Calcium storage in multivesicular endo-lysosome

It is now established that endo-lysosomes, also referred to as late endosomes, serve as intracellular calcium store, in addition to the endoplasmic reticulum. While abundant calcium-binding proteins provide the latter compartment with its calcium storage capacity, essentially nothing is known about the mechanism responsible for calcium storage in endo-lysosomes. In this paper, we propose that the structural organization of endo-lysosomal membranes drives the calcium storage capacity of the compartment. Indeed, endo-lysosomes exhibit a characteristic multivesicular ultrastructure, with intralumenal membranes providing a large amount of additional bilayer surface. We used a theoretical approach to investigate the calcium storage capacity of endosomes, using known calcium binding affinities for bilayers and morphological data on endo-lysosome membrane organization. Finally, we tested our predictions experimentally after Sorting Nexin 3 depletion to decrease the intralumenal membrane content. We conclude that the major negatively-charge lipids and proteins of endo-lysosomes serve as calcium-binding molecules in the acidic calcium stores of mammalian cells, while the large surface area of intralumenal membranes provide the necessary storage capacity.


Introduction
The importance of calcium as a regulator of cellular function is underscored by the significant energy expenditure, and complexity of regulators that establish and maintain sizable spatiotemporal gradients in calcium concentration in the various parts of the cell.
In most cells, the cytoplasmic concentration of free Ca 2+ is kept at least three orders of magnitude less than in the extracellular space (Morgan et al 2011, Scott andGruenberg 2011), while specific organelles serve as 'calcium stores' .These stores are the source of calcium ions released as part of the signal transduction of various fundamental signalling and trafficking pathways in a variety of biological contexts (Clapham 2007, Giorgi et al 2018).In mammalian cells, the endoplasmic reticulum (ER), mitochondria, and late compartments of the endo-lysosomal system (also referred to as acidic calcium stores) serve this storage function, providing an internal source of Ca 2+ .While much is known about the mechanism of ER calcium storage and the calcium binding proteins that serve as the major reservoir of calcium ions (Coe and Michalak 2009), the nature of the calcium binding molecules that play an analogous function in the acidic calcium stores is completely mysterious.Yet, estimates indicate that up to 99.9% of the calcium present in the acidic store is chelated to some unknown storage matrix consistent with the notion that such a buffer must exist (Morgan et al 2011).
In yeast and plant cells, the vacuole, an organelle analogous to the lysosome (Scott et al 2014), also functions as a calcium store and uses large amounts of inorganic polyphosphates to increase the storage capacity of the store for calcium (Lander et al 2016, Wild et al 2016), yet such easily detectible material is not seen in late endosomes and lysosomes of mammalian cells.As mentioned previously, the ER relies on a high density of calcium-binding proteins to maximize the calcium-carrying capacity of the organelle (Coe and Michalak 2009), but these too have not been reported in the endocytic system.This led us to ask what is the identity of the calcium-binding storage material that is enabling endo-lysosomes to function as an efficient calcium store?One of the defining characteristics of late endosomes or endo-lysosomes is the highly pleiomorphic and multivesicular nature of the membranes of this compartment (Scott et al 2014).Multivesicular late endosomes contain abundant intralumenal vesicles (ILVs) that mediate the selective transport of proteins destined to be degraded, including downregulated signalling receptors, to the lysosomes (Bissig and Gruenberg 2013).In principle, the large surface area of these lipid membranes could act to adsorb large amounts of calcium detected in the acidic calcium store as has been observed in other membrane contexts (McDonald et al 1976, Akutsu and Seelig 1981, Miller et al 1982, Macdonald and Seelig 1987, Huster et al 2000).In addition, the membranes of the late endosome uniquely contain high (∼15 mol%) amounts of the atypical phospholipid lysobisphosphatidic acid (LBPA), a highly negatively charged phospholipid known to interact with divalent cations (Kobayashi et al 1998, Matsuo et al 2004).Importantly, the capacity of calcium to bind negatively charged lipids is a universal principle (Melcrova et al 2016).Typically, much energy is used by cells to flip negatively charged lipids from the outer to the inner leaflet of the plasma membrane, facing the high calcium concentration of the blood.Indeed, the presence of negatively-charged lipids on the outer leaflet, which is readily detected by binding of the calciumbinding protein Annexin V, serves as 'eat me' signal for the clearance of apoptotic cells (Kay and Grinstein 2013).
Therefore, in addition to the composition of the endosomal membranes, the structural organization of the organelle likely is a key determinant of the calcium storage capacity of endosomes.The multivesicular structure typical of late endosomes (endo-lysosomes) would be predicted to have a significant impact on the surface-to-volume ratio, and would provide large amount of bilayer surface to mediate calcium adsorption thus increasing the calcium storage capacity of the organelle.In the present study, we set out to investigate the contributions of both endosome morphology, and bilayer membrane lipid composition, on the calcium storage capacity of endosomes using a theoretical approach.We used reported calcium binding affinities for membrane bilayers (table 1), as well as morphological data on the membrane organization of endo-lysosomes (Griffiths et al 1989, Pons et al 2008, Edgar et al 2014), to assess which factors are most important in creating calcium storage capacity.Finally, we tested those predictions experimentally.

Physical description of endo-lysosomal calcium dynamics
To assess which factors of the endo-lysosome were most relevant for determining calcium storage capacity we set up a continuum description of the calcium dynamics in various endosomal geometries.The corresponding dynamic equations for the densities of intraendosomal calcium account for the diffusion of calcium in the geometry of endosomes.Importantly, calcium binds to the surfaces that are accessible within endosomes.These correspond to the lumenal leaflets of the endosome limiting membrane and ILVs.Previous descriptions of calcium release focused on situations, where calcium in an organelle was either free or bound to a diffusible buffer (Falcke 2004), but neglected the possibility of binding to the organelle internal surfaces.We focus on the latter and do not account for a possible buffer present in the endosome.
Explicitly, the dynamic equations for the intraendosomal calcium ion concentration n i read: In these expressions, j is the calcium current and D the diffusion constant.Equation (1) expresses mass conservation and equation (2) states that the calcium current is proportional to spatial gradients in the calcium concentration (Fick's 1st law).When the expression for the current (2) is inserted into equation (1), we obtain the diffusion equation.
The presence of the intralumenal surfaces to which calcium can bind is captured by 'boundary conditions' , that is, expressions for the current j in equation ( 1) at these surfaces.Whereas there are no constraints on the current parallel to the surface, the perpendicular component of the current is determined by two processes: on one hand calcium binds to and is released from membranes, and on the other hand calcium leaves from the endosome through channels.The exchange of calcium between lumen and membrane is determined by the binding rate k a and the unbinding rate k d .The first contribution fixes the outward directed component of the current, and the second the inward directed component.This can be written as (3) In this expression, n i | mem denotes the endosomal calcium concentration at the membrane and n m the concentration of calcium bound to the membrane.Note, that the molecular nature of the calcium binding and release process is irrelevant at this level of description.
The current across the channels can be written as: where the constant α quantifies the current through a channel at a given difference between the cytoplasmic density n e and the intraendosomal density n i at the channel.We take n e to be constant in space and in time.
The geometries we will study in the following prohibit an analytic solution of the dynamic equations.We used COMSOL (COMSOL Multiphysics ® v. 5.3a 2017), as described below in the methods.

Endosome morphology greatly influences calcium storage capacity in the theory
To assess the contribution of the calcium-membrane interaction on efflux of calcium from an endosome without ILVs, we varied the ratio of the association constants and dissociation constants, K Ca , across the range reported for calcium-lipid, and calciummembrane interactions (table 1) in our simulations, first with an idealized multivesicular endosome structure with a single channel (schema shown in figure 1(A); early state of COMSOL simulation 1D).
Varying the binding constants over 6 orders of magnitude of plausible biological values (see methods) produced essentially no changes in the depletion kinetics of the luminal [Ca 2+ ] after opening of the channel (data not shown), and a very marginal difference in the appearance of Ca 2+ in the volume of the cytoplasm adjacent to the endosome (figure 1(B)).In contrast, monitoring the calcium bound to the inner leaflet of the endosome was highly dependent on the K Ca parameter as expected (figure 1(C)).These results suggest that the association/dissociation rates of calcium with the membrane are not a primary factor determining the storage capacity of an endolysosome.It is unlikely that a specific membrane composition would have binding kinetic parameters that vary sufficiently to influence the calcium storage capacity of an endo-lysosome.These calculations led us to reject the hypothesis that atypical calcium binding interactions of endosome-specific proteins or lipids, like LBPA, are providing additional storage capacity for calcium for the geometry used in the simulation (figure 1(D)).Additional calcium channels added to the model did not change the effect of varying calcium-membrane binding constants except that depletion was faster in all conditions as expected (data not shown).
Given these results, we next sought to determine the influence endosome morphology has on the storage capacity of endocytic compartments.As was described, late endosomes (endo-lysosomes) in mammalian cells display a diverse complexity of structure and in particular abundant ILVs, which provide additional membranous surface area to sink free calcium.To study this, we used an endosome (figure 2(A)) of the reported typical diameter (0.5 µm) (Bissig and Gruenberg 2013) and varied the number of ILVs of the average size reported (∼50 nm diameter) within.
As shown in figure 2(B), decreasing the number of ILVs present in the endosome had a profound effect on the calcium storage capacity of the endosome.While the two-dimensional projection of an endosome reduced the maximum number of ILVs possible in our model endosome, there was a profound change in the rate of calcium efflux as the number of ILVs was reduced from 16 (approaching a completely filled endosome in our two-dimensional model) to zero (empty endosome).This, despite the reduced absolute amount of free calcium ions due to volume exclusion by the presence of ILVs.The extended time to empty also changed the character of the calcium signal 'sensed' by the endosomal surface, influencing not only the intensity, but the time course of the calcium sensed by the near-endosomal cytoplasmic environment (figure 2(C)).Together, these results clearly mark ILVs as important elements enabling these organelles to function as calcium stores.While initially surprising, this marked difference in the characteristics of calcium efflux from the endosome after varying number of ILVs in our simulation is explained by the considerably increased calcium storage a highly vesicular morphology provides.Given the initial state of our simulation was at equilibrium, significant amounts of calcium were bound to the surface of the membrane and served as a calcium store effecting the dramatic difference in efflux behaviour, analogous to the biological situation.
This finding leads us to re-examine an analytic approach to describe the effect of increased endosomal internal surface area on endosomal calcium and release.The total amount of calcium N tot in an endosome has two contributions, free and membrane-bound, N tot = N i + N m with N i = ´Ωl n i d 3 r and N m = ´∂mΩl n m d 2 r.In these expressions, Ω l is the region of the endosome in which calcium can diffuse freely, and ∂ m Ω l the boundary of this region given by the membrane.The time evolution of N i is given by: where ∂ p Ω l is part of the endosome boundary given by the channels.The problem of solving the above equations is non-trivial when considering the complicated geometry of a typical endo-lysosome-this is the reason we used the COMSOL simulations described above.However, there is a limiting case where we can make analytical progress.If the diffusion constant D is very large such that the concentration of free calcium in the endo-lysosome is essentially homogenous, Here, we also consider that the concentration of membrane-bound calcium n m is homogenous, n m (r, t) = n m (t) ≡ Nm Am .In these expressions, V l , A m , and A p denote the volume and surface area of Ω l , ∂ m Ω l , and ∂ p Ω l respectively.
The steady state solution for the total amount of Ca 2+ in the endo-lysosome is The slowest time scale τ on which the steady state is reached is given by This result shows that the relaxation time depends on the amount of membrane, given here by the parameter A m .Since this dependence is hard to infer from this expression, we consider the limit of fast exchange between the membrane and the lumen of the endolysosome.Explicitly, we take the limit k a , k d → ∞ with k a /k d finite in equation ( 10).The result is It shows that the relaxation time increases with A m in agreement with our numerical solutions of the full equations (figure 2) and describes the dominant effect of surface area on calcium release from endosomes: τ increases as A m increases.

Endo-lysosomal morphology strongly affects calcium homeostasis in HeLa cells
To examine the relationship between the calcium capacity of endosomes and endosome morphology obtained from our simulations and equations, we performed direct measurements of endo-lysosomal calcium using the methods of Christensen et al (2002) in HeLa cells transfected with small interfering RNAs (siRNAs) known to influence ILV morphology.The HeLa cells were selected as they are amenable to both siRNA silencing and live-cell imaging, and are a commonly used model cell line to study the structure and function of the endocytic pathway.Briefly, this approach used internalized dextrans coupled to either Fura-2, or a pH-indicator to simultaneously measure calcium and pH in the lumen of endo-lysosomes and then corrected for the pH-dependence of the calcium indicator by modelling.This dual-ratiometric approach accounts for the pH-dependence of the calcium sensor by simultaneously measuring the local environment with a second fluorophore with compatible wavelengths.This allows a robust and direct determination of free calcium inside the organelle, something that has proved a technical challenge.
For these experiments we targeted Sorting Nexin 3 (SNX3), a small phosphoinoside-binding protein that when knocked-down, results in the striking phenotype of near-empty endosomes (Pons et al 2008(Pons et al , 2012)).HeLa cells were transfected with siRNAs to SNX3 for 3 d and endo-lysosomes loaded overnight with the ion probes before a 90 min chase to label specifically the later endocytic compartments (figure 3(A)).
As shown in figure 3(B), the endo-lysosomes of cells treated with siRNAs to SNX3 had a mean free calcium concentration of 600 µM, around a 50% increase from the control cells (∼400 µM).Intriguingly, this increase was in qualitative agreement with the increase of free calcium of endosomes as predicted by our model and simulation upon depletion of ILVs (figure 2(B)), which predicts an increase in free endosomal calcium under conditions with reduced surface membrane area available to sink calcium.This is consistent with the hypothesis that the surface of intralumenal structures serve as major storehouse of intra-endosomal calcium and contributes significantly to the capacity of the acidic calcium store.
Together, these observations suggest that endolysosome morphology significantly influences calcium homeostasis and our modelling suggests that it is this influence, rather than the specific composition of the membrane that is the more likely primary determinant of the storage capacity of the acidic calcium stores.

Discussion
In total, these results suggest that unlike calcium storage in the ER or the yeast vacuole that is mediated by a specific calcium substrate (calcium-binding proteins and inositol phosphates respectively), the acidic calcium store primarily uses the large membrane surface area of the multilamellar/multivesicular late endosomes as storage sites for calcium ions.Our models and simulations suggest the morphological structure of the endosome as the dominant feature determining calcium binding capacity in the endosome (figures 1 and 2) and direct measurements of endosomal calcium in SNX3-silenced cells (figure 3) support this notion.This supports the idea that while the specific interactions of endosomal lipids and proteins with calcium are important to mediate calcium signalling and homeostasis, it is the morphology and size of the organelle which is the dominant feature contributing to bulk calcium storage capacity of the acid calcium store.Altogether our findings provide novel insights into the mechanisms regulating the calcium content of acidic calcium stores in mammalian cells.
Our simulations and analytical solutions do have limitations.The morphology used in the COMSOL simulation was based on an idealized endosome with only a single pore to approximate an open calcium channel.In the biological context, a complex balance of calcium pumps and channels (and more generally, ion transporters), as well as membrane fission and fusion events would be mediating calcium flux.Further, the simulation was only performed in two-dimensions, and all of this allows only qualitative insights into how differences in calcium binding kinetic parameters and organellar morphology may influence calcium storage.More work is necessary to understand the fundamental biology of calcium dynamics in the endocytic pathway and to inform more comprehensive models, however our approach is still valid to provide insights as described herein.
Comparison of the reported binding affinities of calcium for various membranes (table 1) imply that major binding sites available for calcium are provided by the integral membrane proteins or other elements not present in the synthetic model bilayers.Likely, a major component of this binding capacity takes the form of the negatively charged carbohydrates moieties attached to many proteins after translation.Obvious candidates for providing such calcium-binding capacity in the late endosome are the abundant proteins LAMP1 and LAMP2, which contribute to about 50% of all membrane proteins in late endosomes and lysosomes (Eskelinen 2006).Each protein contains 15-20 potential N-linked oligosaccharides (LAMP1: 17-20; LAMP2: 16−17) and Oglycans, which may make up ≈60% of the total protein mass (Noguchi et al 1989, Eskelinen et al 2003).If one sialylated oligosaccharide side chain could bind 2-5 calcium atoms, one LAMP molecule may in turn bind 30-100 calcium atoms-LAMP molecules are not fully glycosylated in non-highly metastatic cells (Saitoh et al 1992).LAMP proteins are restricted to the endo-lysosome limiting membrane (Griffiths et al 1989), and the density of LAMP1 on endo-lysosomal membranes is ≈2600 molecules µm −2 (Wilke et al 2012).One can thus estimate that an endo-lysosome with a typical diameter = 0.5 µm may contain 2041 LAMP1 molecules, which in turn may bind a total of ≈80 000-260 000 calcium atoms.Another candidate is the tetraspannin CD63, a protein also extensively glycosylated (Metzelaar et al 1991, p 63), but abundant in ILVs (Escola et al 1998), in contrast to LAMP1.
Another characteristic feature of the late endosome is the dramatic enrichment of the atypical phospholipid LBPA as described above.While the exact molecular mechanism remain unresolved, LBPA is clearly involved in directing endosome structure and transport functions (Matsuo et al 2004, Scott et al 2014) and likely contributes to the intricate multivesicular structure providing the large surface area.In addition, LBPA binds the endosomal sorting complexes required for transport (ESCRT) nucleator apoptosis linked gene 2 interacting protein X (ALIX) (Bissig and Gruenberg 2013), which in turn recruits ESCRT-III to endosomes, and thus drives the formation of ILVs, together with the canonical ESCRT pathway (Bissig et al 2013, Larios et al 2020).Given our results, and the significant difference in reported calcium-binding abilities of simple model membranes versus those of protein-containing bilayers (table 1), it is likely that LBPA functions in a regulatory role directing organelle structure and thus indirectly calcium binding capacity of the late endosome.However, we can estimate that an endosome with a diameter of 0.5 µm and 50 ILVs (Falguières et al 2008, Edgar et al 2014) may contain 168 000 molecules of LBPA in its inner leaflet (accessible to calcium)with LBPA accounting for 15% of the total endosome phospholipids (Kobayashi et l 1998) and phospholipids for 60% of the membrane (Ksenofontov et al 2008) and with 1 phospholipid ≈0.63 nm 2 (van Meer et al 2008).With 1-3 Ca atoms bound per headgroup (Melcrova et al 2016), LBPA may thus bind ≈170 000 calcium atoms, representing approximately the calcium binding capacity of sialylated LAMP1 in non-cancer cells.However, to our knowledge, no kinetic studies of calcium binding to LBPAcontaining membranes have been performed, so we cannot rule out an unexpectedly high binding affinity of LBPA-containing membranes for calcium contributing more directly to the calcium storage capacity of the endo-lysosome.
While our findings provide insight on the characteristics of the endosome relevant to calcium storage, the molecular factors and their relative importance in filling, maintaining, and emptying the acidic calcium store remain incompletely understood.While free [Ca 2+ ] in the ER has been robustly estimated to ≈0.5 mM (Coe and Michalak 2009), [Ca 2+ ] in the endosomal system is poorly characterized (Scott and Gruenberg 2011).While a difficult technical challenge, some determination of [Ca 2+ ] along the endocytic pathway have been reported.After internalization from the calcium-rich (mM) extracellular milieu, the [Ca 2+ ] of a nascent endosome decreased rapidly (to <5 µM) concurrent with the acidification of the organelle (Gerasimenko et al 1998).Yet measurements of the calcium content of the lysosome either by endocytosed fluorescent indicators (Christensen et al 2002) as used in this study, or by lysis of the organelle and measurement of calcium released into the cytoplasm (Duman et al 2006), estimate a much larger (∼500 µM) concentration of [Ca 2+ ] present.This suggests either a progressive reaccumulation of calcium along the endo-lysosomal pathway from either the extracellular environment or uptake from the cytoplasm, or possibly the existence of a specific lysosomal calcium accumulation machinery that exchanges [Ca 2+ ] with the other calcium stores in the cell (Garrity et al 2016, Demaurex andGuido 2017).
Cytosolic calcium flux or changes in concentration have been proposed to play key roles in several endosome-related processes.Among these is not only the regulation of homo-and heterotypic fusion of endocytic compartments themselves (Luzio et al 2007, Tian et al 2015) but also of interactions with autophagosomes (Medina and Ballabio 2015, Tian et al 2015, Garcia-Rua et al 2016) and the plasma membrane (Andrews et al 2014).Further, changes in local calcium levels have been implicated in the escape of the coronavirus from the late endosome (Gunaratne et al 2018, Millet andWhittaker 2018), and even directly on membrane dynamics such as tubulation in model membranes (Ali Doosti et al 2017).Finally, the ANX6-dependent export of cholesterol from the same compartment is influenced by calcium (Enrich et al 2017, Rentero et al 2018).This important role of calcium in coordinating endosomal transport processes is consistent with the reported dysfunction of calcium observed in various lysosome storage disorders (Lloyd-Evans et al 2008, Shen et al 2012, Gomez et al 2018).Finally, efflux of calcium from damaged endosomes has been identified as a signal mediating ESCRT-mediated repair processes (Skowyra et al 2018), presumably via changes in endosomal membrane tension (Mercier et al 2020), underscoring the central role of this ion in directing endosome function and trafficking.
It therefore is not surprising that links between impaired calcium homeostasis and both impaired cellular function and human pathologies are so widely reported.However, the intimate link between endosome function, structure and calcium homeostasis does make it difficult to untangle primary effects from secondary changes resulting from an impaired molecular function.

COMSOL simulation
For the solution of our dynamic equations, we used COMSOL (COMSOL Multiphysics ® v. 5.3a 2017).It is a numeric solver of partial differential equations based on the finite element method.To this end, we created idealized geometries based on the current understanding of multivesicular endosome structure (figure 1(A)) and used estimates of calcium and calcium-membrane interactions to parameterize the simulation.We decided to perform our analysis to assess the gross effects of geometry on calcium dynamics in two spatial dimensions, which should be generalizable to three dimensions, a strategy that has been used by others (Denizot et al 2019).
A review of measured calcium association and dissociation constants with both model and biological membranes reported in the literature (table 1) provides plausible constraints for the kinetics of calcium expected in the endosome.In general, the surface of phospholipid membranes has a substantial binding capacity for calcium (Melcrova et al 2016).Many studies have been performed over decades to measure the ability of artificial membranes and isolated biological membranes to bind calcium and determine the binding constants of this interaction by various techniques (table 1).This includes the analysis of artificial membranes containing phosphatidylcholine (PC), phosphatidylethanolamine (PE), and phosphatidylserine (PS), the primary negatively charged lipids found in cellular membranes (Akutsu and Seelig 1981, Macdonald and Seelig 1987, Huster et al 2000, Sinn et al 2006, Melcr et al 2018), and of isolated cellular membranes (McDonald et al 1976, Miller et al 1982).While the range of binding constants is diverse (table 1), all these studies found a high capacity for bilayercalcium binding consistent with molecular modelling studies predicting multiple calcium ions interaction with each lipid molecule (Melcrova et al 2016, Melcr et al 2018).The significantly increased binding affinity of cellular membranes when compared to artificial membranes containing lipids could be explained by the charged moieties present on the integral membrane proteins present in these preparations.We used these reports to bound the range of calcium affinities tested in the simulation.
As depicted in figure 1, we simulated the opening of a single calcium channel in our model endosome.
The exact number and nature of the endo-lysosome calcium transporters is not known but would typically be in the hundreds or thousands per organelle and therefore was not practical to use in the simulation.As a result, the time scale of depletion does not align with the biological time scale so depletion times were normalized as described in the figure legends.
Calcium-membrane parameters used for the COMSOL simulation were estimated as described.For the initial state of the simulation, bound and free Ca 2+ were set at equilibrium such that the free Ca 2+ was ∼500 µM in agreement with published reports (Christensen et al 2002, Duman et al 2006).In addition, the following parameters were used in the simulation: endosome radius, 250 nm (Griffiths et al 1989); ILV radius, 25 nm (Pons et al 2008); bulk diffusion, 5 × 10 −11 m 2 s −1 (Donahue and Abercrombie 1987); channel (pore) width, 12 nm (Chen et al 2017), membrane bilayer width, 10 nm (Saftig et al 2010); cytoplasm diameter, 1 µm (arbitrary area around model endosome).

Cells, media, reagents and antibodies
HeLa MZ cells were from Lucas Pelkmans (University of Zurich) and cultured as per ATCC recommendations.HeLa cells are not on the list of commonly misidentified cell lines maintained by the International Cell Line Authentication Committee.Our HeLa-MZ cells were authenticated by Microsynth (Balgach, Switzerland), and are mycoplasma-negative as tested by GATC Biotech (Konstanz, Germany).Reagents were sourced as follows: oligonucleotides and siRNA from QIAGEN.Other chemicals and reagents were obtained from Sigma-Aldrich (St. Louis, MO).Transfections of siRNAs was performed using Lipofectamine RNAiMax (Invitrogen; Basel, Switzerland) using the supplier's instructions.

Figure 1 .
Figure 1.Dependence of calcium release on lipid-calcium binding constants.(A) Schema of idealizes endosome used for simulations.(B) COMSOL simulation of depletion time of an empty endosome with varying the KCa constants.KCa was tested over six orders of magnitude.(C) Amount of Ca 2+ bound to the inner limiting membrane of the model endosome over time in the same simulation as (B).(D) Example Ca 2+ profile of the endosome depletion simulation of (B) and (C) values in panels (B) and (D) are relative values, independent of the units and scales.The local calcium concentration is indicated by the colour indicated in the legend below.Time is expressed in units relative to the half-time of depletion of the Kca = 1 simulation.

Figure 2 .
Figure 2. Effect of endosomal organization on calcium release.(A) Calcium of profile of model endosome containing 16 ILVs shortly after the start of the simulation.(B) COMSOL simulation of calcium depletion of model endosomes with varying numbers of ILVs.(C) Relative free calcium concentration in the near-endosomal area for the same simulation in (B).Time is expressed in units relative to the half-time of depletion of an empty endosome.

Figure 3 .
Figure 3. Endo-lysosomal calcium determination in SNX3-knock down cells.(A) Distribution of the endocytosed ion indicators after loading protocol in HeLa cells.(B) Effect of SNX3 depletion on endo-lysosomal calcium.

Table 1 .
Reported calcium binding constants for various membrane compositions.
n.d.no data reported.
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