Computer modeling of gastric parietal cell: significance of canalicular space, gland lumen, and variable canalicular [K⁺]

Abstract

A computer model, constructed for evaluation of integrated functioning of cellular components involved in acid secretion by the gastric parietal cell, has provided new interpretations of older experimental evidence, showing the functional significance of a canalicular space separated from a mucosal bath by a gland lumen and also shedding light on basolateral Cl⁻ transport. The model shows 1) changes in levels of parietal cell secretion (with stimulation or H-K-ATPase inhibitors) result mainly from changes in electrochemical driving forces for apical K⁺ and Cl⁻ efflux, as canalicular [K⁺] ([K⁺]_can) increases or decreases with changes in apical H⁺/K⁺ exchange rate; 2) H-K-ATPase inhibition in frog gastric mucosa would increase [K⁺]_can similarly with low or high mucosal [K⁺], depolarizing apical membrane voltage similarly, so electrogenic H⁺ pumping is not indicated by inhibition causing similar increase in transepithelial potential difference (V_t) with 4 and 80 mM mucosal K⁺; 3) decreased H⁺ secretion during strongly mucosal-positive voltage clamping is consistent with an electroneutral H-K-ATPase being inhibited by greatly decreased [K⁺]_can (Michaelis-Menten mechanism); 4) slow initial change (“long time-constant transient”) in current or V_t with clamping of V_t or current involves slow change in [K⁺]_can; 5) the Na⁺-K⁺-2Cl⁻ symporter (NKCC) is likely to have a significant role in Cl⁻ influx, despite evidence that it is not necessary for acid secretion; and 6) relative contributions of Cl⁻/HCO₃⁻ exchanger (AE2) and NKCC to Cl⁻ influx would differ greatly between resting and stimulated states, possibly explaining reported differences in physiological characteristics of stimulated open-circuit Cl⁻ secretion (≈H⁺) and resting short-circuit Cl⁻ secretion (>>H⁺).

availability of modern computer software for modeling of complex, dynamically functioning systems led us to attempt modeling of acid secretion by the mammalian gastric parietal cell, incorporating active and passive ion transport mechanisms, together with effects on membrane potentials, with all components required to work interdependently. Objectives were to see how simple a model could reproduce the fundamental functions of the parietal cell and to mimic specific published experimental results, showing how the fully integrated actions of known components can yield those results.

The effort began with the basic mechanisms commonly seen in most textbook diagrams of the cell, with the apical membrane directly facing a mucosal medium (or main gastric cavity). A problem of excessively hyperpolarized apical membrane voltage quickly became apparent with a typical bathing medium of high [Cl⁻] and low [K⁺], resulting in a mucosal-positive transcellular voltage, contrary to experimentally determined values (39). Modeling of the deep apical membrane invaginations called canaliculi (11) as a defined space and addition of a simple tube acting as a gland lumen (16) that presents a diffusional barrier (37) between canaliculi and bath (Figs. 1 and 2) not only solved that problem but allowed wide fluctuations in canalicular [K⁺] ([K⁺]_can), which are found to be critical to the understanding of many experimental results described here.¹

Fig. 1.

Modeled secreting gastric parietal cell: functional components and positioning in gland. Lamina propria, with extracellular fluid, is to left. Symbols for transport mechanisms: slashed, ATPases; dotted, passive transporters; clear, conductive pathways; see text for Na⁺ black box. “Canaliculus” does not show extent and complexity of canalicular system. Modeled representative parietal cell is 300 μm from a gastric pit, into which mucosal bath is considered to extend.

Fig. 2.

Berkeley Madonna “Flowchart” of the parietal cell model. An “infinite” serosal bath is at left. “Reservoirs” (e.g., CytCl) hold amounts of ions (μequiv) in cytosol, canaliculus, and mucosal bath. Most flow modules (large arrows) carry ions according to specific formulas to, from, or between reservoirs. Thin arrows indicate inputs of values used by flow modules. A few reservoirs are used simply to hold values that can be used in other formulas. At the bottom is a cluster of modules used to simulate externally applied constant current. Many additional formulas, constants, and variables are maintained in a nongraphic list to keep the Flowchart from becoming too visually cluttered.

The canaliculi have long been seen as greatly increasing apical membrane area (11), allowing stimulatory insertion of an enormous number of “proton pumps” (H-K-ATPase) (19), which, in conjunction with K⁺ and Cl⁻ channels (22, 57), drive a high rate of HCl secretion, recycling K⁺ to the cell (8). The model now reveals how separating the canalicular space from the main gastric cavity helps couple active H⁺/K⁺ exchange by the pump to the passive effluxes of K⁺, Cl⁻, and water.

The model offers explanations for the following observations: 1) increased pump rate increases parietal cell secretion, even though equal exchange of H⁺ for K⁺ (46) is not, in itself, a net ion flux in either direction; 2) inhibition of stimulated H⁺/K⁺ exchange by proton-pump inhibitors (PPIs), without decreased ion conductance, greatly decreases total secretion, rather than converting secretion from high HCl to high KCl (23, 26); 3) intact gastric mucosae seemed to display electrogenic proton pumping (39, 45), although the H-K-ATPase exhibited electroneutral H⁺/K⁺ exchange in isolated membrane vesicles (46); 4) in secreting mucosae at open circuit, H⁺ secretion ≈ Cl⁻ secretion, deemed “acidic” Cl⁻, but in short-circuited resting mucosae Cl⁻ >> H⁺, the excess deemed “active, nonacidic” Cl⁻ secretion, with the two Cl⁻ pathways displaying different anion selectivity (20, 29); 5) NKCC is prominently located in parietal cell basolateral membranes (32), but its inhibition by bumetanide or elimination by gene knockout leaves H⁺ secretion near normal (33); and 6) clamping of transmucosal voltage or current causes initial changes in current or voltage far too large and slow to be due to capacitance (7, 22).

CONSTRUCTION OF THE PARIETAL CELL MODEL

The model, built with Berkeley Madonna software, was designed to represent quantitatively the activity of all parietal cells (Fig. 1) in 1 cm² of adult mammalian fundic/corpic gastric mucosa, with mucosal thickness of 0.1 cm (16), for a volume of 0.1 cm³. Parietal cells have been reported to be ∼14% of mucosal volume in humans (1) and we approximated aggregate parietal cell cytosolic volume as 0.01 cm³/cm² mucosa, fluctuating somewhat with changes in cytosolic ion content. Examination of many of our micrographs of adult rabbit gastric mucosae revealed ∼200 gastric glands per linear cm, thus ∼40,000 glands/cm². Diameter of a single gland lumen, modeled as a simple cylindrical tube, was approximated as 3 μm (35, 48, 49), resulting in a total ∼0.003 cm² of cross-sectional luminal area through which parietal cell secretion would flow to exit 1 cm² of flattened mucosa. A gland luminal length of 300 μm was chosen for distance from mucosal bath to an average parietal cell (16).

Concentrations of relevant ions in an “infinite” serosal bath [extracellular fluid (ECF)] are, in mM, 142 Na⁺, 4 K⁺, 120 Cl⁻, and 24 HCO₃⁻. Initial concentrations in the mucosal bath are, in mM, 145 Na⁺, 4 K⁺, 1 H⁺, and 150 Cl⁻. For mimicking of tests done on frogs, intra- and extracellular ion concentrations were left at mammalian levels. Figure 2 is the Berkeley Madonna graphic representation of the model's basic structure.

Modeled stimulation (Fig. 3) increases electroneutral H-K-ATPase activity (18) and most ion conductances (Table 1) via a timed sigmoidal curve (55), with maximal H⁺ pumping set at 43 μeq·h⁻¹·cm⁻². Ion permeabilities, whether channels or unspecified “leaks,” are modeled as simple conductances, without such specifically identified characteristics as rectification or sensitivity to voltage or pH. The chord conductance equation,

$$V_{\text{m}}=\left(E_{\text{K}}\cdot G_{\text{K}}+E_{\text{Na}}\cdot G_{\text{Na}}+E_{\text{Cl}}\cdot G_{\text{Cl}}\right)/\left(G_{\text{K}}+G_{\text{Na}}+G_{\text{Cl}}\right),$$

Fig. 3.

Modeled transition from resting state to stimulated state. A: resting rates of H⁺ and K⁺ secretion are low and similar. Stimulation (starting at min 5) greatly increases H⁺ and Cl⁻ secretion, as lowering of canalicular [K⁺] ([K⁺]_can) greatly increases driving forces for K⁺ and Cl⁻ efflux (C) and as ion conductances increase (Table 1). K⁺ secretion only modestly increases as most of increased conductive apical K⁺ efflux is returned to the cell by the pump. See text for multiple mechanisms of Cl⁻ transport and for transient Na⁺ secretion. B: [K⁺]_can decreases with combination of increased K⁺ return to cell by the pump and increased washout by high HCl secretion, the latter also washing out Na⁺_can, both cations being replaced by greatly increased [H⁺]_can. C: decreased [K⁺]_can hyperpolarizes E_K, as [K⁺]_can/cytostolic [K⁺] ([K⁺]_cyt) diminishes, also hyperpolarizing membrane voltage (V_m) and greatly increasing driving forces (V_m−E_K and V_m−E_Cl) for conductive efflux. Difference between apical and basal V_m decreases, depolarizing transepithelial voltage (V_t). D: time required for [K⁺]_can to decrease causes increase in conductive K⁺ efflux to lag behind increase in K⁺ back-pumping, so net apical K⁺ efflux transiently decreases, even as K⁺ secretion increases with increased washout of K⁺_can. Greatest difference coincides with steepest decline in [K⁺]_can.

Table 1.

Modeled conductance ranges, resting to maximally stimulated

	Apical		Basolateral
	Resting	Stimulated	Resting	Stimulated
Cl−	0.012	0.072	0.02	0.024
K+	0.02	0.08	0.035	0.04
Na+	1.6 × 10−5	8.6 × 10−5	0.002	0.002
H+	1.0 × 10−6	5.0 × 10−6

Values are in Siemens/cm² mucosa.

is used for membrane voltages, with resistances of other cell types and tight junctions considered high enough to be ignored (43, 50). An Ohm's-law equation is used for ion fluxes: Eq/s = G_ion·(V_m−E_ion)/F. An alternate version of the model has been maintained with Goldman-Hodgkin-Katz equations for ion flux and membrane voltage, allowing ion concentration to affect conductance. It displays essentially the same phenomena with only small differences in absolute numerical values. The version presented here simplifies description of conductive ion flux and allows easy conversion of conductance to resistance, making it useful in analyzing experimental methods of determining transepithelial resistance (see results and discussion).

The total canalicular space is modeled as a constant 0.001 cm³, a tenth of cytosolic volume. Some dilation of canaliculi and gland lumina would be expected with stimulation but would be somewhat limited in the intact tissue, in which glands are tightly packed and constrained by connective tissue of the lamina propria and submucosa. The constant-volume simplification facilitates modeling of ion fluxes through these spaces.

Formulas for net flux of each ion between canalicular space and mucosal bath involve balancing net flux across the apical membrane, advective (liquid-driven) flux, and net diffusion along the gland lumen, the last possibly against total liquid flow or in an electrical gradient during voltage clamping. Luminal Cl⁻ flux involves tiny changes in the virtually constant 150 mM Cl⁻_can. Assuming that all monovalent ions are fully dissociated and have equal osmotic activity, 1 mole = 1 equivalent = 1 osmole. Although an osmotic gradient is necessary for secreted osmoles to “pull” water with them, water permeability of the membranes is considered high enough for the model to treat all compartments as isotonic and to treat water as “moving with” osmoles, without osmotic gradients. With isotonicity (mammalian 300 mosM) and fixed canalicular volume assumed, secretory liquid flow is directly proportional to net apical ion efflux, the latter equaling total advective ion flux to the mucosal bath, although the proportions of different cations within that flux can be altered by diffusive fluxes between canaliculus and bath. Diffusion within a few micrometers is fast enough that the canaliculus is modeled as having no concentration gradients within it; its ion concentrations are treated as those at the cellular end of the luminal tube, contacting the apical membrane.

The modeled basolateral membrane includes transport pathways to account for ion fluxes through the entire cell to maintain homeostasis and to allow the mimicking of transepithelial voltage clamping. A Cl⁻/HCO₃⁻ exchanger (AE2) and a Na⁺-K⁺-2Cl⁻ symporter (NKCC) are used for Cl⁻ loading, functioning according to equilibrium formulas modified by rate constants that are set to bring cytosolic [Cl⁻] ([Cl⁻]_cyt) to within an experimentally determined range of ∼45–60 mM (56), opposing Cl⁻ loss via basolateral Cl⁻ conductance modeled as intermediate between G_K and very low G_Na (47, 53). Based on experimental evidence that cytosolic pH changes very little between resting and stimulated states (56), pH_cyt is modeled as a constant 7.1 and [HCO₃⁻]_cyt a constant 12 mM. A homeostatic function (“black box” in Figs. 1 and 2) covers multiple Na⁺-transporting mechanisms not specifically modeled, moving Na⁺ to balance charge and osmolarity in the cytosol, using estimates of impermeant cytosolic anions and their average charge per osmotically active particle. A simply modeled Na-K-ATPase drives [K⁺]_cyt toward, but not above, 150 mM, exchanging Na⁺ and K⁺ in the established 3:2 ratio.

Voltage clamping is simulated with a procedure that alters membrane voltages in proportion to each membrane's share of the total transcellular resistance, dynamically calculated from all instantaneous conductance values (including tiny apical “leaks” of H⁺ and Na⁺), such that the difference is the desired transcellular voltage (V_t). Forcing membrane voltages away from their open-circuit values causes net anion secretion to differ from net cation secretion, the difference being a net charge flux seen as the negative equivalent of an externally applied current. To mimic a constant current, the model initiates a voltage clamp, the immediately resulting current then held at that value (±tiny fluctuations) with a feedback routine that rapidly adjusts V_t. For ion diffusion along the gland lumen, a Nernst-Planck equation (31) is used to account for both electrical and chemical gradients.

RESULTS AND DISCUSSION

Resting and stimulated parietal cell secretion.

Although the H-K-ATPase (“pump”) is modeled as electroneutral (18, 46), with H⁺ and K⁺ exchanged equally (30, 46), increased pump activity increases total net apical ion efflux (Fig. 3A) by lowering [K⁺]_can (Fig. 3B), which increases electrochemical driving forces (V_m−E_K and V_m−E_Cl, Fig. 3C) for conductive K⁺ and Cl⁻ efflux through increased G_K and G_Cl (Table 1). The pump and various ion conductances are simultaneously activated, although they might be activated over different time courses in the real cell. Most of the conductive K⁺ efflux is exchanged for H⁺, but, with no direct link between the K⁺ efflux and return of K⁺ to the cytosol by the pump, some K⁺ is left in the final “secretion,” defined here as net flux into the mucosal bath. Modeled stimulated secretion (Fig. 3A) resembles the strongly stimulated gastric secretion, mostly HCl with some KCl, seen in human test subjects when parietal cell secretion overwhelms the much lower secretion from other gastric mucosal cells (16, 36) not included in the model.

The resting state is modeled with some pump activity, yielding H⁺ secretion that is 2% of maximal. The normal stomach maintains a pH of ∼2 in the absence of food (21, 28), requiring that basal acid secretion exceed surface-cell HCO₃⁻ secretion (41). In addition, the parietal cell's H2 histamine receptors have been found to have a basal level of activity that can be further lowered by “H2 blockers” that are now known to function as “inverse agonists” (51).

Modeled secretion rates are a combination of advective and diffusive fluxes between canaliculus and bath. As modeled here, net diffusion of H⁺ and K⁺ is nearly always in the same direction as advective flux, while net Cl⁻ diffusion is ≈0 (except with voltage clamping), since [Cl⁻]_can ≈ [Cl⁻]_muc ≈ 150 mM. In the special case of Na⁺ in the resting state, back-diffusion from a bath of standard saline against low outward liquid flow (velocity: ≈10 μm/s) leads to moderately high [Na⁺]_can. Na⁺ flux through the apical membrane is negligible because modeled G_Na is tiny, so advective luminal efflux of Na⁺ is mostly a “flushing” of Na⁺ back-diffusing from the bath and Na⁺ secretion is ≈0 in any steady state. Stimulation increases total ion efflux, and thus the velocity of liquid flow (reaching maximum of ≈300 μm/s), increasingly opposing Na⁺ back-diffusion while flushing out most Na⁺_can in a transient Na⁺ “secretion.”

While total secretion increases in proportion to net apical ion efflux, the canalicular concentration of each cation species determines its share of total advective cation efflux from the canaliculus, so secretion of each cation species can differ from its net apical efflux during transitional states, changing its canalicular concentration. During any steady state, net K⁺ flux from cytosol to canaliculus should equal net K⁺ flux from canaliculus to bath, if solutions are isotonic and canalicular volume constant. In a resting state, low advective K⁺ flux toward the bath and low K⁺ recycling to the cytosol result in [K⁺]_can being high enough (Fig. 3B) to drive sufficient diffusive efflux (≈advective K⁺ flux) through the gland lumen for K⁺ secretion to equal the net apical K⁺ efflux (Fig. 3D), with the latter being low because high [K⁺]_can decreases the driving force for conductive K⁺ efflux and apical G_K is low. As stimulation increases net apical ion efflux (mostly HCl), increased liquid flow increases advective flushing of canalicular ions, with diffusive flux becoming a very small part of total secretion. Back-pumping of K⁺ increases faster than conductive K⁺ efflux, because increase of the latter depends partly on the slower decrease in [K⁺]_can, so net apical K⁺ efflux transiently decreases even as increased advective flux increases K⁺ secretion. The decrease in [K⁺]_can reflects the difference between these two fluxes. A smaller [K⁺]_can/[K⁺]_cyt ratio makes E_K much more negative, also hyperpolarizing apical V_m (Fig. 3C), consistent with stimulatory hyperpolarization of apical V_m found in the acid secreting oxyntic cells of the amphibian Necturus (6). Although net apical K⁺ efflux eventually increases, it lags behind the increasing K⁺ secretion until a steady stimulated state is achieved and [K⁺]_can reaches its lowest value (≈15 mM). Conductive K⁺ efflux ultimately increases more than the back-pumping of K⁺, modestly increasing K⁺ secretion in the steady stimulated state, an increase that has been seen in vivo with stimulation of gastric secretion in several mammalian species, including human (34, 36, 57).

Not shown is that when the model is run with ion conductances maximally increased, but no increase in pump rate, H⁺ and K⁺ secretions slightly decrease and increase, respectively, with no increase in total secretion. However, with pump rate maximally increased and no increase in conductances, H⁺ secretion increases to 68% of the maximal rate in Fig. 3. Thus increased secretion is seen to result mainly from increased H⁺/K⁺ exchange greatly decreasing [K⁺]_can and increasing the driving forces for conductive ion efflux, with increased conductances potentiating that result.

We have not tried to model multiple specifically identified candidate apical K⁺ channels (23), but the model and research reports suggest involvement of two or more such channels. Tests on KCNQ1-knockout mice one wk after birth (52) showed that mice of that age had no other channel to supply the K⁺_can for recycling. However, a strong case has been made that, in parietal cells of adult mice and rabbits, KCNJ15 is a prominent apical K⁺ channel that moves from a cytoplasmic vesicular pool in the resting state to the apical membrane in the stimulated state (15, 58). The modeled fourfold increase in G_K with maximal stimulation may be consistent with adults having both an apical-resident K⁺ channel and another K⁺ channel that is mostly sequestered in a cytoplasmic pool in the resting state (e.g., KCNJ15). Late appearance of KCNJ15 might help to explain a seeming discrepancy between stimulatory V_t hyperpolarization in neonatal mice (52) or piglets (9) and the modeled result of stimulatory V_t depolarization in adult mammals (Fig. 3C). If apical G_K is greatly increased with stimulation in adults, apical V_m should be hyperpolarized, as in Necturus (6), thus depolarizing V_t, as seen in frogs (18) and consistent with a stimulatory decrease in potential difference found between venous blood and mucosal bath in ex vivo canine stomach preparation (24).

Modeled maximal stimulation causes net loss of Cl⁻_cyt, decreasing [Cl⁻]_cyt from 59.5 to 52.6 mM, similar to the decrease of ∼60 to ∼45 mM reported for parietal cells of isolated rabbit gastric glands (56). In the modeled resting conditions, the electroneutral transporters AE2 and NKCC would be at equilibrium with ∼60 and ∼70 mM Cl⁻_cyt, respectively, so NKCC might help AE2 compete with conductive Cl⁻ loss to raise resting [Cl⁻]_cyt toward 60 mM. A stimulatory decrease in [Cl⁻]_cyt increases driving forces for Cl⁻ loading to match increased apical Cl⁻ efflux. With fractional increase in the difference between actual and equilibrium [Cl⁻]_cyt being much greater for AE2 than for NKCC, modeled maximal stimulation increases Cl⁻ loading 16-fold via AE2 but only 1.6-fold via NKCC. The difference would be expected to be even greater if modeled pH_cyt were not held constant and [HCO₃⁻]_cyt could increase slightly. AE2 is well established to bring Cl⁻ into the parietal cell in exchange for HCO₃⁻ (42, 54), especially in a stimulated state when apical H⁺ secretion leaves excess cytosolic base, which must quickly leave basolaterally (5, 55) for pH_cyt to remain nearly constant. NKCC accomplishes most Cl⁻ loading in the modeled resting state when [Cl⁻]_cyt is very near 60 mM, mainly balancing basolateral conductive Cl⁻ loss.

Cl⁻ transport through the full epithelium was long seen as a combination of “acidic” and “nonacidic” fluxes (7), the former linked one-for-one with H⁺ secretion, the latter in excess of H⁺ secretion and especially dominating during short-circuiting in the resting state (see Fig. 7). Different physiological characteristics were experimentally found for the two fluxes, including different anion selectivity (29). The model suggests that the differences might result from AE2 and NKCC making very different relative contributions to Cl⁻ loading in the resting and stimulated states.

Fig. 7.

Modeled effects of steady-state voltage clamping on ion secretion. Results of clamping at 10-mV increments (mucosal relative to serosal) are shown in the resting (A) and fully stimulated (B) states, after initial transient changes (which are shown for short circuit in Fig. 9). Chloride (graphed as positive to aid in comparison) balances charge sum of cations and current. In both states, clamping up to 10 or 20 mV (hyperpolarizing apical V_m, see Fig. 9) causes secretion of K⁺ (exiting cell conductively) to decrease proportionately more than secretion of H⁺ (neutrally “pumped”).

Tests with NKCC-knockout mice and inhibition by bumetanide seem to show that NKCC is not necessary for acid secretion (33), although it is found prominently located in parietal cell basolateral membranes (32, 33). When NKCC is eliminated from the model, both resting and stimulated [Cl⁻]_cyt are substantially lowered, but stimulated H⁺ secretion decreases very little.

Experimentally determined [Cl⁻]_cyt is far higher than would be in equilibrium with basolateral V_m, requiring Cl⁻ loading to be at least indirectly actively driven (38). In the model, the Na-K-ATPase makes a major contribution to the long-perceived “active” serosal to mucosal (s→m) Cl⁻ flux (20) by creating basolateral [Na⁺] and [K⁺] gradients, the latter mainly responsible for a V_m that tends to make [Cl⁻]_cyt much lower than [Cl⁻]_ECF. The [Cl⁻] gradient can then, independently of V_m, help to drive Cl⁻ influx via AE2 and, along with the [Na⁺] gradient, drive NKCC symport against the opposing [K⁺] gradient. The H-K-ATPase would be the second “active” driver of s→m Cl⁻ flux, increasing apical V_m−E_Cl (Fig. 3C) and (in the real cell, but not modeled here) increasing the AE2 rate by increasing [HCO₃⁻]_cyt through apical loss of H⁺.

With modeled stimulation as in Fig. 3, a decrease in [Cl⁻]_cyt is accompanied by loss of K⁺_cyt and Na⁺_cyt for electroneutrality but retention of impermeant cytosolic polyanions limits total ion loss and keeps [K⁺]_cyt and [Na⁺]_cyt nearly constant as cytosolic volume decreases ∼8%. Consistent with the objective of simplicity, no attempt was made to mimic Na/H-exchanger-mediated correction of stimulation-associated cytoplasmic shrinkage in isolated parietal cells (2), the modeled 0.01 cm³ aggregate cytosolic volume being restored with return to the resting state.

PPIs decrease total parietal cell secretion without ion channel inhibition.

A puzzling aspect of H-K-ATPase inhibition by a PPI (e.g., omeprazole) is that blocking of H⁺/K⁺ exchange in the stimulated state does not simply replace HCl secretion with equally voluminous KCl secretion. Sustained omeprazole treatment in vivo has been shown to drive parietal cells to a morphologically extreme stimulated state (13), a result seemingly caused by elevated serum gastrin that results, in turn, from decreased gastric acidity (25) and consistent with ion conductances remaining at stimulated levels. Experimentally, a PPI is usually introduced in a stimulated state to maximize its concentration and activation in the acidic canalicular space (12). Therefore, we have modeled PPI inhibition (Fig. 4) by starting in a fully stimulated state and then decreasing the pump rate sigmoidally (40) by 80%, with no decrease in ion conductances. Modeled parietal cell secretion drops toward resting levels. In human test subjects, omeprazole also greatly decreased total gastric secretion, but proportionately less than acid secretion (26).

Fig. 4.

Modeled 80% inhibition of pump by proton-pump inhibitor (PPI). A: strongly inhibiting exchange of K⁺ for H⁺ greatly decreases total secretion, rather than simply changing secretion from high HCl to high KCl (PPI added at time = 0). B: net apical K⁺ efflux transiently increases with inhibited back-pumping of K⁺ and no decrease in G_K, but eventually decreases as slower increase in [K⁺]_can decreases V_m−E_K. Transient increase in K⁺ secretion is smaller than increase in net apical K⁺ efflux, contributing to increase in [K⁺]_can. Decreased HCl secretion and high [K⁺]_can cause total secretion to decrease. (With G_K remaining high, stimulatory effect in Fig. 3D is not exactly inverted.) C: apical E_K and V_m are depolarized by rising [K⁺]_can, greatly decreasing the driving forces for conductive K⁺ and Cl⁻ efflux, while V_t is hyperpolarized.

Modeled inhibition of the pump starts decreasing K⁺ recycling, initiating a rise in [K⁺]_can. A slower decrease in conductive K⁺ efflux (due to slowly rising [K⁺]_can) follows and, without a decrease in G_K, is enough slower than the decrease in K⁺ recycling for both net apical K⁺ efflux and K⁺ secretion to increase transiently, but the latter increases less, as the faster decrease in pump rate decreases both total secretion and advective flushing of K⁺_can (Fig. 4B). Resulting rise in [K⁺]_can makes apical E_K and V_m less negative, reducing driving forces for conductive efflux of both K⁺ and Cl⁻ (Fig. 4C) even while G_K and G_Cl remain high, reversing the transient increase in K⁺ efflux and hyperpolarizing V_t. The decreasing total flow then keeps K⁺ secretion lower than apical K⁺ efflux, further raising [K⁺]_can until a steady inhibited state is reached. Since the pump does not directly drive a net flux of ions, its inhibition decreases total secretion essentially through elevation of [K⁺]_can, which could not occur without some length of gland lumen separating canaliculi from main gastric cavity.

The process resembles return to a resting state but without changes in ion conductance. In mounted mucosae, very strong pump inhibition has been seen to increase transmucosal resistance, but PPIs are not known to inhibit any ion channels (23) and the increased resistance is thought to result from decreased gland luminal diameter (not modeled here) at very low secretory rates (43, 44). Extended daily omeprazole dosing in adult rabbits gradually increased permeability of gastric secretory membranes to H⁺ (3), but only the simpler case of acute inhibition with no change in H⁺ permeability is modeled here.

Although the modeled 80% inhibition results in an ultimate decrease in K⁺ secretion, reported rates of K⁺ secretion during PPI inhibition have been mixed (24, 37). The model predicts that experimental measurements of K⁺ secretion would be affected by time for the PPI to take effect, the ultimate degree of inhibition, and the timing of secretory measurement. An initial increase is predicted at all levels of inhibition, its onset steeper with increasing strength of inhibition (Fig. 5), reflecting the time lag between decreasing K⁺ recycling and more slowly increasing [K⁺]_can. It is followed by a decline if inhibition is strong. When a steady inhibited state is reached, modeled [K⁺]_can has risen (as in Fig. 4) from a stimulated 14.7 mM to 16.7, 24.3, 38.9, and 56.9 mM, at 10, 40, 75, and 98% inhibition, respectively.

Fig. 5.

K⁺ secretion during onset of PPI inhibition. Initially, modeled K⁺ secretion increases (see also Fig. 4B), more steeply with stronger pump inhibition. It then remains elevated in the steady state during weak to moderate inhibition, but greatly decreases during strong inhibition. Ninety-eight percent inhibition is reached by 1 h.

In the steady inhibited state, K⁺ secretion may be higher or lower than the preceding stimulated rate, depending on a nonlinear relationship between V_m and E_K (varying in a Nernstian manner with [K⁺]_can) and the pump rate. Steady-state K⁺ secretion (as at far right of Fig. 5) for 25 runs of the model with inhibition ranging from 0 to 99% is shown in Fig. 6, along with pump rate and V_m−E_K. At weakest inhibition, decrease in steady-state V_m−E_K is proportionately less steep than the decrease in K⁺ recycling (pump rate), moderately increasing K⁺ secretion, but at highest inhibition it is much steeper, greatly decreasing K⁺ secretion. A low K⁺ secretion continues at strongest inhibition, with high [K⁺]_can driving a modest diffusive efflux.

Fig. 6.

Steady-state K⁺ secretion at increasing degrees of pump inhibition (0 to 99%) involves nonlinear (Nernstian) change in V_m−E_K. In the model, V_m−E_K decreases proportionately less steeply than pump rate with weak to moderate inhibition, but more steeply with strong inhibition, modestly increasing K⁺ secretion during <50% pump inhibition, but greatly decreasing K⁺ secretion during very strong inhibition.

Other factors may affect experimentally measured K⁺ secretion. When modeled H⁺ secretion is lowered to a rate typical of stimulated frog mucosa (∼5 μeq·h⁻¹·cm⁻²) (45) and the lumen is greatly shortened to mimic frog oxyntic cells closer to the gastric pits, 90% inhibition of stimulated H⁺ secretion slightly increases the sustained K⁺ secretion (not shown). Diffusive efflux of K⁺_can to the bath increases with decreased luminal length and [K⁺]_can is modestly lowered, increasing the driving force for conductive apical K⁺ efflux to match the increased diffusive flux. In these conditions, although advective K⁺ flux is decreased by pump inhibition, diffusive K⁺ efflux increases proportionately more, increasing net K⁺ secretion. In addition, with part of a low rate of H⁺ secretion by intact mucosae being neutralized by HCO₃⁻ from surface cells, actual inhibition might not be as complete as measured (41), thus not as far to the right of Fig. 6, where the modeled decrease in K⁺ secretion is most extreme.

The ex vivo canine preparation used by Larsen et al. (24) would seem closest to our model in that it was mammalian, with parietal cells farther separated from the mucosal bath than are frog oxyntic cells (16, 17), and it retained blood circulation for adequate supply of oxygen and nutrients to those cells. Examining 30-min cumulative secretion after initiation of various levels of intravenous omeprazole, they found that K⁺ secretion increased during weak to moderate inhibition, but decreased during strong inhibition, results qualitatively consistent with the model.

PPI inhibition and the electroneutral pump.

Inhibition by PPI is known to increase V_t (40), an effect that could be consistent either with a rise in [K⁺]_can (resulting from inhibited electroneutral H⁺/K⁺ exchange) depolarizing apical E_K and V_m (Fig. 4C), or with inhibition of electrogenic H⁺ pumping. Rehm et al. (45) calculated that, with a mounted frog mucosa in the stimulated state, raising [K⁺]_muc from 4 to 80 mM would raise [K⁺] to 64 mM 300 μm down a simply modeled lumen (full depth of frog gland). There could then be little further fractional increase in the [K⁺]_can/[K⁺]_cyt ratio with omeprazole, thus no significant increase in V_t due to further depolarization of E_K. Experimentally, they found that omeprazole inhibition increased V_t roughly the same with 4 and 80 mM K⁺_muc (11.4 and 14 mV, difference not significant) and deduced that the similar inhibitory ΔV_t at both [K⁺]_muc levels could only result from similarly decreased outward transport of positive charge by an electrogenic pump.

The argument relied partly on underestimated luminal flow of 15.9 μeq·h⁻¹·cm⁻². With the frog's ECF osmolarity of ∼210 mosM (17), secretory [H⁺] could not be much above ∼100 mM, requiring secretory flow of ∼42 μeq·h⁻¹·cm⁻² for their own reported H⁺ secretion of ∼4.2 μeq·h⁻¹·cm⁻². They overestimated luminal cross-sectional area as 0.035 cm² per cm² mucosa, requiring >10-μm diameter per lumen, given two glands per 100 μm (17), resulting in extremely low flow velocity of 0.000125 cm/s. Assuming that uninhibited H⁺/K⁺ exchange returns virtually all conductive apical K⁺ efflux to the cell, they treated back-diffusion of K⁺ from the bath as the only source of K⁺_can in the stimulated state and used a formula, expressed in our terms as [K⁺]_can = [K⁺]_muc·e^−vL/D, that yielded [K⁺]_can of 64 mM when [K⁺]_muc = 80 mM (with L = 0.03 cm and D = 1.7·10⁻⁵ cm²/s). Reasonable flow of 42 μeq·h⁻¹·cm⁻² and luminal diameter of 3 μm, with 40,000 glands/cm² (17), result in v ≈ 0.004 cm/s and, in their formula, [K⁺]_can of 0.07 mM.

In our more fully integrated model, [K⁺]_can is determined overwhelmingly by efflux of K⁺ and total liquid from the cell, rather than by back-diffusion of K⁺ from the bath, especially in the stimulated state. Table 2 shows [K⁺]_can, calculated by our model (with cells 200 μm from bath) in four conditions, stimulated (frog rate: v = 0.004 cm/s) or 98% inhibited (0.00008 cm/s), with 4 or 80 mM K⁺_muc. Raising [K⁺]_muc from 4 to 80 mM increases [K⁺]_can very little in the stimulated state (+2.6 mM), somewhat more in the inhibited state (+9.9 mM). Inhibition causes larger increases in [K⁺]_can, +20 mM with 4 mM K⁺_muc and even more, +27.3 mM, with 80 mM K⁺_muc, which would make apical E_K and V_m less negative and increase V_t with either [K⁺]_muc. Thus the reported experimental increases in V_t are consistent with an electroneutral pump.

Table 2.

Modeled effect of omeprazole inhibition on [K⁺]_can

[K+]muc	4 mM	80 mM
Stimulated	31.7	34.3
98% Inhibited	51.7	61.6

Modeled effect of omeprazole inhibition on [K⁺] (in mM) in canaliculi of cells 200 μm from a mucosal bath containing either 4 or 80 mM K⁺. Inhibition causes a substantial increase in cannicular [K⁺] ([K⁺]_can) with low or high mucosal [K⁺] ([K⁺]_muc), which would depolarize apical membrane voltage (V_m) and hyperpolarize transepithelial voltage (V_t) in both cases (frog secretion rates were used).

Voltage-clamp results do not support an electrogenic proton pump.

Formulas for voltage clamping and passage of constant current were added to the model, allowing it to mimic, but also explain, many reported electrophysiological results. Modeled ion secretion at various steady-state clamped V_t in the resting and fully stimulated states is shown in Fig. 7. As in experiments with mounted frog gastric mucosae (20), clamping to a V_t less mucosal-negative than open-circuit V_t increases Cl⁻ secretion (electrically negative but graphed as positive for comparison of magnitudes), with clamp current also graphed as charge flux (Eq/s = I/F). Ignoring a tiny apical Na⁺ leak in the modeled cell, clamp current is the negative of the charge sum of net Cl⁻, H⁺, and K⁺ secretion in resting or stimulated state. The current is seen as roughly matching the portion of Cl⁻ secretion that was long perceived as “nonacidic” and “active” in that it seemed unpaired to H⁺ and occurred even with no (or mucosal-negative) V_t, as well as against an m→s [Cl⁻] gradient.

Stronger mucosal-positive voltage clamping of a secreting frog mucosa, up to 150 mV, was reported to reduce H⁺ secretion nearly to zero, implying electrogenic proton pumping (39). With our model stimulated to 20% of maximal (conductances and H⁺ rate closer to frog), clamping up to 0 mV markedly decreases both K⁺ secretion and [K⁺]_can (Fig. 8), but minimally affects H⁺ secretion (see also Fig. 7). H⁺ secretion becomes steeply decreased as clamping approaches 122 mV, where [K⁺]_can drops to 0.6 mM, the modeled K_m, estimated from data in Lorentzon et al. (27), for activation of the pump by luminal K⁺. The effect is a Michaelis-Menten mechanism decreasing electroneutral pump activity as [K⁺]_can is driven very low by extreme hyperpolarization of apical V_m (−143 mV at clamped V_t of 122 mV). This mechanism is consistent with the frog results, which did not show a decrease in H⁺ secretion until clamped V_t reached 50 mV and, with further 25-mV steps, showed the largest decrease from 100 to 125 mV. According to the model, the Michaelis-Menten mechanism alone would not fully stop H⁺ secretion, even with V_t at 200 mV. Although some of the tested frog mucosae were reported to resume H⁺ secretion as the clamp was reduced from 150 mV, others were irreversibly damaged by clamping at 150 mV, suggesting that dielectric breakdown of the apical membranes (4) or some other nonspecific cell damage occurred near V_t of 150 mV (−163 mV modeled apical V_m), collapsing the apical [H⁺] gradient and further decreasing H⁺ secretion. Reported alkalinization of the mucosal medium under these conditions (39) may also have resulted from secretion of HCO₃⁻ through surface cells or through shunts opened by the voltage clamping.

Fig. 8.

Extreme mucosal-positive voltage clamping decreases H⁺ secretion by a Michaelis-Menten mechanism. In the model stimulated to 20% of maximal (open-circuit V_t = −25.6 mV), moderate steady-state voltage clamping only slightly affects H⁺ secretion, but greatly changes both K⁺ secretion and [K⁺]_can. H⁺ secretion is more steeply decreased when more extremely positive clamping pushes [K⁺]_can nearer the estimated K_m for pump activation, consistent with the effect in frog mucosa. Inhibition of H⁺ secretion seems not to be a direct electrical effect on cation efflux but a Michaelis-Menten effect of very low [K⁺]_can on the electroneutral pump. B expands the bottom part of A.

The long time-constant transient with clamping of voltage or current.

With experimental short-circuiting (SC) of a gastric mucosa, there is a slow initial change in applied current, lasting many seconds, rather than milliseconds, called the “long time-constant transient” (22, 43). Modeled SC in the resting state rapidly hyperpolarizes apical V_m (Fig. 9), enormously increasing the driving force (V_m−E_Cl) for purely conductive apical Cl⁻ efflux and sharply but transiently reversing the driving force (V_m−E_K) for conductive apical K⁺ flux. A sharp spike of clamp current decays from a peak, 26.9 μeq/h (0.72 mA), that is 2.7 times greater than the initial sharp increase in Cl⁻ secretion, with the spike reflecting a transient reversal of net cation flux, shown as net flux of K⁺ through the apical membrane into the cell. A net loss of K⁺_can, mostly to the cytosol, more slowly decreases [K⁺]_can from 47.4 to 16.5 mM (when [K⁺]_muc = 4 mM). Not shown is that K⁺ passes through the whole cell and the lost K⁺_can is replaced mostly by Na⁺ from the mucosal bath (145 mM Na⁺_muc).

Fig. 9.

Transient changes occurring at start of short circuit (“long time-constant transient”). Apical and basal membrane voltages are quickly brought to the same value (so V_t = 0). Driving force for Cl⁻ efflux (V_m−E_Cl) is greatly increased, while driving force for K⁺ flux (V_m−E_K) is transiently reversed, sending K⁺ back through cell (negative “net apical K⁺ flux”) and lowering [K⁺]_can. Decrease in [K⁺]_can more slowly hyperpolarizes E_K, further hyperpolarizing apical V_m. The latter makes an increasing contribution to short circuiting, requiring less current to maintain V_t = 0 (see text).

A new steady state is reached in which E_K is again more negative than V_m and K⁺ secretion returns to a small net s→m flux (if [K⁺]_muc <28 mM). In that steady state, the driving force for apical Cl⁻ efflux has been further increased and nearly all the ion flux to balance the steady-state SC current is the increased s→m flux of Cl⁻ (see also Fig. 7). In a modeled stimulated state, SC reaches a steady state much more quickly (not shown), because open-circuit V_t is closer to zero, apical G_K is higher, and Δ[K⁺]_can is much smaller (14.7→10.7 mM).

During the initial adjustment to steady-state SC, the modeled ion conductances do not change, so transepithelial resistance (R_t) should not change. Yet, while the current decays, R_t calculated with Ohm's law, from ΔV_t/ΔI, would increase. Durbin and Heinz (7) skeptically mentioned the possibility of huge and slow capacitative charge accumulations, a possibility later more quantitatively rejected by Rehm et al. (43). The alternate explanation proposed by Durbin and Heinz was a slow change in any electromotive force (emf) within the mucosa, which would make an increasing contribution to the ΔV_t, entailing a compensatory change in the applied current to keep clamped V_t constant. The model locates the slowly changing emf mainly in apical E_K. With initial hyperpolarization of apical V_m driving a loss of [K⁺]_can, the decreasing [K⁺]_can/[K⁺]_cyt ratio further hyperpolarizes apical E_K and V_m, with basolateral V_m also changing as V_t = 0 (Fig. 9). SC is maintained in the subsequent steady state by the combined effect of a decreased externally applied current and the added emf of hyperpolarized apical E_K. The very beginning of SC is the only point at which V_t is driven to zero solely by the applied current. With the use of ΔV_t and ΔI from the model to calculate resting R_t, 35.19 mV divided by the steady-state current of 0.36 mA/cm² after the initial spike yields 97.7 Ω·cm². Using the peak current of 0.7211 mA/cm² (first 0.01 s) results in 48.80 Ω·cm², very closely approaching the R_t calculated from the resting ion conductances (Table 1) converted to resistances (R_Bas = 17.544 Ω·cm²; R_Ap = 31.233 Ω·cm²; total = 48.777 Ω·cm²). The model thus supports and explains the established experimental method of determining R_t from ΔV_t/ΔI measured during very brief (≤1 s) current pulses during an otherwise steady open-circuit state (43).

While seen as a slow decay of current after initiation of voltage clamp, the long time-constant transient manifests itself as a slow change in V_t after initiation of constant current. Durbin and Heinz (7) showed that, when a constant current was passed through a frog gastric mucosa, there was a sudden change in V_t, but V_t then continued to change more gradually in the same direction, at an exponentially decreasing rate, until a new steady state was reached in 2–3 min. A mirrored reversal of these V_t changes occurred when the current was stopped, while an opposite current inverted the entire pattern. Later, Kidder and Rehm (22) and Rehm et al. (43) reported a similar result and proposed a mathematical model to account for the slow V_t changes. Although they perceived the phenomenon to involve “polarization of emfs,” their model was far from physiological, with KCl the only ions in bathing media and basolateral E_K altered by a substantial change in [K⁺]_cyt. Kidder and Rehm acknowledged that homeostatic mechanisms would make large changes in [K⁺]_cyt unlikely in a real cell, so the experimental result remained inadequately explained.

Those reported V_t changes are closely matched in our model (Fig. 10), but [K⁺] changes 11.5% in the small canalicular space and negligibly in the cytosol, with the major change in emf being in apical, rather than basolateral, E_K. A −41-μA constant current (direction opposite to that for short-circuiting, slightly depolarizing apical V_m) causes an initial 2-mV hyperpolarization of V_t followed by the further long time-constant polarization and recovery after the end of the current pulse, all in the resting state. In this case, initial depolarization of apical V_m suddenly increases the driving force (V_m−E_K) for conductive K⁺ efflux, causing a transient excess of net apical K⁺ efflux over more moderately increased K⁺ secretion. A resulting rise in [K⁺]_can slowly depolarizes apical E_K and further depolarizes V_m, but the former more than the latter, decreasing V_m−E_K. This brings net apical K⁺ efflux back toward the rate of K⁺ secretion, while slowly hyperpolarizing V_t toward a new steady state, reached in ∼3 min. When the current stops, these changes are reversed, with net apical K⁺ efflux transiently lower than K⁺ secretion, decreasing [K⁺]_can to its open-circuit resting level in ∼3 min.

Fig. 10.

The long time-constant polarization following initiation or ending of constant current is explained by slow changes in [K⁺]_can. A constant current of −41 μA causes rapid initial hyperpolarization of V_t and depolarization of apical V_m, followed by slower change in E_K and V_m as [K⁺]_can rises due to transient spike of apical K⁺ efflux exceeding K⁺ secretion. Rising [K⁺]_can brings apical K⁺ efflux back toward K⁺ secretion in ∼3 min. Changes are inverted after end of current. Driving force for conductive apical K⁺ flux (V_m−E_K) is shown in mV at several points. When current stops, “net apical K⁺ flux” transiently drops lower than might be expected from V_m−E_K, since it is conductive flux minus back-pumped K⁺.

Mimicking of these experiments with a model that lacks other cell types and tight junctions is consistent with an interpretation that parietal/oxyntic cells dominate the total conductance of the acid-secreting mucosa (43) and that tight junctions are very “tight” (50), as they can sustain a million-fold Δ[H⁺] in the stimulated state. Kidder and Rehm (22) used only −10 μA with frog mucosa to cause the initial ΔV_t of 2 mV, which required −41 μA in our model. This might be expected since adult mammals have a much higher maximal gastric secretory rate per cm² mucosa (45) and more extensive canaliculi (10, 14), both consistent with higher total ion conductance. When all resting conductances in the model are halved and the system has stabilized to a new resting V_t, half as much current drives the same initial ΔV_t, but with a longer time constant for the slow hyperpolarization, because of slower K⁺ flux through lower G_K. However, when the canalicular space is halved with conductances unchanged, the time constant is shortened, since the slow hyperpolarization requires half as much net K⁺ flux into the canaliculus to achieve the same increase in [K⁺]_can. That our first effort to mimic constant current yielded results so closely matching the Kidder and Rehm results in shape and timing might be attributed to a felicitous combination of smaller canalicular volume and lower ion conductance in the frog.

The output of the model, especially this mimicking and explaining of the long time-constant transient, indicates that the many simplifications in the model do more than merely ease the difficulty of its construction. They enable the fundamental results of ion flux through the compartmental sequence of cytosol, canaliculus, gland lumen, and mucosal bath to emerge clearly from what might otherwise be a “background noise” of many other variables at work in intact tissue.

Conclusion.

A dynamically functioning model in which all components must work interactively and that can adjust to changes in selected parameters by seeking, and stabilizing at, a new state in a manner consistent with experimental results can help us to understand underlying processes that yield those results by showing exactly what each component is doing. While the model presented here offers new insights into Cl⁻ transport by the parietal cell, the major revelation is the functional significance of a canalicular space at some distance from the gastric cavity.

Because the canalicular space is extracellular, but completely isolated from the main pool of ECF, it is not subject to the homeostatic mechanisms that keep [K⁺] and [Na⁺] narrowly controlled in cytosol and ECF. With the gland lumen imposing a diffusional restriction between canaliculi and mucosal bath in the resting state and with high outward advective flow in the stimulated state, canalicular ion concentrations not only can be quite different from those in cytosol and mucosal bath, but can change greatly between resting and stimulated states or when a current is passed through a mounted mucosa. The model reveals how and why such changes occur, most significantly in [K⁺]_can, along with electrical effects seen to be consistent with an electroneutral H-K-ATPase, thus helping to explain some previously puzzling experimental results.

Although having acid-secreting cells in long, tubular glands clearly increases the number of such cells per unit area of gross mucosa, compared with a flat epithelium, the model now shows the important functional advantage of separating those cells from the main gastric cavity. The clustering of acid-secreting cells at a medium depth in the mammalian gland, compared with the more uniform distribution in shallower frog glands, may reflect a gradual evolutionary selection of that advantage.

The model should now provide a useful framework for examining more extreme experimental manipulation of ion concentrations in bathing media and for prediction of the integrated functioning of additional, or more specifically characterized, ion-transport mechanisms.

GRANTS

This work was supported by National Institute of Diabetes and Digestive and Kidney Diseases Grant AM-10141-34.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

J.M.C. and J.G.F. conception and design of research; J.M.C. performed experiments; J.M.C., J.G.F., and T.E.M. analyzed data; J.M.C., J.G.F., and T.E.M. interpreted results of experiments; J.M.C. prepared figures; J.M.C. drafted manuscript; J.M.C. and T.E.M. edited and revised manuscript; J.M.C. and T.E.M. approved final version of manuscript.