Conformational characteristics of peptides and unanticipated results from crystal structure analyses

Preferred conformation and types of molecular folding are some of the topics that can be addressed by structure analysis using x-ray diffraction of single crystals. The conformations of small linear peptide molecules with 2-6 residues are affected by polarity of solvent, presence of water molecules, hydrogen bonding with neighboring molecules, and other packing forces. Larger peptides, both cyclic and linear, have many intramolecular hydrogen bonds, the effect of which outweighs any intermolecular attractions. Numerous polymorphs of decapeptides grown from a variety of solvents, with different cocrystallized solvents, show a constant conformation for each peptide. Large conformational changes occur, however, upon complexation with metal ions. A new form of free valinomycin grown from DMSO exhibits near three-fold symmetry with only three intramolecular hydrogen bonds. The peptide is in the form of a shallow bowl with a hydrophobic exterior. Near the bottom of the interior of the bowl are three carbonyl oxygens, spaced and directed so that they are in position to form three ligands to a K+, e.g., complexation can be completed by the three lobes containing the beta-bends closing over and encapsulating the K+ ion. In another example, free antamanide and the biologically inactive perhydro analogue, in which four phenyl groups become cyclic hexyl groups, have essentially the same folding of backbone and side chains. The conformation changes drastically upon complexation with Li+ or Na+. However, the metal ion complex of natural antamanide has a hydrophobic globlar form whereas the metal ion complex of the inactive perhydro analogue has a polar band around the middle. The structure results indicate that the antamanide molecule is in a complexed form during its biological activity. Single crystal x-ray diffraction structure analyses have identified the manner in which water molecules are essential to creating minipolar areas on apolar helices. Completely apolar peptides, such as membrane-active peptides, can acquire amphiphilic character by insertion of a water molecule into the helical backbone of Boc-Aib-Ala-Leu-Aib-Ala-Leu-Aib-Ala-Leu-Aib-OMe, for example. The C-terminal half assumes an alpha-helix conformation, whereas the N-terminal half is distorted by an insertion of a water molecule W(1) between N(Ala5) and O(Ala2), forming hydrogen bonds N(5)H...W(1) and W(1)...O(2). The distortion of the helix exposes C = O(Aib1) and C = O(Aib4) to the outside environment with the consequence of attracting additional water molecules. The leucyl side chains are on the other side of the molecule. Thus a helix with an apolar sequence can mimic an amphiphilic helix.     

Intramolecular hydrogen bonds and conformation of the lincomycin molecule in organic solvents

IR spectra (1600-1800 and 3000-3650 cm-1) of lincomycin base solutions in inert (CCl4 and C2Cl4), proton acceptor (dioxane, dimethylsulfoxide and triethyl amine) and proton donor (CHCl3, CD3OD and D2O) solvents were studied. Analysis of the concentration and temperature changes in the spectra revealed that association in lincomycin in the inert solvents was due to intramolecular hydrogen linkage involving amide and hydroxyl groups. Disintegration of the associates after the solution dilution and temperature rise was accompanied by formation of intramolecular bonds stabilizing the stable conformation structure of the lincomycin molecule. The following hydrogen linkage in the conformation was realized: NH...N (band v NH...N at 3340 cm-1), OH...O involving the hydroxyl at C-7 and O atoms in the D-galactose ring (band v OH...O at 3548 cm-1), a chain of the hydrogen bonds OH...OH...OH in the lincomycin carbohydrate moiety (band v OH...O at 3593 cm-1 and v OH of the end hydroxyl group at 3625 cm-1). Bonds NH and C-O of the amide group were located in transconformation. Group C-O did not participate in the intramolecular hydrogen linkage.     

Spectroscopic study on structure of horseradish peroxidase in water and dimethyl sulfoxide mixture

The structure of horseradish peroxidase (HRP) in phosphate buffered saline (PBS)/dimethyl sulfoxide (DMSO) mixed solvents at different compositions is investigated by IR, electronic absorption, and fluorescence spectroscopies. The fluorescence spectra and the amide I spectra of ferric HRP [HRP(Fe3+)] show that overall structural changes are relatively small up to 60% DMSO. Although the amide I band of HRP(Fe3+) shows a gradual change in the secondary structure and a decrease in the contents of a helices, its fluorescence spectra indicate that the distance between the heme and Trp173 is almost constant. In contrast, the changes in the positions of the Soret bands for resting HRP(Fe3+) and catalytic intermediates (compounds I and II) and the IR spectra at the C-O stretching vibration mode of carbonyl ferrous HRP [HRP(Fe2+)-CO] show that the microenvironment in the distal heme pocket is altered, even with low DMSO contents. The large reduction of the catalytic activity of HRP even at low DMSO contents can be attributed to the structural transition in the distal heme pocket. In PBS/DMSO mixtures containing more than 70 vol % DMSO, HRP undergoes large structural changes, including a large loss of the secondary structure and a dissociation of the heme from the apoprotein. The presence of the components of the amide I band that can be assigned to strongly hydrogen bonding amide C=O groups at 1616 and 1684 cm(-1) suggests that the denatured HRP may aggregate through strong hydrogen bonds.     

Beware of proteins in DMSO

The effect on the secondary structure of representative alpha-helical, beta-sheet and disordered proteins by varying concentrations of dimethyl sulphoxide (DMSO) in 2H2O has been investigated by Fourier transform infrared spectroscopy. Significant perturbations of protein secondary structure are induced by DMSO and DMSO/2H2O mixtures. For highly structured proteins, such as myoglobin and concanavalin A, the infrared spectra point to a progressive destabilisation of the secondary structure until at moderate DMSO concentrations (around 0.33 mol fraction) intermolecular beta-sheet formation and aggregation are induced, as indicated by the appearance of a strong band at 1621 cm-1. This is a direct consequence of the disruption of intramolecular peptide group interactions by DMSO (partial unfolding). At higher DMSO concentrations (above 0.75 mol fraction), such aggregates are dissociated by disruption of the intermolecular C = O...2H-N deuterium bonds. The presence of a single amide I band at 1662 cm-1 corresponding to free amide C = O groups indicates that at high concentrations and in pure DMSO the proteins are completely unfolded, lacking any secondary structure. While low concentrations of DMSO showed no detectable effect upon the gross secondary structure of myoglobin and concanavalin A, the thermal stability of both proteins was markedly reduced. In alpha-casein, a highly unstructured protein, the situation is one of direct competition. The amide I maximum in 2H2O, at 1645 cm-1, is typical of unordered proteins with C = O groups deuterium-bonded predominantly to 2H2O. Addition of DMSO disrupts such interactions by competing with the peptide C = O group for the deuterium bond donor capacity of the 2H2O, and so progressively increases the amide I maximum until it stabilizes at 1663 cm-1, a position indicative of free C = O groups.     

Theoretical and experimental study of the complexation of valinomycin with ammonium cation

The interactions of valinomycin, macrocyclic depsipeptide antibiotic ionophore, with ammonium cation NH4+ have been investigated. Using quantum mechanical density functional theory (DFT) calculations, the most probable structure of the valinomycin-NH4+ complex species was predicted. In this complex, the ammonium cation is bound partly by three strong hydrogen bonds to three ester carbonyl oxygen atoms of valinomycin and partly by somewhat weaker hydrogen bonds to the remaining three ester carbonyl groups of the valinomycin ligand. The strength of the valinomycin-NH4+ complex was evaluated experimentally by capillary affinity electrophoresis. From the dependence of valinomycin effective electrophoretic mobility on the ammonium ion concentration in the background electrolyte, the apparent binding (association, stability) constant (Kb) of the valinomycin-NH4+ complex in methanol was evaluated as log Kb = 1.52 +/- 0.22.     

Investigation of the thermal stability of porin from Paracoccus denitrificans by site-directed mutagenesis and Fourier transform infrared spectroscopy

The folding of membrane proteins was addressed using outer membrane protein porin from the soil bacterium Paracoccus denitrificans (P. den.). IR spectroscopy and sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) analysis were used to probe the effect of mutagenesis on the thermal stability of the protein. Secondary structure analysis by amide I ir spectroscopy showed that the wild-type protein was predominantly composed of beta-sheet, which supports the x-ray crystal structure information (A. Hirsch, J. Breed, K. Saxena, O.-M. H. Richter, B. Ludwig, K. Diederichs, and W. Welte, FEBS Letters, 1997, Vol. 404, pp. 208-210). The mutants E81Q, W74C, and E81Q/D148N were shown to have similar secondary structure composition as the wild type. Wild-type protein and the mutants in detergent micelles underwent irreversible denaturation as a result of heating. Transition temperature calculated from the amide I analysis revealed that mutant porins were slightly less stable compared to the wild type. The protein in micelles showed complete monomerization of the trimer above 85 degrees C. In native-like conditions (provided by liposomes), no change was observed in the secondary structure of the protein until 95 degrees C. This is supported by SDS-PAGE as no change in quaternary structure was observed, proving that the proteins are structurally thermostable in liposomes as compared to micelles. Our studies demonstrated that porins resistant to detergents and proteases are highly thermostable as well.     

A study of the conformations of valinomycin in solution phase

Vibrational absorption and vibrational circular dichroism (VCD) spectra of valinomycin are measured, in different solvents, in the ester and amide carbonyl stretching regions. The influence of cations, namely Li(+), Na(+), K(+), and Cs(+), in methanol-d(4) solvent is also investigated. Ab initio quantum mechanical calculations using density functional theory and 6-31G* basis set are used to predict the absorption and VCD spectra. A bracelet-type structure for valinomycin that reproduces the experimental absorption and VCD spectra in inert solvents is identified. For the structure of valinomycin in polar solvents, a propeller-type structure was optimized, but further investigations are required to confirm this structure. A symmetric octahedral environment for the ester carbonyl groups in the valinomycin-K(+) complex is supported by the experimental VCD spectra. The results obtained in the present study demonstrate that even for large macrocyclic peptides, such as valinomycin, VCD can be used as an independent structural tool for the study of conformations in solution.     

Optimization of the binding properties of a synthetic anion receptor using rational and combinatorial strategies

The solution conformations of tetrameric and hexameric cyclopeptides containing alternating L-proline and 6-aminopicolinic acid subunits strongly depend on solvent polarity. Whereas in polar solvents, such as d6-DMSO, both peptides prefer on average symmetric conformations with converging NH groups, in less polar chloroform intramolecular hydrogen bonds to the peptide NH groups stabilize other, and in the case of the hexapeptide, non-symmetrical conformations. Independent of the solvent, both peptides interact with anions via their NH groups but whereas anion binding requires a cleavage of the intramolecular hydrogen bonds accompanied by a conformational reorganization in chloroform, in polar solvents the peptides are already well preorganized for anion complexation. Complex formation between anions and the cyclic hexapeptide was even detected in highly competitive D2O/CD3OD or H2O/CH3CN mixtures, which was attributed to the special sandwich-type structure of the complexes formed. Stabilizing these 2:1 aggregates by covalently linking two cyclopeptide rings together affords ditopic receptors with a high anion affinity in protic solvents. Complex stability depends on the structure of the linker with which the two receptor moieties are connected and even more potent anion receptors were obtained by a dynamic combinatorial optimization of this linking unit.     

Etude par Spectroscopie Infrarouge de la Transformation Hélice—Chaine Statistique des Polypeptides. I. Etude Comparée de l'Interaction de la Poly-L-alanine et d'un Amide Modèle avec l'Acide Trifluoroacétique

Infrared spectra of poly-L -alanine in trifluoroacetic acid-chloroform mixtures have been investigated and compared with those of a model amide (N-methylacetamide). The purpose of this work is to determine the nature of peptide-acid specific interactions responsible for the helix-random coil transition of polymer chains. Analysis is made in using amide (A, I, II, III) and acid (νC?O, νOH) vibrations which are specially sensitive to molecular interactions. We examined a model compound to determine the spectral characteristics of the different complexes or species formed between amide and acid. At a low acid concentration, hydrogen-bonded complexes: ? (NH) C?O…?HOOCCF₃ (1) are evidenced but no association between amide NH and acid CO groups (complexes A) is observed. For higher acid concentrations complexes (I) are progressively changed into ions pairs and free ions, which result from amide protonation by acid, according to the exothermic equilibrium (I)?? (NH)COH⁺, ^?OOCCF₃(II). Amidium and carboxylate bands are localized between 1680–1705 cm^?1 and 1620–1625 cm^?1, respectively. If the cation band is always clearly seen, the anion band is only observed for the most acidic solutions. For the polymer, a gradual complexation of type (I) is observed for all acid concentrations. From our results, the assumption of an (A) type interaction seems very unlikely but cannot be excluded. Moreover, proton transfer—similar to that observed with a model amide—is never evidenced since, in particular, the amidium band characteristic of protonation is never seen. In contrast to previous investigations, we conclude that the helix-random coil transition of polypeptides is not due to the protonation of the peptide functions. This transition does suggest a strong interaction by hydrogen bonds between polymer and acid molecules.     

Structure of macrocyclic K+, Rb+-complexon of meso-valinomycin monohydrate, cyclo[-(D-Val-Hyi-Val-D-Hyi)3-].H2O, in a crystalline complex with dioxane by x-ray structural data]

The crystal structure of a valinomycin analogue, cyclo[-(D-Val-Hyi-Val-D-Hyi)3-]x(C60H102N6O18) crystallized with dioxane and water molecules, has been solved by X-ray direct methods. The conformation found is analogous to one established for free meso-valinomycin crystallized from other organic solvents. It is characterized by a centrosymmetric bracelet form, stabilized by six intramolecular 4----1 type hydrogen bonds between amide N-H and C = O groups. One water molecule is fixed asymmetrically by hydrogen bonds in the internal negatively charged cavity of the complexon. The meso-valinomycin molecule "bracelets" in the crystal form stacks alternatively with dioxane molecules.     

Structural stability of the erythrocyte anion transporter, band 3, in native membranes and in detergent micelles.

The exothermic thermal denaturation transition of band 3, the anion transporter of the human erythrocyte membranes, has been studied by differential scanning calorimetry, in ghost membranes and in nonionic detergent micelles. In detergent micelles the transmembrane domain of band 3 gave an irreversible denaturation transition (C transition). However, no thermal transition was observed for the N-terminal cytoplasmic domain when band 3 was solubilised in detergent micelles. A reduction in enthalpy (190-300 kcal mol-1) with an accompanying decrease in thermal denaturation temperatures (48-60 degrees C) for the C transition was observed in detergent solubilised band 3 when compared with ghost membranes. Unlike ghost membranes, two thermal transitions for band 3 in detergent micelles were observed for the C transition when in the presence of excess covalent inhibitor, 4,4'-diisothiocyanostilbene-2,2'-disulphonate (DIDS), which derive from the thermal unfolding of a single protein with two different thermal stabilities; DIDS-stabilised (75 degrees C) and DIDS-insensitive (62 degrees C). A reduction in the denaturation temperature for the transmembrane domain of band 3 was observed when compared with intact band 3 although no significant differences was observed in the corresponding enthalpy values. This indicates some cooperativity of the two domains of band 3 in maintaining the transmembrane conformation. The results presented in this study show that detergents of intermediate micelle size (e.g. Triton X-100 and C12E8) are required for optimal thermal stability of band 3.     

The crystal and molecular structure of cyclo-[-(D-Val-Hyi-Val-D-Hyi)3-] (meso-valinomycin,C60H102N6O18)

The crystal structure of the valinomycin analog, cyclo-[(-D -Val-Hyi-Val-D -Hyi-)₃-] (meso-valinomycin, C₆₀H₁₀₂N₆O₁₈) has been determined by direct x-ray diffraction procedures. The crystals are triclinic, space group P1 , number of molecules per unit cell Z = 1, and cell parameters a = 11.831, b = 13.815, c = 14.889 Å, α = 109.54°, β = 116.10°, γ = 98.89°. The atomic coordinates for the C,N,O atoms were refined in the anisotropic thermal motion approximation and for the H atoms in the isotropic approximation to R = 0.07. The structure is centrosymmetric and has a threefold axis of pseudosymmetry. The depsipeptide chain is in the form of a bracelet stabilized by six identical intramolecular 4 → 1 hydrogen bonds between the amide C?O and NH groups. The ester carbonyls are oriented towards the symmetry axis, their O atoms forming an ellipsoidal molecular cavity. The isopropyl side chains are located on the molecular periphery. The structure found differs considerably from the conformation of the crystalline naturally occurring antibiotic, valinomycin, but completely resembles that of valinomycin and meso-valinomycin in nonpolar solvents. In the crystal, meso-valinomycin molecules form stacks. The molecular cavities situated in the stacks one above the other along the pseudo-C₃ axis form a continuous channel, the internal surface of which is lined by O atoms. The possible conformations of depsipeptides of the valinomycin series and their mode of action in membranes are discussed in the light of the data obtained.     

Evidence for a folded structure of Met-enkephalin in membrane mimetic systems: 1H-nmr studies in sodiumdodecylsulfate, lyso-phosphatidylcholine, and mixed lyso-phosphatidylcholine/sulfatide micelles

¹H-nmr spectra of Met-enkephalin dissolved in aqueous solution of sodiumdodecylsulfate (SDS) micelles are reported as a function of pH and temperature. The temperature behavior of the amide protons is compared with that observed for the same peptide dissolved in aqueous solution of lyso-phosphatidylcholine (LPC) and lyso-phosphatidylcholine-sulfatide (LPC-SH) micelles. The temperature coefficients are affected by the micelle polarity, which suggests that the peptide backbone is not remote from the micelle surface. pH titration performed in the presence of SDS micelles gives a number of intrinsic and extrinsic pK_a values, indicative of a folded structure of the opioid molecule. This conformation is characterized by the existence of an intramolecular hydrogen bond involving the Met-5 amide proton and an interaction of the N-terminal residue with the aliphatic side chains of both Phe-4 and Met-5.     

The relationship of bound water to the IR amide I bandwidth of albumin

Four different types of ir experiments, involving changes in pH, changes in pressure, and the use of nonaqueous solvents, and with either albumin molecules dissolved in saline or adsorbed albumin films, support the hypothesis that the bandwidth of the amide I vibration of albumin is directly related to the amount of bound water in this protein. From the amide I band narrowing and the amide I shift to higher frequencies, it is proposed that a more ordered helix structure results as the amount of bound water is decreased.     

Crystal structure and solution conformation of S,S'-bis(Boc-Cys-Ala-OMe): intramolecular antiparallel beta-sheet conformation of an acyclic cystine peptide

The conformation of the acyclic biscystine peptide S,S'-bis(Boc-Cys-Ala-OMe) has been studied in the solid state by x-ray diffraction, and in solution by 1H- and 13C-nmr, ir, and CD methods. The peptide molecule has a twofold rotation symmetry and adopts an intramolecular antiparallel beta-sheet structure in the solid state. The two antiparallel extended strands are stabilized by two hydrogen bonds between the Boc CO and Ala NH groups [N...O 2.964 (3) A, O...HN 2.11 (3) A, and NH...O angle 162 (3) degrees]. The disulfide bridge has a right-handed conformation with the torsion angle C beta SSC beta = 95.8 (2) degrees. In solution the presence of a twofold rotation symmetry in the molecule is evident from the 1H- and 13C-nmr spectra. 1H-nmr studies, using solvent and temperature dependencies of NH chemical shifts, paramagnetic radical induced line broadening, and rate of deuterium-hydrogen exchange effects on NH resonances, suggest that Ala NH is solvent shielded and intramolecularly hydrogen bonded in CDCl3 and in (CD3)2SO. Nuclear Overhauser effects observed between Cys C alpha H and Ala NH protons and ir studies provide evidence of the occurrence of antiparallel beta-sheet structure in these solvents. The CD spectra of the peptide in organic solvents are characteristic of those observed for cystine peptides that have been shown to adopt antiparallel beta-sheet structures.     

The conformational analysis of peptides using fourier transform IR spectroscopy

Fourier transform infrared spectroscopy (FTIR) can be used for conformational analysis of peptides in a wide range of environments. Measurements can be performed in aqueous solution, organic solvents, detergent micelles as well as in phospholipid membranes. Information on the secondary structure of peptides can be derived from the analysis of the strong amide I band. Orientation of secondary structural elements within a lipid bilayer matrix can be determined by means of polarized attenuated total reflectance–FTIR spectroscopy. Hydrogen–deuterium exchange can be monitored by the analysis of the, amide II band. This review gives some example of peptide systems studied by FTIR spectroscopy. Studies on alamethicin and α-aminoisobutyric acid containing peptides have shown that FTIR spectroscopy is a sensitive tool for identifying 3₁₀-helical structures. Changes in the structure of the magainins upon interaction with charged lipids were detected using FTIR spectroscopy. Tachyplesin is an example of a β-sheet containing membrane active peptide. Polarized ir spectroscopy reveals that the antiparallel β-sheet structures of tachyplesin are oriented parallel to the membrane surface. Synthesis of peptides corresponding to functionally/structurally important regions of large proteins is becoming increasingly popular. FTIR spectroscopy has been used to analyze the structure of synthetic peptides corresponding to the ion-selective pore of the voltage-gated potassium channel. In biomembrane systems these peptides adopt a highly helical structure. Under conditions, where these peptides are aggregated the presence of some intermolecular β-sheet structure can also be detected. © 1994 John Wiley & Sons, Inc.     

A circular dichroism study of valinomycin barium ion complex

Complex formation of valinomycin with Ba²⁺ ions was investigated by circular dichroism spectroscopy. The results indicated that Ba²⁺ forms entirely different types of complexes when compared with K⁺. The data with perchlorate salt showed evidence for the formation of less stable V₂C (peptide sandwich), VC (1:1), and VC₂ (ion sandwich) complexes followed by a stable final complex upon gradual addition of salt (V stands for valinomycin and C for the cation). This final complex possibly has a flat structure with no internal hydrogen bonds, similar to that of valinomycin in highly polar solvents. The possible complexation mechanism and the role played by anions and isopropyl side chains are highlighted.     

Characterization of β-bend ribbon spiral forming peptides using electronic and vibrational CD

Terminally blocked (L-Pro-Aib)_n and Aib-(L-Pro-Aib)_n sequential oligopeptides are known to form right-handed β-bend ribbon spirals under a variety of experimental conditions. Here we describe the results of a complete CD and ir characterization of this subtype of 3₁₀-helical structure. The electronic CD spectra were obtained in solvents of different polarity in the 260-180 nm region. The vibrational CD and Fourier transform ir (FTIR) spectra were measured in deuterochloroform solution in the amide I and amide II (1750-1500 cm^?1) regions. The critical chain length for full development of the β-bend ribbon spiral structure is found to be five to six residues. Spectral effects related to concentration-induced stabilization of the structures of the longer peptides were seen in the resolution-enhanced FTIR spectra. Comparison to previous studies of (Aib)_n and (Pro)_n oligomers indicate that the low frequency of the amide I mode is due to the interaction of secondary and tertiary amide bonds and not to a strong difference in conformation from a regular 3₁₀-helix. © 1995 John Wiley & Sons, Inc.     

Influence of chirality,amino acid sequence,and protecting groups on the intramolecular interaction behavior of dipeptide and tripeptide derivatives

The intramolecular interaction of protected dipeptides and tripeptides containing the amino acid units Ala, Phe, and Val was studied by means of ir spectroscopy. The NH and CO regions of the compounds dissolved in carbon tetrachloride clearly show the existence of different intramolecular hydrogen bonds. Using solvents with higher polarity such as chloroform and methylene chloride, the association bands disappear. Investigating the substances with the same amino acid sequence but opposite chirality of the central C atom in the peptide chain, we observed different band shapes in the CO and NH regions. Large effects were found when the chirality of the Phe unit in the second position was changed. This is probably due to the steric hindrance originated by the rotation of the aromatic ring in the side chain. The protecting groups, Z (benzyloxycarbonyl) or Boc (tert-butyloxycarbonyl) residues at the N-terminal group and methyl- or tert-butyl esters at the C-terminal group, influence the solubility of the substances in nonpolar solvent, as well as the NH and CO association band profiles in the methylene chloride solutions. The consequences of changing the sequence of the amino acids are discussed for the tripeptide derivatives. Besides a qualitative discussion, some quantitative considerations concerning the intramolecular interaction are also given to illustrate the different stabilities of the associates. © 1996 John Wiley & Sons, Inc.     

Characterization of the solubilization of lipid bilayers by surfactants

This communication addresses the state of aggregation of lipid-detergent mixed dispersions. Analysis of recently published data suggest that for any given detergent-lipid mixture the most important factor in determining the type of aggregates (mixed vesicles or mixed micelles) and the size of the aggregate is the detergent to lipid molar ratio in these aggregates, herein denoted the effective ratio, Re. For mixed bilayers this effective ratio has been previously shown to be a function of the lipid and detergent concentrations and of an equilibrium partition coefficient, K, which describes the distribution of the detergent between the bilayers and the aqueous phase. We show that, similar to mixed bilayers, the size of mixed micelles is also a function of the effective ratio, but for these dispersions the distribution of detergent between the mixed micelles and the aqueous medium obeys a much higher partition coefficient. In practical terms, the detergent concentration in the mixed micelles is equal to the difference between the total detergent concentration and the critical micelle concentration (cmc). Thus, the effective ratio is equal to this difference divided by the lipid concentration. Transformation of mixed bilayers to mixed micelles, commonly denoted solubilization, occurs when the surfactant to lipid effective ratio reaches a critical value. Experimental evaluation of this critical ratio can be based on the linear dependence of detergent concentration, required for solubilization, on the lipid concentration. According to the 'equilibrium partition model', the dependence of the 'solubilizing detergent concentration' on the lipid concentration intersects with the lipid axis at -1/K, while the slope of this dependence is the critical effective ratio. On the other hand, assuming that when solubilization occurs the detergent concentration in the aqueous phase is approximately equal to the critical micelle concentration, implies that the above dependence intersects with the detergent axis at the critical micelle concentration, while its slope, again, is equal to the critical effective ratio. Analysis of existing data suggests that within experimental error both these distinctively different approaches are valid, indicating that the critical effective ratio at which solubilization occurs is approximately equal to the product of the critical micelle concentration and the distribution coefficient K. Since the nature of detergent affects K and the critical micelle concentration in opposite directions, the critical ('solubilizing') effective ratio depends upon the nature of detergent less than any of these two factors.