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Ouabain modulation of cellular calcium stores and signaling

¹Department of Chemical and Biological Engineering, Tufts University, Medford, Massachusetts; and ²Departments of Medicine and Physiology, University of Maryland School of Medicine, Baltimore, Maryland

Submitted 30 May 2007 ; accepted in final form 27 July 2007

	ABSTRACT

TOP ABSTRACT METHODS RESULTS DISCUSSION REFERENCES

 
Ouabain-like factors modulate intracellular Ca²⁺ concentrations and Ca²⁺ stores. Recently, a role for Na⁺-K⁺-ATPase Na⁺ transport inhibition as a pivotal event in ouabain signaling was questioned (Kaunitz JD. Am J Physiol Renal Physiol 290: F995–F996, 2006). In the present study, we used a mathematical model of Ca²⁺ trafficking in cytoplasm and subplasmalemmal microdomains to simulate the pathways through which ouabain can affect Ca²⁺ signaling: inhibition of active transport by Na⁺-K⁺-ATPase ₁- and ₂-isoforms, activation of inositol trisphosphate (IP₃) production, and increased IP₃ receptor (IP₃R) conductance. A fundamental prediction is that Na⁺-K⁺-ATPase inhibition favors sarcoplasmic reticulum Ca²⁺ store loading, whereas Src-mediated increases in IP₃ production and IP₃R sensitization favor store depletion. The model predicts that ₂-isoform inhibition generates a peak-and-plateau pattern of cytosolic Ca²⁺ concentration ([Ca²⁺]_cyt) elevation, whereas ₁-isoform inhibition yields a monophasic rise. The effects of ouabain-mediated increases in IP₃ production or IP₃R conductance on [Ca²⁺]_cyt depend on their relative distributions between cellular microdomains and the bulk cytoplasm. Simulations suggest that the intracellular localization of IP₃ production is a pivotal determinant of the changes in compartmental Ca²⁺ concentrations that can be induced by ouabain. As a consequence of sequestration of the ouabain-sensitive ₂-isoform into microdomains, inhibition of the ₂-isoform in rodents is not predicted to significantly affect cytosolic Na⁺ concentration. Model simulations support the hypothesis that ouabain can enhance agonist-evoked [Ca²⁺]_cyt transients when its predominant effect is to inhibit ₂-isoform Na⁺ transport and, thereby, increase Ca²⁺ loading into sarcoplasmic reticulum stores.

sodium-potassium-adenosine triphosphatase; sodium-calcium exchange; inositol trisphosphate; pericyte; mathematical model

Recently, we provided a mathematical simulation of Ca²⁺ trafficking between the extracellular space, subplasmalemmal microdomains, SR stores, and cytoplasm in vascular smooth muscle cells (VSMC) (13). The model accounted for major ion transport pathways, IP₃ production, IP₃R and ryanodine receptor (RyR) sensitization, intracellular Ca²⁺ buffering, and localization of ouabain-sensitive ₂-isoform Na⁺ pumps into putative subplasmalemmal microdomains. The model successfully predicted that [Ca²⁺]_cyt and the magnitude of SR store loading with Ca²⁺ can be modulated by variation of the activity of microdomain Na⁺ pumps. To achieve the latter effect, it proved critical to sequester microdomains, so as to limit diffusional exchange of Na⁺ with the "bulk" cytoplasm (4, 6, 19). Given the importance of ouabain-like factors (OLF) in the modulation of Ca²⁺ signaling and hypertension, we have investigated the predictions of the model with respect to the actions of ouabain to inhibit microdomain ₂-isoform Na⁺ pumps (6) and/or activate IP₃ production after Src kinase activation (42). The simulations support the contention that isolated inhibition of Na⁺ pumps by ouabain can elevate [Ca²⁺]_cyt and enhance loading of Ca²⁺ into the SR. Interestingly, however, the model predicts that the SR Ca²⁺ content will be limited, or even depleted, if IP₃ production and IP₃R activation are the dominant effects of the interaction of ouabain and Na⁺-K⁺-ATPase.

	METHODS

TOP ABSTRACT METHODS RESULTS DISCUSSION REFERENCES

 
Our model accounts for the characteristics of the channels, transporters, and pumps that exchange ions between the extracellular space, the bulk cytosol, the microdomains, and SR stores. These compartments are denoted by the superscripts or subscripts "out," "cyt," "md," and "sr," respectively.

As described previously (see Fig. 1 in Ref. 13), the following channels and pumps are taken to be uniformly distributed over the plasma membrane: inward rectifier K⁺ channels, delayed rectifier K⁺ channels, ATP-activated K⁺ channels, Ca²⁺-activated K⁺ channels, voltage-activated Na⁺ channels, nonselective cation channels, Ca²⁺ pumps, and L-type voltage-dependent Ca²⁺ channels. In contrast, we assume that the ₂-isoforms of Na⁺-K⁺-ATPase pumps (I_NaK,2) and the NCX are expressed exclusively in the region of the cell membrane directly above the microdomains, whereas the ₁-isoforms (I_NaK,1) are restricted to the region of the cell membrane directly above the bulk cytosol (4, 6, 19). The interfaces between the SR and cytosol and between the SR and microdomains are populated by sarco(endo)plasmic reticulum Ca²⁺-ATPase (SERCA) pumps, RyR, and IP₃R.

View larger version (6K): [in this window] [in a new window]   Fig. 1. Intracellular Ca2+ and Na+ concentrations ([Ca2+] and [Na+]) as a function of time (in seconds). At 300 s, the 2-isoform of Na+-K+-ATPase is entirely inhibited. Inhibition of the 2-isoform elevates microdomain [Na+] ([Na+]md), thereby reducing current through Na+/Ca2+ exchangers (NCX) and raising microdomain [Ca2+] ([Ca2+]md). Ensuing increase in Ca2+ uptake by microdomain sarco(endo)plasmic reticulum Ca2+ (SERCA) pumps results in sarcoplasmic reticulum (SR) Ca2+ loading, which increases Ca2+ release by the inositol trisphosphate (IP3) receptor (IP3R) at the SR-cytosol interface to favor elevation of cytosolic [Ca2+] ([Ca2+]cyt).

Where possible, inputs for the model were taken from recent studies of descending vasa recta pericytes (7, 8, 28) and cerebrovascular arteries (40). When parameters were not available for VSMC, they were extrapolated from data for cardiac cells (24, 33). Equations describing ionic currents across Na⁺-K⁺-ATPase pumps, NCX, store-operated channels (SOC), IP₃R, and SERCA pumps are summarized below. All other model equations and parameter values can be found in the previous study (13). The predicted resting values of all 44 variables of the model are summarized in Table 1. The adopted convention is that exit of positive charge from the cell is a positive current.

(1)

(2)

(3)

(4)

where [Na⁺] and [K⁺] represent Na⁺ and K⁺ concentration, respectively, V_m is transmembrane potential, K_m,K is K⁺ half-saturation constant, K_m,Na,1 and K_m,Na,2 are Na⁺ half-saturation constants for Na⁺-K⁺-ATPase ₁- and ₂-isoform currents, is ionic potential, F is Faraday's constant, R is gas constant, T is temperature, and is electrical conductivity. The maximum currents through the ₁-isoform (I_NaK,1,max) and the ₂-isoform (I_NaK,2,max) are estimated as 15.8 and 2.37 pA, respectively (13). Implicit in the calculations is the assumption that the ratio of the number of ₂- to ₁-isoforms is 20:80, as reported for astrocytes (14) and mesenteric arteries (44), and that the ratio of ₂- to ₁-isoform turnover is 0.6 (32). The values of K_m,K, K_m,Na,1, and K_m,Na,2 are taken as 1.5, 12, and 22 mM, respectively (24, 43).

NCX current. We assume that all NCX are localized above the microdomains (4, 6, 19). We assume that NCX has asymmetric affinities on the internal and external sides of the membrane and that the NCX current (I_NaCa) is given by

(5)

(6)

(7)

(8)

(9)

The maximum current (I_NaCa,max) is taken as 200 µA/µF (i.e., 2.42 x 10³ pA), the external and internal half-saturation constants for Na⁺ and Ca²⁺ (K_m,Nao, K_m,Nai, K_m,Cao, and K_m,Cai) as 87.5 mM, 12.29 mM, 1.3 mM, 3.59 µM, respectively, the constant for NCX (K_d-Act) as 0.256 µM, the NCX saturation factor at negative potential (k_sat) as 0.27, and the constant for voltage dependence of NCX () as 0.35 (33).

SOC current. Decreases in SR Ca²⁺ load stimulate SOC activity. The SOC Ca²⁺ current in compartment j [I(j = cyt or md)] is calculated as

(10)

where G is maximum conductance of the SOC Ca²⁺ current and the Nernst potential (E) of ion i (valence z_i) is calculated on the basis of the concentration difference between the extracellular compartment and the intracellular compartment j (j = cyt or md)

(11)

where [i] is ion concentration. We assume a Ca²⁺-to-Na⁺ permeability ratio (P/P) = 8, and we use the Goldman-Huxley-Katz current equation to relate the SOC Na⁺ and Ca²⁺ currents in compartment j

(12)

The maximum Ca²⁺ conductances of cytosolic and microdomain SOC are taken as 20 and 3.5 pS, respectively, and the value of K_SOC is taken as 100 µM (13).

IP₃R release current. Following the approach of De Young and Keiser (9), the net generation of IP₃ in compartment j is calculated as

(13)

where ₄ is the maximum rate of IP₃ production, I_r is the rate constant for IP₃ consumption, [IP] is a constant, and ₄ determines the strength of the Ca²⁺ feedback on IP₃ production. The parameters I_r and k₄ are taken as 1 s^–1 and 1.1 µM (9), respectively, and we assume that ₄ = 0.5. The baseline value of ₄ is chosen as 1.84 s^–1, so that the resting value of [IP₃]_cyt is equal to [IP], i.e., 240 nM (9). I_IP3R in compartment j [I(j = cyt, md)] is then calculated as

(14)

where ₁ is the Ca²⁺ conductivity of IP₃R, x₀₁₀ is the fraction of receptors bound by one activating Ca²⁺, d₁ is a ratio of kinetic rate constants (0.13 µM), and vol_sr is the SR volume (0.07 pl). The baseline value of ₁ is taken as 6 s^–1 (9), and x₀₁₀ is calculated as described previously (13).

SERCA pump current. We assume that the SERCA pumps are located at the cytosol-SR interface and the microdomain-SR interface and that the uptake current depends on concentrations on the internal and external sides of the SR membrane

(15)

where I is SERCA pump current (j = md or cyt) and f is fraction of membrane surface above microdomain or cytosol. The maximum current (I_SERCA,max) is chosen as 100 pA, a midrange value (33, 40). The forward and reverse half-saturation constants (K_mf and K_mr) are taken as 400 nM and 1.7 mM, respectively, and the Ca²⁺-ATPase constant (H) as 1.787 (13).

Electrodiffusive flux from microdomain to cytosol. The electrodiffusive flux of ion i (J_i,diff) is calculated as follows, such that J_i,diff yields a positive current into the cytosol when cations flow down their electrochemical gradient from microdomain to cytosol

(16)

(17)

(18)

where A is the cross-sectional area at the interface between the microdomains and the cytosol (taken as 7.8 x 10^–9 cm²), D_i is the diffusivity of ion i, L is the distance from the center of the microdomains to the center of the cytosol (estimated as 0.5 µm), _i is normalized electrical potential difference, h is a hindrance factor (0 h 1) that lumps together steric and charge-related effects and P_i,diff is a permeability (in m/s). The whole cell diffusivity of Ca²⁺ is taken as 0.3 x 10^–5 cm²/s. The Na⁺-to-Ca²⁺ and K⁺-to-Ca²⁺ diffusivity ratios are assumed to be 1.33:0.79 and 1.96:0.79, i.e., the ratios of the diffusivities in dilute solution. The baseline value of h is chosen as 2.5 x 10^–3 (13) to reflect significant sequestration of the microdomains from the bulk cytosol. Note that the electrodiffusive current of ion i is given by I_i,diff = z_iF·J_i,diff.

Numerical methods. As described previously (13), the values of the 44 model variables are obtained by solving a system of ordinary differential equations. The latter is programmed with MATLAB and solved numerically on a personal computer with an Intel-based processor.

	RESULTS

TOP ABSTRACT METHODS RESULTS DISCUSSION REFERENCES

 
To investigate the relative importance of hypothetical mechanisms by which ouabain might alter Ca²⁺ signaling, we sequentially examined its predicted effects on Na⁺-K⁺ATPase activity, IP₃ production, and IP₃R conductance. For convenient reference, to facilitate the interpretation of the results, the progression of the simulations is summarized in Table 2.

₂-Isoform inhibition.

View larger version (13K): [in this window] [in a new window]   Fig. 2. Ionic currents (in pA) as a function of time (in seconds). At 300 s, the 2-isoform of Na+-K+-ATPase is entirely inhibited. Solid and dashed-dotted lines denote cytosolic and microdomain currents, respectively. INaK, current through Na+-K+ATPase pumps; INaCa, current through NCX; Idiff, electrodiffusive current between microdomains and cytosol; ISOC, current through store-operated channels (SOC); ISERCA, current through SERCA pumps; IIP3R, current through IP3 receptors (IP3R). Current through the ryanodine receptor (RyR) is negligible in comparison and not shown.

View larger version (9K): [in this window] [in a new window]   Fig. 3. Increases in [Ca2+]cyt, relative to its resting value, after graded inhibition of the 1- or 2-isoform.

₁-Isoform inhibition.

Inhibition of the ₁-isoform raises [Na⁺]_cyt sufficiently (cf. Fig. 4 with Fig. 1) to reverse the direction of the intercompartmental electrodiffusive Na⁺ flux (Eqs. 16–18), which then carries Na⁺ from the cytosol into the microdomains. The subsequent large rise in [Na⁺]_md reverses the operating mode of NCX, which then exports Na⁺ and imports Ca²⁺ into the microdomains. The ensuing rise in [Ca²⁺]_md enhances Ca²⁺ loading into the SR, thereby stimulating RyR- and IP₃R-mediated Ca²⁺ release into the cytosol, markedly elevating [Ca²⁺]_cyt. Thus, despite the presumed lack of NCX above the cytosol, ₁-isoform inhibition is predicted to have a marked effect to elevate [Ca²⁺]_cyt.

View larger version (7K): [in this window] [in a new window]   Fig. 4. Intracellular [Ca2+] and [Na+] as a function of time (in seconds). At 300 s, the 1-isoform of Na+-K+-ATPase is entirely inhibited. Time scale is longer than in Fig. 1. Inhibition of the 1-isoform raises [Na+]cyt sufficiently to reverse the direction of the intercompartmental electrodiffusive Na+ flux, thereby significantly raising [Na+]md. Subsequent NCX-mediated rise in [Ca2+]md enhances Ca2+ loading into the SR, thereby stimulating RyR- and IP3R-mediated Ca2+ release into the cytosol and markedly elevating [Ca2+]cyt.

IP₃ production. In the above-described simulations, there is only limited stimulation of IP₃ production, resulting solely from [Ca²⁺]_md and [Ca²⁺]_cyt elevations and the resultant feedback effect of Ca²⁺ that enhances PLC activity. In contrast, it has been shown that ouabain can independently phosphorylate PLC-₁ downstream of Src kinase activation (30, 42). In LLC-PK₁ cells, this has been shown to increase the production of IP₃ and is accompanied by tyrosine phosphorylation of the type 2 isoform of IP₃R, presumably enhancing its sensitivity to IP₃ (42). To distinguish the consequences of these two Src-stimulated effects of ouabain (henceforth denoted "Src-related effects") from ouabain-mediated inhibition of Na⁺ pump isoforms, we separately examined stimulation of IP₃ production and enhancement of IP₃R conductance as isolated events, without the accompanying ₁- or ₂-isoform inhibition (Table 2).

In LLC-PK₁ cells, 100 nM ouabain increased phosphatidylinositol bisphosphate hydrolysis and IP₃ production by 50–100% (see Fig. 5 in Ref. 42). We simulated this increase in phosphatidylinositol bisphosphate hydrolysis and IP₃ production by increasing the production rate of IP₃ through an increase in the parameter ₄ in Eq. 13. Figure 5 shows the effect of a 100% increase in ₄ starting at t_s = 300 s on intracellular IP₃ and ion concentrations. Data describing the time dependence of changes in IP₃ concentration after ouabain stimulation are not available. We therefore examined two cases: 1) a long-lasting, 100% increase

(19a)

and 2) a very rapid increase in ₄ followed by a slow exponential decrease toward a plateau level that remains 10% higher than the preinhibition level

(19b)

After the step change in ₄, IP₃ concentrations in cytosol and microdomain ([IP₃]_cyt and [IP₃]_md) rise rapidly in both cases, from 240 and 251 nM to 500 and 570 nM, respectively. Note that [IP₃]_md > [IP₃]_cyt, since [Ca²⁺]_md > [Ca²⁺]_cyt and, therefore, exerts a greater stimulation of IP₃ production. As IP₃R-mediated Ca²⁺ release subsequently increases, [Ca²⁺]_cyt and [Ca²⁺]_md rise rapidly and [Ca²⁺]_sr drops sharply to 45 µM. The subsequent increase in the rate of Ca²⁺ uptake by SERCA pumps halts the [Ca²⁺]_cyt and [Ca²⁺]_md increase, accounting for the first, brief peak. The first [Ca²⁺]_cyt and [Ca²⁺]_md transient is followed by a more significant peak-and-plateau effect, as unloading of SR Ca²⁺ stores increases transmembrane SOC currents, thereby greatly increasing Ca²⁺ import into the bulk cytosol. In the absence of cytosolic SOC channels, this secondary peak would be negligible (dashed-dotted line on the [Ca²⁺]_cyt profile in Fig. 5). Furthermore, the increase of the SOC current significantly raises [Na⁺]_md and [Na⁺]_cyt, activating Na⁺-K⁺-ATPase. A pertinent conclusion is that, for nanomolar ouabain to induce a change in [Na⁺]_cyt, activation of IP₃ production would have to accompany the inhibition of the ouabain-sensitive Na⁺ pump ₂-isoform (cf. Fig. 1 with Fig. 5).

View larger version (13K): [in this window] [in a new window]   Fig. 5. Intracellular [Ca2+], [Na+], and IP3 concentration ([IP3]) as a function of time (in seconds). At 300 s, IP3 production (4) is increased everywhere by a factor of 2 (A). Increase in 4 is sustained in time (see Eq. 19) (B). Step increase in 4 is followed by a slow exponential decrease (see Eq. 19b). Note varying time scales. Dashed-dotted line represents [Ca2+]cyt temporal variations predicted in the absence of cytosolic SOC channels. These simulations suggest that IP3 production reduces SR Ca2+ stores.

The model also predicts that the intracellular localization of IP₃ production is a pivotal determinant of the changes in compartmental Ca²⁺ concentrations that can be induced by ouabain. Figure 6 shows a simulation in which ouabain-stimulated IP₃ production (i.e., 100% increase in ₄) occurs only in the cytosol, and not in the microdomains. In that case, the ouabain-induced increase in [Ca²⁺]_cyt is predicted to be much greater. The peak rise is 260 vs. 165 nM, stimulation in the cytosol vs. both compartments. The reason is that when IP₃ production increases in both compartments, the depletion of SR stores is greater, thereby limiting the availability of Ca²⁺ that can be released to the cytosol. Specifically, when IP₃ production is stimulated in both compartments, store Ca²⁺ falls from 0.674 fg to 0.247 or 0.598 fg (sustained vs. transient stimulation, Eq. 19, a and b, respectively). In contrast, when IP₃ production is stimulated in the cytosol alone, store Ca²⁺ drops to only 0.381 or 0.639 fg.

View larger version (8K): [in this window] [in a new window]   Fig. 6. Effect of a transient 2-fold increase in 4 (i.e., IP3 production) on [Ca2+]cyt when IP3 production increases in cytosol and microdomains, in cytosol only, or in microdomains only. In isolation, microdomain IP3 production reduces [Ca2+]cyt. When combined with cytosolic IP3 production, it blunts [Ca2+]cyt elevation. Intracellular location of IP3 production is predicted to be a pivotal determinant of ouabain-stimulated changes in compartmental [Ca2+].

Increase in IP₃R conductance. Studies suggest that ouabain also increases the sensitivity of the IP₃R through its tyrosine phosphorylation by Src kinase (42). We modeled this effect by varying ₁, the Ca²⁺ conductivity of IP₃R (Eq. 14). The dependence of ₁ on time was modeled according to Eq. 19, a and b (i.e., a sustained elevation or an abrupt increase followed by an exponential decay). Again, simulations were performed as an isolated effect, without simultaneous inhibition of transport by Na⁺-K⁺-ATPase (Table 2).

The effects of a twofold increase in ₁ on intracellular Ca²⁺ and Na⁺ concentrations are similar to those of a twofold increase in ₄, albeit smaller in magnitude. After an increase in ₁, Ca²⁺ release via IP₃R rises, leading to elevation of [Ca²⁺]_cyt and [Ca²⁺]_md, which results in concomitant increases in [IP₃]_cyt and [IP₃]_md via Ca²⁺ stimulation of IP₃ production. The model predicts that the ₁-mediated increases in I and I immediately following the step change are significantly smaller than the equivalent ₄-mediated increases (3.6 and 3.7 vs. 13.1 and 11.8 pA, respectively) and, hence, the lower [Ca²⁺]_md peak (300 nM) and the smaller [Ca²⁺]_cyt rise (115 nM) mediated by the former. Since the depletion of SR Ca²⁺ stores and the subsequent SOC stimulation are less significant (Table 3), the elevations of [Na⁺]_cyt and [Na⁺]_md are also lower.

As in the case of increasing IP₃ production (see above) the [Ca²⁺]_cyt increase would be higher if the enhancement of IP₃R conductance occurred only in the cytosol, and not in the microdomains. Conversely, [Ca²⁺]_cyt would decrease if the change in IP₃R conductance occurred only in the microdomains (results not shown).

Concentration-dependent effects of ouabain on IP₃ production and IP₃R conductance. Graded increases in ouabain concentration, from the physiological (pM to nM) to the pharmacological (mM) range, are often used to test its experimental effects. To examine parallel modeling predictions, we performed simulations driven by the following assumptions.

The effect of ouabain on ₄ and ₁ was estimated on the basis of the experimental data of Yuan et al. (42) in porcine LLC-PK₁ cells, where the Na⁺-K⁺-ATPase ₁-isoform is ouabain sensitive. In their experiments with 100 nM ouabain, they found that 1) ouabain enhanced the interaction between the ₁-isoform and PLC-₁ approximately twofold (see Fig. 3 in Ref. 42), which we simulated as a rise in ₄ of 13, and 2) ouabain enhanced tyrosine phosphorylation of IP₃R and the interaction between the ₁-isoform and IP₃R approximately twofold, which we simulated as a rise in ₁ of Eq. 14.

Given that the effects of ouabain on the interactions between the ₁-isoform and PLC-₁ and between the ₁-isoform and IP₃R are comparable in magnitude (cf. Figs. 3C and 6D in Ref. 42), we calculated their average and assumed for simplicity that variations in ₄ and ₁ are equal. We then extrapolated the results to correlate relative increases in cytosolic ₄ and ₁ (RI_,cyt) to the percentage of ₁-isoform inhibition (PI₁) as described in Table 4. The concentration of ouabain that inhibits 50% of the pump activity (IC₅₀) in LLC-PK₁ cells was taken as 1 µM (15). The data were best fitted to a power law, and the following regression equation was obtained

(20)

View this table: [in this window] [in a new window]   Table 4. Relationship between percent 1-isoform inhibition and 4 and 1 increases in the cytosol

50,i

Src-related effects of ouabain on the ₂-isoform.

2

,md

,md

,md

View larger version (8K): [in this window] [in a new window]   Fig. 7. Predicted effects of stimulation with 10 nM ouabain (at 300 s) on intracellular [Ca2+] and [Na+], where ouabain inhibits Na+-K+-ATPase, stimulates IP3 production, and enhances IP3R conductance (Table 2). In case A, IP3-related effects of ouabain binding to the 2-isoform are identical to those of the 1-isoform. In case B, IP3-related effects of ouabain binding to the 2-isoform are 10% smaller than those of the 1-isoform. In case C, ouabain stimulates cytosolic (1-isoform-mediated) but not microdomain (2-isoform-mediated) IP3 production and IP3R conductance. Ouabain-mediated effects on 4 and 1 were taken to decrease with time (according to Eq. 19b) in these simulations and the remainder of this study. These simulations predict that microdomain IP3 production (case A) decreases [Ca2+]cyt, because significant diminution of SR Ca2+ stores accompanies [Ca2+]md elevation.

Clearly, model predictions based on the assumptions of case A are not compatible with those experimental measurements (31, 42) that have shown a peak-and-plateau pattern of [Ca²⁺]_cyt elevation on ouabain application. The model predicts such a pattern at 10 and 100 nM only when microdomain IP₃ production and IP₃R sensitization are minimal, as in cases B and C.

We then examined the effects of varying other parameters: the affinity of the ₁- or ₂-isoform to ouabain, the time constant characterizing the exponential decay of ₄ and ₁ following the step increase (Eq. 19b), and the distribution of NCX between the microdomains and the cytosol. Since the initial [Ca²⁺]_cyt drop is due to the transient depletion of SR Ca²⁺ stores, the subsequent variations in IP₃R-mediated Ca²⁺ release into the cytosol, and Ca²⁺ uptake into the SR, we also varied the rate of SERCA uptake. In all those cases, the predicted [Ca²⁺]_cyt pattern corresponded to experimental observations only in cases B and C (results not shown). We therefore subsequently focused on simulations where the binding of ouabain to the ₂-isoform has a minimal effect to stimulate microdomain IP₃ production or microdomain IP₃R conductance.

Dose-dependent effects of ouabain on [Ca²⁺]_cyt and [Na⁺]_cyt. With baseline parameters, [Ca²⁺]_cyt is predicted to peak at 121 nM after application of 10 nM ouabain (Fig. 7, case C), whereas [Na⁺]_cyt variations are negligible. Indeed, the ₁-isoform is inhibited by only 0.1% at that concentration. As expected, stimulation with 100 nM ouabain (i.e., 1% ₁-isoform inhibition) is found to elicit a higher [Ca²⁺]_cyt peak (145 nM) and equilibrium value (117 nM); [Na⁺]_cyt is not predicted to vary significantly.

At >10 µM ouabain, ₁-isoform inhibition becomes significant, and the [Ca²⁺]_cyt profile is concomitantly altered (Fig. 8A). As an isolated effect, ₁-isoform inhibition raises [Ca²⁺]_cyt monotonically (Fig. 4), whereas a peak-and-plateau pattern emerges when it is combined with a step increase in cytosolic ₁ and/or ₄ (IP₃R conductance and IP₃ production, respectively; Fig. 5). Stimulation with <1 µM ouabain does not significantly inhibit the ₁-isoform, hence, the predicted [Ca²⁺]_cyt peak-and-plateau pattern. If ouabain concentration is >10 µM (the value of IC₅₀ for the ₁-isoform in rodents), then ₁-isoform inhibition is significant, and the model predicts a secondary increase in [Ca²⁺]_cyt after the initial peak.

View larger version (8K): [in this window] [in a new window]   Fig. 8. Predicted effects of ouabain stimulation on [Ca2+]cyt and [Na+]cyt as a function of ouabain concentration (1 nM–1 mM). To optimize display and interpretation, timing of ouabain stimulation is staggered, so that the resultant curves do not overlap. Ouabain concentration that inhibits 50% of Na+-K+-ATPase activity (IC50) is taken as 1.3 nM for 2-isoforms and 10 µM (A and B; baseline case) or 1.3 nM (C and D) for 1-isoforms.

In the preceding simulations (Figs. 7, 8A, and 8B), we assumed that the affinity for ouabain of the ₁- and ₂-isoforms of the Na⁺-K⁺-ATPase pump differs by several orders of magnitude, as observed in rodents. In many other species, including primates, the affinity difference between the two isoforms is much smaller. Therefore, we also investigated the model predictions of the effects of ouabain on [Ca²⁺]_cyt and [Na⁺]_cyt when the affinities of the ₁- and ₂-isoforms are high and equal (IC_50,1 = IC_50,2 = 1.3 nM). As shown in Fig. 8, C and D, the general shape of the [Ca²⁺]_cyt and [Na⁺]_cyt profiles is the same as that for rodent isoforms (₁-isoform affinity << ₂-isoform affinity), but the curves are shifted with respect to ouabain concentration. Thus, if it is assumed that other cellular components are similar in primates, our results suggest that picomolar ouabain concentrations may be sufficient to elicit significant increases in [Ca²⁺]_cyt (Fig. 8C), whereas in rodents, ouabain concentration must be in the nanomolar range to exert comparable changes (Fig. 8A). Saturation is also predicted to occur at much lower ouabain concentrations in primates: the threshold ouabain concentration beyond which no further changes in [Ca²⁺]_cyt are seen is 100 nM in primates and 100 µM in rodents (Fig. 8, A and C). Similarly, our model suggests that, to significantly raise [Na⁺]_cyt, ouabain concentration must be >1 µM in rodents (Fig. 8B) but only 100 pM in primates (Fig. 8D).

Dose-dependent effects of ouabain on SR Ca²⁺ stores. As described above, in isolation, Na⁺-K⁺-ATPase inhibition increases Ca²⁺ loading in the SR, because it leads to inhibition of NCX, favoring an increase in [Ca²⁺]_md. Conversely, increases in IP₃ production and IP₃R conductivity (₁ and ₄, Eqs. 13 and 14) tend to deplete SR Ca²⁺ stores by augmenting Ca²⁺ release through IP₃R. These trends are summarized in Fig. 9. If it is assumed that the increase in ₄ and ₁ is transient, the model predicts that, at equilibrium, the mass of Ca²⁺ in the SR will rise after ouabain exposure (Table 3). If the increase is sustained, however, the SR Ca²⁺ content of rodents (₁-isoform affinity << ₂-isoform affinity) will achieve a net increase only at <1 µM ouabain.

View larger version (12K): [in this window] [in a new window]   Fig. 9. A and B: mass of Ca2+ in SR stores at equilibrium (ordinate, in 10–18 g) after exposure to increasing concentrations of ouabain, considering the effects of ouabain on Na+-K+-ATPase inhibition only, Src-mediated increases in cytosolic IP3 production and IP3R conductance only, or both. Value of IC50 for 1-isoforms is taken as 10 µM (A; baseline case) or 1.3 nM (B). C: mass of Ca2+ in SR stores after isolated increases in IP3 production (4) and IP3R conductivity (1) in the cytosol only, the microdomains only, or both. Abscissa denotes increase in 4 and 1 relative to baseline. Model predicts that Na+-K+-ATPase inhibition per se increases Ca2+ loading in the SR, whereas increases in IP3 production and IP3R sensitivity per se tend to deplete SR Ca2+ stores by augmenting Ca2+ release through IP3R.

	DISCUSSION

TOP ABSTRACT METHODS RESULTS DISCUSSION REFERENCES

 
Cardiotonic steroids such as digitalis and ouabain bind to the NH₂-terminal extracellular loop of the Na⁺-K⁺-ATPase -subunit at a site that is conserved in evolution. Endogenous OLF are synthesized by the adrenal gland and hypothalamus and circulate in picomolar-to-nanomolar concentrations. Taken together, these observations support the interpretation that ouabain-Na⁺ pump interactions serve a fundamental physiological role (16, 41). Blaustein and colleagues (3, 5) hypothesized that ouabain-induced inhibition of Na⁺ export from cells elevates localized subplasmalemmal Na⁺ concentrations, leading to secondary reduction of Ca²⁺ export, or enhanced import, via the NCX. Those events were proposed to favor an increase in cellular Ca²⁺ concentrations and the overall mass of Ca²⁺ in SR stores (3, 5). In rodents, the abundant ₁-isoform of Na⁺-K⁺-ATPase, which ubiquitously maintains transcellular Na⁺ and K⁺ gradients, is ouabain insensitive. In contrast, other less abundant rodent isoforms (₂–₄) retain ouabain sensitivity (6, 23) and possess an NH₂-terminal sorting motif that tethers them to cellular microdomains (35). In turn, those microdomains provide an interface between the plasma membrane and SR stores. Colocalization of ₂-isoform Na⁺ pumps with endoplasmic reticulum/SR protrusions that abut the plasma membrane has been verified (4, 6, 19).

Secondary blockade of NCX is not the only means by which ouabain influences Ca²⁺ signaling. Tian et al. (36) and Xie and Cai (39) elegantly demonstrated that binding of ouabain to Na⁺-K⁺-ATPase stimulates tyrosine phosphorylation through activation of Src kinase. In LLC-PK₁ cells, stimulation of PLC-₁, leading to IP₃ generation and [Ca²⁺]_cyt elevation, was demonstrated (42). Those events appear to be dependent on spatial relationships and protein-protein interactions within caveolae and can involve surface-expressed Na⁺-K⁺-ATPase, which resides in a "nonpumping" pool (22). Recently, on the basis of those observations, the importance of Na⁺ pump inhibition in ouabain signaling has been questioned (20). The predictions of this model bear directly on this issue; the IP₃ generation and IP₃R sensitization that occur downstream of Src and PLC-₁ activation do not readily account for the enhancement of Ca²⁺ store loading observed in a number of studies (2, 6, 31). That is best ascribed to secondary inhibition of NCX related to Na⁺-K⁺-ATPase inhibition (Figs. 8 and 9). Although this model provides a perspective from which to explore implications of Src- and NCX-mediated ouabain signaling, in combination and separately, it seems likely that various cell types may function in vivo by emphasizing one or the other.

A great deal of evidence exists to demonstrate control of Ca²⁺ signaling by ouabain. For example, ouabain enhances agonist-induced Ca²⁺ release from cellular stores in smooth muscle and endothelium (2, 31) and increases resting cytoplasmic Ca²⁺ and myogenic tone in isolated mesenteric arterioles (44). The role of ouabain-sensitive Na⁺ pumps and NCX in the control of microvessel contractility and salt-dependent hypertension has been extensively studied. Chronic infusion of ouabain into rodents induces hypertension (25), and a substantial fraction of humans with essential hypertension have high circulating OLF (37). Recent observations in transgenic mice have provided key evidence that supports a causal role for OLF in the induction of salt-dependent hypertension (6, 17). Reduction of expression of ₂-isoform Na⁺ pumps, mirroring ouabain inhibition of Na⁺-K⁺-ATPase in rodents, leads to salt-dependent hypertension. Expression of a mutant, ouabain-insensitive ₂-isoform eliminates the ability of ACTH infusion to induce hypertension in mice (11). SEA-0400, a selective inhibitor of NCX, eliminates ouabain-induced hypertension and selectively treats salt-sensitive, but not salt-insensitive, hypertension in rat models (14, 17). Similarly, smooth muscle overexpression of an SEA-0400-insensitive NCX1.3 isoform eliminates the antihypertensive properties of that NCX inhibitor (10, 18). These topics have been reviewed recently (5, 6, 17, 25, 37, 39).

Motivated by the importance of ouabain and OLF in modulation of myocyte contractility and generation of hypertension, we simulated the pathways through which ouabain affects Ca²⁺ signaling in cells: 1) inhibition of active transport by Na⁺-K⁺-ATPase ₁- and ₂-isoforms; 2) activation of PLC-₁, leading to IP₃ production; and 3) stimulation of tyrosine phosphorylation of IP₃R, leading to an increase in its conductance.

Model simplifications. We recognize that our investigation into the effects of ouabain on Ca²⁺ signaling, IP₃ generation, and IP₃R activation is limited by the paucity of detailed data and the need to combine and extrapolate information that was obtained in studies of effects in different cell types. Nonetheless, it provides an opportunity to explore the implications of signaling pathways that may exist separately or, to some degree, in combination and dispute contentions that one or the other may be predominant in a given setting (6, 20). Stated another way, it may provide some insight into which actions of ouabain best account for the relative plethora of experimental observations concerning [Ca²⁺]_cyt changes, store Ca²⁺ loading, and IP₃-mediated effects.

To the best of our knowledge, the effects of ouabain to enhance IP₃ production and IP₃R conductance have not been fully quantified with respect to their spatial and temporal changes within cells or as a function of ouabain concentration. We therefore extrapolated the data of Yuan et al. (42) concerning the ouabain dependence of the interaction of the Na⁺-K⁺-ATPase ₁-isoform with PLC-₁ and IP₃R to yield a correlation between increases in IP₃ production (₄) and IP₃R conductivity (₁) with ₁-isoform inhibition. Furthermore, our assumption that tyrosine phosphorylation of IP₃R simply raises its conductance is most likely an oversimplification. It is probable that the spatiotemporal Ca²⁺ release properties of the channel are altered in more complex ways, as reported for serine and threonine phosphorylation events (29). The extent to which phosphorylation leads to modulation of IP₃R sensitivity to Ca²⁺ or IP₃ is similarly uncertain. In the absence of more specific data, we chose to simply retain the kinetics of the model of De Young and Keiser (9) previously used to simulate IP₃R Ca²⁺ currents, while varying the Ca²⁺ conductivity of IP₃R (₁).

Comparisons with experimental measurements of [Ca²⁺]_cyt. Our simulations indicate that the net effect of ouabain on intracellular concentrations depends on the relative changes in ₁- and ₂-isoform transport, IP₃ production (i.e., ₄), and IP₃R conductivity (i.e., ₁). The model predicts that ₂-isoform inhibition generates a peak-and-plateau pattern for [Ca²⁺]_cyt (Fig. 1), whereas ₁-isoform inhibition results in a monophasic increase (Fig. 4). Perhaps most importantly, the effects of increases in ₄ or ₁ on [Ca²⁺]_cyt depend on how they are distributed between the microdomains and the bulk cytoplasm. Specifically, when we assumed that the Src-related effects of ouabain, mediated through its binding to the ₂-isoform (i.e., PLC-₁ activation and the subsequent increase in IP₃ production and IP₃R conductance), are identical to those of the ₁-isoform, the model predicted that nanomolar ouabain would induce a significant, transient drop in [Ca²⁺]_cyt (Fig. 7). The reason for this prediction is that ₂-isoforms are exclusively expressed above the microdomains, and their sensitivity to ouabain in rodents is 10³ times higher than that of the ₁-isoform, so they extensively bind ouabain, even at nanomolar concentrations. Hence, if it is assumed that variation of ₄ and ₁ is regulated by that binding, nanomolar ouabain increases ₄ and ₁ to a much greater extent in the microdomains than in the cytosol. Therefore, the model predicts a substantial elevation of [Ca²⁺]_md, a diminution of SR Ca²⁺ stores, and a reduction of [Ca²⁺]_cyt. Given that such a reduction of [Ca²⁺]_cyt has not been observed experimentally, we surmise that the binding of ouabain to the ₂-isoform may have minimal effects on IP₃ production and IP₃R sensitivity in microdomains. That might be explained, for example, if microdomain protein-protein interactions are such that ₂-isoform binding partners do not include Src, PLC-₁, or IP₃R or if the ₂-isoform resides outside signaling complexes in caveolae (39). No current data address this issue, and measurement of IP₃ release and its effects in microdomains, separate from those in the bulk cytosol, might be prohibitively difficult.

When cells are acutely exposed to ouabain, investigators observed a variety of temporal patterns of [Ca²⁺]_cyt changes. Monophasic increases have been described in some cells (12, 44), whereas peak elevation followed by a stable plateau has been observed in others (31, 42). Finally, [Ca²⁺]_cyt oscillations have been described in cell lines of renal epithelial origin (1, 26). The predictions of this model illustrate a few paradigms involving cellular transporter distributions and signaling molecule generation through which cells might display such variable patterns in experimental settings.

SR Ca²⁺ stores. Our results suggest that Na⁺-K⁺-ATPase inhibition per se favors SR Ca²⁺ loading (Fig. 9, A and B), since it induces NCX to inhibit Ca²⁺ export or enhance its import, depending on the balance of membrane potential and transmembrane Ca²⁺ and Na⁺ concentrations. On the other hand, increases in IP₃ production and IP₃R conductance are predicted to augment Ca²⁺ release by the receptors and, therefore, partly deplete SR Ca²⁺ stores (Fig. 9C).

In rats, nanomolar concentrations of ouabain enhance cytosolic Ca²⁺ transients evoked by agonists such as bradykinin and serotonin (2, 31). A likely explanation for this enhancement is that the SR Ca²⁺ load increases after ouabain application, thereby increasing receptor-mediated Ca²⁺ release on exposure to agonists. Our predictions support this hypothesis (Table 6), with the caveat that it depends on minimization of the extent of stimulation of IP₃ production and IP₃R conductance by ouabain in the cell type under study (42).

[Na⁺]_cyt variations. Our model also provides insight into which experimental maneuvers might be expected to affect [Na⁺]_cyt. It predicts that isolated inhibition of the ouabain-sensitive ₂-isoform in rodents, as might be accomplished with nanomolar ouabain or genetic manipulations, does not significantly affect [Na⁺]_cyt (Fig. 1). This is largely a consequence of ₂-isoform sequestration above the microdomains. In contrast, inhibition of the predominant ₁-isoform, above the bulk cytosol, leads to a progressive and significant [Na⁺]_cyt elevation. Selective increases in ₄ and/or ₁, whether in the bulk cytosol and/or the microdomains, also raise [Na⁺]_cyt, because they trigger the partial depletion of SR Ca²⁺ stores, thereby stimulating SOC activity and increasing Na⁺ import into the cell.

Arnon et al. (2) observed that low concentrations (3–100 nM) of ouabain augment Ca²⁺ transients in rat arterial smooth muscle without raising cytosolic Na⁺. This is also predicted by our model, if we assume that the binding of ouabain to the ₂-isoform does not elicit significant changes in microdomain IP₃ production and IP₃R conductance (Fig. 8B). If, however, the latter changes were significant, [Na⁺]_cyt would be predicted to rise by >1 mM (Fig. 7). In other words, comparison between experimental and theoretical profiles of [Ca²⁺]_cyt and [Na⁺]_cyt evoked by nanomolar ouabain strongly suggests that binding of the ₂-isoform by ouabain has small effects on IP₃R-mediated Ca²⁺ release in the microdomains, at least in some rodent cell types.

An interesting and testable prediction of the model is that, in species where the ouabain affinity of the ₁-isoform is high and comparable to that of the ₂-isoform, ouabain concentrations as low as 100 pM–1 nM might be sufficient to raise cytosolic Na⁺ (Fig. 8D).

Conclusion. We simulated in the present study the pathways through which ouabain affects Ca²⁺ signaling in cells. The model predicts that ₂-isoform inhibition generates a peak-and-plateau pattern for [Ca²⁺]_cyt, whereas ₁-isoform inhibition results in a monophasic increase. The effects of ouabain-mediated increases in IP₃ production or IP₃R conductance on [Ca²⁺]_cyt depend on their relative distributions between the microdomains and the bulk cytoplasm. Comparison between experimental data and predictions suggests that the binding of ouabain to the ₂-isoform may have minimal effects on IP₃ production and IP₃R conductance in microdomains. Our model also predicts that isolated inhibition of the ouabain-sensitive ₂-isoform in rodents does not significantly affect [Na⁺]_cyt, given sequestration of the ₂-isoform above the microdomains. Finally, our results suggest that Na⁺-K⁺-ATPase inhibition favors SR Ca²⁺ store loading, whereas increases in IP₃ production and IP₃R conductance favor store depletion, pointing to possible explanations for experimental observations obtained in studies of various cell types. In a particular cell type, the balance of those two effects might govern the characteristics of responses to ouabain and OLF.

	FOOTNOTES

 

Address for reprint requests and other correspondence: A. Edwards, Dept. of Chemical and Biological Engineering, Tufts Univ., 4 Colby St., Medford, MA 02155 (e-mail: aurelie.edwards{at}tufts.edu)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

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