Intrinsic Membrane Permeability to Small Molecules - ACS Publications

Review Cite This: Chem. Rev. XXXX, XXX, XXX−XXX

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Intrinsic Membrane Permeability to Small Molecules Christof Hannesschlaeger, Andreas Horner, and Peter Pohl*

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From the Institute of Biophysics, Johannes Kepler University Linz, Gruberstrasse 40, 4020 Linz, Austria ABSTRACT: Spontaneous solute and solvent permeation through membranes is of vital importance to human life, be it gas exchange in red blood cells, metabolite excretion, drug/ toxin uptake, or water homeostasis. Knowledge of the underlying molecular mechanisms is the sine qua non of every functional assignment to membrane transporters. The basis of our current solubility diffusion model was laid by Meyer and Overton. It correlates the solubility of a substance in an organic phase with its membrane permeability. Since then, a wide range of studies challenging this rule have appeared. Commonly, the discrepancies have their origin in ill-used measurement approaches, as we demonstrate on the example of membrane CO2 transport. On the basis of the insight that scanning electrochemical microscopy offered into solute concentration distributions in immediate membrane vicinity of planar membranes, we analyzed the interplay between chemical reactions and diffusion for solvent transport, weak acid permeation, and enzymatic reactions adjacent to membranes. We conclude that buffer reactions must also be considered in spectroscopic investigations of weak acid transport in vesicular suspensions. The evaluation of energetic contributions to membrane translocation of charged species demonstrates the compatibility of the resulting membrane current with the solubility diffusion model. A local partition coefficient that depends on membrane penetration depth governs spontaneous membrane translocation of both charged and uncharged molecules. It is determined not only by the solubility in an organic phase but also by other factors like cholesterol concentration and intrinsic electric membrane potentials.

CONTENTS 1. 2. 3. 4. 5.

Introduction Driving Forces for Membrane Translocation Determinants of the Partition Coefficient Membrane Permeation of Neutral Substances Activation Energy of Permeation in a One-Slab Model: Eyring−Zwolinski Equation 6. Unstirred Layers 7. Water Diffusion across Lipid Membranes 7.1. Measurements of Pm,H2O: Osmotic Permeabilities 7.2. Measurements of Pm,H2O: Diffusional Permeabilities 8. Weak Acids/Bases 8.1. Steady-State Measurements on Planar Lipid Bilayers 8.2. Kinetic Measurements on Vesicular Systems 8.3. Limitations of Kinetic Measurements on Vesicles 9. Membrane Permeation of CO2 9.1. Pore Access Resistance to Solutes 9.2. Unstirred Layers 9.3. Pm,CO2 Measurements by Mass Spectrometry 9.4. Additional Approaches Aimed at Characterizing Membranes as CO2 Barrier 9.5. Pm,CO2 from Scanning Electrochemical Microscopy 10. Ion Permeation 10.1. Proton/Hydroxide Permeation 11. Conclusion Author Information © XXXX American Chemical Society

Corresponding Author ORCID Notes Biographies Acknowledgments Abbreviations References

A B C D E E G

Y Y Y Y Z Z Z

1. INTRODUCTION Passive membrane transport of small molecules is important for many physiological processes. For example, it ensures (i) the exchange of O2 and CO2 across the membrane of red blood cells1 or (ii) cell signaling by allowing second messengers like H2S to reach their target.2,3 Cellular uptake of many pharmaceuticals relies on passive membrane diffusion.4,5 The corresponding transmembrane flux density J is usually assumed to be proportional to the transmembrane concentration gradient Δc of the membrane permeable substance: J = −Pm·Δc (1)

I J L L M N O O Q Q

The membrane permeability Pm serves as the proportionality factor. Yet, the seemingly simple process of transmembrane diffusion is subject to many controversies. They culminated in the complete denial of passive membrane transport phenomena, i.e., the postulate that all membrane transport is mediated by carriers, channels and pumps.6,7 More subtle versions of the very

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Special Issue: Biomembrane Structure, Dynamics, and Reactions Received: September 11, 2018

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DOI: 10.1021/acs.chemrev.8b00560 Chem. Rev. XXXX, XXX, XXX−XXX

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As part of a special issue that is devoted to membrane transport phenomena at the interface between computational and experimental biology, we made a special effort to underline (i) mechanistic aspects of transport as well as (ii) the potential link between permeability and thermodynamic parameters like activation energy, enthalpy, and entropy. Moreover, we show that membrane permeability of both neutral solutes and ions is well described by the solubility-diffusion model. To underline the common denominator, we focused on the role of hydrophobicity in ion transport and departed from a mathematical description that is mainly based on rate constants.

same claim are more substrate specific, like the one about “facilitated” CO2 transport by aquaporins.8 The confusion about the role of membrane transport proteins is fueled by a large scatter of membrane permeability values that are obtained for the lipid matrix. An unconsidered presentation of partition coefficients versus membrane permeabilities reveals no more than a cloud,7 and yet we know that Overton’s rule applies.9−12 This ruling is not undermined by observing (i) fast translocation of selected charged molecules versus slow moving neutral molecules or (ii) bigger molecules permeating at higher rates than smaller molecules (Figure 1).

2. DRIVING FORCES FOR MEMBRANE TRANSLOCATION Any description of transmembrane translocation has to take into account the driving forces. For the sake of simplicity, we consider a one-dimensional, isothermal and isobaric case. Magnetic or gravitational influences are not taken into account. The one-dimensional simplification is justified by the small membrane thickness of a few nanometers. The lateral extension of a bilayer is at least 1 order of magnitude larger. The smallest membrane structures of interest are small unilamellar vesicles with a minimum diameter of 30 nm that is given by the edge energy.29 Without convection or sinks or sources, mass transport (flux density J in mol/m/s) is caused by a force F̅ (in N). F̅ acts on single particles or molecules. It is created by a gradient of the corresponding chemical potential μ (eq 2, NA is Avogadro’s constant).30,31

Figure 1. Absolute value of Pm is not simply determined by the size or charge of a substance. Nevertheless, if two structure-wise almost similar compounds such as the neutral salicylic acid or its deprotonated form, anionic salicylate, are compared, the Pms behave relatively to each other as one would expect from a charged and an uncharged substance.13 Membrane permeabilities for different classes of substances are taken from different following sources: (i) Nonelectrolytes smaller than 100 g/mol (red): CO2,14 H2S,2 ammonia,15 acetic acid,16 H2O,17 ethylene glycol,18 glycerol,18 urea.19 (ii) Nonelectrolytes larger than 100 g/mol (green): salicylic acid,20 triethylamine,21 codein,22 sorbitol,23 ascorbic acid,24 glucose.23 (iii) Anions (blue): TPB−,25 3,4-dinitrophenol,25 Cl−,26 salicylate.25 (iv) Cations (purple): TPA+,27 K+,26 Na+.28 Pms are measured with various methods on various lipids.

F̅ = −

1 dμ · NA dx

(2)

F̅ causes the molecules to move with velocity v (in m/s). v depends on their mobility u (in kg/s). (3)

v = u·F ̅

From the Einstein−Smoluchowski relation (D = u·kBT with D the diffusivity, T the absolute temperature, and kB the Boltzmann constant) and the consideration that a flux density J is proportional to the concentration of moving particles, one obtains eq 4.

The scope of the current paper is to outline the origin for the large scatter in published permeability values and to identify modern approaches that are suitable to perform precise membrane permeability measurements. We show here the importance of unstirred layer (USL) phenomena and buffer effects. The insight comes mostly from scanning electrochemical microscopy that displays the concentration distribution of solutes within the stagnant water layers adjacent to the membrane. The method allows an exact quantification of USL contribution, both as additional diffusion barriers and as space with a special microenvironment for chemical reactions. Transferring the knowledge about the importance of buffer effects to a completely different experimental system, to large unilamellar vesicles, allowed a much better quantitative understanding of the respective permeation processes. As an illustrative example, we analyze methodological caveats in studies of CO2 membrane transport. We show how severe shortcomings in the treatment of unstirred layer phenomena and buffer effects led to the misconception that the lipid bilayer may act as a barrier to CO2 diffusion. Tearing down this barrier leaves no room for facilitated CO2 transport, i.e., there is no role for aquaporins in the maintenance of the acid base equilibrium.

J=−

dμ D 1 D dμ · ·c· =− ·c· kBT NA dx RT dx

(4)

where R is the gas constant. The total chemical potential μ′ of a substance of interest in the presence of external fields can have various contributors as gravitation, magnetic fields, or electrical fields in addition to the internal chemical potential μ (F is Faraday’s constant, z the valence of an ion, Φ an electrical potential, M is a molecule’s molar mass, g is the standard gravitation, and h the absolute height).32 μ′ = μ +

∑ Xj·∂xj = μ + F ·z·Φ + M·g ·h + ... j

0

= μ + RT ·ln(c) + F ·z ·Φ + M ·g ·h + ...

(5)

Under physiological conditions, only electrical fields are relevant. Consequently, eq 5 can be simplified to yield the electrochemical potential: μ′ = μ0 + RT ·ln(c) + F ·z ·Φ B

(6) DOI: 10.1021/acs.chemrev.8b00560 Chem. Rev. XXXX, XXX, XXX−XXX

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Hence, the flux amounts to J=−

dμ′ D D d ·c· =− ·c· (μ0 + RT ·ln(c) + F ·z ·Φ) RT dx RT dx (7) 0

For a homogeneous medium (μ = const), eq 7 reduces to the Nernst−Plank equation: D d ·c· (RT ·ln(c) + F ·z ·Φ) RT dx F ·z dΦ zy i dc zz = −D·jjj + ·c· RT dx { k dx

J=−

(8)

At the border of two phases 1 and 2 with standard chemical potentials μ01,2, that is, at the membrane water interface, eq 7 transforms into: ij 1 dμ0 dc F ·z dΦ yzz J = −D·jjjc· + + ·c· z j RT dx dx RT dx zz{ k

(9)

In equilibrium, i.e. in the absence of a net flux, the electrochemical potential in the two phases is equal: μ10 + RT ·ln(c1) + F ·z ·Φ1 = μ 20 + RT ·ln(c 2) + F ·z ·Φ2 (10)

From eq 10 we find for the ratio of the two concentrations: ij μ 0 − μ 02 + z ·F ·(Φ1 − Φ2) yz c1 zz = expjjj− 1 zz j c2 RT k { 0 ji Δμ + z ·F ·ΔΦ zyz = expjjj− zz: = K p j z RT k {

Figure 2. The total energy barrier ΔW that opposes solute transport across a neutral lipid membrane has four constituents (eq 12): (1) The neutral energy term (green). It accounts for all effects that cannot be attributed to the charge of the permeant (solid line, hydrophilic substances; dashed line, hydrophobic substance). (2) The electrostatic self-energy (Born energy) describes the expense in energy for moving an ion from the aqueous solution into the hydrophobic interior of the membrane. A charged solute near the boundary between two mediums of different ϵ has a polarizing effect. The polarization of the distant medium can be represented by an image charge. The corresponding image energy (3) acts to lower the Born energy. The sum of (2 + 3) is shown in blue and does not depend on the sign of the charge. The sum of (1 + 2 + 3) results in a local minimum for hydrophilic ions at the water−lipid interface. Oriented dipoles, mostly the carbonyls of the lipid ester bonds and the interfacial water molecules, induce a so-called membrane dipole potential Φdipole (4, red). Because Φdipole is positive inside the membrane, it increases anion partition and reduces cation partition. ΔW, the sum of all contributions (1 + 2 + 3 + 4) is thus different for hydrophobic and hydrophilic substances and for negatively and positively charged ions (orange).

(11)

The last definition introduces the dimensionless partition coefficient Kp for the distribution of solutes between the aqueous solution and the hydrophobic interior of a membrane. For a single substance of interest, the standard chemical potential is equal to the standard Gibbs free energy G0 = H0 − T·S0. Thus, eq 11 becomes ij ΔG° + z ·F ·ΔΦ yz zz K p = expjjj− zz j RT k { ° ° i ΔW yz ji ΔH − T ·S + z ·F ·ΔΦ zyz zz zz ∼ expjjj− = expjjj− j z RT k RT { k {

partitioning.35 However, they depend on the nature of the organic solvent that is used to determine Kp. For example, octanol can form hydrogen bonds with solutes via its hydroxyl group and its high water content (mole fraction of 0.29 at saturation).36 In contrast, alkanes lack such hydrogen bonding capacity. Thus, the difference between Kp,oct and Kp,alk provides a measure of solute hydrogen bonding capacity.37,38 It allows distinguishing between hydrophobic and hydrogen bonding effects.39 One of the first to argue that hydrogen bonding can play a role in this process was Stein.40 In favor of this perception are (i) activation energy (EA) measurements for solute (e.g., glycol) diffusion40 and (ii) permeation through vesicular membranes.41 The number of possible hydrogen bonds (acceptor and donor) corrected for the possibility of intramolecular hydrogen bonds in isolated molecules, multiplied by the energy to break one hydrogen bond (∼5 kcal/mol) are in excellent agreement with these EA values. This is in line with the reported correlation between EA of nonelectrolytes and number of H-bonds they

(12)

In the absence of external fields, ΔW harbors four terms: (1) the neutral energy term accounts for the energetic barrier that the molecule would face if it was electrically neutral, (2) a term that accounts for the self-solvation energy (Born energy), (3) a term expressing the attraction of an ion by a dielectric surface (image energy), and (4) a dipole potential term.33 These contributions are schematically shown in Figure 2 for solutes that are solved at equal concentrations in the aqueous solutions at both sides of an uncharged membrane. We will first dwell on the simplest case, the permeation of a neutral substance (section 4), before considering the permeation of anions and cations (section 10).

3. DETERMINANTS OF THE PARTITION COEFFICIENT Because the partition coefficient Kp governs Pm, considerable efforts have been invested into prediction methods.34 Hydrogen bonding characteristics were identified to be most relevant to C


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form with water.42 This number was hypothesized to govern the energy barrier to membrane transport because nonelectrolytes were thought to penetrate into the hydrophobic core as single, fully dehydrated molecules.41 In this case, the lipid composition should play a minor role. However, permeants having the same number of H-bonding groups may exhibit permeability differences on the order of 1 order of magnitude,43 indicating a simple count of hydrogen bonding groups may (i) miss the true hydrogen bonding potential, as some groups may be better hydrogen donors or acceptors than others44−47 and (ii) does not account for other determinants of the overall permeability. Newly formed intramolecular hydrogen bonds represent one of those factors. They reduce the resistance to transport48 and increase cell permeability49,50 because only the number of hydrogen bonds, which is lost during dehydration, is of relevance. Accounting for hydrogen bond strength, i.e., for the type of heteroatom involved, inductive and steric effects51,52 also helps to predict Kp. As a result of an extensive analysis of H-bond acidity and H-bond basicity functional group constants were introduced.53,54 The packing density of a lipid bilayer represents another of those factors. That is, a densely packed bilayer may oppose solute movement across the membrane. This phenomenon is best described in terms of local partition coefficients in a multislab model, as demonstrated by molecular dynamics simulations of cholesterol rich membranes.21 It may result in large variations in solute permeability depending on the lipid. Glycerol provides a prominent example.55,56

Figure 3. One-slab model: According to the homogeneous solubility diffusion model (Meyer−Overton rule), the membrane is viewed as one homogeneous oil layer.11 Pm is determined by the partition coefficient Kp between aqueous and oil phase, the membrane thickness d, and the substance’s diffusivity Dm inside the membrane: Pm = Km·Dm/d. Threeslab model: To enter or leave the homogeneous hydrocarbon core, a substance has to pass the slabs that are occupied by lipid headgroups. These two layers are characterized by permeability Ph that is distinct from the permeability Pc of the lipid core. Ph may be quite large if substances accumulate in these slabs. The accessibility of the core, which is similarly treated as with the homogeneous solubility diffusion model, is geometrically limited by the area occupancy of the head Ah and the membrane area per lipid Ac.57 As long as the substance is not expended inside the membrane, the flux across each slab is constant in steady state and hence the total permeability is Pm = (2/Ph + 1/Pc)−1 with P h = K h ·D h /d h ·(A c − A h )/A c . Multislab model: In the inhomogeneous solubility diffusion model, the membrane is viewed as consecutive layers of thickness di, local diffusivity Di, and partitioning Ki. Each layer has a local permeability Pi that contributes to the total permeability as in the three-slab model. One has to be careful when calculating the Pi from local partition coefficients of subsequent single slabs. Even though particles partition between adjacent slabs, the Ki′ used to calculate Pi via Pi = Ki′·Di/di is relative to the aqueous bulk, hence K i = K i′/∏i − 1 K i . Geometrical occlusions are not explicitly taken into account. Molecular dynamics simulations revealed that cholesterol did not alter diffusivity but the local partitioning.21 The three-slab and the multislab models are computationally more demanding and thus seldom used in experimental studies.

4. MEMBRANE PERMEATION OF NEUTRAL SUBSTANCES For neutral substances eq 7 transforms into Fick’s first law. In steady state (time independent flux), the flux across a thin layer membrane of thickness d in which the substrate of interest has the diffusivity Dm is a linear function of the concentration difference: J = −Dm ·

dc m Δc = −Dm · m dx d

The effect may be rationalized by imaging the membrane as being embedded into two aqueous slabs that each offers permeability PUSL1 and PUSL2 that may be lower than Pm. A brief discussion of unstirred layer phenomenon follows in section 6. In more general terms we can write, according to mass conservation, for the total permeability Ptot of subsequent slabs of permeability Pi of thickness di with different local diffusivities Di and partition coefficients Ki′ (in reference to the aqueous bulk solution):

(13)

where the index m indicates the membrane layer and d membrane thickness. A transmembrane flux requires partitioning of the molecules from the aqueous solution into the bilayer on one interface and partitioning from the bilayer into the aqueous solution on the other. Assuming that Kp is identical at both interfaces leads to the common definition of membrane permeability Pm = Kp·Dm/d. J = −Pm·Δcs

ij yz ij di yzz zz Ptot = jjjj∑ Pi−1zzzz = jjjj∑ j i z j i K i′·Di zz (15) k { k { The use of partition in reference to the bulk aqueous solution is necessitated by the assumption of the same partitioning left and right of the slab that led to eq 14. The partition coefficient Ki′ is the product of the local partition coefficients Ki of all layers up to layer I. It can easily be shown that Ptot is lower than any Pi. A definition as in eq 15 can also be conveniently used to account for membrane heterogeneities in the direction of transmembrane flow. That is, the one-slab model of eq 14 may be substituted for a three-slab model: a hydrocarbon core slab and two headgroup slabs (Figure 3).57 The benefit is that the threeslab model incorporates the permeability dependence on the −1

(14)

where Δcs is the concentration difference between the aqueous concentrations at the two surfaces of the membrane. The simplest model for membrane permeation of a neutral substance is the solubility diffusion model (eq 14, Figure 3). It is based on the Meyer−Overton rule that relates Kp to the hydrophobicity of the permeating molecules. The model views the membrane as one homogeneous slab of constant Dm. Despite the apparent simplicity of eq 14, Pm may be difficult to determine. For example, stagnant water layers adjacent to the membrane may lead to severe underestimations of Pm. Transport across these so-called unstirred layers (USL) occurs only by diffusion. Imposing an additional resistance to the diffusion of fast permeating substances, they act to decrease Δcs. D

−1


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area per lipid molecule (created by the outer slabs) without abandoning the solubility diffusion model (inner slab). The disadvantage of the three-slab model is that it does not work for cholesterol containing membranes. The reason is that cholesterol modulates local partition coefficients at the lipid headgroups and at the lipid tails oppositely. Thus, increasing the total slab number far beyond three and calculating local partition coefficients may sometimes be beneficial for predicting the permeability of multicomponent bilayers.21 We discuss the different permeation models on the example of the permeation of water and other small molecules in section 7.

d ln(Pm) ΔHP 1 = + dT T RT 2

Hence, the experimentally determined EA value exceeds ΔHP by 1 RT.59 Equation 18 assumes that there are no changes in bilayer properties that would render the experimental EA temperature dependent. Otherwise Arrhenius plots result in erroneous EAs.28 Measurement of EA does not necessarily require knowledge of Pm. A quantity proportional to Pm can be used instead. For example, the osmotic membrane water permeability Pf can be substituted in eq 19 for the exponential rate τvs of osmotically induced vesicle shrinkage because τvs ∼ Pf.60 Unfortunately, calculating Pm from EA is not feasible because the entropic penalty ΔSP is unknown (eq 18). The latter can only be calculated if Pm, EA, λ, and d are known.28 Yet a very rough estimation of Pm from known EA values and vice versa of EA from values is still possible. The accuracy is sufficient to distinguish between facilitated transport and passive membrane diffusion. To illustrate the usefulness of such an approach, we provide the recent example of an attempt to measure the water permeability of very narrow carbon nanotubes: Tunuguntla et al. claimed that the nanotubes channel water molecules more efficiently than aquaporins and that EA = 24.1 kcal/mol.61 Because EA values >12 kcal/mol are not compatible with facilitated water transport, it is safe to conclude that the authors measured water transport through the lipid matrix instead of monitoring water transport through nanotubes.62 The hallmark of facilitated water transport by water-filled channels is an EA value in the range of 4 kcal/mol, i.e., a value that is close to the activation energy for the selfdiffusion of water.63

5. ACTIVATION ENERGY OF PERMEATION IN A ONE-SLAB MODEL: EYRING−ZWOLINSKI EQUATION Zwolinski et al.58 formulated the permeation through a membrane based on absolute rate theory. Diffusion is imagined as consecutive steps from one equilibrium position to another separated by a distance λ.59 The equilibrium positions have the same level of free energy but are separated by a free energy barrier of height ΔGD. The resulting diffusion coefficient is (h is Planck’s constant, kB is Boltzmann’s constant) D = λ2·

kBT i ΔGD yz zz ·expjjj− h k RT {

(16)

Combining eq 16 with Pm = Kp·Dm/d and eq 12 results in the Eyring−Zwolinski equation (for an uncharged particle): Pm = λ 2 · = λ2·

i ΔG° yz kBT i ΔGD zy zz zz·expjjjj− ·expjjj− j RT zz h·d k RT { k {

kBT i ΔGP yz zz ·expjjj− h·d k RT {

6. UNSTIRRED LAYERS In addition to the membrane properties, the unstirred layer (USL) adjacent to the membrane also act as barriers to permeation.64 The unstirred layers are not to be mixed with the thin layer of interfacial water molecules adjacent to surfaces: The layer of interfacial water molecules constitutes the membrane hydration shell. Typically, it consists of less than five layers of ordered water molecules.65 That is, water molecules assume the properties of bulk-like water within less than 2 nm from the interface. Consequently, the time required for diffusion across the thin interfacial water layer is negligible, even if the diffusion coefficient was an order of magnitude smaller than in bulk water. In contrast, unstirred layers are much thicker. They may well be comparable to the sizes of the LUVs or GUVs they are adhering to. Consequently, the time required for diffusion across these layers can only be ignored for LUVs, but not for GUVs or cells. If the membrane permeability to a substance is higher than the USL permeability, transport across the USL becomes rate limiting. That is, a concentration gradient appears in the USL of thickness δ. In the extreme case, this gradient is so large that the transmembrane gradient becomes negligible. That is, the USL offers the entire resistance to transmembrane diffusion. This is equivalent to the depletion of the rapidly permeating substance within the immediate membrane vicinity of the donating compartment (Case V in Figure 4). The unstirred layer permeability PUSL is defined as 1 D PUSL = · sol 2 δ USL (21)

(17)

Using the one-slab representation (i.e., a single Kp) is a simplification because lateral diffusion and perpendicular diffusion do not necessarily occur at the same speed. Nevertheless, only perpendicular motion is of importance for permeation. Equation 17 introduces the total free energy barrier ΔGP that a particle faces when passing through a homogeneous membrane. According to the definition of the Gibbs free energy, eq 17 can be split into temperature dependent and temperature independent terms:28 kBT i ΔGP yz zz ·expjjj− h·d k RT { kT i ΔS y i ΔHP zy zz = λ 2 · B ·expjjj P zzz·expjjj− h·d R k { k RT {

Pm = λ 2 ·

(18)

where ΔSP and ΔHP denote the respective molecule’s entropy and enthalpy changes upon membrane permeation. Comparing eq 18 to the Arrhenius equation: i E y Pm = A ·expjjj− A zzz k RT {

(20)

(19)

where A denotes a temperature independent constant reveals that the activation energy EA is only an approximate representation of ΔHP. Besides the exponential temperature dependence, also a linear temperature term exists if eq 18 is transformed:

where the factor 1/2 accounts for the presence of two layers. Unstirred layer limitations occur when the apparent (total) E


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are made: (i) solvent flow is absent, (ii) the solutions surrounding the membrane are well agitated, and (iii) the compartments are so large that the bulk concentrations remain virtually unaltered during the experiment. Hence, a steady state establishes. The two limiting cases of (α) the lack of membrane permeation (case Kp = 0) and (β) the lack of USL limitations (case Kp ≪ 1) are shown as well as a few cases in between. Kp stands for the biphasic oil (or hexadecane)−water partition coefficient. Note that the limiting situation (β) only holds for solutes and not for solvents, because solvents cannot be depleted from the USL. USLs were initially defined as layers that are entirely free of convection. In volume flow this definition led to the absurd prediction that the largest concentration gradient localizes not to the membrane water interface but to the boundary between the USL and the well stirred aqueous solution.67 This problem is solved when a gradually increasing stirring velocity is incorporated into the model.17 That is, the speed of mass transport by convection varies with the distance to the membrane. Volume transport is characterized by an additional peculiarity: water movement across the membrane is itself a source for agitation (see chapter 7.1 for a more detailed discussion on transmembrane water flux). The linear velocity v’ of volume flux gives rise to a convective flux density of molecules dissolved in the aqueous solution:

Figure 4. Unstirred layer phenomena. Effect of the partition coefficient on solute concentration polarization. The membrane is viewed as a continuous slab. Solvent (water) flux vH2O is absent. There is no concentration shift in the case of a nonpartitioning substance (case I: Kp = 0). Case II describes a poorly partitioning (hydrophilic) substance with 0 < Kp < 1. Case III displays the case for Kp = 1, where no concentration jump occurs at the water−membrane interface. Case IV shows the profile for a very hydrophobic substance. Case V shows the limiting case of pure unstirred layer limitation: resistance to solute flux is entirely due to diffusion through the USL. The flux across the membrane is associated with negligible resistance. The unstirred layer thickness δUSL is defined as the first derivative of solute concentration d[solute]/dx at zero distance from the membrane surface, x = 0.

Jconvection = c·v′

(23)

Consequently, the width δUSL of the USL depends on solvent flux density (Figure 5, left panel),17 stirring strength (Figure 5, middle panel),17 and solute diffusivity (Figure 5, right panel).68 It is important to note that the relative contributions of flux density, stirring, and diffusivity may vary. For example, vigorous stirring may keep δUSL constant even though the flux density varies.13,17 Outside of the membrane, the substance of interest can be consumed or produced by chemical reactions (eq 24 with the local rate of expenditure R in chemical reactions).15,16 Thus, chemical reactions have to be carefully considered when calculating the transmembrane flux Jm and the transmembrane solute gradient:

permeability Ptot of a membrane contains a non-negligible contribution of PUSL:66 1 1 1 = + Ptot PUSL Pm (22) Thus, for planar bilayers with a typical diameter of 150 μm, δUSL of ∼100 μm and Dsol ∼ 2 × 10−5 cm2/s, we find PUSL ∼ 10−3 cm/s. The corresponding concentration distribution of permeable solute that moves along a transmembrane gradient is schematically depicted in Figure 4 for different partition coefficients in a one-slab membrane. The following assumptions

Figure 5. Unstirred layer determinants in solvent flow. Solvent flow affects the concentration distribution of membrane impermeable solutes (case 1 in Figure 4). (left) Effect of different solvent volume flux densities (linear transmembrane volume flux velocities) vH2O (unit: m/s). δUSL increases proportionally to vH2O. From the distribution of the impermeable solute and vH2O, the water membrane permeability Pf can be calculated (see section 7).17 (middle) δUSL can only be reduced, but not fully abolished, by vigorous stirring. Solute induced osmotic water flux across the membrane results in solute dilution on the hyperosmotic site and solute concentration increase on the hypoosmotic side. As a result, the osmotic gradient diminishes and, hence, also vH2O. Thus, vH2O depends both on stirring and on the difference in bulk osmolarity.17 (right) Diffusion of every solute is characterized by its individual δUSL.68 That is, δUSL is different for different solutes even though both stirring and transmembrane solvent flux density are kept constant. The higher the Dsol the smaller δUSL gets.68,69 F


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Figure 6. Unstirred layers in weak acid and base transport. (left) Permeating substances undergo chemical reactions at the membrane water interface. The diffusion, expenditure in chemical reactions, and translocation across the membrane have to be taken into account. Exemplarily, the relevant processes for a weak acid AH and weak bases B are outlined. AH can deprotonate to form the conjugated base A−, and B can protonate to form the conjugated acid BH+. (right) Effect of chemical reactions on transmembrane flux. The conjugated forms A− and BH+ serve as reservoirs from which the acid or base can be produced right next to the membrane. For illustrative purposes, an acid with Kp = 1 is chosen. The A− pool at the interface allows transmembrane fluxes to be higher than would be predicted from PUSL. Permeation of acid augments pH in USL of the donating compartment and drops pH in the opposing USL. Pm can be calculated from the resulting pH profiles. For mild buffering (red), the USL is depleted from acid molecules because there is hardly any buffer that can supply enough protons to protonate the conjugated base. Buffer abundance (blue) serves as a protons source, ensuring a high transmembrane gradient of acid. In turn, elevated transmembrane flux is observed.

dJm dx

=R

(24)

Chemical reactions at the membrane water interface may help to reduce or overcome flux limitations by PUSL − as has been shown on the example of salicylic acid,9 CO2,14 and H2S.2 Ptot in the range of cm/s are achievable under favorable buffer conditions as depicted in Figure 6. Because of high concentrations of the conjugated anion and rapid proton uptake reactions at the interface, diffusion of the deprotonated weak acid across the USL contributes to the total flux. That is the protonated weak acid is produced or expended right next to the membrane.70,71 Figure 6 assumes that the chemical reactions are in equilibrium, i.e., that translocation across USLs and the membrane occurs at a much slower rate than protonation or deprotonation. This is not necessarily true for the abovementioned CO2 involving reactions. In the absence of the enzyme, carbonic anhydrase, the CO2 hydration and bicarbonate dehydration are very slow. In consequence, there would be no equilibrium throughout both unstirred layers.72 By adjusting the enzyme concentration, it is possible to arrive at intermediate situations, where membrane translocation and chemical reaction compete with each other. Such conditions may be physiologically meaningful as they provide the opportunity to regulate transmembrane CO2 flux.73 From the above said, it follows that the extension of the near membrane aqueous layer, in which the reaction occurs (= reaction layer) depends on the concentration of the aqueous enzyme. We have demonstrated this fact on the example of alcohol dehydrogenase (AlDH):74 Subsequent to its membrane permeation, acetaldehyde transformed into ethanol in the presence of the enzyme alcohol dehydrogenase. The reaction consumed NADH and protons (Figure 7). This process augmented pH within the reaction layer of the receiving compartment, as has been visualized by scanning pH electrodes that were moved perpendicular to the membrane. Remarkably enough, the peak of the pH value was observed at some distance to the membrane water interface, provided that proton were allowed to freely pass the membrane.75 Increasing acetaldehyde concentrations moved the pH peak closer to the membrane water interface, indicating a shortening of the reaction layer. At the highest enzyme concentrations, the pH profile was

Figure 7. Visualization of the reaction layer adjacent to the membrane. Acetaldehyde (CH3COH, purple) translocates across the membrane from the donating to the receiving compartment, where it is enzymatically converted to ethanol (CH3CH2OH) by alcohol dehydrogenase (AlDH, turquoise). Per molecule CH3COH, one proton and one molecule of NADH are consumed. Proton release from membrane permeable buffer molecules (acetic acid) counteracts large pH changes. The pH profiles peak far from the membrane at low AlDH concentrations (blue). At high enzyme concentrations, monotonic pH profiles are observed (red).

monotonic, indicating that the chemical reaction reached equilibrium. In consequence, the aldehyde concentration was minimized in the receiving compartment and the acetaldehyde concentration gradient across the membrane was maximized, as was the transmembrane acetaldehyde flux.75 We conclude that the interplay between diffusion and chemical reactions within the unstirred layer serves to modulate transmembrane flux. Thus, USLs may decrease solvent flux by allowing the osmolyte to be swept away and they may provide the microclimate for chemical reactions that acts to enhance solute flux.

7. WATER DIFFUSION ACROSS LIPID MEMBRANES Diffusion of small nonelectrolytes across lipid bilayers is best discussed using the example of water, simply because G


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Figure 8. Lipid properties known to influence membrane permeabilities to water molecules and hydrophobic substances. Cholesterol (red) intercalates between the lipids, thereby increasing the spacing in the headgroup region and, in turn, facilitating solute and solvent partition into this region. In the hydrocarbon region, where cholesterol sits, void space is reduced and hence partition of the permeant drops.21 Sphingolipids (yellow) are able to reduce Pm,H2O by an order of magnitude by virtue of amide mediated hydrogen bond formation with each other (indicated by black dashed line), cholesterol and ceramides inducing a lipid ordered phase.55,85−87 Hence, lipid packing increases, which in turn decreases the partition of the permeant into the bilayer. Permeation can be further reduced if temperature drops below the main phase transition temperature of the bilayer lipid, resulting in tighter packing. For example, the acetic acid permeability of dipalmitoylphosphatidylcholine rises about a hundredfold once the lipids melt.88 In contrast, unsaturated lipids enhance the passage ability due to more void space in the hydrocarbon core.79,80

depends on bilayer thickness, which should be reflected by prominent permeability changes. The transient pore model (Figure 9) appears especially appealing because it is often thought to provide a plausible explanation for the high permeability of lipid membranes to protons. That is, these transient water “wires” would provide a pathway for faster proton movement through the bilayer according to Grotthuss’ mechanism.92,93 If that was the case, proton and water permeabilities should go hand in hand, i.e., it should be possible to predict proton permeability from Pm,H2O. This is not the case. For example, archaeol lipids 3-fold decrease the apparent proton permeability while they reduce water permeability 5-fold as compared to diphytanoyl lipids.56 Pm,H2O and Pm,H+ of the phosphatidyl choline bilayers varied 67- and 3fold, respectively, with increasing temperature.77 Generally, membrane proton permeability is only weakly influenced by fluidity.77,94 The opposite observation has been made for Pm,H2O, suggesting markedly different permeation mechanisms for water and protons. This conclusion is in line with the following criticism of the pore model: (a) Membrane permeability to small molecules depends too weakly on bilayer thickness. Instead of the exponential dependence that was predicted from the pore model, augmentation of the carbon number in the lipid acyl chains from 14 to 24 carbon atoms resulted in a linear Pm,H2O decrease.89,94 The conclusion is corroborated by an NMR study that found a less than 2-fold difference between Pm,H2O of C14 and C18 lipids (dimyristoylphosphatidylcholine vs distearoylphosphatidylcholine) containing membranes.82

permeation of water has been studied more extensively than that of any other molecule.76 Water transport is in full agreement with the solubility diffusion model. That is, its translocation rate depends on membrane partitioning and mobility within the bilayer. Water permeability Pm,H2O strongly correlates with membrane fluidity.77 Both cholesterol and sphingomyelin act to reduce Pm,H2O.78 Unsaturation serves to increase Pm,H2O.79,80 Below the lipid phase transition temperature, Pm,H2O is 30−100-fold reduced compared to the liquid state above the phase transition temperature (Figure 8).81,82 This is reflected by an up to 10 kcal/mol large increase in activation energy EA for water permeation across synthetic lecithin lipid bilayers when going from above to below the phase transition temperature.83,84 Apart from the well-known solubility diffusion model,89 water was proposed to permeate the lipid bilayer through transient defects, arising from thermal fluctuations (Figure 9).90,91 Slipping through such transient pores is thought to lower EA and thus increase permeability because water would not partition into the hydrophobic bilayer interior. According to the pore model, the probability for defect formation strongly

(b) The activation energy EA provides another argument against the pore theory. EA for water transport across pores would be expected to be in the range of 4−7 kcal/ mol.62,95 In contrast, EA for nonfacilitated transport across lipid membranes is generally between 10 and 20 kcal/ mol.78,79 In contrast, the predictions of the solubility diffusion model were confirmed experimentally: (a) For fluid membranes, the value of water permeability is accurately predicted by Kp.96

Figure 9. Permeation models for lipid bilayers. (left) The three-layer theory represents the most recent model which includes the area/lipid, the hydrocarbon core thickness, and the strong correlation of permeability upon the partition coefficients of general solutes in hydrocarbon environments, also known as the Overton’s rule.109 (middle) The pore model assumes molecules traversing the hydrocarbon core through transient defects, arising from thermal fluctuations. The permeant is surrounded by hydrocarbons.92,93 (right) On the border of membrane patches of different phases (liquid order/ disordered), membrane spanning water filled pores form.102,103

(b) Pm,H2O weakly depends on membrane thickness.94 H


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decrease in the area per lipid.111 Yet, there is no clear correlation between Pm,H2O and hydrophobic thickness, if both saturated and unsaturated lipids are included in the study.109 This observation can be explained by an increase in fluidity due to unsaturation (depending on the position of the double bond).112 Thus, a weighted assessment of the contributions of hydrophobic thickness and unsaturation to Pm,H2O is only possible via the analysis of the cross-sectional areas of head groups and acyl chains. This area criterion cannot be substituted for bilayer bending modulus or area compressibility modulus as neither of them correlates well with Pm,H2O.109 The result appears to be counterintuitive because both moduli depend on both unsaturation and hydrophobic thickness of the bilayer.113 However, their impact on bending and area compressibility moduli may well be quantitatively different from that on Pm,H2O. Unfortunately, the three-slab model does not cover cholesterol mediated effects. That is, cholesterol containing membranes reduce Pm,H2O beyond the level that would be expected from the reduction in area per lipid.109 This observation agrees very well with the finding that cholesterol reduces the local partitioning of permeating substances within the hydrophobic core.21 The statement can be rationalized in terms of a multislab model for the hydrophobic core. Movement in the direction to the bilayer center from one slab to the next may be associated with its own partition coefficient. Cholesterol acts to reduce one or more of these local coefficients due to spatial constraints, very much like a reduced area per lipid acts in the three-slab model.21 Notably, the reduction in Pm,H2O is in line with an increase of the activation energy EA from 10 to 21 kcal/ mol.81

(c) Membrane fluidity is a major determinant of the osmotic water permeability Pf = Pm,H2O. For example Pf increases with the unsaturation for monoglyceride membranes.78 The micropipette aspiration technique revealed a 5-fold increase in Pf from 30 to 150 μm/s when saturated PC lipids (18:0−18:0) were substituted for lipids with six double bonds (18:3−18:3).97 The same holds for diffusive water permeability Pd. 17O NMR measurements of diffusion-controlled water permeation revealed a 6-fold increase (at 10 °C) in Pd for an increase in the number of double bonds from one to 12 per lipid (i.e., from 18:0− 18:1 PC to 22:6−22:6 PC). The effect is comparable to that of six double bonds because the acyl chain length increased as well, which is known to decrease Pf. Nevertheless, the pore mechanism may work at the boundary between gel and liquid−lipid phases (Figure 9). That is, the membrane water permeability shows a maximum close to the phase-transition temperature of membrane lipids, where crystalline phases partially coexist.82,97 Other nonelectrolytes and electrolytes also show a peak in permeability.98−101 The increased permeability at phase transition strongly depends on the size of the permeating molecule.97 Spontaneous lipid pore formation is thought to be due to increased area fluctuations because a maximum in the lateral compressibility may be observed close to the chain-melting temperature.102,103 Conceivably, the increased compressibility lowers the work necessary to create membrane defects, thereby facilitating pore formation.102 The fluctuations are highest at domain boundaries.99 Consequently, the latter represent the most likely location for the permeation pathway.102 This hypothesis was supported by computer simulations.104,105 It is important to note that lipid phase transitions do not exclusively occur at the phase transition temperature of the individual lipid, but they may be shifted to other temperatures by protein lipid interactions106,107 as well as by interactions of the lipid with other membrane-embedded molecules. For instance, membrane inserted carbon nanotubes are thought to tightly bind adjacent lipid molecules leading to a strong order of lipid tails similar to the order of lipids in the gel phase.108 Hence, carbon nanotube insertion into lipid bilayers is likely to induce permeation events at the boundary between the highly ordered lipids adjacent to the tubes and the fluid lipids farther away. The resulting permeation events may easily be mistaken as water and ion passage across the tubes.62 The popularity of the transient pore model was fueled by the observation that the permeation of very small molecules was not well described by the simplest version of the solubility diffusion model, the one-slab version. Only when excluding small molecules Walter and Gutknecht found a one-to-one correlation of membrane permeability to the partition coefficient.96 Nagle et al. subsequently rationalized the permeability dependence on the volume of the permanent by proposing the three-slab model.57,109 The additional outer two slabs govern the access of the permeating molecule to the inner slab. Their resistance is determined by the area that is accessible for passage of solutes into the hydrocarbon core. This area is given by the difference between the cross-sectional areas of head groups and acyl chains (Figure 3). This three-slab model57 satisfactorily describes most lipid effects on Pm,H2O.109 For example, an increase in hydrocarbon thickness results in an increase of the attractive van der Waals forces between hydrocarbon tails, which for lipids with the same degree of unsaturation leads to a greater lipid order110 and a

7.1. Measurements of Pm,H2O: Osmotic Permeabilities

Water permeability can be quantified in two different ways: in terms of an osmotic water permeability Pf or a diffusional water permeability Pd. Pf is the transmembrane volume flow in response to an osmotic or hydrostatic gradient. Pd arises from the diffusional movement of water across membranes in the absence of driving forces.114 In the absence of membrane channels the two ways of assessment yield the same result, i.e., Pd = Pf = Pm,H2O. Pf can be studied in two principally different ways: (i) by kinetic techniques where the changes of a membrane encapsulated volume are observed as a function of time, or (ii) by steady-state approaches where much larger volumes are involved: (i) Larger objects, like Xenopus oocytes, are monitored directly by light microscopy, and the increment in volume after osmotic challenge is extracted from the image.115,116 The technique does not work very well for objects of intermediate size, like giant unilamellar vesicles (GUVs). Here the micropipette aspiration technique is the method of choice. Instead of trying to resolve tiny changes in diameter, vesicle projection into a ∼10 μm wide pipet is studied.80 Calculation of Pf may result in underestimated values because extended internal and external unstirred layers (USLs) may exist in the vicinity of these micrometer (GUVs) or millimeter (Xenopus oocytes) sized objects. Interference by USLs may be avoided by using large unilamellar vesicles (LUVs).11 These objects are too small to be studied by light microscopy. Resolving their volume changes is thus possible only by monitoring the quenching of encapsulated fluorescent dyes or by registering the intensity of scattered light I.60,117 The latter technique is used most I


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frequently. I increases upon osmotic deflation in spite of the size decrease. The reason is the increment in the refractive index due to the concentration increase of the encapsulated solutes.117 I(t)=I0+a ·V (t ) + b·V (t )2

experimentally observed concentration distributions within the USLs, it is mandatory to account also for fluid convection that is caused by stirrer bars. That is, at the membrane−water interface, the nonslip condition is obeyed, but the velocity of fluid movement gradually increases as ast·x2, where ast is the stirring parameter and x the distance to the membrane.17,123,124 The sum of diffusive flux and convection due to water flow and stirring amounts to

(25)

a and b are commonly fitting parameters. However, they can also be found analytically from the refractive indices of all encapsulated components.117 Independent of the size of the particle, Pf can be extracted from the observed volume change:117,118 i V y d V (t ) = A ves ·Pf ·VW ·jjjj 0 ·cin,0 − cout zzzz dt k V (t ) {

i dc y J = Dsol ·jjj sol zzz + (vH2O − ast ·x 2) ·csol = 0 k dx {

Equation 28 can be solved by using the boundary condition that the solute concentration csol at the membrane surface csol(0) = cs:

(26)

where Vw, V0, Aves, cin,0, and cout are the molar volume of water, vesicle volume at time zero, surface area of the vesicle, the initial osmolyte concentration inside the vesicles, and the externally applied osmolyte concentration, respectively. Now an accurate analytical solution is available that may replace previously used inaccurate approximations:117 V (t ) =

3

csol = cs·e(−[vH2O·x / Dsol]+[ast·x /3·Dsol])

(29)

vH2O and ast are fitting parameters. Once obtained by fitting eq 29 to an experimental concentration profile, Pf can be calculated: vH 2 O Pf = csol·Vw (30)

V0 cin,0 + cout

ÉÑ | ÅÄÅ l ij c − c o ÅÅ cout − cin,0 o o A ves · Pf · Vw · cout 2 ÑÑÑÑyzzzo in,0 jj out Å ×o + · − · 1 L exp t } ÑÑzzo Å m ÅÅ c jjj c o o Ñ z o o · V c Ñ Å o in,0 in,0 0 in,0 Ñ Å Ö Ç {o k ~ n

where Vw is the molecular volume of water. An alternative method of monitoring solute dilution in the immediate membrane vicinity is provided by fluorescence correlation spectroscopy. Instead of the concentration of an ion, the concentration of an aqueous fluorescent dye is observed as a function of the distance to the membrane.125,126 So far, that method has been only applied to observe water transport across epithelial monolayers. The microelectrode approach offers an enormous potential as it allows investigating planar lipid bilayers that (i) mimic the immense compositional heterogeneity127 of biological systems and (ii) display permeability changes in response to lipid protein interactions.128 Here we illustrate that point by reproducing our study of water passage through asymmetric bilayers.87 Previous studies on vesicular bilayers had only revealed that symmetrical membranes with the composition of the outer leaflet of epithelial cells (MDCK type 1 cells) offered an 18-fold higher resistance to water transport then symmetrical bilayers that compositionally mirrored the inner leaflet of epithelial cells.55 However, the permeability of the asymmetric bilayer as well as the contributions of the individual leaflets to it were not known. The question was answered by forming planar lipid bilayers: one leaflet consisted of highly charged and phosphatidylethanolamine rich lipids, and the outer leaflet was built of cholesterol, sphingomyelin, and cerebroside.55 The microelectrode measurements confirmed that the single leaflets offer an independent and additive resistance to water permeation (Figure 10):

(27) L(x)

where L is the Lambert function: L(x)e = x. (ii) Steady-state approaches of determining Pf of lipid membranes are commonly restricted to the use of planar lipid bilayers. In the early days, the bilayers were formed on the tip of a microsyringe.78,81,119 Water flux into the syringe was accompanied by an increment in hydrostatic pressure, which, in turn, resulted in bilayer bulging. Subsequent adjustment of the available volume by moving the piston flattened the bilayer again. Controlling bilayer area by capacitance measurements allowed long-term measurements of volume flux. However, quantitative analysis was hampered by unstirred layer effects.120−122 That is, transmembrane water flux resulted in osmolyte dilution in the immediate membrane vicinity. As a result, osmotic water permeability was often underestimated. The problem can be solved by measuring solute dilution within the USLs. This is easily achieved by moving an ionsensitive microelectrode toward or away from the lipid bilayer.17,123,124 When the microelectrode touches the bilayer, a steep potential change is observed that serves as reference position for the bilayer. The actual distance of the microelectrode to the bilayer can then be calculated from the known speed of microelectrode movement. Calculation of membrane permeability is possible from the simple consideration that in steady state there exists no net flux of an impermeable solute across the unstirred layers. At linear velocity vH2O the transmembrane osmotic flow sweeps solute away from the membrane in the hypotonic USL and sweeps solute toward the membrane in the hypotonic USL. It thus lowers the solute concentration csol (diffusivity Dsol) at one interface and raises the solute concentration at the other interface. Solute diffusion in the opposite direction counters this convection driven solute flux. In the steady state, the diffusion driven flux Dsol ·

(28)

1 1 1 = + PAB PA PB

(31)

where PAB, PA, and PB are the water permeabilities of the asymmetric bilayer, of leaflet A, and of leaflet B, respectively. An increased EA of 22.1 kcal/mol for the exofacial lipids reflects the tighter lipid packing.81 7.2. Measurements of Pm,H2O: Diffusional Permeabilities

A variety of physical approaches has been exploited to measure Pd: the sensitivity of a fluorescent dye to the surrounding water isotope, the difference in the refractive indices between H2O in D2O, the dilution of a radioactive label, and nuclear magnetic

dcsol dx

( ) and the convective flow must be equal to

each other for membrane impermeable substances. To describe J


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the accurate and instantaneous measurement of transepithelial diffusional water permeability Pd in perfused kidney tubules138 was extended to simultaneous measurements of Pf and Pd with high accuracy and low sample requirement139 (Figure 11). The method results in similar values compared to NMR.139

Figure 11. Diffusional and osmotic water permeabilities in red cell ghosts measured by fluorescence and scattering, respectively. The ghosts contain water channels (aquaporins) that can be inhibited by mercurial compounds. The isotope and osmotic gradients were imposed by mixing the ghosts with an equal volume of D2O containing buffer, resulting in a 100 mM inward sucrose gradient. Please note the requirement for a much faster detection system for the isotope measurements (compare eq 34). Although Pd amounted to only 5.1 ± 0.5 × 10−3 cm/s and 2.8 ± 0.5 × 10−3 cm/s without and with HgCl2, respectively, the stopped flow apparatus was brought close to its limit (the dead time commonly amounts to 1 ms). The samples were illuminated at 380 nm. The fluorescence of the encapsulated fluorophore ANTS was detected at >450 nm. Simultaneously scattered light was detected at 380 nm (measured at 25 °C). Calculation of Pf revealed values of 2.1 ± 0.4 × 10−2 cm/s and 2.2 ± 0.3 × 10−3 cm/s without and with HgCl2, respectively. Reproduced with permission from ref 139. Copyright 1989 American Chemical Society.

Figure 10. Water permeability of symmetric and asymmetric planar lipid membranes. (top) Measurement scheme. Sodium sensitive microelectrodes were moved perpendicular to the bilayer. Main graph: Na+ concentration as a function of the distance to the membrane. The profiles were recorded at the hypoosmotic side of planar lipid bilayers at 36 °C. Water flux was induced by 1 M transmembrane gradient of urea. The black and red sodium concentration profiles correspond to lipid bilayers formed from exofacial and cytoplasmic lipids, respectively. The green profile refers to an asymmetrically formed membrane with exofacial lipids in one monolayer and cytoplasmic lipids in the other. Inset: Bar chart of the different water permeabilities. Figure adapted with permission from ref 87. Copyright 2001 Rockefeller University Press.

Pd measurements require much higher time resolution than Pf measurements (Figure 11). To illustrate this circumstance, we take the Pf/Pd ratio. That purpose requires substitution of eq 27 for a recently published, rather accurate approximate solution:60

resonance (NMR). For example, NMR has been extensively used to study red blood cells,129−134 kidney cells,135 as well as lipid vesicles.79 Pd measurements in vesicular systems require a time resolution in the lower ms time range due to the small volume V0 in which the isotope is exchanged: 1 Pd = τd·(A ves /V0) (32)

Pf =

cin,0 + cout r0 · 2 3·Vw ·τf 2·cout

(33)

Taking into account that for channel free bilayers Pf = Pd, we find from eqs 32 and 33: τf 1 cin,0 + cout = · 2 τd Vw 2·cout

where Aves is the surface area of the vesicle. For example, 17O NMR assessed the diffusion controlled water permeation by monitoring changes of the 17O water resonance.79 Because of the presence of paramagnetic magnesium ions in the vesicles, the relaxation time within the vesicles was much shorter than the relaxation time outside the vesicles. Discrimination between the H2O/D2O content is also possible with fluorescence markers like indol136,137 or aminonapthelane trisulfonic acid (ANTS).138 For example, ANTS exhibits a 3.2-fold increase in quantum yield in D2O compared to H2O,138 which is 10 times greater than for indol.137 The change in fluorescence occurs due to collisional quenching with a response time of 0.1 ([C18O16O]in denotes the intravesicular C18O16O concentration),173 amounts to 0.16 cm s−1 for the vesicle experiments.168 The analysis of the authors may be confounded by a substantial intravesicular acidification that was visualized with an encapsulated pH sensitive dye under comparable conditions.174 Because intravesicular volume was R


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also the control with lysed vesicles is absent from the paper. This control would have shown whether the concentrations of encapsulated carbonic anhydrase in the two vesicle populations (30% and 70% cholesterol) were equal to each other (Figure 20). Cholesterol has already been shown to reduce encapsulation efficiency by ∼40%.178 Thus, a variable amount of encapsulated carbonic anhydrase alters the rate of the catalytic reaction, what in turn could have been misinterpreted as a change in Pm,CO2. The different vesicle populations (30% and 70% cholesterol) are likely to differ in their radii because the extrusion step in their production introduces a dependency of the final radius on stiffness. Accordingly, it has long been recognized that cholesterol increases vesicle size by up to 70% upon extrusion through 200 nm wide pores.178 In contrast, the uniformity of vesicle size (150 nm in diameter), as claimed by the authors of the mass spectrometry paper,168 appears unreasonable. The more so as neither the electron microscopy picture nor the width of vesicle size distribution is provided.168 Resulting differences in the surface to volume ratio lead to a variability in 12C18O16O uptake, which may have been misinterpreted as alterations in Pm,CO2. We conclude that the large variability in both r and in the rate of the catalyzed reaction is likely to have hampered the mass spectrometry experiments. This appears the more likely as the actual changes in isotope kinetics are rather small (Figure 20). We extracted krd by fitting an exponential decay function that contained an additional linear term to the experimental data. Augmenting the cholesterol concentration from 30 to 70% increased krd from 0.081 s−1 to 0.086 s−1, i.e., altered krd by only ∼6%. Unstirred layers (USLs) represent yet an additional source for erroneous Pm,CO2 estimates by the mass spectrometry setup. They are known to exist in the immediate vicinity of the membrane that separates the aqueous solution from the gaseous phase.179 Together with the membrane itself, USLs constitute the so-called boundary layer that acts to decrease the C18O16O concentration in the gas phase below that in the aqueous phase (Figure 21). Because of the huge concentration polarization effect, solute concentration at the membrane surface often amounts to only one-tenth or less of the concentration in the bulk solution.180 The reason for the near-membrane C18O16O depletion within the USL is the much faster transport in the gas phase. That is, mass transfer is limited by the slow aqueous diffusion across the USL181 If the concentration polarization at the liquid−membrane interface controls solute transfer,179 we may estimate USL size from the characteristic time 1/krd ≈ 12 s. Transforming the latter into the corresponding half time t1/2 = 3/4 krd = 9 s allows using the relationship t1/2 = 0.38 δ2/D64 to find δ: δ=

9s × 2 × 10−5 cm 2 s−1 = 47 μm 0.38

Figure 21. Pervaporation separation of dilute solutes. The external C18O16O concentration in the vesicle solution reduces significantly in the USL of the Teflon membrane. That is, the mass transfer boundary layer resistance adjacent to the Teflon membrane may significantly disturb both kinetics and absolute readout values of the mass spectrometer. μCO2 denotes the chemical potential of CO2. The subscripts b, s, 1, and 2 stand for bulk, the aqueous solution adjacent to the Teflon surface, the gaseous phase adjacent to the vapor side of the membrane, and the gaseous phase adjacent to the aqueous interface of the membrane, respectively.

did not provide evidence that cholesterol containing bilayers may represent a barrier to CO2. Similar criticism applies to experiments conducted with cells: The rate of the catalyzed reaction inside the cells is likely to (i) be lowered by internal acidification,174 (ii) be masked by transfer kinetics across the boundary layers adjacent to the Teflon membrane, and (iii) suffer from ambiguities that are caused by a large number of unknown fitting parameters. Along with the pH dependent enzymatic reaction rate, bicarbonate, and water permeabilities, now also the sizes of internal and external USLs adjacent to the plasma membrane need to be extracted by fitting a mathematical model to the data. The authors claim to have these USLs determined by altering the viscosity of buffer solutions. However, the viscosity effect on the boundary layer adjacent to the Teflon membrane (Figure 21) must have been much more pronounced. Our conclusion is supported by the finding that the calculated sizes182 of 0.5 and 0.2 μm for the outer and inner USLs of red blood cells are unreasonably small. Rather, the whole interior of the erythrocyte acts as an USL. Support for this hypothesis comes from the observation that solute diffusion in the cytoplasm of erythrocytes is restricted by the high concentration of hemoglobin:183 Cytoplasmic diffusivity of calcein was measured to be 47.8 ± 5.95 μm2/s,183 as compared to ∼600 μm2/s in water.184 Last but not least, the ambiguities in the interpretation of the mass spectrometry data are also documented: (i) Back in 1998, Pm,CO2 was determined to be 2 cm/s.185 Seven years later, similar mass spectrometry recordings yielded a more than 10-fold smaller value.186 No comment about the origin of the discrepancy was offered. (ii) In the presence of an inhibitor of the Cl−HCO3− exchanger, a Pm,HCO3− of 4 × 10−3 cm/s was measured,186 a value that is 4 orders of magnitude larger than the value that would be expected for the lipid matrix.72 This

(61)

For a Teflon membrane with a radius of rTM = 0.3 mm,169 the result is quite reasonable. It indicates vigorous stirring, as can be judged from measurements of δ by scanning electrochemical microscopy in the vicinity of similarly sized planar lipid bilayers. Thus, the time course of mass spectrometry kinetics (Figure 20) is compatible with the view that diffusion across the unstirred layer adjacent to the Teflon membrane is rate limiting. We conclude that the vesicle experiments that were carried out with the mass spectrometry device are not conclusive. They S


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observation opens the distinct possibility that in addition to Pm,HCO3− also Pm,CO2 is also orders of magnitude off. We conclude that mass spectrometry experiments on cells cannot provide evidence for a membrane barrier to CO2. 9.4. Additional Approaches Aimed at Characterizing Membranes as CO2 Barrier

We will shortly review three additional approaches that have been applied to claim low membrane permeability to CO2: 1. Heterologous protein expression in oocytes along with site directed mutagenesis has served to assign CO2-conducting functions to aquaporins.8,187,188 The maximal increment in pH, ΔpHooc, at cell surface served to separate CO2-channeling membrane pores from nonconducting proteins. It was obtained by pushing pH-sensitive microelectrodes against the oocyte surface.187 ΔpHooc was directly taken as a quantitative measure of CO2 permeability. However, ΔpHooc is not a measure of Pm,CO2. ΔpHooc may only serve as an indicator for the size of the CO2 influx, i.e., ΔpHooc, is related to the number np of protons that per unit time recombined with HCO3− to form the oolemma permeating CO2 molecules. Their number nCO2 declines with time because CO2 accumulates within the oocyte, while the external concentration cCO2,o remains constant. In other words, the influx diminishes with the transmembrane CO2 concentration gradient ΔcCO2. Thus, the time dependence of oocyte surface pH mirrors the time dependence of the CO2 concentration [CO2]i inside the oocyte. To find that function, we write the influx JCO2 of nCO2 across the oocyte plasma membrane with area Aooc as JCO2 =

Figure 22. Microelectrode measurements of oocyte surface pH. Exposure to 5% CO2/33 mM HCO3− resulted in a sudden increase in pH. The increment ΔpHooc was larger for oocytes expressing rat aquaporin-5 (red trace) than for control oocytes (blue trace). The data are taken from Geyer at al.188 We obtained the time constant τ for the pH decay by fitting the data with an exponential function (eq 65). The black fits yielded τ values of 38.7 and 48.8 s, respectively. Inset: The resistance to CO2 flux that is offered by oocyte’s unstirred layer is at least 3 orders of magnitude larger than the resistance that is caused by the oolemma. The resistors in the drawing differ in size by only 1 order of magnitude. Thus, altering oolemma resistance by aquaporin expression cannot have a measurable effect on CO2 uptake. The difference between the red and the blue traces must be of different origin. For example, a change in the size of the unstirred layer is noticeable.

V d[CO2 ]i 1 dnCCO2 · = ooc · ·(1 + 10 pH − pK ) Aooc dt Aooc dt

larger.189,190 Accounting for the intracellular acidification of about 0.3 pH units191 reduces the factor 1 + 10pH−pK (eq 66) from 21 at pH 7.4 to only 6 at pH 6.9. As a result, Ptot diminishes and, in turn, δUSL increases to about 100 μm. But even if the underestimated δUSL value was correct, our calculation clearly indicates that an oolemma with Pm,CO2 = 11 cm/s (Figure 17) makes an immeasurable contribution to Ptot (eq 22): 1 1 1 1 1 = + = + Ptot Pm PUSL 11 cm s−1 8.7 × 10−3 cm s−1 1 ≈ (67) 8.7 × 10−3 cm s−1

(62)

where Vooc is the oocyte volume. The factor 1 + 10pH−pK accounts for the chemical reaction insight the oocyte, i.e., for the transformation of CO2 into HCO3−. JCO2 is determined by the apparent (total) permeability, Ptot: JCO2 = Ptot·([CO2 ]o − [CO2 ]i ) = Ptot·Δ[CO2 ]

(63)

Inserting eq 63 into eq 62 yields Ptot·dt =

dΔ[CO2 ] r ·(10 pH − pK + 1) · 3 Δ[CO2 ]

(64)

Equation 64 assumes that there is no pH shift inside the vesicle. Assuming ΔcCO2(t = 0) ≈ cCO2,o, (i.e cCO2,i(t = 0) ≈ 0) allows solving eq 64: Δ[CO2 ](t ) = [CO2 ]o ·e[−3·Ptot / r·(1 + 10

pH − pK

)]·t

Representing the reverse permeabilities of both membrane and unstirred layer as resistances in series illustrates the impossibility of detecting aquaporin mediated changes in the membrane resistance to CO2 (Figure 22). 2. Stopped flow fluorescence spectroscopy of cholesterol containing vesicles was claimed to reveal a CO2 barrier.149 Using stopped flow for this purpose appears to be questionable because the time resolution is insufficient.11 Eq 66 yields a time constant of τ = 13 μs for vesicles with radius r = 75 nm and Pm,CO2 = 11 cm s−1 (Figure 17). Even if we take into account the internal vesicle acidification, i.e., assume a final pH value of 7.0, the resulting τ value of 38 μs would still be immeasurable, because the mixing time of the stopped flow apparatuses is in the order of 1 ms. The study claims Pm,CO2 = 0.01 cm/s for cholesterol containing membranes.149 This appears unconvincing for several reasons: a. This is a one point measurement at the resolution limit of the device. A cholesterol doses effect was not demonstrated.

(65)

ΔpHooc is a measure of Δ[CO2](0) = [CO2]o and thus, it does not reflect Ptot. Both Δc CO2 and surface pH diminish exponentially with time. Because intravesiclar pH changes and buffer effects are ignored, the time constant τ can only be used as a very rough indicator of Ptot: r (1 + 10 pH − pK ) Ptot = (66) 3·τ From an exponential fit to typical experimental traces (Figure 22), we find τ ∼ 40 s. Equation 66 returns Ptot ≈ 8.7 × 10−3 cm/s for oocytes with radius r = 0.5 mm. Ptot corresponds to CO2 diffusion across an aqueous layer of δUSL ∼ DCO2/PUSL = 23 μm. This is a clear underestimation because USLs in oocytes are usually ∼10 times T


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b. Cholesterol is known to affect both encapsulation efficiency and vesicle radius. Small cholesterol mediated variations in radius or carboanhydrase encapsulation efficiency would produce alterations in τ, which in turn may have been misinterpreted as cholesterol induced changes in Pm,CO2. c. The mathematical model that the authors use for calculating Pm,CO2 assumes constant buffer capacity. At the same time they calculate a drop from pH = 7.5 at the beginning of the experiment to pH = 7.0 at the end of the experiment. Clearly, the buffer capacity of the encapsulated HEPES molecules is pH dependent. This inconsistency must hamper the calculation of Pm,CO2, because τ depends on buffer capacity (Figure 15). We conclude that the stopped flow measurements did not produce evidence in favor of a cholesterol mediated reduction in Pm,CO2. 3. Plant aquaporins were reported to confer CO2 permeability to otherwise gastight triblock- copolymer membranes made from poly-2-methyloxazoline (PMOXA) and polydimethylsiloxane (PDMS).192 Several arguments speak against that conclusion: a. Functional reconstitution was never verified, and the methodology of film formation (codissolution of polymer and aquaporin in decane) seems suspect, as solvation of aquaporin in decane may result in formation of ion conducting pores.193 b. PDMS is a prototypical elastomeric or rubbery polymer. The latter commonly have relatively high gas permeabilities.194 Moreover, PDMS is used (i) as a membrane selective layer for separation of CO2/N2, with CO2 being more permeable,195 and (ii) as a CO2-permeable barrier in microfluidic devices to help regulate CO2 levels in cell culture.196 There is no reason to believe that PDMS as part of a PMOXA−PDMS−PMOXA triblock copolymer (in water) would have permeation properties that differ greatly from bulk PDMS. The second polymer constituent, PMOXA, has recently been reported to conduct solutes, in agreement with Overton’s rule.197 That is, the higher the partition coefficient in oil, the higher the PMOXA permeability. Taken together, the PMOXA− PDMS−PMOXA polymer should be perfectly permeable to CO2. c. It is thus unclear as to why two of the tested triblock copolymer films were found to be CO2 impermeable, while a third PMOXA−PDMS−PMOXA film was CO2 permeable.192 The permeable third film had the largest PDMS block, and thus, if anything, this film should be the least permeable due to the increased PDMS thickness. We conclude that the study192 cannot be taken as evidence for the CO2 channeling function of aquaporins. 9.5. Pm,CO2 from Scanning Electrochemical Microscopy

Figure 23. Scanning electrochemical microscopy reveals that cholesterol and sphingomyelin containing membranes do not represent a barrier to CO2 permeation. CO32− and HCO3− do not permeate the membrane as shown in the scheme on the top. Their conversion into to CO2 is catalyzed by carbonic anhydrase. It is accompanied by H+ release (CO2 donating compartment). The reverse reaction on the CO2 receiving side of the membrane consumes H+. Scanning pH microelectrodes serve to record the resulting pH changes in steady state. Representative pH values in the receiving compartment are shown (bottom) as a function of the distance to the membrane for (i) a pure DPhPC bilayer (green), (ii) a DPhPC bilayer tightened by cholesterol and sphingomyelin (pink), and (iii) a bilayer designed to mimic the red cell plasma membrane (orange). It was composed of egg phosphatidylcholine, egg phosphatidylethanolamine, brain phosphatidylserine, cholesterol, and egg sphingomyelin. The donating compartment contained 8 mM NaHCO3 and 3.2 mM Na2CO3. Both compartments enclosed 30 mM CAPSO, 66 mM NaCl (pH = 9.6). A mathematical model that takes into account all chemical reactions (including the reactions of the buffer molecules) revealed a lower limit for Pm,CO2 of 3.2 cm/s. Reproduced with permission from ref 14. Copyright 2008 American Society for Biochemistry and Molecular Biology.

We have employed scanning electrochemical microscopy to measure Pm,CO2.14 We validated the method many times by assessing the Pm to acetate,16 NH3,15 H2S,2 and ascorbic acid.24 In the presence of carbonic anhydrase, a transmembrane HCO3− gradient was imposed. The CO2 flux across the membrane resulted in an acidification in the near membrane unstirred layers of the receiving compartment. This acidification was measured by moving a pH-sensitive microelectrode perpendicular to the membrane.14 Bulk pH was augmented to 9.6 (Figure 23). In consequence, the HCO3− flux across the

unstirred layers was more than 1000-fold larger than the CO2 flux across the unstirred layer. Yet the HCO3− molecules that arrived at the membrane water interface were rapidly converted by carbonic anhydrase into CO2 and thus contributed to the transmembrane CO2 flux. This trick helped to diminish the unstirred layer effects and enabled determining a lower limit of Pm,CO2. It was equal to 3.2 cm/s for pure phosphatidylcholine membranes as well as for membranes containing cholesterol and sphingomyelin (Figure 23). U


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This lower limit is in perfect agreement with the prediction Pm,CO2 = 12 cm/s made by the solubility diffusion model (Figure 17). It is also in line with the results of molecular dynamics simulation that showed a much lower energy barrier for CO2 permeation through the pure lipid bilayer than through aquaporins.198 Although the central pore of some aquaporins appeared gas permeable, it provided only a very small crosssectional area. Replacement of the aquaporin tetramer for a lipid patch therefore augmented membrane permeability to CO2.198 Another simulation study came to the same result: Calculated potentials of mean force for solute permeation along aquaporin channels were 3−5-fold larger than for the alternative pathway across the lipid bilayer.199 The inability of lipid bilayers to form a barrier to CO2 is an apparent contrast to the existence of epithelial layers that may block CO2 diffusion. For example, the kidney excretes acidic urine, resulting in a partial CO2 pressure in the urine of PCO2 = 80−100 mmHg. It is thus 3−4-fold higher than blood PCO2.200−202 Yet the failure of CO2 to diffuse across the wall of the bladder is not due to a membrane barrier or a barrier provided by the dense uroplakin layer on top of the membrane.73 It must solely be attributed to the lack of carbonic anhydrase in the cells of the bladder wall. The observed dependence of PCO2 on carbonic anhydrase activity suggests that the tightness of biological membranes to CO2 may uniquely be regulated via carbonic anhydrase expression.73 We suspect that a report about CO2 tight epithelia203 was actually a report about primary cultured cells that accidentally lacked carbonic anhydrase. It is not uncommon for primary cells to lose some properties of their parent cells during cultivation. In line with these considerations this preparation of primary cultured cells was not tested for carbonic anhydrase activity.203 We conclude that CO2 membrane permeation is well described by the solubility diffusion model. It is not limited by a membrane barrier but by CO2 availability, which in turn is regulated by carbonic anhydrase.

(

z 2·F 2·Pm cion,c − cion,g ·exp − i = U· · z·F ·U RT 1 − exp − RT

(

i = U·

(70)

z 2·F 2·Pm ·cion RT

(71)

According to eq 71, i is proportional to the applied voltage, just as in Ohm’s law. Consequently, a constant specific membrane conductivity g = i/U may be expected: g=

z 2·F 2·Pm ·cion RT

(72)

Membrane conductivity measurements for various ions on planar lipid bilayers formed from a variety of different lipids (protons/hydroxide,207 Na+/Cl−,208 K+/Cl−,209 phenylated cations,210 organic anions25) show that the current−voltage characteristics of ion permeation are supralinear. Such peculiar dependence of current on voltage is due to the trapezoidal shape33,211 of the intrinsic electrical potential barrier that ions face in membranes (Figure 24). The main determinants specific to ion permeation are: • Self Solvation The transfer of an ion from one dielectric medium (water with permittivity εw ∼ 80) into another (membrane with permittivity εm ∼ 2) results in the following energetic penalty:212

1 (z ·e)2 ijj 1 1 yzz · ·jj − z εw zz{ 4π ·ε0 2·rion jk εm (73) where rion is the ionic radius, e is the elementary charge, and ε0 is the vacuum permittivity. The Born penalty is the same for similarly sized but oppositely charged molecules. In contrast, the corresponding permeabilities differ by orders of magnitude,213 suggesting a barrier component that is sensitive to the sign of the charge (dipole potential).214 • Image Energy A charged solute near the boundary between two mediums of different ϵ has a polarizing effect. The polarization of the distant medium can be represented by an image charge. The corresponding image energy (Figure 2) acts to lower the Born energy by roughly 10%.215 • Dipole Potential Φdipole This electrical potential is mainly generated by oriented water molecules and the polar carbonyl groups of ester bonds.216−218 The length of the acyl chains, i.e., the number of CH2 groups of the acyl chains provides a negligible contribution to membrane dipole potential in lipid bilayers.219 In general, it is positive inside the membrane,220 thereby favoring the partition of anions and disfavoring the partition of cations.221 • Surface Potential Φsurface A charged surface (characterized by an electrical potential Φsurface) attracts or repells cations and anions, respectively. This creates a double layer that compensates this surface charge. The application of the theories of Gouy,222 Chapman,223 and Stern224 to ion transport across lipid bilayers are well described ΔG Born =

(68)

In contrast to uncharged particles where no net flux occurs in absence of a concentration gradient, ions can be driven by an electrical field dΦ/dx originating from an electrical potential Φ. In a one-dimensional case, the Nernst−Plank equation expresses the current density for ions in a homogeneous medium: i dc F ·z dΦ yz zz · cm· i = −z ·F ·Dm ·jjj m + RT dx { k dx i dc F ·z dΦ yz zz = −z ·F ·Dm ·K p·jjj w + ·c w · RT dx { k dx

)

)

where cion,c and cion,g are aqueous solute concentrations. The indices g and c denote the command-electrode side and the ground-electrode side of the membrane, respectively. Pm = Kp· Dm/d is the permeability of the bilayer for the ion. For symmetrical concentrations (cion,c = cion,g = cion), eq 70 simplifies to

10. ION PERMEATION Because of their charged nature, the flux density J of an ion of valency z is related to electric current density i (eq 68, F is Faraday’s constant). i = z·F ·J

z·F ·U RT

(69)

where cm stands for the concentration inside the membrane. For a membrane in its simplest view as a single-slab, cm is linked to the concentration in the aqueous solution cion by the partition coefficient Kp. Assuming a linear drop of the applied voltage U across the membrane, one obtains the Goldman−Hodgkin− Katz flux equation.204−206 V


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ij z ·F ·Φ boundary yz zz K p ∝ expjjj− zz j RT k {

(74)

If a voltage U(Φext) is applied to a membrane, the initially symmetrically distributed ions (as depicted for anions in Figure 24) are driven across the membrane. The constant field approximation reveals, that the superposition of Φext and Φboundary results in a total potential that favors ion partition into the bilayer on one side and ion exit into the aqueous solution on the opposing side. In addition to the electrical field that drives the process, an ion concentration gradient builds up inside the membrane that also fuels permeation. The constant field approximation carries information about the shape of the trapezoidal barrier.227 The ratio of g in the presence of an applied voltage (g(U)) to g in absence of an applied voltage (g0, eq 72) is as follows:207,229

( z·F·U ) ( )

g (U ) b sinh 2·RT = · g0 d sinh b · z·F·U d 2·RT

Taylor at U = 0 ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ 1 +

z 2 · F 2 d 2 − b2 2 · ·U 24·R2·T 2 d2

+ O(U 4)

(75)

where b and d are the widths at top (inner barrier thickness) and the bottom (membrane thickness) of the trapezoidal barrier, respectively. The combination of eqs 71, 72, and 75, and yields j ≈ U· Figure 24. Electrical potential barriers of a charged lipid bilayer. Besides the self-solvation energy (Born energy), several membrane-intrinsic electrical potentials33,211 affect the permeation of an ion. At the interface of the bilayer, the surface potential (Φsurface) causes a thin layer of up-concentrated or diluted electrolytes, depending on the sign of their charge. Oriented water molecules and oriented carbonyl moieties of the lipids give rise to a positive dipole potential (Φdipole). Φdipole strongly favors anion (purple spheres) partitioning and disfavors cation membrane partitioning. The boundary potential Φboundary = Φsurface + Φdipole. The top panel shows symmetric electric potential profiles of trapezoidal shape (red line; base width d is the membrane thickness; b is the width of inner barrier). The lower panel shows the effect of an external potential (Φext). It drives anions toward the left side. Φext partly drops across the hydrocarbon core (yellow) and partly across the dipole potential region (brown). Φext adds to Φsurface and Φdipole, resulting in an asymmetric membrane potential profile. In turn, ion partitioning is altered. In addition to the field driving anions to the left, also a concentration gradient drives anions toward the left side. In consequence, anion flux is not linearly related to Φext but shows supralinearity in the form of a sinus hyperbolicus which can be Taylor expanded resulting in a third-power dependence.210,227,228

ij z 2·F 2·Pm z 2·F 2 d 2 − b2 2yzz ·cion·jjj1 + · ·U zz RT 24·R2·T 2 d2 k {

(76)

Thus, the supralinearity in eq 76 only depends on the geometric shape of the barrier. Eq 76 is time-independent. Application of a constant U should result in a steady current. However, in the (for ions) rare case that Pm ≫ PUSL or in case of slow partitioning into the bilayer, kinetically decaying currents are recorded (e.g., tetraphenylborate).27,230 Extracting Pm values from such measurements may be misleading. Nevertheless, membrane absorption and translocation of lipophilic ions can be separated in voltage jumpcurrent relaxation experiments.231 Even if the USL is not limiting, the permeation of hydrophobic ions can saturate at elevated ion concentrations.25,232 This behavior has been attributed to saturation at both interfaces, which is equivalent to complete occupancy of presumed interfacial binding sites at high concentrations.232 Transport from the donating interface to the receiving interface can only occur once the binding site at the receiving interface has been emptied. Consequently, ion desorption is rate limiting.232 If this interpretation was correct, a reduction of the central barrier to membrane ion transport, i.e., a drop of membrane dipole potential Φdipole, should remain without effect on membrane conductance. Yet, a Φdipole mediated increase of the transport rate of positively charged ions216 and a decrease of the transport rate of negatively charged ions233 was observed. This observation did not vanquish the hypothesis about a limited number of binding sites: A location of ion binding sites deep inside the membrane, and thus an effect of Φdipole on ion adsorption and desorption, appeared possible. Yet the replacement of ester bonds in phosphatidylcholine or phosphatidylethanolamine by ether bonds had little effect on

in papers by McLaughlin.225,226 For natural lipid mixtures, Φsurface is negative. The sum of Φsurface and Φdipole is called boundary potential Φboundary. The simplest model of ion permeation describes a three-step process: partition from the donating aqueous compartment onto the top of the trapezoidal barrier, transmembrane diffusion, partition from the top of the barrier into the receiving aqueous phase. The partition coefficient Kp is proportional to a term containing Φboundary (eq 11) via: W


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ion binding, although it decreases Φdipole by about ΔΦd = 100 mV.216 Perturbation of the dipolar layer of the membrane by the comparatively large hydrophobic ions may provide an alternative explanation of the saturation kinetics. That is, the hydrophobic ions are hypothesized to augment the energetic barrier that opposes their permeation in a concentration dependent fashion. Support for an ion induced augmentation of Φdipole is provided by a comparison of the ion translocation rates through membranes that exhibit 100 mV difference in their Φdipole: This ΔΦdipole yielded a much smaller effect than the expected 100-fold difference in membrane conductances.216 A clear demonstration that ions modulate their own permeability via Φdipole augmentation is not yet available. Thus far, only uncharged molecules are described to alter Φdipole upon permeating the membrane. Phloretin is a prominent example. It decreases Φdipole. The effect saturates at high phlorentin concentrations.234,235 Yet its interaction with the membrane cannot be described by a Langmuir adsorption isotherm alone, because phloretin alters lipid packing.236 In contrast to ions, the permeation of the uncharged phloretin across the membrane is not affected by the decrease in Φdipole. That is, the transmembrane phloretin flux does not saturate at higher phloretin concentrations.237 The view of a three-slab model with an oily core as determinant of ionic permeability is supported by the observation that Pm correlates with the hexadecane/water partition coefficient Kp. A large set of anions with Pm’s spanning 11 orders of magnitude has been tested and yielded very convincing linear relationship (Figure 25).25 The validity of the solubility diffusion model also extends to cations. Unfortunately, data that would support this supposition are scarce. The positive sign of Φdipole strongly disfavors partition of cations into the middle of the bilayer. The resulting low electrical conductivity renders cation permeability measurements very demanding. Recently the translocation of an organic cation with attached acyl chains across lipid bilayers was studied.239 The rate of translocation increased with the length of the hydrocarbon chain as it is expected from the increased solubility in the organic phase. The authors explained their results by assuming that the more hydrophobic molecules adopted a different orientation as compared to the more hydrophilic derivatives and that this new orientation facilitated the flip-flop across lipid bilayer. They used such a complicated explanation because they assumed an invariant adsorption plane for all derivatives, i.e., a position of the positive charge that does not depend on the length of the acyl chain. This assumption does not seem to be very plausible: The energy of hydrophobic interactions scales with the surface area of the acyl chain,240 while the Born energy that counteracts the movement of the molecule into the membrane stays invariant. Thus, it appears possible that the more hydrophobic cations partitioned both in greater numbers and deeper into the bilayer due to the increment in hydrophobic interaction energy. This view is in line with the recently found dependence of the pKa value of free fatty acids on both length and unsaturation of their acyl chains.241 Being tagged deeper into the lipid bilayer the more hydrophobic free fatty acids displayed a higher shift toward basic pKa values and a lower tendency toward dissociation. In conclusion, both anion and cation permeations obey the solubility diffusion model. In contrast to neutral substances, ion permeation depends not only on concentration gradients (Fick’s law) but also on applied voltages (Nernst−Plank equation). If

Figure 25. Solubility diffusion model works also for anions. Pm was determined from membrane conductivity measurements and revealed a correlation of log(Pm) = 0.6(±0.05)·log(Kp) + 4.8(±0.9) (gray line; RSME = 0.74(18), r = 0.95). The blue triangles denote substances for which only upper limits of Pm were accessible. The hexadecane/water partition coefficients Kp were computed according to the “Conductorlike Screening Model for Realistic Solvation” (COSMO-RS) theory.238 The compounds listed with increasing Kp are (for substance that are weak acids or bases as, e.g., salicylic acid, the anion is actually the deprotonated species): anthracene-9-carboxylic acid, 9,10-dimethoxyanthracene-2-sulfonate, salicylic acid, sulcotrione, 4-octylbenzenesulfonate, diclofenac, 4-Np, 3,5-Dcp, flufenamic acid, warfarin, 2,4-Dnp, bromol, 3,4-Dnp, 4-nitro-2-(trifluoromethyl)-1H-benzimidazole, coumachlor, triclosan, bromoxynil, dinoseb, PCP, dino2terb, bis(fluorosulfonyl)azanide, 6-OH-BDE47, CCCP, and TPB. Plotted data are from Ebert et al.25

the permeation is fast, USL limitations can occur. As a result the current−voltage characteristics deviate from eq 76. 10.1. Proton/Hydroxide Permeation

The membrane permeability to protons seems to be the only accepted exception from Overton’s rule. At neutral pH values the membrane proton permeability coefficient Pm,H+ ranges between 10−6 - 10−5 cm/s for both vesicular and planar bilayer systems.242 Pm,H+ is orders of magnitude larger than the predictions made on the basis of the partition coefficient. A Born energy of ∼108 kBT can be calculated for a hydronium ion.215 The potassium ion has a comparable size and thus a comparable Born energy, yet its permeability is 6−7 orders of magnitude smaller. The second peculiarity of proton flux is its surprising independence on pH, i.e., proton flux changes no more than 10-fold when pH increases from near 1 to 11.157,243−245 As a result, Pm,H+ depends on pH. Two hypotheses have been put forward to explain these two anomalous observations, but neither one allows a satisfactory quantitative description of the high pH-dependent Pm,H+ values. Because both theories have been extensively reviewed (e.g., refs 246,247), we restrict ourselves to a very short summary of the major points. (i) The first hypothesis states that weak acids/bases generate the unusually large permeability. They are present in membranes as contaminants,207 e.g., fatty acids that may be generated by lipid hydrolysis. Even if the deprotonated weak acid would initially reside in both monolayers at equal concentrations, membrane voltage would lead to an X


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three slab model in which the additional two new slabs regulate the access to the “old” inner slab. Addition of (i) cholesterol to the bilayer or (ii) charges to the permeant requires a multislab model in which partition changes continuously from the membrane water interface to the membrane center. That is, local partition coefficients are necessary to capture alterations of Pm due to (i) geometrical constrains, i.e., altered packing in the acyl chain area and (ii) intrinsic electric membrane potentials. Such a multislab model is well capable of describing membrane translocation of volatile molecules, hydrophobic as well as hydrophilic substances, and anions as well as cations.

accumulation of these anions at one interface. Some of the anions would then pick up a proton and the acid would move along the concentration gradient of the uncharged form across the membrane. Subsequently, the anion is driven back by the membrane potential. Thus, instead of the positive charge of the proton, a negative charge moves across the membrane. The view is supported by the observation that a phloretin induced decrease of membrane dipole potential significantly reduces the measured electric conductance.246 If a positively charged substance (e.g., H3O+) was permeating the membrane, the conductance should have increased. However, at low pH, a significant residual H+/OH− conductance remains that is not explained by the model because at pH ≪ pK, all acid is protonated and does not yield charge carrying anions.246

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. ORCID

(ii) The inability of the weak acid model to explain the largely pH independent proton flux in its entirety promoted the development of a second model. It involves transient hydrogen-bonded chains of water.248 These water wires serve as railways for protons that cross the bilayer according to Grotthus’ mechanism.249 To explain the pH independence of such structural diffusion, three different hypotheses were discussed:248 (a) The turning defect in the water wire is rate limiting. That is, the water molecules are thought to reorient after having conducted a proton and the rate of this reorientation is limited by the probability of breaking hydrogen bonds between neutral water molecules. (b) The water wires are too unstable to conduct more than one proton. The pH independent probability of forming the wires limits proton conductance. (c) The water wires span only one monolayer. Thus, two wires are required for conductance. The first wire is conducting H+ across one leaflet, the second wire is conducting OH− across the opposing monolayer. Electrostatic attraction is thought to increase the otherwise minute probability of H+ and OH− encounter.250 Two important observations argue against the transient hydrogen bonded chain model: (1) The likelihood of water wires formation must increase if bilayer water permeability increases. However, no such correlation was found.251 (2) The probability of forming a membrane spanning wire of hydrogen bonded water molecules is extremely low. It requires to overcome a 108 kJ/mol high energy barrier.252 Moreover, the lifetime of a water wire in the lipid bilayer is in the order of 0.01 ns253 or shorter.253 For comparison, a water molecule requires about 1 ns to cross highly conductive single file water channels.95 Even if we assume that, similar to water molecules in aquaporins, the protons retain bulk mobility while moving along a transient membrane spanning water file, they would require at least 0.4 ns to cross the membrane. It is thus unlikely the transient water wires may quantitatively explain the experimentally observed proton transport.

Peter Pohl: 0000-0002-1792-2314 Notes

The authors declare no competing financial interest. Biographies Christof Hannesschlaeger received his diploma in technical physics (specialization on biophysics) from the Johannes Kepler University (JKU) Linz in 2013. The topics of his doctoral research in the group of Prof. Peter Pohl covered different fields of membrane permeation ranging from acid flux into vesicles under the influence of buffering agents to self-inhibition effects accompanying the membrane permeation of a certain ionic liquid. He was awarded with a Ph.D. in 2017 and continues his work as university assistant at the JKU with special interest in the quantification of the permeability via various experimental approaches. Andreas Horner received both his diploma in technical physics (specialization on biophysics) in 2007 and his Ph.D. in 2012 from the Johannes Kepler University (JKU) Linz (Austria). Under the supervision of Prof. Peter Pohl at the Institute of Biophysics, he studied binding of peptides and proteins to artificial lipid membranes and its accompanying membrane cluster formation with special emphasis on interleaflet coupling. He was a visiting research scientist at the lab of Prof. Francisco Bezanilla at the Department of Biochemistry at the University of Chicago for 7 months in 2007. Since 2013, he has been working as an assistant professor at the JKU Linz, where he is establishing his own research group. His research is focused on finding determinants for water and solute transport through narrow transmembrane channels and transporters. His group uses artificial lipid bilayer systems with reconstituted membrane proteins to quantify membrane and protein permeabilities. Prof. Dr. Peter Pohl obtained his diploma in Biophysics at the Piragov Institute Moscow in 1989 and his M.D. at the Martin Luther University Halle (Saale) in 1994. After having completed his habilitation in 2001, he joined the Leibniz Institute of Molecular Pharmacology in Berlin as Heisenberg fellow of the Deutsche Forschungsgemeinschaft. He then became guest professor at the Institute of Biology of the Humboldt University Berlin in 2002−2003 and was appointed full Professor of Biophysics in 2004 at the Physics Department of the Johannes Kepler University Linz. His research focuses on (i) spontaneous and facilitated membrane transport of water and other small molecules in reconstituted systems, (ii) proton migration along membranes, (iii) protein translocation through membranes, and (iv) the coupling of membrane leaflets.

11. CONCLUSION Membrane transport is governed by a queue of partition processes. In the simplest case, it is sufficient to regard the partition from the aqueous environment into a bulk organic phase to predict Pm with an error that in most cases does not exceed 1 order of magnitude. Capturing effects of (i) the permeant’s size or (ii) lipid composition on Pm already requires a Y


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ACKNOWLEDGMENTS

kb Kp krd k+w L LUV NA PA PAB PB pc Pd Pf Pm Pm+c ps R rion rves S SP T Tdiff

We thank Mark Zeidel and John C. Mathai for critically reading the manuscript.

ABBREVIATIONS [A‑] conjugated base concentration [A]tot total acid concentration [AH] acid concentration [B]tot total base concentration μ chemical potential μ′ total chemical/electrochemical potential μo standard chemical potential A temperature independent constant in Arrhenius Law A− conjugated base to the acid AH acid AIDH alcohol dehydrogenase ast stirring parameter Aves surface area of the vesicle Ah surface area of a hemisphere (same radius as Ap) Ap surface area of a pore containing protein in the membrane b the top width of the trapezoidal electric potential barrier B base BH+ conjugated acid to the base cin,0 initial osmolyte concentration inside the vesicle (osmolarity) cm concentration inside the membrane cout osmolyte concentration outnside the vesicle (osmolarity) cs surface concentration in aqueous solution csol solute concentration cw concentration of water d membrane thickness Dm diffusion coefficient in membrane Dsol solute diffusion coefficient e elementary charge EA activation energy f area fraction of a membrane that is devoid of channels F Faraday’s constant G Gibbs free energy g specific membrane conductivity g̅ electrical single channel conductivity g(U) specific membrane conductivity in the presence of an applied voltage G0 standard Gibbs free energy g0 specific membrane conductivity in the absence of an applied voltage GD Gibbs free energy barrier for diffusion GP Gibbs free energy barrier for permeation GUV giant unilamellar vesicle H enthalpy HP enthalpy of permeation I scattered light intensity i electric current density I0 scattered light intensity at time zero J flux density J̅ flux Jm transmembrane flux k− deprotonation rate k+ protonation rate Ka acid dissociation constant

tH2O+ t+ U USL V v′ V0 vH2O Vw W x z β δ ε0 εm εw λ τ+ τd τf τvs Φ Φboundary Φdipole Φext Φsurface

Boltzmann constant partition coefficient C18O16O depletion rate rate of water self-dissociation Lambert function large unilamellar vesicle Avogadro’s constant water permeability of symmetric lipid bilayer of lipid A water permeability of asymmetric lipid bilayer water permeability of symmetric lipid bilayer of lipid B single channel permeability diffusional membrane water permeability osmotic membrane water permeability membrane permeability permeability of a channel containing membrane pore access permeability universal gas constant ionic radius vesicle radius entropy entropy of permeation absolute temperature time, it requires a particle to diffuse from the membrane of a particle toward the vesicle center time that passes between two water self-dissociation events inside a vesicle time that passes between two deprotonation events of a weak acid inside a vesicle voltage applied across the membrane unstirred layer vesicle volume linear solvent velocity vesicle volume at time zero linear transmembrane volume flux molar volume of water work distance to membrane valence of ion buffer capacity USL thickness vacuum permittivity permittivity of lipid membrane permittivity of water distance between two equilibrium positions time constant of deprotonation exponential rate constant of fluorescence response due to passive D2O diffusional exponential rate constant of osmotically induced vesicle shrinkage exponential rate of osmotically induced vesicle shrinkage electrical potential boundary potential dipole potential externally applied potential equal to U surface potential

REFERENCES (1) Klocke, R. A. Velocity of CO2 Exchange in Blood. Annu. Rev. Physiol. 1988, 50, 625−637. (2) Mathai, J. C.; Missner, A.; Kugler, P.; Saparov, S. M.; Zeidel, M. L.; Lee, J. K.; Pohl, P. No Facilitator Required for Membrane Transport of Z


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Review

Hydrogen Sulfide. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 16633− 16638. (3) Paul, B. D.; Snyder, S. H. H2s Signalling through Protein Sulfhydration and Beyond. Nat. Rev. Mol. Cell Biol. 2012, 13, 499−507. (4) Sugano, K.; Kansy, M.; Artursson, P.; Avdeef, A.; Bendels, S.; Di, L.; Ecker, G. F.; Faller, B.; Fischer, H.; Gerebtzoff, G.; et al. Coexistence of Passive and Carrier-Mediated Processes in Drug Transport. Nat. Rev. Drug Discovery 2010, 9, 597. (5) Smith, D.; Artursson, P.; Avdeef, A.; Di, L.; Ecker, G. F.; Faller, B.; Houston, J. B.; Kansy, M.; Kerns, E. H.; Kramer, S. D.; et al. Passive Lipoidal Diffusion and Carrier-Mediated Cell Uptake Are Both Important Mechanisms of Membrane Permeation in Drug Disposition. Mol. Pharmaceutics 2014, 11, 1727−1738. (6) Kell, D. B.; Dobson, P. D.; Oliver, S. G. Pharmaceutical Drug Transport: The Issues and the Implications That It Is Essentially Carrier-Mediated Only. Drug Discovery Today 2011, 16, 704−714. (7) Dobson, P. D.; Kell, D. B. Carrier-Mediated Cellular Uptake of Pharmaceutical Drugs: An Exception or the Rule? Nat. Rev. Drug Discovery 2008, 7, 205−220. (8) Boron, W. F. Sharpey-Schafer Lecture: Gas Channels. Exp. Physiol. 2010, 95, 1107−1130. (9) Saparov, S. M.; Antonenko, Y. N.; Pohl, P. A New Model of Weak Acid Permeation through Membranes Revisited: Does Overton Still Rule? Biophys. J. 2006, 90, L86−88. (10) Missner, A.; Kugler, P.; Antonenko, Y. N.; Pohl, P. Passive Transport across Bilayer Lipid Membranes: Overton Continues to Rule. Proc. Natl. Acad. Sci. U. S. A. 2008, 105, No. E123, author reply E124 . (11) Missner, A.; Pohl, P. 110 Years of the Meyer-Overton Rule: Predicting Membrane Permeability of Gases and Other Small Compounds. ChemPhysChem 2009, 10, 1405−1414. (12) Di, L.; Artursson, P.; Avdeef, A.; Ecker, G. F.; Faller, B.; Fischer, H.; Houston, J. B.; Kansy, M.; Kerns, E. H.; et al. Evidence-Based Approach to Assess Passive Diffusion and Carrier-Mediated Drug Transport. Drug Discovery Today 2012, 17, 905−912. (13) Saparov, S. M.; Pfeifer, J. R.; Al-Momani, L.; Portella, G.; de Groot, B. L.; Koert, U.; Pohl, P. Mobility of a One-Dimensional Confined File of Water Molecules as a Function of File Length. Phys. Rev. Lett. 2006, 96, 148101. (14) Missner, A.; Kugler, P.; Saparov, S. M.; Sommer, K.; Mathai, J. C.; Zeidel, M. L.; Pohl, P. Carbon Dioxide Transport through Membranes. J. Biol. Chem. 2008, 283, 25340−25347. (15) Antonenko, Y. N.; Pohl, P.; Denisov, G. A. Permeation of Ammonia across Bilayer Lipid Membranes Studied by Ammonium Ion Selective Microelectrodes. Biophys. J. 1997, 72, 2187−2195. (16) Antonenko, Y. N.; Denisov, G. A.; Pohl, P. Weak Acid Transport across Bilayer Lipid Membrane in the Presence of Buffers. Theoretical and Experimental pH Profiles in the Unstirred Layers. Biophys. J. 1993, 64, 1701−1710. (17) Pohl, P.; Saparov, S. M.; Antonenko, Y. N. The Effect of a Transmembrane Osmotic Flux on the Ion Concentration Distribution in the Immediate Membrane Vicinity Measured by Microelectrodes. Biophys. J. 1997, 72, 1711−1718. (18) Lippe, C.; Gallucci, E.; Storelli, C. Permeabilities of Ethylene Glycol and Glycerol through Lipid Bilayer Membranes and Some Epithelia. Arch. Int. Physiol. Biochim. 1971, 79, 315−318. (19) Finkelstein, A. Water and Nonelectrolyte Permeability of Lipid Bilayer Membranes. J. Gen. Physiol. 1976, 68, 127−135. (20) Missner, A.; Horner, A.; Pohl, P. Cholesterol’s Decoupling Effect on Membrane Partitioning and Permeability Revisited: Is There Anything Beyond Fick’s Law of Diffusion? Biochim. Biophys. Acta, Biomembr. 2008, 1778, 2154−2156. (21) Zocher, F.; van der Spoel, D.; Pohl, P.; Hub, J. S. Local Partition Coefficients Govern Solute Permeability of Cholesterol-Containing Membranes. Biophys. J. 2013, 105, 2760−2770. (22) Orbach, E.; Finkelstein, A. The Nonelectrolyte Permeability of Planar Lipid Bilayer Membranes. J. Gen. Physiol. 1980, 75, 427−436.

(23) Wood, R. E.; Wirth, F. P., Jr.; Morgan, H. E. Glucose Permeability of Lipid Bilayer Membranes. Biochim. Biophys. Acta, Biomembr. 1968, 163, 171−178. (24) Hannesschlaeger, C.; Pohl, P. Membrane Permeabilities of Ascorbic Acid and Ascorbate. Biomolecules 2018, 8, 73. (25) Ebert, A.; Hannesschlaeger, C.; Goss, K. U.; Pohl, P. Passive Permeability of Planar Lipid Bilayers to Organic Anions. Biophys. J. 2018, 115, 1931−1941. (26) Hauser, H.; Oldani, D.; Phillips, M. C. Mechanism of Ion Escape from Phosphatidylcholine and Phosphatidylserine Single Bilayer Vesicles. Biochemistry 1973, 12, 4507−4517. (27) Pickar, A. D.; Benz, R. Transport of Oppositely Charged Lipophilic Probe Ions in Lipid Bilayer Membranes Having Various Structures. J. Membr. Biol. 1978, 44, 353−376. (28) Papahadjopoulos, D.; Nir, S.; Ohki, S. Permeability Properties of Phospholipid Membranes: Effect of Cholesterol and Temperature. Biochim. Biophys. Acta, Biomembr. 1972, 266, 561−583. (29) Fromherz, P.; Röcker, C.; Rüppel, D. From Discoid Micelles to Spherical Vesicles. The Concept of Edge Activity. Faraday Discuss. Chem. Soc. 1986, 81, 39−48. (30) Eliaz, N.; Banks-Sills, L. Chemical Potential, Diffusion and Stress - Common Confusions in Nomenclature and Units. Corros. Rev. 2008, 26, 87−103. (31) Crank, J. The Mathematics of Diffusion, 2nd ed.; Clarendon Press: Oxford, UK, 1975. (32) Han, G. Z.; Wang, H. J. Generalized Expression of Chemical Potential with Influence of External Fields and Its Applications: Effect of Charged Particles on Droplet Condensation. Fluid Phase Equilib. 2013, 338, 269−273. (33) Flewelling, R. F.; Hubbell, W. L. The Membrane Dipole Potential in a Total Membrane Potential Model. Applications to Hydrophobic Ion Interactions with Membranes. Biophys. J. 1986, 49, 541−552. (34) Mannhold, R.; Poda, G. I.; Ostermann, C.; Tetko, I. V. Calculation of Molecular Lipophilicity: State-of-the-Art and Comparison of Logp Methods on More Than 96,000 Compounds. J. Pharm. Sci. 2009, 98, 861−893. (35) Collander, R.; Lindholm, M.; Haug, C. M.; Stene, J.; Sörensen, N. A. The Partition of Organic Compounds between Higher Alcohols and Water. Acta Chem. Scand. 1951, 5, 774−780. (36) Dallas, A. J.; Carr, P. W. A Thermodynamic and Solvatochromic Investigation of the Effect of Water on the Phase-Transfer Properties of Octan-1-Ol. J. Chem. Soc., Perkin Trans. 2 1992, 2155. (37) Toulmin, A.; Wood, J. M.; Kenny, P. W. Toward Prediction of Alkane/Water Partition Coefficients. J. Med. Chem. 2008, 51, 3720− 3730. (38) Ermondi, G.; Visconti, A.; Esposito, R.; Caron, G. The Block Relevance (Br) Analysis Supports the Dominating Effect of Solutes Hydrogen Bond Acidity on Δlogpoct−Tol. Eur. J. Pharm. Sci. 2014, 53, 50−54. (39) Burton, P. S.; Conradi, R. A.; Hilgers, A. R. (B) Mechanisms of Peptide and Protein Absorption: (2) Transcellular Mechanism of Peptide and Protein Absorption: Passive Aspects. Adv. Drug Delivery Rev. 1991, 7, 365−385. (40) Stein, W. D. The Molecular Basis of Diffusion across Cell Membranes. In The Movement of Molecules across Cell Membranes; Academic Press: New York, 1967; pp 65−125. (41) De Gier, J.; Mandersloot, J. G.; Hupkes, J. V.; McElhaney, R. N.; Van Beek, W. P. On the Mechanism of Non-Electrolyte Permeation through Lipid Bilayers and through Biomembranes. Biochim. Biophys. Acta, Biomembr. 1971, 233, 610−618. (42) Cohen, B. E. The Permeability of Liposomes to Nonelectrolytes. J. Membr. Biol. 1975, 20, 205−234. (43) Mayer, P. T.; Xiang, T. X.; Niemi, R.; Anderson, B. D. A Hydrophobicity Scale for the Lipid Bilayer Barrier Domain from Peptide Permeabilities: Nonadditivities in Residue Contributions. Biochemistry 2003, 42, 1624−1636. (44) Mayer, P. T.; Anderson, B. D. Transport across 1,9-Decadiene Precisely Mimics the Chemical Selectivity of the Barrier Domain in Egg Lecithin Bilayers. J. Pharm. Sci. 2002, 91, 640−646. AA


Chemical Reviews

Review

(67) Pedley, T. J.; Fischbarg, J. The Development of Osmotic Flow through an Unstirred Layer. J. Theor. Biol. 1978, 70, 427−447. (68) Pohl, P.; Saparov, S. M.; Antonenko, Y. N. The Size of the Unstirred Layer as a Function of the Solute Diffusion Coefficient. Biophys. J. 1998, 75, 1403−1409. (69) Pedley, T. J. Calculation of Unstirred Layer Thickness in Membrane Transport Experiments: A Survey. Q. Rev. Biophys. 1983, 16, 115−150. (70) Gutknecht, J.; Tosteson, D. C. Diffusion of Weak Acids across Lipid Bilayer Membranes: Effects of Chemical Reactions in the Unstirred Layers. Science 1973, 182, 1258−1261. (71) Antonenko, Y. N.; Yaguzhinsky, L. S. The Role of pH Gradient in the Unstirred Layers in the Transport of Weak Acids and Bases through Bilayer Lipid Membranes. Bioelectrochem. Bioenerg. 1984, 13, 85−91. (72) Gutknecht, J.; Bisson, M. A.; Tosteson, D. C. Diffusion of Carbon Dioxide through Lipid Bilayer Membranes. Effects of Carbonic Anhydrase, Bicarbonate and Ustirred Layers. J. Gen. Physiol. 1977, 69, 779−794. (73) Zocher, F.; Zeidel, M. L.; Missner, A.; Sun, T. T.; Zhou, G.; Liao, Y.; von Bodungen, M.; Hill, W. G.; Meyers, S.; et al. Uroplakins Do Not Restrict CO2 Transport through Urothelium. J. Biol. Chem. 2012, 287, 11011−11017. (74) Antonenko, Y. N.; Pohl, P. Steady-State Nonmonotonic Concentration Profiles in the Unstirred Layers of Bilayer Lipid Membranes. Biochim. Biophys. Acta, Biomembr. 1995, 1235, 57−61. (75) Antonenko, Y. N.; Pohl, P.; Rosenfeld, E. H. Visualization of the Reaction Layer in the Immediate Membrane Vicinity. Arch. Biochem. Biophys. 1996, 333, 225−232. (76) Bellissent-Funel, M.-C.; Hassanali, A.; Havenith, M.; Henchman, R.; Pohl, P.; Sterpone, F.; van der Spoel, D.; Xu, Y.; Garcia, A. E. Water Determines the Structure and Dynamics of Proteins. Chem. Rev. 2016, 116, 7673−7697. (77) Lande, M. B.; Donovan, J. M.; Zeidel, M. L. The Relationship between Membrane Fluidity and Permeabilities to Water, Solutes, Ammonia, and Protons. J. Gen. Physiol. 1995, 106, 67−84. (78) Fettiplace, R. The Influence of the Lipid on the Water Permeability of Artificial Membranes. Biochim. Biophys. Acta, Biomembr. 1978, 513, 1−10. (79) Huster, D.; Jin, A. J.; Arnold, K.; Gawrisch, K. Water Permeability of Polyunsaturated Lipid Membranes Measured by O17 NMR. Biophys. J. 1997, 73, 855−864. (80) Olbrich, K.; Rawicz, W.; Needham, D.; Evans, E. Water Permeability and Mechanical Strength of Polyunsaturated Lipid Bilayers. Biophys. J. 2000, 79, 321−327. (81) Fettiplace, R.; Haydon, D. A. Water Permeability of Lipid Membranes. Physiol. Rev. 1980, 60, 510−550. (82) Jansen, M.; Blume, A. A Comparative Study of Diffusive and Osmotic Water Permeation across Bilayers Composed of Phospholipids with Different Head Groups and Fatty Acyl Chains. Biophys. J. 1995, 68, 997−1008. (83) Blok, M. C.; van Deenen, L. L.; De Gier, J. Effect of the Gel to Liquid Crystalline Phase Transition on the Osmotic Behaviour of Phosphatidylcholine Liposomes. Biochim. Biophys. Acta, Biomembr. 1976, 433, 1−12. (84) Carruthers, A.; Melchior, D. L. Study of the Relationship between Bilayer Water Permeability and Bilayer Physical State. Biochemistry 1983, 22, 5797−5807. (85) Slotte, J. P. The Importance of Hydrogen Bonding in Sphingomyelin’s Membrane Interactions with Co-Lipids. Biochim. Biophys. Acta, Biomembr. 2016, 1858, 304−310. (86) Smaby, J. M.; Momsen, M.; Kulkarni, V. S.; Brown, R. E. Cholesterol-Induced Interfacial Area Condensations of Galactosylceramides and Sphingomyelins with Identical Acyl Chains. Biochemistry 1996, 35, 5696−5704. (87) Krylov, A. V.; Pohl, P.; Zeidel, M. L.; Hill, W. G. Water Permeability of Asymmetric Planar Lipid Bilayers: Leaflets of Different Composition Offer Independent and Additive Resistances to Permeation. J. Gen. Physiol. 2001, 118, 333−340.

(45) Abraham, M. H. Scales of Solute Hydrogen-Bonding: Their Construction and Application to Physicochemical and Biochemical Processes. Chem. Soc. Rev. 1993, 22, 73−83. (46) Abraham, M. H. Hydrogen-Bonding 0.31. Construction of a Scale of Solute Effective or Summation Hydrogen-Bond Basicity. J. Phys. Org. Chem. 1993, 6, 660−684. (47) Abraham, M. H.; Ibrahim, A.; Zissimos, A. M.; Zhao, Y. H.; Comer, J.; Reynolds, D. P. Application of Hydrogen Bonding Calculations in Property Based Drug Design. Drug Discovery Today 2002, 7, 1056−1063. (48) Conradi, R.; Hilgers, A.; Burton, P.; Hester, J. Epithelial Cell Permeability of a Series of Peptidic Hiv Protease Inhibitors: Aminoterminal Substituent Effects. J. Drug Targeting 1994, 2, 167−171. (49) Over, B.; McCarren, P.; Artursson, P.; Foley, M.; Giordanetto, F.; Grönberg, G.; Hilgendorf, C.; Lee, M. D.; Matsson, P.; et al. Impact of Stereospecific Intramolecular Hydrogen Bonding on Cell Permeability and Physicochemical Properties. J. Med. Chem. 2014, 57, 2746−2754. (50) Alex, A.; Millan, D. S.; Perez, M.; Wakenhut, F.; Whitlock, G. A. Intramolecular Hydrogen Bonding to Improve Membrane Permeability and Absorption in Beyond Rule of Five Chemical Space. MedChemComm 2011, 2, 669. (51) Epshtein, L. M. Hydrogen Bonds and the Reactivity of Organic Compounds in Proton Transfer and Nucleophilic Substitution Reactions. Russ. Chem. Rev. 1979, 48, 854. (52) Joesten, M. D. Hydrogen-Bonding and Proton-Transfer. J. Chem. Educ. 1982, 59, 362−366. (53) Abraham, M. H.; Chadha, H. S.; Whiting, G. S.; Mitchell, R. C. Hydrogen Bonding. 32. An Analysis of Water-Octanol and WaterAlkane Partitioning and the Delta Log P Parameter of Seiler. J. Pharm. Sci. 1994, 83, 1085−1100. (54) Abraham, M. H.; Platts, J. A. Hydrogen Bond Structural Group Constants. J. Org. Chem. 2001, 66, 3484−3491. (55) Hill, W. G.; Zeidel, M. L. Reconstituting the Barrier Properties of a Water-Tight Epithelial Membrane by Design of Leaflet-Specific Liposomes. J. Biol. Chem. 2000, 275, 30176−30185. (56) Mathai, J. C.; Sprott, G. D.; Zeidel, M. L. Molecular Mechanisms of Water and Solute Transport across Archaebacterial Lipid Membranes. J. Biol. Chem. 2001, 276, 27266−27271. (57) Nagle, J. F.; Mathai, J. C.; Zeidel, M. L.; Tristram-Nagle, S. Theory of Passive Permeability through Lipid Bilayers. J. Gen. Physiol. 2008, 131, 77−85. (58) Zwolinski, B. J.; Eyring, H.; Reese, C. E. Diffusion and Membrane Permeability. J. Phys. Colloid Chem. 1949, 53, 1426−1453. (59) Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rate Processes; the Kinetics of Chemical Reactions, Viscosity, Diffusion and Electrochemical Phenomena, 1st ed.; McGraw-Hill: New York, London, 1941. (60) Hannesschlager, C.; Barta, T.; Siligan, C.; Horner, A. Quantification of Water Flux in Vesicular Systems. Sci. Rep. 2018, 8, 8516. (61) Tunuguntla, R. H.; Henley, R. Y.; Yao, Y. C.; Pham, T. A.; Wanunu, M.; Noy, A. Enhanced Water Permeability and Tunable Ion Selectivity in Subnanometer Carbon Nanotube Porins. Science 2017, 357, 792−796. (62) Horner, A.; Pohl, P. Comment on ″Enhanced Water Permeability and Tunable Ion Selectivity in Subnanometer Carbon Nanotube Porins. Science 2018, 359, eaap9173. (63) Wang, J. H.; Robinson, C. V.; Edelman, I. S. Self-Diffusion and Structure of Liquid Water 0.3. Measurement of the Self-Diffusion of Liquid Water with H-2, H-3, and O-18 as Tracers. J. Am. Chem. Soc. 1953, 75, 466−470. (64) Barry, P. H.; Diamond, J. M. Effects of Unstirred Layers on Membrane Phenomena. Physiol. Rev. 1984, 64, 763−872. (65) Laage, D.; Elsaesser, T.; Hynes, J. T. Water Dynamics in the Hydration Shells of Biomolecules. Chem. Rev. 2017, 117, 10694− 10725. (66) Dainty, J.; House, C. R. Unstirred Layers in Frog Skin. J. Physiol. (Oxford, U. K.) 1966, 182, 66−78. AB


Chemical Reviews

Review

(88) Xiang, T. X.; Anderson, B. D. Permeability of Acetic Acid across Gel and Liquid-Crystalline Lipid Bilayers Conforms to Free-SurfaceArea Theory. Biophys. J. 1997, 72, 223−237. (89) Paula, S.; Volkov, A. G.; Deamer, D. W. Permeation of Halide Anions through Phospholipid Bilayers Occurs by the SolubilityDiffusion Mechanism. Biophys. J. 1998, 74, 319−327. (90) Deamer, D. W.; Bramhall, J. Permeability of Lipid Bilayers to Water and Ionic Solutes. Chem. Phys. Lipids 1986, 40, 167−188. (91) Lawaczeck, R.; Pitterich, H. Pathways of Water through Erythrocyte Membranes. Routes Along Defect Structures. J. Theor. Biol. 1988, 135, 401−407. (92) Agmon, N.; Bakker, H. J.; Campen, R. K.; Henchman, R. H.; Pohl, P.; Roke, S.; Thämer, M.; Hassanali, A. Protons and Hydroxide Ions in Aqueous Systems. Chem. Rev. 2016, 116, 7642−7672. (93) Nagle, J. F.; Morowitz, H. Molecular Mechanisms for Proton Transport in Membranes. Proc. Natl. Acad. Sci. U. S. A. 1978, 75, 298− 302. (94) Paula, S.; Volkov, A. G.; Vanhoek, A. N.; Haines, T. H.; Deamer, D. W. Permeation of Protons, Potassium Ions, and Small Polar Molecules through Phospholipid Bilayers as a Function of Membrane Thickness. Biophys. J. 1996, 70, 339−348. (95) Horner, A.; Pohl, P. Single-File Transport of Water through Membrane Channels. Faraday Discuss. 2018, 209, 9−33. (96) Walter, A.; Gutknecht, J. Permeabilities of Small Neonelectrolytes through Lipid Bilayer Membranes. J. Membr. Biol. 1986, 90, 207−217. (97) Blok, M. C.; Van Der Neut-Kok, E. C. M.; Van Deenen, L. L. M.; De Gier, J. The Effect of Chain Length and Lipid Phase Transitions on the Selective Permeability Properties of Liposomes. Biochim. Biophys. Acta, Biomembr. 1975, 406, 187−196. (98) Antonov, V. F.; Petrov, V. V.; Molnar, A. A.; Predvoditelev, D. A.; Ivanov, A. S. The Appearance of Single-Ion Channels in Unmodified Lipid Bilayer Membranes at the Phase Transition Temperature. Nature 1980, 283, 585−586. (99) Papahadjopoulos, D.; Cowden, M.; Kimelberg, H. Role of Cholesterol in Membranes Effects on Phospholipid-Protein Interactions, Membrane Permeability and Enzymatic Activity. Biochim. Biophys. Acta, Biomembr. 1973, 330, 8−26. (100) Nicholls, P.; Miller, N. Chloride Diffusion from Liposomes. Biochim. Biophys. Acta, Biomembr. 1974, 356, 184−198. (101) Blicher, A.; Wodzinska, K.; Fidorra, M.; Winterhalter, M.; Heimburg, T. The Temperature Dependence of Lipid Membrane Permeability, Its Quantized Nature, and the Influence of Anesthetics. Biophys. J. 2009, 96, 4581−4591. (102) Nagle, J. F.; Scott, H. L. Lateral Compressibility of Lipid Monoand Bilayers. Theory of Membrane Permeability. Biochim. Biophys. Acta, Biomembr. 1978, 513, 236−243. (103) Heimburg, T. Mechanical Aspects of Membrane Thermodynamics. Estimation of the Mechanical Properties of Lipid Membranes Close to the Chain Melting Transition from Calorimetry. Biochim. Biophys. Acta, Biomembr. 1998, 1415, 147−162. (104) Corvera, E.; Mouritsen, O. G.; Singer, M. A.; Zuckermann, M. J. The Permeability and the Effect of Acyl-Chain Length for Phospholipid Bilayers Containing Cholesterol: Theory and Experiment. Biochim. Biophys. Acta, Biomembr. 1992, 1107, 261−270. (105) Cruzeiro-Hansson, L.; Mouritsen, O. G. Passive Ion Permeability of Lipid Membranes Modelled Via Lipid-Domain Interfacial Area. Biochim. Biophys. Acta, Biomembr. 1988, 944, 63−72. (106) Mouritsen, O. G.; Bloom, M. Mattress Model of Lipid-Protein Interactions in Membranes. Biophys. J. 1984, 46, 141−153. (107) Killian, J. A. Hydrophobic Mismatch between Proteins and Lipids in Membranes. Biochim. Biophys. Acta, Rev. Biomembr. 1998, 1376, 401−416. (108) Vögele, M.; Köfinger, J.; Hummer, G. Molecular Dynamics Simulations of Carbon Nanotube Porins in Lipid Bilayers. Faraday Discuss. 2018, 209, 341−358. (109) Mathai, J. C.; Tristram-Nagle, S.; Nagle, J. F.; Zeidel, M. L. Structural Determinants of Water Permeability through the Lipid Membrane. J. Gen. Physiol. 2008, 131, 69−76.

(110) Pan, J.; Tristram-Nagle, S.; Nagle, J. F. Effect of Cholesterol on Structural and Mechanical Properties of Membranes Depends on Lipid Chain Saturation. Phys. Rev. E Stat Nonlin Soft Matter Phys. 2009, 80, 021931. (111) Kucerka, N.; Heberle, F. A.; Pan, J.; Katsaras, J. Structural Significance of Lipid Diversity as Studied by Small Angle Neutron and X-Ray Scattering. Membranes (Basel, Switz.) 2015, 5, 454−472. (112) Kučerka, N.; Nieh, M.-P.; Katsaras, J. Fluid Phase Lipid Areas and Bilayer Thicknesses of Commonly Used Phosphatidylcholines as a Function of Temperature. Biochim. Biophys. Acta, Biomembr. 2011, 1808, 2761−2771. (113) Rawicz, W.; Olbrich, K. C.; McIntosh, T.; Needham, D.; Evans, E. Effect of Chain Length and Unsaturation on Elasticity of Lipid Bilayers. Biophys. J. 2000, 79, 328−339. (114) Finkelstein, A. Water Movement through Lipid Bilayers, Pores, and Plasma Membranes; Wiley & Sons: New York, 1987. (115) Echevarria, M.; Frindt, G.; Preston, G. M.; Milovanovic, S.; Agre, P.; Fischbarg, J.; Windhager, E. E. Expression of Multiple Water Channel Activities in Xenopus Oocytes Injected with Mrna from Rat Kidney. J. Gen. Physiol. 1993, 101, 827−841. (116) Zampighi, G. A.; Kreman, M.; Boorer, K. J.; Loo, D. D.; Bezanilla, F.; Chandy, G.; Hall, J. E.; Wright, E. M. A Method for Determining the Unitary Functional Capacity of Cloned Channels and Transporters Expressed in Xenopus Laevis Oocytes. J. Membr. Biol. 1995, 148, 65−78. (117) Horner, A.; Zocher, F.; Preiner, J.; Ollinger, N.; Siligan, C.; Akimov, S. A.; Pohl, P. The Mobility of Single-File Water Molecules Is Governed by the Number of H-Bonds They May Form with ChannelLining Residues. Science Advances 2015, 1, No. e1400083. (118) Illsley, N. P.; Verkman, A. S. Serial Permeability Barriers to Water Transport in Human Placental Vesicles. J. Membr. Biol. 1986, 94, 267−278. (119) Levitt, D. G.; Elias, S. R.; Hautman, J. M. Number of Water Molecules Coupled to the Transport of Sodium, Potassium and Hydrogen Ions Via Gramicidin, Nonactin or Valinomycin. Biochim. Biophys. Acta, Biomembr. 1978, 512, 436−451. (120) Rosenberg, P. A.; Finkelstein, A. Water Permeability of Gramicidin a-Treated Lipid Bilayer Membranes. J. Gen. Physiol. 1978, 72, 341−350. (121) Cass, A.; Finkelstein, A. Water Permeability of Thin Lipid Membranes. J. Gen. Physiol. 1967, 50, 1765−1784. (122) Finkelstein, A.; Cass, A. Effect of Cholesterol on the Water Permeability of Thin Lipid Membranes. Nature 1967, 216, 717−718. (123) Saparov, S. M.; Antonenko, Y. N.; Koeppe, R. E.; Pohl, P. Desformylgramicidin: A Model Channel with an Extremely High Water Permeability. Biophys. J. 2000, 79, 2526−2534. (124) Pohl, P.; Saparov, S. M. Solvent Drag across Gramicidin Channels Demonstrated by Microelectrodes. Biophys. J. 2000, 78, 2426−2434. (125) Erokhova, L.; Horner, A.; Kugler, P.; Pohl, P. Monitoring Single-Channel Water Permeability in Polarized Cells. J. Biol. Chem. 2011, 286, 39926−39932. (126) Erokhova, L.; Horner, A.; Ollinger, N.; Siligan, C.; Pohl, P. The Sodium Glucose Cotransporter Sglt1 Is an Extremely Efficient Facilitator of Passive Water Transport. J. Biol. Chem. 2016, 291, 9712−9720. (127) van Meer, G.; Voelker, D. R.; Feigenson, G. W. Membrane Lipids: Where They Are and How They Behave. Nat. Rev. Mol. Cell Biol. 2008, 9, 112−124. (128) Pohl, P.; Saparov, S. M.; Pohl, E. E.; Evtodienko, V. Y.; Agapov, I. I.; Tonevitsky, A. G. Dehydration of model membranes induced by lectins from Ricinus communis and Viscum album. Biophys. J. 1998, 75, 2868. (129) Herbst, M. D.; Goldstein, J. H. A Review of Water Diffusion Measurement by Nmr in Human Red Blood Cells. Am. J. Physiol.-Cell Physiol. 1989, 256, C1097−C1104. (130) Benga, G. Comparative Studies of Water Permeability of Red Blood Cells from Humans and over 30 Animal Species: An Overview of AC


Chemical Reviews

Review

20 years of Collaboration with Philip Kuchel. Eur. Biophys. J. 2013, 42, 33−46. (131) Wong, K. R.; Verkman, A. S. Human Platelet Diffusional Water Permeability Measured by Nuclear Magnetic Resonance. Am. J. Physiol. - Cell Physiol. 1987, 252, C618−C622. (132) Benga, G.; Borza, T.; Popescu, O.; Porutiu, D.; Matei, H. Comparative Nuclear Magnetic Resonance Studies of Diffusional Water Permeability of Red Blood Cells from Sheep and Cow. Comparative biochemistry and physiology 1993, 104, 589−594. (133) Benga, G.; Borza, T. Diffusional Water Permeability of Mammalian Red Blood Cells. Comp. Biochem. Physiol., Part B: Biochem. Mol. Biol. 1995, 112, 653−659. (134) Fabry, M. E.; Eisenstadt, M. Water Exchange across Red Cell Membranes: Ii. Measurement by Nuclear Magnetic Resonancet1,T2, Andt12 Hybrid Relaxation. The Effects of Osmolarity, Cell Volume, and Medium. J. Membr. Biol. 1978, 42, 375−398. (135) Verkman, A. S.; Wong, K. R. Proton Nuclear Magnetic Resonance Measurement of Diffusional Water Permeability in Suspended Renal Proximal Tubules. Biophys. J. 1987, 51, 717−723. (136) Lawaczeck, R. On the Permeability of Water Molecules across Vesicular Lipid Bilayers. J. Membr. Biol. 1979, 51, 229−261. (137) Lawaczeck, R. Water Permeability through Biological Membranes by Isotopic Effects of Fluorescence and Light Scattering. Biophys. J. 1984, 45, 491−494. (138) Kuwahara, M.; Verkman, A. S. Direct Fluorescence Measurement of Diffusional Water Permeability in the Vasopressin-Sensitive Kidney Collecting Tubule. Biophys. J. 1988, 54, 587−593. (139) Ye, R.; Verkman, A. S. Simultaneous Optical Measurement of Osmotic and Diffusional Water Permeability in Cells and Liposomes. Biochemistry 1989, 28, 824−829. (140) Gerweck, L. E.; Vijayappa, S.; Kozin, S. Tumor pH Controls the in Vivo Efficacy of Weak Acid and Base Chemotherapeutics. Mol. Cancer Ther. 2006, 5, 1275−1279. (141) Brodie, B. B.; Hogben, C. A. M. Some Physico-Chemical Factors in Drug Action. J. Pharm. Pharmacol. 1957, 9, 345−380. (142) Gutman, M.; Nachliel, E. The Dynamic Aspects of ProtonTransfer Processes. Biochim. Biophys. Acta, Bioenerg. 1990, 1015, 391− 414. (143) Gutknecht, J.; Tosteson, D. C. Diffusion of Weak Acids across Lipid Bilayer Membranes - Effects of Chemical Reactions in Unstirred Layers. Science 1973, 182, 1258−1261. (144) Antonenko, Y. N.; Bulychev, A. A. Measurements of Local pH Changes near Bilayer Lipid Membrane by Means of a pH Microelectrode and a Protonophore-Dependent Membrane Potential Comparison of the Methods. Biochim. Biophys. Acta, Biomembr. 1991, 1070, 279−282. (145) Pohl, P.; Antonenko, Y. N.; Rosenfeld, E. H. Effect of Ultrasound on the pH Profiles in the Unstirred Layers near Planar Bilayer Lipid Membranes Measured by Microelectrodes. Biochim. Biophys. Acta, Biomembr. 1993, 1152, 155−160. (146) Hannesschlaeger, C.; Barta, T.; Pechova, H.; Pohl, P. The Effect of Buffers on Weak Acid Uptake by Vesicles. Biomolecules 2019, 9, 63. (147) Li, S.; Hu, P. C.; Malmstadt, N. Imaging Molecular Transport across Lipid Bilayers. Biophys. J. 2011, 101, 700−708. (148) Li, S.; Hu, P.; Malmstadt, N. Confocal Imaging to Quantify Passive Transport across Biomimetic Lipid Membranes. Anal. Chem. 2010, 82, 7766−7771. (149) Tsiavaliaris, G.; Itel, F.; Hedfalk, K.; Al-Samir, S.; Meier, W.; Gros, G.; Endeward, V. Low CO2 Permeability of CholesterolContaining Liposomes Detected by Stopped-Flow Fluorescence Spectroscopy. FASEB J. 2015, 29, 1780−1793. (150) Eyer, K.; Paech, F.; Schuler, F.; Kuhn, P.; Kissner, R.; Belli, S.; Dittrich, P. S.; Kramer, S. D. A Liposomal Fluorescence Assay to Study Permeation Kinetics of Drug-Like Weak Bases across the Lipid Bilayer. J. Controlled Release 2014, 173, 102−109. (151) Sezer, D.; Oruc, T. Protonation Kinetics Compromise Liposomal Fluorescence Assay of Membrane Permeation. J. Phys. Chem. B 2017, 121, 5218−5227.

(152) Verkman, A. S. Optical Methods to Measure Membrane Transport Processes. J. Membr. Biol. 1995, 148, 99−110. (153) Verkman, A. S.; Dix, J. A.; Seifter, J. L. Water and Urea Transport in Renal Microvillus Membrane Vesicles. Am. J. Physiol. 1985, 248, F650−655. (154) Allen, P. B.; Milne, G.; Doepker, B. R.; Chiu, D. T. PressureDriven Laminar Flow Switching for Rapid Exchange of Solution Environment around Surface Adhered Biological Particles. Lab Chip 2010, 10, 727−733. (155) Stillinger, F. H. Proton Transfer Reactions and Kinetics in Water. In Theoretical Chemistry: Advances and Perspectives; Eyring, H., Henderson, D., Eds.; Academic Press: New York, 1978; Vol. 3, pp 177− 234. (156) Marsh, D. CRC Handbook of Lipid Bilayers; CRC Press: Boca Raton, FL, 1990. (157) Nichols, J. W.; Deamer, D. W. Net Proton-Hydroxyl Permeability of Large Unilamellar Liposomes Measured by an AcidBase Titration Technique. Proc. Natl. Acad. Sci. U. S. A. 1980, 77, 2038− 2042. (158) Simon, S. A.; Gutknecht, J. Solubility of Carbon Dioxide in Lipid Bilayer Membranes and Organic Solvents. Biochim. Biophys. Acta, Biomembr. 1980, 596, 352−358. (159) Widomska, J.; Raguz, M.; Subczynski, W. K. Oxygen Permeability of the Lipid Bilayer Membrane Made of Calf Lens Lipids. Biochim. Biophys. Acta, Biomembr. 2007, 1768, 2635−2645. (160) Wolosin, J. M.; Ginsburg, H. The Permeation of Organic Acids through Lecithin Bilayers. Resemblance to Diffusion in Polymers. Biochim. Biophys. Acta, Biomembr. 1975, 389, 20−33. (161) Battino, R.; Evans, F. D.; Danforth, W. F. The Solubilities of Seven Gases in Olive Oil with Reference to Theories of Transport through the Cell Membrane. J. Am. Oil Chem. Soc. 1968, 45, 830−833. (162) Hille, B. Ionic Channels in Nerve Membranes. Prog. Biophys. Mol. Biol. 1970, 21, 1−32. (163) Hall, J. E. Access Resistance of a Small Circular Pore. J. Gen. Physiol. 1975, 66, 531−532. (164) Tamimi, A.; Rinker, E. B.; Sandall, O. C. Diffusion-Coefficients for Hydrogen-Sulfide, Carbon-Dioxide, and Nitrous-Oxide in Water over the Temperature-Range 293−368-K. J. Chem. Eng. Data 1994, 39, 330−332. (165) Neher, E.; Sandblom, J.; Eisenman, G. Ionic Selectivity, Saturation, and Block in Gramicidin a Channels. J. Membr. Biol. 1978, 40, 97−116. (166) Thompson, A. N.; Posson, D. J.; Parsa, P. V.; Nimigean, C. M. Molecular Mechanism of pH Sensing in Kcsa Potassium Channels. Proc. Natl. Acad. Sci. U. S. A. 2008, 105, 6900−6905. (167) Boron, W. F.; Endeward, V.; Gros, G.; Musa-Aziz, R.; Pohl, P. Intrinsic CO2 Permeability of Cell Membranes and Potential Biological Relevance of CO2 Channels. ChemPhysChem 2011, 12, 1017−1019. (168) Itel, F.; Al-Samir, S.; Oberg, F.; Chami, M.; Kumar, M.; Supuran, C. T.; Deen, P. M. T.; Meier, W.; Hedfalk, K.; et al. CO2 Permeability of Cell Membranes Is Regulated by Membrane Cholesterol and Protein Gas Channels. FASEB J. 2012, 26, 5182−5191. (169) Hoch, G.; Kok, B. A Mass Spectrometer Inlet System for Sampling Gases Dissolved in Liquid Phases. Arch. Biochem. Biophys. 1963, 101, 160−170. (170) Itada, N.; Forster, R. E. Carbonic Anhydrase Activity in Intact Red Blood Cells Measured with 18o Exchange. J. Biol. Chem. 1977, 252, 3881−3890. (171) Holz, R.; Finkelstein, A. The Water and Nonelectrolyte Permeability Induced in Thin Lipid Membranes by the Polyene Antibiotics Nystatin and Amphotericin B. J. Gen. Physiol. 1970, 56, 125−145. (172) Forster, R. E.; Dodgson, S. J.; Storey, B. T.; Lin, L. Measurement of Carbonic Anhydrase Activity inside Cells and Subcellular Particlesa. Ann. N. Y. Acad. Sci. 1984, 429, 415−429. (173) Forster, R. E.; Gros, G.; Lin, L.; Ono, Y.; Wunder, M. The Effect of 4,4’-Diisothiocyanato-Stilbene-2,2’-Disulfonate on CO2 Permeability of the Red Blood Cell Membrane. Proc. Natl. Acad. Sci. U. S. A. 1998, 95, 15815−15820. AD


Chemical Reviews

Review

(174) Yang, B. X.; Fukuda, N.; van Hoek, A.; Matthay, M. A.; Ma, T. H.; Verkman, A. S. Carbon Dioxide Permeability of Aquaporin-1 Measured in Erythrocytes and Lung of Aquaporin-1 Null Mice and in Reconstituted Proteoliposomes. J. Biol. Chem. 2000, 275, 2686−2692. (175) Tasgin, E.; Nadaroglu, H.; Demir, Y.; Demir, N. Purification and Properties of Carbonic Anhydrase from Bone Marrow. Asian J. Chem. 2009, 21, 5117. (176) Demir, Y.; Demir, N.; Nadaroglu, H.; Bakan, E. Purification and Characterization of Carbonic Anhydrase from Bovine Erythrocyte Plasma Membrane. Prep. Biochem. Biotechnol. 2000, 30, 49−59. (177) Elleby, B.; Chirica, L. C.; Tu, C.; Zeppezauer, M.; Lindskog, S. Characterization of Carbonic Anhydrase from Neisseria Gonorrhoeae. Eur. J. Biochem. 2001, 268, 1613−1619. (178) Szoka, F.; Olson, F.; Heath, T.; Vail, W.; Mayhew, E.; Papahadjopoulos, D. Preparation of Unilamellar Liposomes of Intermediate Size (0.1−0.2 Μm) by a Combination of Reverse Phase Evaporation and Extrusion through Polycarbonate Membranes. Biochim. Biophys. Acta, Biomembr. 1980, 601, 559−571. (179) Psaume, R.; Aptel, P.; Aurelle, Y.; Mora, J. C.; Bersillon, J. L. Pervaporation: Importance of Concentration Polarization in the Extraction of Trace Organics from Water. J. Membr. Sci. 1988, 36, 373−384. (180) Wijmans, J. G.; Athayde, A. L.; Daniels, R.; Ly, J. H.; Kamaruddin, H. D.; Pinnau, I. The Role of Boundary Layers in the Removal of Volatile Organic Compounds from Water by Pervaporation. J. Membr. Sci. 1996, 109, 135−146. (181) Raghunath, B.; Hwang, S. T. Effect of Boundary Layer Mass Transfer Resistance in the Pervaporation of Dilute Organics. J. Membr. Sci. 1992, 65, 147−161. (182) Endeward, V.; Gros, G. Extra- and Intracellular Unstirred Layer Effects in Measurements of CO2 Diffusion across Membranes–a Novel Approach Applied to the Mass Spectrometric 18o Technique for Red Blood Cells. J. Physiol. 2009, 587, 1153−1167. (183) Richardson, S. L.; Swietach, P. Red Blood Cell Thickness Is Evolutionarily Constrained by Slow, Hemoglobin-Restricted Diffusion in Cytoplasm. Sci. Rep. 2016, 6, 36018. (184) Richards, M.; Lomas, O.; Jalink, K.; Ford, K. L.; Vaughan-Jones, R. D.; Lefkimmiatis, K.; Swietach, P. Intracellular Tortuosity Underlies Slow Camp Diffusion in Adult Ventricular Myocytes. Cardiovasc. Res. 2016, 110, 395−407. (185) Wunder, M. A.; Gros, G. 18o Exchange in Suspensions of Red Blood Cells: Determination of Parameters of Mass Spectrometer Inlet System. Isot. Environ. Health Stud. 1998, 34, 303−310. (186) Endeward, V.; Cartron, J. P.; Ripoche, P.; Gros, G. Red Cell Membrane CO2 Permeability in Normal Human Blood and in Blood Deficient in Various Blood Groups, and Effect of Dids. Transfus Clin Biol. 2006, 13, 123−127. (187) Musa-Aziz, R.; Chen, L. M.; Pelletier, M. F.; Boron, W. F. Relative CO2 /NH3 Selectivities of Aqp1, Aqp4, Aqp5, Amtb, and Rhag. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 5406−5411. (188) Geyer, R. R.; Musa-Aziz, R.; Qin, X.; Boron, W. F. Relative CO2 /NH3 Selectivities of Mammalian Aquaporins 0−9. American Journal of Physiology-Cell Physiology 2013, 304, C985−C994. (189) Fischbarg, J.; Kuang, K. Y.; Hirsch, J.; Lecuona, S.; Rogozinski, L.; Silverstein, S. C.; Loike, J. Evidence That the Glucose Transporter Serves as a Water Channel in J774 Macrophages. Proc. Natl. Acad. Sci. U. S. A. 1989, 86, 8397−8401. (190) Fischbarg, J.; Kuang, K. Y.; Vera, J. C.; Arant, S.; Silverstein, S. C.; Loike, J.; Rosen, O. M. Glucose Transporters Serve as Water Channels. Proc. Natl. Acad. Sci. U. S. A. 1990, 87, 3244−3247. (191) Nakhoul, N. L.; Davis, B. A.; Romero, M. F.; Boron, W. F. Effect of Expressing the Water Channel Aquaporin-1 on the CO2 Permeability of Xenopus Oocytes. Am. J. Physiol. 1998, 274, C543−C548. (192) Uehlein, N.; Otto, B.; Eilingsfeld, A.; Itel, F.; Meier, W.; Kaldenhoff, R. Gas-Tight Triblock-Copolymer Membranes Are Converted to CO2 Permeable by Insertion of Plant Aquaporins. Sci. Rep. 2012, 2, 538.

(193) Ehring, G. R.; Zampighi, G.; Horwitz, J.; Bok, D.; Hall, J. E. Properties of Channels Reconstituted from the Major Intrinsic Protein of Lens Fiber Membranes. J. Gen. Physiol. 1990, 96, 631−664. (194) Ghosal, K.; Freeman, B. D. Gas Separation Using Polymer Membranes: An Overview. Polym. Adv. Technol. 1994, 5, 673−697. (195) Scholes, C. A.; Stevens, G. W.; Kentish, S. E. The Effect of Hydrogen Sulfide, Carbon Monoxide and Water on the Performance of a Pdms Membrane in Carbon Dioxide/Nitrogen Separation. J. Membr. Sci. 2010, 350, 189−199. (196) Mäki, A. J.; Peltokangas, M.; Kreutzer, J.; Auvinen, S.; Kallio, P. Modeling Carbon Dioxide Transport in Pdms-Based Microfluidic Cell Culture Devices. Chem. Eng. Sci. 2015, 137, 515−524. (197) Werber, J. R.; Elimelech, M. Permselectivity Limits of Biomimetic Desalination Membranes. Sci. Adv. 2018, 4, eaar8266. (198) Wang, Y.; Cohen, J.; Boron, W. F.; Schulten, K.; Tajkhorshid, E. Exploring Gas Permeability of Cellular Membranes and Membrane Channels with Molecular Dynamics. J. Struct. Biol. 2007, 157, 534−544. (199) Hub, J. S.; de Groot, B. L. Mechanism of Selectivity in Aquaporins and Aquaglyceroporins. Proc. Natl. Acad. Sci. U. S. A. 2008, 105, 1198−1203. (200) Weinstein, A. M. A Mathematical Model of the Inner Medullary Collecting Duct of the Rat: Pathways for Na and K Transport. Am. J. Physiol. 1998, 274, F841−855. (201) DuBose, T. D., Jr. Hydrogen Ion Secretion by the Collecting Duct as a Determinant of the Urine to Blood Pco2 Gradient in Alkaline Urine. J. Clin. Invest. 1982, 69, 145−156. (202) Ryberg, C. Some Investigations on the Carbon Dioxide Tension of the Urine in Man. Acta Physiol. Scand. 1948, 15, 123−139. (203) Waisbren, S. J.; Geibel, J. P.; Modlin, I. M.; Boron, W. F. Unusual Permeability Properties of Gastric Gland Cells. Nature 1994, 368, 332−335. (204) Goldman, D. E. Potential, Impedance, and Rectification in Membranes. J. Gen. Physiol. 1943, 27, 37−60. (205) Hodgkin, A. L.; Katz, B. The Effect of Sodium Ions on the Electrical Activity of Giant Axon of the Squid. J. Physiol. 1949, 108, 37− 77. (206) Hille, B. Ionic Channels of Excitable Membranes; Sinauer Associates, 1984. (207) Gutknecht, J. Proton/Hydroxide Conductance through Phospholipid Bilayer Membranes: Effects of Phytanic Acid. Biochim. Biophys. Acta, Biomembr. 1987, 898, 97−108. (208) Gambale, F.; Robello, M.; Usai, C.; Marchetti, C. Properties of Ionic Transport through Phospholipid-Glycolipid Artificial Bilayers. Biochim. Biophys. Acta, Biomembr. 1982, 693, 165−172. (209) Baba, T.; Toshima, Y.; Minamikawa, H.; Hato, M.; Suzuki, K.; Kamo, N. Formation and Characterization of Planar Lipid Bilayer Membranes from Synthetic Phytanyl-Chained Glycolipids. Biochim. Biophys. Acta, Biomembr. 1999, 1421, 91−102. (210) Miyauchi, S.; Ono, A.; Yoshimoto, M.; Kamo, N. Membrane Transport of Tetraphenylphosphonium and Its Homologues through the Planar Phospholipid Bilayer: Concentration Dependence and Mutually Competitive Inhibition in Membrane Passive Transport. J. Pharm. Sci. 1993, 82, 27−31. (211) Neumcke, B.; Lauger, P. Nonlinear Electrical Effects in Lipid Bilayer Membranes. Ii. Integration of the Generalized Nernst-Planck Equations. Biophys. J. 1969, 9, 1160−1170. (212) Born, M. Volumen Und Hydratationswärme Der Ionen. Eur. Phys. J. A 1920, 1, 45−48. (213) Liberman, E. A.; Topaly, V. P. Permeability of Bimolecular Phospholipid Membranes for Fat-Soluble Ions. Biofizika 1969, 14, 452−461. (214) DeLevie, R.; Rangarajan, S.; Seelig, P.; Andersen, O. S. On the Adsorption of Phloretin onto a Black Lipid Membrane. Biophys. J. 1979, 25, 295−300. (215) Parsegian, A. Energy of an Ion Crossing a Low Dielectric Membrane: Solutions to Four Relevant Electrostatic Problems. Nature 1969, 221, 844−846. AE


Chemical Reviews

Review

(216) Benz, R.; Lauger, P. Transport Kinetics of Dipicrylamine through Lipid Bilayer Membranes. Effects of Membrane Structure. Biochim. Biophys. Acta, Biomembr. 1977, 468, 245−258. (217) Gawrisch, K.; Ruston, D.; Zimmerberg, J.; Parsegian, V. A.; Rand, R. P.; Fuller, N. Membrane Dipole Potentials, Hydration Forces, and the Ordering of Water at Membrane Surfaces. Biophys. J. 1992, 61, 1213−1223. (218) Pohl, E. E. Dipole Potential of Bilayer Membranes, 1st ed.; Elsevier, 2005. (219) Peterson, U.; Mannock, D.; Lewis, R.; Pohl, P.; McElhaney, R.; Pohl, E. E. Origin of Membrane Dipole Potential: Contribution of the Phospholipid Fatty Acid Chains. Chem. Phys. Lipids 2002, 117, 19−27. (220) Latorre, R.; Hall, J. E. Dipole Potential Measurements in Asymmetric Membranes. Nature 1976, 264, 361−363. (221) Pohl, E. E.; Krylov, A. V.; Block, M.; Pohl, P. Changes of the Membrane Potential Profile Induced by Verapamil and Propranolol. Biochim. Biophys. Acta, Biomembr. 1998, 1373, 170−178. (222) Gouy, M. Sur La Constitution De La Charge É lectrique À La Surface D’un É lectrolyte. J. Phys. Theor. Appl. 1910, 9, 457−468. (223) Chapman, D. L. Li. A Contribution to the Theory of Electrocapillarity. London, Edinburgh, and Dublin philosophical magazine and journal of science 1913, 25, 475−481. (224) Stern, O. The Theory of the Electrolytic Double-Layer. Z. Elektrochem 1924, 30, 1014−1020. (225) McLaughlin, S. In Current Topics in Membranes and Transport; Elsevier, 1977; Vol. 9. (226) McLaughlin, S. The Electrostatic Properties of Membranes. Annu. Rev. Biophys. Biophys. Chem. 1989, 18, 113−136. (227) Hladky, S. B. The Energy Barriers to Ion Transport by Nonactin across Thin Lipid Membranes. Biochim. Biophys. Acta, Biomembr. 1974, 352, 71−85. (228) Benz, R.; McLaughlin, S. The Molecular Mechanism of Action of the Proton Ionophore Fccp (Carbonylcyanide P-Trifluoromethoxyphenylhydrazone). Biophys. J. 1983, 41, 381−398. (229) Baba, T.; Minamikawa, H.; Hato, M.; Handa, T. In Membrane Science and Technology; Elsevier, 2003; Vol. 7. (230) Benz, R.; Lauger, P.; Janko, K. Transport Kinetics of Hydrophobic Ions in Lipid Bilayer Membranes. Charge-Pulse Relaxation Studies. Biochim. Biophys. Acta, Biomembr. 1976, 455, 701−720. (231) Jordan, P. C.; Stark, G. Kinetics of Transport of Hydrophobic Ions through Lipid Membranes Including Diffusion Polarization in the Aqueous Phase. Biophys. Chem. 1979, 10, 273−287. (232) Ketterer, B.; Neumcke, B.; Lauger, P. Transport Mechanism of Hydrophobic Ions through Lipid Bilayer Membranes. J. Membr. Biol. 1971, 5, 225−245. (233) Smejtek, P.; Paulis-Illangasekare, M. Modification of Ion Transport in Lipid Bilayer Membranes in the Presence of 2,4Dichlorophenoxyacetic Acid. Ii. Suppression of Tetraphenylborate Conductance and Changes of Interfacial Potentials. Biophys. J. 1979, 26, 467−487. (234) de Levie, R.; Rangarajan, S. K.; Seelig, P. F.; Andersen, O. S. On the Adsorption of Phloretin onto a Black Lipid Membrane. Biophys. J. 1979, 25, 295−300. (235) Reyes, J.; Greco, F.; Motais, R.; Latorre, R. Phloretin and Phloretin Analogs - Mode of Action in Planar Lipid Bilayers and Monolayers. J. Membr. Biol. 1983, 72, 93−103. (236) Cseh, R.; Benz, R. The Adsorption of Phloretin to Lipid Monolayers and Bilayers Cannot Be Explained by Langmuir Adsorption Isotherms Alone. Biophys. J. 1998, 74, 1399−1408. (237) Pohl, P.; Rokitskaya, T. I.; Pohl, E. E.; Saparov, S. M. Permeation of Phloretin across Bilayer Lipid Membranes Monitored by Dipole Potential and Microelectrode Measurements. Biochim. Biophys. Acta, Biomembr. 1997, 1323, 163−172. (238) Eckert, F.; Klamt, A. Fast Solvent Screening Via Quantum Chemistry: Cosmo-Rs Approach. AIChE J. 2002, 48, 369−385. (239) Rokitskaya, T. I.; Korshunova, G. A.; Antonenko, Y. N. Effect of Alkyl Chain Length on Translocation of Rhodamine B N-Alkyl Esters across Lipid Membranes. Biophys. J. 2018, 115, 514−521.

(240) Smith, R.; Tanford, C. Hydrophobicity of Long Chain N-Alkyl Carboxylic Acids, as Measured by Their Distribution between Heptane and Aqueous Solutions. Proc. Natl. Acad. Sci. U. S. A. 1973, 70, 289− 293. (241) Pashkovskaya, A. A.; Vazdar, M.; Zimmermann, L.; Jovanovic, O.; Pohl, P.; Pohl, E. E. Mechanism of Long-Chain Free Fatty Acid Protonation at the Membrane-Water Interface. Biophys. J. 2018, 114, 2142−2151. (242) Deamer, D. W. Proton Permeation of Lipid Bilayers. J. Bioenerg. Biomembr. 1987, 19, 457−479. (243) Cafiso, D. S.; Hubbell, W. L. Electrogenic H+/Oh- Movement across Phospholipid Vesicles Measured by Spin-Labeled Hydrophobic Ions. Biophys. J. 1983, 44, 49−57. (244) Gutknecht, J. Proton/Hydroxide Conductance through Lipid Bilayer Membranes. J. Membr. Biol. 1984, 82, 105−112. (245) Perkins, W. R.; Cafiso, D. S. An Electrical and Structural Characterization of H+/Oh- Currents in Phospholipid Vesicles. Biochemistry 1986, 25, 2270−2276. (246) Gutknecht, J. Proton Conductance through PhospholipidBilayers - Water Wires or Weak Acids. J. Bioenerg. Biomembr. 1987, 19, 427−442. (247) Decoursey, T. E. Voltage-Gated Proton Channels and Other Proton Transfer Pathways. Physiol. Rev. 2003, 83, 475−579. (248) Nagle, J. F. Theory of Passive Proton Conductance in Lipid Bilayers. J. Bioenerg. Biomembr. 1987, 19, 413−426. (249) Nagle, J. F.; Morowitz, H. J. Molecular Mechanisms for Proton Transport in Membranes. Proc. Natl. Acad. Sci. U. S. A. 1978, 75, 298− 302. (250) Nichols, J. W.; Abercrombie, R. F. A View of Hydrogen/ Hydroxide Flux across Lipid Membranes. J. Membr. Biol. 2010, 237, 21−30. (251) Gutknecht, J. Proton Hydroxide Conductance and Permeability through Phospholipid-Bilayer Membranes. Proc. Natl. Acad. Sci. U. S. A. 1987, 84, 6443−6446. (252) Marrink, S. J.; Jahnig, F.; Berendsen, H. J. C. Proton Transport across Transient Single-File Water Pores in a Lipid Membrane Studied by Molecular Dynamics Simulations. Biophys. J. 1996, 71, 632−647. (253) Karathanou, K.; Bondar, A. N. Dynamic Water Hydrogen-Bond Networks at the Interface of a Lipid Membrane Containing PalmitoylOleoyl Phosphatidylglycerol. J. Membr. Biol. 2018, 251, 461−473.

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