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First published online 11 December 2007
doi: 10.1242/jcs.013383
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Research Article |
1 Cellular Biophysics Group (BIOMS), German Cancer Research Center, Bioquant Center, Im Neuenheimer Feld 267, D-69120 Heidelberg, Germany
2 Biomedical Computer Vision Group, Department of Bioinformatics and Functional Genomics, IPMB, University of Heidelberg, Im Neuenheimer Feld 267, D-69120 Heidelberg, Germany
3 German Cancer Research Center, D-69120 Heidelberg, Germany
* Author for correspondence (e-mail: m.weiss{at}dkfz.de)
Accepted 17 October 2007
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Summary |
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Key words: Biophysical modelling, Domain formation, Membrane traffic, Systems biology
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Introduction |
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), which are highly conserved in organisms from yeasts to human (Mellman and Warren, 2000). The COPII coat consists of the small Ras-like GTPase Sar1p and two larger heterodimeric coat complexes, Sec23p-Sec24p and Sec13p-Sec31p (Bannykh et al., 1996; Barlowe et al., 1994; Kuge et al., 1994), which both stimulate GTP hydrolysis by Sar1p in vitro (Antonny et al., 2001). During the past decade, the COPII proteins have been characterized in detail (Barlowe et al., 1993; Barlowe et al., 1994; Bi et al., 2002; Huang et al., 2001; Lederkremer et al., 2001; Matsuoka et al., 2001; Stagg et al., 2006; Yoshihisa et al., 1993) and their sequential assembly has been elucidated (Antonny et al., 2001; Matsuoka et al., 1998), thereby revealing the cycle of COPII coat (dis)assembly: while being cytosolic in its GDP-bound form, Sar1p associates firmly with ER membranes upon nucleotide exchange at the transmembrane factor Sec12p (Barlowe and Schekman, 1993). Subsequently, Sar1p recruits Sec23p-Sec24p and Sec13p-Sec31p to yield a mature COPII complex whose components dissociate sequentially from the ER membrane after GTP hydrolysis by Sar1p (Forster et al., 2006). In fact, a full COPII complex is an intrinsically unstable entity owing to the hydrolysis-stimulating action of Sec23p-Sec24p and Sec13p-Sec31p (Antonny et al., 2001). In addition, the Sec23p-Sec24p heterodimer has been implicated in cargo selection (Aridor and Traub, 2002; Miller et al., 2003), whereas the membrane bending during vesicle budding and pinch-off is most likely mediated by Sar1p (Lee et al., 2005) and the Sec13p-Sec31p complex (Stagg et al., 2006). In virtually all mammalian cells, the described turnover of COPII proteins and the formation of vesicles appears to be restricted to a small portion of the ER, the so-called ER exit sites (ERES). Typical mammalian cells display a few hundred ERES (Hammond and Glick, 2000), each of which has a diameter of several hundred nanometres. The kinetics of turnover of COPII proteins at individual ERES have been shown to be on the scale of a few seconds (Forster et al., 2006; Sato and Nakano, 2005), in good agreement with previous in vitro data (Antonny et al., 2001).
While the kinetic aspects of COPII binding have received considerable attention, much less is known regarding how ERES self-assemble and which dynamic events underlie their self-organization. This point acquires additional importance when bearing in mind that ERES are functionally disassembled during mitosis and are re-established after cytokinesis (Dudognon et al., 2004; Farmaki et al., 1999; Hammond and Glick, 2000). Furthermore, differentiated cells can show alternative ERES phenotypes despite the conservation of essential COPII components (Lu et al., 2001). Also, the yeast Saccharomyces cerevisiae does not show visible ERES at the level of light microscopy, whereas Pichia pastoris shows large ERES with rather intriguing dynamics (Bevis et al., 2002; Rossanese et al., 1999): ERES have been shown to be mobile in the ER and are able to fuse upon contact; also they were shown to form de novo and to have a distinct size (Bevis et al., 2002). Given the remarkable dynamics and the various phenotypes in eukaryotic cells, it becomes apparent that the mere conservation of COPII components is insufficient to explain the formation of (visible) ERES. Rather, the spatiotemporal dynamics of the COPII machinery is likely to be the crucial ingredient.
Here, we have formulated and tested the first computational model to investigate the generic mechanisms that drive formation of ERES. Based on a few experimentally well-supported assumptions, the model is not only capable of reproducing the patterns of ERES in the physiological parameter range, but we were also able to derive experimentally testable predictions. In particular, the model predicts that ERES show a lattice-like arrangement in undifferentiated cells, while their sizes and mobilities are strongly dependent on the cargo-modulated kinetics of COPII turnover. These predictions are in favorable agreement with our experimental observations on GFP-tagged COPII proteins in Chinese hamster ovary (CHO) cells by means of fluorescence microscopy. Based on the model and our experimental observations, we suggest that cooperative binding of COPII proteins (mediated, for example, by an additional regulatory protein) is a necessary condition for the robust self-assembly of ERES, whereas a lack of cooperativity might explain the apparent loss of visible ERES in organisms such as S. cerevisiae. By contrast, the change of the ERES phenotype during mitosis is most likely a consequence of an alteration in the kinetics of COPII turnover, which is predicted to be an efficient means to change the size of ERES. Moreover, we show that increasing the average size of ERES is an advantageous strategy when trying to enhance the anterograde secretory flux, whereas increasing the number of (small) ERES has little effect.
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Results |
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), we also considered the fusion events to be a non-reversible phenomenon. To gain a high computational efficiency, we considered for simplicity only a single-particle species that might represent, for example, a full COPII complex, rather than modeling the individual COPII proteins and their sequential binding or dissociation (Antonny et al., 2001; Forster et al., 2006).
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; Connerly et al., 2005; Watson et al., 2006) might mediate this biased binding.
To equip the simulations with physiologically reasonable parameters, we have chosen Kon and Koff in accordance with the reported binding kinetics of Sec23p-Sec24p in vivo (Forster et al., 2006) and imposed physiologically reasonable diffusion parameters (see Materials and Methods). Unless stated otherwise, we have chosen Pfuse=1 for simplicity. We also estimated the density of COPII complexes in a single ERES (diameter, 400 nm) from the size of a COPII vesicle (diameter, 60 nm, area
0.01 µm2) and the need for 48 COPII complexes per COPII vesicle (Stagg et al., 2006) to be 
=4250/µm2 – that is, a COPII complex has a radius of 
10 nm. Assuming that ERES and COPII vesicles have the same density of COPII proteins, a single ERES hosts 600 COPII complexes (=12 COPII vesicles). Given that a cell (diameter= 30 µm, ER area1000 µm2) contains 200 ERES (Hammond and Glick, 2000) (M.W. et al., unpublished) and estimating the ratio between ERES-bound and cytoplasmic pool to be roughly equal (Forster et al., 2006), a total pool of 300 COPII complexes (=particles) per square micron of simulated ER membrane was used for the simulations.
The steady state of the simulations: ERES-like clusters keep their distance
The basic read-out of the simulations was the steady-state time-course of the sizes and positions of membrane-bound ERES-like clusters. Each cluster was made up of n monomers with 1
nnmax, where nmax denoted the size of the largest cluster. We have monitored the cluster positions and sizes in intervals of 4 seconds over a period of 30 minutes (after an initial equilibration period of 3 minutes, at which a dynamic steady state had emerged). Note that, for each time point, the value of nmax can vary, whereas the total number of considered particles (membrane and cytoplasmic pool) was fixed throughout the simulation. To allow for a comparison with experimental data (fluorescence images), we have converted the numerical data into microscopy-like images by blurring the position of each particle with a theoretical Gaussian point-spread function (width 250 nm). Similar to fluorescence microscopy images, this approach highlighted the largest ERES-like clusters, with sizes n=nmax,..., nmax/10. Smaller clusters such as monomers, dimers etcetera only gave rise to a dim background.
Running the simulations with physiological parameters (see Materials and Methods), we obtained a dynamic steady-state pattern that was strikingly similar to the punctate ERES pattern observed in living cells (Fig. 2a). To quantify the spatial arrangement of the visible clusters, we utilized the distribution p(s) of (normalized) nearest-neighbor distances s, which has been a valuable tool to characterize, for example, neighborhood relations of energy levels in complex quantum spectra (Haake, 2001). To be compatible with the processing of fluorescence images, we only included visible clusters with sizes n>nmax/10 (or n>48, the size of a single COPII vesicle, when nmax/10<48; see Materials and Methods for details). If the ERES-like clusters were arranged in a perfect crystalline state, p(s) should show only a single peak at s=1 – that is, p(s)=
(s–1), with (x) being Dirac's delta distribution. If they were distributed randomly over the membrane without `knowing' the position of each other, a time-space Poisson process would adequately describe the pattern (cf. Eqn 1, Materials and Methods; shown dashed in Fig. 2b). In contrast to this naïve expectation of randomly and independently distributed clusters, the statistic p(s) showed a strong suppression of small and large distances (Fig. 2b) while concentrating around the mean <s>=1, with only small fluctuations. A very good heuristic fit to the data was given by Eqn 2 (Materials and Methods) that had been derived from random matrix theory in another context (Haake, 2001). In other words, the ERES-like clusters `know' about the position of their neighbors and the suppression of small and large distances is indicative of a crystalline-like arrangement of the clusters. We would like to stress that the spatial arrangement was not sensitive to the detailed parameters of the simulations but appeared as a robust feature of the model – that is, we reproduced the very same statistic p(s) for a wide range of binding kinetics (Kon, Koff), using free or biased binding. In particular, reducing the probability for fusion from Pfuse=1 to Pfuse=10–3 did not alter the spatial arrangement (data not shown).
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ERES-like clusters interact through depletion zones
As the ERES-like clusters seemed to prefer to maintain their separations, we asked which interactions were responsible for the observed pattern. Clearly, long-range (repelling) forces, for example through microtubules, could be excluded as they were not part of the simulation. We therefore hypothesized that the effect solely emerges owing to a competition for particles – that is, larger clusters recruit smaller clusters and monomeric particles from their vicinity, therefore creating a `depletion zone' around themselves that suppresses the emergence of another cluster in their vicinity. To test our hypothesis with a stochastic approach, we considered a circular `cell' of 15 µm radius and sequentially picked 200 ERES locations at random. Each ERES was assumed to have a hard-core radius of 200 nm, and ERES were not allowed to overlap. Without any further constraints, this stochastic approach yielded an excellent agreement of p(s) with Eqn 1 as the ERES did not `feel' each other (Fig. 3a). Only very small distances s were suppressed owing to the imposed hard-core exclusion. When we considered a Gaussian depletion zone around each ERES – that is, when we suppressed picking a new ERES location near to a pre-existing ERES with a Gaussian filter (see Materials and Methods), strong deviations from Eqn 1 became visible and the data were again well described by Eqn 2 (Fig. 3b). Thus, the concept of competition for limiting particles – that is, the formation of a depletion zone around an ERES-like cluster – yields an excellent agreement with the results of the model simulations. Using a cell-wide patterning, for example, fewer ERES in the center of the cell owing to the nucleus or even an annular accumulation of ERES around the cell center (supplementary material Fig. S1) did not alter this result (data not shown). In vivo, the envisaged competition might not be (solely) focused on COPII complexes, but also certain lipids or (regulatory) proteins might participate.
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Koff. This effect is anticipated as accelerating the turnover decreases the residence time of a particle on the membrane, the membrane-bound particles having less time to search for binding partners through diffusion. In other words, before acquiring enough mass, a cluster already disperses by losing particles to the cytoplasmic pool. As a consequence of the decreasing size of ERES-like clusters, an increased average diffusive mobility of ERES is predicted for an accelerated turnover.
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In fact, an accelerated turnover of Sec23p-Sec24p has been observed as a consequence of the reduction of transport-competent cargo, for example by treatment with the protein synthesis inhibitor cycloheximide (Forster et al., 2006). Thus, the increased turnover mimics the effect of cargo depletion. The model therefore predicts a decrease of ERES sizes upon reducing the amount of transport-competent cargo. It is also noteworthy that imposing a biased binding considerably increases the mean cluster size as new particles are preferentially bound to the membrane in the vicinity of pre-existing clusters (compare Fig. 4a versus 4b). The search time for recruiting new material is therefore decreased and, consequently, the average cluster size is larger. Thus, changing the cooperativity of the COPII membrane association provides a sensitive switch that allows for a drastic change of ERES sizes. Depending on the actual turnover kinetics, the size can become even so small that individual clusters do not appear as visible entities any more but only contribute to a blurred fluorescence background. It is tempting to speculate that this effect underlies the phenotypic difference between S. cerevisiae and P. pastoris (see also discussion below).
Reducing the probability for fusion of adjacent clusters (Pfuse) only had a minor effect on the mean cluster size as long as Pfuse>10–2 as the main contribution to cluster growth relies on individual particles (i.e. `clusters' of size n=1) that frequently probe for fusion owing to their high diffusive mobility. Beyond Pfuse=10–2, fusion became more and more unlikely so that individual particles exhausted their residence time on the membrane in unsuccessfully trying to bind to neighboring clusters. Consequently, we observed a decrease of the mean cluster size <n>.
In contrast to the mean size <n>, the probability distribution of normalized cluster sizes [p(a) with a=n/<n>] showed a fairly broad and featureless form in all cases (Fig. 4c). Only the lower cut-off that was imposed by the visibility of the clusters (n=nmax/10 or n=48, respectively) changed owing to the varying average cluster size (cf. Fig. 4a,b). The model therefore predicts a heterogeneous size distribution of an ERES population in vivo.
Exit sites show a quasi-crystalline pattern in vivo
To test the model predictions about the spatial arrangement of ERES, we transfected CHO cells with GFP-tagged Sec23p and determined by (confocal) fluorescence microscopy and image processing the distribution of (normalized) distances, p(s), between nearest neighbors in the ERES population of a cell (see Materials and Methods). For better comparison with the model, we again employed the normalized distance s. The representative average distance (corresponding to s=1) was 950 nm. Owing to the fitting with Gaussian profiles, which is similar in spirit to the nanometre-precise position determination of a latex bead in an optical trap, the image processing was even able to identify closely adjacent spots with a distance of <120 nm (see supplementary material Fig. S2 for a representative picture). As predicted from the model, the experimentally obtained statistic p(s) showed a strong suppression of small and large distances (Fig. 5). This result was the same regardless of whether we considered distances in the three-dimensional cell (using confocal slices) or in the two-dimensional projection (image taken with an open pinhole); it was also independent of the COPII marker used (e.g. using GFP-tagged Sec31p; data not shown). In agreement with the observations in the simulations, the shape of p(s) was robust and did not change significantly when we applied drugs such as cycloheximide (CHX), brefeldin A (BFA) or nocodazole (NOC) that, respectively, stopped protein synthesis, disrupted the Golgi apparatus or broke down microtubules (Fig. 5 and data not shown). Enhancing the amount of transport-competent cargo through overexpression of the temperature-sensitive mutant ts-O45-G of the vesicular stomatitis virus G protein (see Materials and Methods) also did not affect p(s). Hence, the model correctly predicted the spatial arrangement of ERES in living cells.
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Exit sites show a broad and cargo-dependent distribution of sizes in vivo
We next turned to the size of individual ERES. At first glance, the ERES population seemed to have a fairly uniform size when inspecting the fluorescence images of CHO cells expressing Sec23p-GFP. To gain more-quantitative data on this aspect, we acquired stacks of confocal slices for several cells and determined from that the total fluorescence F of individual ERES (see Materials and Methods), which is a measure of the number n of COPII proteins participating in an ERES (n is the basic observable in the simulation). To become independent of detector and laser settings, we extracted the mean fluorescence `size' <F> of the ERES population in every cell by defining a normalized ERES size a=F/<F> and inspected the distribution of normalized ERES sizes, p(a), derived from many cells. In qualitative agreement with the model predictions, the experimental histogram showed a broad distribution irrespective of the particular GFP-tagged COPII protein (Fig. 6). Most of the determined sizes are considerably smaller than the mean, and a non-negligible fraction of large ERES was observed in the `tail' of p(a). In fact, the distribution fitted well to a lognormal distribution (Materials and Methods, Eqn 3), indicating that the arithmetic mean <a>=1 of the population does not yield a good estimate for the size of individual ERES. Rather, the position of the most likely value for a (i.e. the peak of the distribution) yields a good estimate for the typical ERES size.
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). We therefore monitored below the diffusional movement of individual ERES under various treatments.
The model also predicted that slowing down the COPII kinetics beyond the native level would give rise to larger ERES (cf. Fig. 4). We tried to reach this condition by overexpressing ts-O45-G (see Materials and Methods), as the presence of transport-competent cargo modulates the turnover kinetics of Sec23p (Forster et al., 2006). We fixed cells for imaging 10 minutes after shifting to the permissive temperature, after folding had occurred and proper transport had set in (de Silva et al., 1993). Similar to the spatial arrangement (see above), the size distribution p(a) was not significantly altered. This observation presumably indicates that the kinetics of COPII were already strongly modulated by the endogenous amount of cargo such that ts-O45-G did not have a strong effect. However, in line with our model predictions, a recent report by Guo and Linstedt (Guo and Linstedt, 2006) indicated a slight increase in ERES size after drug washout when cells had been treated with BFA and H89, which strongly increases the concentration of Golgi-resident proteins and secretory cargo in the ER.
Exit sites show a rapid, cargo-dependent motion in vivo
Based on time-lapse microscopy, ERES have been reported to display a rapid, short-range motion in P. pastoris (Bevis et al., 2002) and mammalian cells (Stephens et al., 2000). To quantify thoroughly the mode of motion of ERES, we have tracked individual ERES with confocal fluorescence microscopy and deduced from that the average diffusion coefficient of the ERES population (see Materials and Methods). In particular, we determined the squared displacement (SD) of each ERES for two frames of the time series with a time lag 
and fitted the cumulative distribution of all SDs as a function of to deduce the apparent diffusion coefficient D() averaged over the ERES population. As can be seen from Fig. 6c, the average diffusion coefficient initially decreases with time , indicating a subdiffusive process on short time scales [see Weiss and Nilsson for an introduction to anomalous diffusion (Weiss and Nilsson, 2004)]. For larger times , however, D() converges towards a quite low diffusion constant D01.3x10–3 µm2/second in untreated cells. In agreement with previous observations (Stephens et al., 2000), the disruption of microtubules with NOC reduced the diffusion coefficient drastically (D03.2x10–4 µm2/second), which indicates that part but, not all, of the apparent diffusion of ERES in untreated cells originates from microtubule-induced random movements of the entire ER. However, under both conditions, application of CHX did result in an approximately twofold enhanced diffusion (D02.8x10–3 µm2/second and D0=8x10–4 µm2/second, respectively), showing that cargo reduction rendered the ERES more mobile. The increase in the average diffusion coefficient upon treatment with CHX is consistent with the above rationale that cargo depletion leads to an increased fraction of small, and thus more mobile, ERES. Hence, cargo reduction not only reduces the size of ERES but also renders them more mobile, as predicted by the model.
Further predictions of the model
Having confirmed that the proposed model indeed is capable of predicting ERES features that are observed in living cells, we would like to put forward below some more speculative predictions that hopefully will fuel future research on the spatiotemporal organization of ERES.
Given the fact that ERES can be regarded as the origin of the secretory pathway, one might ask which strategy is better for a cell to achieve a maximum secretory flux. Should the cell aim at maximizing the number of (small) ERES or is it more advantageous to grow a smaller number of ERES to larger size? We have approached this question by monitoring the number of ERES (NERES) and the number of vesicles produced during the simulation (after equilibration) for varying turnover kinetics Kon of the COPII machinery (keeping Kon=Koff fixed). From the total number of vesicles produced, we determined the rate of vesicle production Rves. While enhancing the turnover of COPII increased the number of ERES for both free and biased binding, the vesicle production rate decreased concomitantly (Fig. 7). The decrease in Rves is due to the fact that not only the number of ERES increases but, at the same time, their average size decreases considerably (cf. Fig. 4). Thus, ERES become smaller and less stable towards fluctuations – that is, they might be exhausted by the sending of a single vesicle. Also, they are less capable of recruiting new material owing to their smaller circumference, meaning that replenishing the material that has been despatched as a vesicle might take longer than the ERES can survive. From this observation, it seems plausible that growing the size of the ERES is the most advantageous strategy when aiming at a proper secretory flux.
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Another topical problem that can be addressed with the help of the model is the self-assembly of ERES after mitosis. Indeed, the model easily reproduces the self-assembly without any scaffold as the steady state (as shown, for example, in Fig. 1) emerged from an entirely empty membrane as a starting condition (see Materials and Methods). In fact, it is conceivable that formation of ERES is blocked at the start of mitosis by transient posttranslational changes in Sec24p (Dudognon et al., 2004), hence removing all COPII complexes from the ER membrane. This corresponds to Kon=0 in the model and leads to a membrane devoid of any COPII-like complex. Reverting this transient modification leads directly to the self-assembly process described by the model. Thus, altering the turnover kinetics might be key to the disappearance of ERES during mitosis and their subsequent reassembly.
A puzzling observation is the apparent difference of the ERES pattern in the yeasts S. cerevisiae and P. pastoris. While P. pastoris shows distinct ERES at the level of light microscopy, S. cerevisiae only shows a hazy, dotty pattern (Connerly et al., 2005). From the results of our model, we propose, however, that both yeast strains indeed make use of the same self-assembly process (cf. Fig. 1). As altering the turnover kinetics and/or the binding scheme (free versus biased) strongly influences the size of ERES, S. cerevisiae might operate in a regime where only small clusters/ERES are formed that are hard to distinguish against the fluorescent background, whereas P. pastoris might operate in a regime where large and distinct ERES emerge. Owing to the apparent role of Sec16p as an organizer of ERES and the observed differences of the SEC16 gene among species, the phenotypic difference most likely is based on a difference in the binding scheme. In other words, S. cerevisiae might utilize the free binding approach (yielding small ERES), whereas mammals and P. pastoris most likely use Sec16p to establish a biased binding (yielding distinct, large ERES). In agreement with this hypothesis, a knockdown of Sec16p in mammalian cells has been shown to cause disintegration of ERES (Bhattacharyya and Glick, 2006; Watson et al., 2006).
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) for an introduction]. The predictions of the model of a quasi-crystalline arrangement of ERES (reminiscent of molten colloidal crystals) and a cargo-dependent size and mobility were in good agreement with experimental data obtained by fluorescence microscopy. For simplicity, we have assumed in the model that diffusion of COPII complexes in the cytoplasm is fast, meaning that the cytoplasmic pool is well mixed. Given the typical residence time of COPII complexes in the cytoplasm before binding to ER membranes (1/Kon2 seconds) and the diffusion coefficients of soluble proteins [15 µm2/second (Elsner et al., 2003)], this assumption appears reasonable as a COPII complex would explore roughly half of the interior of a cell before binding to the membrane. For simplicity, we also considered a single particle species only, instead of modeling the different components of the COPII coat. Considering a more elaborate binding scheme including all COPII proteins, for example the one reported in Forster et al. (Forster et al., 2006), is possible but will massively slow down the computation and will introduce more (partially unknown) parameters, while it is unlikely that the gross features of the predictions will change.
A basic prediction from the model is that the competition for limiting material leads to the observed spatial arrangement of ERES. While it is likely that ER-bound COPII proteins themselves constitute a limiting pool of material, it is also anticipated that certain lipids and regulatory proteins might be involved. The model further predicts that cooperative (`biased') binding of COPII proteins enlarges ERES and stabilizes them. Such cooperativity might be mediated by cargo proteins and/or Sec16p that has been shown to participate in the organization of ERES in the yeast P. pastoris (Connerly et al., 2005) and in mammalian cells (Bhattacharyya and Glick, 2006; Watson et al., 2006). In fact, Sec16p might serve as a COPII-linked primary docking factor for recruiting further COPII proteins. In agreement with the predictions of our model, a knockdown of Sec16p indeed resulted in disintegration of ERES (Bhattacharyya and Glick, 2006; Watson et al., 2006). Similarly, a loss of Sec16p function in S. cerevisiae that lacks distinct, visible ERES might be responsible for the altered phenotype in comparison with that of P. pastoris. In the light of our findings, it will be interesting to elucidate whether Sec16p indeed acts as a mediator of cooperative binding of COPII to ERES.
One might also ask whether alternatives to the proposed model exist. Given the simplicity of the scheme in Fig. 1 and the crucial role of the COPII proteins for the functioning of ERES, the choice of alternative models appears limited. One could consider, for example, a lipid and/or protein scaffold that is responsible for the observed spatiotemporal ERES features, thus shifting the self-organization of ERES to the problem of scaffold self-assembly. While a (fairly slow) segregation of lipids, that might underlie the scaffold formation, has been observed in artificial membranes (see Baumgart et al., 2003), there is currently no evidence on similar mechanisms in the ER. Moreover, ER membranes are active in the sense that GTPases and ATPases drive the lipid bilayer out of thermal equilibrium, and little is known regarding whether this supports or hampers the formation of lipid domains. Given these caveats, it seems appropriate to use the scheme outlined in Fig. 1 as a working model based on current experimental results.
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) was performed using FuGene 6 (Roche) and the manufacturer's protocol (0.5 µg DNA, 1.5 µl FuGene 6 in a total volume of 50 µl supplement-free MEM). The medium was refreshed 12-24 hours after transfection. For microscopy, cells were grown on glass coverslips in 12-well dishes or on Lab-Tek chambered cover-glass (two-well, thickness #1; Nunc). Cells were either fixed with methanol at –20°C and mounted with Fluoromount-G (SouthernBiotech) 30 hours post transfection or imaged directly using CO2-free imaging medium (MEM without phenol-red, plus 25 mM HEPES), with the appropriate concentration of drugs where applicable.
Transfection with the temperature-sensitive GFP-tagged VSVG mutant ts-O45-G (Runz et al., 2006) and mCherry-tagged Sec23A was performed using the above protocol. Co-transfected cells and controls (transfected only with mCherry-Sec23A) were incubated for 24 hours at the nonpermissive temperature (39.5°C) and were fixed 10 minutes after a temperature shift to the permissive temperature (32°C) for confocal imaging and the subsequent image analysis.
To disrupt microtubules, 20 µM nocodazole (Acros Organics) was added to the medium, cells were put on ice for 10 minutes and then grown for 4-6 hours at 37°C. Disruption of the Golgi apparatus was accomplished by adding 5 µg/ml brefeldin A (Invitrogen) to the medium 1 hour before microscopy. To shut down protein synthesis, cycloheximide (Sigma) was added at a concentration of 100 µg/ml 3 hours before fixation or live imaging.
Confocal imaging was performed with a Leica SP2 confocal microscope using a 63x 1.4 NA oil-immersion objective, an excitation wavelength of 488 nm and a 500-600 nm detection bandpass for GFP and 594 nm excitation with a 600-700 nm bandpass for mCherry. For live imaging, the climate chamber of the microscope was kept at 37°C. Two-dimensional (2D) pictures (512x512 pixels, 12 bit) were obtained with an open pinhole (2.6 Airy units). For three-dimensional (3D) stacks, the pinhole was set to 1 Airy unit, and 50 confocal sections were taken with a spacing of 0.12 µm. For tracking individual ERES, 2D time series with 200 images (652 mseconds/frame, 8 bit) were acquired with a zoom area of 7.44x7.44 µm.
Note that widefield pictures of the transfected CHO cells sometimes showed clusters of ERES in a juxtanuclear position (near to the Golgi apparatus). This apparent accumulation of ERES, however, turned out to be an artifact of there being a larger amount of ER membrane near to the nucleus as confocal slicing of the cells revealed that ERES kept the distance along the z-direction. In other words, the area density of ERES on ER membranes did not vary systematically. Interestingly, this apparent accumulation was somewhat stronger in HeLa cells (data not shown).
Image processing and quantification of spot size
To localize and estimate automatically the size and contrast of spot-like subcellular structures in 2D and 3D fluorescence microscopy images, we have considered a two-step approach for automatic segmentation and quantification based on parametric intensity models (anisotropic Gaussian models). Gaussian models well approximate small spot-like structures that are blurred by the point-spread function of the microscope (Santos and Young, 2000; Thomann et al., 2002).
To reduce the image noise, we first convolved the images with a 2D/3D Gaussian filter (standard deviation 
=1), respectively. We then clipped all intensity values below a threshold Tclip. As the optimal value of Tclip depends on the background intensity, the image contrast and the amount of image noise, the value of Tclip is generally different for different images. To avoid manual setting of values of Tclip for different images, we devised an automatic procedure for an optimal value of Tclip that is computed from the image histogram – that is, Tclip=µh + cxh, where µh and h denote the mean and standard deviation of the histogram, respectively, and c is a constant. In our case, c=2.8 yielded good results for all images. Altering the clipping by moderately changing the parameter c did not alter the derived statistics p(a) and p(s) significantly. We next performed a local-maxima search for spot detection within quadratic or cubic regions of interest (ROIs). For 2D/3D images, we have chosen a ROI of 5x5 pixels and 5x5x5 voxels, respectively. As a result, we obtained for each candidate spot a (coarse) center position.
In the second step of our approach, we fitted a Gaussian intensity G3D(x,y,z)=a0+(a1–a0)exp[–x2/(2x2)-y2/(2y2)-z2/(2z2)] to the candidate spots. Here, a0 and a1 are the intensities of the local background and the peak, respectively, while x, y and z denote the standard deviations of the Gaussian. To obtain a fine-tuned fit, each Gaussian was then translated and rotated for a maximum overlap with the spot. For 2D images, the appropriate Gaussian G2D(x,y) was used. For segmenting the spots, we applied a least-squares fit (Levenberg/Marquardt) of the Gaussian to the image intensities within the ROIs of the original image. For each candidate spot, the starting values of the model parameters were automatically initialized based on the parameters of the detected spot from the first step.
As the images contained spots of different sizes, it was not possible to use the same ROI size for all spots. We therefore varied the ROI sizes in the range RROI,min=3 and RROI,max=10 and kept the smallest ROI, for which model fitting terminated with valid parameters. From this, we obtained for each spot an estimate of all model parameters, obtaining the position (x,y,z) of each spot, its maximum contrast a1–a0, and the half-width x, y, z in each direction. From the latter, we calculated the fluorescence sizes of each ERES spot in a given cell through the Gaussian integral as A=(2
)3/2(a1–a0)xyz. For each cell, we divided these fluorescence sizes by the arithmetic mean of the considered ERES to obtain the normalized fluorescence sizes a. A representative picture of the image analysis is shown in supplementary material Fig. S2.
Nearest-neighbor statistics
From the position of ERES obtained by the above image processing, we determined the spatial arrangement of ERES in a given cell by considering the distribution p(s) of (normalized) distances s between nearest neighbors (NN) in the ERES population. A similar strategy is commonly used to characterize the spectra of complex quantum systems (Haake, 2001). If point-like objects, for example ERES, without any interaction are dispersed randomly in a circular area, one obtains a distribution (Haake, 2001):
 | (1) |
For interacting ERES, the experimental and numerical data are empirically best described by an expression that has been derived for the spectra of random matrices belonging to the Gaussian symplectic ensemble:
 | (2) |
To be independent of the size of the cell and the number of ERES per cell, we have quantified the NN distances for each cell and then divided them by their arithmetic mean. We then used a collection of these normalized distances from a population of cells to obtain p(s) with good statistics.
Tracking of single ERES and deduction of the diffusion coefficient
The motion of individual ERES was analyzed with RYTRACK (developed by Ryan Smith and Gabe Spaulding, http://titan.iwu.edu/~gspaldin/rytrack.html) running under IDL 6.1 (Visual Numerics). Settings for RYTRACK were chosen such that only spots were considered in the analysis that could be identified and tracked over at least five subsequent frames of the time series. From RYTRACK, we obtained the squared displacement (SD) 
x2 of each individual ERES for two frames of the time series having a lag time T. From the cumulative distribution of SDs, P(x2), of a tracked particle for a fixed lag time T, one can infer the diffusion coefficient of the tracked particles (Guigas and Weiss, 2006). Owing to the heterogeneous motion and size of the ERES, assuming a single diffusion coefficient did not yield a good fit for the cumulative distribution of SDs of all tracked ERES for a fixed lag time T. We therefore have modified the fitting procedure by assuming a lognormal distribution of diffusion coefficients of the considered ERES:
 | (3) |
By optimizing µL and L, we obtained extremely good fits to the experimental data, from which we calculated the mean diffusion coefficient D(T)=exp{µT+T2/2} of the ERES population. To account for the limited accuracy when determining the center-of-mass position of ERES, P(x2) was only fitted in the range x > 50 nm.
Statistical model for the spatial arrangement of ERES
To elucidate the statistical characteristics of the spatial arrangement of ERES in a cell, we considered a circular region (radius 15 µm) and randomly selected sequentially 200 ERES positions (hard-core radius 200 nm) within this area. Without further constraints, Eqn 1 yielded a very good description of the next-neighbor distance statistics p(s) (cf. Fig. 3a); only very small distances were suppressed owing to the hard-core exclusion. To create a `depletion zone' around an ERES position, we did the following: to determine the n+1st ERES position, we drew a random point within the circle and asked for the distances d1,n+1,..., dn,n+1 to the n already accepted ERES positions. We rejected the position when it failed to obey the hard-core exclusion criterion. Otherwise, the new position was only accepted if a random number 0<
<1 fulfilled the condition:
 | (4) |
Spatiotemporal model of ERES assembly
The model sketched in Fig. 1 was studied numerically with a Brownian dynamics simulation that, for simplicity, only considered a single particle species (e.g. a full COPII complex). An extension of the simulation to include individual COPII proteins and their sequential binding is feasible, yet the computational effort increases considerably and more unknown parameters will have to be considered.
A total pool of Ntot=Ncyt+Nmem particles with radii rc=10 nm [the putative radius of a COPII complex (Stagg et al., 2006)] was considered, with Ncyt and Nmem being the particle numbers of the cytosolic and membrane-bound pools, respectively. The total area of the (flat) ER membrane was set to 400 µm2 and periodic boundary conditions were used to reduce finite size effects. Particles from the cytoplasm were allowed to attach with rate Kon to the ER membrane, reflecting a simplified version of the rapid assembly of COPII complexes after nucleotide exchange (GDP to GTP) and firm binding of Sar1p to ER membranes (Antonny et al., 2001; Forster et al., 2006). The imposed detachment of any individual particle from the membrane with rate Koff essentially captured the dissociation of the COPII complex from ER membranes owing to GTP hydrolysis by Sar1p.
To mimic a biased binding of particles from the cytoplasm to ERES-rich membrane regions, we divided the membrane into 50x50 nm squares, determined the amount of particles nij in each patch (i,j) and calculated the associated probability density of particles Wij=nij/Ntot, which was typically a number in the interval [0, 0.001]. While the number of attaching particles was solely dictated by the rate Kon, the probability to bind to a locus in patch (i,j) was additionally enhanced by 3x105xwij, meaning that, in ERES-rich regions, the association was favored 100-fold with respect to a naked membrane.
While being on the membrane, individual particles were subject to diffusion. Diffusing particles were able to fuse and hence build larger clusters. For simplicity, all clusters were assumed to have a circular shape; a single particle was interpreted as a cluster of size unity. In general, two clusters at positions 
and 
consisting of m1, m2 individual particles (i.e. having radii 
; i=1,2) were allowed to fuse and build a new cluster consisting of m1+m2 particles when their distance d=|
| was smaller than the sum of the individual radii (dR1+R2). In other words, only if two clusters overlapped or were touching did fusion occur. The new cluster was assigned the spatial position of the largest contributing cluster. Within a cluster of size m, all m individual particles were allowed to dissociate from the membrane and join the cytoplasmic pool with rate Koff. The diffusion coefficient of the clusters was determined by the relation D(m)=D0/(1+m/mc)2, with D0=0.05 µm2/second and mc=100. This simplified relationship accounts for the fact that, in the regime of small radii, the diffusion coefficient hardly depends on the size of the particle (Guigas and Weiss, 2006; Saffman and Delbruck, 1975), whereas, for larger sizes, hydrodynamics and internal degrees of freedom lead to a strong reduction of D owing to the reticular structure of the ER.
Vesicle transport, being a collective loss of Nves particles from a cluster owing to the pinch-off of a COPII vesicle, was considered only for clusters that consist of m>Nves particles. Such a cluster tried to pinch off m÷Nves vesicles, each containing Nves particles, with budding rate 
=10–3/seconds ("÷" denotes a division that only yields the integer part of the result). We estimated the number of COPII vesicles that could be produced in a single cell per minute. Photobleaching experiments indicated that the turnover time for the Golgi stack is 60 minutes (Zaal et al., 1999), meaning that the typical time to replace only the cis cisterna (area depending on cell type, 5-10 µm2) by newly arriving membranes is 20 minutes. Supporting the formation of a new Golgi cisterna therefore requires 500-1000 COPII vesicles per 20 minutes. Of course, retrograde transport from the medial cisterna might also contribute to the newly emerging cis cisterna, thus indicating a reduced number of COPII vesicles. However, retrograde transport already sets in en route towards the Golgi apparatus (Stephens et al., 2000), meaning that a fraction of the COPII-derived membranes never make it to the Golgi, which indicates that more COPII vesicles are produced than are actually needed for maintaining the Golgi. Assuming that the latter two contributions approximately cancel, the production of 500-1000 COPII vesicles per 20 minutes appeared to be a reasonable benchmark. In all simulations, the steady-state appearance was not altered significantly when we produced at least this number of vesicles, indicating that vesicle formation is only a small perturbation of the ERES assembly phenomenon.
All kinetic reactions were treated in the spirit of the Gillespie algorithm. Diffusion of each cluster was simulated by the associated overdamped Langevin equation – that is, 
, where is a two-dimensional random vector, with each entry being a Gaussian random number with zero mean and variance 2D(m)t. For the simulations, we have chosen a time increment t=2 mseconds. We equilibrated the system for a real time of 200 seconds and then monitored the evolution over 2000 seconds. For the physiological regime, we chose the binding kinetics to be Kon=0.1/second, 0.2/second, 0.3/second and fixed Koff=Kon/2, Kon, 2Kon for each of the values (yielding nine combinations). In that way, 2/3, 1/2 or 1/3 of the COPII population was membrane bound. The time for exchanging the membrane-bound pool was thus given by a few seconds and agreed with the previously reported Sec23p-Sec24p turnover half-time of 3.5 seconds (Forster et al., 2006) when we used Kon=Koff=0.1/second. In accordance with the considerations given to physiological constraints in the main text, we used Nves=48 as the number of COPII complexes per vesicle and a total particle pool of Ntot=120,000 for a membrane area of 400 µm2.
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