Article |
Address correspondence to Dr. Thomas Haller, Department of Physiology, University of Innsbruck, Fritz-Pregl-Str. 3, A-6020 Innsbruck, Austria. Tel.: 0043-512-507-3770. Fax: 0043-512-507-2853. E-mail: thomas.haller{at}uibk.ac.at
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Abstract |
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Key Words: alveolus; exocytosis; lamellar bodies; lung; surfactant secretion
* Abbreviations used in this paper: FM 1-43, N-(3-triethylammoniumpropyl)-4-(4-[dibutylamino]styryl) pyridinium dibromide; [Ca2+]i, intracellular Ca2+ concentration; LB, lamellar body; LSM, laser scanning microscopy; SEM, scanning electron microscopy; TEM, transmission electron microscopy.
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Introduction |
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Less attention is drawn to exocytosis in epithelial cells than to excitable cells, although the basic mechanisms (involving Ca2+ and PKC) turn out to be very similar (Frick et al., 2001). The alveolar type II cell has its predominant role in synthesizing pulmonary surfactant, which is essential to maintain normal lung function (Clements, 1997). The release from the cells proceeds by exocytosis of large vesicles containing surfactant in characteristic arrangements, the lamellar bodies (LBs) (Fig. 2 A illustrates the distinction we made between vesicles and LBs). Consequently, fusion of vesicles with the plasma membrane and formation of exocytotic fusion pores are the key steps linking cellular synthesis of surfactant to its delivery into the alveolar space. The initial opening of fusion pores can be visualized by entry of extracellular N-(3-triethylammoniumpropyl)-4-(4-[dibutylamino]styryl) pyridinium dibromide (FM 1-43), an amphiphilic fluorescent dye (Betz et al., 1996), into the lumen of fused vesicles. Intercalation of this dye into LBs leads to localized fluorescence (Haller et al., 1998), its onset coinciding with step capacitance changes (Mair et al., 1999). Importantly, fluorescence-labeled LBs remain closely attached to the cellular surface. Occasionally, stained protrusions are clearly discernible, which we interpreted as LBs undergoing release (Dietl and Haller, 2000). Both observations suggested that LBs reside within a fused vesicle for a certain period of time, and prompted us to investigate whether fusion pore geometry is rate limiting for their release. This seems quite reasonable in that LBs are hydrophobic and not subject to the rapid dispersal characteristics of the more soluble vesicle constituents found in other cells.
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Results |
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The rate of IFM 1-43 recovery in released LBs and the time needed to reach completion varied considerably (Fig. 2 Ca). The mean correlation coefficient of curve fits, applying Eq. A3 to 51 of these recovery experiments, was 0.967 ± 0.006, and the mean diameter of these LBs was 1.45 + 0.07 µm (0.68 < d < 3.24). These data strongly suggest that released LBs behave like a homogeneous sphere with respect to FM 1-43 uptake; therefore, DLB could be calculated from these experiments to be 9.37 ± 1.04 x 1011cm2/s. This value seems to be low, but may be due to the complicated arrangement of the highly packed lipids in LBs. However, even this small value allows FM 1-43 to pass the distance of a membrane (10 nm) in 1 s, and fits quite well with the observations that a typical FRAP lasts
1 min for an LB of 1 µm in diameter.
The determination of DLB enables to describe FM 1-43 uptake into fused LBs, and therefore to calculate the fusion pore area by Eq. A4 (see Appendix). The validity of this extended model was checked again by fitting experimental data of the FM 1-43 uptake into fused LBs revealing r values 0.99. In addition, by measuring corresponding LB diameter from LSM images, the pore area of fused LBs have been calculated. Finally, as shown in Fig. 2 E, this model also applies to the complex situation of a compound exocytosis (see Discussion).
Initial states of fusion pores
Fluorescence of initially fused LBs developed in four distinct phases, as illustrated in Fig. 3. The IFM 1-43 increase could be very fast (small LB with 1.2 µm ), resulting in a rapid exponential rise to a maximum (Fig. 3 a;
= 48 s; fit of the experimental result by Eq. A4 reveals a relatively large pore area of 1.09 µm2, r = 0.996). In contrast, a large LB (Fig. 3 b;
= 2.7 µm) showed a much slower increase. The fit of these data by the model with r = 0.995 predicts a pore area of only 0.34 µm2. Occasionally, a faster rise in IFM 1-43 was preceded by a "foot" (Neher, 1993; Betz and Angleson, 1998; Travis and Wightman, 1998), lasting up to several min (Fig. 3 c). This biphasic pattern was not observed with released LBs, indicating that it reflects transitions between different states of dye accessibility into fused LBs pointing to the expansion of a formerly smaller pore. The model predicts a small pore area of 0.15 µm2 for the preceding foot, followed by a small expansion of the pore up to 0.18 µm2 (LB
= 1.3 µm, r = 0.998). In contrast to the observation of pore expansion, other experiments demonstrated dramatic spontaneous pore size reductions (Fig. 3 d; LB
= 1.7 µm). This LB has probably already been released to a great extent (predicted pore area = 4.52 µm2, r = 0.983), but for unknown reasons was retracted and the pore area has been restricted down to 0.34 µm2 (r = 0.98).
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Late states of fusion pores
An example of a type II cell after stimulation is shown in Fig. 1 A. As demonstrated, FM 1-43stained LBs remain located at the site of vesicle fusion, suggesting that fusion pore restriction impedes their release into the extracellular space. In analogy to IFM 1-43 measurements of initial fusion pores as described above, and after careful validation of the feasibility of FRAP measurements (Fig. 2, BD), we sought to restore destained conditions of fused LBs for repeated IFM 143 recovery measurements. The LSM images in Fig. 4 A show part of an ATP-stimulated cell exhibiting four fused LBs. Scanning the same region with the unattenuated laser led to a disappearance of IFM 143, followed by recoveries of different rates that were quite stable during several repeats (Fig. 4, B and C). However, fluorescence of some LBs (LB no. 3 in Fig. 4 A and data in Fig. 4 D) developed progressively from a slow initial into a fast recovery in subsequent measurements. The model (Eq. A4) describes best (r > 0.995) the characteristics of this particular LB (1.8 µm ) by the supposition of a variable pore area in the observation interval of 34 min. At the beginning of the first FRAP measurement (10 min after initial fusion), the pore area is calculated to be 0.07 µm2, raising linearly to 0.48 µm2 after 200 s. 10 min later, when starting an additional FRAP experiment, the pore area was enlarged to 0.58 µm2 followed by a further expansion (arrow) up to 2.24 µm2 during the next 3 min. After beginning the last experiment in this series (30 min), full expansion of the pore (3.14 µm2) occurred. Such very large areas during late stages of secretion most likely reflect LBs during the process of release, which is accompanied by large scale surface expansions as seen by transmission electron microscopy (TEM) (see Fig. 8 C). Under these conditions (dramatic change in LB morphology), model calculations will inevitably lead to a pore area overestimation.
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Ca2+: a key regulator of fusion pore dynamics
Ionomycin leads to cytoplasmic Ca2+ transients and stimulates exocytosis (Sano et al., 1987; Pian et al., 1988). Furthermore, perfusion with ionomycin caused the steady-state IFM 1-43 of fused LBs to shift to higher levels (Fig. 5 B, lower graph), indicating fusion pore dilation. The effect of ionomycin-induced increase in [Ca2+]i on fusion pores was further analyzed by FRAP (Fig. 6). The frequency distribution of time constants of constitutive fusion events (i.e., without exogenous stimulation = control) was assessed. In comparison to released LBs (Fig. 6 C, right), this distribution indicates limitation of FM 1-43 access into fused LBs due to the restricted area of the fusion pore. Treatment of the cells with ionomycin significantly increased IFM 1-43 recovery rates (Fig. 6, AC). This effect was not observed in the cell-free situation (Fig. 2 Cb), excluding that ionomycin per se affects the partition characteristics of FM 1-43 with LBs. Applying Eq. A4 on the results of Fig. 6 A, a fusion pore area of 1.17 µm2 was calculated for this particular LB (1.66 µm , r = 0.999) shifting to the pore area of 2.43 µm2 after treatment with ionomycin (r = 0.998). In the summary of the experiments (Fig. 6 B), the model predicts a fusion pore area dilation by ionomycin from 0.55 to 1.41 µm2 (mean
of fused LBs was 1.62 µm). Therefore, the mean time constant decreased from 231 ± 31 s to 95 ± 10 s. Additional theoretical opening of the fusion pore area up to the entire surface of the LB causing unlimited access of FM 1-43 to the LB (representing the configuration of released LBs) predicts a time constant of 17 s, which is in the range of the experimentally determined
(29 ± 3 s) of released LBs (Fig. 6 B).
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Discussion |
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In line with this assumption, fusion pore formation significantly precedes surfactant release. The time course of lipid accumulation in cell supernatants is usually gradual and in the range of hours following application of secretagogues like ATP (Gilfillan and Rooney, 1987; Griese et al., 1993). In contrast, vesicle fusion as determined by the FM 1-43 and capacitance techniques (Haller et al., 1998; Mair et al., 1999) starts within seconds and terminates after several minutes. Because these methods record the time of fusion pore formation with a minimum delay (<<1 s), we proposed that the release process has to be considerably slower than the fusion events with the plasma membrane (Haller et al., 1998). Consistently, we found that most exocytosed LBs remain closely attached to the cellular surface at the site of fusion (Fig. 1 A). Stirring, perfusion, or other forms of mechanical perturbation led to removal of only a portion, if at all, of stained LBs, suggesting that the remainder is retained by a structural component, presumably the fusion pore. This is supported by LSM, demonstrating floating, tubular protrusion of stained material out of fused vesicles (Fig. 7 C), resembling LB material caught in the process of release by our EM studies (Fig. 8). All of these findings are consistent with the idea that a narrow pore slows down or even prevents LB release. In fact, the LSM images are intriguing because LBs seem to be virtually squeezed through these pores, consistent with published data using TEM (Williams, 1977; Mason et al., 1985; Rooney et al., 1994). Accordingly, fusion pores in type II cells are probably rather stable structures that do not readily collapse into the plasma membrane as is generally assumed for fast secretory cells (Betz and Angleson, 1998).
Fusion pore modeling
EM studies suggest a morphological situation of fused LBs as depicted in Fig. 2 A, showing a negligibly small space between LB and the surrounding vesicular membrane, and direct access of FM 1-43 into fused LBs via pores of the plasma membrane. From Fick's law we derived a solution (Eqs. 3 and 4) by which experimental results of FM 1-43 uptake into released and fused LBs could be well described (r > 0.96). Determination of DLB in released LBs, and measurements of LB diameters, enabled us to calculate pore areas by application of this diffusion model for each experiment. Although we cannot test the validity of our model with simultaneous patch clamp experiments (i.e., the prerequisite of a freely conducting granule content is probably not given; Monck and Fernandez, 1992), the extraordinarily high correlation (r > 0.99) between measured dye uptake rates into fused LBs and model calculations (Eq. A4) strongly supports the validity of our model. Additional confirmation raised from an experiment demonstrating FRAP on a compound exocytosis (Mair et al., 1999) as shown in Fig. 2 E. The fused LB 1 ( 1.48 µm) has access to extracellular dye by a pore area of 0.5 µm2 (r = 0.99), whereas the following LBs (LB 2,
1.6 µm; LB 3,
1.8 µm; LB 4,
1.66 µm) are coupled to the first one in a linear row. Extending the diffusion model to such a linear coupled system, where the access to FM 1-43 is dependent on the outer adjacent LBs, the experimental data can be fit best by introducing particular contact areas between adjacent LBs. Furthermore, these calculated areas (2 µm2 between LB 1 and 2; 3.1 µm2 between LB 2 and 3; 1.5 µm2 between LB 3 and 4) fairly agree with estimations derived from the LSM pictures, thereby providing a direct reference of calculated pore areas by the model. Finally, TEM of compound exocytosis (Fig. 8 C) indeed demonstrate that these contact areas are in the range of the respective LB sizes. The extended model should also be able to predict dye uptake rates into all four LBs after ionomycin-induced pore dilation of LB 1. As demonstrated in Fig. 2 Eb, this is indeed the case, and for LB, a pore area enlargement to 0.85 µm2 could be calculated (r = 0.995). Taken together, the fairly good description of all experimental results indicates a correct estimation of fusion pore areas by our model.
Fusion pore dynamics
In many cells, fusion pores undergo transitions from initially small to expanded states (Monck and Fernandez, 1992). Owing to the potentially high physiological importance of fusion pore dynamics, this issue is intensively discussed (Rahamimoff and Fernandez, 1997). However, major emphasis has been put on secretion of small, highly diffusive solutes in various specialized cell types, making a generalization on exocytotic processes, in particular with regard to release of macromolecular compounds difficult. Fusion pores in expanded states, often referred to as -shaped profiles, have been shown for example in pancreatic acinar cells to persist for up to 8 min (Nemoto et al., 2001). Similar persisting structures have been described in neuroendocrine cells, probably retaining the FM 1-43stained contents of dense core vesicles for considerable time after fusion (Cochilla et al., 2000). In the present study, we show that fusion pores in alveolar type II cells are stable for even longer periods, which might allow mechanistic insights of pore growth to be gained more readily than for other cells. Furthermore, the study of pore dynamics by FM 1-43 may be applied for a variety of other cell types containing some amount of lipophilic materials, in a way similar to the studies on compound exocytosis performed in lactotrophs (Cochilla et al., 2000).
In addition to the arguments above, the concept of slowly developing pores in alveolar type II cells is supported by the fact that a swift expansion of fusion pores would certainly tend to lead to a homogeneous pore size distribution. However, this was neither observed in our SEM and TEM studies, nor by reevaluating the available literature (Williams, 1977; Hollingsworth and Gilfillan, 1984; Mason et al., 1985; Risco et al., 1994; Rooney et al., 1994; Dobbs et al., 1997). Also, the probability of detecting fusion pores would be considerably lower if fusion pore expansion and vesicle collapse into the plasma membrane are instantaneous events. Instead, fusion pores of different sizes could be observed by SEM even 1 h after stimulation. These findings are in favor of slowly, though discontinuously expanding pores, arrested at various stages of the expansion process, and entirely consistent with the repeated and continuous photobleaching measurements reported in this study. In particular, the continuous photobleaching assay revealed spontaneous shifts in the steady-state IFM 1-43 of single fused LBs (Fig. 5 B). Perhaps these results are the most convincing evidence for late fusion pore expansion, as all potential sources of artifacts are minimized in these protocols.
The Ca2+ dependence of fusion pore expansion is supported by several observations. (A) The flash photolysis experiments using caged Ca2+ revealed a significant Ca2+ dependence of the time constants of fluorescence staining during initial fusion pore formations (Fig. 1 D), pointing to an accelerated pore expansion under conditions of high [Ca2+]i. (B) Perfusion with ionomycin increased the frequency of IFM 143 shifts during continuous photobleaching measurements (Fig. 5 B). As these changes occurred closely after ionomycin treatment, they are not likely caused by spontaneous fusion pore expansions, which occurred rarely. (C) Ionomycin enhanced the recovery rates of single fused LBs (Fig. 6). Although highly significant, this was not uniformly seen in all experiments (i.e., some LBs showed no response). However, the ionomycin effect was most pronounced at high values ( > 6 min; Fig. 6 C), which is in agreement with the finding that the ionomycin effect seemed to be inversely related to the level of steady-state IFM 1-43 during continuous photobleaching measurements (Fig. 5 B). This suggests that small fusion pores are more susceptible to changes in [Ca2+]i than those in an already expanded state. (D) ATP is a potent physiological agonist of surfactant secretion (Warburton et al., 1989), and that its stimulatory effect is mediated primarily by an increase of [Ca2+]i although additional mechanisms are indicated (Rooney, 1998). By SEM, we found that ATP treatment significantly increased the number of expanded pores compared with unstimulated cells, corroborating the above results of Ca2+-induced fusion pore expansion (Fig. 8). To investigate how these expansion processes are related to the Ca2+ signals we applied combined FM 1-43 and fura-2 image analysis of ATP-stimulated cells. Previous investigations already disclosed that the number of fusion events is proportional to the [Ca2+]i integral over time (Frick et al., 2001). In addition, we found that fusion of many vesicles coincides with [Ca2+]i spikes during the late phase of Ca2+ entry into the cells, occurring as spike-like or oscillatory elevations, lasting for several min. Here we report that cells with marked oscillatory Ca2+ patterns showed many floating LB protrusions at the end of the measurements, most likely as a direct consequence of Ca2+-induced fusion pore expansion (Fig. 7). However, our experiments revealed that these protrusions develop only slowly (>> min). It is therefore impossible to definitely relate each event with a Ca2+ spike. For that reason, the quantitative assessment of these processes is problematic. Thus, the correlation between Ca2+ oscillations and LB protrusions remains an observation, although a consistent one, and further investigations are required to definitely relate the dynamics of fusion pore expansion to LB release.
Mechanisms by which Ca2+ regulates fusion pores
LB-releasing vesicles are often surrounded by actin-like material (Kapanci et al., 1979; Tsilibary and Williams, 1983; Manabe and Ikeda, 1986). Presumably, it is this scaffold of cytoskeletal elements that stabilizes fusion pores as purse stringlike invaginations (Becker and Hart, 1999), prompting speculation that fusion pores might be controlled by molecular motors and other cytoskeletal elements. Here, the effects of Ca2+ on fusion pores might be severalfold. By activating F-actinsevering proteins, Ca2+ could promote transformation of the cortical actin in its gel state. This "smoothing" effect could allow fusion pores to expand, presumably in response to forces exerted by other cytoskeletal components, by intravesicular factors (i.e., hydration and swelling of LB), or by forces of extracellular origin (i.e., membrane stretch). Despite other possible explanations, this model is plausible and would fit many published observations, implicating cytoskeletal components in the regulation of surfactant secretion (Tsilibary and Williams, 1983; Rice et al., 1984; Rose et al., 1999). This assumption is further strengthened in parallel studies applying optical tweezers to measure forces on cellular structures, in which we demonstrate the fusion pore being a Ca2+-dependent mechanical barrier for release (Singer, W., S. Bernet, M. Pitsch-Marte, M. Frick, T. Haller, and P. Dietl. 2001. Biophys. Soc. 80:140a.). In particular, our model emphasizes a dual role of the cytoskeleton/Ca2+ interactions with respect to exocytosis: Ca2+ facilitates vesicle movements by abrogating cytoskeletal "barriers," and promotes fusion pore expansion. Both effects would assist in increased secretion, although by completely different mechanisms. Furthermore, it is widely accepted that mechanical factors acting on the alveolar epithelium during ventilation are major determinants of surfactant secretion in vivo (Wirtz and Dobbs, 1990; Liu et al., 1999; Ashino et al., 2000). In addition to initiating vesicle fusions, such mechanical factors could assist in widening fusion pore diameters, facilitating release of LBs into the alveolar space. Alternatively, alveolar distension could modify LB morphology by affecting fusion pore geometry, as originally proposed by Kliewer et al. (1985), explaining why the mode of mechanical ventilation would affect surfactant forms in vivo (Savov et al., 1999). That the well-established enhancement of surfactant turnover by high tidal volumes (Wirtz and Schmidt, 1992) is also mediated in part by fusion pore expansion, is a likely scenario and its elucidation a challenging issue in future lung physiology research.
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Materials and methods |
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Measurement of exocytosis
The method is described in previous studies (Haller et al., 1998; Mair et al., 1999). In brief, FM 1-43 is a fluorescent styryl dye intercalating at, but not penetrating, lipid/water interfaces due to its amphiphilic nature. The quantum efficiency of FM 1-43 is low in water but considerably enhanced by insertion into lipids. Because LBs predominantly consist of phospholipids, entry of this dye through fusion pores leads to bright, localized fluorescence intensity of FM 1-43 (IFM 1-43) at 480 nm excitation, exceeding the faint signal originating from the plasma membrane (Fig. 1 A). FM 1-43 was permanently present in the extracellular solution at a concentration of 1 µM.
Microscopy and image analysis
Coverslips with adherent cells were mounted into a perfusion chamber placed on the stage of an inverted microscope (Zeiss 100), equipped for polychromatic illumination and image analysis (TILL Photonics). [Ca2+]i is expressed as background-corrected fura-2 fluorescence ratio (350:380 nm excitation), measured from cells preincubated in DME with 1 µM fura-2 AM at 37°C for 15 min. IFM 1-43 was measured simultaneously to fura-2 at 480 nm excitation and >530 nm emission. Flash photolosis was performed on cells loaded with caged Ca2+ (NP-EGTA AM, 10 µM, 30 min in culture conditions) by a pulsed xenon arc lamp as described (Haller et al., 1999).
Confocal FRAP and continuous photobleaching measurements
These experiments were performed on a Zeiss Laser Scan Microscope (LSM 410 invert). FM 1-43 was excited at the 488-nm wavelength of the argon laser passing a Plan-Apochromat 100x/1.4 NA oil objective, and emitted light was directed through a 515-nm long pass filter. The nominal output power of the laser (60 mW) could be attenuated by neutral density filters in the light path. Each FRAP measurement was started by scanning a square of usually 8 x 8 µm in the specimen plane 20 times with the unattenuated laser (100% transmission) at a rate of one full frame/0.4 s in the nonconfocal mode. The high number of consecutive repeats was necessary for bleaching due to the high photostability of FM 1-43. Typically, a 20x scan yielded a bleach to <1% of original IFM 1-43. Subsequently (after 6 s; this time was required due to instrument handling), images were captured at regular intervals at a reduced intensity (0.32% transmission) to minimize bleaching during data acquisition. From these images, IFM 1-43 values were obtained by calculating mean pixel intensities within defined areas of vesicular fluorescence.
Continuous photobleaching was performed at 32% laser transmission. This value was selected because it caused partial bleaching of FM 1-43 stained LBs (Results). Partial bleaching can be considered as the result of an equilibrium between bleaching and restaining of LBs by FM 1-43. To avoid out of focus movements of LBs during measurement, stacks of eight horizontal scans in the confocal mode (8 x 8 µm each, one full frame/0.4 s, 1 µm step size, 8 s/stack, confocal setting = 40) were performed at regular intervals. IFM 1-43 was calculated as the sum of integrated pixel intensities from all scans in each stack, yielding one single data point of the IFM 1-43 tracings shown in Fig. 5. The confocal mode was chosen to enhance image contrast and resolution. This was also necessary to avoid shifts in steady-state IFM 1-43 due to additional fusion events within the observed region. Analysis of the point spread function using fluorescent beads revealed that this type of analysis yields sufficiently stable signals, even when LBs completely move through the focal planes. To exclude dye depletion within the scanned fluid volume and mechanical perturbations of the cells caused by pipetting, all measurements were performed under constant slow perfusion (0.8 µl/s) of the experimental chamber using a precision peristaltic pump. IFM 1-43 was normalized to 100% (LB intensity at the beginning of each experiment) and 0% (instrumental background).
Fluorescence data were analyzed with DatGraf (Cyclobios), TILLvisION, Adobe Photoshop and Excel (Microsoft). The time constant was uniformly calculated within the first 2 min following the onsets of IFM 1-43 increase. Statistics were performed by unpaired t tests, and data are reported as arithmetic mean ± SEM (unless otherwise indicated).
EM
For SEM, the cells were fixed with 2.5% glutardialdehyde in 0.15 M cacodylate buffer (pH 7.3). A brief washing in the same buffer was followed by 1 h of postfixation with 1% aqueous OsO4, gradual dehydration with ethanol, and critical point drying (Bal-Tec CPD 030; Balzers). Specimens were mounted with colloidal silver on aluminum stubs, sputtered with 10 nm Au/Pd (Balzers), and examined with a Zeiss scanning electron microscope (Gemini 982). Data analysis (Fig. 8 D) was performed by a technician unaware of the experimental protocol ("blind analysis"). Furthermore, selection of the microscopic areas for that analysis was done at random.
For TEM, the cells were rinsed with fresh culture medium, slam-frozen and freeze-substituted with acetone containing 1% OsO4 and 0.5% uranyl acetate as described (Hess and Siljander, 2001). For further fixation and contrast enhancement the samples were taken out of the substitution media at 65°C and immediately transferred into 2% aqueous OsO4 at room temperature for 1 h (Dalen et al., 1992). Finally the cells were embedded in Epon. 80-nm thin serial sections cut perpendicularly to the plane of the monolayer were viewed at 60 kV with a JEM-1200 EX (Jeol).
Solutions and materials
Bath solution contained, in mM: 140 NaCl, 5 KCl, 1 MgCl2, 2 CaCl2, 5 glucose, and 10 Hepes (pH 7.4). Fura-2 AM, NP-EGTA AM, FM 1-43, SP-DiOC18(3), and calcein AM were purchased from Molecular Probes. All other chemicals were obtained from Sigma-Aldrich. ATP and ionomycin were applied at 10 µM each. All experiments were performed at room temperature.
Calculation of the diffusion constant DLB and the pore area A'
Diffusion processes (characterized, i.e., by the diffusion constant D and the concentration of the diffusible substance c) dependent on time (t) and distance (x) are generally described by Fick's law c/
t = D
2c/
x2. However, analytical solutions of this complex differential equation, can only be achieved by introducing adequate start and boundary conditions, usually after simplification of the physical reality.
For determination of DLB of released LBs, we used an adapted solution of the problem derived previously, and proved for the measurement of many diffusion constants of molecules in variable matrices for technical applications (Muhr and Blanshard, 1982; Fergg, 1999). Leaving the beginning of FRAP experiments (i.e., the first few seconds) out of consideration, we can assume quasistable conditions leading to linearized concentration profiles with time dependent gradients. The material balances for FM 1-43 in both compartments (surrounding buffer and LB) are then given as:
(A1a)cVe/
t = 1/Ve [AD (cVe cLB)/r]
and
(A1b)cLB/
t = 1/VLB [AD (cVe cLB)/r]
where cVe represents the concentration of FM 1-43 in the extracellular volume Ve; cLB the concentration of FM 1-43 in an LB of the volume VLB; and A and r the surface and the radius of the LB, respectively. Having a closed system as used in our experimental design, these Eqs. are coupled because of mass conservation (the decrease of the FM 1-43 concentration in the buffer equals the uptake of FM 1-43 into the LB), and therefore we can solve:
(A2)(cVe cLB)/
t = [1/Ve +1/VLB ][AD (cVe cLB)/r]
for (cVe cLB) simply by separation of the variables getting:
ln{[cVe (t) cLB (t)]/[cVe (t0) cLB (t0)]} = AD (t t0)/(VLB r).
On the assumption of a spherical and homogeneous LB under the boundary and starting conditions of Ve >> VLB, cVe const = cVe (t), cLB(t=0) = 0, t0 = 0, we have the final solution for released LBs:
(A3)cLB(t) = cVe [1 exp(3DLBt/r2)].
From the fit of the experimental data obtained from FRAP experiments of released LBs, and the respective LB radius, DLB could be calculated from the slope of the trendline of each set of linearized data if the correlation coefficient of the fit was sufficiently high (r > 0.95). Extending the model to a situation where the diffusion area of the LB is not represented by the entire surface but restricted by a smaller area (the pore area A'), the concentration of FM 143 (IFM 143) in fused LBs is given by:
(A4)cLB(t) = cVe {1 exp[(A' DLB t)/(r VLB)]} .
Achieving a sufficient fit of the experimental data by this equation, the pore area A' for a particular LB has been determined.
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Acknowledgments |
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This work was supported by grants from the Austrian National Bank (7413 to T. Haller) and the Austrian Science Foundation (P12974 to P. Dietl; P12337 and P13041 to M. Paulmichl). Parts of this work were presented at the Meeting of the American Society for Cell Biology (Washington, DC, 1999), the FASEB Summer Research Conference (Saxtons River, VT, 2000), and the Meeting of the Society for Experimental Biology (Cambridge, UK, 2000).
Submitted: 20 February 2001
Revised: 13 August 2001
Accepted: 13 September 2001
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