Charged Biological Membranes Repel Large Neutral Molecules by Surface Dielectrophoresis and Counterion Pressure.

Macromolecular crowding is the usual condition of cells. The implications of the crowded cellular environment for protein stability and folding, protein-protein interactions, and intracellular transport drive a growing interest in quantifying the effects of crowding. While the properties of crowded solutions have been extensively studied, less attention has been paid to the interaction of crowders with the cellular boundaries, i.e., membranes. However, membranes are key components of cells and most subcellular organelles, playing a central role in regulating protein channel and receptor functions by recruiting and binding charged and neutral solutes. While membrane interactions with charged solutes are dominated by electrostatic forces, here we show that significant charge-induced forces also exist between membranes and neutral solutes. Using neutron reflectometry measurements and molecular dynamics simulations of poly(ethylene glycol) (PEG) polymers of different molecular weights near charged and neutral membranes, we demonstrate the roles of surface dielectrophoresis and counterion pressure in repelling PEG from charged membrane surfaces. The resulting depletion zone is expected to have consequences for drug design and delivery, the activity of proteins near membrane surfaces, and the transport of small molecules along the membrane surface.

PEG Equilibrium Partitioning in the α-Hemolysin Channel: Neutral Polymer Interaction with Channel Charges.

We study the interaction of neutral polyethylene glycol (PEG) molecules of different molecular weights (MWs) with the charged residues of the α-hemolysin channel secreted by Staphylococcus aureus. Previously reported experiments of PEG equilibrium partitioning into this nanopore show that the charge state of the channel changes the ability of PEG entry in an MW-dependent manner. We explain such an effect by parameter-free calculations of the PEG self-energy from the channel 3D atomic structure that include repulsive dielectrophoretic and hydrostatic forces on the polymer. We found that the pH-induced shift in the measured free energy of partitioning ΔΔGexp from single-channel conductance measurements agrees with calculated energy changes ΔΔEcalc. Our results show that the PEG-sizing technique may need corrections in the case of charged biological pores.

Scaling Behavior of Ionic Transport in Membrane Nanochannels.

Ionic conductance in membrane channels exhibits a power-law dependence on electrolyte concentration ( G ∼ cα). The many scaling exponents, α, reported in the literature usually require detailed interpretations concerning each particular system under study. Here, we critically evaluate the predictive power of scaling exponents by analyzing conductance measurements in four biological channels with contrasting architectures. We show that scaling behavior depends on several interconnected effects whose contributions change with concentration so that the use of oversimplified models missing critical factors could be misleading. In fact, the presence of interfacial effects could give rise to an apparent universal scaling that hides the channel distinctive features. We complement our study with 3D structure-based Poisson-Nernst-Planck (PNP) calculations, giving results in line with experiments and validating scaling arguments. Our findings not only provide a unified framework for the study of ion transport in confined geometries but also highlight that scaling arguments are powerful and simple tools with which to offer a comprehensive perspective of complex systems, especially those in which the actual structure is unknown.

Corneal Equilibrium Flux as a Function of Corneal Surface Oxygen Tension.

PURPOSE: Oxygen is essential for aerobic mammalian cell physiology. Oxygen tension (PO2) should reach a minimum at some position within the corneal stroma, and oxygen flux should be zero, by definition, at this point as well. We found the locations and magnitudes of this "corneal equilibrium flux" (xmin) and explored its physiological implications. METHODS: We used an application of the Monod kinetic model to calculate xmin for normal human cornea as anterior surface PO2 changes from 155 to 20 mmHg. RESULTS: We find that xmin deepens, broadens, and advances from 1.25 µm above the endothelial-aqueous humor surface toward the epithelium (reaching a position 320 µm above the endothelial-aqueous humor surface) as anterior corneal surface PO2 decreases from 155 to 20 mmHg. CONCLUSIONS: Our model supports an anterior corneal oxygen flux of 9 µL O2 · cm · h and an epithelial oxygen consumption of approximately 4 µL O2 · cm · h. Only at the highest anterior corneal PO2 does our model predict that oxygen diffuses all the way through the cornea to perhaps reach the anterior chamber. Of most interest, corneal oxygen consumption should be supported down to a corneal surface PO2 of 60 to 80 mmHg but declines below this range. We conclude that the critical oxygen tension for hypoxia induced corneal swelling is more likely this range rather than a fixed value.

Effects of extreme pH on ionic transport through protein nanopores: the role of ion diffusion and charge exclusion.

We combine electrophysiological experiments with the structure-based Poisson-Nernst-Planck 3D calculations to investigate the transport properties of the bacterial porin OmpF under large pH gradients and particularly low salt concentrations. We show that under extreme pH conditions protons and hydroxyls contribute decisively to the overall measured current, challenging the traditional interpretation of some electrokinetic parameters such as channel selectivity and rectification properties. We analyze with unprecedented detail the two intertwined factors ruling the ionic permeation through the channel, namely the differences between cation and anion mobilities and the electrostatic exclusion due to the interaction between permeating ions and channel ionizable residues.

Modeling Corneal Oxygen with Scleral Gas Permeable Lens Wear.

PURPOSE: The main goal of this current work is to use an updated calculation paradigm, and updated boundary conditions, to provide theoretical guidelines to assist the clinician whose goal is to improve his or her scleral gas permeable (GP) contact lens wearing patients' anterior corneal oxygen supply. METHODS: Our model uses a variable value of corneal oxygen consumption developed through Monod equations that disallows negative oxygen tensions within the stroma to predict oxygen tension at the anterior corneal surface of scleral GP contact lens wearing eyes, and to describe oxygen tension and flux profiles, for various boundary conditions, through the lens, tears, and cornea. We use several updated tissue and boundary parameters in our model. Tear exchange with GP scleral lenses is considered nonexistent in this model. RESULTS: The majority of current scleral GP contact lenses should produce some levels of corneal hypoxia under open eye conditions. Only lenses producing the thinnest of tear vaults should result in anterior corneal surface oxygen tensions greater than a presumed critical oxygen tension of 100 mmHg. We also find that corneal oxygen tension and flux are each more sensitive to modification in tear vault than to changes in lens oxygen permeability, within the ranges of current clinical manipulation. CONCLUSIONS: Our study suggests that clinicians would be prudent to prescribe scleral GP lenses manufactured from higher oxygen permeability materials and especially to fit without excessive corneal clearance.

Quatsomes: vesicles formed by self-assembly of sterols and quaternary ammonium surfactants.

Thermodynamically stable nanovesicle structures are of high interest for academia and industry in a wide variety of application fields, ranging from preparation of nanomaterials to nanomedicine. Here, we show the ability of quaternary ammonium surfactants and sterols to self-assemble, forming stable amphiphilic bimolecular building-blocks with the appropriate structural characteristics to form in aqueous phases, closed bilayers, named quatsomes, with outstanding stability, with time and temperature. The molecular self-assembling of cholesterol and surfactant cetyltrimethylammonium bromide (CTAB) was studied by quasi-elastic light scattering, cryogenic transmission electron microscopy, turbidity (optical density) measurements, and molecular dynamic simulations with atomistic detail, upon varying the cholesterol-to-surfactant molar ratio. As pure species, CTAB forms micelles and insoluble cholesterol forms crystals in water. However, our molecular dynamic simulations reveal that the synergy between CTAB and cholesterol molecules makes them self-assemble into bimolecular amphiphiles and then into bilayers in the presence of water. These bilayers have the same structure of those formed by double-tailed unimolecular amphiphiles.

A three-dimensional model to describe complete human corneal oxygenation during contact lens wear.

We perform a novel 3D study to quantify the corneal oxygen consumption and diffusion in each part of the cornea with different contact lens materials. The oxygen profile is calculated as a function of oxygen tension at the cornea-tear interface and the oxygen transmissibility of the lens, with values used in previous studies. We aim to determine the influence of a detailed geometry of the cornea in their modeling compared to previous low dimensional models used in the literature. To this end, a 3-D study based on an axisymmetric volume element analysis model was applied to different contact lenses currently on the market. We have obtained that the model provides a valuable tool for understanding the flux and cornea oxygen profiles through the epithelium, stroma, and endothelium. The most important results are related to the dependence of the oxygen flux through the cornea-lens system on the contact lens thickness and geometry. Both parameters play an important role in the corneal flux and oxygen tension distribution. The decline in oxygen consumption experienced by the cornea takes place just inside the epithelium, where the oxygen tension falls to between 95 and 16 mmHg under open eye conditions, and 30 to 0.3 mmHg under closed eye conditions, depending on the contact lens worn. This helps to understand the physiological response of the corneal tissue under conditions of daily and overnight contact lens wear, and the importance of detailed geometry of the cornea in the modeling of diffusion for oxygen and other species.

Dynorphin A induces membrane permeabilization by formation of proteolipidic pores. Insights from electrophysiology and computational simulations.

Dynorphins are endogenous neuropeptides that function as ligands for the κ-opioid receptor. In addition to opioid activity, dynorphins can induce several pathological effects such as neurological dysfunctions and cell death. Previous studies have suggested that Dynorphin A (DynA) mediates some pathogenic actions through formation of transient pores in lipid domains of the plasma membrane. Here, we use planar bilayer electrophysiology to show that DynA induces pore formation in negatively charged membranes. We find a large variability in pore conformations showing equilibrium conductance fluctuations, what disregards electroporation as the dominant mechanism of pore formation. Ion selectivity measurements showing cationic selectivity indicate that positive protein charges of DynA are stabilized by phosphatidyl serine negative charges in the formation of combined structures. We complement our study with computational simulations that assess the stability of diverse peptide arrangements in the hydrophobic core of the bilayer. We show that DynA is capable of assembling in charged membranes to form water-filled pores that conduct ions.

A refined model on flow and oxygen consumption in the human cornea depending on the oxygen tension at the interface cornea/post lens tear film during contact lens wear.

The study of oxygen consumption rate under" in vivo" human cornea during contact lens wear has been technically a challenge and several attempts have been made in the last 20 years to model the physiology of the human cornea during contact lens wear. Unfortunately, some of these models, based on a constant corneal oxygen consumption rate, produce areas on the cornea where the oxygen tension is negative, which has no physical sense. In order to avoid such inconsistency, different researchers have developed alternative models of oxygen consumption, which predict the likely oxygen metrics available at the interface cornea/post lens tear film by determination of oxygen flux, oxygen consumption, and oxygen tension through the different layers (endothelium, stroma, and epithelium). Although oxygen deficiency produces corneal edema, corneal swelling, hypoxia, acidosis, and other abnormalities, the estimation of the oxygen distribution below the impact of a contact lens wear is interesting to know which lens transmissibility was adequate to maintain the cornea and avoid epithelial and stromal anoxia. The estimation of minimum transmissibility for a lens for extended wear applications will be very useful for both clinicians and manufacturers. The aim of this work is to present a complete discussion based on Monod kinetics model that permits give an estimation of oxygen partial pressure distribution, the profile distribution of corneal flux and oxygen consumption rate, and finally the estimation of the relaxation mechanism of the cornea depending on the oxygen tension at the interface cornea/post lens tear film. Relaxation time in this context can quantify the capability of the corneal tissue to adapt to increasing concentrations of oxygen. It is proposed this parameter as a biological meaningful indicator of the interaction between contact lens polymers and living tissues such as the corneal cellular layer.

Big dynorphin is a neuroprotector scaffold against amyloid ß-peptide aggregation and cell toxicity.

Amyloid ß-peptide (Aß) misfolding into ß-sheet structures triggers neurotoxicity inducing Alzheimer's disease (AD). Molecules able to reduce or to impair Aß aggregation are highly relevant as possible AD treatments since they should protect against Aß neurotoxicity. We have studied the effects of the interaction of dynorphins, a family of opioid neuropeptides, with Aß40 the most abundant species of Aß. Biophysical measurements indicate that Aß40 interacts with Big Dynorphin (BigDyn), lowering the amount of hydrophobic aggregates, and slowing down the aggregation kinetics. As expected, we found that BigDyn protects against Aß40 aggregates when studied in human neuroblastoma cells by cell survival assays. The cross-interaction between BigDyn and Aß40 provides insight into the mechanism of amyloid pathophysiology and may open up new therapy possibilities.

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.

Access resistance in protein nanopores. A structure-based computational approach.

Single-channel conductance measurements in biological pores have demonstrated the importance of interfacial effects in nanopores, particularly in protein channels with low aspect ratio (length over aperture radius). Access resistance (AR), the contribution to the total measured resistance arising from the electrodiffusive limitation that ions experience in passing from bulk solution to confinement within the pore, becomes essential in the description of ionic transport across these biological channels. Common analytical estimates of AR are based on idealized nanopore models, cylindrical in shape, electrically neutral and embedded in a neutral substrate. Here we calculate the AR of five protein channels by using their atomic structure and a mean-field approach based on solving 3D Poisson and Nernst-Planck equations. Our approach accounts for the influence of the protein charged ionizable residues, the geometry of the pore mouth and the ion concentration gradients near the pore. We compare numerical calculations with the few available AR measurements and show for several protein channels that analytical predictions tend to overestimate AR for physiological concentrations and below. We also discuss the relationship between AR and the size of the channel aperture in single-pore channels and three-pore channels and demonstrate that in the latter case, there is an enhancement of AR.

Corneal relaxation time estimation as a function of tear oxygen tension in human cornea during contact lens wear.

The purpose is to estimate the oxygen diffusion coefficient and the relaxation time of the cornea with respect to the oxygen tension at the cornea-tears interface. Both findings are discussed. From the experimental data provided by Bonanno et al., the oxygen tension measurements in vivo for human cornea-tears-contact lens (CL), the relaxation time of the cornea, and their oxygen diffusion coefficient were obtained by numerical calculation using the Monod-kinetic model. Our results, considering the relaxation time of the cornea, observe a different behavior. At the time less than 8 s, the oxygen diffusivity process is upper-diffusive, and for the relaxation time greater than 8 s, the oxygen diffusivity process is lower-diffusive. Both cases depend on the partial pressure of oxygen at the entrance of the cornea. The oxygen tension distribution in the cornea-tears interface is separated into two different zones: one for conventional hydrogels, which is located between 6 and 75 mmHg, with a relaxation time included between 8 and 19 s, and the other zone for silicone hydrogel CLs, which is located at high oxygen tension, between 95 and 140 mmHg, with a relaxation time in the interval of 1.5-8 s. It is found that in each zone, the diffusion coefficient varies linearly with the oxygen concentration, presenting a discontinuity in the transition of 8 s. This could be interpreted as an aerobic-to-anaerobic transition. We attribute this behavior to the coupling formalism between oxygen diffusion and biochemical reactions to produce adenosine triphosphate. © 2019 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater 108B:14-21, 2020.

Ion selectivity of a biological channel at high concentration ratio: insights on small ion diffusion and binding.

The ionic selectivity of the bacterial porin OmpF has been investigated in several chloride salts of alkali metal cations under a wide range of concentration ratios. We report a novel way of studying the several factors contributing to ionic selectivity of large channels: measuring reversal potential beyond the gradients commonly used in channel selectivity experiments, i.e., over 50-fold salt concentration ratios. Our results reveal an additional channel feature slipped by in previous studies: the interaction of mobile ions with the protein channel transforms noticeably the ion intrinsic diffusivities. The cation/anion diffusivity ratios in the channel are approximately half of their bulk values for all alkali metal cations studied (KCl, NaCl, LiCl, and CsCl). The binding of cations to certain acidic channel residues is likely to be involved, and its contribution is essential to account for the observed traits. A simple molecular model based on statistical thermodynamics provides qualitative explanations to the experimental findings and can be useful for future, more elaborated treatments.

Electrostatic properties and macroscopic electrodiffusion in OmpF porin and mutants.

The bacterial porin OmpF found in the outer membrane of E. coli is a wide channel, characterized by its poor selectivity and almost no ion specificity. It has an asymmetric structure, with relatively large entrances and a narrow constriction. By applying continuum electrostatic methods we determine the ionization states of titratable amino acid residues in the protein and calculate self-consistently the electric potential 3-D distribution within the channel. The average electrostatic properties are then represented by an effective fixed charge distribution along the pore which is the input for a macroscopic electrodiffusion model. The theoretical predictions agree with measurements performed under different salt gradients and pH. The sensitivity of reversal potential and conductance to the direction of the salt gradient and the solution pH is captured by the model. The theory is also able to explain the influence of the lipid membrane charge. The same methodology is satisfactorily applied to some OmpF mutants involving slight structural changes but a large number of net charges. The correlation found between atomic structure and ionic selectivity shows that the transport characteristics of wide channels like OmpF and its mutants are mainly regulated by the collective action of a large number of residues, rather than by the specific interactions of residues at particular locations.

Blocking of an ion channel by a highly charged drug: modeling the effects of applied voltage, electrolyte concentration, and drug concentration.

We present a simple physical model to estimate the blocked pore probability of an ion channel that can be blocked by a highly charged drug in solution. The model is inspired by recent experimental work on the blocking of the PA(63) channel, involved in the anthrax toxin infection, by a highly charged drug [Karginov PNAS 102, 15075 (2005)]. The drug binding to the pore is highly specific but the strong dependence of blocking on the applied voltage and electrolyte concentration suggests that long range electrostatic interactions are important. Since basic electrostatic concepts rather than detailed molecular models are considered, the microscopic details of the channel blocking are ignored, although the model captures most of the qualitative characteristics of the problem.

Selectivity of Protein Ion Channels and the Role of Buried Charges. Analytical Solutions, Numerical Calculations, and MD Simulations.

The preference of large protein ion channels for cations or anions is mainly determined by the electrostatic interactions of mobile ions with charged residues of the protein. Here we discuss the widely spread paradigm that the charges determining the channel selectivity are only those that can be considered solvent-accessible because of their location near the permeation pathways of ions and water molecules. Theoretical predictions for the electric potential and average ion densities inside the pore are presented using several approaches of increasing resolution: from analytical and numerical solutions of electrostatic equations in a model channel up to all-atom molecular dynamics simulations and continuum electrostatic calculations performed in a particular biological channel, the bacterial porin OmpF. The results highlight the role of protein dieletric properties and the importance of the initial choice of the residue ionization states in the understanding of the molecular basis of large channel selectivity irrespective of the level of resolution of the computational approach used.

Oxygen diffusion and edema with modern scleral rigid gas permeable contact lenses.

PURPOSE: We defined the theoretical oxygen tension behind modern scleral contact lenses (CLs) made of different rigid gas permeable (RGP) materials, assuming different thickness of the tear layer behind the lens. A second goal was to show clinically the effect of the postlens tear film on corneal swelling. METHODS: We simulated the partial pressure of oxygen across the cornea behind scleral CLs made of different lens materials (oxygen permeability Dk, 75-200 barrer) and different thickness (Tav, 100-300 µm). Postlens tear film thicknesses (Tpost-tear) ranging from 150 to 350 µm were considered. Eight healthy subjects were fitted randomly with a scleral lens with a thin and a thick postlens tear layer in two different sessions for a period of 3 hours under open-eye conditions. RESULTS: The CLs with less than 125 barrer of Dk and a thickness over 200 µm depleted the oxygen availability at the lens-cornea interface below 55 mm Hg for a postlens tear film of 150 µm. For a postlens tear film thickness of 350 µm, no combination of material or lens thickness will meet the criteria of 55 mm Hg. Our clinical measures of corneal edema showed that this was significantly higher (P < 0.001, Wilcoxon signed ranks test) with the thicker compared to the thinner Tpost-tear (mean ± SD, 1.66 ± 1.12 vs. 4.27 ± 1.19%). CONCLUSIONS: Scleral RGP CLs must be comprised of at least 125 barrer of oxygen permeability and up to 200 µm thick to avoid hypoxic effects even under open eye conditions. Postlens tear film layer should be below 150 µm to avoid clinically significant edema.