The permeability of liposomes to nonelectrolytes. I. Activation energies for permeation.

The effect of temperature on the permeability of nonelectrolytes across liposomal membranes above and below their transition temperature has been studied by using an osmotic method. Below their transition temperature, liposomes are osmotically insensitive structures but, on addition of gramicidin A, the water permeability so increased that the permeability of solutes could be studied. The measured activation energies for permeation of a variety of nonelectrolytes has been found to increase when a) there is an increase in the capability of the solutes to form hydrogen bonds in water, b) the cholesterol concentration in the membranes increases and c) the membranes pass from a liquid-crystalline to a solid-crystalline state. The change in the activation energy for permeation per hydrogen bond is about 1.8 kcal/mole for all the different liposome systems investigated; the only solute tested that deviated from this correlation was urea, whose activation energy for permeation across a gramicidin-containing system was much lower than expected from its hydrogen-bonding capacity. This finding suggests that urea is permeating across the gramicidin pore. Although the literature contains only incomplete data relating the activation energies for permeation of nonelectrolytes across biological membranes to their hydrogen-bonding capacity, the available evidence suggests that there is a similar correlation to that found in liposomes. Thus, the average increase in the activation energy per hydrogen bond for permeation across ox red cell membranes (Jacobs, Glassman & Parpart, J. Cell. Comp. Physiol. 7:197, 1935) is 2.2 plus or minus 0.4 kcal/mole, a value that is similar to that obtained in liposomes. However, the activation energies for water and urea are - in such a system - very much lower than expected, suggesting that they, too, are permeating by some parallel route such as an aqueous pore.     

A bulk water-dependent desolvation energy model for analyzing the effects of secondary solutes on biological equilibria

A new phenomenological model for interpreting the effects of solutes on biological equilibria is presented. The model attributes changes in equilibria to differences in the desolvation energy of the reacting species that, in turn, reflect changes in the free energy of the bulk water upon addition of secondary solutes. The desolvation approach differs notably from that of other solute models by treating the free energy of bulk water as a variable and by not ascribing the observed shifts in reaction equilibria to accumulation or depletion of solutes next to the surfaces of the reacting species. On the contrary, the partitioning of solutes is viewed as a manifestation of the different subpopulations of water that arise in response to the surface boundary conditions. A thermodynamic framework consistent with the proposed model is used to derive a relationship for a specific reaction, an aqueous solubility equilibrium, in two or more solutions. The resulting equation reconciles some potential issues with the transfer free energy model of Tanford. Application of the desolvation energy model to the analysis of a two-state protein folding equilibrium is discussed and contrasted to the application of two other solute models developed by Timasheff and by Parsegian. Future tabulation of solvation energies and bulk water energies may allow biophysical chemists to confirm the mechanism by which secondary solutes influence binding and conformational equilibria and may provide a common ground on which experimentalists and theoreticians can compare and evaluate their results.     

Hydration and conformational equilibria of simple hydrophobic and amphiphilic solutes.

We consider whether the continuum model of hydration optimized to reproduce vacuum-to-water transfer free energies simultaneously describes the hydration free energy contributions to conformational equilibria of the same solutes in water. To this end, transfer and conformational free energies of idealized hydrophobic and amphiphilic solutes in water are calculated from explicit water simulations and compared to continuum model predictions. As benchmark hydrophobic solutes, we examine the hydration of linear alkanes from methane through hexane. Amphiphilic solutes were created by adding a charge of +/-1e to a terminal methyl group of butane. We find that phenomenological continuum parameters fit to transfer free energies are significantly different from those fit to conformational free energies of our model solutes. This difference is attributed to continuum model parameters that depend on solute conformation in water, and leads to effective values for the free energy/surface area coefficient and Born radii that best describe conformational equilibrium. In light of these results, we believe that continuum models of hydration optimized to fit transfer free energies do not accurately capture the balance between hydrophobic and electrostatic contributions that determines the solute conformational state in aqueous solution.     

A CFF 91-based Continuum Solvation Model: Solvation Free Energies of Small Organic Molecules and Conformations of the Alanine Dipeptide in Solution

Abstract

For molecular mechanics simulations of solvated molecules, it is important to use a consistent approach for calculating both the force field energy and the solvation free energy. A continuum solvation model based upon the atomic charges provided with the CFF91 force field is derived. The electrostatic component of the solvation free energy is described by the Poisson-Bolzmann equation while the nonpolar comonent of the solvation energy is assumed to be proportional to the solvent accessible surface area of the solute. Solute atomic radii used to describe the interface between the solute and solvent are fitted to reproduce the energies of small organic molecules. Data for 140 compounds are presented and compared to experiment and to the results from the well-characterized quantum mechanical solvation model AM1-SM2. In particular, accurate results are obtained for amino acid neutral analogues (mean unsigned error of 0.3 kcal/mol). The conformational energetics of the solvated alanine dipeptide is discussed.     

Partitioning of tryptophan side-chain analogs between water and cyclohexane.

We have measured the partitioning of the tryptophan side-chain analogs 3-methylindole and N-methylindole between water and cyclohexane over the temperature range 8-55 degrees C to investigate the relative contribution of the imine-NH- to the free energy of transfer. We take advantage of the fact that the indole imine nitrogen is blocked by a methyl group in N-methylindole. Unlike previous studies, we take into account the water present in the cyclohexane phase. Free energies of partitioning were calculated using mole-fraction, volume-fraction, and Flory-Huggins-corrected volume-fraction partition coefficients [De Young, L. R., & Dill, K. A. (1990) J. Phys. Chem. 94, 801-809; Sharp, K. A., Nicholls, A., Friedman, R., & Honig, B. (1991) Biochemistry 30, 9686-9697]. These approaches account for configurational entropy changes in different ways and thus lead to different values for the calculated free energies of transfer. There is a 2-3-fold difference in the free energies calculated from our measurements, using the different units. Independent of units, the partitioning of both compounds involves identical entropy changes. However, 3-methylindole has an additional unfavorable enthalpic contribution to partitioning into cyclohexane of +1.6 kcal/mol (independent of units) which is presumably the cost of removing the indole -NH- group from water and transferring it to cyclohexane. In cyclohexane, 3-methylindole forms hydrogen bonds with water that cause water to copartition into cyclohexane with the solute. A method is described which allows the partitioning process to be examined independent of subsequent interactions with water in the solvent.     

The Barrier Domain for Solute Permeation Varies With Lipid Bilayer Phase Structure

The chemical selectivities of the transport barriers in lipid bilayers varying in composition and phase structure (gel-phase DPPC and DHPC bilayers and liquid-crystalline DPPC/CHOL/50:50 mol% bilayers) have been investigated by determining functional group contributions to transport of a series of α-substituted p-toluic acid analogs obtained in vesicle efflux experiments. Linear free energy relationships are established between the free energies of transfer for this series of compounds from water to the barrier domain and corresponding values for their transfer from water into six model bulk solvents (hexadecane, hexadecene, decadiene, chlorobutane, butyl ether, and octanol) determined in partitioning experiments to compare the barrier microenvironment to that in these model solvents. The barrier microenvironment in all bilayers studied is substantially more hydrophobic than octanol, thus establishing the location of the barrier beyond the hydrated headgroup interfacial region, as the interface is expected to be more hydrophilic than octanol. The chemical nature of the barrier domain microenvironment varies with bilayer phase structure. The barrier regions in non-interdigitated DPPC and interdigitated DHPC gel-phase bilayers exhibit some degree of hydrogen-bond acceptor capacity as may occur if these domains lie in the vicinity of the ester/ether linkages between the headgroups and the acyl chains. Intercalation of 50 mol% cholesterol into DPPC bilayers, which induces a phase transition to a liquid-crystalline phase, substantially increases the apparent barrier domain hydrophobicity relative to gel-phase bilayers to a nonhydrogen bonding, hydrocarbonlike environment resembling hexadecene. This result, combined with similar observations in liquid-crystalline egg-PC bilayers (J. Pharm. Sci. (1994), 83:1511–1518), supports the notion that the transition from the gel-phase to liquid-crystalline phase shifts the barrier domain further into the bilayer interior (i.e., deeper within the ordered chain region). Received: 16 September 1997/Revised: 14 May 1998     

The nature of the hydrophobic binding of small peptides at the bilayer interface: implications for the insertion of transbilayer helices

One method of obtaining useful information about the physical chemistry of peptide/bilayer interactions is to relate thermodynamic parameters of the interactions to structural parameters obtained by diffraction methods. We report here the results of the application of this approach to interactions of hydrophobic tripeptides of the form Ala-X-Ala-O-tert-butyl with lipid bilayers. The thermodynamic constants (delta Gt, delta Ht, and delta St) for the transfer of the tripeptides from water into DMPC vesicles were determined for X = Leu, Phe, and Trp and found to be consistent with those expected for hydrophobic interactions above the phase transition of DMPC. Combining these results with the earlier ones of Jacobs and White [(1986) Biochemistry 25, 2605-2612], the favorable free energies of transfer with different amino acids in the -X- position increase in the order Gly less than Ala less than Leu less than Phe less than Trp in agreement with the Nozaki and Tanford [(1971) J. Biol. Chem. 246, 2211-2217] hydrophobicity scale. Determination of the location of Ala-[2H5]Trp-Ala-O-tert-butyl in oriented DOPC bilayers by neutron diffraction shows that the most hydrophobic peptide of the series is confined to the bilayer headgroup/water region. Refinement of the diffraction measurements shows that only 13% of the tryptophan is associated with the hydrocarbon core. The distribution of the water tends to mirror that of the peptide. Unlike peptide-free bilayers, 5% of the water penetrates the hydrocarbon, which is about 100-fold greater than expected. A quantitative thermodynamic analysis of the interfacial binding of the peptides suggests that (1) the hydrophobic interactions are 60-70% complete upon binding at the bilayer interface, (2) the interface is likely to play an important role in helix formation and insertion, (3) the hydrogen bond status of amino acid side chains is crucial to insertion, and (4) an a priori lack of knowledge of the status of such bonds could limit the precision of hydrophobicity plots. We introduce an interfacial hydrophobicity scale, IFH(h), with a variable hydrogen bond parameter (h) that permits one to consider explicitly hydrogen bonding in transbilayer helix searches.     

Hydrophilicity of polar amino acid side-chains is markedly reduced by flanking peptide bonds

Several amino acid side-chain hydropathy scales have been devised on the basis of solubility and water/organic solvent partitioning data obtained with free amino acids or side-chain analogs. In nearly all cases, these scales are based upon the structure-additivity assumption; it has been assumed that the transfer free energies of the amino acid side-chains are the same in these model compounds as they are in a polypeptide. This assumption is probably wrong. In the present study, deviations from additivity for amino acid side-chains are demonstrated by comparing a theoretically derived scale, which N-acetylamino acid amides. The results show that the flanking peptide bonds dramatically reduce the hydrophilicity of the polar side-chains, with deviations up to several kilocalories (1 kcal = 4.184 kJ) for the charged side-chains at pH 7.0. Further calculation shows that these deviations are due to reductions of 40 to 85% in the unfavorable transfer free energy of the polar functional groups. In addition, proximity of the neighboring amide bonds in the parent molecule (N-acetylglycine amide) decreases the hydrophilicity of the -CONH-backbone unit by 36%. This decrease is expected to be twice as large for -CONH- units in the interior of a polypeptide backbone. The significance of these observations is: (1) valid hydropathy scales can be obtained only with model peptides; (2) deviations from additivity are expected in all solvent systems, including non-polar solvents that are thought to mimic the interior of a membrane; (3) the spontaneous insertion of polypeptides into membranes is likely to occur much more readily than has been previously thought. In order to estimate the free energy of transferring the side-chains and the polypeptide backbone from water to the interior of a lipid bilayer, the results of this study are used to construct a hydropathy scale based upon the partitioning of solutes between water and non-polar solvents. The validity of hydropathy scales that are based on criteria other than solubility and water/organic solvent partitioning data is also discussed.     

The importance of the membrane interface as the reference state for membrane protein stability

The insertion of nascent polypeptide chains into lipid bilayer membranes and the stability of membrane proteins crucially depend on the equilibrium partitioning of polypeptides. For this, the transfer of full sequences of amino-acid residues into the bilayer, rather than individual amino acids, must be understood. Earlier studies have revealed that the most likely reference state for partitioning very hydrophobic sequences is the membrane interface. We have used μs-scale simulations to calculate the interface-to-transmembrane partitioning free energies ΔG_S→TM for two hydrophobic carrier sequences in order to estimate the insertion free energy for all 20 amino acid residues when bonded to the center of a partitioning hydrophobic peptide. Our results show that prior single-residue scales likely overestimate the partitioning free energies of polypeptides. The correlation of ΔG_S→TM with experimental full-peptide translocon insertion data is high, suggesting an important role for the membrane interface in translocon-based insertion. The choice of carrier sequence greatly modulates the contribution of each single-residue mutation to the overall partitioning free energy. Our results demonstrate the importance of quantifying the observed full-peptide partitioning equilibrium, which is between membrane interface and transmembrane inserted, rather than combining individual water-to-membrane amino acid transfer free energies.     

Interactions of small nonpolar molecules with biological membranes: an exactly solvable model

An exactly solvable model of the interaction of small nonpolar molecules with biological membranes is developed. This model, which is based upon a “decorated dimer model” extension of Nagle's membrane model, is demonstrated to qualitatively reproduce many of the changes in the order-disorder phase transition seen when biological membranes are exposed to anesthetic gases. The decorated dimer model is itself interesting because it provides an example of an exactly solvable monomer-dimer model in which phase transitions can occur in the presence of monomers.     

Effect of substitution of hydrogen oxide by deuterium oxide on thermotropic transition between the interdigitated gel phase and the ripple phase of dihexadecylphosphatidylcholine.

Thermotropic transitions of dihexadecylphosphatidylcholine (DHPC) dispersions in hydrogen oxide (1H2O) and deuterium oxide (2H2O) were investigated by differential scanning calorimetry (DSC). In DHPC dispersions, transition temperature between interdigitated gel phase (L beta I) and ripple phase (P beta') is lower in 2H2O than in 1H2O, and transition between the ripple phase (P beta') and fluid phase (L alpha) in 2H2O occurs at a temperature slightly higher than in 1H2O. In dipalmitoylphosphatidylcholine (DPPC) dispersions, on the other hand, transition temperature between lamellar gel phase (L beta') and ripple phase is higher in 2H2O than in 1H2O. These results suggest that the interdigitated gel phase is more stable in 1H2O than in 2H2O. To account for the shift of transition temperature by the water substitution, difference of interfacial energies between these aqueous environments is discussed.     

Behaviour of small solutes and large drugs in a lipid bilayer from computer simulations

To reach their biological target, drugs have to cross cell membranes, and understanding passive membrane permeation is therefore crucial for rational drug design. Molecular dynamics simulations offer a powerful way of studying permeation at the single molecule level. Starting from a computer model proven to be able to reproduce the physical properties of a biological membrane, the behaviour of small solutes and large drugs in a lipid bilayer has been studied. Analysis of dihedral angles shows that a few nano seconds are sufficient for the simulations to converge towards common values for those angles, even if the starting structures belong to different conformations. Results clearly show that, despite their difference in size, small solutes and large drugs tend to lie parallel to the bilayer normal and that, when moving from water solution into biomembranes, permeants lose degrees of freedom. This explains the experimental observation that partitioning and permeation are highly affected by entropic effects and are size-dependent. Tilted orientations, however, occur when they make possible the formation of hydrogen bonds. This helps to understand the reason why hydrogen bonding possibilities are an important parameter in cruder approaches which predict drug absorption after administration. Interestingly, hydration is found to occur even in the membrane core, which is usually considered an almost hydrophobic region. Simulations suggest the possibility for highly polar compounds like acetic acid to cross biological membranes while hydrated. These simulations prove useful for drug design in rationalising experimental observations and predicting solute behaviour in biomembranes.     

Theory of lipid monolayer and bilayer phase transitions: Effect of headgroup interactions

Summary Headgroup and soft core interactions are added to a lipid monolayer-bilayer model and the surface pressure-area phase diagrams are calculated. The results show that quite small headgroup interactions can have biologically significant effects on the transition temperature and the phase diagram. In particular, the difference in transition temperatures of lecithins and phosphatidyl ethanolamines is easy to reproduce in the model. The phosphatidic acid systems seem to require weak transient hydrogen bonding which is also conjectured to play a role in most of the lipid systems. By a simple surface free energy argument it is shown that monolayers under a surface pressure of 50 dynes/cm should behave as bilayers, in agreement with experiment. Although the headgroup interactions are biologically very significant, in fundamental studies of the main phase transition in lipids they are secondary in importance to the hydrocarbon chain interactions (including the excluded volume interaction, the rotational isomerism, and the attractive van der Waals interaction).     

Cooperative transition between two helical conformations in a linear system: Poly-L-proline I ⇌ II. I. Equilibrium studies

The solvent-induced conformational transition between the two helical forms of poly-L -proline is studied as a model for cooperative order ? order transitions. The chain length dependent equilibrium data in two solvent systems are described by Schwarz's theory, which is based upon the most general formulation of the linear Ising model with nearest neighbor interactions. The parameter σ which describes the difficulty of nucleation of a I (II) residue in an uninterrupted II (I)-helix is 10^?5 in both solvent systems. The ratios of the nucleation difficulties of states I and II at the ends of the chains β′ and β″ are very different in the two systems. Nucleation difficulty within the chain is interpreted as being due to unfavorable excess interaction energies at the I–II and II–I junctions, which add up to 7 kcal/mole of nuclei as calculated from the σ value. A similar value is computed from the atomic interactions at the junctions. In contrast to this intrinsic properly of poly-L -proline, the energies of I and II residues at the ends are heavily influenced by interactions of the endgroups with the solvent. The above values of the nucleation parameters are determined by a new least-square fitting procedure which does not necessitate the assumption of the dependence of the equilibrium constant s for propagation upon the external parameters, but yields this function from the experimental transition data. A quantitative explanation of this experimental s function through the binding of solvent is attempted. In the transition region a very small free energy change (about 0.1 kcal/mole), arising from a preferential binding of solvent molecules to one of the conformational states, is sufficient for a complete conversion from one helical form to the other.     

Polymer selection for biphenyl degradation in a solid-liquid two-phase partitioning bioreactor

The commercially available thermoplastic polymer Hytrel was selected as the delivery phase for the hydrophobic model compound biphenyl in a solid-liquid two-phase partitioning bioreactor (TPPB), and 2.9 g biphenyl could successfully be degraded in 1-L TPPBs by a pure culture of the biphenyl-degrading bacterium Burkholderia xenovorans LB400 in 50 h and by a mixed microbial consortium isolated from contaminated soil in 45 h. TPPBs consist of an aqueous cell-containing phase and an immiscible second phase that partitions toxic and/or poorly soluble substrates (in this case biphenyl) on the basis of maintaining a thermodynamic equilibrium. This paper illustrates a rational strategy for selecting a suitable solid polymeric substance for the delivery of the poorly water-soluble model compound biphenyl. The partitioning of biphenyl between the selected polymers and water was analogous to partitioning of solutes between two immiscible liquid phases. The partitioning coefficients varied between 180 for Nylon 6.6 and 11,000 for Desmopan, where the later numerical value is comparable to biphenyl partitioning coefficients between water and organic solvents. Employing a solid delivery phase enabled the utilization of a surfactant-producing microbial mixed culture, which could not be cultivated in liquid-liquid TPPBs and thereby extended the range of biocatalysts that can be employed in TPPBs.     

Solubilization of ubiquinone-10 in the lamellar and bicontinuous cubic phases of aqueous monoolein

Using X-ray diffraction measurements and polarizing microscopy, the solubilization of ubiquinone-10 (UQ10) was investigated in the lamellar and reversed bicontinuous cubic phases of aqueous monoolein (MO, 86 wt% of monooleoylglycerol). At 25 degrees C and UQ10 content below 0.5 wt%, a partial phase diagram of the MO/UQ10/H2O system indicated the same sequence of hydration-induced phases as found in the MO/H2O system. This low amount of coenzyme had no effect on the MO bilayer thickness and swelling behavior of phases, but it promoted thermotropic Q230-->HII phase transition. We suggested that the effect was determined by the UQ10 partitioning into the HII phase regions where the MO chains must be stressed upon the phase transition. At UQ10 contents above 0.5 wt%, a solid 'UQ10-rich' phase appeared inside the initially homogeneous phases within a few days. It was proposed that this process was driven by the coenzyme lateral diffusion in the MO bilayer.     

Static compression of articular cartilage can reduce solute diffusivity and partitioning: implications for the chondrocyte biological response.

Chondrocytes depend upon solute transport within the avascular extracellular matrix of adult articular cartilage for many of their biological activities. Alterations to bioactive solute transport may, therefore, represent a mechanism by which cartilage compression is transduced into cellular metabolic responses. We investigated the effects of cartilage static compression on diffusivity and partitioning of a range of model solutes including dextrans of molecular weights 3 and 40 kDa, and tetramethylrhodamine (a 430 Da fluorophore). New fluorescence methods were developed for real-time visualization and measurement of transport within compressed cartilage explants. Experimental design allowed for multiple measurements on individual explants at different compression levels in order to minimize confounding influences of compositional variations. Results demonstrate that physiological levels of static compression may significantly decrease solute diffusivity and partitioning in cartilage. Effects of compression were most dramatic for the relatively high molecular weight solutes. For 40 kDa dextran, diffusivity decreased significantly (p<0.01) between 8% and 23% compression, while partitioning of 3 and 40 kDa dextran decreased significantly (p<0.01) between free-swelling conditions and 8% compression. Since diffusivity and partitioning can influence pericellular concentrations of bioactive solutes, these observations support a role for perturbations to solute transport in mediating the cartilage biological response to compression.     

A model for the modulation of microvessel permeability by junction strands

To investigate the effect of junction strands on microvessel permeability, we extend the previous analytical model developed by Fu et al. (1994, J. Biomech. Eng., 116, pp. 502-513), for the interendothelial cleft to include multiple junction strands in the cleft and an interface between the surface glycocalyx layer and the cleft entrance. Based on the electron microscopic observations by Adamson et al. (1998, Am. J. Physiol., 274(43), pp. H1885-H1894), that elevation of intracellular cAMP levels would increase number of tight junction strands, this two-junction-strand and two-pore model can successfully account for the experimental data for the decreased permeability to water, small and intermediate-sized solutes by cAMP.