A Method For Estimating The Cholesterol Affinity Of Integral Membrane Proteins From Experimental Data

The cholesterol affinities of many integral plasma membrane proteins have been estimated by molecular computation. However, these values lack experimental confirmation. We therefore developed a simple mathematical model to extract sterol affinity constants and stoichiometries from published isotherms for the dependence of the activity of such proteins on membrane cholesterol concentration. The binding curves for these proteins are sigmoidal with strongly-lagged thresholds attributable to competition for the cholesterol by bilayer phospholipids. The model provided isotherms that matched the experimental data using published values for the sterol association constants and stoichiometries of the phospholipids. Three oligomeric transporters were found to bind cholesterol without cooperativity with dimensionless association constants of 35 for Kir3.4* and 100 for both Kir2 and a GAT transporter. (The corresponding ρG° values were -8.8, -11.4 and -11.4 KJ/mol, respectively.) These association constants are significantly lower than those for the phospholipids which range from ∼100 to 6,000. The BK channel, the nicotinic acetylcholine receptor and the M192I mutant of Kir3.4* appear to bind multiple cholesterol molecules cooperatively (n = 2 or 4) with subunit affinities of 563, 950 and 700, respectively. The model predicts that the three less avid transporters are approximately half-saturated in their native plasma membranes; hence, sensitive to variations in cholesterol in vivo. The more avid proteins would be nearly saturated in vivo. The method can be applied to any integral protein or other ligand in any bilayer for which there are reasonable estimates of the sterol affinities and stoichiometries of the phospholipids.


INTRODUCTION
Cholesterol is bound to many plasma membrane proteins, affecting their disposition and activity in diverse ways.][3][4][5][6][7][8][9][10] Two cardinal features of the interaction of the proteins and sterols are the strength of their association and their binding stoichiometry.We have found only one experimental determination in the literature of the affinity of cholesterol for an integral membrane protein in situ. 11However, that study is not secure. 1215][16][17][18][19][20][21] Here, we describe an indirect method to characterize the binding of cholesterol to integral proteins and other membrane-embedded ligands.3][24] The sterol dependence of the activity of the proteins is consequently constrained by the sterol affinity and stoichiometry of the membrane phospholipids.Using literature values for the latter, one can obtain estimates of the sterol affinity and stoichiometry of these proteins by matching computer-simulated binding isotherms to experimental cholesterol dependence curves for protein activity.In other words, competition by phospholipids with known cholesterol affinity provide a quantitative gauge of the binding of the sterol to integral membrane proteins.
At one extreme, very avid proteins outcompete the phospholipids for the cholesterol and so bind it with nearly hyperbolic isotherms.At the other extreme, very weak proteins bind cholesterol poorly until the phospholipids become saturated with sterol at their stoichiometric equivalence point and the uncomplexed excess sterol becomes increasingly available to the protein. 25Between these extremes, proteins have sigmoidal sterol dependence curves with shapes and thresholds determined both by the ligands and the phospholipids (see Results).We assume that two forms of cholesterol are available to the protein: (a) that extracted from membrane phospholipid complexes by strong competition; and (b) an uncomplexed fraction readily available to the protein beyond the stoichiometric equivalence point of the phospholipid complexes. 25

METHODS
The model.This model simulates the association of sterol molecules with ligands such as proteins within a phospholipid bilayer so as to estimate the affinity and stoichiometry of the binding reaction of the ligand.It resembles an earlier model that treats the binding of watersoluble ligands such as cytolysins to membrane sterols. 25In contrast, the present version places the ligand in the same membrane compartment as the sterol and the phospholipid.It utilizes the simplest formalism consistent with the experimental data: competitive binding of sterols to phospholipids constrains their binding to the proteins.Applying values for the former allows values for the latter to be obtained through computed simulations.
We assume that a ligand (L) associates with cholesterol (C) in competition with membrane phospholipids (P).The essential parameters are therefore the sterol association constants and stoichiometries for these reactants.The compartment size is  = (CT + PT + LT), where the subscript T denotes total.The chemical activities of the reactants are ideal and expressed as their concentrations in mole fractions.These are Cf/α, Pf/α and Lf /α , where f denotes their free or unbound form.CPr denotes lipid complexes with a stoichiometry of one cholesterol to r phospholipid molecules.CnL denotes cholesterol-ligand (e.g., protein) complexes with a stoichiometry of n cholesterol molecules per ligand.
The association equilibrium for the sterol and phospholipid is: The dimensionless association constant for complexes is then Many integral membrane proteins such as the transporters considered here are oligomeric. 26,27  simplicity, we allow the ligand (L) to be an oligomer composed of identical subunits that bind n sterol molecules in a fully cooperative all-or-none fashion; a concerted rather than sequential reaction. 28Hence, Designating the dimensionless association constant for the formation of an n-mer of L as KLn, we have Application of the model.Eqs.1-4 were used to generate isotherms that simulate the binding of an integral membrane protein to cholesterol in competition with the phospholipids.
Simulations are numerical solutions computed in MATLAB.The computer code is presented in the S2 section of the Supporting Information.Reactant quantities are in moles.The abundance of the phospholipid (PT) was set to unity and the mole fraction of the sterol (CT/) was varied across its physiologic range, from zero to 60 mol%.The abundance of the protein (LT) was set at 1 x 10 -3 for biological membranes and 1 x 10 -5 for planar bilayers.(The concentration of the protein affected the results by far less than one percent--nor should competition by extraneous proteins matter because of the large molar excess of the sterol and phospholipids.) Cholesterol/protein binding ratios of n = 1 to 5 were examined.
Accurate values for the sterol affinity and stoichiometry of the phospholipid mixtures (i.e., KP and CPr in Eq. 2) were not available.We therefore used plausible estimates based on a published data set. 29We assumed that the stoichiometry of the binding of phospholipid to cholesterol, r, was one or two. 24,25,29 Te program allows membranes to contain two types of phospholipids with different cholesterol affinities and stoichiometries in different proportions.The membrane sterol concentration was expressed as mol% cholesterol; i.e., 100 x moles cholesterol / (moles cholesterol + moles phospholipid).
Assuming plausible values for the cholesterol affinity and stoichiometry of the phospholipids, we tested a range of values for each protein by matching computed isotherms to the experimental data by eye.The experimental data were kept in their published form, scaled on the left-hand ordinates of the figures.No data points were omitted.Simulated isotherms were scaled from zero to one on the right-hand ordinates.In addition to the cholesterol binding affinity and stoichiometry of a protein, KLn and n, the simulations yielded cholesterol-dependence curves for the fractional saturation of the protein (CnL/LT), the fraction of each phospholipid associated with the sterol (r x CPr/PT) and the fraction of uncomplexed sterol (Cf/CT).Free energies of sterol binding were calculated as G o = -RT ln KL1 at 298 o K.
A satisfactory match of simulation to data was found in each case.However, estimates of KLn depended on KP.Consequently, the experimental data could be matched by various pairs of values for KP and KL.Thus, the delivered association constants were not uniquely determined and were therefore not definitive.
It is shown in Section S3.a of the Supporting Information that, at half-saturation of the protein, Eq. ( 5) implies that the half-saturation of a protein is independent of the assumed sterol binding stoichiometry, n, and, furthermore, that the cholesterol-dependent isotherms of a protein will all intersect at (Cf)1/2 (not shown).
In addition, note that the calculated isotherms in each of several figures intersect close to the same total cholesterol concentration (CT) for all values of n.As shown in Section S3.b of the Supporting Information, this intersection point is given by: Thus, the membrane concentration of cholesterol at the half-saturation point of a protein with affinity KLn is essentially independent of n.

Many integral plasma membrane proteins associate with cholesterol (see Introduction).
However, sterol-dependent activity curves suitable for our analysis are few. 30Six such isotherms were tested here.
GAT.These oligomeric transporters facilitate the recovery of secreted -aminobutyric acid (GABA) across presynaptic plasma membranes, symported by gradients of NaCl. 31The data in Figure 1 show the cholesterol dependence of the transport activity of a purified rat brain GAT reconstituted in liposomes. 32The overall sterol affinity of the phospholipids employed was not known, so we tested some relevant KP values. 29A very good match to the data was obtained by assuming an affinity of the phospholipid for the sterol of KP = 200, a protein affinity of KL1 = 100 and a protein stoichiometry of n = 1 (curve 3 in Figure 1).Because the protein competes moderately well with the phospholipids, the isotherm has a gentle sigmoidicity and ascends well before the appearance of free cholesterol at its presumed stoichiometric equivalence point with the phospholipids, 43 mol% (curve 6).This behavior shows that the protein extracts cholesterol from the phospholipid complexes.
The other curves in Figure 1 explore the model.Curve 1 shows that, in the presence of phospholipids with low sterol affinity, avid proteins will bind cholesterol strongly with a nearly hyperbolic isotherm.Curves 2 and 4 show the effect of doubling and halving the sterol shown in Table 1. 29The stoichiometric equivalence point of such bilayers is 43 mol% cholesterol.Curve 6 shows free cholesterol in moles/mol phospholipid in the absence of protein.Free cholesterol Red dash affinity of the best-matched phospholipids (curve 3).The spread among curves 2, 3 and 4 gives an indication of the sensitivity to phospholipid affinity of the sterol-protein interaction.Curve 5 illustrates how the cholesterol binding curve of a protein is shifted to the right when the bilayer phospholipids are very avid.
We also matched the experimental data to simulations that assumed that the protein has two or four identical sterol binding sites; that is, n = 2 and 4. The affinity of the monomer was again taken to be KL1 = 100.The curves had lagged thresholds and very acute ascents and so did not match the experimental data well (not shown).We infer that the binding of cholesterol to the GAT is not cooperative.Nevertheless, multiple cholesterol molecules might associate with the oligomer at non-interacting sites.
KIR3.4*.This recombinant homotetramer was derived from a subunit of the G proteinactivated potassium channel, GIRK. 8In the study shown in Figure 2, the protein was reconstituted into planar bilayers and single channel activities were recorded as a function of membrane cholesterol concentration. 33Curve 2 provides a good match to the data using KL1 =  Free cholesterol Red dash Kir2.As seen in Figure 3, the activity of this tetrameric inward rectifier potassium channel is inhibited by cholesterol. 34,35 he simulation of these data is considered to be slightly clamping cultured bovine aortic endothelial cells that had been treated with methyl-βcyclodextrin plus varied cholesterol to adjust the plasma membrane sterol. 34The plasma membrane was represented by a mixture of equal proportions of two phospholipids with stoichiometries of C:P = 1:1 and 1:2 and affinities of 5,000 and 2,500, respectively. 24,25 he resting plasma membrane cholesterol concentration, here normalized to 1.0, was therefore 43 mol% (mole fraction = 0.43 or C/P = 0.75). 24The simulations used the protein values given in better for n = 1 (curve 1) than for n = 4 (curve 2), both by eye and from the value of R 2 (Table 3).
Curves for n = 2 and 3 fell between these two extremes (not shown).It appears that the protein does not extract appreciable cholesterol from the avid phospholipid complexes but depends on the uncomplexed cholesterol emerging at the stoichiometric equivalence point of the plasma membrane.This undermines the estimation of the stoichiometry, n, which depends on the shape of the isotherm.
BK.This voltage-gated potassium channel is activated by cytoplasmic calcium ions with high positive cooperativity. 37,38 owever, as shown in Figure 4, it is inhibited by cholesterol. 38,39  simulation for n = 4 (curve 2; R 2 =0.73) was better matched to the data than that for n = 1 (curve 1; R 2 = 0.58).Rejecting the stray point at ~20 weight % further favored the match for n = 4 over that for n = 1 (R 2 = 0.90 vs. 0.66).The sterol affinity of a putative subunit was KL1 = 563 (Table 4).Thus, BK was much more avid for cholesterol than the three transporters analyzed above.represent the open probability (Po) of single channels in a planar bilayer composed of a 1:1 mixture of 1-palmitoyl-2-oleoyl-phosphatidylserine (POPS) plus 1-palmitoyl-2-oleoylphosphatidylethanolamine (POPE) in the presence of 0.1 mM CaCl2. 39We assumed that the two phospholipids had stoichiometries of C:P = 1:2 and 1:1 and affinities of KP = 210 and 130, respectively. 29The stoichiometric equivalence point of such bilayers is 43 mol% cholesterol.To convert the experimental cholesterol concentrations from the reported percent of total lipid weight to mol%, we assumed molecular weights of 387 and 740 for C and P, respectively.The midpoint of the curve was 8.3 weight % which corresponds to 12.7 mol% cholesterol.The protein values for BK listed in Table 4 were used in the simulations.As predicted by the model, the curves intersect at their half-saturation values (see Methods).was recently characterized. 41The cholesterol dependence of its conductance was altered by the mutation in three ways.First, while cholesterol activated the wild type (Figure 2), it inhibited the variant (Figure 5).Second, whereas the open probability of the unmodified channel in Figure 2 appeared to have first-order dependence on cholesterol concentration, the data for the mutant were better matched by assuming n = 4 rather than n = 1.Third, the mutant protein was far more avid for cholesterol than was the wild type (i.e., KL1 = 700 versus 35, respectively).
Consequently, its sterol threshold was shifted far to the left.Figure 1 shows that the sterol affinity of the phospholipid strongly influences the binding isotherm of a protein.But, given that the Kir3.4* and the M192I variant were analyzed in the same bilayer environment, the striking difference in their isotherms can be ascribed to the alteration in the protein.1-palmitoyl-2-oleoyl-phosphatidylethanolamine (POPE). 41We assumed that the two phospholipids had C:P stoichiometries of 1:2 and 1:1 and affinities of Kp = 210 and 130, respectively. 29The stoichiometric equivalence point of such bilayers is 43 mol% cholesterol.The computed curves used the protein values listed in Table 5.As predicted by the model, the curves intersect at their half-saturation values (see Methods).

Nicotinic acetylcholine receptor (AChR)
. This pentameric cation channel has complex allosteric behavior and specific binding sites for cholesterol. 42,43 he data in Figure 6 show the sterol-dependence of a conformational switch in the receptor from a desensitized to a resting state. 44Simulation with n = 1 (curve 1) gives a poor match to the data, and the threshold for n = 5 (curve 3) is too sharp.On the other hand, assuming modest cooperativity (i.e., n = 2, curve 2) dioleoylphosphatidylcholine:dioleoylphosphatidic acid (DOPC:DOPA). 44We assumed sterol affinities of KP = 930 and 200, respectively, for the two phospholipids and a C:P stoichiometry of 1:2 for both. 29The stoichiometric equivalence point of such bilayers is 33 mol% cholesterol.The simulations used the protein values listed in Table 6.As predicted by the model, the curves intersect at their half-saturation values (see Methods).provides an excellent match.Calculations using n = 3 or n = 4 give intermediate simulations while varying the affinity of the phospholipids moves these cooperative curves to lower and higher thresholds as in Figure 1 (not shown).The threshold of the curve was far to the left of that predicted for the phospholipids.Thus, both the cooperativity of the protein and competition with the phospholipids contributed to the position and contour of curve 2, the best-matched simulation.
The sterol affinity of the protein subunit, KL1 = 950, is an order of magnitude greater than that of the proteins shown in Figures 1-3.The corresponding free energy change is G o = -17.2KJ/mol.An earlier molecular dynamics simulation suggested an energy of interaction of cholesterol with subunits of the receptor of -25 to -50 KJ/mol. 45However, those determinations were performed in vacuo rather than in a bilayer.
Simulated isotherms for five transporters in cell membranes.The model posits that the value for KLn does not vary with the phospholipid environment of a protein.This allowed us to apply the KLn values obtained above to model five of those proteins in a plasma membrane bilayer (Figure 7).(We did not include the M192I mutant of Kir3.4* from Figure 5 because its biological relevance is uncertain.)The midpoints of the simulations for the three low-affinity transporters (curves 3, 4 and 5 in Figure 7) fell near the resting cholesterol concentration assumed for the plasma membrane, ~43 mol%. 24In contrast, the two high-affinity transport proteins with n = 4 (curve 2) and n = 2 (curve 1) had thresholds to the left of the physiological rest point; this predicts that they are saturated with the sterol in the resting plasma membrane.curves for the proteins in their native environment, the plasma membrane.The bilayer was represented by a 1:1 mixture of two phospholipids with stoichiometries of C:P = 1:1 and 1:2 and sterol association constants of 5,000 and 2,500, respectively. 24,25 he stoichiometric equivalence point of such bilayers is 43 mol% cholesterol.The values for the affinities of the proteins are given in Table 7.  Endomembranes (i.e., the cytoplasmic organelles taken as a whole) appear to have a very low cholesterol content (namely,  10 mol%) and a very low cholesterol affinity. 24,25 t was of interest to simulate the association of the integral membrane proteins with cholesterol in such an environment.Figure 8 suggests that proteins with modest cholesterol affinity (namely, those characterized in Figures 1-3) would be partially filled with cholesterol in the weakly-avid intracellular compartment while the oligomers with high affinity and cooperativity for five of the transporters studied above and endomembranes that contained a 30/70 mixture of two phospholipids with stoichiometries of C:P = 1:1 and 1:2 and sterol association constants KP = 21 and 10, respectively. 24The stoichiometric equivalence point of such bilayers is 39 mol% cholesterol The characteristics of the proteins are given in Table 8.  would be essentially saturated.Of course, the cholesterol content of various organelles such as the endoplasmic reticulum and distal Golgi membranes differ, and the maturation and modifications of these proteins presumably varies among them.Thus, this exercise is simply heuristic.

DISCUSSION AND CONCLUSIONS
Cholesterol affects the structure and function of a variety of plasma membrane proteins (see Introduction).As illustrated by the figures, the activity of these proteins can have a deeply sigmoidal dependence on membrane cholesterol concentration.These thresholds will reflect both the cooperative binding of the sterol by oligomeric proteins and competition by membrane phospholipids for cholesterol. 46Here, we have explored a computational model that estimates the cholesterol association constants and binding stoichiometries of integral membrane proteins based on their competition for the sterol with the membrane phospholipids.
The approach was tested by matching simulations to the cholesterol dependence curves for the activities of six integral membrane proteins.GAT, Kir2 and Kir3.4* did not appear to bind cholesterol cooperatively; that is, n = 1 gave the best matches in Figures 1-3.Even so, these proteins could have bound multiple cholesterol molecules non-cooperatively.The deep sigmoidicity of the isotherms suggests that their sterol affinities are weak (namely, KL1 = 35-100) compared to those of typical phospholipids, the KP values of which are in the range of 100-5,000. 29Figure 7 suggests that the cholesterol dependence of these proteins would have a threshold near stoichiometric equivalence with the plasma membrane phospholipids, ~43 mol%.This is the homeostatically-regulated physiologic setpoint of plasma membrane cholesterol. 24us, as previously proposed, such proteins might have evolved to respond acutely to small variations in the concentration of plasma membrane cholesterol at its resting level. 30he data for the other three oligomers were not well fit using n = 1 (Figures 4-6).Rather, they appeared to bind the sterol cooperatively.Furthermore, their subunit association constants were roughly an order of magnitude greater than those of the three non-cooperative proteins (Table 9). Figure 7 suggests that this form of the BK channel and the acetylcholine receptor are saturated with cholesterol at the physiological setpoint of the plasma membrane; all else being equal, they might therefore be insensitive to small variations in its sterol concentration in vivo.The present analysis has limitations.(a) The experimental data sets were sparse, undermining the precision of the estimates of the sterol association constants and, especially, the binding stoichiometries which depend strongly on the contour of the isotherm.In this model, however, the curves computed for all binding stoichiometries of a protein intersect at the same membrane cholesterol concentration and therefore have the same KL1 value (see Methods).
Consequently, good estimates of the sterol affinity of the subunit of an oligomer can be secured even when its stoichiometry is uncertain.(b) The model may be too simple, given the complex behavior of many membrane proteins. 47For example, a protein might not be an ideal oligomer with n values that are integers, as assumed here.Also, the model stipulates that the only effect of the bilayer on the binding of the sterol to the protein is through competition by the phospholipids while, in reality, other kinds of interactions may obtain. 4On the other hand, the matches of simulation to data were satisfactory without the need for a more elaborate model.(c) In vitro may not replicate in vivo.For example, the nearly complete inhibition by cholesterol of the type of BK channel studied in Figure 4 might not obtain in vivo where factors such as cytoplasmic calcium, membrane voltage and accessory proteins serve as physiologic regulators. 38,40 n this regard, the model could be useful in comparing values obtained for a plasma membrane protein in vitro and in vivo.

Figure 1 .
Figure 1.Simulation of the binding of cholesterol to a GAT transporter.Experimental data

Figure 3 .
Figure 3. Simulation of the binding of cholesterol to Kir2 channels.Experimental data (symbols;

Figure 4 .
Figure 4. Simulation of the binding of cholesterol to BK channels.(These were presumably tetramers of the alpha subunit. 40) Experimental data (symbols; taken from Figure 4 in ref. 39)

Figure 5 .
Figure 5. Simulation of the binding of cholesterol to Kir3.4* M182I channels.Experimental data

Figure 7 .
Figure 7. Simulation of the association of cholesterol with five transporters in a hypothetical

Figure 8 .
Figure 8. Simulation of the association of cholesterol with proteins in membranes with the (d) The analysis does not enumerate individual sterol binding sites on a protein or report on dynamics or other molecular features.Rather, it characterizes the equilibrium binding reaction that affects protein activity.(e) The KLn values obtained depend on characteristics assumed for the phospholipid mixtures.Only approximations are available for some of these.29This might not be a big problem, however.For example, doubling or halving the KP value assigned to curve 3 in Figure1(namely, changing the KP from 200 to 100 or 400) yielded KL1 values of 55 and 190 rather than the best match, KL1 = 100.The flanking KL1 estimates correspond to G o values of -9.9 and -13.0, not far from the best match: G o = -11.4KJ/mol.Thus, the KLn values we have obtained should be meaningful despite their uncertain accuracy.(f) Could the experimental sigmoidal isotherms simply reflect cooperative cholesterol binding by the protein without competition by the phospholipids?Some of our simulations were consistent with this supposition (not shown).However, the extensive

Table 3 .
36 predicted by the model, the curves intersected at their half-saturation values (see Methods).[Much of the excess sterol loaded into the cells presumably moved to intracellular organelles.36However,thisshould not have affected the derivedKLn.]