, there are few, if any, natural or designed peptides that have this property. Here we show that the 26-residue peptide "MelP5", a synthetically evolved gain-of-function variant of the bee venom lytic peptide melittin identified in a high-throughput screen for small molecule leakage, enables the passage of macromolecules across bilayers under conditions where melittin and other pore-forming peptides do not. In surface-supported bilayers, MelP5 forms unusually high conductance, equilibrium pores at peptide:lipid ratios as low as 1:25000. The increase in bilayer conductance due to MelP5 is dramatically higher, per peptide, than the increase due to the parent sequence of melittin or other peptide pore formers. Here we also develop two novel assays for macromolecule leakage from vesicles, and we use them to characterize MelP5 pores in bilayers. We show that MelP5 allows the passage of macromolecules across vesicle membranes at peptide:lipid ratios as low as 1:500, and under conditions where neither osmotic lysis nor gross vesicle destabilization occur. The macromolecule-sized, equilibrium pores formed by MelP5 are unique as neither melittin nor other pore-forming peptides release macromolecules significantly under the same conditions. MelP5 thus appears to belong to a novel functional class of peptide that could form the foundation of multiple potential biotechnological applications.

Monitoring and quantifying the passive transport of molecules through patch-clamp suspended real and model cell membranes

Transport of active molecules across biological membranes is a central issue for the success of many pharmaceutical strategies. Herein, we combine the patch-clamp principle with amperometric detection for monitoring fluxes of redox-tagged molecular species across a suspended membrane patched from a macrophage. Solvent- and protein-free lipid bilayers (DPhPC, DOPC, DOPG) patched from single-wall GUV have been thoroughly investigated and the corresponding fluxes measurements quantified. The quality of the patches and their proper sealing were successfully characterized by electrochemical impedance spectroscopy. This procedure appears versatile and perfectly adequate to allow the investigation of transport and quantification of the transport properties through direct measurement of the coefficients of partition and diffusion of the compound in the membrane, thus offering insight on such important biological and pharmacological issues.

A membrane-translocating peptide penetrates into bilayers without significant bilayer perturbations

Using a high throughput screen, we have identified a family of 12-residue long peptides that spontaneously translocate across membranes. These peptides function by a poorly understood mechanism that is very different from that of the well-known, highly cationic cell penetrating peptides such as the tat peptide from HIV. The newly discovered translocating peptides can carry polar cargoes across synthetic bilayers and across cellular membranes quickly and spontaneously without disrupting the membrane. Here we report on the biophysical characterization of a representative translocating peptide from the selected family, TP2, as well as a negative control peptide, ONEG, from the same library. We measured the binding of the two peptides to lipid bilayers, their secondary structure propensities, their dispositions in bilayers by neutron diffraction, and the response of the bilayer to the peptides. Compared to the negative control, TP2 has a greater propensity for membrane partitioning, although it still binds only weakly, and a higher propensity for secondary structure. Perhaps most revealing, TP2 has the ability to penetrate deep into the bilayer without causing significant bilayer perturbations, a property that may help explain its ability to translocate without bilayer permeabilization.

Synthetic molecular evolution of pore-forming peptides by iterative combinatorial library screening

We previously reported the de novo design of a combinatorial peptide library that was subjected to high-throughput screening to identify membrane-permeabilizing antimicrobial peptides that have β-sheet-like secondary structure. Those peptides do not form discrete pores in membranes but instead partition into membrane interfaces and cause transient permeabilization by membrane disruption, but only when present at high concentration. In this work, we used a consensus sequence from that initial screen as a template to design an iterative, second generation library. In the 24-26-residue, 16,200-member second generation library we varied six residues. Two diad repeat motifs of alternating polar and nonpolar amino acids were preserved to maintain a propensity for non-helical secondary structure. We used a new high-throughput assay to identify members that self-assemble into equilibrium pores in synthetic lipid bilayers. This screen was done at a very stringent peptide to lipid ratio of 1:1000 where most known membrane-permeabilizing peptides, including the template peptide, are not active. In a screen of 10,000 library members we identified 16 (~0.2%) that are equilibrium pore-formers at this high stringency. These rare and highly active peptides, which share a common sequence motif, are as potent as the most active pore-forming peptides known. Furthermore, they are not α-helical, which makes them unusual, as most of the highly potent pore-forming peptides are amphipathic α-helices. Here we demonstrate that this synthetic molecular evolution-based approach, taken together with the new high-throughput tools we have developed, enables the identification, refinement, and optimization of unique membrane active peptides.

The electrical response of bilayers to the bee venom toxin melittin: evidence for transient bilayer permeabilization

Melittin is a 26-residue bee venom peptide that folds into amphipathic α-helix and causes membrane permeabilization via a mechanism that is still disputed. While an equilibrium transmembrane pore model has been a central part of the mechanistic dialogue for decades, there is growing evidence that a transmembrane pore is not required for melittin's activity. In part, the controversy is due to limited experimental tools to probe the bilayer's response to melittin. Electrochemical impedance spectroscopy (EIS) is a technique that can reveal details of molecular mechanism of peptide activity, as it yields direct, real-time measurements of membrane resistance and capacitance of supported bilayers. In this work, EIS was used in conjunction with vesicle leakage studies to characterize the response of bilayers of different lipid compositions to melittin. Experiments were carried out at low peptide to lipid ratios between 1:5000 and 1:100. The results directly demonstrate that the response of the bilayer to melittin at these concentrations cannot be explained by an equilibrium transmembrane pore model.