Surface pressure-dependent conformation change of apolipoprotein-derived amphipathic α-helices.

Amphipathic α-helices (AαH) are the primary structural motif of exchangeable apolipoproteins. AαHs in exchangeable apolipoproteins adsorb, remodel, and desorb at the surface of plasma lipoproteins in response to changes in their size or composition. A triolein/water (TO/W) interface was used as a model surface to study adsorption and desorption of AαHs at a lipoprotein-like interface. We previously reported that AαH peptides spontaneously adsorb to a TO/W interface, but they only partially desorb from the surface when the excess peptide was removed from the system. This finding suggests that “exchangeable” apolipoproteins are in fact partially exchangeable and only desorb from a surface in response to compression or change in composition. Here, we develop a thermodynamic and kinetic model to describe this phenomenon based on the change in the interfacial pressure (Π) of the C-terminal 46 amino acids of apolipoprotein A-I (C46) at a TO/W interface. This model suggests that apolipoproteins have at least two interfacial conformations that are in a surface concentration and Π-dependent equilibrium. This two-state surface equilibrium model, which is based on experimental data and is consistent with dynamic changes in Π(t), provides insights into the selective metabolism and clearance of plasma lipoproteins and the process of lipoprotein remodeling.

High-density lipoproteins (HDL) are protein-lipid assemblies that circulate in blood plasma and have a role in reverse cholesterol transport, detoxifi cation, and infl ammation response. HDL is commonly known as "good cholesterol" because it prevents the development of atherosclerotic plaques. HDL removes cholesterol and oxysterols from foam cell macrophages, preventing the progression of fatty streak development. Fatty streak development is an initial step in plaque formation. Therefore by removing sterols solution with peptide free buffer, called a "washout" ( 17,(21)(22)(23). If the peptide was in equilibrium with the bulk peptide, one would expect ⌸ to fall to 0 mN/m when the peptide was removed from the surrounding solution because when the surface peptide desorbed, the surface would not be replenished with bulk peptide. If the peptide was nonexchangeably bound to the TO/W interface (i.e., not in equilibrium with the bulk solution), one would expect no change in ⌸ during a washout, as occurs with amphipathic ␤ -sheet peptides ( 17 ). Surprisingly, when some A ␣ H peptides, such as C46 or N44, were removed from the surrounding solution, ⌸ reached a new equilibrium value, which was lower than the prewashout ⌸ but higher than 0 mN/m. This phenomenon was termed "partial exchangeability" ( 17 ). Partial exchangeability occurs in washout experiments with most exchangeable apolipoprotein-derived A ␣ H peptides we have tested, including apoC-I, short apoA-I-derived peptides (N44 and C46), and apolipoprotein mimetic peptides (Refs. 17, 24 , and unpublished observations). Partial exchangeability also occurred when the N-terminus of apoA-I (N44), C46, and full-length apoA-I were adsorbed to a TO/POPC/W interface and washed out ( 24,25 ). When partial exchangeability was originally reported in 2009, we did not have an explanation ( 17 ). In this article, we present a two-surface state thermodynamic and kinetic model that adequately describes the change in ⌸ during a washout, using C46 as a model A ␣ H-forming peptide. This model is used to speculate on the interfacial conformation and remodeling of C46 at a lipoprotein-like interface, and it may describe how exchangeable apolipoproteins remodel and exchange in response to changes in lipoprotein composition and size.

Methods
All experiments were performed with an IT Concepts Oil-Drop Tensiometer (Longessaigne, France) ( 26 ). See supplementary Fig. I for more detail about the instrument. A 16 l drop of TO was formed at the tip of a J-tube submerged in 6 ml of bulk buffer. The bulk buffer was 2 mM sodium phosphate buffer (PB) at a pH of 7.4 ± 0.1. The drop was >99.7% pure TO (Nu-Chek Prep, Elysian MN). A 0.5-250 l of the C46 stock solution (see below) was added to the 6 ml of bulk solution. For most experiments, 25 l of 1 mg/ml C46 stock was added for a fi nal concentration of ‫ف‬ 4.2 g/ml. C46 spontaneous adsorbs to the triolein/ water interface, and raises the ⌸ ( 18 ). The peptide was removed from the bulk solution by fl owing 220 ml of peptide-free bulk buffer through the cuvette. This effectively depleted the bulk peptide by >99.9% ( 17,(21)(22)(23). The process is referred to as a "washout." In general, after the washout, the drop either i ) rapidly compressed and then reexpanded repeatedly or ii ) slowly expanded linearly and then linearly compressed. In some experiments, peptide was readded to the bulk buffer after a washout. During the experiments, drop volume, area, and surface tension ( ␥ ) were recorded. ⌸ was calculated by subtracting the ␥ of a TO/C46/W interface from the ␥ of a clean TO/W interface ( ⌸ = 32 Ϫ ␥ ). The specifi c details of individual experiments are given in the Results section. Apolipoprotein (apo)A-I is the principal protein component of HDL and is present in the surface of chylomicrons and VLDL. The structure of apoA-I is a series of A ␣ Hs ( 3 ). The core of apoA-I (aa 44-185) is a series of homologous 11/22 mer tandem repeats of A ␣ Hs (called A-and B-type helices), which are separated by prolines to encourage bend, turn, or loop formation ( 2,4 ). The N-terminus (aa 1-43) and C terminus (aa 186-243) of apoA-I also contain some A ␣ Hs but do not have the repeated sequence of the core helices ( 5,6 ). By forming a series of A ␣ Hs with fl exible loops between each helix, apoA-I can form soluble monomers in water at low concentration by forming a hydrophobic protein core. It can also bind to a lipoprotein with its amphipathic helices interacting with the lipids ( 2,7,8 ). The conformation of apoA-I at a lipid interface likely depends on the lipid composition and protein surface concentration. For example, at near-saturated protein conditions (when apoA-I was in excess), only the C terminus of apoA-I bound to egg phosphatidyl choline (EPC) vesicles, and the remaining N-terminus (aa 1-198) did not interact with lipid ( 9 ). When EPC surface was in excess, the entire protein appeared to interact ( 9 ). This suggests a bulk concentration dependence on the apoA-I interfacial structure in which only the C terminus of apoA-I directly interacts with lipid at a high protein surface concentration and presumably lipoprotein surface pressure ( ⌸ ).
An unanswered question in lipoprotein physiology is how exchangeable apolipoproteins transfer between lipoprotein particles. One possibility is that lipid-bound apolipoproteins are in a concentration-dependent equilibrium with soluble plasma apolipoproteins. In other words, the exchangeable apolipoproteins are constantly adsorbing and desorbing from a lipoprotein surface. To test this hypothesis, Small et al. adsorbed small A ␣ H peptides to a pendant triolein (TO) drop and examined their compressibility and exchangeability (17)(18)(19)(20). A TO drop is an adequate model for a lipoprotein core in which lipoprotein surface components can be adsorbed to the triolein/water (TO/W) interface, thus creating a lipoprotein-like surface. The surface pressure ( ⌸ ) and area of the drop can be monitored with a drop tensiometer (supplementary Fig. I).
A ␣ H peptides adsorbed to a TO/W interface and increased ⌸ by 10-17 mN/m (17)(18)(19)(20). After the A ␣ H peptides were adsorbed to the surface, the soluble peptide was removed from the system by exchanging the surrounding area, ⌸ returned to a lower value than before the compression. The difference in ⌸ means that the peptide desorbed from the surface after a compression. Compression of the surface caused the peptide surface concentration ( ⌫ ) to increase. The increase in ⌫ caused some of the nonexchangeable peptide on the surface to become exchangeable and desorb from the surface. Therefore, compression of C46 caused the peptide to desorb from the surface. However, C46 does not fully desorb spontaneously without a compression.

Model of partial exchangeability
Using this data, a two-surface state model of C46 or N44 was developed ( Fig. 3 ). The most reasonable conclusion from this data is that the soluble state (S) of the peptide is in bulk concentration-dependent adsorption-desorption equilibrium with the exchangeable (Ex) surface state of the peptide. The Ex and nonexchangeable (NE) states are in a surface concentration ( ⌫ )-and/or ⌸ -dependent equilibrium. The Ex conformation of the peptide can exert more ⌸ on the surface, but the NE conformation occupies a larger area. The peptide maximizes ⌸ by adopting both the Ex and NE conformations when there is not an excess of surface peptides. A quantitative thermodynamic model would better describe this system and allow testing of these hypotheses about helix exchangeability.
We make the assumption that the soluble state of the peptide is a random unfolded coil. Zhu and Atkinson ( 5 ) found that at concentrations of 5 g/ml, a random coil circular dichroism spectrum was obtained, and they concluded that protein was unfolded and only folded at higher concentrations, reaching a fully folded state only about concentration of 100 g/ml. This is well above the concentration of this study. While it is possible that the soluble peptide at this concentration might exist in many partly folded states that only exist for a very short time (<1 msec), we have chosen to assume that the "soluble state" of the peptide is a single state.
The state variables of the system can be defi ned from fi rst principles. A mass balance can be used to defi ne the number of moles in each state: Where N is the number of molecules, and the subscripts Ex, NE, and S represent the exchangeable, nonexchangeable, and soluble states of the peptide. A useful defi nition is the number of surface molecules (N Sur ): The area is defi ned as: Where APM is the area per molecule in each state, C v is the number of vacant binding site, and A B is the area per binding site. At equilibrium, C V A B will make a small contribution to A, so the fi rst assumption is C V A B = 0, simplifying equation 3 to:
The peptide was lyophilized and stored long-term at Ϫ 80°C. A stock solution of peptide was made by adding 2 mM PB, pH 7.4, to a fi nal peptide concentration of 1 mg/ml. The stock solution was stored at 4°C for up to a week. For drop tensiometery experiments, 0.5-250 l of the stock solution was added to the 6 ml of bulk solution. For most experiments, 25 l of 1 mg/ml peptides stock was added for a fi nal concentration of ‫ف‬ 4.2 g/ml.

Characterization of partial exchangeability
C46 is partially exchangeable at a TO/W interface. Partial exchangeability was demonstrated by washing the peptide out of the solution surrounding a TO drop after adsorption ( Fig. 1A , B ). Partial exchangeability is characterized by a change in ⌸ during a washout, without ⌸ returning to the ⌸ of a peptide-free TO/W interface (i.e., ⌸ = 0 mN/m). Partial exchangeability is a thermodynamic phenomenon; thus, by developing a thermodynamic model of the process, we can better understand and potentially prove the mechanism. One requirement for using thermodynamic analysis is that the change must be reversible. To prove reversibility, we readded the peptide to the surrounding solution at the prewashout concentration ( Fig. 1A ). Readding the peptide caused ⌸ to return to the prewashout value; therefore, the change in ⌸ caused by the washout is reversible. Washing out and readding the peptide was repeated up to four times with a similar result (data not shown).
In 2007, Wang et al. demonstrated that the prewashout equilibrium ⌸ was dependent on the bulk concentration of C46 adsorbed at a TO/W interface ( 18 ). In this article, we confi rm those results ( Fig. 1A ) and show that the postwashout ⌸ was independent of the prewashout bulk concentration. Four examples of the washout intervals at different initial concentrations are shown in Fig. 1B . The relationship between prewashout and postwashout equilibrium surface tension ( ␥ ) is shown in Fig. 1C, D . The prewashout ␥ did not change above a concentration of ‫ف‬ 10 g/ml, which was used to defi ne the saturated pressure ( ⌸ SAT = 32 Ϫ ␥ SAT ). The ⌸ after a washout was independent of prewashout bulk concentration and was defi ned as the washout pressure ( ⌸ WO = 32 Ϫ ␥ WO ). This indicates that the exchangeable state is in equilibrium with the solution, whereas the nonexchangeable state is not.
Wang et al. showed that prewashout compression of a TO/ C46/W interface caused the peptide to be expelled from the surface but that the peptide readsorbed when the surface was reexpanded ( 18 ). Postwashout compressions and reexpansions of C46, also known as a stress-response experiment, are shown in Fig. 2 . When a TO/C46/W interface was rapidly compressed and then reexpanded to the original Partial surface pressure ( ) is thermodynamically defi ned as: By combining equations 4-7 , the surface equilibrium constant is defi ned as: Surface pressure ( ⌸ ) can be defi ned by the law of partial pressures adapted for two dimensions: Where is the partial surface pressure of the Ex or NE state and x is the fraction of the area occupied by each state, defi ned as:  ( 18 ), but the postwashout ␥ was independent of the prewashout bulk concentration. The prewashout ␥ was higher at a higher bulk C46 concentration, e.g., at 16.6 g/ml (blue) the equilibrium ␥ was 1.5 mN/m lower than that at 0.16 g/ml (purple). (C and D) The prewashout ⌸ was dependent on bulk concentration (black diamonds, top). Before the washout, ⌸ was related to [C46] by the relation ⌸ = 1.12log([C46])+15.162 (R 2 = 0.946) . ⌸ was saturated at a bulk concentration >10 g/ml. The ⌸ at the saturated concentration is defi ned as ⌸ SAT . The postwashout ␥ was not dependent on bulk concentration (gray squares, bottom). The ⌸ after a washout is defi ned as ⌸ WO . ⌸ was calculated by subtracting the ␥ of a TO/C46/W interface from the ␥ of a clean TO/W interface ( ⌸ = 32 Ϫ ␥ ). centration (>10 g/ml; see Fig. 1B ). In the fi rst case, we assume that, after a washout, the number of soluble and exchangeable peptide molecules is effectively zero: Fig. 1C ), which according to equations 1 and 5 is equal to NE . Therefore:

NE WO
In the second case, after a washout, there is an excess of surface molecules in the system. When there is an excess of bulk peptide to saturate ⌫ , most of the peptide will be in the smaller APM conformation. The Ex form has a smaller APM than the NE form because compressing the surface postwashout ( Fig. 3 ) causes the NE to convert to the Ex state. If the NE had a smaller APM, expanding the surface postwashout would cause NE to convert to Ex, which is not the case. Therefore, we can assume that when ⌸ is saturated by having a high bulk concentration of peptide, the number of NE molecules is negligible because there will be a much larger population of Ex than NE molecules. Thus, we have assumed: The ⌸ at saturated concentration equals ⌸ SAT (defi ned in Fig. 1D ), which according to equations 2 and 5 , is equal to Ex :

Ex SAT
Calculating the structural factor NE Ex APM APM fi rst requires consideration of how a TO/C46/W interface responds to a rapid compression (shown in Fig. 2 ). When the surface was compressed, ⌸ rapidly rose and then slowly fell over the next 3-5 min. The change in ⌸ was accompanied by a decrease in the number of peptide molecules on the surface. There are two steps to the conversion of NE to S molecules. The fi rst step is a conformational arrangement of the protein on the surface to go from NE to Ex, presumably through protein remodeling and two-dimensional diffusion. In the second step, Ex molecules desorb from the surface. In general, protein remodeling events occur on the timescale of nanoseconds to microseconds . On the other hand, protein desorption occurs on the timescale of milliseconds to hours. Therefore, it is reasonable to assume that NE and Ex reach an equilibrium much faster than the Ex and S forms. After a rapid compression, ⌸ rapidly decreases. Since NE and Ex reach an equilibrium quickly (meaning faster than the sampling rate of ‫ف‬ 2 points/sec), ⌬ G Ex → NE will equilibrate before a signifi cant amount of peptide has desorbed from the surface. The larger the compression, the more favorable the Ex form will be. If a compression is large enough, such that ⌸ immediately after a compression is very close to ⌸ SAT , the ratio of the area before and after a compression will be equal to the ratio of the APM of the NE and Ex forms. Mathematically stated: A derivation of Sur eq K is included in the supplemental materials. Equation 10 can be used to defi ne the surface Gibbs free energy between the two surface states as: Where R is the universal gas constant, and T is the temperature.
Equation 10 is an insightful formula, which requires some thought to appreciate. It defi nes the relative number of molecules in the two surface states as a function of an experimentally measureable parameter ( ⌸ , which is based on the difference in conformation of the two states, and two energy constants ( NE , Ex ), which are related to the interfacial activity of the two surface states. These parameters defi ne Sur eq K . The constants in this equation ( NE , Ex , and NE Ex APM APM ) can be calculated from drop tensiometry data. With these constants known, the surface equilibrium of NE and Ex can be quantitatively defi ned.

Two-state surface equilibrium model constants
Calculating the value of NE and Ex is reasonably straightforward by analyzing two cases: i ) after a washout and ii ) before a washout at saturating bulk peptide con- Fig. 2. Postwashout compressions caused ⌸ to rapidly rise and then recovered to a new equilibrium value near the precompression ⌸ . When the surface was reexpanded, ⌸ was lower than the precompression ⌸ . This indicates that some of the peptide was expelled from the surface by compression. In other words, the nonexchangeable state can convert to the exchangeable state of the peptide by a compression. Where k A is the adsorption constant, C V is the number of vacated binding sites, and k D is the desorption constant.
This kinetic model now introduces a new assumption and three new unknowns to the system of equations. Fortunately, after a washout N S will be equal to zero, therefore r A will also be equal to zero (see equation 13 ). With this in mind, equation 14 can be combined with the two state thermodynamic model to predict the ⌸ (t) during a washout: See the supplementary material for the derivation of these two kinetic equations in proof V .
Although these are complex equations, all the parameters in these equations are known from experimental data except k D . One set of experiments can be used to correlate k D using the known values of NE , Ex , and  can be used to calculate ⌬ G Ex → NE during adsorption, during a washout, and after a postwashout rapid compression. The value of ⌬ G Ex → NE during these events is shown in Fig. 5 . During the adsorption, ⌬ G Ex → NE increased until a new equilibrium value near 7 kJ/mol. During a washout, ⌬ G Ex → NE decreased sigmoidally to a value of Ϫ 7 kJ/mol. When the surface was compressed, ⌬ G Ex → NE immediately increased, then slowly decreased to a new equilibrium value near the postwashout value.

Kinetic model of desorption
Although this is a fully defi ned surface equilibrium model, the validity of the model would be strengthened by demonstrating its ability to predict a change in ⌸ (t) either during a washout or after a postwashout compression. Unfortunately, the thermodynamic data has been exhausted in determining Sur eq K . To test the validity of the two-state equilibrium model of Sur eq K , a kinetic model must be invoked to predict either a washout or the compression response over 3-5 min. Without any information about the order of the kinetics, a fi rst-order adsorption and desorption model is the best possible assumption. By again assuming that NE and Ex reach equilibrium much faster than Ex and S, the rate equations can be simplifi ed to the rate of adsorption (r A ) and the rate of desorption (r D ):  At 47 min (arrow), the surface was rapidly reduced by ‫ف‬ 30% to 20.6 mm 2 . After the compression, peptide slowly desorbed from the surface. Gibbs free energy is defi ned as: Pressure is traced in black and Gibbs free energy is traced in gray. larger compressions (see supplementary Fig. IV). When ⌸ remained below ⌸ WO , the compressions were reversible, and when ⌸ exceeded ⌸ WO , there was a loss of area during the next compression (supplementary Fig. IV).

DISCUSSION
In circulation, plasma lipoproteins remodel as their composition and size change due to enzyme-mediated fl ux of hydrophobic core lipids. For example, lecithin-cholesterol acyltransferase (LCAT) esterifi es amphipathic cholesterol with a fatty acid-forming hydrophobic cholesterol ester on the surface of HDL. Lipid-bound apoA-I is a cofactor for LCAT. The esterifi cation causes the cholesterol to transfer from the surface to the core, thus increasing the number of core lipids. Due to LCAT and other plasma factors, HDL particles can grow as they accumulate cholesterol ester. Presumably as the particle grows, ⌸ decreases due to less surface crowding. In other words, as the surface area increases, the surface pressure decreases. Lipoprotein particles can also shrink in circulation due to the enzymatic activity of lipoprotein lipase (LPL). LPL requires apoC-II on the surface of chylomicrons or VLDL as a cofactor ( 27 ). On the surface of lipoproteins, LPL hydrolyzes hydrophobic triacylglyceride to two free fatty acids and a monoacylglyceride. The products of this reaction are amphipathic and surface active. Therefore, LPL-mediated hydrolysis results in a depletion of the lipoprotein core and an increased number of molecules on the surface, causing surface crowding. The surface crowding and decrease in surface area result in an increase in the ⌸ of a lipoprotein.
Alternate methods of exchange have been employed by others. The presence of exchange and rate of exchange depend on the system employed and the methods. In an in vitro system, after incubating chylomicrons with increasing supplementary Figs. II and III. The good agreement between the model and experimental data indicates that the twosurface state thermodynamic model and fi rst-order kinetics adequately describe partial exchangeability of C46. In addition, the constants derived from this model are physically reasonable.

Linear isotherm of a TO/C46/W interface
The ⌸ -A relationship during a linear compression of C46 can be related to the two-state thermodynamic model. The ⌸ -A relationship was determined by adsorbing the peptide to the surface, washing out the excess peptide, linearly expanding to the maximum area, and then linearly compressing ( Fig. 7A ). The compression isotherm is shown in Fig. 7B . The rate of compression ( ⌬ ⌬ A, ‫ف‬ 2.7 mm 2 /min) was fast relative to the desorption constant (0.3 min Ϫ 1 ). During the compression when ⌸ was below ⌸ WO , ⌸ was predicted to be inversely proportional to area by the relationship: When ⌸ is > ⌸ WO and < ⌸ SAT , both surface states will be in equilibrium, and the ⌸ will be dependent on both time and area by the relationship: As the compression proceeds, Ex will accumulate on the surface because the compression converts NE to EX faster than the rate of Ex desorption. This causes Ex to plateau at ⌸ SAT . The reversibility was tested by repeatedly linearly compressing and expanding the surface with progressively a lipoprotein shrinks, ⌸ increases, which prefers the compact Ex conformation. As a lipoprotein grows, ⌸ decreases, encouraging an apolipoprotein to spread and convert to the NE conformation.
According to the two-state thermodynamic model, the interfacial structure affects both APM and partial pressure ( ). Without any information about the absolute number of molecules on the surface, there is no way to calculate the APM of each surface state. was inversely related to APM, and thus, was also unknown. However, the relative areas and 's of surface transition states were directly calculated from experimental data. This can be related to the structure by making an educated guess about all the possible interfacial structures of each transition state. The possible interfacial structure combinations of high and low ⌸ states are related to the structure and energy factors, which can be used to relate structure and thermodynamics. To address this question, we can consider each A ␣ H as an independent lipid-binding unit. In this model, when a helix adsorbs to a hydrophobic interface, the entire hydrophobic face binds. The helix also desorbs as a single unit. Between each helix is a fl exible loop or proline. Aside from the peptide backbone constraints between the two helices, the A ␣ Hs were independent of one another in regard to their adsorption/desorption behavior. The desorption of the exchangeable form of C46 was quite slow (k D = 0.2 Ϫ 0.35 min Ϫ 1 ), suggesting that helix desorption was a rare event on a molecular scale that occurs stochastically. If only one helix was bound, the rare desorption events still allowed C46 to diffuse away from the surface. When a second helix binds, the peptide cannot diffuse from the surface because it was anchored by the lipid-bound helix. Both helices desorbing simultaneously is unlikely. The protein can only adsorb when all helices are detached. The NE form became exchangeable upon compression because at least one helix was pushed off by reduced area and the remaining helix desorbed stochastically.
There are three potential helices in C46, which are punctuated with prolines at aa 209 and 220 to disrupt amounts of HDL for 1 h, the apoA-1 (but not apoA-II) mass moved from HDL to nascent chylomicrons. However, when apoA-1-labeled chylomicrons were injected into live monkeys in vivo, the labeled chylomicron apoA-1 was transferred to HDL for the fi rst ‫ف‬ 3 h, showing that, unlike the in vitro system, chylomicron apoA-1 moves to HDL.
The difference in these systems shows that apoA-1 movement off of chylomicrons to HDL is driven by a number of factors in plasma, especially LPL activity and possibly a host of other plasma enzymes, coeffectors, and transfer proteins. We demonstrated that compression is suffi cient to exchange amphipathic ␣ -helices independent of other plasma factors.
As lipoproteins remodel, the exchangeable apolipoprotein profi le changes. In general, larger, low ⌸ lipoproteins, such as VLDL and chylomicrons, have more exchangeable apolipoproteins than smaller, high ⌸ lipoproteins, such as LDL. Exchangeable apolipoproteins are unable to bind a high ⌸ surface ( 28,29 ) and desorb when compressed (17)(18)(19)(20). The ⌸ where a lipoprotein is incapable of binding a lipoprotein surface is defi ned as the exclusion pressure ( 28,29 ). Apolipoproteins remodel their conformation in response to changes in ⌸ . The two-state thermodynamic model implies that the adsorption and remodeling are independent events. The binding of an exchangeable apolipoprotein is likely initiated by the most hydrophobic portion of the protein interacting with a lipoprotein surface with a ⌸ below its exclusion pressure. After interacting, the apolipoprotein can remodel to a NE surface conformation in which the apolipoprotein spreads on the surface. The ⌸dependent equilibrium between the interfacial conformations of an exchangeable apolipoprotein is defi ned by the surface equilibrium constant ( equation 10 ): The Ex conformation of an apolipoprotein has a smaller APM and higher than the NE conformation. As an independent lipid-binding unit, there are only seven potential interfacial structures: only one helix on the surface (H1, H2, or H3); two helices on the surface (H1 + H2, H2 + H3, or H1 + H3); or all three helices on the surface (H1 + H2 + H3).
Treating A ␣ Hs as independent binding units allows thermodynamics to be related to lipid-bound structure. To establish this relationship, we must make two assumptions: i ) the APAA was similar for in all A ␣ Hs (i.e., EX NE PAA PAA PAA A A A ) and ii ) ⌬ G W → O (calculated from the White-Wimley hydrophobicity scale) was roughly proportional to ⌬ G W → S .
These assumptions led to the following feasibility criteria (see the supplementary material for a deriva- Both of these criteria are directly related to experimental data and were used to determine the feasible lipidbound structures of C46 as a function of ⌸ . There are seven potential structure in either the Ex or NE form (supplementary Table I ( 2, 4-6, 12, 16, 30 ). A rough structure of the potential ␣ -helices can be identifi ed by making a helical wheel diagram. See Fig. 8 for a summary of the predicted helices of C46. The helical wheel predicts the amino acids in the hydrophobic face of an A ␣ H and thus the potential protein in contact with the lipid. Two parameters were deduced from the helical wheel diagram: i ) the number of amino acids in contact with the surface in that helix (# AA ) and ii ) the Gibbs free energy of transfer from water to oil of that helix ( ⌬ G W → O ). The # AA was determined by simply counting the number of amino acids in the hydrophobic face. The ⌬ G W → O was the sum of the ⌬ G W → O of all the amino acids in the hydrophobic face. The ⌬ G W → O was determined using the White-Wimley hydrophobicity scale (31)(32)(33). The # AA and ⌬ G W → O of each potential structure (where different sets of helices were on the surface) was calculated by summing the values of each individual helix in supplementary Table II. The N-terminal helix is aa 198-208. In most models of full-length apoA-I, this helix extends to aa 189 ( 2,5,(10)(11)(12)(13)16 ). There are three amino acids in the hydrophobic face of the A ␣ H (LAL), with a total ⌬ G W → O = Ϫ 8.4 kJ/mol, based on the White/Wimley hydrophobicity scale. The second helix, which spans aa 210-219, has four amino acids in the hydrophobic face (ALLL) and a ⌬ G W → O = Ϫ 13.6 kJ/mol. The third helix, aa 219-243, is distinguished from the other two helices because it is longer and has three aromatic amino acids in the face. For helix 3, # AA = 7 (VAFYFLL) and ⌬ G W → O = Ϫ 31.8 kJ/mol. If each helix is considered Fig. 8. Lipid binding of C46 induces the formation of A ␣ Hs. C46 is predicted to form three potential helices separated by prolines at aa 209 and 220. In full-length apoA-I, the fi rst helix (198-209) likely extends to aa ‫ف‬ 189. The C-terminal helix, helix 3 aa 220-238, is the longest and most hydrophobic in C46. The number of amino acids in the hydrophobic face (# AA ) and the Gibbs free energy of transfer from water to oil ( ⌬ G W O ) of each helix were determined based on the helical wheel diagrams based on the White/Wimley (W/W) and GES hydrophibicity scales. forms dictates the rate of lipoprotein lipase and thus how triacylglyceride is distributed. Conversely, apoE only binds to LDLr (or lipoprotein receptor-related protein) when it is associated to high ⌸ remnant particles ( 35 ). This model suggests that apoE must be in the compressed form (Ex) to clear chylomicron remnants, and although apoE is associated with low ⌸ chylomicrons, it only binds LDLr when it is compressed. These hypotheses are only speculation. ApoA-I is multifunctional and likely has multiple ⌸ -dependent surface conformations, each of which dictates the metabolic state of the lipoprotein. The remodeling and clearance of lipoproteins is dependent on both the apolipoproteins associated with the particle and their conformation.