Regulation of organelle acidity

Abstract

Intracellular organelles have characteristic pH ranges that are set and maintained by a balance between ion pumps, leaks, and internal ionic equilibria. Previously, a thermodynamic study by Rybak et al. (Rybak, S., F. Lanni, and R. Murphy. 1997. Biophys. J. 73:674-687) identified the key elements involved in pH regulation; however, recent experiments show that cellular compartments are not in thermodynamic equilibrium. We present here a nonequilibrium model of lumenal acidification based on the interplay of ion pumps and channels, the physical properties of the lumenal matrix, and the organelle geometry. The model successfully predicts experimentally measured steady-state and transient pH values and membrane potentials. We conclude that morphological differences among organelles are insufficient to explain the wide range of pHs present in the cell. Using sensitivity analysis, we quantified the influence of pH regulatory elements on the dynamics of acidification. We found that V-ATPase proton pump and proton leak densities are the two parameters that most strongly influence resting pH. Additionally, we modeled the pH response of the Golgi complex to varying external solutions, and our findings suggest that the membrane is permeable to more than one dominant counter ion. From this data, we determined a Golgi complex proton permeability of 8.1 x 10(-6) cm/s. Furthermore, we analyzed the early-to-late transition in the endosomal pathway where Na,K-ATPases have been shown to limit acidification by an entire pH unit. Our model supports the role of the Na,K-ATPase in regulating endosomal pH by affecting the membrane potential. However, experimental data can only be reproduced by (1) positing the existence of a hypothetical voltage-gated chloride channel or (2) that newly formed vesicles have especially high potassium concentrations and small chloride conductance.

Figure 1

(A) A prototypical mammalian cell showing the major organelles that exhibit distinct lumenal pHs along with typical pH values. These compartments tend to be in the secretory or endocytic pathways. Arrows indicate the progression along these pathways. (B) Cartoon of an organelle illustrating the principle elements influencing organelle pH regulation. (1) V-ATPase activity can be directly regulated, e.g., by dissociation of V₁; (2) passive proton leaks; (3) buffering by the lumenal polyelectrolyte matrix; (4) chloride channels; (5) potassium channels; (6) sodium channels; and (7) the Na,K-ATPase.

Figure 2

Performance surfaces. (A) The proton pumping rate [H⁺/s] for a single V-ATPase is plotted as a function of lumenal pH and membrane potential across the bilayer. The bulk cytoplasmic pH is 7.4, but the proton concentration at the membrane is modified by a −50-mV surface potential. The free energy of ATP hydrolysis is 21 k_BT. In principle, the pumping surface can be measured empirically. However, in the absence of such measurements, we have computed the surface based on the mechanochemical model for the V-ATPase as described in Grabe et al. 2000. The parameters used in the computations are given in Table S1 (see Online Supplemental Material available at http://www.jgp.org/cgi/content/full/117/4/329/DC1). (B) The pumping rate for a single Na,K-ATPase plotted as a function of lumenal potassium concentration and membrane potential. Bulk cytoplasmic potassium and sodium concentrations are maintained constant at 140 and 20 mM, respectively. Membrane values of these concentrations are also modified by a −50-mV surface potential as in A. The free energy of ATP hydrolysis is 21 k_BT, and the lumenal sodium is fixed at 145 mM. The pumping profile was computed from the composite model found in Online Supplemental Material. See Table S2 (available at http://www.jgp.org/cgi/content/full/117/4/329/DC1) for a complete list of all parameters.

Figure 3

(Top) Modeling the ATP-dependent acidification of a single endocytic vesicle from rat kidney. The model (dashed) is compared against the experiments (solid) of Shi et al. 1991. Simulations include the effects of V-ATPases, proton leaks, passive potassium channels, Donnan equilibrium, and buffering capacity. Table lists all parameters. (A) Acidification with a constant buffering capacity of 40 mM/pH, as reported by Shi et al. 1991. The vesicle is initially in osmotic equilibrium with an external solution having an osmolarity of 291 mM. The efflux of potassium upon acidification results in a decrease of osmotically active particles; thus, shrinking occurs. Cross-sectional areas of the initial spherical vesicle and an ellipsoid corresponding to the final volume of the vesicle are drawn to scale. The osmotic activity of the protons and the potassium ions is given in Table . The shapes of the acidification curves with and without water flow are indistinguishable at this scale.(B) An approximation to the buffering data reported by Van Dyke and Belcher for MVB endosomes was used to model the acidification curve in A. This buffering curve can be seen in Figure S5 (available at http://www.jgp.org/cgi/content/full/117/4/329/DC1). The lumenal buffering capacity has a noticeable influence on the models ability to fit the data.

Figure 4

(Top) Modeling the ATP-dependent acidification of vesicles in rat liver from two different stages of endocytosis. Model predictions are shown in solid lines and the experimental data points were provided by Van Dyke and Belcher 1994. Controls include the following: V-ATPases, proton leaks, passive chloride channels, passive potassium channels, Donnan equilibrium, and buffering capacity. See Table for all parameters. (A) The acidification of the receptor recycling compartment (RRC). The buffering capacity is extrapolated from experimental values determined by Van Dyke and Belcher. (B) Acidification of the much larger multivesicular bodies (MVB). Fitting the data required a pump density on the MVB vesicles approximately eight times greater than the RRC vesicles. (Bottom) Steady-state membrane potential as a function of external chloride concentration. The presence of chloride enhances acidification by allowing chloride to enter the vesicle to reduce the membrane potential against which the pump must operate. Both C and D show that increasing the external chloride concentration is an effective way to reduce the resting membrane potential. (C) For the RRC population, the dependence of the membrane potential on the external chloride concentration matches experimental observations with the same parameters for the simulations in A. (D) A fivefold decrease in the number of proton pumps relative to B is required to describe the MVB population's dependence on the external chloride concentration.

Figure 4

(Top) Modeling the ATP-dependent acidification of vesicles in rat liver from two different stages of endocytosis. Model predictions are shown in solid lines and the experimental data points were provided by Van Dyke and Belcher 1994. Controls include the following: V-ATPases, proton leaks, passive chloride channels, passive potassium channels, Donnan equilibrium, and buffering capacity. See Table for all parameters. (A) The acidification of the receptor recycling compartment (RRC). The buffering capacity is extrapolated from experimental values determined by Van Dyke and Belcher. (B) Acidification of the much larger multivesicular bodies (MVB). Fitting the data required a pump density on the MVB vesicles approximately eight times greater than the RRC vesicles. (Bottom) Steady-state membrane potential as a function of external chloride concentration. The presence of chloride enhances acidification by allowing chloride to enter the vesicle to reduce the membrane potential against which the pump must operate. Both C and D show that increasing the external chloride concentration is an effective way to reduce the resting membrane potential. (C) For the RRC population, the dependence of the membrane potential on the external chloride concentration matches experimental observations with the same parameters for the simulations in A. (D) A fivefold decrease in the number of proton pumps relative to B is required to describe the MVB population's dependence on the external chloride concentration.

Figure 5

The effect of surface area and volume on steady-state pH. Simulations include V-ATPases, proton leaks, chloride channels, Donnan equilibrium (120 mM), and buffering capacity (10 mM/pH unit). The density of proton pumps and the proton permeability were held constant at 10⁹ pumps/cm² and 10⁻⁴ cm/s, respectively. Constant steady-state pH is plotted as a function of the surface area and volume in the absence (top) or presence (bottom) of 5 mM chloride (140 mM of impermeant potassium is assumed to be present internally). The bulk cytoplasmic pH is 7.4. Even at low counter ion concentrations, the effect of changes in the vesicle shape on the steady-state pH is small. The bottom panel shows highlighted regions corresponding to reported surface areas and volumes for specific organelles: (1) normal rat kidney Golgi complex (Ladinsky et al. 1999); (2) rat kidney endosomes (Shi et al. 1991); and (3) rat liver endosomes (Van Dyke and Belcher 1994).

Figure 6

Counter ion regulation of Golgi complex pH in living HeLa cells. Wu et al. 2000 have shown that the steady-state pH of the Golgi complex is not affected by removal of chloride from the cytoplasmic solution (solid circles). These simulations include V-ATPases, proton leaks, passive chloride channels, passive potassium channels, Donnan equilibrium, and buffering (see Table for parameter values). At time zero, the external chloride is removed. Three theoretical curves are shown with increasing counter ion concentration. When the bulk potassium concentration is 1 mM (dotted line), the lumenal pH rises half a pH unit in response to the removal of chloride. The presence of as little as 14 mM counter ion concentration (dashed line) significantly suppresses pH changes because of chloride removal, whereas the pH change in the presence of 140 mM counter ion concentration (solid line) is imperceptible. This last case is most likely if the membrane is permeable to potassium as well as chloride. (Inset) Determination of the passive leak of protons out of bafilomycin-inhibited Golgi complex. The cytoplasm has been preacidified in sodium-free conditions that inhibit plasma membrane Na⁺/H⁺ exchangers. At time zero, sodium is reintroduced, and the cytoplasmic pH quickly rises due to the exchangers. This experimental curve (circles) is described by a single exponential (solid line). The Golgi complex response to the rise in cytoplasmic pH (solid line) is then fit, using the model, to the experimentally measured data (solid circles). We estimate the permeability constant of the Golgi complex to be P = 8.1 × 10⁻⁶ cm/s. The Golgi complex volume and surface area are estimated from the detailed EM tomography experiments performed by Ladinsky et al. 1999. These measurements were performed on a different cell type, and they may not be representative of the Golgi complex from HeLa cells. Since the characteristic time scale for a passive channel is given by the quantity P×(surface area), errors in the estimate of the surface area lead to uncertainties in our prediction of the permeability constant.

Figure 7

Endosomal acidification in the selective presence (− ouabain) or absence (+ ouabain) of Na,K-ATPase. We model the acidification of a single 163-nm-diam spherical endosome in the presence (top curves) or absence (bottom line) of 350 Na,K-ATPases. All three simulations include the following: 16 V-ATPases, a proton leak with a permeability of 8.24 × 10⁻⁵ cm/s, chloride channels, passive potassium channels, 140 mM of Donnan particles, and 40 mM/(pH unit) buffering capacity. The initial lumenal concentrations of sodium and potassium were assumed equal to standard extracellular values (Table ). A significant increase in lumenal pH is achieved by incorporating Na,K-ATPases into the vesicle (dashed curve). However, the addition of a voltage-gated chloride channel, which is inactivated above 133 mV, is necessary to obtain the experimentally measured full pH difference (top curve). Data points have been adapted from Cain et al. 1989. The model endosome begins acidifying at a single instance, hence, a kink in the pH is present at time zero. The experimental points are smoother since only a small fraction of the what will be the entire endosomal population has begun acidifying near time zero. We have shaded the graph at later times to highlight the portion of the curves best modeled by a single endosome.