Mechanism of Long-Chain Free Fatty Acid Protonation at the Membrane-Water Interface

Abstract

Long-chain free fatty acids (FFAs) play an important role in several physiological and pathological processes such as lipid fusion, adjustments of membrane permeability and fluidity, and the regulation of enzyme and protein activities. FFA-facilitated membrane proton transport (flip-flop) and FFA-dependent proton transport by membrane proteins (e.g., mitochondrial uncoupling proteins) are governed by the difference between FFA’s intrinsic pK_a value and the pH in the immediate membrane vicinity. Thus far, a quantitative understanding of the process has been hampered, because the pK_a value shifts upon moving the FFA from the aqueous solution into the membrane. For the same FFA, pK_a values between 5 and 10.5 were reported. Here, we systematically evaluated the dependence of pK_a values on chain length and number of double bonds by measuring the ζ-potential of liposomes reconstituted with FFA at different pH values. The experimentally obtained intrinsic pK_a values (6.25, 6.93, and 7.28 for DOPC membranes) increased with FFA chain length (C16, C18, and C20), indicating that the hydrophobic energy of transfer into the bilayer is an important pK_a determinant. The observed pK_a decrease in DOPC with increasing number of FFA double bonds (7.28, 6.49, 6.16, and 6.13 for C20:0, C20:1, C20:2, and C20:4, respectively) is in line with a decrease in transfer energy. Molecular dynamic simulations revealed that the ionized carboxylic group of the FFAs occupied a fixed position in the bilayer independent of chain length, underlining the importance of Born energy. We conclude that pK_a is determined by the interplay between the energetic costs for 1) burying the charged moiety into the lipid bilayer and 2) transferring the hydrophobic protonated FFA into the bilayer.

Introduction

Interfacial protons have attracted much attention and yet there is no consensus on whether the concentration of protons increases or decreases even at boundaries as simple as the air-water interface (1). The situation is even more complicated at the interface of biological membranes; in addition to the propensity of the protons to accumulate there (2), the majority of titratable groups show a pK_a value that is different from their pK_a in bulk water. Part of the apparent difference can be attributed to the proton’s attraction to the negative charge of the deprotonated species (3). But even if the actual surface proton concentration is accounted for, i.e., the intrinsic pK_a is calculated (compare Eq. 2), the carboxyl groups of fatty acids in membranes exhibit significantly different pK_a values in the membrane than in bulk water (4).

In addition to the vital biological roles as a nutrient and substrate for signaling molecules, long-chain free fatty acids (FFAs) play an important role in physiological and pathological processes as modifiers of biophysical properties of lipid membranes (e.g., fluidity), sources of energy, and activators/inhibitors of enzymes and membrane proteins (e.g., uncoupling proteins, G-protein-coupled receptors), etc. (5, 6, 7). FFA-facilitated membrane proton transport (flip-flop (3, 8, 9, 10)), and FFA-dependent proton transport by mitochondrial membrane proteins, are governed by the difference between FFA’s pK_a and the pH in the immediate membrane vicinity (11, 12).

The exact pK_a values of biologically important FFAs are mostly unknown. The few reported values scatter widely: e.g., for stearic or oleic acids from 6 to 10.5 (3, 10, 13, 14, 15, 16, 17, 18, 19, 20). However, there is consensus that pK_a of the carboxyl group, which is ∼4.75 in water, is shifted to higher values in a hydrophobic environment (21). The question of whether and how pK_a depends on FFA structure is also controversially discussed. Nuclear magnetic resonance revealed no difference between pK_a values of stearic and palmitic acids (22). In contrast, titration of fatty acid salts led to the conclusion that their pK_a increases from 6.5 to ∼9.0, as their chain length increases from C8 to C16 (23). The pK_a values for unsaturated FFAs decreased from 10.15 to 8.28 with an increasing number of double bonds (17).

The mechanism behind the divergent pK_a shifts of membrane-standing FFAs also remains elusive. The discussion so far focuses on the local dielectric permittivity ε of the medium, on the surface net charge, on the interactions between charged moieties, on the water organization, and on the local electrical field (22, 24, 25, 26).

This study aimed to elucidate the major determinants of FFA protonation at the water-membrane interface. First, we obtained the apparent pK_a values, pK_a,a, from ζ-potential measurements (10) and calculated the intrinsic pK_a values of biologically important FFAs with different chain lengths and saturation degrees. Second, we compared the positions of the protonated and deprotonated FFA forms and the positions of different FFA anions in the membrane using molecular dynamics (MD) simulations.

Materials and Methods

Chemicals

1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine (SOPC), and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) were obtained from Avanti Polar Lipids (Alabaster, AL). Stearic, oleic, γ-linolenic, arachidic, cis-11-eicosenoic, cis-11,14-eicosadienoic and arachidonic acids, and cholesterol, MES, TRIS, β-alanine, and Na₂SO₄ were purchased from Sigma-Aldrich (Schnelldorf, Germany).

Liposome preparation and ζ-potential measurements

Quantities of 60 mol % DOPC (or SOPC) and 40 mol % FFA were mixed in chloroform and evaporated under argon flow until a thin film was formed on the wall of the glass vial. Then buffer containing 20 mM Na₂SO₄, 10 mM MES, 10 mM TRIS, and 10 mM β-alanine was added and the vial was vortexed until the full transition of the lipid to water phase occurred. Liposomes were formed by the Mini-Extruder (Avanti Polar Lipids) using a membrane filter with a pore diameter of 100 nm at the required pH of the buffer (3, 4, 5, 6, 7, 8, 9, 10) to ensure that pH values inside and outside of liposomes were the same and that no difference in the FFA amount at the inner and outer leaflets existed. The final liposome concentration was 0.2 mg/mL.

The ζ-potential (Φ_ζ) of FFA-containing liposomes was obtained with the Zetasizer Nano (Malvern Instruments, Malvern, UK) as described in (10). In brief, the velocity of liposome movement in the electrical field was deduced from the Doppler shift of a scattered laser beam. The Smoluchowski model was applied to calculate the Φ_ζ. Assuming that the distance to the shear plane is δ = 0.2 nm, we calculated surface potential, Φ_s, from Φ_ζ. The value Φ_s depends on the ratio of dissociated [A⁻] and non-dissociated [HA] FFA in the liposomes and is related to pH and pK_a,a according to the Henderson-Hasselbalch equation, Eq. 1:

$$\text{pH}={\text{pK}}_{\text{a,}a}+\log \left(\left[{\text{A}}^{-}\right]/\left[\text{HA}\right]\right).$$ (1)

To obtain the pK_a,a we presented Φ_s as a function of bulk pH and fitted the experimental data with the four-component sigmoidal curve to find the inflection point, which corresponds to pK_a,a (Fig. 1 A). To take into account that pH changed with dissociation of the fatty acid, we corrected the obtained pK_a values using Eq. 2 (27):

$$p{K}_a=p{K}_{\text{a,}a}+\frac{F{\Phi }_s}{2.303RT},$$ (2)

where F, R, and T are the Faraday’s constant, universal gas constant, and absolute temperature, respectively.

Figure 1.

Surface potential and pK_a values of saturated free fatty acids. (A) Dependence is shown of the liposome’s surface potential, Φ_s, on buffer pH. Liposomes were either made from pure DOPC (black spheres) or from DOPC reconstituted with palmitic acid (black squares), or stearic acid (black uptriangles), or arachidic acid (black downtriangles). (B) Dependence is shown of pK_a on the FFA chain length. The buffer solution contained 20 mM Na₂SO₄, 10 mM Tris, 10 mM MES, and 10 mM β-alanine. pK_a,a and pK_a are the apparent and intrinsic pK values of the corresponding FFAs. To see this figure in color, go online.

Alternatively, we calculated pH at the membrane surface from bulk pH according to Eq. 1 (27). Both approaches gave similar results (data not shown).

Giant unilamellar vesicle formation and imaging

For the electroformation of giant unilamellar vesicles (GUVs), stock solutions of 12.5 mM DOPC and 12.5 mM arachidic acid, both dissolved in chloroform, were mixed at a ratio of 0.6:0.4. Alternatively, GUVs were prepared from an equal mixture of 12.5 mM DOPC:DPPC:Cholesterol each, dissolved in chloroform at a ratio 0.35:0.35:0.3. Subsequently, a quantity of 6 μL of the lipid mixture was placed on two platinic wires and dried with nitrogen. Then both platinic wires were put into a chamber containing 600 μL buffer consisting of 5 mM HEPES, 200 mM sucrose at pH 7.4. For GUV generation, platinic wires were connected to a function generator and an AC field (10 Hz sine wave, 3 V peak-to-peak voltage) was applied for 2 h. Afterwards, 200 μL of the GUV solution was added to 400 μL of a buffer containing glucose (5 mM HEPES, 200 mM glucose, pH 7.4) for sedimentation of the GUVs (for at least 1 h). During sedimentation, GUVs were labeled with the lipophilic dye DiIC18 (5)-DS (end concentration 820 nM; Invitrogen/Molecular Probes, Eugene, OR). Finally, GUVs were imaged with a Zeiss Axiovert 200M microscope (Carl Zeiss, Oberkochen, Germany) containing a mercury short-arc lamp HXP 120C at room temperature (25°C) or at 6°C.

MD simulations

MD simulations were performed for DOPC lipid bilayers embedded with different protonated FFAs and their corresponding anions in aqueous solutions. In particular, DOPC bilayers consisted of 128 lipids on an 8 × 8 grid forming a bilayer of two monolayers each containing 64 individual lipid molecules. Furthermore, we randomly inserted an additional 34 FFA molecules or FFA anions, respectively, in DOPC bilayers. For MD simulations, we studied palmitic (16:0), stearic (18:0), arachidic (20:0), eicosenoic (20:1), eicosadienoic (20:2), and arachidonic acids (20:4) as well as their deprotonated forms, respectively. All MD simulations were performed at 310 K and 1 bar of pressure.

DOPC bilayers and FA were described with an SLipids (28, 29, 30) force field and all missing bonding and Lennard-Jones parameters of FFAs and their anions were updated with compatible CHARMM36 parameters (31). Atomic charges for protonated FA and their anions were calculated by the Merz-Singh-Kollman scheme (32) with B3LYP/6-31G(d) optimized geometry and a single point ESP charge calculation using the B3LYP/cc-pVTZ method. A final charge refinement of the molecule of interest was performed with the RESP method (33). All systems were placed in a unit cell and solvated by ∼11,500 TIP3P water molecules (34). In the case of FA anions, a corresponding number of Na⁺ counterions were added to the systems to make them electroneutral. The size of the unit cell was ∼7 × 7 × 11.0 nm. Three-dimensional periodic boundary conditions with long-range electrostatic interactions beyond the nonbonded cutoff of 1 nm were accounted for with the particle-mesh Ewald procedure (35) using a Fourier spacing of 0.12 nm. The real-space Coulomb interactions were cut off at 1 nm and van der Waals interactions were cut off at 1.4 nm. All MD simulations were performed with semi-isotropic pressure coupling (independently in the directions parallel and perpendicular to the bilayer normal) using the Parrinello-Rahman algorithm (36) at 1 bar with a coupling constant of 10 ps⁻¹. All simulations were performed at 310 K employing the Nosé-Hoover thermostat (37) independently for the lipid/FA and water subsystems with a coupling constant of 0.5 ps⁻¹. All bond lengths were constrained using the LINCS algorithm (38), whereas water bond lengths were kept constant employing the SETTLE method (39). Equations of motion were integrated using the leap-frog algorithm with a time step of 2 fs.

Initially, lipid bilayer membranes were equilibrated until a constant area per lipid was obtained (i.e., for at least 10 ns), with a subsequent 100 ns of simulation time used for analysis. MD simulations were performed with the GROMACS program package, version 4.6.3 (40), whereas quantum chemical calculations were performed using Gaussian 09 (41).

Results

pK_a of biologically important FFAs that differ in chain length and saturation

We first measured the electrophoretic mobility of liposomes made from DOPC, reconstituted with saturated palmitic (C16), stearic (C18), or arachidic (C20) acids at pH from 3 to 11. Then, we calculated the corresponding Φ_ζ and Φ_s (Fig. 1 A) values. The observed broadening of the curve indicates an increase in pK_a with an increase in chain length (Fig. 1 A). The pK_a values amounted to 6.25 ± 0.07, 6.93 ± 0.12, and 7.28 ± 0.09 for palmitic, stearic, and arachidic acids, respectively (Fig. 1 B).

The increase in chain length acts to increase the interaction energy between the host bilayer and the FFA molecules. To test whether this interaction was confounded by DOPC’s notorious demixing tendency, we repeated the experiments while substituting DOPC for SOPC. The observation that the pK_a values of the three FFAs were similar to their corresponding values in DOPC (Table S1) ruled out the demixing hypothesis (see Discussion).

In contrast, the presence of double bonds decreased pK_a. We made this observation with FFAs of two different carbon chain lengths—C20 (Fig. 2 A) and C18 (Fig. 2 B). pK_a adopted the values 7.28 ± 0.09, 6.49 ± 0.15, 6.16 ± 0.08, and 6.13 ± 0.08 for C20:0, C20:1, C20:2, and C20:4 FFAs, and 6.93 ± 0.11, 6.44 ± 0.12, and 6.11 ± 0.1 for C18:0, C18:1, and C18:2 FFAs, respectively.

Figure 2.

Dependence of pK_a values of unsaturated FFAs on the number of double bonds. Liposomes were made from DOPC reconstituted with (A) arachidic (20:0), eicosenoic (20:1), eicosadienoic (20:2), and arachidonic (20:4) acids or (B) stearic (C18:0), oleic (C18:1), or γ-linolenic (C18:3) acids. The buffer solution contained 20 mM Na₂SO₄, 10 mM Tris, 10 mM MES, and 10 mM β-alanine. pK_a,a and pK_a are the apparent and intrinsic pK values of the corresponding FFAs. To see this figure in color, go online.

We can also exclude that a nonnegligible fraction of the fatty acids exists in solution, which would, by way of a charge-dependent redistribution, affect the experimental results (Fig. S1 A). First, the vesicles were formed from a lipid-FFA mixture and the low critical micelle concentration forbids FFA exit in significant amounts. Second, if such an exit occurred, it would be most probable for the anionic form because it has the highest water solubility. A simple calculation shows that this is not the case: 40 mol % of fatty acids correspond—when fully charged—to a surface charge density of ∼1 negative charge per 1 nm². According to the Gouy-Chapman theory, such density corresponds to a Φ_ζ in the order of ∼−65 mV at an ionic strength of 40 mM. This represents an upper boundary, because the total energy of FFA bilayer insertion ΔG_T (see below) reduces the fraction of deprotonated FFA well below 100%. For FFA with the lowest pK_a = 6.25, i.e., the FFA with the highest deprotonated fraction, the ζ-potential = −58 mV was reasonably close to that upper boundary.

Visualization of FFA position in the bilayer membrane by MD simulations

Our MD simulations suggest that the difference in pK_a is not related to the position of the FFA anions in the membrane. The calculated number density profiles of choline and phosphate groups are similar for both protonated and deprotonated palmitic acid molecules (Fig. 3). However, the position of the protonated carboxyl group is shifted toward the membrane midplane due to hydrogen bonding of the -OH group with both the P=O and the carbonyl moieties of DOPC (Fig. 3, A and B). On the other hand, the deprotonated form is deprived of these hydrogen bonds, because it acts as a hydrogen acceptor just like DOPC’s carbonyl and phosphate groups. In consequence, the deprotonated carboxyl groups occupy a position closer to the aqueous phase, which favors the formation of hydrogen bonds with the surrounding water molecules (Fig. 3, C and D). The outward movement removes the density maximum of the terminal carbon atoms from the bilayer center (Fig. 3 C) that is clearly visible for the protonated palmitic acid (Fig. 3 A). It was previously observed experimentally (42) that protonated FFAs with attached anthroyloxy- and carbazole probes are located deeper into the bilayer when compared to deprotonated ones.

Figure 3.

Position of the carboxyl oxygen atom in protonated and deprotonated palmitic acids. (A and B) Number density profile and MD snapshot are given for the protonated palmitic acid. (C and D) Number density profile and MD snapshot are given for the deprotonated palmitic acid. The red, orange, green, black, and blue colors denote the nitrogen atom of the DOPC choline group, the phosphorous atom of the DOPC phosphate group, the oxygen carboxyl atom of the FFA, the terminal carbon atom of the DOPC lipid tail, and the water oxygen atom, respectively. In MD snapshots, the blue color corresponds to the protonated FFA in van der Waals representation (B). The red color indicates the deprotonated FFA in the van der Waals representation (D). To see this figure in color, go online.

A visual inspection of the MD snapshots does not show clustering of fatty acids and/or lipids, i.e., the simulations do not support a phase separation in the system (see below).

The localization of the FFA anion in the bilayer does not depend on FFA chain length as revealed by MD simulations of palmitic (C16, Fig. 4, A and B), stearic (C18, Fig. 4, C and D), and arachidic (C20, Fig. 4, E and F) acids. In all four cases, the deprotonated carboxyl group is confined at a larger distance from the membrane center than the protonated moiety. The increase in chain length only results in an increasing density of the terminal carbon atoms in the bilayer center.

Figure 4.

Number density profiles of deprotonated saturated acids (terminal carbon in the FFA anion). (A and B) Number density profiles and MD snapshot are given for the deprotonated palmitic acid. (C and D) Number density profiles and MD snapshot are given of the deprotonated stearic acid. (E and F) Number density profiles and MD snapshot are given of the deprotonated arachidic acid. The color code is as in Fig. 3. To see this figure in color, go online.

The number density profiles for protonated and deprotonated unsaturated arachidonic acid show a similar shift in the position of the carboxylic anion away from the bilayer center (Fig. 5, A and C). In contrast, the localization of the terminal carbon atom of the unsaturated FFA is less well defined. The presence of four double bonds allows for higher structural flexibility, so that part of the tail density is found in regions close to the bilayer interface (Fig. 5, B and D).

Figure 5.

Comparison of carboxyl oxygen atom position in protonated and deprotonated unsaturated arachidonic acid. (A and B) Number density profiles and an MD snapshot are given for the protonated arachidonic acid. (C and D) Number density profiles and an MD snapshot are given for the deprotonated arachidonic acid. The color code is as in Fig. 3. To see this figure in color, go online.

The carboxyl groups of both the protonated saturated and unsaturated FFAs sink deeper into the bilayer than their anionic counterparts. The distance, h_d, between them (C1) and the phosphate groups of the adjacent lipids varies between 5.1 and 6.2 Å. In contrast, the deprotonated carboxylic group is placed much closer to the surface; h_d adopts values between 1 and 1.6 Å (Fig. 6, A, C, and E; Table S2). Snapshots from MD simulations also indicate that DOPC restricts the free rotation around double bonds in unsaturated FFAs (Fig. 6, B, D, and F).

Figure 6.

Number density profiles of deprotonated unsaturated fatty acids. (A and B) Number density profiles and MD snapshot are given of the deprotonated eicosenoic acid. (C and D) Number density profiles and MD snapshot are given of the deprotonated eicosadienoic acid. (E and F) Number density profiles and MD snapshot are given of the deprotonated arachidonic acid. The color code is as in Fig. 3. To see this figure in color, go online.

Measurements of phase separation using fluorescence microscopy

Our MD simulations suggested that FFA clustering (i.e., soap formation) does not occur (Figs. 4 and 6). Because the close proximity of carboxylic anions to each other would have important implications for FFAs’ pK_a, we verified the lack of clusters experimentally. Therefore, we formed GUVs from mixtures of DOPC and arachidic acid (0.6:0.4). The uniform distribution of the lipophilic dye DiIC18 (5)-DS demonstrated the presence of one homogeneous phase (Fig. 7 A). As a positive control, we prepared GUVs from a DOPC:DPPC:cholesterol mixture (0.35:0.35:0.30). Dye enrichment in some regions of the GUV indicates the formation of domains (Fig. 7 B). These data confirm the previously reported lack of FFA clustering in analogous systems that consisted of mixtures of stearic acid with the DMPC or DSPC (43).

Figure 7.

Fluorescence images of GUVs labeled with the lipophilic dye DiIC₁₈ (5)-DS. (A) GUVs prepared from a DOPC/arachidic acid (0.6:0.4) lipid mixture at 25°C show no domain structures. (B) Domain structures in GUVs were prepared from a DOPC/DPPC/Cholesterol lipid mixture (0.35:0.35:0.30) at 25°C. Scale bars, 10 μm. To see this figure in color, go online.

Discussion

According to experimental results, pK_a increases with FFA chain length and decreases with an increasing number of double bonds (Figs. 1 and 2). Obviously, alterations of the local relative dielectric permittivity ε of the medium are not responsible, because neither chain length nor the level of unsaturation had an effect on the position of FFA’s carboxylic group relative to the aqueous bulk phase (Figs. 4 and 6), and the carboxylic moieties of all investigated fatty acids were exposed to the same ε.

We can similarly rule out that the electrostatic attraction of protons by the negatively charged membrane may be important, because we have accounted for proton up-concentration by calculating the intrinsic pK_a from pK_a,a value. An interfacial proton affinity beyond that expected from the Gouy-Chapman theory (2, 44) is also unlikely to contribute to the observation, because the accompanying increase in the proton association rate (45) should be roughly identical for all FFAs.

We can also exclude FFA segregation into microscopically visible domains from being involved in the pK_a changes. They would require tight packing of the soaps (fully ionized FFAs) without interspersing lipid molecules, i.e., soap clustering into islands (23). Such self-association to lamellar or liquid-crystalline aggregates has been observed at intermediate degrees of ionization, i.e., with mixtures of saturated (10–18 carbons) or ω-9 monounsaturated (18:1) FFAs and their potassium soaps (46), but not for lipid-FFA mixtures. Accordingly, the embedment of FFAs into lipid bilayers in our experiments precluded clustering at ambient temperatures, as we confirmed by fluorescence microscopy of giant liposomes (Fig. 7) and MD simulations (Figs. 4 and 6).

The lack of microscopically observable domains does not exclude nonideal mixing that favors transient contacts between the saturated FFA chains. DOPC is notorious for its demixing tendencies. This nonideal behavior would increase with chain length. A neutral FFA hitting another FFA would form a contact that persists a little longer and, hence, would become more likely to be found than a contact with an oleic acid of DOPC. This contact would decrease the energy of the system but could not persist if both carbonyls were charged. Thus, if demixing was responsible for the dependence of pK_a on chain length, we should be unable to observe it in a mixed chain lipid like SOPC. However, substituting DOPC for SOPC did not abolish the effect. This observation rules out nanoscopic demixing as a possible mechanism for the pK_a dependence on chain length.

The FFAs in this study vary differently in their potential to interact with the acyl chains of the surrounding lipids. We may take their energy of transfer from the aqueous solution into the bilayer as a measure for the interaction energy ΔG_H. It is proportional to the surface area of the cavity created by the solute in the aqueous solution (47). Each -CH₂- group contributes ∼1.4 kT (850 cal/mol) to the transfer energy (48). In turn, the increment in ΔG_H increases the probability of submerging the carboxyl group in the bilayer.

The burial is opposed by the extreme costs that arise when a charged moiety is immersed into the hydrophobic interior of the bilayer. The corresponding costs can be roughly estimated by calculating Born’s energy, ΔG_B (Eq. 3):

$$\mathit{\Delta }{G}_B=\frac{q^2}{8\mathit{\pi }{\mathit{\epsilon }}_0\text{a}}\left(\frac{1}{{\epsilon }_2}-\frac{1}{{\epsilon }_1}\right),$$ (3)

where q and ε₀ are the charge of the carboxylic moiety and the dielectric permittivity of vacuum. Assuming a radius a of the carboxylic moiety of 5 Å and relative electrical permittivities ε₁ and ε₂ of 70 and 9 (49) in the two positions of the charged and uncharged forms of palmitic acid (∼17 and 14 Å away from the bilayer center), we find a ΔG of ∼5.4 kT.

This very rough estimation holds for all FFAs, because ε is estimated to change slightly between 12 and 14 Å (the position of most protonated carboxylic moieties) from the bilayer center. For large ions, image potential and membrane dipole potential tend to decrease ΔG by roughly one-fourth. Thus, the estimate shows that moving the carboxylic anion from 17 to 14 Å costs roughly as much energy as is gained by adding four methylene groups (i.e., an increment in chain length from C16 to C20). In other words, increasing the chain length is bound to noticeably shift the equilibrium between the two forces: the force with which the charged carboxylic group opposes movement in the direction of the bilayer center—and the force with which the carboxylic group is pulled toward the bilayer center. Acyl chain unsaturation shifts that equilibrium into the opposite direction—every double bond acts as if a -CH₂- group was removed (48). We can look at this equilibrium as a tug-of-war where the sum of the energetic contributions, ΔG_T, affects the probability of protonation (Eq. 4):

$$\mathit{\Delta }{G}_T=\mathit{\Delta }{G}_H\mathrm{-}\mathit{\Delta }{G}_B.$$ (4)

In the case where the hydrophobic forces (ΔG_H) win, the buried carboxylic moiety must pick up a proton to approach the energetic minimum; if they lose, the carboxylic group retains its charge and occupies its usual position at the interface (Fig. 8). As a result, not only the pK_a depends on the chain length, but also the maximum surface charge of the membrane that is contributed by the fatty acid: the longer the FFA, the smaller the surface charge it may donate to a lipid vesicle (Fig. 1 A).

Figure 8.

Energy balance of FFA in lipid bilayers. (A) The position of FFAs in lipid bilayers is governed by two counteracting energetic contributions: 1) the Born energy, ΔG_B, pushes the anionic form of FFA toward the aqueous phase, and 2) the hydrophobic interaction energy, ΔG_H, pulls FFA toward the hydrophobic membrane interior. (B) The probability of FFAs getting deprotonated increases for ΔG_B > ΔG_H. (C) An increase in FFA length augments ΔG_H, which pulls a higher FFA fraction deeper into the bilayer. In contrast, an increasing number of double bonds decreases ΔG_H (one double bonds acts as if one -CH₂- group were lost), thereby increasing the FFA’s probability of being deprotonated. To see this figure in color, go online.

Conclusions

• 1)The experimentally measured pK_a values increase (6.25, 6.93, and 7.28) with an increase of FFA chain length (C16, C18, and C20) and decrease (7.28, 6.49, 6.16, and 6.13) with an increase in the number of double bonds (C20:0, C20:1, C20:2, and C20:4).
• 2)MD simulations reveal that anionic and neutral FFA forms have different positions regarding the bilayer membrane center: i.e., the ionized carboxylic group is shifted toward the lipid-water interface, the localization of the charged carboxylic FFA moiety depends neither on chain length nor on the amount of double bonds, and no FFA clustering occurs.
• 3)Differences in the hydrophobic interactions between lipid acyl chains and FFA explain the dependency of pK_a on the chain length and number of double bonds.

Author Contributions

A.A.P. and E.E.P. designed the project. A.A.P., L.Z., and O.J. performed the experiments. M.V. performed MD simulations. P.P. and E.E.P. wrote the manuscript. All authors analyzed the data and edited the manuscript.

Editor: Alemayehu Gorfe.