Introduction

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Modulation of the BAR in airway smooth muscle, through desensitization and resensitization, has been well studied both in vitro and in vivo (Barnes, 1995, and references cited therein). Although clinical desensitization (tolerance and tachyphylaxis) of the long-term therapeutic effects of BAR agonists has been reported both in patients with obstructive airway disease (Repsher et al., 1984; Georgopoulos et al., 1990) and in normal human subjects (Galant et al., 1978), desensitization of BAR during a short exposure to agonists does not appear to represent a significant phenomenon. Recent data suggest that the absence of detectable desensitization may be due to the large BAR reserve in airway smooth muscle (reviewed by Barnes, 1995). A rapid fade of the relaxation response to BAR agonists in the isolated guinea pig trachea has been reported (Raper and Malta, 1973; Jeppsson et al., 1992; Linden et al., 1993); however, it was characterized as neither a desensitization nor a time-dependent process.

Much effort has been directed toward the understanding of the molecular structure and regulation of BAR in cells in culture. Hall and collaborators performed second messenger measurements of the desensitization of the BAR in cultured human airway smooth muscle myocytes (Hall et al., 1992, 1993; Hall and Kotlikoff, 1995). Furthermore, hypotheses based on these cellular models have been tested in tissues from multiple organs and species, including rabbit aorta (Keitz et al., 1990), guinea pig stomach fundus (Ball et al., 1991), human bronchi (Nials et al., 1993) and guinea pig lung parenchyma (Zaagsma et al., 1983). The high density of BAR in the guinea pig trachea makes this tissue a sensitive model for the study of BAR agonist activity and for the modulation of airway responses to these drugs (van der Heijden et al., 1984; Fernandes et al., 1988).

A resensitization of desensitizing BAR at the cellular level has been described (Yu et al., 1993; Pippig et al., 1995), but the contribution of the resensitization process to the clinical efficacy of inhaled BAR agonists has yet to be demonstrated. In the current study, we hypothesized that, after BAR activation, a steady state was established between desensitization and resensitization of BAR in the isolated guinea pig trachea. We used a three-compartment phenomenological model to assess the kinetics of these processes and proposed that desensitization and resensitization of BAR were distinct concurrent events whose net result actively maintained a sustained partial relaxation response to BAR agonists.

	Methods

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Isolated guinea pig trachea. Male Hartley guinea pigs (300-500 g) were sacrificed, by CO₂ asphyxiation, up to 16 hr before an experiment, and the entire trachea from larynx to carina was rapidly excised. The trachea was immediately cleaned of surrounding muscle and connective tissue and was placed into Krebs-bicarbonate buffer saturated at low temperature (0-4°C) with 95% O₂/5% CO₂. The trachea remained in this buffer at 4°C until it was used. At that time, each trachea was divided into four approximately equal segments. In some experiments, the tracheal epithelium was mechanically removed with a cotton-tipped applicator; epithelial removal was confirmed histologically. The four tracheal segments were suspended between stainless steel hooks in 20-ml organ baths. The baths contained Krebs-bicarbonate buffer, through which was bubbled 95% O₂/5% CO₂ to maintain a pH of 7.4 ± 0.1 at 37 ± 1°C. The tissues were initially set to 2 g of mechanical tension ("basal tone") and the buffer was drained and replaced ("washed") a minimum of three times over a period of not less than 1 hr, with periodic readjustment to 2-g tension. After the tissues had been stabilized at 2-g tension, they were primed by eliciting a contraction with 10 µM CARB. Drugs were removed from the bath by replacing the Krebs buffer (washing).

Solutions. Krebs-bicarbonate buffer contains the following components (in mM), in glass-distilled water: NaCl, 110; KCl, 5; MgSO₄, 1.2; CaCl₂, 2.35; KH₂PO₄, 1.2; NaHCO₃, 25; glucose, 11. A modified Krebs solution, with 40 mM NaCl and 75 mM KCl, was used to elicit a contractile response to KCl. All drug solutions were prepared in glass-distilled water on the day of the experiment. The cumulative volume of added drugs never exceeded 300 µl or 1.5% of the organ bath volume.

Sequential responses to BAR agonists. The relaxation response to ()-ISO or to (±)-SALB was elicited and assessed with tissues maintained at basal tone and with tissues preconstricted with CARB or KCl. A typical protocol is illustrated in figure 1. After the 1 µM CARB-elicited constriction reached a plateau, 130 nM ISO was added to the organ bath. A rapid (over 350 sec) decrease of the tissue tone (relaxation) was followed by a slower (over 1500 sec) partial reestablishment of the tone (fade; desensitization). After the tissue tone had reached a steady-state level, the tissues were washed with fresh Krebs buffer. During the following 1 hr, no drugs were added, and the tissues were washed three to six times to completely remove the drugs from the tissue and to allow for a full recovery of tissue responsiveness. This protocol allowed for several reproducible assays to be conducted on the same tracheal segment. The magnitude of the first response of a given tracheal segment to BAR agonists was consistently smaller than that of the subsequent responses. Therefore, all data in this study were obtained from tissues that were treated twice, with 1) exposure to 1 µM CARB and, 2) after 20 to 30 min of wash, exposure to 1 µM CARB followed by the saturating concentration of the tested BAR agonist. With this protocol of pretreatment of the tissues, the subsequent responses of tracheal segments to BAR stimulation were consistent and reliable and could be used for multiple assays for >12 hr.

View larger version (22K): [in this window] [in a new window]   Fig. 1.   Time-dependent response of a segment of guinea pig trachea to ISO. The dots are digitized data of the analog response to 1 µM CARB and then to 130 nM ISO. For purposes of clarity, only 10% of the acquired data points are shown. The tissue was initially set to a mechanical tone of 2 g. Addition of CARB to the organ bath elicited a constriction that reached a limiting value, Tmax, of 3.41 g. Asterisks (*) denote times of drug addition. The first 70 sec of the relaxation response, the time lag, were not included in the data analysis (fig. 9). Equation 11 was fitted to the digitized data that describe the remainder of the response to ISO, which yielded curve 2. The nonlinear parameter estimation yielded the following parameters (mean ± S.E.): k1 = 50 ± 2 × 104 sec1, k2 = 21 ± 0.8 × 104 sec1, k3 = 5 ± 0.09 × 104 sec1 and Rmax = 2.27 ± 0.05 g (see table 1 for the mean values of these parameters determined on 89 tissues). The parameter t0 was assessed by subtracting the value of telap (872 sec) from the collected data. At steady state, Rss = 0.44 g (eq. 4), such that the fractional sustained response (Rss/Rmax) = 0.19. Of note, the visually assessed Rss = 0.45 g, confirming the Rss values derived by eq. 4. Two additional sets of data are depicted. Curve 1 [(Rmax)A(t) + Tmin] is the calculated tissue tension when k2 = 0, and curve 3 [(Rmax)C(t) + Tmin] is linearly related to the contribution of state C to the tissue tension. The shaded area indicates the portion of the data that is reproduced in figure 9.

Collection of data points. Isometric contractions were measured with Grass FT03C linear force-displacement transducers connected to a Grass polygraph (model 7D; Grass Co., Quincy, MA). Signals from the amplifier driver were fed through a universal interface module (UIM100; BIOPAC Systems, Inc., Goleta, CA) to a 16-channel digital-to-analog converter and data acquisition unit (MP100; BIOPAC). The signals were then processed on an Apple Macintosh SE with the software package AcqKnowledge 3.0 (BIOPAC) to control data acquisition and handle file management commands. Data points corresponding to tension were collected at a frequency of 1 Hz. Digital values were transferred to an Apple Macintosh Power PC 7100/66 or 7100/80 for nonlinear regression analysis with KaleidaGraph (Synergy Software, Reading, PA).

Data analysis. Figure 1 illustrates the time course of the response to 130 nM ISO of a trachea segment preconstricted with 1 µM CARB. We considered several kinetic models and chose the simplest one that could describe the observed kinetics. The following is the three-compartment phenomenological model:

(1)

This kinetic model assumes that the tissue consists of a large number of similarly activated units that may exist in one of three states, A, B or C. At the start of the response, immediately after addition of BAR agonist to the constricted tissue, every unit activated by this agonist concentration exists in state A. In this state, all units that may be potentially activated by agonist are occupied. As a result of this activation, state A converts with a rate constant k₁ to state B, a state associated with tissue relaxation. State B converts to state C, a state associated with a physiological loss of the relaxation and with an "alteration" of the unit such that it becomes less active. This conversion occurs with rate constant k₂. The units may return to their highly active state, state B, from state C with rate constant k₃. In developing the integrated form of the three-compartment model, we assume that each activated unit contributes to the constriction of the tissue according to its state; the contribution of a unit in state B is smaller than that of units in state A or state C. It is also assumed that the contribution to the constriction of a unit in state A is similar to that contributed by a unit in state C. These assumptions imply that, at a given concentration, T_min occurs when all units activated by this concentration of the BAR agonist are in state B. Similarly, T_max is elicited when all units activated by this concentration of the constrictor are in state A or in state C. R_max is defined as (T_max  T_min). This model enables us to calculate the level of tissue tension, T, at any given time t (see "Appendix" for derivation): Because B = 1  A  C (see eq. 7 in "Appendix"), T(t) is described by and in a final form

(2)

B(t) is the integrated form of the three-compartment phenomenological model described in "Appendix" (eq. 9). In eq. 2, T(t) contains four parameters, k₁, k₂, k₃ and T_min, that are determined by means of nonlinear regression analysis; T_max is the observed level of constriction at the time of BAR agonist addition. The value of T_max is positive, whereas T_min may have either a positive or negative value, depending on the relative magnitudes of the stimuli for constriction and relaxation. The three kinetic parameters, k₁, k₂ and k₃, represent the rate constants for relaxation, desensitization and resensitization, respectively.

Determination of time 0. The kinetic model of the response (eq. 2) describes most of the observed time course of the response. However, it is not applicable to a short time period at the start of the relaxation response during which there is a lag of the response, which begins at the time of BAR agonist addition and ends at the inflection point of the initial relaxation response (see fig. 9). The time lag, which is not considered by the three-compartment model, may be caused by drug diffusion and by an initial nonhomogeneous distribution of the tested BAR agonist in the tissue. This discrepancy between the model and the observed data required that the theoretical curve be fitted to the observed data without the time lag; also, instead of using the actual time of addition of a drug as time 0, a corrected time, t₀, was used to produce the best fit. Thus, an additional parameter was introduced with A(t), B(t) and C(t), i.e., t_elap. For example, eq. 3 shows the B(t) function with the inclusion of the t_elap parameter. A(t) and C(t) functions were similarly altered. In each assay, the collection of data points started a few seconds before the addition of the constrictor (CARB or KCl) to the organ bath. The value of t_elap was defined as the time period that started with this addition and ended at t₀, such that, at t₀, t  t_elap = 0 (see figs. 1 and 9 and "Appendix").

(3)

Substituting eq. 3 into eq. 2 yields eq. 11, which was used to calculate the tissue tension throughout this study. The values of the four-model parameters in eq. 11 (T_min, k₁, k₂ and k₃), as well as t_elap, were determined simultaneously by means of a nonlinear parameter estimation, whereas T_max was measured directly from the experimental data.

View larger version (18K): [in this window] [in a new window]   Fig. 9.   Short time lag before the onset of a monotonic response in the observed relaxation response to ISO. Shown is a portion (150 to +400 sec) of the digitized response to 130 nM ISO, after constriction with 1 µM CARB (see fig. 1 for the complete time course of this response). *, time of ISO addition, followed by a 70-sec time lag, which ends at the inflection point of the curve where a monotonic relaxation response develops. The position of the inflection point was estimated visually, and the experimental data before this point were eliminated from analysis. The telap is the time period that starts with addition of CARB (not shown; see fig. 1) and ends with the extrapolated t0. The values of Rmax and telap, in addition to the kinetic parameters, are determined when eq. 11 is fitted to the experimental data. Note that t0 is not congruent with the time of ISO addition.

(4)

Statistics. The following statistical methods were used: 1) cumulative frequency plot of the residuals (e.g., fig. 10) to assess the goodness of the fit, 2) ² test of the residuals, 3) Kruskal-Wallis H test (Mendenhall et al., 1986), 4) linear regression analysis and 5) nonlinear regression analysis (KaleidaGraph; Synergy Software, Reading, PA). A short description of these methods is found in the "Appendix."

View larger version (14K): [in this window] [in a new window]   Fig. 10.   Curves showing that the goodness of a curve fit may be used to justify the rejection of a data set. Shown are digitized data of the original analog responses that are examples of "good" and "bad" curve fits. A, the fit closely follows the curve of data points, with random variation around this line. The nonlinear parameter estimation yielded the following parameters: Rmax = 3.5 g, k1 = 75 × 104 sec1, k2 = 8 × 104 sec1, k3 = 3 × 104 sec1 and Rss = 0.98 g. B, there is systematic deviation of the fit from the data curve, most notably in the area of maximal relaxation and at the desensitization plateau, where large portions of the curve are not fit. Insets, cumulative frequency plots for the respective curve fits. The residuals are plotted as a function of their cumulative percentage frequencies. Except for the extreme values, in the case of a satisfactory fit the points in the cumulative frequency plot form a straight line, as shown in A, inset. B, inset, is an example of a nonlinear array of residual points, indicating that the curve fit is unsatisfactory. The above conclusions about the goodness of the curve fits are confirmed by means of the 2 test of the residuals (see "Appendix"): 2 = 17.29, .05 < P < .1, for the data in A, inset; 2 = 176.28, P < .001, for the data in B, inset.

Drugs. ()-ISO, CARB, (±)-SALB, epinephrine, (±)-PROP, forskolin, NECA, (±)-metaproterenol and indomethacin were obtained from Sigma Chemical Co. (St. Louis, MO); (±)-atenolol and ICI 118-551 were obtained from RBI (Natick, MA). SALM was generously donated by the Glaxo Pharmaceutical Company. All other chemicals were of the highest grade available.

	Results

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BAR agonists elicited a sustained, PROP-sensitive, relaxation response in tracheal segments maintained at basal tone. When tested on a mechanically applied basal tissue tone of 2 g, 130 nM ISO elicited a robust relaxation response that completely eliminated this tone (n = 36 tissues). Therefore, we tested the relaxation response to this concentration of ISO on tissues set to 4 to 6 g of mechanical tension. Figure 2A illustrates digitized data collected from one tissue. Addition of 130 nM ISO elicited an initial rapid relaxation that was completed within 500 sec, followed by a further, slower loss of tissue tone (500-2000 sec). The relaxation response was assayed for up to 45 to 60 min. The original basal tone was restored after removal of ISO from the organ bath by washing. Addition of 3 µM (±)-PROP to an ISO-relaxed tissue reversed the relaxation response (fig. 2A). The relaxation response could be reelicited three to five times over 10 to 12 hr in a given tissue without a detectable loss of the relaxation magnitude. Consistently, within a range of mechanically applied tone intended to mimic the range of tone inducible by 1 µM CARB (up to 7 g), there was no fade of the response to ISO within the 45- to 60-min assay. Similar sustained, PROP-sensitive relaxation responses were elicited from tissues maintained at basal tone by other BAR agonists, such as 10 µM SALB and 20 µM (±)-metaproterenol (data not shown).

View larger version (13K): [in this window] [in a new window]   Fig. 2.   PROP sensitivity of the ISO-elicited relaxation response in both nondesensitized and partially desensitized responses. A, addition of 130 nM ISO to an organ bath with a tissue set to 6 g of mechanical tension elicited a biphasic elimination of tone, consisting of a rapid partial relaxation followed by slower prolonged elimination of tone. Addition of 3 µM PROP to the tissue (*) elicited a complete restoration of the original basal tone, but no additional gain of tone, analogous to the PROP-sensitive relaxation response shown in B (n = 3). B, tissue set to 2 g of basal tone developed tension above basal tone in response to addition of 1 µM CARB. Subsequent addition of 130 nM ISO elicited a relaxation that fully eliminated the CARB-induced constriction, further eliminated 0.25 g of the preset basal tone and was followed by a regain of tone (see curve 2 in fig. 1). This experiment was repeated on nine tissues from three animals. Addition of 3 µM PROP to the tissue (*) eliminated the remainder of the ISO-induced relaxation, with no additional gain of tone beyond the CARB-induced constriction (n = 9) (see fig. 6 for similar effects of ICI 118-551 on the response to ISO).

In contrast to experiments on tissues whose tone was increased by mechanical stretching, the relaxation response to BAR agonists underwent an incomplete fade when elicited on tissues preconstricted with CARB or with KCl. Cumulative concentration-response curves for CARB yielded two response parameters, i.e., EC₅₀ (pEC₅₀ = 6.56 ± 0.25, n = 4; EC₅₀ = 0.31 µM) and slope index (0.96 ± 0.2, n = 4) (for definition of the slope index, see Clancy and Maayani, 1985). Similarly, 75 mM KCl was found to elicit a maximal contractile response.

The relaxation response and its incomplete fade are mediated through the BAR subtype. The receptor that mediates a relaxation response in mammalian airways (Barnes, 1995), including guinea pig trachea (Jeppsson et al., 1992; Kallstrom et al., 1994), has been classified as the BAR subtype. Because of antagonist interference with the kinetics of agonist action (Clancy et al., 1987), we confirmed this classification with two selective BAR partial agonists, SALB and SALM (beta-2/beta-1 = 1,375 and 85,000, respectively; reviewed by Johnson and Coleman, 1995). We also characterized interactions between the responses to these drugs; the relaxation response to both drugs was followed by a partial fade (fig. 3). After a complete response to 10 µM SALM (relaxation and partial fade), subsequent addition of 10 µM SALB did not elicit a relaxation response (n = 6; data not shown), whereas a robust response was elicited by this concentration of SALB in the absence of SALM (fig. 3). This response indicates that SALB and SALM address the same site of action. Finally, the response to an EC₅₀ concentration of the nonselective BAR agonist ISO (200 nM) was abolished in tissues preexposed to 10 µM SALB (fig. 4). Taken together, these results are consistent with the hypothesis that the contribution of the beta-1 adrenoceptor to the observed kinetics of the response to the tested BAR agonists is negligible.

View larger version (19K): [in this window] [in a new window]   Fig. 3.   Partial BAR agonism of SALB and SALM, relative to ISO. Shown are three sets of experimental data collected on two segments of guinea pig trachea; one set is a response to 10 µM ISO, one a response to 10 µM SALB and the third a response to 10 µM SALM. The observed Tmax values in response to 3 µM CARB were set to 100%. Curves shown were computer-fitted to eq. 11. The nonlinear parameter estimation yielded the following parameters for the responses to ISO, SALB and SALM, respectively: Rmax = 3.91, 3.03 and 1.46 g; k1 = 353.1 × 104, 291.8 × 104 and 46.3 × 104 sec1; k2 = 8.9 × 104, 39.5 × 104 and 12.9 × 104 sec1; k3 = 6.4 × 104, 13.3 × 104 and 12.9 × 104 sec1; and Rss = 1.63, 0.76 and 0.88 g. This experiment was repeated on 78 tissues (10 µM ISO), 64 tissues (10 µM SALB) or 30 tissues (10 µM SALM). Mean values of the parameters based on these repetitions of ISO, SALB and SALM, respectively, include k1 = 215.0 × 104, 282.7 × 104 and 66.7 × 104 sec1; k2 = 9.4 × 104, 32.3 × 104 and 15.2 × 104 sec1; k3 = 7.0 × 104, 11.1 × 104 and 14.3 × 104 sec1; Rmax = 4.47, 3.35 and 1.99 g; and Rss = 1.87, 0.93 and 0.89 g.

View larger version (15K): [in this window] [in a new window]   Fig. 4.   Elimination by 10 µM SALB of the subsequent relaxation response to 200 nM ISO. Shown is the second half of digitized data of the original analog tracing of the sequential responses of a segment of guinea pig trachea to SALB and then to ISO. In the first portion of the assay (not shown), 200 nM ISO was added to a preconstricted tissue (1 µM CARB). After completion of the normal response, the tissue was washed. Fifty minutes later, the tissue was constricted a second time with 1 µM CARB and, after the addition of 10 µM SALB and the establishment of the Rss, the kinetics of the response to 200 nM ISO were assayed. Compared with the control, this response to ISO was minimal and could not be analyzed. This experiment was repeated on eight tissues from three animals.

The fade met criteria for its classification as a homologous desensitization at the BAR level. Seven experiments were performed to characterize the nature of the fade. 1) We first tested the possibility that the fade was a result of a gradual, time-dependent formation of a stable BAR "antagonist." The Krebs solution was rapidly transferred at the completion of a relaxation and a fade into another organ bath containing a preconstricted tissue whose solution had been drained (bath replacement experiment). The second tissue developed a response to ISO (relaxation followed by a fade) with a magnitude consistent with control experiments in which the tissue was challenged with CARB and ISO in the standard fashion (n = 3). 2) We tested whether the added ISO was eliminated during the fade and, if so, whether this elimination was responsible for the partial restoration of tissue tone. A second addition of the agonist to an organ bath, after the full relaxation and fade response of a tissue to an initial exposure, did not elicit a second relaxation response (fig. 5). Of note, the protocol illustrated in figure 5 called for saturating concentrations of CARB (30 µM) as well as ISO (30 µM). This study was repeated multiple times (n = 36), varying the BAR agonist [i.e., ()-epinephrine, SALB or metaproterenol]. 3) We tested the possibility that the fade resulted from the release of a stable constrictor that functionally antagonized the stable relaxation response. Addition of 3 µM PROP reversed the remaining relaxation only to the original constriction level, implying the absence of a stable constrictor and confirming the presence of intact and functioning BAR (fig. 2B). Similar results were observed with ICI 118-551 (fig. 6) (Bilski et al., 1983). It should be noted that 1 µM CARB (3 × EC₅₀) did not elicit the maximal contractile response of the tissue, because other constrictors, such as 100 µM histamine, or higher concentrations of CARB could elicit additional constriction on top of the existing CARB response. 4) Addition of either 10 µM forskolin (n = 3; data not shown) or 10 µM NECA (an adenosine A₂ agonist) (fig. 5) to ISO-exposed tissues, after the relaxation and fade, resulted in additional relaxation responses consistently similar to those of tissues not exposed to ISO. This response implies that the relaxation elicited by activation of adenosine A₂ receptors with NECA or by direct activation of adenylyl cyclase with forskolin was not altered after the fade of the response to BAR agonists. 5) Mechanical removal of the epithelial cells from the trachea segments (n = 9; see "Methods") did not affect the qualitative or time-dependent characteristics of either the relaxation or the fade, indicating that these responses do not depend on the presence of intact epithelial cells. 6) Similarly, 30-min incubation with 1 µM indomethacin did not affect the qualitative characteristics of either the relaxation or the fade (n = 8), indicating that these responses are not completely dependent on prostaglandin synthesis. Of interest, both removal of epithelium and inhibition of prostaglandin synthesis did modulate quantitative aspects of the relaxation and fade responses to ISO. These findings are currently under investigation. 7) Cross-reactivity between BAR agonists was investigated through the addition of a second BAR agonist to the organ bath at the end of a fade caused by a first BAR agonist. Neither ISO (30 µM) nor SALB (30 µM) elicited a second relaxation response after an initial relaxation and fade response to 30 µM ISO (fig. 5). We tested several combinations of two BAR agonists (ISO, SALB and epinephrine), all with similar qualitative results (fig. 5). This apparent cross-reactivity between all tested BAR agonists is consistent with the fact that these drugs share general pharmacological characteristics, are thought to act through the same receptor and should therefore be similar with respect to their ability to elicit a relaxation and fade response.

View larger version (16K): [in this window] [in a new window]   Fig. 5.   Mediation of desensitization of the relaxation response to ISO through homologous desensitization of the BAR. Shown are data collected from a tissue incubated with 10 µM (±)-atenolol, a beta-1 adrenoceptor antagonist, for 30 min before constriction with 30 µM CARB. The tissue reached a limiting value of constriction, Tmax = 5.0 g, followed by relaxation and desensitization in response to 30 µM ISO. Subsequent addition of BAR agonists, such as 30 µM ISO or 30 µM SALB, had no effect on tissue tone. Addition of 10 µM NECA, an adenosine A2 agonist, resulted in a relaxation of the tracheal segment that was similar to the relaxation obtained in the presence of NECA alone. This experiment was repeated several times using different combinations of agonists, including ISO, SALB, epinephrine and metaproterenol, both with and without prior incubation with atenolol (n = 12), with similar results.

View larger version (18K): [in this window] [in a new window]   Fig. 6.   ICI 118-551 sensitivity of the relaxation response to ISO. Addition of 10 µM ICI 118-551 to a tissue 30 min before the addition of CARB (3 µM) eliminated the relaxation response to a subsequent addition of 10 µM ISO. This inhibition lasted >8 hr (not shown). Addition of 10 µM ICI 118-551 to a second tracheal segment prepared from the same animal at the steady-state level of the response reversed the Rss to the original level of tissue constriction, Tmax. This experiment was repeated on eight tissues from four animals.

A phenomenological kinetic model accurately describes the observed data. A phenomenological model (see "Methods") enabled us to fit three kinetic parameters (k₁, k₂ and k₃) and a steady-state parameter (T_min) to the observed data. The kinetic parameters allowed for the assessment of R_ss (eq. 4). Shown in figure 1 are data of the response of one tissue segment to 1 µM CARB, followed by 130 nM ISO. Superimposed upon the digitized data is a computer-generated nonlinear regression fit to eq. 11 (see "Appendix"). Using the three-compartment model, the time-dependent change from state A, a state of tissue constriction, to state B, a state of tissue relaxation, and state C, a loss of the relaxation, was simulated from the fitted values of the observed response (see legend to fig. 1). The initial rapid elimination of state A occurs concurrently with a slower formation of states B and C, whose steady state is described by R_ss. The ratio R_ss/R_max represents the fraction of the response that remains active at steady state. Table 1 summarizes the mean values (and their standard deviation) of these parameters collected from 89 tissues from 32 animals.

View this table: [in this window] [in a new window]   TABLE 1 Kinetics and steady-state parameters of the response to 130 nM ISO in guinea pig trachea segments preconstricted with 1 µM CARB Shown are mean values ± S.D. observed in 89 segments from 32 animals. Correlation between each parameter and the Tmax values was assessed by testing (t test) whether the slope of the linear regression was significantly different from 0. Six of the eight parameters shown were related to Tmax (at P < .001) (slope ± S.D.), as follows: k1 (14.4 ± 3.7 × 104), k2 (5.0 ± 0.74 × 104), k3 (5.7 ± 1.5 × 105), Rmax (0.32 ± 0.099), Rss/Tmax (0.07 ± 0.01) and Rmax/Tmax (0.288 ± 0.0395). The slopes of the linear regressions describing Rss and Rss/Rmax vs. Tmax were not significantly different from 0.

The interaction between the stimulus for constriction and the kinetics of the response to a BAR agonist was investigated by altering CARB concentrations. Figure 7 illustrates sequential responses of a single tissue to a saturating concentration (10 µM) of SALB after constriction with several CARB concentrations (0.1-10 µM). Constriction with CARB concentrations below the EC₅₀ (e.g., 0.1 µM) did not support partial desensitization; in contrast, CARB concentrations at or above the EC₅₀ altered the rate and magnitude of desensitization and resensitization. Consequently, the steady-state portions of the curves were reached more rapidly at higher CARB concentrations. Similar results were observed with 3 µM ISO (n = 3; not shown). The same sequential addition of KCl could not be performed due to the lack of a graded constrictor response to this compound.

View larger version (22K): [in this window] [in a new window]   Fig. 7.   Alteration by increasing CARB concentrations of the kinetics of the subsequent response to 10 µM SALB. Shown are digitized data of the original analog responses of the same guinea pig trachea segment to 10 µM SALB, after constriction with the indicated CARB concentrations. Tissues were constricted with concentrations of CARB below the EC50 (0.1 µM, n = 5), at the EC50 (0.3 µM, n = 7) and above the EC50 to a saturating concentration (1 µM, n = 14; 3 µM, n = 7; 10 µM, n = 14). There was no evidence of partial desensitization for up to 50 min, after either mechanical constriction (fig. 2A) or 0.1 µM CARB treatment, whereas constriction with CARB concentrations at or above the EC50 (inset) did result in a partially desensitized response. Comparison of Rmax/Tmax values (analysis not shown) confirmed the expected progressive functional antagonism, because these values decreased as CARB concentrations increased (Rmax/Tmax = 3.35, 1.30, 1.29, 0.98 and 0.70 for concentrations of 0.1, 0.3, 1, 3 and 10 µM, respectively).

The kinetics of desensitization and resensitization of the response to the partial BAR agonists SALB and SALM were faster than those observed with the response to ISO. Figure 3 illustrates sequential responses of a single, preconstricted (3 µM CARB) tracheal segment to saturating concentrations of ISO (10 µM), SALB (10 µM) and SALM (10 µM). In another set of experiments (data not shown), the kinetics of the response to ISO and to SALB were assessed at concentrations of 1 × EC₅₀ (130 nM and 200 nM, respectively) on tissues preconstricted with 1 µM CARB. A summary of mean values of the kinetic and steady-state parameters for ISO and SALB is presented in table 2. The partial agonist nature of SALB vs. that of ISO was confirmed at both concentrations as tested by the calculated ratio between values of the steady state parameters, R_max (0.39 and 0.61 for the EC₅₀ and saturating concentrations, respectively) (table 2), R_ss (0.67 and 0.32) and R_max/T_max (0.56 and 0.59). By using the Kruskal-Wallis H test (Mendenhall et al., 1986), we found that the rate constant of relaxation (k₁) was statistically indistinguishable between the two drugs. In contrast, compared with ISO, and at both concentrations, the values of the rate constants of desensitization (k₂) and resensitization (k₃) were significantly larger with SALB. These results were confirmed by studies with SALM; at saturating concentrations, both the partial agonist nature of SALM (calculated ratios, R_max = 0.44, R_ss = 0.48 and R_max/T_max = 0.36) and its larger values of k₂ and k₃, compared with ISO, were demonstrated (fig. 3).

Preconstriction of guinea pig trachea with KCl slowed the relaxation, compared with that with CARB, but did not change the kinetics of desensitization and resensitization of the response to ISO. Potassium chloride at 75 mM elicited a smaller contractile response (2.02 ± 0.44 g; n = 11), compared with that observed with 1 µM CARB (2.93 ± 0.86 g; n = 10) (table 3). The kinetics of the response to 1 µM ISO were assessed on tissues preconstricted sequentially with CARB and KCl (fig. 8). The rate constant of the relaxation response to ISO (k₁) with 75 mM KCl was 3.7-fold smaller than that observed with 1 µM CARB (table 3). In contrast, the rate constants of desensitization (k₂) and resensitization (k₃) were statistically indistinguishable, according to the Kruskal-Wallis H test. The calculated R_max for ISO elicited in the presence of KCl (2.69 g) was significantly smaller than that observed in the presence of CARB (4.69 g), despite the somewhat smaller constriction elicited by KCl. Of interest, even maximal concentrations of the partial agonist SALB were not sufficient to functionally antagonize the KCl-induced response; no response to 10 µM SALB was observed on tissues preconstricted with 75 mM KCl. Attempts to use lower concentrations of KCl to optimize this functional antagonism with SALB resulted in erratic and unreliable responses.

View larger version (17K): [in this window] [in a new window]   Fig. 8.   Kinetics of responses to 1 µM ISO of tissues preconstricted with CARB or with KCl. Shown are two sets of experimental data collected on two segments that were prepared from the same guinea pig trachea; one set shows a response to ISO of a tissue preconstricted with 1 µM CARB and the other a response to ISO of tissue preconstricted with 75 mM KCl. Curves shown were computer-fitted to eq. 11. The nonlinear parameter estimation yielded the following parameters for the response to ISO in the presence of CARB and KCl, respectively: Rmax = 4.3 and 2.5 g, k1 = 61 × 104 and 55 × 104 sec1, k2 = 9 × 104 and 9 × 104 sec1, k3 = 2 × 104 and 2 × 104 sec1 and Rss = 1.21 and 0.44 g. This experiment was repeated on 10 tissues (CARB) or 11 tissues (KCl) from four animals (table 3).

	Discussion

Top Abstract Introduction Methods Results Discussion References

The results of this study allow us to tentatively identify and, using a phenomenological model, to quantify the kinetics of three concurrent processes elicited by three BAR agonists in the isolated guinea pig trachea, i.e., a relaxation response, its short-term desensitization and its resensitization. Desensitization is defined as a decreasing response to a constant stimulus, assessed at either the cellular or tissue level; the clinical terms are tachyphylaxis or tolerance (Gershengorn, 1994). Resensitization is defined as the restoration of the desensitized responsiveness, either in the continued presence or in the absence of the stimulus. Molecular details of BAR desensitization and resensitization have been elucidated in cells in culture (Perkins et al., 1991, and references cited therein), including the kinetics of the response to BAR activation (Shear et al., 1976), desensitization (Su et al., 1980) and resensitization (Kurz and Perkins, 1992; Yu et al., 1993; Pippig et al., 1995). Cellular studies of desensitization of BAR in cultured human airway smooth muscle myocytes were reported by Hall and collaborators (Hall et al., 1992, 1993; Hall and Kotlikoff, 1995). These studies of the underlying biochemical mechanism of BAR desensitization appear to provide information similar to that reported in established cultured cell lines. Some of these cellular hypotheses involving desensitization and resensitization of BAR have been addressed in isolated tissues (Fernandes et al., 1988), but the counteracting dynamic nature of these events has not been previously reported in isolated tissues. We have created a kinetic model for the analysis of the short-term response to BAR agonists in the isolated guinea pig trachea. In addition to the kinetics of the relaxation response, we assessed those of its desensitization and resensitization. The results of this analysis appear to support the notion that, in the ongoing presence of BAR stimulus, there is a concurrent resensitization of desensitizing BAR. We propose that the protocol used in this study, coupled with the phenomenological model used for data analysis, are powerful tools for assessing the kinetics of these and other overlapping responses in tissue preparations.

The guinea pig trachea preparation has been widely used as a model to study the physiology and the pharmacology of BAR agonists in vitro (Castillo and De Beer, 1947; Watanabe et al., 1976; Douglas et al., 1977; Fernandes et al., 1988). The high density of BAR in the guinea pig trachea (Zaagsma et al., 1984) makes it a sensitive model for the study of BAR and its modulation by BAR agonists. Furthermore, the ability of BAR in the isolated trachea to undergo short-term desensitization offers an integrated system whereby cellular events can be probed at the level of a relatively intact organ system (van der Heijden et al., 1984; Fernandes et al., 1988).

We described the relaxation, desensitization and resensitization responses by a phenomenological kinetic model, consisting of states A, B and C (see "Methods"). We have tested several more complex models, such as the one in which state A converts to state B in a reversible manner and in which state C converts irreversibly to state A. However, the model we have chosen (eq. 1) not only is the simplest one but also is an identifiable model, in which the three parameters proposed (k₁, k₂ and k₃) may be identified with known cellular processes. In contrast, more complex models define large sets of adjustable parameter values that may not identify specific cellular processes. Currently, we are performing additional experiments using more complex protocols to exclude these alternative models.

We propose that the fade of the relaxation response to BAR agonists is a receptor-mediated event, consistent with desensitization of BAR. A series of control experiments supports this proposition. There was neither formation of a tentative stable antagonist or a constrictor nor elimination of the BAR agonist during the fade. Although both removal of epithelium and inhibition of prostaglandin synthesis failed to eliminate desensitization, these manipulations did alter some characteristics of the response. Thus, the hypotheses that the epithelium (Goldie et al., 1986) or de novo synthesis of prostaglandins (Berti et al., 1982; Omini et al., 1984) contributes to the desensitization response could not be rejected. The desensitization was homologous; relaxation responses to both NECA (fig. 5) and forskolin were not altered by BAR desensitization. Desensitization induced by one BAR agonist resulted in cross-desensitization to other BAR agonists (van der Heijden et al., 1984) (figs. 4 and 5). Finally, BAR selectivity was confirmed. We previously reported on the interference of antagonist kinetics with those of agonists (Clancy et al., 1987). Consequently, we have currently confirmed this classification by testing two selective BAR agonists, SALB and SALM (see "Results"). Under the selected experimental conditions, SALB appeared to activate the BAR and not the beta-1 adrenoceptor, because the proportion of beta-1/beta-2 binding sites in airways is less than 1:4 (Barnes, 1995). Furthermore, there is no receptor reserve for the partial agonist SALB on the BAR. Thus, if the ratio between the binding sites reflects the true ratio between the densities of the two active receptor subtypes, then 200 nM SALB and 10 µM SALM activated 1,375 and 85,000 × 4-fold more BAR than beta-1 adrenoceptors, respectively. However, we cannot rule out the contribution of beta-1 adrenoceptors in the observed response to ISO. The lack of a response to the EC₅₀ concentration of ISO (200 nM) in the presence of 10 µM SALB (fig. 4) supported the notion that the response to ISO was also mediated through activation of the BAR.

Several lines of evidence, at both the cellular and tissue levels, are consistent with the hypothesis that the short-term desensitization of responses to BAR agonists is incomplete, despite full receptor occupancy. Our kinetic studies on isolated rabbit aorta (Keitz et al., 1990; Osman et al., 1990) and on guinea pig trachea (this study) have demonstrated that the initial relaxation response to a saturating ISO concentration undergoes a slower partial desensitization, culminating in a PROP-sensitive (fig. 2A) and ICI 118-551-sensitive (fig. 6) steady state. In both tissues, we found that removal of ISO restored the original response within 60 min, confirming the work of others with guinea pig trachea (Fernandes et al., 1988; Herepath and Broadley, 1992). Similarly, short-term, partial, reversible desensitization of the response to BAR agonists has been demonstrated in cells in culture (Perkins et al., 1991). There is a reported range of 50 to 55% (Su et al., 1980; Kelsen et al., 1995) to 82% (Mukherjee et al., 1976; Fernandes et al., 1988) loss in the ability of the cells to respond to ISO stimulation after incubation with ISO, a process that is fully reversible after removal of agonist (Yu et al., 1993; Pippig et al., 1995).

Although our study does not explore the molecular nature of BAR desensitization or resensitization, our data do support the general notion of concurrent resensitization of desensitizing BAR. The strongest evidence for the existence of the resensitization process is based on the properties of R_ss. The initial, unstable relaxation response to both ISO and SALB (k₁ and R_max) evolved into a smaller, more stable relaxation response (R_ss). The properties of both responses were characteristic of BAR activation; however, the initial response partially desensitized, whereas R_ss did not. Desensitization of the initial relaxation response was incomplete, regardless of the level of BAR occupancy for both tested BAR agonists (R_ss/R_max values) (tables 1-3). We propose that there is a counteracting process that prevents full desensitization of the response, allowing for 18 to 50% activity at steady state. We further propose that the short-term desensitization of BAR in the isolated trachea is incomplete due to a concurrent, balancing, resensitization process that continuously restores the responsiveness of the desensitizing BAR.

The kinetic parameters summarized in table 1 may be expressed as half-life values (t_1/2 = ln 2/k) and thus may be compared with t_1/2 values reported for cells in culture, where the time course of cyclic AMP formation in cells is a measure of the kinetics of the response to BAR agonists. The fastest response in the trachea is the relaxation (k₁), with t_1/2 = 1.7 min. This t_1/2 value is similar to that found in B₅₀ neuroblastoma cell monolayers (t_1/2 = 0.44 min) (McCrea and Hill, 1993) and in S49 mouse lymphoma cells (Shear et al., 1976). The kinetics of the desensitization (k₂) of the relaxation response in the trachea (t_1/2 = 4.3 min) are similar to reported kinetics in cells (t_1/2 = 3 min) (Su et al., 1979, 1980; Waldo et al., 1983). However, resensitization (k₃) of desensitized BAR, elicited in cells by removal of the BAR agonist, proceeded with t_1/2 of 3 to 7 min (Su et al., 1980; Yu et al., 1993). Kurz and Perkins (1992) described similar kinetics of receptor externalization, in both the presence and absence of agonist (t_1/2 = 3-4 min). These kinetics are different from those in the isolated trachea, in which t_1/2 is 28 min. Thus, although the kinetics of relaxation and desensitization of BAR in the trachea appear to be similar to those reported in cells, the resensitization of BAR in cells in culture displayed faster kinetics than seen in the isolated trachea. This discrepancy may be explained by an interaction that occurs between receptors and their effectors in the intact tissue system, accelerating or slowing various processes, in contrast to single cells. We propose, however, that, despite these different kinetics, the effective resensitization of desensitized BAR is an intrinsic property of this receptor in both systems.

Each of the three kinetic parameters (eq. 1) may be related to a subset of biochemical processes elicited by BAR activation. The subset of processes defined collectively by k₁ may include rates of events such as cyclic AMP production and opening of K⁺ channels (Lohse, 1993; Barnes, 1995, and references cited therein). Similarly, k₂ may represent a series of cellular events implicated in BAR desensitization, such as kinase-activated receptor phosphorylation by protein kinase A and/or BAR kinase (Lefkowitz and Williams, 1978; Benovic et al., 1986; Pitcher et al., 1992), -arrestin binding to the phosphorylated receptor (Pippig et al., 1993) or sequestration of phosphorylated receptors to internal membrane compartments (Lohse et al., 1990; Lohse, 1993), which is associated with a diminished adenylyl cyclase response. This agonist-induced sequestration may be the first step in the set of events characterizing k₃, the third rate constant. The internal vesicles are rich in phosphatases that dephosphorylate BAR and reactivate them. They are then recycled to the cell membrane (Barak et al., 1994; Pippig et al., 1995), a process that has been shown to occur even in the continued presence of agonist (Kurz and Perkins, 1992). Furthermore, there is good temporal correlation between the recycling of internalized BAR back to the plasma membrane and the recovery of ISO-stimulated adenylyl cyclase activity (Garcia-Higuera and Mayor, 1994).

Thus, the steady state that we observe (R_ss) may reflect two simultaneous competing cellular processes, i.e., receptor phosphorylation (short-term desensitization) and receptor sequestration and dephosphorylation (resensitization) (Yu et al., 1993). We propose that these events overlap in time (fig. 1) and that, by applying a phenomenological model, they may be separated and quantified. We previously attempted to implement a phenomenological kinetic model for the analysis of responses to ISO in isolated rabbit aorta (Keitz et al., 1990; Osman et al., 1990). However, the Keitz model assumes a temporal separation, not overlap, between the relaxation and its desensitization. In addition, the Keitz model does not allow for characterization of the resensitization process.

The three-compartment phenomenological model that we describe here addresses these outstanding elements in the description of the observed data, namely the temporal overlap of the three counteracting processes, and allows for assessment of three kinetic and one steady-state parameter (fig. 1). The differential kinetics of the three processes (k₁ > k₂ > k₃) (tables 1-3) resulted in the observed unique time course of the response to ISO (fig. 1) and to SALB (fig. 3). A comparison of the t_1/2 values for each of these processes, as well as the relative values of the kinetic parameters (e.g., for the response to ISO, k₁/k₂ = 2.64 and k₂/k₃ = 5.50; n = 56) (table 1), indicate that there is, indeed, temporal overlap between them. If this is true, then the magnitude of the observed relaxation response is an underestimate of the correct measure of the potential full relaxation response to ISO stimulation [(T_max  T_min)/observed relaxation = 1.7] (fig. 1). The efficiency of the resensitization processes is demonstrated by the high value of the ratio R_ss/R_max that is derived from the values of k₂ and k₃ (eq. 4). Under all experimental conditions tested in this study (three different concentrations of ISO, two of SALB, two of CARB and one of KCl), R_ss varied from 18 to 44% of R_max (tables 1-3).

Experimental conditions required for detecting BAR desensitization in the isolated trachea appear to be different from those described for cells in culture. In the cell studies, BAR desensitization has been elicited by incubation with a BAR agonist alone. In the isolated trachea, however, desensitization of the response to BAR agonists could be measured only when a constriction was elicited through activation of the muscarinic receptor by CARB at concentrations above its EC₅₀ (fig. 7) or through membrane depolarization of the tissue by 75 mM KCl (fig. 8), and it failed to occur in their absence (fig. 2A) (van der Heijden et al., 1984). Furthermore, the k₂/k₃ ratio may be altered by an interaction between the desensitization response pathways and those of active constriction, because we observed that gradual increases in the CARB stimulus for constriction affected