Solubility and Permeation of Hydrogen Sulfide in Lipid Membranes

Hydrogen sulfide (H2S) is mainly known for its toxicity but has recently been shown to be produced endogenously in mammalian tissues and to be associated with physiological regulatory functions. To better understand the role of biomembranes in modulating its biological distribution and effects; we measured the partition coefficient of H2S in models of biological membranes. The partition coefficients were found to be 2.1±0.2, 1.9±0.5 and 2.0±0.6 in n-octanol, hexane and dilauroylphosphatidylcholine liposome membranes relative to water, respectively (25°C). This two-fold higher concentration of H2S in the membrane translates into a rapid membrane permeability, Pm = 3 cm s−1. We used a mathematical model in three dimensions to gain insight into the diffusion of total sulfide in tissues. This model shows that the sphere of action of sulfide produced by a single cell expands to involve more than 200 neighboring cells, and that the resistance imposed by lipid membranes has a significant effect on the diffusional spread of sulfide at pH 7.4, increasing local concentrations. These results support the role of hydrogen sulfide as a paracrine signaling molecule and reveal advantageous pharmacokinetic properties for its therapeutic applications.


Introduction
For years, the toxicity of hydrogen sulfide (H 2 S, IUPAC recommended name dihydrogen sulfide) has been recognized and explored [1], but only recently it has been associated with an intrinsic physiological role in mammals. The discovery of endogenous H 2 S-producing enzymatic pathways and the measurement of significant H 2 S levels in several tissues was followed by the implication of H 2 S in numerous biochemical functions, and latest investigations propose that H 2 S could play signaling and cytoprotective roles, revealing its potential for pharmacological applications [2].
Hydrogen sulfide is a secondary product of the transsulfuration pathway. It is produced by two pyridoxal-phosphate-dependent enzymes, cystathionine b-synthase (CBS) [3] and cystathionine clyase (CGL) [4], and by the detoxifying enzyme mercaptopyruvate sulfurtransferase [5]. The physiological targets vary according to the tissue, for example, in brain and nervous system, H 2 S can modulate NMDA receptors [2], whereas in the vasculature H 2 S mediates vasorelaxation by opening K ATP channels [6]. It could also act as an oxidant scavenger, but the recent determination of the relatively low rate constants [7] together with the fairly low physiological levels [8], suggest that this action would depend on H 2 S being able to achieve high local concentrations.
If H 2 S were a hydrophobic molecule, then a higher local concentration of H 2 S could be achieved in the hydrophobic core of lipid membranes, and promote reactions with physiological targets. For instance, the reaction of nitric oxide with oxygen, which yields oxidizing and nitrosating species, occurs thirty times more rapidly inside lipid membranes than in aqueous media [9,10,11]. Considering that the permeability coefficient of a membrane to a solute (P m ) is directly proportional to the partition coefficient (K P ) [12], another consequence of a high solubility of H 2 S in lipid membranes would be a high membrane permeability. Mathai et al. have recently measured the permeability coefficient using planar lipid bilayers and found that diffusion through the membrane was fast indeed (P m = 0.560.4 cm s 21 , [13]). As discussed by these authors, this value may actually be an underestimation, which prompted us to find a better estimate. Diffusion of H 2 S through membranes and aqueous solution is very important because it will determine the extent of H 2 S action. If H 2 S could diffuse practically unhindered through lipid membranes, it could act at places distant from the site of formation supporting mechanisms of transient paracrine communication.
Understanding the interactions of H 2 S with lipid membranes and its overall diffusion is essential to rationalize the biological properties and the pharmacological potential of this newly recognized signaling molecule. Herein, we determined the partition coefficient of H 2 S in the organic solvents hexane and n-octanol, relative to water. We also developed a method and successfully measured the partition coefficient of H 2 S in dilauroylphosphatidylcholine liposome membranes. This solubility value allowed us to estimate the permeability coefficient of phospholipid membranes to H 2 S. Finally, we modeled the diffusional spread of H 2 S from a single cell, illustrating how far and how many neighboring cells could H 2 S affect, and analyzed the impact of lipid membranes on the macroscopic diffusion of H 2 S.

Hydrogen sulfide solutions
Stock solutions contained sodium hydrosulfide (NaHS, Sigma-Aldrich) in water and their concentration was determined by iodometric titration [7]. The working solutions contained a mix of H 2 S and HS 2 (hydrosulfide anion) in dependence with pH (pK a1 = 7.0 and pK a2 ,17 [14]). At pH 7.4 total sulfide distributes 72% as HS 2 , 28% as H 2 S and S 22 (sulfide) is insignificant. At pH 3.8 HS 2 becomes negligible (0.06%) and solutions can be considered 100% H 2 S.

Determination of partition coefficients in hexane and noctanol
Partition coefficients (K P ) were calculated as the ratio of organic solvent/buffer total sulfide concentration. Hexane and n-octanol were pre-equilibrated with sodium formate buffer (0.1 M, pH 3.8) overnight. Sealed tubes were prepared with a mix of buffer, sodium hydrosulfide (10 mM) and solvent with minimal headspace. Tubes were allowed to reach thermodynamical equilibrium (gentle agitation during 1 h at 25uC) and were centrifuged (10 min, 200 g) to separate the phases. Then, aliquots from both phases were removed with a gas-tight syringe and H 2 S was measured by an adaptation of the methylene blue assay [7,15]. Samples taken at different times confirmed that the systems had reached equilibrium after one hour. No interference of the solvents in the quantification method was detected according to controls.

Determination of the partition coefficient in DLPC liposomes
In the case of the dispersed liposomes, it is not possible to measure the concentration of H 2 S directly in the lipid phase, which does not separate from the aqueous phase. Thus, the partition coefficient was measured indirectly, according to the following reasoning: Consider two closed vials, one containing buffer only and the other a suspension of liposomes in buffer, both with a relatively large headspace. H 2 S will distribute in the three phases (gas, aqueous, lipid). If the same amount of H 2 S is added to both vials and H 2 S has a favorable partitioning in lipid membranes, it is expected that more H 2 S will be present in the liquid phase containing buffer and liposomes, than in the one containing buffer only. The inverse would happen if H 2 S had an unfavorable partitioning.
Large multilamellar liposomes were prepared by mechanical dispersion using dilauroylphosphatidylcholine (DLPC, Avanti Polar Lipids, 100 mg/mL) in formate buffer (0.1 M, pH 3.8). Septum-sealed vials (1980 mL) were prepared containing either liposomes in formate buffer or just formate buffer (100 mL), to which 20 mM H 2 S were added (10 mL) and allowed to reach equilibrium at 25uC (2 h, gentle agitation). Aliquots were withdrawn from the aqueous and the gaseous phase with a gastight syringe and H 2 S was measured by the methylene blue assay. Calibration curves included DLPC.
The method to determine K P in membranes is based on the one previously used for nitric oxide ( ? NO) [16]. For H 2 S, we must consider the 3 phases to determine the K P between membranes and water. Using mass conservation relationships, we could arrive to a simple expression, Equation 1 (the complete derivation of this equation is shown in Text S1) to calculate the partition coefficient, K P mem/w , the ratio of lipid/buffer H 2 S concentrations at equilibrium (25uC): where ½H 2 S lip aq and ½H 2 S lip g are aqueous and gas concentrations in the samples with liposomes, K g is a partition-like expression of Henry's constant ([H 2 S] g /[H 2 S] aq ), which can be calculated from the results obtained with buffer-only samples, and a is the lipid fractional volume, calculated taking into account lipid concentration and lipid specific volume (0.97 ml/g, see Text S1). Typical experimental concentration values are shown in Table S1. Measured K g values, 0.460.1, were similar to previous reports [17].

Modeling the 3D diffusional spread of H 2 S from a single cell
We wanted a mathematical model that could represent the diffusion of H 2 S in tissue. For that reason we chose a three dimensional model where the source is spherical and H 2 S diffuses from the surface. Furthermore, we chose a continuous source to better represent H 2 S cellular production. The corresponding solution of Fick's second law of diffusion is [18]: where C is the concentration at a given distance r from the center of the sphere, a is the radius of the sphere, set to 5 mm, D is the diffusion coefficient of H 2 S, q is the rate of production of H 2 S and erfc is the complementary error function. q was set so that the concentration of H 2 S on the surface of the sphere would be 100.0 arbitrary units at infinite time (q = 1.46610 7 ) in aqueous media (without membrane resistance, D w = 2.32610 25 cm 2 s 21 ).

Partitioning in organic solvents
Because of the difficulty involved in measuring the solubility of molecules in lipid membranes, organic solvents are usually used as surrogates. Octanol has been widely used for this purpose, and measuring a drug's partition coefficient in n-octanol is a common practice used to estimate the drug's biodistribution properties [19,20]. At pH 3.8, where H 2 S predominates (pK a = 7.0 [14]), the partition coefficient for H 2 S in n-octanol/buffer at 25uC resulted to be 2.160.2 (Table 1). Hexane was also used, as a completely non-polar solvent that could approximate the environment experienced by H 2 S in the mid-bilayer. The partition coefficient for H 2 S in hexane/buffer systems was 1.960.5 (Table 1). These values mean that H 2 S is twice as soluble in the organic solvents as in water. At the physiological pH of 7.4, the measured ratio was 0.6460.05 for n-octanol. This lower apparent K P is explained by the ionization of H 2 S to HS 2 in the aqueous phase, which has a negligible solubility in the organic phase [21]. This is in full agreement with the calculated partition coefficient (K P oc/w = 0.6 at pH 7.4) using K P oc/w = 2.1 for H 2 S, mass balance and Henderson-Hasselbach equilibrium considerations (Equation 3). In addition, at a pH of 6.5, which approximates ischemic tissue acidosis, the apparent K P oc/w can be calculated to be 1.6.
Partitioning in phospholipid membranes Although K P oc/w may already provide a valuable insight into the lipophilicity of H 2 S, considering that lipid membranes are intrinsically different from bulk solvent and constitute heterogeneous phases with high ordering, molecular packing and charge density [22], we proceeded to determine the partition coefficient of H 2 S between membranes of dilauroylphosphatidylcholine (DLPC) liposomes and water. According to our experimental data, the partition coefficient between phospholipid membranes and buffer was 2.060.6 ( Table 1) at 25uC.
One potential consequence of this two-fold higher local concentration is the acceleration of reactions of H 2 S within the membrane. H 2 S is known to inhibit mitochondrial respiration by reacting with cytochrome c oxidase [23]. This is a transmembrane protein complex that has many of its metallic prosthetic groups located deep in the transmembrane domain. It is very likely that the two-fold higher concentration of H 2 S in the hydrophobic core of the membrane plays a role in facilitating the reaction of H 2 S with these metallic centers and inhibiting its activity.
We mentioned earlier that the hydrophobicity of H 2 S could enhance its antioxidant potential in lipid membranes where low molecular weight thiols such as glutathione are scarce. This was an interesting possibility, but there is a problem. We have recently shown that most of the reactions ascribed to H 2 S such as disulfide reduction, nucleophilic substitution and free radical scavenging are actually done by HS 2 , which is a better nucleophile, more reactive and is present in higher amounts at physiological pH [7]. The dissociation of H 2 S to HS 2 in a lipid environment is thermodynamically unfavorable, so that, paradoxically, the net effect in lipid membranes should be a decrease in reactivity despite the favorable partitioning of H 2 S.
Another important consequence of the higher solubility of H 2 S in membranes than in water is a high membrane permeability, as will be discussed below.

Estimation of the diffusion of H 2 S through lipid membranes
A recent work by Mathai et al. using planar lipid bilayers indicated that transport of H 2 S through biological membranes is indeed extremely fast [13]. In their report, a free-standing bilayer lipid membrane made of E. coli total lipid extract was used and measurements were made with microelectrodes near the membrane, assuming a steady-state approach. A lower limit for H 2 S permeability of 0.560.4 cm s 21 was reported. However, it was observed that addition of cholesterol and sphingomyelin to E. coli lipid membranes, which cause bilayer tightening and generally lead to a decrease in membrane permeability, had no effect on the measured P m , indicating that unstirred layer effects were very important and that the determined P m is very likely an underestimation [13]. We tried to obtain better estimates through different approaches. Experimentally, we used stopped-flow to monitor H 2 S entrance into phospholipid liposomes, where we confirmed a very fast H 2 S permeation, in fact too fast to be measured (see Figure S1 and Text S2 for details). In a semitheoretical approach, we used membrane permeability data for similar molecules to estimate the permeability coefficient of H 2 S.
According to the current view of the permeation process, one of the main factors controlling permeability is the solubility of the molecule in the membrane [24]. The permeability coefficient of a membrane is proportional to K P and the diffusion coefficient in the membrane (D m ), and inversely proportional to the width of the bilayer (dx in Equation 4) [24].
Partition coefficients found here (Table 1) suggested a permeability coefficient for H 2 S higher than reported. The permeability of lipid bilayers to molecules comparable to H 2 S, such as hydrogen chloride or carbon dioxide, is high: 2.9 and .3.2 cm s 21 , respectively. Considering the molecular volume, water solubility and partition coefficients ( Table 2) we would then expect a permeability coefficient of H 2 S in lipid bilayers equal to or higher than 3 cm s 21 . Note that ? NO and O 2 may not be the best models for H 2 S behavior given their low solubility in water and larger K P oc/w ( Table 2). Taking the value of 3 cm s 21 for the permeability coefficient and with the partition value for membranes of 2.0 determined herein, we can estimate a diffusion coefficient of 6610 27 cm 2 s 21 for H 2 S in lipid membranes (D m in Equation 4). This value is significantly lower than the diffusion coefficient in water, D w = 2.32610 25 cm 2 s 21 at 35uC [25]. So, are lipid membranes effective barriers to H 2 S transport? We can easily calculate the resistance to H 2 S flux imposed in a cell by lipid membranes. If all sulfide consisted of H 2 S, as at acidic pHs, considering P m = 3 cm s 21 , the resistance of one 4 nm-thick (dx) phospholipid membrane would be 1/P m = 0.33 cm 21 s. The resistance of an equally thick layer of water would be 1/P w = 0.017 cm 21 s (using a permeability of 58 cm s 21 , calculated as P w = D w /dx, analogous to Equation 4 [25]). Several membranes would behave as resistances in series [24], so that considering the contribution of several 4 nm-thick layers of water (a-n) and membranes (n), a weighed apparent total resistance (1/P T ) for the whole process can be calculated using Equation 5: Assuming that simple diffusion in a cell of 10 mm in diameter equals diffusion in a = 2500 layers, 4 nm each, of water, it can be calculated that a single membrane (n = 1) would result in a very small decrease in diffusion (0.7%). Even assuming that H 2 S must diffuse across several organelle membranes accounting for 20 lipid Lowering the pH would result in an increase in apparent diffusion. In ischemia, for instance, there is tissue acidosis, and the pH can decrease to 6.5. At this pH, the apparent P m would be 2.3 cm s 21 and the apparent diffusion would decrease 16.4% in the presence of membranes.
Overall, lipid membranes will offer a low resistance to the diffusion of H 2 S that will not limit its transport across cells to a great extent. The effect of multiple cells and lipid membranes (''tissue'') on H 2 S macroscopic diffusion is discussed next.

Modeling the diffusional spread of H 2 S from a single cell
The relatively low barrier to transport offered by lipid membranes indicates that H 2 S produced in one cell can diffuse and exert effects on distant cells, complying with the requirements of a paracrine signaling molecule. Although it has often been compared with ? NO and CO [26], no attempt to model H 2 S diffusion in tissues has been made. In contrast to early onedimensional point-source models of ? NO diffusion [27,28] here we used a 3D diffusion model involving a spherical source (''the cell'') that produces H 2 S in a continuous manner from the surface. By using a spherical model, we include many sources of H 2 S (collection of enzymes) while avoiding the complexities derived of trying to use multiple single-point sources in a 3D model. We can calculate the change in the concentration of H 2 S as a function of time and distance from the source. Since there is still some debate about how much H 2 S is generated by cells and how much is necessary to activate different functions, we used a generic model where we set the rate of H 2 S production so that the concentration of H 2 S at the surface of the cell is 100.0 arbitrary units at infinite time in the absence of membrane resistance. The sphere of action was arbitrarily set at the distance in which the concentration of H 2 S drops to 10.0. Another reason to use a generic model with arbitrary units is that it can be conveniently scaled to any concentration. If we knew the actual concentration of H 2 S in the surface of a cell, we could rescale Figure 1B directly, and obtain the actual concentration distribution of H 2 S away from a cell.
Considering the free diffusion of H 2 S in an aqueous medium with no membranes, we can see that after production starts, the sphere of action expands very rapidly and has a radius of 32 mm after 1 s and 42 mm after 10 s ( Figure 1C). By calculating how many spheres of 10 mm diameter (representing cells) can fit within spheres of 32 and 42 mm radii, we can estimate that H 2 S would be able to reach 260 and 590 neighboring cells, respectively. After incorporating the resistance imposed by lipid membranes to H 2 S (n = 20, D T = 2.02610 25 cm 2 s 21 ), we found that, for the same rate of production, the concentration close to the cell was significantly increased (Figure 1B). At pH 7.4, where ionization to HS 2 decreases the apparent membrane permeability (D T, 7.4 = 1.51610 25 cm 2 s 21 ), the increase in concentration was even more remarkable. For example, at 20 mm from the surface of the cell after 1 s of production, the concentration of sulfide was 40% higher than in the absence of membranes. By slowing down diffusion, total sulfide spreads more slowly and a higher concentration is achieved close to the source. As defined here, the sphere of action in absolute numbers is actually larger for the hindered diffusion model ( Figure 1C), but expectedly decreases when the concentration at the source is re-normalized to 100.0. This effect of hindered diffusion may help to build up a higher local concentration of H 2 S, focusing the signaling function close to the site of H 2 S production (see also Figure S2). At the pH of 6.5 typical of tissue acidosis, the focusing effect of the membranes was lower than at pH 7.4 ( Figure 1B), consistent with a higher proportion of H 2 S being protonated at this pH (D T, 6.5 = 1.94610 25 cm 2 s 21 ).
The size of the sphere of action will also depend on how fast H 2 S is consumed as it spreads in a tissue. The decay of H 2 S will be determined by the presence of molecular targets like disulfide bonds, oxidants, mitochondrial membrane proteins and metallic centers among others, and on how fast H 2 S reacts with these targets. In rat blood, for instance, the half-life of sulfide has been reported to be 151 s [29]. Considering that in 15 seconds H 2 S covers 90% of the space covered at infinite time ( Figure 1C), while only ,7% of the starting H 2 S has been consumed, such a rate of decay will have minimal effects on H 2 S spread. In summary, H 2 S produced at one site should easily reach proximal cell layers at concentrations close to those in the source ( Figure 1A-C), and the layers further away at decreasing concentrations, supporting the role of hydrogen sulfide as a paracrine signaling molecule. More studies on the rate and concentration of H 2 S that can be produced by cells in different tissues are needed to define the real extent and range of physiological effects of H 2 S.

H 2 S diffusion and partitioning in ischemia-reperfusion
It has been shown that exogenous H 2 S can protect cardiac muscle cells from ischemia-reperfusion injury when it is added during reperfusion, reducing significantly the infarct size and subsequent inflammation [30,31]. In a study, exogenous H 2 S reduced the infarct size by 70% in the hearts of mice subjected to ischemia-reperfusion [30]. This high degree of myocardial protection is likely due to the high membrane permeability and diffusivity of H 2 S, further enhanced by tissue acidosis that allows H 2 S to go deep in the myocardium. Partitioning of H 2 S in the mitochondrial membranes may also be involved in protecting against ischemia-reperfusion injury, since part of the protective actions of H 2 S is ascribed to the inhibition of cytochrome c oxidase [30]. As discussed earlier, the reaction of H 2 S with this protein complex is likely enhanced by the two-fold higher solubility of H 2 S in membranes relative to water. The high membrane permeability and partitioning of H 2 S are undoubtedly very advantageous pharmacokinetic properties.

Conclusions
We found that H 2 S is twice as soluble in lipid membranes as in water (K P = 2.060.6), and similar results were found with noctanol and hexane (K P = 2.1 and 1.9, respectively). The estimated high membrane permeability coefficient of H 2 S (3 cm s 21 ) indicates a very low barrier to intercellular transport. A 3D mathematical model of H 2 S diffusion in tissues at pH 7.4 shows that the low but significant resistance imposed by lipid membranes slows down diffusion in tissues and leads to a local accumulation of H 2 S near the source. In these conditions, the sphere of action, defined by the distance at which the concentration of H 2 S is 10% that at the source, involves more than 200 neighboring cells within 1 s of formation. These results support the role of hydrogen sulfide as a paracrine signaling molecule and reveal advantageous pharmacokinetic properties for its therapeutic applications.

Supporting Information
Text S1 Derivation of Equation 1.  The model consists of a single spherical cell producing H 2 S at a constant rate. We interrogate how the concentration of total sulfide (H 2 S+HS 2 ) changes as a function of time and distance from the source cell with or without surrounding cells. The sphere of action is defined by the distance from the source cell at which the concentration of total sulfide is 10.0 arbitrary units. B) Expansion 1s after formation starts, with membranes at acidic pH (green), with membranes at pH 7.4 (red), with membranes at pH 6.5 (gray) and without membrane resistance (blue) C) Expansion of the sphere of action as a function of time, without membrane resistance (blue), with membranes at acidic pH (green), with membranes at pH 7.4 (red) and at pH 6.5 (gray). Plots are derived from Equation 2. The resistance imposed by the membranes was weighed into the aqueous diffusion coefficient (Equation 5) so that 20 membranes would cause the apparent diffusion coefficient of H 2 S to decrease from D w = 2.32610 25 cm 2 s 21 (H 2 S in water, blue line) to 2.02610 25 cm 2 s 21 (green line). Considering ionization to HS 2 , the apparent diffusion coefficient of H 2 S/HS 2 drops to 1.51610 25 cm 2 s 21 at pH 7.4 (red line) and to 1.94610 25 cm 2 s 21 at pH 6.5 (gray line). doi:10.1371/journal.pone.0034562.g001 Figure S2 Diffusional spread dependence on membrane resistance. A) Concentration profiles of total sulfide (H 2 S+HS 2 ) as a function of time and distance considering a spherical and continuous source (''cell'') with unhindered diffusion (r = 5 mm, D = 2.32610 25 cm 2 s 21 ); B) with a resistance of 20 membranes per cell (D = 2.02610 25 cm 2 s 21 ); and C) with a resistance of 20 membranes per cell at pH 7.4 (D = 1.51610 25 cm 2 s 21 ). The gray line at 10.0 concentration units indicates the limit of the putative sphere of action. As better exemplified in C, an important consequence of slowing down diffusion is increasing the concentration of H 2 S near the origin and throughout the system. The spreading does occur more slowly, but a higher concentration can be achieved near the source. Concentration profiles were calculated using Equation 2 and expressed as arbitrary units. (TIF)