Partitioning of Pyrene-Labeled Phospho- and Sphingolipids between Ordered and Disordered Bilayer Domains

Abstract

Here we have studied how the length of the pyrene-labeled acyl chain (n) of a phosphatidylcholine, sphingomyelin, or galactosylceramide affects the partitioning of these lipids between 1), gel and fluid domains coexisting in bovine brain sphingomyelin (BB-SM) or BB-SM/spin-labeled phosphatidylcholine (PC) bilayers or 2), between liquid-disordered and liquid-ordered domains in BB-SM/spin-labeled PC/cholesterol bilayers. The partitioning behavior was deduced either from modeling of pyrene excimer/monomer ratio versus temperature plots, or from quenching of the pyrene monomer fluorescence by spin-labeled PC. New methods were developed to model excimer formation and pyrene lipid quenching in segregated bilayers. The main result is that partition to either gel or liquid-ordered domains increased significantly with increasing length of the labeled acyl chain, probably because the pyrene moiety attached to a long chain perturbs these ordered domains less. Differences in partitioning were also observed between phosphatidylcholine, sphingomyelin, and galactosylceramide, thus indicating that the lipid backbone and headgroup-specific properties are not severely masked by the pyrene moiety. We conclude that pyrene-labeled lipids could be valuable tools when monitoring domain formation in model and biological membranes as well as when assessing the role of membrane domains in lipid trafficking and sorting.

INTRODUCTION

In recent years, evidence has accumulated suggesting that segregated lipid domains, or “rafts,” exist in the plasma membrane as well as in some other membranes of eukaryotic cells (Simons and Ikonen, 1997). There is presently a wide interest in membrane rafts and other membrane domains since they are thought to play a crucial role in many important cellular phenomena, like signal transduction and intracellular sorting of membrane proteins and lipids (Brown and London, 2000; Anderson and Jacobson, 2002; Simons and Ehehalt, 2002; Edidin, 2003). The actual lipid composition of rafts is not known, but they are thought to be rich in cholesterol and sphingolipids and therefore to exist in liquid-ordered (l_o) phase in contrast to the liquid-disordered (l_d) phase, a state that most natural glycerophospholipids exist in at physiological temperatures (Ipsen et al., 1987; Sankaram and Thompson, 1990; Vist and Davis, 1990; Almeida et al., 1992; Schroeder et al., 1994, 1998; Ahmed et al., 1997).

The major unresolved issues regarding rafts relate to their composition, size, and lifetime, and whether or not the rafts include both monolayers of the bilayer (Maxfield, 2002; Edidin, 2003; Silvius, 2003). Fluorescent lipid analogs are potentially useful tools to study these issues because of the sensitivity of fluorescence detection and the possibility to use both spectroscopic and microscopic approaches. However, to be useful as a raft probe, the fluorescent analog should partition effectively to the raft domains. Because the lipids in rafts are thought to be conformationally ordered and tightly packed together, one would assume that fluorescent lipids containing a bulky and fairly polar fluorophore in the acyl chain would be largely excluded from rafts. Conversely, probes with long, saturated alkyl/acyl chains are expected to interact favorably with conformationally ordered lipids and thus partition to rafts. These predictions seem to be largely correct as indicated by recent studies (Mesquita et al., 2000; Wang et al., 2000; Wang and Silvius, 2000; Samsonov et al., 2001).

Pyrene lipids have been extensively used to study lateral organization of membranes (reviewed in Pownall and Smith, 1989; Somerharju, 2002). The main reason for this is that an excited pyrene lipid molecule can form excimers upon collision with another pyrene lipid in the ground state, and that the rate of excimer formation is proportional to the local pyrene lipid concentration. The ratio of excimer/monomer fluorescence intensities (E/M) thus provides information on the lateral distribution and mobility of pyrene lipids in the bilayer (Galla and Sackmann, 1975). Partitioning of pyrene lipids between gel-state and fluid-state (liquid-crystalline) domains has been investigated by recording the E/M ratio as a function of temperature (Chong and Thompson, 1985; Somerharju et al., 1985; Hresko et al., 1986, 1987; Jones and Lentz, 1986; Ollmann et al., 1987; Viani et al., 1988). In those studies, however, only a single, or few, pyrene lipid species were employed and therefore systematic information on the effect of the acyl chain length or the lipid backbone/polar headgroup structure on the partitioning behavior is lacking. Second, in those earlier studies the bilayer matrix usually consisted of a single saturated phospholipid species and was thus quite different from natural membranes. Therefore, additional studies with more natural-like systems are needed to determine how pyrene lipids partition between different membrane domains and whether they could be used to study raft formation and properties. Such information is also crucial when pyrene lipids are employed to investigate lipid trafficking and sorting in cells (Masserini et al., 1990; Agmon et al., 1991; Kasurinen and Somerharju, 1995; Tanhuanpää and Somerharju, 1999; Heikinheimo and Somerharju, 2002).

Here we have studied the effect of the length of the labeled acyl chain of Pyr_nPC, Pyr_nSM, and Pyr_nGalCer (n = the number of carbons in the labeled acyl chain) on the partitioning of the parent lipid between 1), gel and fluid domains coexisting in BB-SM and BB-SM/spin-labeled PC bilayers or 2), between l_d and l_o domains in BB-SM/spin-labeled PC/cholesterol bilayers. The partitioning was determined based either on E/M versus temperature curves or quenching of the pyrene monomer fluorescence by spin-labeled PC molecules. The key result is that whereas the pyrene lipids with a short labeled chain strongly preferred the fluid/l_d domains, those with a long chain had a markedly higher affinity for gel/l_o domains. The lipid headgroup/backbone had a modest effect on partitioning.

MATERIALS AND METHODS

Lipids and other reagents

BB-SM, dioleoylphosphatidylcholine (DOPC), 1-palmitoyl-2-(7-doxyl)-stearoylphosphatidylcholine (7-SLPC), and 1-palmitoyl-2-(12-doxyl)-stearoylphosphatidylcholine (12-SLPC) were purchased from Avanti Polar Lipids (Alabaster, AL). Sphingosylphosphorylcholine and lysogalactosylceramide were obtained from Larodan (Malmö, Sweden) and the other chemicals from Sigma (St. Louis, MO). The 1-palmitoyl-2-pyrenylacyl-phosphatidylcholine (Pyr_nPC) species were synthesized as described previously (Somerharju et al., 1987). Pyrenylacylsphingomyelins (Pyr_nSM) and pyrenylacylgalactosylceramides (Pyr_nGalCer) were synthesized essentially as described elsewhere (Ahmad et al., 1985) and purified on a Licrosphere 100 DIOL column (5-μm particle size, 250 × 4.6 mm; Alltech, Deerfield, IL) using a solvent system described previously (Silversand and Haux, 1997). All lipids were >98% pure and were stored in chloroform/methanol (4:1, v/v) <−20°C.

Preparation of multilamellar liposomes

To prepare multilamellar vesicles (MLV), the lipids were mixed in chloroform and the solvent was evaporated under a nitrogen stream at 55°C to 60°C and samples were then kept in a vacuum desiccator for 3 to 16 h. The lipids were dispersed in 20 mM Tris-HCl, 1 mM EDTA, and 150 mM NaCl, at pH 7.4 (TEN) buffer for fluorometry, and 0.5 mM phosphate, 1 mM EDTA, 50 mM NaCl, and 0.02 mg/ml NaN₃, at pH 7.4 (PEN) buffer for calorimetry. The samples containing Pyr_nPC or Pyr_nSM were hydrated at 65°C and the samples containing Pyr_nGalCer at 85°C. The samples for E/M ratio versus temperature measurements and calorimetry were first incubated at the hydration temperature for 10 min in the dark, vortexed for 1 min, and again incubated at the hydration temperature for 2 min. This sequence was repeated twice, after which the samples were allowed to cool to room temperature and kept at 4°C for at least 16 h before the measurement. For fluorometric analysis the total lipid concentration was adjusted to 16.1 μM and for calorimetry to 1.7–3.3 mM (with 2 mol % of a pyrene lipid). For the fluorescence quenching assays, MLVs with a total lipid concentration of 50 μM (with 0.3 mol % pyrene lipid) were prepared as described previously (Wang et al., 2000; Wang and Silvius, 2000). The samples were incubated for 15 min at 45°C, 1 min at 75°C, vortexed twice for 10 s, incubated for 15 min at 45°C, and then allowed to cool to the desired temperature at which they were kept for 2–4 h before the measurement.

Fluorometry

The E/M versus temperature measurements were performed on a PTI Quantamaster (Lawrenceville, NJ), fluorescence spectrophotometer equipped with two emission monochromators and detectors. The excitation wavelength was set to 345 nm (bandwidth 2 nm), and the emission wavelengths to 378 nm (bandwidth 4.5 nm) and 475 nm (bandwidth 22 nm), for the pyrene monomer and excimer fluorescence, respectively. The temperature in the cuvette was regulated with a Braun Thermomix UB (Melsungen, Germany), temperature bath under computer control and was recorded with a probe placed in the cuvette. The samples were maintained at 10°C for 10 min and then heated to 80°C at a rate of 1°C/min. The fluorescence quenching assays were performed on a Varian Cary Eclipse fluorometer (Varian, Cary, NC) equipped with a thermostated cuvette holder. The excitation (345 nm) and emission (378 nm) bandwidths were as described above. After incubating the samples for the quenching assays at the temperature of measurement for 2–4 h, they were placed into the thermostated cuvette, incubated in the dark for 30 s at the same temperature, and fluorescence intensity was determined using a signal integration time of 5 s. The quenching curves were not significantly altered if the preincubation at the temperature of measurement was extended to 10 h, in agreement with previous studies (Wang et al., 2000; Wang and Silvius, 2000). Other control experiments also indicated that the systems studied were at or close to an equilibrium.

Differential scanning calorimetry

The MLVs dispersed in PEN buffer were degassed for 10 s in a sonicating bath and then introduced into the sample cell of a 6100 Nano II differential scanning calorimeter (Calorimetry Sciences, American Fork, UT). The reference cell contained an equal volume of the PEN buffer. The temperature was maintained at 10°C for 10 min and then raised to 80°C at the rate of 1°C/min.

Other methods

The molecular species of BB-SM were quantified by electrospray mass-spectrometry as described previously (Koivusalo et al., 2001). The concentrations of lipid stocks were determined based on a phosphate assay (Bartlett and Lewis, 1970).

RESULTS

E/M versus temperature plot as an indicator of gel/liquid-domain partitioning of pyrene lipids

Previous studies have indicated that partitioning of pyrene-labeled lipids between fluid and gel bilayer domains can be studied by measuring the pyrene excimer/monomer (E/M) emission intensity ratio as a function of temperature (Galla and Sackmann, 1975; Somerharju et al., 1985; Hresko et al., 1986, 1987; Jones and Lentz, 1986). Whereas in those studies homogenous, saturated PC species were used as the matrix lipid, we chose to use BB-SM which is a mixture of several molecular species containing 16:0, 18:0, 20:0, 22:0, 24:1, and 24:0 fatty acyl residues as determined by mass-spectrometry. As shown in Fig. 1 A, BB-SM undergoes a gel-to-fluid phase transition between ∼15 and 47°C, in agreement with earlier data (Barenholz et al., 1976; Calhoun and Shipley, 1979). This transition actually consists of at least three subtransitions as indicated by the complex peak shape and deconvolution (Fig. 1 A). The presence of several transitions is obviously due to the acyl chain heterogeneity of BB-SM. The subtransitions at ∼36°C and ∼41°C may be attributed to domains consisting of species with long and saturated acyl chains, whereas the transition at ∼26°C probably derives from the melting of the species with shorter and/or more unsaturated chains. Notably, the BB-SM liposomes used for the calorimetry also contained 2 mol % of Pyr₆PC to allow direct comparison with E/M versus temperature curves (see below). Very similar calorimetric curves were obtained if Pyr₆PC was replaced with any other Pyr_nPC/SM/GalCer species or if no pyrene lipid was included (data not shown).

FIGURE 1.

Relationship between E/M versus temperature curves and phase behavior of short-chain pyrene lipids. Multilamellar vesicles consisting of 98 mol % BB-SM and 2 mol % of Pyr₆PC lipid were prepared and the heat capacity (A) and the E/M ratio (B) were measured as a function of temperature as detailed in Materials and Methods. C relates the E/M ratio to the distribution of Pyr₆PC below T_m (left panel), at the phase transition region (middle panel), and above T_m of BB-SM (right panel). The shaded areas represent gel and the open areas fluid domains, whereas the solid dots represent Pyr₆PC molecules.

Fig. 1 B shows an E/M versus temperature plot obtained for Pyr₆PC/BB-SM MLVs. Similarly to the earlier studies (Somerharju et al., 1985; Hresko et al., 1986, 1987; Jones and Lentz, 1986), we interpret this plot as follows (cf. Fig. 1 C). When the BB-SM bilayer is initially cooled to a low temperature, the Pyr₆PC molecules cluster because of their low solubility in gel-state BB-SM domains (far left panel in Fig. 1 C). These clusters most probably also contain some low-melting, i.e., unsaturated/short-chain BB-SM molecules, which probably explains why only a relatively modest increase in excimer formation occurs upon probe clustering. The exclusion of Pyr₆PC from the BB-SM gel domains can be attributed to a poor fit (perturbation) of the bulky pyrene moiety into the tightly packed lipids in such domains (see Discussion). Upon heating, E/M gradually increases until the gel-to-liquid phase transition of BB-SM is reached. At this point, E/M decreases abruptly due to a gradual disappearance of the Pyr₆PC cluster domains upon melting of the matrix lipid (middle panel of Fig. 1 C). Any further increase in temperature results in a monotonous increase in E/M due to increasing lateral diffusion of the pyrene lipid molecules fully dispersed in the fluid BB-SM matrix (far right panel of Fig. 1 C). Consistent with this interpretation, the cooling curves fully coincided with the heating curves (data not shown).

The E/M versus temperature curves obtained for each Pyr_nPC species (n = 6–14) are shown in Fig. 2 A. Clearly, the length of the pyrene-labeled chain has a remarkable effect on the shape of the curve. The abrupt decrease of E/M observed for Pyr_nPC in the phase transition region of BB-SM upon heating became less evident with increasing chain length and disappeared when n = 12. For Pyr₁₄PC even an increase in E/M was observed. The shape of the curves strongly suggests that partitioning of Pyr_nPC to the gel domains becomes increasingly favorable as n increases.

FIGURE 2.

Excimer/monomer intensity ratio versus temperature curves for different pyrene lipids incorporated in BB-SM bilayers. Two mol percent of the indicated pyrene lipid was incorporated in multilamellar BB-SM liposomes and E/M was determined as a function of increasing temperature as described in Materials and Methods. (A) Pyr_nPC, (B) Pyr_nSM, and (C) Pyr_nGalCer (n = 6, 8, 10, 12, or 14). The experiment was repeated three times with essentially identical results. Practically identical curves were also obtained in cooling runs.

Pyr_nSM behaved similarly to Pyr_nPC (Fig. 2 B); i.e., the longer the labeled acyl chain, the smaller is the deflection in E/M curve, thus indicating that partitioning to the gel phase domains increases systematically with n. Careful comparison of the curves in Fig. 2, A and B, indicates that each Pyr_nSM may partition somewhat less to the gel domains than Pyr_nPC with equal n. We also tested how the length of the labeled acyl chain affects the partitioning of a glycosphingolipid derivative, Pyr_nGalCer (Fig. 2 C). Also in this case the plots clearly indicate that partitioning to the gel domains increases systematically with increasing chain length. However, the curves deviated again somewhat from those obtained for Pyr_nPC, thus supporting the notion that partitioning of pyrene-labeled lipids between gel and fluid domains is not determined merely by the length of the labeled acyl chain (see below).

Quantitative analysis of pyrene lipid distribution between gel and liquid domains in BB-SM bilayers based on E/M versus temperature plots

To assess more quantitatively the gel/liquid partition of the different pyrene-labeled lipids an empirical model was constructed (see Appendix 1). Notably, only two subtransitions, i.e., those centered at ∼36°C and ∼28°C (Fig. 1 A), were taken into account when applying this model here. The transition at ∼41°C was neglected simply because none of the probes seemed to respond significantly to this subtransition (Fig. 2). The most probable explanation for this lack of response is that the pyrene-labeled lipids do not partition significantly to the corresponding gel domains probably consisting mainly of the long-chain and saturated SM species. A low affinity of pyrene lipids containing the rather bulky pyrene moiety for such domains with tightly packed acyl chains would not be unexpected.

Fig. 3 shows the experimental and modeled E, M, and E/M versus temperature curves for a short- and long-chain Pyr_nPC species (Pyr₆PC and Pyr₁₄PC). As can be seen, a reasonable fit was obtained in each case. Similar results were obtained for all other pyrene lipids (not shown). The gel versus liquid partition coefficients obtained from those fits are plotted as a function of labeled chain length in Fig. 4. The model provides two partition coefficients: one for partitioning between the fluid domains and the gel domains with T_m of ∼36°C (K_g/f(36°C)), and the other for partitioning between the fluid domains and gel domains with T_m of ∼28°C (K_g/f(28°C)). As would be expected from the data shown in Fig. 2, the probes with a short labeled chain partitioned mainly to the fluid domains at 36°C, whereas those with a long chain partitioned equally to both types of domains, or even slightly preferred the gel domains. The long-chain Pyr_nGalCer derivatives (n = 10 or 12) partitioned somewhat more to the gel domains than the corresponding Pyr_nPC and Pyr_nSM derivatives (Fig. 4 A). This indicates, that beside the lipid backbone, the headgroup also has an effect on pyrene lipid partitioning between gel and fluid domains. Interestingly, the pyrene lipids partitioned nearly equally between the fluid and gel domains with T_m of ∼28°C independent of the length of the pyrene-labeled chain and other structural details (Fig. 4 B). The cause for such structure independent partitioning could be that these low-melting domains probably consist of BB-SM species with a short and/or unsaturated acyl chain and are thus less ordered and more accommodative than the higher melting domains.

FIGURE 3.

Experimental and modeled excimer, monomer, and excimer/monomer versus temperature curves for Pyr₆PC and Pyr₁₄PC. Experimental curves (open circles) obtained for liposomes containing 2 mol % of Pyr₆PC (A–C) or Pyr₁₄PC (D–F) are shown together with curves (dotted line) obtained by fitting of an empirical model (Appendix 1) to the data. It is important to note that a global fitting protocol was used here, i.e., the temperature, cooperativity, and maximal fractional area of the individual transitions were forced to be identical for all Pyr_nPC, Pyr_nSM, and Pyr_nGalCer species.

FIGURE 4.

Gel/fluid partition coefficients for pyrene lipids obtained by modeling of the excimer and monomer fluorescence versus temperature curves. The gel/fluid partition coefficients were obtained by fitting of the model described in Appendix 1 to the experimental curves as shown in Fig. 3 and are plotted as a function of pyrenylacyl chain length (n). (A) Partition coefficients at 36°C (K_g/f(36°C)). (B) Partition coefficients at 28°C (K_g/f(28°C)). The error in the partition coefficients was tested with selected samples by determining how systematic variation of the partition coefficient affects the fit quality. Already when the partition coefficient obtained by fitting was changed by 10%, the modeled curve deviated clearly more from the experimental one than what was the typical deviation between experimental curves from different experiments. Based on this finding, we estimate that the error in the partition coefficients is <10%.

In line with the present results, making use of the E/M ratio Jones and Lentz calculated that Pyr₁₀PC partitions seven times more to fluid DOPC-rich domains than to coexisting solid DPPC-rich domains (Jones and Lentz, 1986). Another, qualitative study also indicated that Pyr₁₀PC partitions preferentially to the fluid domains in neat DPPC bilayers (Hresko et al., 1986).

Reliable information on the lateral distribution of pyrene-labeled lipids can be obtained from the E/M versus temperature plots only if the pyrene lipid does not cluster significantly in the fluid matrix (Hresko et al., 1987). To study this, E/M versus temperature plots were measured for all Pyr_nPC, Pyr_nSM, or Pyr_nGalCer species present at a concentration of 2 mol % in DOPC bilayers. E/M increased smoothly with temperature at least to 90°C in each case (data not shown). This suggests that pyrene lipids do not have a significant tendency to cluster in a fluid bilayer; otherwise one would expect to see deviations in the E/M versus temperature curve due to melting of the clusters. We also measured the E/M ratio for representative pyrene lipids (Pyr₆PC, Pyr₆SM, Pyr₆GalCer, Pyr₁₀PC, Pyr₁₀SM, Pyr₁₀GalCer, Pyr₁₄PC, and Py₁₄SM) versus their concentration (0–10 mol %) in BB-SM bilayers at 50°C. The plots were essentially linear and coincided independent of the headgroup/backbone structure when n was equal (data not shown). Collectively, these results strongly suggest that none of pyrene lipids have any significant tendency to segregate in fluid bilayers at the concentrations used in this study.

Partitioning of pyrene lipids between gel and liquid domains in BB-SM/7-SLPC bilayers as deduced from fluorescence quenching

Earlier studies have demonstrated that partitioning of a fluorescent probe between fluid and gel-like membrane domains can be determined by incorporating the probe into bilayers consisting of a quencher lipid (having a spin-labeled or brominated acyl chain and closely mimicking natural unsaturated PC species) with a low T_m and of an unlabeled lipid with a high T_m, e.g., BB-SM (London and Feigenson, 1981a,b; Huang et al., 1988; Spink et al., 1990; Wang et al., 2000; Wang and Silvius, 2000, 2003). Whereas 12-SLPC has been generally used as the quencher lipid (Ahmed et al., 1997; Wang et al., 2000; Wang and Silvius, 2000; Xu and London, 2000), we chose to use 7-SLPC, inasmuch as this species quenched pyrene lipid fluorescence equally independent of the length of the pyrene-labeled chain in homogenous fluid bilayers (see below), whereas for 12-SLPC significant differences were found (data not shown). The gel-to-liquid phase transition temperature of 7-SLPC was ∼8°C as determined by differential scanning calorimetry (our unpublished data). Thus this lipid is in the fluid state at 15°C, the temperature at which the partitioning experiments were carried out.

We first studied the quenching of Pyr₆PC and Pyr₁₄PC, i.e., species with a short or a long labeled chain in homogenous, fluid bilayers consisting of DOPC and 7-SLPC. As can be seen in Fig. 5 A, the quenching curves obtained for these lipids are essentially superimposable, thus indicating that the pyrene lipid fluorescence is quenched equally by 7-SLPC independent of the length of the pyrene-labeled chain in the absence of domain segregation. Such chain-length independent quenching, which is a prerequisite for obtaining reliable partitioning information in segregated bilayers (Wang et al., 2000), was also observed for other lipids studied, namely Pyr₆PC, Pyr₁₄PC, Pyr₆SM, and Pyr₁₄SM, in BB-SM/7-SLPC bilayers at 50°C, i.e., when the entire bilayer is in the fluid state (data not shown).

FIGURE 5.

Analysis of pyrene lipid partition between coexisting gel and fluid domains as determined by pyrene fluorescence quenching. Multilamellar liposomes containing 0.3 mol % of the indicated pyrene lipid and 0–100 mol % of 7-SLPC, a quencher of pyrene fluorescence, were prepared and the pyrene monomer fluorescence intensity was determined at 15°C as detailed in Materials and Methods. (A) Pyr₆PC and Pyr₁₄PC in DOPC/7-SLPC bilayers, (B) Pyr₆PC, Pyr₁₀PC, and Pyr₁₄PC in BB-SM/7-SLPC bilayers, (C) Pyr₆SM, Pyr₁₀SM, and Pyr₁₄SM in BB-SM/7-SLPC bilayers, and (D) Pyr₆GalCer and Pyr₁₂GalCer in BB-SM/7-SLPC bilayers. Data is shown only up to 7-SLPC mole fraction of 0.4 since complete quenching of each pyrene lipid was observed at higher mole fractions. Each data point represents an average from two to three experiments with three replicate samples. The error bars indicate the standard deviation.

Fig. 5 B shows the quenching curves obtained for Pyr_nPC in BB-SM/7-SLPC bilayers at 15°C, a temperature at which BB-SM-rich gel domains coexist with fluid domains consisting mainly of 7-SLPC over a wide composition range. In contrast to the homogenous bilayers discussed above, the quenching was significantly dependent on the length of the pyrene-labeled chain, i.e., Pyr₆PC and Pyr₁₀PC were quenched more efficiently than Pyr₁₄PC. This indicates that the former species partition significantly less to the BB-SM gel domains than the latter one. Analogously, Pyr₆SM and Pyr₁₀SM were quenched more efficiently than Pyr₁₄SM (Fig. 5 C) and Pyr₆GalCer more efficiently than Pyr₁₂GalCer (Fig. 5 D; Pyr₁₄GalCer was not available, therefore the Pyr₁₂ species was used instead). The data clearly indicate that the length of the labeled chain plays an important role in partitioning of the pyrene-labeled lipids between the fluid and gel domains in BB-SM/7-SLPC bilayers. London and Feigenson have previously constructed a model which allows one to determine quantitatively the partitioning of a fluorescent probe between co-existing gel and fluid domains from quenching data (London and Feigenson, 1981b). However, this model is valid only when the quenching is static, i.e., for probes with a relatively short (few nanoseconds) fluorescence lifetime (London and Feigenson, 1981b). The fluorescence lifetime of pyrene lipids in bilayers is >100 ns (Sassaroli et al., 1995), which allows diffusional quenching to take place as well. To account for this, an empirical model was constructed to analyze pyrene lipid partitioning (see Appendix 2). This model assumes that 1), the quenching can be either static or dynamic (diffusional) and 2), the quencher can be either a single quencher lipid molecule or a domain consisting (mostly) of the quencher lipid. Quenching by these two entities are characterized by specific quenching constants, i.e., k_mon and k_dom, respectively. The value of k_mon can be determined for each lipid from quenching at low quencher concentrations (<∼1.5 mol %), i.e., when the bilayer is homogenous. Knowing the value of k_mon then allows one to determine both the gel/fluid partition coefficients of the probes as well as k_dom which in turn can be used to estimate the average size of the quencher lipid domains. The fitting results indicate that the pyrene lipids with a Pyr₆ or Pyr₁₀ acyl chain species strongly prefer the liquid domains, independent of the headgroup or backbone structure (Fig. 6). The Pyr₁₄ species appear to partition more to the gel domains than the shorter chain species, albeit they also prefer the fluid domains. A very small value (∼0.04) was obtained for k_dom from which one can deduce (see Appendix 2) that the quencher domains are quite large, i.e., consist minimally of several hundreds of lipid molecules.

FIGURE 6.

Gel/fluid partition coefficients pyrene lipids. The partition coefficients (K_g/f) were obtained by fitting an equation given in Appendix 2 to the quenching data in Fig. 5, B–D.

Partitioning of pyrene lipids between liquid-disordered and liquid-ordered domains coexisting in BB-SM/7-SLPC/cholesterol bilayers

Partitioning of the pyrene lipid between l_o and l_d domains was assessed by varying the quencher lipid content in phospholipid fraction while maintaining the cholesterol content of the bilayer constant (33 mol %). Based on earlier data, BB-SM/cholesterol-rich l_o-domains are present in such bilayers at 37°C when the BB-SM mole fraction is ∼0.05–0.85 (Ahmed et al., 1997; Wang et al., 2000; Wang and Silvius, 2000). However, contrary to expectations, only minor differences in quenching between the Pyr₆ and Pyr₁₄ species were observed at this temperature (data not shown), which has also been observed for different indolyl-labeled lipids (Wang and Silvius, 2003). This could be due to the long excited state lifetime of pyrene as well as the small size and/or lifetime of the BB-SM-rich l_o domains at this temperature. We therefore measured the samples at 25°C where the l_o domains are expected to be significantly larger and more stable. The basic characteristics of l_o and l_d domains at this temperature should, however, be similar to those at 37°C as shown for similar systems (cf. Silvius, 1992).

The quenching curves obtained for Pyr₆PC, Pyr₁₀PC, and Pyr₁₄PC in BB-SM/7-SLPC/cholesterol bilayers at 25°C are shown in Fig. 7 A. Pyr₆PC is quenched significantly more efficiently than either Pyr₁₀PC and Pyr₁₄PC, thus indicating that this short-chain species partitions significantly less to l_o domain than those with a longer chain. Interestingly, the curves obtained for Pyr₁₀PC and Pyr₁₄PC cross at 7-SLPC mole fraction of ∼0.2–0.3, indicating that partitioning of the pyrene lipids is critically dependent on the position of the pyrene in the bilayer as well as the composition of the coexisting domains. The SM and GalCer derivatives behaved similarly to Pyr_nPC, i.e., the short-chain species appeared to partition less into l_o domains than the long-chain ones (Fig. 7, B and C). However, the Pyr₁₄SM and Pyr₁₂GalCer species were less quenched at low 7-SLPC mole fractions than Pyr₁₄PC, indicating that they partition more to the BB-SM-rich domains than the PC derivative. As a control, we also determined quenching of Pyr₆PC and Pyr₁₄PC in DOPC/7-SLPC/cholesterol bilayers in which no domain segregation should exist (Ahmed et al., 1997; Wang et al., 2000). The quenching curves (Fig. 7 D) were virtually identical for the two probes, thus indicating that the intrinsic efficiency of pyrene lipid quenching by 7-SLPC is independent of the length of the pyrene-labeled chain also in the presence of cholesterol.

FIGURE 7.

Analysis of pyrene lipid partition between coexisting liquid-ordered and liquid-disordered domains as determined by fluorescence quenching. Multilamellar DOPC/7-SLPC/cholesterol (33 mol %) or BB-SM/7-SLPC/cholesterol (33 mol %) liposomes containing the indicated mole fractions of 7-SLPC in the nonsterol fraction were prepared and the fluorescence intensity was measured as detailed in Materials and Methods. (A) Pyr₆PC, Pyr₁₀PCm, and Pyr₁₄PC in BB-SM/7-SLPC/cholesterol bilayers, (B) Pyr₆SM, Pyr₁₀SM, and Pyr₁₄SM BB-SM/7-SLPC/cholesterol bilayers, (C) Pyr₆GalCer, Pyr₁₂GalCer, and Pyr₁₀TAG in BB-SM/7SLPC/cholesterol bilayers, and (D) Pyr₆PC and Pyr₁₄PC in DOPC/7-SLPC/cholesterol bilayers. Each value represents an average of two to three experiments with three replicate samples. The error bars indicate the standard deviation.

Due to the complexity of this ternary system, it is not feasible to obtain absolute partition coefficients from the quenching data. However, it is possible to obtain relative partition coefficients (Wang et al., 2000). Although this generally requires that a fluorescent species is available that partitions exclusively to l_d domains, this is not the case for the pyrene lipids since they are fully quenched in 7-SLPC domains (Fig. 7). Using the slope method of Wang et al. (2000) we determined the relative K_lo/ld values for the different pyrene lipids using Pyr₁₂GalCer as the reference. As shown in Fig. 8 the length of the pyrene-labeled chain has a significant effect on Pyr_nPC partitioning, Pyr₁₀PC showing the highest affinity for the l_o domains. However, when the ratio method of Wang et al. (2000) was used, the K_lo/ld value obtained for Pyr₁₄PC was similar or even higher than that for Pyr₁₀PC at low 7-SLPC mole fractions, as expected from the data in Fig. 7. In case of Pyr_nSM, K_lo/ld increased monotonously and only modestly with n, whereas a more significant chain-length dependency was observed for Pyr_nGalCer.

FIGURE 8.

Relative l_o/l_d partition coefficients for pyrene lipids in BB-SM/7SLPC/cholesterol bilayers. The l_o/l_d partition coefficients (K_lo/ld) were determined by slope method described previously (Wang et al., 2000) and normalized relative to that of Pyr₁₂GalCer and are plotted against the length of the pyrene-labeled acyl chain (n).

As a control, we also determined quenching of a triacylglycerol which contains two oleoyl chains in addition to a Pyr₁₀-acyl chain, and is thus expected to partition largely to the l_d domains (Wang et al., 2000). The shape of the quenching curve obtained for this lipid is indeed consistent with this prediction (Fig. 7 C), i.e., the relative K_lo/ld value obtained with the slope method was only 0.08 (Fig. 8).

DISCUSSION

Partition of the pyrene-labeled lipids between gel and liquid-crystalline domains

Both the E/M versus temperature and the quenching measurements indicated that partitioning of Pyr_nPC, Pyr_nSM, and Pyr_nGalCer shifted in favor of the gel phase when the length of the labeled chain increased (Figs. 4 and 6). The quenching data gave much smaller values for K_g/f than the E/M data. Notably, however, these values cannot be directly compared since 1), the highest melting subtransition of BB-SM (T_m ∼ 41°C) was not considered in the analysis of the E/M data for practical reasons (see Results); 2), the temperature at which the partition coefficients were determined was different in the quenching and E/M vs. T experiments; and 3) the lipid compositions were also different (neat BB-SM vs. BB-SM/7-SLPC).

Why does the length of labeled acyl chain affect the partitioning of the pyrene lipid molecules? In this respect, it is notable that when the nominal length of the pyrene-labeled chain increases, two things happen simultaneously: 1), the effective length of the chain increases and 2), the pyrene moiety moves deeper into the bilayer (Sassaroli et al., 1995). Previous studies have shown that partitioning of lipids (or mimics) containing saturated alkyl chains to gel domains is maximal when the length of the alkyl chains is approximately equal to the length of the chains of the lipid forming the gel domains (Klausner and Wolf, 1980; Spink et al., 1990; Mesquita et al., 2000; Wang and Silvius, 2003). The length of a Pyr₆ acyl chain, including the pyrene moiety, equals to that of an alkyl chain with 11.5 carbon units (Sassaroli et al., 1995), and is thus much shorter than the estimated average length of BB-SM alkyl chains (∼19–20 carbons). On the other hand, the total length of a Pyr₁₄acyl chain is ∼19.5 carbon units and thus very similar to that of the BB-SM chains. Therefore, it is likely that the more avid partitioning of the long-chain pyrene lipids to the gel domains is, at least in part, due to that the length of their acyl chains better matches the length of the chains of the lipids forming those domains.

Regarding the effect of pyrene position in the bilayer, it is worthy to mention that the mean depth of the pyrene moiety attached to a phospholipid acyl chain has been shown to increase systematically with increasing length of the linked chain both in the presence and absence of cholesterol (Eklund et al., 1992; Sassaroli et al., 1995). On the other hand, it is known that in fluid BB-SM bilayers the acyl chains are more ordered, and thus more tightly packed together, close to bilayer surface (acyl carbons 1–10) as compared to the core region (Guo et al., 2002). Such transversal gradient of alkyl chain order is likely to be maintained to some degree also in the gel state due to heterogeneity of acyl chain length (16–24 carbons) and unsaturation (0–1 double bonds) of BB-SM. Thus, when the pyrene is attached to a short acyl chain (n ≤ 8), it will partly reside in the more ordered region of the bilayer, which, due to bulkiness of pyrene, is expected to significantly perturb the packing of BB-SM acyl chains. When the length of the labeled chain increases, the pyrene moiety moves to the less ordered and less tightly packed core region of the bilayer where it is better accommodated than when it is closer to the bilayer surface. Previous studies have shown that addition of a double bond to a saturated acyl chain dramatically shifts the partitioning of the parent lipid or a lipid-like molecule in favor of the fluid phase (Welti and Silbert, 1982; Martin et al., 1990; Mesquita et al., 2000; Wang et al., 2000). A double bond causes the acyl chain to kink and thus perturbs packing of neighboring acyl chains similarly to a pyrene moiety.

Also the lipid backbone and headgroup structures were found to affect, albeit modestly, the distribution of pyrene lipids between gel and liquid-crystalline domains. Visual inspection of the E/M versus temperature curves indicates that Pyr_nPCs partition slightly more to the gel domains than Pyr_nSMs when the chain length is equal (Fig. 2). The K_g/f values determined using the model described in Appendix 1 are consistent with this conclusion, albeit no significant differences were observed for all chain lengths (Fig. 4). One possible explanation for these data is that the pyrene moiety of Pyr_nSM is less deeply inserted in the bilayer than that of corresponding Pyr_nPC. Hoffmann and co-workers have recently proposed that a nitroxide moiety attached to the acyl chain of SM lies ∼1 methylene unit closer to the membrane surface than when the same acyl is attached at the sn-2 position of PC (Hoffmann et al., 2000). These authors attributed this difference to different molecular conformations of SM and PC, as indicated by their crystal structures. An alternative explanation would be that the whole SM molecule is less deeply inserted in the bilayer than PC. SM contains a polar hydroxyl group and a double bond in the upper part of the sphingosine moiety. These are absent in PC and thus SM is more polar than PC containing comparable hydrocarbon chains.

Our data indicates that Pyr_nGalCer has a somewhat higher affinity for the gel domains than either Pyr_nPC or Pyr_nSM when n > 8 (Figs. 4 and 6). This is consistent with the recent data obtained for lipids containing an indolylstearic acid residue (Wang and Silvius, 2003). The higher gel domain affinity of the Pyr_nGalCer derivatives could derive from that these species are better accommodated in such closely packed systems due to their smaller headgroup (Kulkarni et al., 1995). However, the data of Wang and Silvius indicate that no simple relationship between the headgroup size and partitioning between fluid and gel domains may exist (Wang and Silvius, 2003).

As far as we are aware, there are no previous detailed studies on how the position of a fluorophore (or other bulky group) along an acyl chain of a phospho- or sphingolipid affects the partitioning of the labeled lipid between coexisting gel/liquid domains. Beck and colleagues have studied partitioning of two PC species carrying a fluorescent diphenylhexatriene moiety attached either to a long (C₂₂) or a short (C₃) acyl chain between fluid and gel domains coexisting in dielaidoyl-PC/distearoyl-PC bilayers (Beck et al., 1993). They found that the long-chain probe preferred the gel domains whereas the short-chain probe preferred the fluid ones. Huang and co-workers studied the partitioning of anthroyloxy-labeled fatty acids between gel and fluid domains in DPPC or DSPC bilayers (Huang et al., 1988) and found that the probes partitioned preferentially and equally to the fluid domains (K_g/f ≈ 0.25) when the position of the anthroyloxy moiety was varied between the carbons 3 and 12 of a stearic acid. Increased partitioning to the gel domains was observed when the probe was attached to the carbon 16 of a palmitic acid (K_g/f ≈ 0.7). The fact that no effect on probe partitioning was observed until the fluorophore was placed beyond carbon 12 could be due to that in the gel-state DPPC and DSPC bilayers are conformationally more ordered than BB-SM bilayers studied here. In addition, a fatty acid could partition differently from complex lipids like PC and SM (see below).

Partition of pyrene lipids between liquid-ordered and liquid-disordered domains

Partitioning of pyrene lipids between l_o and l_d domains coexisting in BB-SM/7-SLPC/cholesterol bilayers was studied by using the quenching method. In this system, the l_o domains probably consist mainly of BB-SM and cholesterol, whereas the l_d domains consist mainly of 7-SLPC. The relative partition coefficients obtained show that, in general, the affinity for the l_o domains increases with the length of the pyrene-labeled chain (Fig. 8). However, Pyr_nPC is an exception since Pyr₁₄PC partitioned less to the l_o domains than Pyr₁₀PC at higher 7-SLPC mole fractions (Fig. 8). A possible explanation could be that in the l_o domains the pyrene moiety of Pyr₁₄PC interacts unfavorably with the molecules in the opposite leaflet. Thus Pyr₁₄PC would have a lower affinity for such domains than the species with a somewhat shorter chain, e.g., Pyr₁₀PC. The absence of such anomalous chain-length dependency in BB-SM/7-SLPC bilayers (Figs. 4 and 6) could relate to the fact that the SM gel domains are thicker than the SM/cholesterol l_o domains (Maulik and Shipley, 1996a,b) and thus the Pyr₁₄ chain does not reach the opposite monolayer in BB-SM gel domains. These suggestions are consistent with studies carried out with other labeled lipids showing that an optimal chain-length exists for partitioning into l_o domains (Wang et al., 2000; Wang and Silvius, 2003). Notably, the fact that partitioning of Pyr_nSM to l_o domains increased with n with no anomaly (Fig. 8) could be due to a shallower position of the pyrene in these lipids as compared to Pyr_nPC with equal n (see above). However, it cannot be excluded that other factors as well, such as higher affinity of SM for cholesterol (Ramstedt and Slotte, 2002), play a role here.

Although the absolute partition coefficients could not be determined in this study, the shape of the quenching curves (Fig. 7) as well as the much lower relative K_lo/ld value obtained for pyrene triglyceride (Fig. 8) indicate that the long-chain pyrene lipids partition preferentially to the l_o domains, whereas the short-chain ones prefer the l_d domains. Previously, phospho- and sphingolipids with another type of fluorophore attached to short acyl chain were found to partition largely into l_d domains (Wang and Silvius, 2000; Samsonov et al., 2001).

Beside the chain-length per se, the depth of pyrene in the bilayer could also influence domain partitioning, and this effect could be much more pronounced in the presence of cholesterol. Both pyrene and cholesterol have rigid and planar structures and thus their relative depths in the bilayer could have a marked effect on pyrene lipid partitioning to the cholesterol-rich l_o domains. The sign and magnitude of this effect are, however, difficult to estimate from the existing data. The headgroup also influenced the partitioning of pyrene lipids into l_o domains, since the partitioning of long-chain chain pyrene lipids to l_o domains increased in the order PC < SM < GalCer (Fig. 8). This order agrees with that obtained previously for other fluorescent lipids (Wang and Silvius, 2000, 2003).

Implications on the use of pyrene lipids to study raft properties and intracellular lipid trafficking

One of the goals of this study was to estimate whether pyrene-labeled lipids could be used to detect and probe rafts or similar domains in cellular membranes. As was discussed above, the shape of the quenching curves indicates that long-chain pyrene lipids partition significantly to l_o domains. Consistent with this conclusion, we have recently found that when Pyr_nSM species were introduced to human fibroblasts and the cells were then exposed to Triton X-100 at 4°C, ∼60% of Pyr₁₆SM and ∼35% of Pyr₁₂SM was found in insoluble membrane fraction (as were ∼60% of the natural SM species). In contrast, almost all of Pyr₄SM was found in the soluble fraction (unpublished data). These observations strongly suggest that long-chain pyrene lipids partition to rafts or similar domains in cellular membranes and could thus be used to probe these entities.

Pyrene lipids have been proven as useful tools to study intracellular lipid trafficking as was noted in the Introduction. For correct interpretation of the data obtained in such studies it is essential to understand the how the labeled lipids partition between the different domains existing in the various cellular membranes. This is because rafts are likely to play an important role in intracellular lipid sorting and trafficking (van Meer and Lisman, 2002). Strong experimental evidence for domain partition-dependent sorting of lipids comes from a study showing that endocytic sorting of fluorescent lipids and mimics is determined by the length and unsaturation of their alkyl chains (Mukherjee et al., 1999). The differential partitioning of short- and long-chain pyrene lipids as found here could be used to further probe the role of membrane domains in intracellular lipid sorting and trafficking. The recently developed method of Tanhuanpää and Somerharju (1999) and Heikinheimo and Somerharju (2002) allowing the introduction of long-chain pyrene lipids to cells help to make such studies feasible.

Finally, it is worthy to mention that the lipid backbone and headgroup-specific properties do not seem to be severely masked by the pyrene moiety, as indicated by the fact that significant differences in partitioning were observed between Pyr_nPC, Pyr_nSM, and Pyr_nGalCer classes. This conclusion is supported by previous data obtained for different glycerophospholipid classes (Somerharju et al., 1985).

APPENDIX 1. MODELING OF THE EXCIMER AND MONOMER FLUORESCENCE INTENSITY VERSUS TEMPERATURE PLOTS

The partitioning of the pyrene lipids between solid and fluid phases (domains) was analyzed based on a model assuming that 1), N solid phases with different compositions form sequentially in BB-SM bilayers upon cooling as indicated by the calorimetric analysis (cf. Fig. 1) and 2), that partitioning of a pyrene lipid molecule between each solid phase and coexisting liquid phase is defined by a unique partition coefficient. The partitioning coefficients can be determined from the temperature dependency of the excimer (E) and monomer (M) fluorescence intensities as follows.

The temperature dependence of the fractional area covered by a liquid phase n (λ_n) is described by a Hill equation as

(1)

where s_n is the maximum of the fractional area covered by a solid phase n, c is the cooperativity of the transition (the Hill coefficient), and T_m,n is the peak temperature of that transition. The solid fractional area of each component is

(2)

A small yet significant fraction of the lipids may be in the liquid state even at the lowest temperature of measurement, i.e., 10°C. The area fraction occupied by those molecules is denoted by λ₀. Since three solids and one fluid phase can exist in this system, the total fractional area covered by the liquid phase (λ) is

(3)

The total excimer fluorescence intensity is

(4)

where x_l and x_s,n represent the concentrations of the labeled lipid in the fluid phase and each solid phase, and E_l and E_s indicate the fluid and solid phase contributions to the excimer fluorescence, respectively. It is further assumed that

(5a)

and

(5b)

where and are exponential functions describing the temperature dependencies of the excimer fluorescence intensity in the liquid and solid domains, respectively, and and are polynomials describing the probe concentration dependency of the excimer fluorescence intensities when the bilayer is fully in the liquid (T = 50°C) or solid (T = 10°C) states, respectively. The temperature dependency of excimer formation in the fluid and solid phases are described by and , respectively, and are defined as

(6a)

and

(6b)

where and k is the Boltzmann constant, and and indicate the activation energies for excimer formation in the liquid and solid phases, respectively. The parameters of the third-degree polynomials, and , were determined by measuring the excimer intensity as a function of pyrene lipid mole fraction at 10°C and 50°C, respectively.

Analogously, the total monomer intensity is defined by the equation

(7)

where the symbols are analogous to those given above for the total excimer fluorescence. Finally, the concentrations of the probe in the different phases can be coupled by the following equation

(8)

Notably, we also tested an alternative model that included the domain boundaries. However, this did not improve the fits, indicating that the probes do not have a strong tendency to concentrate to the boundaries and therefore it is not useful to employ such a more complex model here.

APPENDIX 2. MODELING OF PYRENE LIPID FLUORESCENCE QUENCHING

The framework of these calculations is given in Fig. 9. To simplify the visualization as well as some calculations, it was assumed that the packing symmetry of phospholipid molecules is hexagonal and that the quencher domains are hexagonal as well. Notably, however, the analysis can be readily generalized to apply to other domain shapes and packing symmetries, including totally random packing as will be shown elsewhere (unpublished data).

FIGURE 9.

The framework used to model pyrene lipid quenching by quencher lipid domains. The open and solid circles represent the unlabeled lipid and quencher lipid molecules, respectively. Some unlabeled lipid molecules residing in the molecular shell next to the quencher domain (n + 1) are shown in shaded representation. See the text for other details.

By denoting the radius of the quencher domains by q, the length of the quencher domain perimeter will the be 6q and its area 3q(q + 1) + 1. Since the unit here is a molecule, the area equals the number of molecules in the domain. For the purpose of calculations, the area surrounding the quencher domain is divided into molecular shells. The first shell (n + 1) consists of the molecules in direct contact with the quencher domain (part of these are shown in shaded representation in Fig. 9), the second shell consists of the molecules outside the first shell, etc.

To calculate the quenching probability one needs to determine the fraction of excited molecules that come in contact with the quenching domain, i.e., reach the first shell during their excitation lifetime. In this analysis it is assumed that the molecular movement takes place in distinct jumps between layers and that the time needed for one jump is constant. Then, the fraction of excited (fluorescent) molecules remaining after one jump, [P*], will be

(9)

where τ_R is the residence time, τ_F is the fluorescence lifetime of the excited molecule, and [P*]₀ is the mole fraction of excited molecules before the jump. The probability for a molecule to move from one shell to another is directly proportional to the length of the border between those shells and thus the quenching probability of a molecule in the second shell (Q₂₁) is

(10)

The first term describes the probability that the molecule jumps directly to the first shell, the second term accounts for molecules that stay in the second shell but will enter the first shell later on (with the probability Q₂₁), whereas the third term accounts for molecules that first jump to the third shell but (with probability Q₃₁) enter the first shell later. Likewise, the quenching probability of a molecule located in the third shell (Q₃₁) is

(11)

where Q₃₂ is the probability that such a molecule enters the second shell, and Q₂₁ is as defined above. Finally, it can be shown that the total number of quenched molecules (M_N,1) in the shells 1–N is given by the following equation,

(12)

where

Equation 4 can thus be expressed briefly as

(13)

where k_dom, the domain quenching constant, is a function of the quencher domain size (q), the fluorescence lifetime (τ_F), and the residence time (τ_R) of the probe. When the quencher domains are small, one also has to take their diffusion into account; i.e., a reduced residence time needs to be used,

(14)

The effective diffusion coefficient (1/τ_R,eff) is thus equal to the sum of the diffusion coefficients of the fluorophore and the quencher domains, as in the case of molecular quenchers (cf. Lacowicz, 1983). The fluorescence intensity is proportional to the total number of excited molecules according to

(15)

where the first term gives the number of excited molecules in the area a_N surrounding a quencher domain and the second term indicates the number of excited molecules that will be actually quenched. In the absence of the quencher , the relative fluorescence F_R measured in the presence of the quencher lipid is

(16)

where x_Q is the quencher mole fraction and a_Q is the area of the quencher domain expressed as the number of molecules. Notably, the standard Stern-Volmer equation relating the relative fluorescence intensity to the quencher concentration is (Lacowicz, 1983)

(17)

The approximation is valid at low quencher concentrations. By comparing Eqs. 7 and 8 one can note that

(18)

if the quencher domains consist of single quencher molecules, k_dom = k_mon, a_Q = 1, and k_Q = k_mon. Thus, we have established the relationship between the quenching rate constant and the size of the quencher domain. Although this result was derived for low quencher concentrations, the quenching constant can be assumed to be (nearly) constant over the whole concentration range.