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CARDIOVASCULAR

Down-Regulation of Na⁺ Pump ₂ Isoform in Isoprenaline-Induced Cardiac Hypertrophy in Rat: Evidence for Increased Receptor Binding Affinity but Reduced Inotropic Potency of Digoxin

Section of Pharmacokinetics, Department of Pharmacology, Martin Luther University Halle-Wittenberg, Halle, Germany

Received September 28, 2004; accepted January 4, 2005.

	Abstract

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Cardiac hypertrophy in rats induces a down-regulation of Na⁺,K⁺-ATPase ₂ isoform, although its functional consequences are poorly understood. Using a mathematical modeling approach that allows differentiation between effects elicited at the receptor and postreceptor level, we studied uptake, receptor binding kinetics, and positive inotropism of digoxin in single-pass Langendorff-perfused hearts of vehicle- and isoprenaline-pretreated rats (2.4 mg/kg per day over 4 days). Digoxin outflow concentration and left ventricular developed pressure data were measured for three consecutive doses (15, 30, and 45 µg) in the absence and presence of the reverse mode Na⁺/Ca²⁺ exchange inhibitor 2-[2-[4-(4-nitrobenzyloxyl-)phenyl]ethyl isothiourea methansulfonate] (KB-R7943) (0.1 µM) in perfusate. In hypertrophied hearts, 1) the amount of ₂ receptors was reduced to 52% of control levels; 2) the digoxin binding affinity was increased 12-fold due to a decrease in dissociation rate constants of ₁ and ₂ receptors, and 3) inotropic responsiveness to digoxin the was attenuated on the stimulus-response level, where the coupling ratio of stimulus to response was reduced to 38% of control values. Only in the lowest dose level (15 µg) was this decrease in inotropic potency counterbalanced by the increase in receptor affinity. The Na⁺,K⁺-ATPase isoform shift was not responsible for the diminished inotropic effect of digoxin. Coadministration of KB-R7943 significantly reduced cellular response generation at higher digoxin doses to the same limiting stimulus-response relationship in both the vehicle and isoprenaline group.

To understand the action of cardiac glycosides, we need a quantitative description of the processes involved. To this end, we recently developed a mechanism-based mathematical model to describe the uptake kinetics, receptor interaction, and positive inotropic effect of digoxin in the single-pass isolated perfused rat heart (Kang and Weiss, 2002; Weiss et al., 2004). Using this model to analyze transient outflow concentration and inotropic response data of digoxin, we were able to estimate model parameters characterizing receptor binding and cellular response generation of digoxin. The findings have helped to unveil the functional receptor heterogeneity in the intact heart and shed new light on the quantitative role of the reverse mode NCX in response generation.

With this background, we have designed experiments in hearts of isoprenaline (ISO)-pretreated rats to study the effect of left ventricular hypertrophy on myocardial uptake and receptor binding kinetics (Na⁺,K⁺-ATPase inhibition) and positive inotropic effect of digoxin. To our knowledge, the function of the Na⁺,K⁺-ATPase has not been previously studied in cardiac hypertrophy induced by a continuous infusion of ISO. The modeling of cardiac distribution and response kinetics of digoxin in the perfused heart is thus used as a tool to characterize the functional receptor heterogeneity and to differentiate between effects elicited at the receptor and postreceptor level. In view of reported changes of NCX activity in cardiac hypertrophy (Sipido et al., 2002; Chorvatova et al., 2004), we were interested to find out how inhibition of the reverse mode NCX by KB-R7943 (KBR) affects inotropic response to digoxin in normal and hypertrophied hearts.

	Materials and Methods

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Drugs. Digoxin and isoprenaline were purchased from Sigma Chemie (Deisenhofen, Germany), and [³H]digoxin (37 Ci/mmol) was purchased from PerkinElmer Life and Analytical Sciences (Boston, MA). KB-R7943 [2-[2-[4-(4-nitrobenzyloxyl)phenyl]ethyl] isothiourea methansulfonate] was kindly donated by Nippon Organon KK (Osaka, Japan). Isoprenaline was dissolved in 0.1% ascorbic acid solution and sterilized via filtration before filling into the ALZET mini-osmotic pump model 1003D (Durect Corp., Cupertino, CA). Digoxin was dissolved in 70% ethanol solution and diluted with Krebs-Henseleit buffer. The final concentration of ethanol in vehicle was 0.7%. [³H]digoxin (1 µCi/ml) was mixed with 50 µg/ml of unlabeled drug to obtain the appropriate specific radioactivity. All other chemicals and solvents were of the highest grade available.

Isoprenaline Pretreatment. Cardiac hypertrophy was induced in male Wistar rats weighing 280 to 330 g (n = 5) by treatment with isoprenaline for 4 days. The control group received vehicle infusion (n = 5). Delivery of drug was achieved by implanting a miniosmotic pump filled with sterilized isoprenaline solution or vehicle (0.1% ascorbic acid). The mean pumping rate was 1.06 ± 0.04 µl/h, and mean fill volume was 93.8 ± 4.5 µl. The miniosmotic pump was implanted underneath the neck skin under ether anesthesia. Isoprenaline was continuously infused at a rate of 2.4 mg/kg/day over 4 days. At the end of treatment, animals were anesthetized with sodium pentobarbital (50 mg/kg i.p.); after the onset of general anesthesia, the heart was excised and subjected to retrograde perfusion with Langendorff technique. After finishing the perfusion experiment, the heart was separated into atrial, right ventricular, and left ventricular (LV) sections. Hypertrophy was monitored by the ratio of myocardial wet weight (each section) to body weight. All aspects of animal care and experimentation were performed in accordance with the Guide for the Care and Use of Laboratory Animals, published by the National Institutes of Health, and were approved by the Animal Protection Body of the State of Sachsen-Anhalt, Germany.

Isolated Perfused Heart Preparation. Hearts excised from vehicle- and ISO-pretreated rats were perfused by the nonrecirculating Langendorff technique as previously described (Kang and Weiss, 2002; Weiss et al., 2004). The Krebs-Henseleit buffer (pH 7.4) consisted of 118 mM NaCl, 4.7 mM KCl, 1.66 mM MgSO₄, 24.88 mM NaHCO₃, 1.18 mM KH₂PO₄, 5.55 mM glucose, 2.0 mM sodium pyruvate, 1.5 mM CaCl₂, and 0.1% bovine serum albumin. Buffer was continuously bubbled with 95% O₂/5% CO₂ and maintained at 37°C. Left ventricular contractility was assessed by measuring isovolumic left ventricular pressure with a fluid-filled balloon placed in the left ventricular chamber. Left ventricular developed pressure (LVDP) was calculated from the difference between left ventricular peak systolic pressure and end-diastolic pressure (LVEDP). LVEDP was adjusted to 5 to 6 mm Hg during the initial equilibration. Coronary flow was maintained at 9.5 ± 0.4 ml/min. The hearts were beating spontaneously at an average rate of 270 beats/min.

Experimental Protocol. Perfused hearts were allowed 20 min of equilibration, then three successive doses of 15, 30, and 45 µg of [³H]digoxin were administered as a 1-min infusion, with an interval of 15 min between the doses. Infusion was performed into the perfusion tube, close to the aortic cannula, using an infusion device. Outflow samples were collected every 5 s for 2 min and every 30 s for the next 5 min (total collection period, 7 min), and the cardiac response was measured. After this first series of digoxin doses, hearts were perfused with buffer containing 0.1 µM KBR, and the experiments were repeated in the presence of KBR in perfusate (15 min after change in buffer). The outflow samples were kept frozen at –20°C until analysis. For determination of [³H]digoxin, the outflow sample (200 µl) was transferred to a vial, and 2 ml of cocktail was added. After vigorous mixing, the radioactivity was measured with a liquid scintillation counter (PerkinElmer Life and Analytical Sciences).

Modeling and Data Analysis. The mathematical model used in this study has been developed previously to analyze the kinetics of digoxin uptake, receptor binding, and inotropic response after infusion in the single-pass perfused heart (Weiss et al., 2004). The nonequilibrium, nonlinear model contains five compartments, describing changes in the amounts of digoxin in the mixing, capillary, and interstitial space as well as in two compartments representing the two saturable digoxin binding sites, i.e., two receptor classes R₁ and R₂ on the sodium pump (Fig. 1). Perfusate flow (Q) (including drug) first passes the mixing volume V₀ (tubing and large vessels where no exchange with tissue occurs) before it enters the vascular space (distribution volume V_vas), where transcapillary transport of the unbound drug between vascular and interstitial space is described by rate constants k_vi and k_iv, respectively, and the apparent permeability surface-area or permeation clearance CL_vi = k_viV_vas is determined by k_vi and V_vas. Assuming passive transport processes, we have k_viV_vas = k_ivV_app,is, where V_app,is denotes the apparent volume that determines initial distribution of digoxin in the interstitial space (exceeding the distribution space V_is due to quasiinstantaneous nonspecific tissue binding). The free concentration in the interstitial space that governs receptor binding is then given by C_is(t) = D_is(t)/V_app,is, where D_is(t) denotes the amount of digoxin in the interstitial space. The model allows for the estimation of the amount of available receptor sites R_tot,i and rate constants for the association and dissociation of digoxin k_i and k_–i (i = 1,2). The latter determine the equilibrium dissociation and affinity constants K_D,i = k_–i/k_i and K_A,i = 1/K_D,i, respectively, of the two receptor populations. The binding rate of digoxin to free membrane receptors (R_tot,I–DR_i) is given by k_i [R_tot,i – DR_i(t)] C_is(t), where DR_i(t) is the amount of digoxin bound at time t to receptor i (receptor occupancy). It is assumed that the receptor amounts R_tot,i (i = 1,2) remain constant during the time course of the experiment (i.e., dR_i(t)/dt = 0). The corresponding differential equations describing the time course of outflow concentration C(t) are listed below.

(1)

(2)

(3)

(4)

(5)

where D₀(t) and D_vas(t) are the digoxin amounts in the mixing and vascular volume, respectively. RATE denotes the dosing rate (1-min infusion of digoxin doses). The resulting outflow concentration is then obtained as C(t) = D_vas(t)/V_vas.

View larger version (13K): [in this window] [in a new window]   Fig. 1. The compartmental model used to analyze cardiac kinetics and inotropic response of digoxin. The model describing distribution and receptor binding of digoxin (boxes) is followed by cellular response generation (circle) with a linear (solid line) and hyperbolic (dashed line) stimulus-response relationship in the absence and presence of the NCX inhibitor KB-R7943, respectively. Vvas and Vapp,is = vascular and interstitial distribution volumes; Cis(t) = Dis(t)/Vapp,is = unbound interstitial digoxin concentration; kvi and kiv = first-order rate constants of transcapillary transport; Ki(t) = ki[Rtot,i – DRi (t)] = fractional rate for saturable receptor binding; ki and k–i = association and dissociation constants; DRi = receptor occupancy; the index i = 1,2 denotes the receptor population i.

Sodium pump inhibition by digoxin [as quantified by DR₁(t) and DR₂(t) obtained by solving eqs. 1–5] ultimately leads to an increase in the force of contraction. In other words, the interaction of the drug with the receptor yields a stimulus that, via cellular processes, causes the response E(t). For our heterogeneous receptor system, this stimulus is the total functional receptor occupation DR_T, which is given by the weighted sum of both isoforms, DR_T(t) = f₁DR₁(t) + (1 – f₁)DR₂(t), where f₁ is the fraction of R₁-occupancy contribution. The correlation between positive inotropic effect E(t) and DR_T(t) is described by the stimulus-response relationship E(t) = [DR_T(t)], where refers to the chain of cellular processes that convert the stimulus into response (Kenakin, 1993). Normally, can be approximated by a linear function (Kang and Weiss, 2002):

(6)

where the coupling ratio e_T represents the effect per amount of stimulus. However, when the cellular response generation (Ca²⁺ influx) is inhibited by KBR, saturation of effectuation process occurs and a Michaelis-Menten-like hyperbolic function had to be used to describe empirically the dependence of response on stimulus, DR_T (Weiss et al., 2004)

(7)

Note that eq. 7 is the stimulus-response model that is commonly used in pharmacology (Kenakin, 1993), where _max and K_DR represent the maximum effect and the amount of stimulus (DR_T) producing 50% of _max, respectively. In addition, a first-order delay with time constant was introduced to account for the fact that under KBR, the time course of E was delayed with respect to that of DR_T, i.e., that the effectuation process was time-dependent (Mager and Jusko, 2001b). Thus, in the presence of KBR, the following differential equation has to be added to describe the stimulus-response relationship:

(8)

For the appropriate initial conditions [D_i(0) = 0 and DR_i(0) = 0], the model eqs. 1–5 and 8) were solved numerically in fitting the C(t) and E(t) data as described below. The LVDP(t) data were used as a measure of inotropic response, i.e., the increase in LVDP with respect to the baseline (predrug) value LVDP₀:

(9)

The terminology "effect", E(t), will be used throughout for the fractional change of LVDP. It is assumed that the low-affinity/high-capacity and high-affinity/low-capacity digoxin binding sites R₁ and R₂ represent the ₁- and ₂ -subunit isoforms of the Na⁺,K⁺-ATPase, respectively (Bers et al., 2003; Verdonck et al., 2003).

The differential equations corresponding to the compartmental model described above (Weiss et al., 2004) were solved numerically in analyzing the data using ADAPT II software (D'Argenio and Schumitzky, 1997). Modeled as the response to three successive doses, the effect E(t) and outflow concentration C(t) data were fitted simultaneously. Although the above model structure is already a minimal model that is reasonably consistent with the physiological knowledge of digoxin uptake and action, the number of parameters to be adjusted is relatively large. Since the information content of the outflow data is inadequate to support such a nonlinear model with a relative rich parameterization, we take advantage of the fact that a priori information on the unknown model parameters is available, e.g., results obtained from in vitro receptor binding experiments of digoxin. Thus, as described in our previous studies (Kang and Weiss, 2002; Weiss et al., 2004), we used a Bayesian approach of parameter estimation (D'Argenio and Schumitzky, 1997), incorporating a priori knowledge on the ratios of the receptor affinities (K_A,2/K_A,1) and capacities (R_tot,1/R_tot,2) of digoxin. Only under this condition could all parameters of the model be uniquely estimated; i.e., the model was structurally identifiable. Based on binding data (Vér et al., 1997) and receptor affinities estimated in rat cardiac myocytes by measuring the Na⁺ pump current (Ishizuka et al., 1996), the ratios K_A,2/K_A,1 = 45 and R_tot,1/R_tot,2 = 3 were selected for the vehicle group (Weiss et al., 2004). For the ISO group, the a priori information was based on the expression of Na⁺,K⁺-ATPase isoforms (protein level) measured by Book et al. (1994) and Magyar et al. (1995) in hypertrophied LV of renovascular hypertensive rats, leading to a capacity ratio of R_tot,1/R_tot,2 = 6. Note that a reduction of the R_tot,2 level by 50% is in accordance with observations in other hypertrophy models (Verdonck et al., 2003). Since only the prior means of the ratios K_A,2/K_A,1 and R_tot,1/R_tot,2 were exploited in using the MAP Bayesian estimator, the fractional standard deviations of these ratios were set to 20% of mean values (assuming log-normal distributions) to ensure that parameter estimation will be governed by data as well as a priori knowledge. No prior information was incorporated for the other parameters; i.e., their estimates will be data driven, except for the volume of the vascular compartment V_vas, which was fixed to a literature value of 0.06 ml/g (Dobson and Cieslar, 1997). Note that we have reparameterized Eqs. 3 through 5 using R_tot,1/R_tot, R_tot,1, K_A,2/K_A,1, k₁, k₂, and k_–2 as primary parameters to estimate R_tot,1 and k_–1 as secondary parameters in ADAPT II. In hypertrophied hearts, the estimation of association and dissociation rate constants was based on a simultaneous fit of both concentration and effect data, since prolonged receptor binding in the terminal phase was too low to be detected in outflow concentration. However, under normal conditions (vehicle group), the receptor binding parameters can be estimated solely on the basis of C(t) data (Kang and Weiss, 2002; Weiss et al., 2004). That digoxin binding to receptors is a determinant of outflow C(t) data in perfused heart experiments is analogous to the concept of "target-mediated drug disposition" (Mager and Jusko, 2001a). The assessment of numerical identifiability was guided by the asymptotic fractional standard deviations (CV) provided by the fitting procedure, which represent the uncertainty in parameter estimates resulting from the fit and correlation coefficients.

Descriptive data are expressed as means ± S.D. To get a quantitative measure of the positive inotropic effect that is independent of the model, we calculated the time integral (over 7 min) of the developed effect ⁷₀ E(t)dt) using trapezoidal rule. The responses in the two groups were compared using two-way analysis of variance, with repeated measures performed on the three dose levels of vehicle and ISO group, followed by Student-Newman-Keuls post hoc test for multiple comparisons. Differences in parameter estimates between the normal and hypertrophied hearts were assessed by Student's t test. For all analyses, a two-tailed p value of <0.05 was used to indicate statistical significance (SigmaStat; SPSS Inc., Chicago, IL).

Model Simulations. To facilitate understanding of the consequences of changes in receptor properties and postreceptor events, time courses of receptor occupancy and occupancy-response curves have been simulated. In addition, the steady-state response behavior has been predicted. At steady state, we obtain for the stimulus (functional receptor occupancy) as a function of concentration, C_ss:

(10)

and steady-state E-versus-C_ss curves in the absence and presence of KBR can be predicted by the substitution of eq. 10 into eqs. 6 and 7, respectively. All simulations were performed with average estimates obtained in each group using MAPLE 8 (Maplesoft, Waterloo, ON, Canada).

	Results

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Baseline Cardiac Function in Vehicle- and ISO-Pretreated Rats. There was a significant increase in total, LV, and atrial weight in animals subjected to continuous ISO infusion over 4 days but no significant elevation in right ventricular weight (Fig. 2). The body weights of vehicle- and ISO-pretreated rats were 315.6 ± 9.48 and 299.0 ± 13.7 g, respectively. In the ISO group, baseline contractility (LVDP₀) was reduced to 70% of vehicle group values (p < 0.001). No significant changes in LVEDP and coronary vascular resistance (CVR) were observed. KBR in perfusate did not affect baseline function of the heart (Table 1).

View larger version (9K): [in this window] [in a new window]   Fig. 2. ISO-induced increase in myocardial wet weight of hypertrophied rat hearts, together with changes in atrial (AT), right ventricular (RV), and LV weight. *, p < 0.05 and ***, p < 0.01 compared with the value of vehicle-pretreated group.

Outflow Concentration and Inotropic Response to Digoxin. Figure 3 shows a typical recording of digoxin outflow concentration, C(t), and inotropic effect, E(t), profiles after three consecutive digoxin doses (15, 30, and 45 µg) measured in hearts of vehicle- and ISO-pretreated rats, respectively, in the absence and presence of KBR. The time-integral ⁷₀ E(t)dt of percentage increase in LVDP(t) caused by digoxin doses of 30 and 45 µg was significantly reduced in hypertrophied versus normal hearts (p < 0.05). These differences were eliminated by 0.1 µM KBR in perfusate, which produced a downward shift in the dose-effect curve and a significant decrease in positive inotropism [time-integrals of E(t)] for digoxin doses greater than 15 µg (Fig. 4).

View larger version (19K): [in this window] [in a new window]   Fig. 3. Representative digoxin outflow concentration (top panel) and percentage of increase in left ventricular developed pressure (bottom panel) after three digoxin doses (15, 30, and 45 µg) in normal and hypertrophied hearts as observed under control conditions and in the presence of 0.1 µM KB-R7943, respectively, together with simultaneous fits of the model (smooth curves) to experimental data (symbols).

View larger version (14K): [in this window] [in a new window]   Fig. 4. Dose-response curves of normal and hypertrophied hearts in the absence and presence of reverse NCX blocker KB-R7943 (0.1 µM), where response is the time-integral of digoxin effect 70 E(t)dt. **, p < 0.01 and ++, p < 0.01, compared with the value of vehicle-pretreated group and before exposure to KB-R7943, respectively.

Model Analysis. Figure 3 shows typical fits of the model to the data obtained for three consecutive digoxin doses (15, 30, and 45 µg) in normal and hypertrophied hearts. As expected from our previous modeling results (Weiss et al., 2004), the model was conditionally identifiable, and parameters were estimated with reasonable precision as suggested by the approximate coefficients of variations obtained in individual fits. The averaged model parameters and averaged estimation errors, as a percentage of related parameter estimates, are listed in Table 2.

Capacity and Affinity of Digoxin Binding Sites. Binding kinetics was determined by a mixture of two receptor subtypes, a low-affinity/high-capacity binding site (₁) and a high-affinity/low-capacity binding site (₂) (Table 2). The capacity ratios R_tot,1/R_tot,2 = 3.12 and 5.98, estimated in normal and hypertrophied hearts, are not much different from the respective a priori values used in the Bayesian estimation procedure, which stem from the literature. In hypertrophied hearts, the ₂ isoform (R₂) was markedly down-regulated to 52% of the level in the vehicle group, whereas the ₁ level remained unchanged. The dissociation rate constants of ₁ and ₂ receptors (k_–1 and k_–2) decreased to 8 and 21%, respectively, of those in the control hearts. Together with a 2-fold increase in the fractional ₂ binding rate (k₂), this leads to a 12-fold increase in digoxin receptor binding affinities. In accordance with the a priori value, no differences in the resulting affinity ratios K_A,2/K_A,1 of about 45 were observed among the groups. The consequences of these alterations in receptor properties are illustrated by the time course of receptor occupancy simulated on the basis of the mean parameter estimates (Fig. 5). Whereas maximum occupancy is not changed in hypertrophied hearts, the washout occurs much slower.

View larger version (12K): [in this window] [in a new window]   Fig. 5. Model simulations of the time course of stimulus [total functional receptor occupancy, DRT(t)] (left), as well as underlying occupancies of 1 and 2 receptors [DRi(t)] (right) in normal and hypertrophied hearts for the 45-µg dose of digoxin, computed with average parameters (Table 2).

Occupancy-Response Relationship. At the postreceptor level, ISO pretreatment reduced the inotropic potency of digoxin, i.e., the slope of the stimulus-response relationship (e_T) to 38% of control hearts (Table 2; Fig. 6). This linear occupancy-response relationship became nonlinear in the presence of the NCX inhibitor KBR; i.e., a hyperbolic stimulus-response function had to be used to fit the response data (Weiss et al., 2004). Under reverse mode NCX inhibition, hypertrophy did not affect the parameters _max and K_DR characterizing the cellular effectuation process (Table 2), as also illustrated by the stimulus-response relationships (Fig. 6).

View larger version (12K): [in this window] [in a new window]   Fig. 6. Stimulus-response relationships as predicted by the model for normal and hypertrophied hearts in the absence and presence of reverse NCX blocker KB-R7943 (0.1 µM). Note that following a 15-µg dose of digoxin, the maximum total receptor occupancy is 0.5 µg.

	Discussion

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Modeling of digoxin receptor binding and response kinetics in ISO-induced hypertrophied rat heart confirmed the down-regulation of the Na⁺ pump ₂ isoform and revealed the functional consequences regarding the action of cardiac glycosides. 1) A decrease in dissociation rate constants of ₁ and ₂ receptors, together with an increase in fractional ₂ binding rate, led to a marked increase in digoxin receptor binding affinities; 2) at the cellular level, hypertrophy substantially reduced the inotropic potency of digoxin (coupling ratio of stimulus to response); and 3) the impaired inotropic response after reverse NCX inhibition was not further diminished by hypertrophy.

The hypertrophy development was comparable to that reported by Boluyt et al. (1995), where after ISO infusion (same dosing) the heart weight-to-body weight ratio and the alterations in gene expression peaked after about 4 days of treatment. The reduced baseline LVDP₀ in the ISO-pretreated group (Table 1) points to a decompensated LV hypertrophy (Badenhorst et al., 2003). Although recent results in pressure-overload hypertrophied hearts (Minakawa et al., 2003) suggest that this contractile failure could be also explained by the decrease in the relative level of sarcoplasmic reticulum Ca²⁺-ATPase (SERCA mRNA) (Boluyt et al., 1995), this question is still under dispute (Badenhorst et al., 2003; Houser and Margulies, 2003; Ward et al., 2003) (vide infra). The lack of right ventricular hypertrophy (Fig. 2) is in accordance with the response observed after continuous infusion of noradrenaline in rats (Irlbeck et al., 1996). Note that gene expression observed in ISO-induced cardiac hypertrophy is similar to that caused by pressure overload (Boluyt et al., 1995).

Our finding obtained by modeling of digoxin receptor binding kinetics that isoprenaline-induced LV hypertrophy is accompanied by the specific down-regulation of Na⁺ pump ₂ isoform parallels the alterations of mRNA and/or protein levels observed in different rat pressure-overload models (Book et al., 1994; Charlemagne et al., 1994; Sweadner et al., 1994; Magyar et al., 1995), as well as in a postinfarction rat model of hypertrophy and cardiac failure (Semb et al., 1998), where ₂ isoform protein was reduced to a similar degree (50%) (for review, see Verdonck et al., 2003). In salt-sensitive rats, the decrease of the ₂ level to about 65 and 40% of control observed with the development of LV hypertrophy and failure, respectively, was accompanied by an increase and decrease, respectively, of the ₁ level (Fedorova et al., 2004). The ability to confirm by receptor binding kinetics in the intact heart the shift in Na⁺,K⁺-ATPase isoforms gene expression seems important in view of quantitative uncertainties of the biochemical methods (e.g., Larsen et al., 1997).

Based on a more rigorous approach, our results on altered functional properties of the Na⁺,K⁺-ATPase in hypertrophied myocardium shed new light on the slower decline of inotropic response to ouabain during washout in hypertrophied rat hearts and the reduced dissociation rate constants measured on isolated vesicles (Lelievre et al., 1986; Berrebi-Bertrand et al., 1990). The 12-fold increase in digoxin binding affinities of both ₁ and ₂ receptors was the result of a decrease in dissociation rate constants of ₁ and ₂ receptors (to 8 and 21%, respectively) and a 2-fold increase in the fractional ₂ binding rate (k₂) (Table 2). Note that Fedorova et al. (2004) observed a 11- and 2.4-fold increase in ouabain binding affinity of ₂ and ₁ receptors, respectively, in cardiac hypertrophy with transition to heart failure.

It was suggested that the down-regulation of the Na⁺ pump ₂ isoform alone could decrease the sensitivity of hypertrophied myocardium to cardiac glycosides (Book et al., 1994), explaining why in rat hypertrophy ouabain is less toxic than normal (Chevalier et al., 1989; Charlemagne and Swynghedauw, 1995). This conclusion is not supported by our results because the reduced inotropic responsiveness could be explained fully by a decrease in coupling efficiency, i.e., effects occurring at postreceptor level. Figure 5 demonstrates for the 45-µg-digoxin dose that the time course of functional receptor occupation in hypertrophied LV differs from the norm only by the slower washout; however, the slope of the stimulus-response curve is reduced (Fig. 6), indicating that the depressed inotropic response of the LV can be solely attributed to alteration in cellular effectuation process. This is also illustrated by the steady-state concentration-response curves simulated with the mean parameter estimates by substituting eq. 10 into eq. 6 (Fig. 7). Only in the low concentration range (<1 µg/ml) could increased receptor affinity in hypertrophied LV compensate for reduced cellular response generation. This is also reflected by the dose-response curve (Fig. 4), where no significant influence of hypertrophy could be detected at the lowest dose level (15 µg). Furthermore, Fig. 7 is in general accordance with dose-response curves to ouabain measured in rat hearts pressure-hypertrophied and sham-operated rat hearts (Berrebi-Bertrand et al., 1990). A reduced positive inotropic effect of ouabain was also previously observed in ISO-induced cardiac hypertrophy by Szabo et al. (1989).

View larger version (11K): [in this window] [in a new window]   Fig. 7. Model simulations of digoxin concentration-response curve at steady state in normal and hypertrophied hearts. Note that following the lowest dose (15 µg), maximum outflow concentrations averaged at 2 µM.

The mechanism behind this contractile dysfunction, i.e., the reduced inotropic response to digoxin per occupied receptor (inhibited Na⁺ pump) is not clarified; possible explanations include 1) chamber dilatation and changes in the extracellular matrix (Badenhorst et al., 2003; Ward et al., 2003); 2) reduced SERCA Ca²⁺-ATPase 2a activity (Charlemagne et al., 1994; Boluyt et al., 1995; Minakawa et al., 2003; Muller-Ehmsen et al., 2003; Schultz et al., 2004); 3) NCX overexpression (Muller-Ehmsen et al., 2003; Bolck et al., 2004); or 4) a combination of these processes. Previous studies indicate that ISO-induced hypertrophy is accompanied by an increase in NCX expression (Golden et al., 2001; Chorvatova et al., 2004) and that NCX and Na⁺,K⁺-ATPase (mainly ₂ isoform) are inversely regulated (Magyar et al., 1995). The fact that at the relatively high intracellular Na⁺ concentration in the rat heart Na⁺ pump inhibition favors Ca²⁺ influx, since the NCX predominantly acts in reverse mode (Bers et al., 2003; Verdonck et al., 2003), makes it difficult to explain how NCX up-regulation could influence the inotropic action of cardiac glycosides (Muller-Ehmsen et al., 2003; Bolck et al., 2004). An inhibition of Ca²⁺ influx by the reverse mode NCX blocker KBR limits the inotropic response in increasing digoxin doses to that of the low dose range (Figs. 4 and 6); this is in accordance with our earlier work (Weiss et al., 2004), where we hypothesized that for a small increase in [Na⁺]_i at low receptor occupancy the inotropic effect may be independent of net Ca²⁺ influx, whereas Ca²⁺ entry via NCX can increase greatly when [Na⁺]_i rises. In other words, the linear relationship between receptor stimulus and inotropic response becomes hyperbolic because the selective inhibition of net Ca²⁺ influx by KBR affects response for doses higher than about 15 µg (Fig. 4), corresponding to receptor occupancies > DR_T 0.5 µg (Fig. 6). That inhibition of response generation by KBR leads to practically the same stimulus-response curves in normal and hypertrophied LV (Fig. 6) may suggest that processes connected with digoxin induced Ca²⁺ influx are responsible for the reduced (hyperbolic) coupling of stimulus with inotropic response in hypertrophied hearts. That KBR inhibits the digoxin-induced inotropy solely under conditions that favor net Ca²⁺ influx via NCX may also explain the difference between our results and earlier findings in rat ventricular myocytes (Satoh et al., 2000).

That positive inotropism is nearly completely mediated through ₂ receptors (Fig. 5) is consistent with data in mice (Dostanic et al., 2003). This simulation also demonstrates that at the time of maximum effect, down-regulation of ₂ isoform in the ISO group increases the occupancy of ₁ receptors from 10 to 20%. Finally, it should be noted that no significant influence of hypertrophy on the kinetics of digoxin uptake into the myocardium, i.e., transcapillary permeation clearance CL_vi and apparent interstitial distribution volume V_app,is, could be detected (Table 2). Thus, it seems unlikely that changes in the onset and offset of inotropic effect are due to changes in myocardial transport processes as previously suggested for ouabain (Berrebi-Bertrand et al., 1990).

Limitations of our study should be considered. The Bayes approach allowed the estimation of all parameters of our relatively complex model but at the cost of using a priori information on the ₁ to ₂ ratios of receptor capacities and affinities. For the normal heart, the values K_A,2/K_A,1 = 45 and R_tot,1/R_tot,2 = 3, taken from independent studies, seem reasonable; however, whereas the a priori value of the capacity ratio for the ISO group was selected according to literature data, the affinity ratio was assumed unchanged since there is no empirical or theoretical evidence that suggests that hypertrophy development influences this ratio (Verdonck et al., 2003). Although this remains to be confirmed in further investigations, it is obvious from Fig. 5 that because of its relatively small contribution to the stimulus, a change in K_A,1 (implied by the unchanged affinity ratio) may be of minor importance compared with the increase in K_A,2. In conclusion, analyzing outflow concentration and inotropic response to digoxin with a mathematical modeling approach can provide insight into mechanisms of hypertrophy-dependent alterations in Na⁺ pump isoforms and digitalis action.

	Acknowledgements

 
We thank Dr. Ingrid Hoffmann-Heinroth for kind assistance in pump implantation.

	Footnotes

 
This study was supported in part by German Research Foundation Grant GRK 134/1-96.

doi:10.1124/jpet.104.078345.

ABBREVIATIONS: NCX, Na⁺/Ca²⁺ exchanger; ISO, isoprenaline; KB-R7943 (or KBR), [2-[2-[4-(4-nitrobenzyloxyl)phenyl]ethyl] isothiourea methansulfonate]; KBR, NCX blocker KB-R7943; LV, left ventricular; LVDP, LV developed pressure; LVEDP, end-diastolic pressure; CVR, coronary vascular resistance; SERCA, sarcoplasmic reticulum Ca²⁺ ATPase.

Address correspondence to: Dr. Michael Weiss, Section of Pharmacokinetics, Department of Pharmacology, Martin Luther University Halle-Wittenberg, 06097 Halle, Germany. E-mail: michael.weiss{at}medizin.uni-halle.de

	References

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