Permeability of composite chondrocyte-culture-millipore membranes to solutes of varying size and shape.

A model connective-tissue system was developed that is amenable to the determination of permeability coefficients of diffusing solutes. The system involves the culture of 13-day chick-embryo chondrocytes on a Millipore filter (HA:0.45 micron pore size) to form what is, in effect, a confluent, extremely thin cartilage slice of uniform thickness. These cultured chondrocyte membranes were used to measure the steady-state flux of radioactively labelled low-molecular-weight solutes and micro-ions. Similarly, the permeability coefficients of either radioactively labelled or enzymically active proteins across the membranes were determined. The membrane was found to have no marked effects on the diffusional behaviour of low-molecular-weight non-electrolytes (water, proline, ribose, glucose, sorbitol, raffinose). For micro-ions (Na+, SO42-, Cl-, glutamate, glucuronate,), the diffusive behaviour was found to be markedly affected by the ionic strength of the solvent used in a manner which was consistent with a Donnan distribution resulting from the immobilized proteoglycans. Globular proteins permeated the membrane at rates which decreased as the molecular size of the diffusing solute increased. The apparent diffusion rates of fibrinogen and of collagen through the membranes were greater than would be expected on the basis of their diffusion coefficients in free solution. Reasons for this behaviour are discussed.     

Permeability of the Isolated Toad Bladder to Solutes and Its Modification by Vasopressin

Measurements have been made of the permeability of the isolated urinary bladder of the toad to a number of small solute molecules, in the presence and absence of vasopressin. Vasopressin has a strikingly specific effect on increasing permeability of the bladder to a group of small, uncharged amides and alcohols while penetration by other small molecules and ions is unaffected. The movement of urea is passive, as indicated by equal flux rates in the two directions. The reflection coefficients for chloride and thiourea indicate a high degree of impermeability of the bladder to these solutes even in the presence of large net movements of water. The low concentration of thiourea in the tissue water when this compound is added to the mucosal bathing medium indicates that the major permeability barrier to thiourea is at the mucosal surface of the bladder. The findings can be accounted for by a double permeability barrier consisting of a fine selective diffusion barrier and a porous barrier in series. The former would constitute the permeability barrier to most small solutes while the latter would be the rate-limiting barrier for water and the amides. It would be the porous barrier which is affected by vasopressin. Reasons are presented which require both barriers to be contained in or near the plasma membrane at the mucosal surface of the bladder.     

Exchange Properties of Isolated Cell Walls of Lemna minor L

From our theoretical treatment which is an extension of the classical Donnan theory, we have estimated the rational selectivity coefficients of the carboxylic groups of the walls during exchanges of divalent ions against monovalent ones (i.e. calcium and potassium or calcium and sodium ions). These coefficients express the interactions between the different ions, those between the counter-ions and the ionized groups of the wall, and the influence of water. These quantitative values are consistent with the great affinity of the carboxylic groups for the calcium ions. They vary with the experimental conditions, showing a purely physicochemical mechanism of “regulation” of the exchanges in the cells walls of Lemna minor L.     

Diffusion and partition of solutes in cartilage under static load

We describe experimental apparatus, methodology and mathematical algorithms to measure diffusion and partition for typical small ionic solutes and inulin (a medium size solute) in statically loaded cartilage. The partition coefficient based on tissue water (K(H(2)O)) of Na(+) increased from 1.8 to 4.5 and for SO(4)(-2) decreased from 0.5 to 0.1, when the applied pressure was raised from zero to 22 atm K(H(2)O) of inulin decreased from 0.3 to 0.05, for an increase in pressure from zero to 11 atm. Our theoretical interpretation of the results is that the partition coefficient can be expressed as a function of fixed charge density (FCD) for both loaded and unloaded cartilage. The partition coefficient shows good agreement with the ideal Gibbs-Donnan equilibrium, particularly when FCD is based on extrafibrillar water (EFW). The diffusion coefficients, D also decreased with an increase in applied pressure; raising the pressure from 0 to 22 atm resulted in the following changes in the values of D: for Na(+) from 2.86 x 10(-6) to 1.51 x 10(-6) cm(2)/s, for SO(4)(-2) from 1.58 x 10(-6) to 7.5 x 10(-7) cm(2)/s, for leucine from 1.69 x 10(-6) to 8.30 x 10(-7) cm(2)/s and for inulin from 1.80 x 10(-7) to 3.30 x 10(-8) cm(2)/s. For the three small solutes (two charged and one neutral) the diffusion coefficient D is highly correlated with the fraction of fluid volume in the tissue. These experimental results show good agreement with the simple model of Mackie and Meares: hence solute charge does not affect the diffusion of small solutes under load. For inulin D & K show some agreement with a modified Ogston model based on two major components, viz., glycosaminoglycans (GAG) and core protein. We conclude that the changes in the partition and diffusion coefficients of small and medium size solutes in statically loaded cartilage can be interpreted as being due to the reduction in hydration and increase in FCD. The change in the latter affects the partition of small ionic solutes and the partition and diffusion of larger molecules. Our results throw light on the ionic environment of chondrocytes in loaded cartilage as well as on the transport of solutes through the matrix.     

Ionic and osmotic equilibria of human red blood cells treated with nystatin

Human red blood cells have been incubated in the presence of nystatin, which allows Na and K, as well as Cl and pH to equilibrate rapidly when cell volume is set with external impermeant sucrose. The intracellular mean ionic activity coefficients, relative to values in the extracellular solution, for KCl and NaCl are 1.01 +/- 0.02 and 0.99 +/- 0.02 (SD, n = 10), respectively, and are independent of external pH, pH o, and of [sucrose]o. With nystatin the dependence of red cell volume on [sucrose]o deviates from ideal osmotic behavior by as much as a factor of three. A virial equation for the osmotic coefficient, phi, of human hemoglobin, Hb, accounts for the cell volumes, and is the same as that which describes Adair's measurements of phi Hb for Hb isolated from sheep and ox bloods. In the presence of nystatin the slope of the acid-base titration curve of the cells is independent of cell volume, implying that the charge on impermeant cellular solutes is independent of Hb concentration at constant pH. By modifying the Jacobs-stewart equations (1947. J. Cell. Comp. Physiol. 30: 79--103) with the osmotic coefficients of Hb and of salts, a nonideal thermodynamic model has been devised which predicts equilibrium Donnan ratios and red cell volume from the composition of the extracellular solution and from certain parameters of the cells. In addition to accounting for the dependence of cell volume on osmotic pressure, the model also describes accurately the dependence of Donnan ratios and cell volumes on pHo either in the presence or absence of nystatin.     

THE RECIPROCAL RELATION BETWEEN THE OSMOTIC PRESSURE AND THE VISCOSITY OF GELATIN SOLUTIONS

1. These experiments confirm the conclusion that protein solutions are true solutions consisting of isolated ions and molecules, and that these solutions may or may not contain in addition solid submicroscopic particles capable of occluding water. 2. The typical influence of electrolytes on the osmotic pressure of protein solutions is due to the isolated protein ions since these alone are capable of causing a Donnan equilibrium across a membrane impermeable to the protein ions but permeable to most crystalloidal ions. 3. The similar influence of electrolytes on the viscosity of protein solutions is due to the submicroscopic solid protein particles capable of occluding water since the amount of water occluded by (or the amount of swelling of) these particles is regulated by the Donnan equilibrium. 4. These ideas are supported by the fact that the more the submicroscopic solid particles contained in a protein solution or suspension are transformed into isolated ions (e.g., by keeping gelatin solution for 1 hour or more at 45°C.) the more the viscosity of the solution is diminished while the osmotic pressure is increased, and vice versa.     

Effects of dielectric saturation on planar electric double layers in salt solutions

The effects of dielectric saturation on planar electric double layers in salt solutions are examined by solving the Poisson-Boltzmann equation analytically where the dielectric constant is given as a function of the electric displacement. The activity and the distribution of small ions, the surface potential and the Donnan potential are calculated. The salt exclusion parameter and the Donnan potential decrease while the surface potential increases as a result of the dielectric saturation. The electrostatic entropy is affected considerably by the dielectric saturation while the electrostatic energy is little influenced. Generally, the effects of dielectric saturation on the distribution of small ions and the thermodynamic properties are enhanced by the addition of salt.     

The distributions and diffusivities of small ions in chondroitin sulphate, hyaluronate and some proteoglycan solutions

The distributions and diffusivities of Na+, Ca2+ and Cl- in chondroitin sulphate (CS), hyaluronate (HA) and proteoglycan solutions were measured using equilibrium dialysis and a capillary tube method. Measurements were made for a range of glycosaminoglycan (GAG) concentrations up to those normally found in dense connective tissue (10% CS, 2.5% HA), ionic strengths up to normal physiological concentrations (0.15 M) and for different combinations of monovalent and divalent cations. The partition coefficients, Ki, of the positive ions increased with increasing matrix concentration and with decreasing ionic strength but with one exception the selectivity coefficient KCaNa = square root of KCa/KNa was close to unity, indicating nearly ideal Donnan distributions. The ionic diffusivities decreased very much like those of small neutral solutes with increasing matrix concentration and with one exception were relatively independent of ionic strength, The exception in both cases was low matrix concentrations and low ionic strengths for which the diffusivity of Ca2+ was an order of magnitude lower and selectivity coefficients were approximately 2. We conclude that at physiological ionic strengths and GAG concentrations the distributions of small ions are determined by simple electrostatic interactions, without binding or condensation, and the diffusivities are not affected by the electrostatic field.     

The effect of non-binding molecules on the gelation of HbS

The influence of an inert globular macromolecule upon the solubility of sickle cell hemoglobin has been determined as a function of the degree of oxygenation. The thermodynamic theory required to treat this and related problems is derived partition function. The treatment includes non-ideal solution behaviour as measured by osmotic pressure of highly concentrated macromolecular. solutions. Application of the theoretical equations demonstrates how the solubility of hemoglobin is influenced by the presence of the binding ligand (oxygen) and the inert macromolecule, bovine serum albumin (BSA). Good agreement is obtained between experimentally determined and theoretically calculated solubilities using 1) oxygen binding curves to solution and gel phases, 2) activity coefficients from osmotic pressure data, 3) one solubility under the condition where oxygen and BSA are absent, and 4) the value of the water content of the gel phase. Examination of the theoretical equations suggests that inert molecules of intermediate size, that are partially excluded from crystalline or gel phases, have the potential of generally increasing the solubility when non-ideal solution effects are small.     

Calculation of self-diffusion coefficients of the [BMIM][TFSA]/water system by molecular dynamics simulation

We performed a molecular dynamics simulation to calculate the self-diffusion coefficients of 1-Butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide and water in a water–ionic liquid mixture. We then compared the simulated self-diffusion coefficients of cation, anion and water molecules with experimental data and with simulated data from the literature. Although the simulation overestimated the self-diffusion coefficients of ions, the simulated results qualitatively reproduced the enhancement of the self-diffusion coefficients of water as the water molar fraction increased. We also calculated the radial distribution functions to investigate the solution structure, i.e. the clustering of water molecules. The clustering of water in ionic liquid was found to play an important role in the enhancement of the diffusion of water molecules in the ionic liquid.     

A Biomechanical Triphasic Approach to the Transport of Nondilute Solutions in Articular Cartilage

Biomechanical models for biological tissues such as articular cartilage generally contain an ideal, dilute solution assumption. In this article, a biomechanical triphasic model of cartilage is described that includes nondilute treatment of concentrated solutions such as those applied in vitrification of biological tissues. The chemical potential equations of the triphasic model are modified and the transport equations are adjusted for the volume fraction and frictional coefficients of the solutes that are not negligible in such solutions. Four transport parameters, i.e., water permeability, solute permeability, diffusion coefficient of solute in solvent within the cartilage, and the cartilage stiffness modulus, are defined as four degrees of freedom for the model. Water and solute transport in cartilage were simulated using the model and predictions of average concentration increase and cartilage weight were fit to experimental data to obtain the values of the four transport parameters. As far as we know, this is the first study to formulate the solvent and solute transport equations of nondilute solutions in the cartilage matrix. It is shown that the values obtained for the transport parameters are within the ranges reported in the available literature, which confirms the proposed model approach.     

Contribution of solvent water to the solution X-ray scattering profile of proteins

A theoretical framework is presented to analyze how solvent water contributes to the X-ray scattering profile of protein solution. Molecular dynamics simulations were carried out on pure water and an aqueous solution of myoglobin to determine the spatial distribution of water molecules in each of them. Their solution X-ray scattering (SXS) profiles were numerically evaluated with obtained atomic-coordinate data. It is shown that two kinds of contributions from solvent water must be considered to predict the SXS profile of a solution accurately. One is the excluded solvent scattering originating in exclusion of water molecules from the space occupied by solutes. The other is the hydration effect resulting from formation of a specific distribution of water around solutes. Explicit consideration of only two molecular layers of water is practically enough to incorporate the hydration effect. Care should be given to using an approximation in which an averaged electron density distribution is assumed for the structure factor because it may predict profiles considerably deviating from the correct profile at large K.     

What befalls the proteins and water in a living cell when the cell dies?

The solvency of solutes of varying molecular size in the intracellular water of freshly-killed Ehrlich carcinoma cells fits the same theoretical curve that describes the solvency of similar solutes in a 36% solution of native bovine hemoglobin--a protein found only in red blood cells and making up 97.3% of the red cell's total intracellular proteins. The merging of the two sets of data confirms the prediction of the AI Hypothesis that key intracellular protein(s) in dying cells undergo(es) a transition from: (1) one in which the polypeptide NHCO groups assume a fully-extended conformation with relatively strong power of polarizing and orienting the bulk-phase water in multilayers; to (2) one in which most of the polypeptide NHCO groups are engaged in alpha-helical and other "introvert" conformations (see below for definition) with much weaker power in polarizing-orienting multilayers of bulk-phase water. This concordance of the two sets of data also shows that what we now call native hemoglobin--supposedly denoting hemoglobin found in its natural state in living red blood cells--, in fact, more closely resembles the water-polarizing, and -orienting intracellular proteins in dead cells. Although in the dead Ehrlich carcinoma cells as well as in the 36% solution of native hemoglobin, much of the protein's polypeptide NHCO groups are engaged in alpha-helical and other "introvert" conformation (Perutz 1969; Weissbluth 1974), both systems produce a weak but nonetheless pervasive and "long-range" water polarization and orientation. It is suggested that in both the dead Ehrlich carcinoma ascites cells and in the 36% native bovine hemoglobin solution, enough polypeptide NHCO groups assume the fully-extended conformation to produce the weak but far-reaching multilayer water polarization and orientation observed.     

The Water and Nonelectrolyte Permeability Induced in Thin Lipid Membranes by the Polyene Antibiotics Nystatin and Amphotericin B

Nystatin and amphotericin B increase the permeability of thin (<100 A) lipid membranes to ions, water, and nonelectrolytes. Water and nonelectrolyte permeability increase linearly with membrane conductance (i.e., ion permeability). In the unmodified membrane, the osmotic permeability coefficient, P_f, is equal to the tagged water permeability coefficient, (P_d)_w; in the nystatin- or amphotericin B-treated membrane, P_f/(P_d)_w ≈ 3. The unmodified membrane is virtually impermeable to small hydrophilic solutes, such as urea, ethylene glycol, and glycerol; the nystatin- or amphotericin B-treated membrane displays a graded permeability to these solutes on the basis of size. This graded permeability is manifest both in the tracer permeabilities, P_d, and in the reflection coefficients, σ (Table I). The "cutoff" in permeability occurs with molecules about the size of glucose (Stokes-Einstein radius 4 A). We conclude that nystatin and amphotericin B create aqueous pores in thin lipid membranes; the effective radius of these pores is approximately 4 A. There is a marked similarity between the permeability of a nystatin- or amphotericin B-treated membrane to water and small hydrophilic solutes and the permeability of the human red cell membrane to these same molecules.     

Water in barnacle muscle. IV. Factors contributing to reduced self-diffusion.

The relative self-diffusion coefficients D/Do, of water in various solutions, in fresh barnacle muscle fibers, and in membrane-damaged fibers equilibrated with several media have been estimated from NMR relaxation rates in the presence of applied field gradients. A model has been developed to account for the contributions to the observed reduction in D/Do from small organic solutes, and from the hydration and obstruction effect of both soluble macromolecules and myofilament proteins. Intracellular ions do not affect D/Do, but all tested organic solutes do. Solute effects are additive. When artificially combined in the proportions found in barnacle muscle ultracentrifugate (measured D/Do = 0.77), organic acids, small nitrogenous solutes, and proteins give D/Do = 0.77. After correcting the D/Do measured in fibers for this value, we calculate the myofilament hydration, Hm, in fresh muscle to be 0.65 g H2O/g macromolecule. Only in membrane-damaged fibers, highly swollen by salt-rich media, was this significantly increased. Because our earlier NMR relaxation measurements indicate only 0.07 g H2O bound/g myofilament protein, we conclude that the "hydration" water measured by reduction of D/Do cannot be described by stationary layers of water molecules; instead, we propose that nonpolar groups on the proteins cause extensive, hydrophobically-induced interactions among a large fraction of solvent molecules, slowing their translational motion.     

Determination of reflection coefficients of liposomes for some non-electrolytes by osmotic pressure measurement

The reflection coefficients of bilayer lipid vesicles (liposomes) of various compositions have been determined for a number of non-electrolytes. The solutes were the same and the method of measurement was essentially the same as those which have been used to estimate an equivalent pore radius for erythrocytes. The method involves matching the osmotic pressure of solutions of a permeant test solute with that of a known inpermeant solute. Reflection coefficients for cholesterol-containing liposomes and those of erythrocytes are, when account is taken of those solutes known to permeate the erythrocyte by specialized pathways, not greatly different. Lipid bilayers can thus account for most of the permeability characteristics of the cell originally interpreted as due to aqueous pores. Reflection coefficients are significantly higher for egg phosphatidylcholine membranes that contain cholesterol than those which do not. There is a strong correlation between relative permeabilities derived from reflection coefficients and oil-water partition coefficients. There is also good agreement between these permeabilities and permeabilities measured by others, which exhibit an inverse dependence on molecular size. It is suggested that this tendency of membranes to pass small molecules more readily than large molecules, other properties being equal, is a consequence of the surface pressure of the constituent monolayers of the membrane.     

Molecular Dynamics Simulation of Limiting Conductance for Na2+, Cl2−, Na°, and Cl° in Supercritical Water

Abstract

We report results of molecular dynamics simulations of the limiting conductance of Na²⁺, Cl^2?, Na°, and Cl° in supercritical water using the SPC/E model for water in conjuction with our previous study (Lee et al., Chem. Phys. Lett. 293, 289 (1998)). The behavior of the limiting conductances of Na²⁺ and Cl^2? in the whole range of water density shows almost the same trend as those of Na⁺ and Cl^?, but the deviation from the assumed linear dependence of limiting conductances of Na²⁺ and Cl^2? on the water density is smaller than that of Na⁺ and Cl^?. The ratio of the limiting conductance of the divalentions to that of the corresponding monovalentions over the whole range of water density is almost constant. In the cases of Na²⁺ and Cl^2?, the dominating factor of the number of hydration water molecules around ions in the higher-density region and the dominating factor of the interaction strength between the ions and the hydration water molecules in the lower-density region are also found as was the cases for Na⁺ and Cl^?. These factors, however, are not so strong as for the corresponding monovalent ions because the change in the energetics, structure, and dynamics are very small mainly due to the strong Coulomb interaction of the divalent ions with the hydration water molecules. The diffusion coefficient of Na° and Cl° monotonically increases with decreasing water density over the whole range of water density. The increase of the diffusion coefficient with decreasing water density is attributed only to the dramatic decrease of the hydration number of water in the first solvation shell around the uncharged species. Among the two important competing factors in the limiting conductance of Na⁺ and Cl^?, the effect of the number of hydration water molecules around the uncharged species is the only existing factor over the whole range of water density since the interaction strength between the uncharged species and the hydration water molecules very small through the LJ interaction. This result has confirmed the dominating factor of the number of hydration water molecules around ions in the higher-density region in the explanation of the limiting conductance of Na⁺ and Cl^? in supercritical water at 673 K.     

DONNAN EQUILIBRIUM AND THE PHYSICAL PROPERTIES OF PROTEINS : IV. VISCOSITY—Continued.

1. The proof is completed that the influence of electrolytes on the viscosity of suspensions of powdered particles of gelatin in water is similar to the influence of electrolytes on the viscosity of solutions of gelatin in water. 2. It has been suggested that the high viscosity of proteins is due to the existence of a different type of viscosity from that existing in crystalloids. It is shown that such an assumption is unnecessary and that the high viscosity of solutions of isoelectric gelatin can be accounted for quantitatively on the assumption that the relative volume of the gelatin in solution is comparatively high. 3. Since isoelectric gelatin is not ionized, the large volume cannot be due to a hydration of gelatin ions. It is suggested that this high volume of gelatin solutions is caused by the existence in the gelatin solution of submicroscopic pieces of solid gelatin occluding water, the relative quantity of which is regulated by the Donnan equilibrium. This would also explain why the influence of electrolytes on the viscosity of gelatin solutions is similar to the influence of electrolytes on the viscosity of suspensions of particles of gelatin. 4. This idea is supported by experiments on solutions and suspensions of casein chloride in which it is shown that their viscosity is chiefly due to the swelling of solid particles of casein, occluding quantities of water regulated by the Donnan equilibrium; and that the breaking up of these solid particles into smaller particles, no longer capable of swelling, diminishes the viscosity. 5. This leads to the idea that proteins form true solutions in water which in certain cases, however, contain, side by side with isolated ions and molecules, submicroscopic solid particles capable of occluding water whereby the relative volume and the viscosity of the solution is considerably increased. This accounts not only for the high order of magnitude of the viscosity of such protein solutions but also for the fact that the viscosity is influenced by electrolytes in a similar way as is the swelling of protein particles. 6. We therefore reach the conclusion that there are two sources for the viscosity of protein solutions; one due to the isolated protein ions and molecules, and the other to the submicroscopic solid particles contained in the solution. The viscosity due to the isolated molecules and ions of proteins we will call the general viscosity since it is of a similar low order of magnitude as that of crystalloids in solution; while the high viscosity due to the submicroscopic solid protein particles capable of occluding water and of swelling we will call the special viscosity of protein solutions. Under ordinary conditions of hydrogen ion concentration and temperature (and in not too high a concentration of the protein in solution) the general viscosity due to isolated ions and molecules prevails in solutions of crystalline egg albumin and in solutions of metal caseinates (where the metal is monovalent) while under the same conditions the second type of viscosity prevails in solutions of gelatin and in solutions of acid-salts of casein; and also in solutions of crystalline egg albumin at a pH below 1.0 and at higher temperatures. The special viscosity is higher in solutions of gelatin than of casein salts for the probable reason that the amount of water occluded by the submicroscopic solid gel particles in a gelatin solution is, as a rule, considerably higher than that occluded by the corresponding particles of casein.     

Studies on the physical state of water in living cells and model systems. X. The dependence of the equilibrium distribution coefficient of a solute in polarized water on the molecular weights of the solute: experimental confirmation of the "size rule" in model studies

The equilibrium distribution of 14 sugars, sugar alcohols, and other nonelectrolytes in solutions of polyethylene oxide (PEO) and of native and alkali-denatured bovine hemoglobin were studied over wide concentration ranges. The results show that the equilibrium concentrations of all the solutes studies are rectilinearly related to their external concentrations. This straight-line relationship demonstrates the existence of these solutes entirely or almost entirely in the aqueous phase of these systems. Therefore the slope of each of these straight lines equals the equilibrium distribution coefficient or q-value of the solute involved. In general, the q-values decrease with increasing molecule weights (M.W.) of the solutes in 15% solutions of PEO, 20% solutions of alkali-denatured hemoglobin (and in 18% gelatin) but not in 39% solution of native hemoglobin. In solutions of PEO, of alkali-denatured hemoglobin studied (and of gelatin) a fraction of the water (20% to 30%) appears to have solvency similar to that of normal liquid water. The experimental findings of M.W.-dependent solute exclusion were discussed in the light of four alternative theories that have been offered to explain this type of phenomena. Among these four theories only the polarized multilayer theory agrees with most, if not all the facts known.     

Distribution of amino acids in a lipid bilayer from computer simulations

We have calculated the distribution in a lipid bilayer of small molecules mimicking 17 natural amino acids in atomistic detail by molecular dynamics simulation. We considered both charged and uncharged forms for Lys, Arg, Glu, and Asp. The results give detailed insight in the molecular basis of the preferred location and orientation of each side chain as well the preferred charge state for ionizable residues. Partitioning of charged and polar side chains is accompanied by water defects connecting the side chains to bulk water. These water defects dominate the energetic of partitioning, rather than simple partitioning between water and a hydrophobic phase. Lys, Glu, and Asp become uncharged well before reaching the center of the membrane, but Arg may be either charged or uncharged at the center of the membrane. Phe has a broad distribution in the membrane but Trp and Tyr localize strongly to the interfacial region. The distributions are useful for the development of coarse-grained and implicit membrane potentials for simulation and structure prediction. We discuss the relationship between the distribution in membranes, bulk partitioning to cyclohexane, and several amino acid hydrophobicity scales.