Preventing Rapid Receptor Desensitization at
the beta-1-Adrenergic Receptor with Agonist/Antagonist Combinations
Abstract
Background: Desensitization is a
serious side effect of many drugs and is also a fundamental problem for modeling
drug-receptor interactions. Although there has been very little theoretical or
experimental work to describe the pharmacological effects of
agonist/antagonist combinations, this study was designed to test both a
theoretical model and a specific method to prevent rapid receptor
desensitization by using agonist/antagonist combinations. Preventing
desensitization may have relevance for many important drugs, including the-adrenergic agonist
drugs, which desensitize yet are frequently used in medical practice to promote
increased heart rate and contractility. Because desensitization is a
serious side effect, these drugs are no longer the logical or preferred treatment
for heart failure. Subsequently, the1-antagonist drugs such as
metoprolol (Lopressor) have replaced the-adrenergic agonist drugs
as a standard treatment for heart failure. From this perspective, it is
important to understand how the -agonist drugs interact
with the -antagonist drugs at the
level of the initial receptor response.
Results: The-agonist drugs
(isoproterenol (Iso) or dobutamine (Dob)) were given as intravenous (IV)
solutions to rats with or without the beta-1-antagonist, metoprolol (Met),
which was given either as a fixed amount or as part of a specific
agonist/antagonist ratio. The initial experiments demonstrated that
desensitization occurred for all of the animals receiving either the Iso or Dob
solutions alone. The theoretical model fit these initial experiments with
biophysical parameters, which were then used in calculateing a specific
agonist/antagonist ratio for making the agonist/antagonist combination solution
to prevent desensitization. Both the Iso/Met and Dob/Met agonist/antagonist
combination solutions significantly prevented desensitization while maintaining
near maximal responses in all of the animals tested. This theoretical
model predicted these responses and fit the experimental data with reasonable
biophysical parameters.
Conclusion: This study supports the concept
that the earliest events of receptor desensitization can be modeled and
controlled at the level of the initial receptor response. The theoretical model
appears to be the only model capable of describing this behavior with
reasonable biophysical parameters. This explanation for rapid desensitization
suggests that the beneficial effects of metoprolol for heart failure may result
from its action on the initial events of receptor activation. This method may
also be useful for describing and preventing desensitization in other drugs
that desensitize their receptors.
Abbreviations
Iso = isoproterenol, Dob
= dobutamine, Met = metoprolol, Iso/Met = the combination of isoproterenol with
metoprolol in the specific ratio, Dob/Met = the combination of dobutamine with
metoprolol in the specific ratio. dP/dt = maximum time-derivative of left
ventricular pressure. LVP = maximum left ventricular pressure. IV =
Intravenous. GPCR = G protein-coupled receptors. GRK = G protein-receptor
kinase.
Background
Receptor desensitization
appears counterintuitive because the addition of more of an activating ligand
lessens the elicited response. Although many of the most rapid and important
biological events desensitize [1-13], the earliest events of the receptor response
haven't been examined with suitable biophysical models that suggest a plausible
mechanism for the events that produce rapid desensitization. The rat has
previously served as a late-stage or chronic desensitization animal model
[14-16]; however, there have been no attempts to both model and test methods to
prevent desensitization at the level of the initial receptor-ligand
interaction. Therefore, this study was designed both to test a theoretical
model and to prevent rapid receptor desensitization using a specific method
[17].
The drugs isoproterenol (Iso) and dobutamine
(Dob) are two b-adrenergic drugs frequently used for the
treatment of patients with a variety of conditions including heart block,
decreased cardiac output, and acute heart failure. They are sympathomimetic
adrenergic agonists that activate the beta-1-adrenergic receptors, and thereby
promote increased heart rate and contractility. The undesirable side effects
that accompany these drugs include desensitization, tachycardia and arrhythmias.
Since many of the abnormalities in adrenergic signaling observed in late-stage
heart failure in both human and animal models are considered a result of
adrenergic desensitization, the adrenergic agonists have gradually lost favor
as the logical treatment for heart failure [13]. Conversely, metoprolol
(Lopressor), a relatively selective beta-1-adrenoreceptor blocker, is now
frequently prescribed for heart failure [18] although the scientific rationale
behind this remains obscure.
Historically beta-1-receptor blockers, such as
metoprolol (Met), were known to depress cardiac function; however, more recent
data have confirmed that moderate doses of beta-1-receptor blockers produce
beneficial effects in most cases of individuals with heart failure [18,19].
Since the scientific rationale for these observations is uncertain, it is
important to understand the interactions which are possible between
beta-1-receptor blockade and -agonist induced
desensitization in the heart. From this perspective, this study tests how
a -adrenergic agonist
combined with a beta-1-receptor antagonist in a known and specified agonist/antagonist
ratio can decrease or prevent the desensitization due to the agonist [17].
Controlling receptor desensitization would offer new methods for improving drug
therapy and provide a scientific rationale for why beta-blockers improve the
cardiac function of patients with heart failure.
Desensitization also represents a fundamental
problem for the theoretical modeling of drug-receptor interactions. Most
theories of receptor activation have difficulty modeling the nonlinear
interactions between receptor desensitization and competitive antagonists with
meaningful biophysical parameters. These difficulties arise primarily because
the competition of an antagonist at the receptor should theoretically block the
receptor binding with an agonist and thereby diminish the response. However,
since some receptor desensitization is very rapid, there must be at least one
alternative explanation for rapid desensitization at the earliest level of
receptor activation. Although the role played by the receptor-G protein
decoupling schemes involving kinases have been most prominent, they are
experimentally difficult to verify for very rapid receptor desensitization and
may be secondary phenomena, which occur after the initial phase of receptor
desensitization has past. Therefore, revealing the relative importance of these
phenomena may assist in placing receptor activation and desensitization into an
appropriate temporal perspective.
Receptor activation or desensitization schemes
usually involve a diagram of the chemical interactions between the ligand and
the receptor. An implicit and often overlooked assumption in these schemes is
the nature of the reaction quotients or approximate steady state chemical
equilibrium constants. These parameters represent collections of various
chemical species, which are often lumped together into a bracket sign
representing a concentration. How these reaction quotients combine and are
altered by unequal ligand binding to two or more receptor states represents a
challenge both to pharmacology and to chemical theory. A better understanding
of how drugs work at the level of the receptor may result from an understanding
of how these reaction quotients are altered and what chemical species they
specifically represent.
An underlying premise in most models is that the
chemical equilibrium of the receptor controls the response; however, it is
increasingly recognized that it is the perturbation in the equilibrium that
determines the receptor response although many theories neglect to calculate
the net change in this parameter as the response of the system. Normally the
underlying chemical ministate equilibria, which compose the overall equilibrium
constant are ignored. These perturbations require a deeper
understanding of how the underlying equilibria interact and combine with each
ministate within the overall chemical equilibrium. This raises much
more complicated questions than we can discuss here; however, we can study
these chemical perturbations in more accessible systems that are more tightly
controlled and easier to recognize. Ironically, the membrane-embedded, cellular
receptor may be a better system to witness these chemical perturbations
directly. From a chemical perspective, the changes in competing ministate
equilibria may be minimized in a large, membrane-embedded molecule such as a
receptor. Since these changes are connected to changes in the initial receptor
equilibrium that produce observable biological responses, they may be more
accessible because these responses often obey Weber's law.
Weber's law gained wide recognition when it was
discovered that all of our sensory perceptions obey this law; however, the
underlying physiological and biochemical basis for this law hasn't been clearly
understood [20]. Weber's law has been previously linked to an equation for the
overall equilibrium that equates equivalent perturbations produced by either
the transfer of a fraction of weight, w, or by an external
weighting given by, S1 and S2,
(1)
Where w1 and w2 are
the weights on each side of a simple balance and S1 and S2 are
the external weights added to each side. Equation (1) represents a simple
equation of equilibrium that also obeys Weber's law [20].
Interestingly, Equation (1) can be shown to
represent a two-state, chemical equilibrium of a cellular receptor by substituting
Langmuir binding expressions, S1=R1(S)/(S+K1)
and S2=R2(S)/(S+K2), for
the binding of a molecule, S, with each receptor state, R1 and
R2. Making these substitutions and substituting R for w into Equation (1)
yields,
(2)
Equation (2) calculates an equivalent
perturbation between two receptor states, R1 and R2, in terms of the competing reaction quotients, K1 and K2 for S, the binding
molecule or ligand. Where R represents the net
transfer of receptor states.
Surprisingly, Equation (2) is identical to a
two-state model that was previously derived and tested for its ability to model
cellular receptor activation and desensitization [17]. With a few minor
substitutions, Equation (2) can also be expressed in terms of this previously
derived, two-state, pharmacological model [17].
For a receptor in an initial chemical equilibrium
between two-states, the selective affinity of agonist drugs, or ligands, for
the high affinity state, RH, will perturb the initial receptor
equilibrium and thereby produce a net shift in this initial equilibrium as the
net receptor response, RH, which is equivalent
to R in Equation
(2). This is similar to most other two-state models with R and R*
states corresponding to inactive and active receptor states except that this
model relates the response to a fundamental equation for physical equilibrium
(Equation (1)), which can be solved for the net shift in the original
equilibrium, RH,
(3)
Where RH and RL represent
the amount of unperturbed receptor existing in initial high and low affinity
states respectively, and D represents the concentration of the binding drug or
ligand. Equation (2), which was derived separately from Equation (3), is
exactly analogous to Equation (3). Equation (3) with the factor of (1+ [I]/ Ki)
for an antagonist, I, binding equally to each receptor state, multiplied times
each of the dissociation constants, KDH and KDL, has
been shown to accurately model the dose-response behaviors for agonists with
and without antagonists in a wide variety of drug-receptor systems [17].
By taking the derivative of Equation (3) with
respect to the dose, D, and setting the derivative to zero for the maximum
response with the factor (1+ [I]/ Ki) for a competitive antagonist
multiplied times each of the dissociation constants, KDH and KDL,
the concentration of the antagonist as a fractional dose of the agonist ([I]=f
[D]) can be derived as,
(4)
Where f is the agonist to antagonist
ratio that is necessary and sufficient to prevent desensitization at the
receptor [17]. This is the specific ratio that was tested for its ability to
prevent desensitization.
For calculations of the model versus the
experimental response, the ratio given by f was inserted into
Equation (3) by altering the inhibition expression (1+ [I]/ Ki) for
a competitive antagonist multiplied times each of the dissociation constants
for the agonist, KDH and KDL. By this alteration the
term (1+ [I]/ Ki) for the competitive antagonist, becomes (1+ f [D]/
Ki) where the antagonist concentration [I] has been replaced by f
[D]. Where f is the fractional dose of antagonist relative to the dose of
the agonist [D] [17]. Substitution produces the following specific
modifications to the agonist dissociation constants: KDH(1+ f [D]/ Ki)
and KDL(1+ f [D]/ Ki). These were then inserted into
Equation (3) in order to model the experimental responses for the
agonist/antagonist combination solutions.
Results
Isoproterenol (Iso) Experiments
The time-derivative of
the blood pressure in the ventricle of the heart (dP/dt) is an accepted
measurement of the contractility of the heart. As the strength of the
contractions in the ventricle of the heart goes up, the rate at which the
pressure in the ventricle rises will increase. Increased dP/dt
therefore implies increased contractility and also serves as a measure of -receptor stimulation and
desensitization.
The initial experiments with Iso alone
demonstrated desensitization to the IV agonist solution and provided data for
the parametric fit of the model (Table 1). From this fit, the
agonist/antagonist ratio was calculated and then used to make the specific
agonist/antagonist ratio for the Iso/Met solution, which was subsequently
tested in the animals. Plots of the experimental responses for the Iso/Met
solution were compared to the responses of the Iso solution alone, and to the
model plots.
As shown in Figure 1A, the plot of the
responses to increasing levels of infusion of the Iso solution shows increasing
dP/dt at the lower dosages, but peaks and rapidly declines at the higher
infusion dosages. This shows the presence of desensitization in these animals
to the agonist solution alone. The fit of the model to these initial
experiments is displayed as a line plot in Figure 1A for comparison with the
experimental plot (compare model (dark circles) with experiment (light
squares)). This initial experiment demonstrates both the degree of
desensitization in these animals and the ability of this model to fit the
experimental data.
Figure 1 - Average responses for the
rats given Iso, Met or Iso/Met solutions
Figure 1A: Plots of the model in dark symbols
compared with the experimental results in light symbols for a group of animals compared
with a separate group of animals that received a fixed infusion of metoprolol
(Met) IV solution at 1mg kg-1min-1 with the Iso
infusions varying. The plots show the responses of the heart "dP/dt
(%)" to increasing infusions of the isoproterenol (Iso) solution alone, or
with Met at a fixed level of infusion (experiment - "Met (fixed)"
(light circles), model - "RH Met (fixed)"
(dark triangles)).
Figure 1B: Plots for both
the model and experimental data to the isoproterenol (Iso) solution (model,
"RH Iso" (dark
circles) and experiment, "Iso" (light squares)), which were also
plotted in Figure 1A for reference. The plots of the Iso/Met IV solution are
significantly different from the Iso solution at the 95% confidence interval
for the infusion rates of 10 mg kg-1min-1 and
above - paired t-test. The Iso/Met solution is also plotted for
comparison with the model (generated by substitution into Equation (3) with the
modified dissociation constants, KDH(1+ f [D]/ Ki) and KDL(1+
f [D]/ Ki)) (compare model, "RH Iso/Met" (dark
triangles) and experiment, "Iso/Met" (light circles)).
Figure 1A also shows a plot for a separate group
of rats that received a fixed concentration of the metoprolol solution, Met
(fixed), at 1.0 mg kg-1min-1, which decreased the dP/dt
response to less than 40% of the peak. This experiment was done to determine
the apparent Ki for Met, and to demonstrate that the Met
solution was acting as an antagonist in these animals. The model successfully
fit this data with the factor of (1+ [I]/ Ki) for the antagonist
multiplied times each of the dissociation constants, KDH and KDL in
Equation (3) for the response.
The Iso/Met IV solution was premixed as a
1:85 mg kg-1min-1 ratio, which was calculated
by Equation (4) with the biophysical parameters derived from the initial
experiments (Table 1). In addition, the expected response was
calculated from Equation (3) for the response with the modifications to the
dissociation constants as mentioned above and in the Methods section, and plotted
for comparison with the experimental results. These animals were tested with
either the IV Iso or Iso/Met solutions. Figure 1B shows the
responses to the Iso solution with the standard error bars for a direct
comparison with the responses to the Iso/Met solution and the predicted
response from the model. The Iso/Met solution increases the dP/dt at
low dosages, but at the higher dosages the dP/dt levels off at an elevated and
sustained level rather than decreasing sharply, as seen previously for the Iso
solution (see Iso (light squares) vs. Iso/Met (light circles) in Figure 1B).
Therefore, compared to the Iso solution, the Iso/Met solution displays a more
sustained and maximal response into infusion ranges where desensitization would
have normally occurred.
Table 1 - Biophysical Parameters from
the Theoretical Model
Experiments:
|
Parameters:
in mg kg-1min-1 or
(approximate nM)
|
|||
KDH
|
KDL
|
Ki for Met
|
Ratios*
"f "
|
|
Isoproterenol (Iso)
|
1.3 (5.2)
|
19 (77)
|
300 (440)
|
1:85 (1:31)
|
Dobutamine (Dob)
|
1.7 (5.2)
|
700 (2100)
|
40 (58)
|
1:1.6 (1:0.8)
|
* Ratios
were calculated by Equation (4), where "f ", represents the agonist
to antagonist ratio that is sufficient to prevent receptor desensitization
[17].
The modified Equation (3), based on the initial
parameters, largely predicted these responses (see model, RH Iso/Met (dark
triangles), and experiment, Iso/Met (light circles), in Figure 1B). The amount
of Met in the Iso/Met IV infusion is insufficient to inhibit the
response as compared with the fixed amount of Met in the initial experiments
(Met (fixed) in Figure 1A). At the infusion level of 10g kg-1min-1,
the dP/dt is sustained at a significantly higher level for the Iso/Met infusion
than the dP/dt for the Iso infusion alone at 10g kg-1min-1. This demonstrates the ability of the agonist/antagonist combination
solution to sustain the maximum response well into infusion ranges that
previously showed severe desensitization with the agonist solution alone.
In Figure 2A and 2B, responses are plotted
individually for three rats that served as their own controls. With the Iso IV
solution alone, the rats initially showed a range of peak responses and
subsequent desensitization; however, their individual responses with the
Iso/Met IV solution were more sustained with much less desensitization. These
plots show that the desensitization is prevented for each of the individual
rats. This might not have been expected given that these rats desensitized at
different levels of infusion and to different magnitudes of depression. Also it
might not have been expected given that the biophysical parameters for making
the Iso/Met solution were derived from initial experiments obtained from a
different set of rats. Comparing the individual responses in Figures 2A and 2B,
the responses of all the animals to the Iso/Met solution show a steady rise to
peak levels of dP/dt and a continuous and sustained response well past
previously measured desensitization levels. Therefore, these results
demonstrate that this method correctly calculates a specific agonist/antagonist
ratio that largely prevents the experimentally observed desensitization.
Figure 2 - Responses of individual
rats to the Iso and Iso/Met solutions
Figure 2A (above): Plots of the dP/dt responses in mmHg
sec-1 of three animals that served as their own controls. With
the higher IV infusion levels of the isoproterenol (Iso) solution the
desensitization is evident as a shape decline in responses for all of the
animals.
Figure 2B (below): The same
animals as in Figure 2A except that they received the Iso/Met IV solution. The
dP/dt responses are significantly different from those for the Iso solution at
the infusion levels of 10 mg kg-1min-1 and above.
Modeling of Spare Receptors
Although the phenomenon
of spare receptors has been observed for many years, pharmacological theories
have had difficulty accounting for this observation in a meaningful,
biophysical model. Therefore, in order to further test the abilities of this
theoretical model, the apparent spare receptor reserve was modeled by comparing
the response curve given by Equation (3) to the total binding curve, which was
calculated as the sum of the Langmuir binding equations for each of the high
and low affinity states (Total Binding = RH(D)/(D+ KDH) +
RL(D)/(D+ KDL)). Previously, Brown, et al. observed
that the plots of beta-adrenoceptor occupancy versus responses for rat left
atria and papillary muscles had a rather large receptor reserve: 50% of maximal
response was produced with only 1-3% of beta-adrenoceptor occupancy [21]. As
shown in Figure 3, the percent of the receptors needed for a fifty percent
maximal response appears to be five percent or less when compared to the amount
of the total bound, which is in good agreement with Brown, et al.
[21].
Figure 3 - Spare receptors for the
isoproterenol response
Two plots of the theoretical model: one is the percent
total binding and the other is the percent response. The total
binding was calculated from the sum of the Langmuir binding equations for the
high and low affinity states, Total Binding = RH(D)/(D+ KDH)
+ RL(D)/(D+ KDL). The response was calculated from
Equation (3). The values for KDH and KDL were
taken from Table 1 for Iso. RH and RL in
Equation (3) were set equal to 10 and 190 respectively, which represents about
5% of the receptors in the high affinity state, RH.
The problem is that there are at least two
binding affinities that affect efficacy and binding. It is the interplay
between these that determines both response and binding. From this model, the
spare receptor reserve arises from the fraction of receptors that are shifted
from the total receptor pool. This results because only a relatively small
fraction of the total receptor states are shifted to increase the amount of the
higher affinity state. Therefore, the phenomenon known as spare receptors
becomes understandable, since the total amount of this shift is, not
surprisingly, some relatively small fraction (deltaRH from Equation
(3)) of the total number of the total bound pool of receptor molecules.
Therefore, this model is consistent with the experimental findings of a large
receptor reserve observed for beta-adrenoceptor agonists in the b1-receptor system of rat
heart.
Dobutamine Experiments
Similar to the procedure
for the Iso experiments, the KDH, KDL and Ki were
derived from the fit of Equation (3) to the average values of the experimental
data for the Dob infused rats. The model fit the experimental findings within
the range of error for these experiments (compare model - RH Dob (dark triangles)
with experiment - Dob (light triangles) in
Figure 4). A separate experiment was performed to determine the Ki for
Met in the animals receiving the Dob IV solution alone (not shown). All of the
parameters, KDH, KDL and Ki, were
inserted into Equation (4) to calculate the specific ratio for making the
Dob/Met agonist/antagonist solution (see Table 1). This solution was prepared
before hand, and subsequently used for the experimental comparisons with the
Dob solution as discussed below. In addition, the calculated ratio, "f
", for Dob/Met was entered into Equation (3), and plotted for a direct
comparison with the experimental results.
Figure 4 - Plots of the average
responses for the dobutamine exposed rats
These plots show the model compared with the
experimental values for either the dobutamine (Dob) solution or the combination
solution of dobutamine plus metoprolol (Dob/Met). At the 200 mg kg-1min-1 infusion
level the response for the Dob/Met infusion (94%±4) was significantly higher
than for the Dob infusion alone (48%±10). The model,
generated by substitution into Equation (3) of the modified dissociation
constants, KDH(1+ f [D]/ Ki) and KDL(1+ f [D]/
Ki), was plotted for comparison with the experimental findings
(compare the model in the dark symbols - "RH Dob" (dark
triangles) and "RH Dob/Met" (dark
circles) with the experiments in the light symbols - " Dob"
(triangles) with "Dob/Met" (squares)).
Similar to the results obtained for the Iso
experiments, the responses of the animals to the Dob IV infusions showed an
initial increase in dP/dt response with the dP/dt reaching an average peak at
20g kg-1min-1 (range:
4-100g kg-1min-1)
followed by a sharp decline ( Dob in Figure 4).
The decline in dP/dt was on average 40% below baseline levels. This decline was
present to some degree in all of the responses (range: 56 to -135%), but had a
wide range of variability. This demonstrates that all of these rats were
sensitive to Dob induced desensitization although some were much more sensitive
than others.
Table 2 - Summary of the Responses to
the Agonist Solutions Compared to the Agonist/Antagonist Solutions
1) Experiments with Iso or Iso/Met solutions:
|
|||
Iso
(g
kg-1min-1)
|
dP/dt (%)*
Iso (n=6) ’ÄÝ
|
Iso/Met
(g
kg-1min-1)
|
dP/dt (%)
Iso/Met (n=3)
|
5
|
55±21
|
5
|
97±3||
|
10
|
-15±35’Ä°
|
10
|
96±2||
|
20
|
-2±7¬ß
|
20
|
85±15
|
2) Experiments with Dob or Dob/Met solutions:
|
|||
Dob
(g
kg-1min-1)
|
dP/dt (%)
Dob (n=9)
|
Dob/Met
(g
kg-1min-1)
|
dP/dt (%)
Dob/Met (n=4)
|
200
|
48±10
|
200
|
94±4
|
400
|
9±14
|
500
|
86±8
|
800
|
-38±28
|
1000
|
73±7
|
* Values of dP/dt (%) are
means±s.e.
’ÄÝThe data for this column include data from the
three paired rats plus three additional rats tested with the Iso solution
alone.
’Ä°At 10g kg-1min-1 for
the Iso IV infusions, arrhythmias occurred in 1 rat therefore the data was
discarded and n is reduced from 6 to 5.
§ At 20g kg-1min-1 for
the Iso IV infusions, arrhythmias occurred in 4 rats therefore the data was
discarded and n is reduced from 6 to 2.
|| P < 0.05 Student's t-test
P < 0.005 Student's t-test
In a separate experiment, the Dob/Met (1.0/1.6g kg-1min-1)
solution was administered as a single IV solution. Comparing the Dob/Met to the
Dob infused group of animals, a maximum response was maintained throughout the
infusion range, whereas the Dob group showed a progressive decline in the
average response to values below baseline (see Figure 4 and Table
2).
At 200g kg-1min-1 the
dP/dt average response for the Dob/Met infusion (94%±4) was significantly
higher than the dP/dt average response for the Dob IV infusion (48%±10)
. In addition, this theoretical model predicted
these experimental findings (compare the model, dark symbols - RH Dob (dark triangles)
and RH Dob/Met (dark circles)
with the experiments, light symbols - Dob (triangles)
with Dob/Met (squares) in Figure 4) based upon Equation (3) with modification
for a competitive antagonist and the ratio from Equation (4).
Discussion
All of the experiments
with the agonist drugs alone rapidly desensitized the dP/dt responses for each
animal at the higher infusion levels. After infusions of either the Iso or Dob
agonist solutions, peak responses occurred on average at 5 g kg-1min-1 (range:
1-5) for the Iso solution or 20g kg-1min-1 (range:
4-100) for the Dob solution and subsequently declined. The declines from these
peaks were variable in their onset with step reductions in responses to as low
as 15% to 40% below baseline levels (Table 2). The increased variability within
the desensitization range (±35% Iso and ±28% Dob see Table 2) also suggests
that there exists the potential for large variations in response when using
these drugs clinically. However, by combining either agonist (Iso or Dob) with
metoprolol in the specified agonist/antagonist ratio, the reductions in
responses were significantly less than the controls (compare Iso (squares) vs.
Iso/Met (circles) in Figure 1B and Dob (triangles)
with Dob/Met (squares) in Figure 4).
Although some animals were much
more sensitive than others to the desensitization potential of these drugs,
there may be a genetic component to the onset of desensitization, which was not
explored. However, both in the concentration of onset and the decline below
baseline values (Figure 2A and Table 2), all of the animals receiving either
the Iso/Met or the Dob/Met agonist/antagonist solutions showed significantly
less desensitization for each individual animal. In addition,
maximum responses were largely sustained for each animal receiving the
agonist/antagonist combination solutions. As seen in Table 2, which summarizes
these experimental results with their statistical significance, the Iso/Met or
Dob/Met solutions produced significantly higher responses past the peak than
the responses for either the Iso or Dob solutions alone.
Interestingly, the group of animals that
received the Dob solution alone did not show cardiac arrhythmias comparable to
the Iso group, but did show a comparable diminution in dP/dt response. This
suggests that arrhythmias and desensitization are not necessarily coupled.
However, using the Iso/Met agonist/antagonist combination solution, the
occurrences of arrhythmias and variations of these responses were both markedly
reduced compare to either of the agonist solutions alone.
These experiments demonstrate that specific
agonist/antagonist combinations prevent rapid receptor desensitization over a
wide range of infusions and also support the hypothesis that desensitization
can be reduced or eliminated at the level of the receptor. This may also relate
to observations that partial agonists appear to cause less desensitization than
full agonists in some receptor systems [5]. In addition, this study further
suggests that a full agonist can be made into a "full partial
agonist" by adding a specific amount of an antagonist. This concept may
have important implications for the modeling of pharmacological drug-receptor
interactions since other receptor reaction schemes appear unable to model these
results with meaningful biophysical parameters.
Since some of the abnormalities observed in
adrenergic signaling in late-stage heart failure are most likely due to
sustained adrenergic stimulation and concomitant receptor desensitization [13],
this study may provide an additional, scientific rationale for how beta-blocker
therapy improves cardiac function in patients with heart failure [18,19]. This
study suggests that this improvement results from the ability of
beta-1-antagonists to inhibit desensitization in the presence of desensitizing
levels of -agonist drugs or the naturally
occurring -agonist hormones such as
epinephrine.
From a modeling perspective, this model was
able to both describe and predict the experimental responses for the animals
receiving either beta-agonist drugs, or beta-agonist/antagonist
combinations (compare the model, dark symbols, with the experiments, light symbols,
in Figures 1B and 4). One reason why other theories of drug-receptor activation
have difficulty modeling these types of agonist/antagonist interactions is
because the additional competition of a competitive antagonist at the receptor
should, theoretically, hinder the receptor binding with an agonist and diminish
the maximal response. Although it appears surprising that the combination of an
agonist with a competitive antagonist in a specific ratio can maintain the
receptor in an active conformational state, this theoretical model predicts
these results and supports the concept that desensitization can be controlled
primarily at the level of the initial receptor response.
Although there have been extensive studies on
the downstream mechanisms associated with receptor desensitization and the
decoupling of receptors from their intracellular signaling pathways, the timing
and sequence of these events in relation to receptor desensitization still need
further clarification. This study raises the prospect that the receptor may
remain in an activated state without being desensitized. Therefore, the theory
that the phosphorylation of receptors by heterotrimeric guanine nucleotide
binding protein (G protein) coupled receptor kinases (GRKs) is a universal
regulatory mechanism that leads to desensitization of G protein signaling (18)
may need revision based upon the findings of this study. Whether activated
GPCRs are first phosphorylated by GRKs and then bound by molecules of arrestin,
which block the binding of the G proteins, or whether there are other states of
GPCRs that are phosphorylated to modulate their activity remains open to
further investigation. However, this study suggests that desensitization can
occur rapidly in the initial binding and activation phase of the receptor and
that a competitive antagonist increases the activation of 1-receptors in the presence
of desensitizing amounts of an agonist. These observations argue against the
belief that GRK-mediated receptor phosphorylation is primarily responsible for
impairment of receptor signaling (18).
This theoretical model advances the understanding
of receptor desensitization and receptor activation in terms of a biophysical
model. Making a distinction between effects on binding and effects on
conformation change is arguably the fundamental problem of modern molecular
studies of receptors; however, in the context of this model, ligand binding and
conformation change are linked by two binding affinities for the two receptor
states. Although, the initial response of the receptor may be far from
equilibrium, it tends toward equilibrium over time. However, it is the net
perturbation (RH) that is the
activation step of the receptor. The biophysical origin of these
separate affinities for each receptor state may result from the charged states
of at least one residue within the receptor (24). Agonists act by shifting the
initial receptor equilibrium toward the active state of the receptor, which may
be the base or negatively charged state (24). Competitive antagonists bind with
each receptor state more or less equally and thereby produce no net shift in
the initial receptor equilibrium states. The quantity of this shift can be
calculated by RH from Equation (3) and
is entirely due to the initial interactions of the ligand with the receptor,
which largely depends upon the electrostatic interactions of the ligands with
the acid and base states of the receptor (24). In the context of this model, an
alternative explanation for rapid desensitization is that the net shift back
toward the inactive receptor state (desensitization in this model) occurs due
to the increased binding of the agonist to the lower affinity state (22,23).
Therefore, desensitization results from the binding of the agonist with the
inactive receptor state, which produces a net shift in RH back toward the
initial receptor equilibrium values (22).
Combining an antagonist with an
agonist in a specific ratio, prevents the binding of the agonist with the
inactive receptor state and thereby prevents the desensitization of the
receptor. The specific ratio of antagonist to agonist can be calculated so
that the competition with the active receptor state is minimized relative to
the competition with the inactive, or lower affinity state, thereby maintaining
the essential agonist interaction with the active receptor state (17).
Conclusions
This study supports the
key concept that the earliest events of receptor desensitization can be modeled
and controlled at the level of the initial receptor response. Since competitive
antagonists bind to the receptor, but do not produce desensitization, the
binding of a molecule to the receptor alone isn’t sufficient to produce
receptor desensitization.
Therefore, what are the crucial differences between
an agonist and antagonist ligand that determines whether or not a receptor will
desensitize? This study has attempted at least a partial answer to this
question. By combining a competitive antagonist with an agonist that would
normally desensitize the receptor, receptor desensitization was prevented.
These experimental observations suggest that the action of each molecule shifts
the net change in the underlying receptor equilibrium according to Equation (1)
of the theoretical model. This equation, with Langmuir binding as the weighting
factor for each side, demonstrates the origin of desensitization as arising
from the inherent competition of an agonist for two receptor states (22,23).
This model describes all of the observed behavior and spare receptors with
reasonable biophysical parameters.
The beneficial effects of Lopressor and
other beta-blockers in enhancing cardiac function in patients with heart
failure may have an improved scientific rationale due to the observations from
this study. Previously, it was uncertain why beta-blockers improved heart
function in these patients; however, by showing that desensitization can be
inhibited by antagonists suggests that for those patients that have
desensitized receptors, beta-antagonists may assist by directly producing more
sensitized receptors.
Methods
Preparation of the animals
For each of the following
experiments Sprague-Dawley rats (weight range 200 g) were anesthetized by
intraperitoneal (IP) injection of 75-mg/kg sodium pentobarbital (Sodium
Nembutal). All appropriate and humane, animal protocols were strictly followed
for all experiments. Following sedation, the neck of the rat was incised and a
tracheotomy was performed, inserting a 14-gauge angiocatheter sheath into the
trachea of the rat and securing it with a silk tie.
The
angiocatheter was connected through a small tube to a small animal respirator
supplied with 1.0 liters of oxygen per minute and set to 95 breaths per minute.
The right carotid artery was next tied off, and after making a small incision,
a Micro-Tip Millar pressure catheter was introduced down through the carotid
artery, placing the end of the catheter into the left ventricular cavity of the
rat’s heart. Position of the catheter tip was determined by the
waveform of the pressure reading. Placement in the left ventricle was presumed
when a diastolic pressure of zero mmHg and a reasonable systolic pressure (70
to 150 mmHg) was observed. Once properly placed, the catheter was
secured to the artery with 1-0 silk ties. Following placement of the Millar
catheter, the right jugular vein of the rat was tied off and cannulated by
incising the side of the vein and introducing a small (0.3 mm internal
diameter), 20 centimeter-long intracatheter pre-loaded with 0.9% saline
solution into the vein. Once a reasonable length of the catheter was
inserted into the vein, it was tied to the vein with 1-0 silk suture to secure
it in place.
The Millar pressure catheter was then connected through a Millar
transducer control unit to a digital/analog recording card in a Sonometrics
computer (Sonometrics Corporation, 1510 Woodcock Street, Unit #12, London,
Ontario, Canada N6H 5S1). The transmitted Millar pressure signal was
then zeroed and calibrated in the Sonometrics SonoLAB data acquisition program.
At this point for each rat, a baseline recording was obtained of the left
ventricular pressure tracing. Cardiac function was assessed after two to three
minutes of each infusion increment, when the heart had stabilized. At each
infusion level, the whole assessment was completed within 10 minutes. Segments
of three to five seconds were recorded, and it was from these recorded tracings
that the maximum left ventricular pressure (reported as LVP), maximum
time-derivative of left ventricular pressure (dP/dt), and heart rate (HR) were
later determined, by analysis with Sonometrics CardioSOFT data analysis
software.
At this point in the experimentation, the
procedure followed differed depending upon which drugs and mixtures were being
examined, as is described in the following paragraphs. The total number of rats
tested for each group were: Iso, n=6; Iso/Met, n=3; Dob, n=9; Dob/Met, n=4; Met
(fixed) with Iso, n=3 and Met alone, n=7.
The IV line was connected to a syringe of
isoproterenol (Isuprel) or dobutamine in solution on a fluid infusion
pump. The isoproterenol was administered at varying rates (see
figures: up to 20-100 g kg-1min-1 or
until arrhythmias occurred); at each rate the LVP tracing was recorded after
several minutes at a constant infusion rate, and the tracing was later analyzed
in the same manner as described above for the baseline LVP
recordings. The same procedure was then performed in the rats using
a solution of metoprolol alone. Again, at each rate, LVP was
recorded for later analysis. The procedure was repeated a third
time, except that the infusion rate of isoproterenol was varied while at the
same time a constant dosage of metoprolol (1 mg kg-1min-1)
was administered. This constant dose was not the calculated ratio, but served
to calculate a Ki for metoprolol in these rats. The Ki for
Met was also calculated for a separate set of rats receiving only Met. This
second Ki was used to determine the ratio for the Dob/Met
infusions.
In the Iso exposed rats, there was a subset
of experiments done with the rats as their own controls. In these
experiments the rats were first given isoproterenol (Iso) alone and infused up
to either 20 g kg-1min-1 or
until arrhythmias occurred. They were then allowed to rest and then
infused with the optimized combination solution of isoproterenol and metoprolol
(Iso/Met), in the calculated ratio of 1.0 g isoproterenol to
85 g metoprolol and given
the Iso/Met solution up to either 20 or 100 g kg-1min-1 dosages
or until arrhythmias occurred. Data were not collected if the animals had
arrhythmias and all measurements were taken only in the absence of arrhythmias.
Metoprolol alone was also administered and showed
a steady decline in dP/dt from baseline values (not shown). This was done to insure
that metoprolol was acting as an antagonist and to calculate the apparent Ki for
metoprolol in these animals.
In another set of rats, the dobutamine
solution (Dob) was first infused at varying rates and tracings were
recorded. In these experiments, the rats were first infused with a
low-concentration solution for accuracy of administered
dosage. After Dob administration had progressed approximately 50 to
100 times the initial dosage, the solution was switched to a high-concentration
(ten time as concentrated as the low-concentration) solution of
dobutamine. This was done to avoid over-loading the rats with too
much fluid volume. After completion of the dobutamine infusion in
rats 1 through 7, the rats were then infused with a metoprolol solution. The
dP/dt, LVP and HR were again recorded for later analysis at each infusion rate.
Four of the rats were infused with the
combination solution of dobutamine and metoprolol, in the calculated ratio of
1.0 g kg-1min-1 dobutamine
to 1.6 g kg-1min-1 metoprolol.
LVP tracings, HR and dP/dt readings were taken at each rate. As was
done in the straight dobutamine infusions, the Dob/Met combination was switched
from a low-concentration solution to a ten-times more concentrated solution
(after the dosage of 100 times the initial dosage), again to avoid over-loading
the rats with excessive fluid volume.
In the second set of rats, the Dob/Met
combination of 1.0 g kg-1min-1 dobutamine
to 1.6 g kg-1min-1 metoprolol
was administered as the calculated ratio. Comparing the Dob/Met to the Dob
group, while the LVP was at first increased, it subsequently stabilized at
baseline levels for the higher dosages. In the nine rats treated with Dob, the
maximum left ventricular pressure (not shown) also showed a parallel effect to
the dP/dt. Heart rate remained largely unaffected.
A separate experiment was done with saline
alone in order to determine whether or not the fluid expansion would produce
any untoward effects on the cardiovascular system of the rats. Only past total
infusion rates above 800 g kg-1min-1, which matched the maximal infusion rate of
Dob/Met, did the fluid expansion decrease the measured parameters (dP/dt, LVP
or HR). All of the values for the reported experiments were within acceptable
infusion rates.
Upon completion of each experiment, the
rats were euthanized by intravenous (IV) overdose of sodium pentobarbital (75
mg kg-1). Gwathmey, Inc. performed all of the animal experiments
under all appropriate and approved guidelines (763 Concord Avenue, Building E,
Cambridge, MA, USA 02138, see www.gwathmey.com). All calculations of the
specific ratios and modeling were done at Bio Balance, Inc. (30 West 86th Street,
New York, NY, USA 10024, see www.bio-balance.com).
The general experimental model
In general each set of
experiments compared the responses of the animals to the Iso and Dob solutions
to those of the Iso/Met and Dob/Met agonist/antagonist combination solutions.
The following is a general outline of the steps taken for each set of
experiments:
1) The initial experiment
determined the desensitization to the agonist and obtained an apparent Ki for
the antagonist.
2) Equation (3) was fit to
the initial experimental data.
3) The parameters, KDH,
KDL and Ki, were obtained from the fit and entered
into Equation (4) to calculate the agonist/antagonist ratio ("f ").
4) The predicted response
for the agonist/antagonist solution was calculated by modifying the
dissociation constants, KDH and KDL to become KDH(1+
f [D]/ Ki) and KDL(1+ f [D]/ Ki) in Equation
(3).
5) The agonist/antagonist
solution was made according to the calculated agonist/antagonist ratio ("f
") obtained from Equation (4).
6) A second set of
experiments tested the agonist/antagonist solution in the animals.
7) Comparisons were made of
the experimental results and the predicted responses from the model.
For each experiment
involving either Iso or Dob desensitization, the model fit the results with the
parameters, KDH, KDL and Ki, obtained
from fits of Equation (3) to the initial experiments. After these initial
experiments, a specific ratio was calculated for each agonist/antagonist
combination given by Equation (4) [17]. This is the ratio used in making the
combination solutions (Iso/Met or Dob/Met solutions). The calculated
ratio was also inserted back into the model and plotted for comparison to the
experimental results. Also the agonist/antagonist combination solutions were
tested and compared to the responses to the agonist solutions and to the
predictions from the theoretical model.
Model calculations
The parameters of the
model were fit to the average values from the initial experiments in order to
obtain KDH and KDL. For the isoproterenol
dose-response relationship, the model was fit to the experimental data with the
assumption that RH and RL are equal, which may
not be true [20]. During this fit, it was found necessary to account for the
total amount of infused isoproterenol that gave an approximation for the total
amount of drug delivered to the animal at each infusion rate. This wasn't
necessary for the dobutamine fit probably due to the smaller half-life of
dobutamine (t1/2 2min.) compared to
isoproterenol. The two-state affinity constants, KDH and KDL,
were initially selected, then iteratively entered back into Equation (3) and
visually inspected to determine the adequacy of the fit. This was done until a
good fit was obtained.
The Ki for the antagonist metoprolol
was also determined in a similar iterative manner from two, separate sets of
experiments (Met fixed) and Met alone. The second Ki calculated
for Met in the Dob treated rats was derived from four of the animals' responses
to Met administered without Iso or Dob. This second Ki was an
order of magnitude different from the Ki for Met in the Iso
experiment (300 vs. 40). This may be due to the dynamic nature of these
experiments, or the varying metabolism that was not measured for these animals.
However, considering the nature of these experiments and the variability
amongst the animals, an order of magnitude difference is reasonable. From the
initial set of experiments with Iso or Dob, the values for KDH, KDL and
Ki were derived and entered into Equation (4). This is the
specific ratio that was used in making the agonist/antagonist combination
solutions Iso/Met and Dob/Met.
In addition, "f " from Equation
(4) was substituted into Equation (3) by altering the inhibition expression (1+
[I]/ Ki) for an antagonist multiplied times each of the dissociation
constants, KDH and KDL. Note that the Ki for
an antagonist is assumed to be equal for the RH and RL receptor
states, which may not always be true. With this alteration (1+ [I]/ Ki)
becomes (1+ f [D]/ Ki) where the antagonist concentration
"I" has been replaced with "f [D]" where [D] is the agonist
concentration [17]. For each of the experiments, these agonist/antagonist
curves were calculated from the model and compared with the experimental results.
Statistical evaluations
Results in figures and
tables are expressed as the mean ±s.e. (standard error of the mean) of n
experiments. The statistical significance of differences was estimated by
paired and non-paired Student's t-test with P-values <0 .05="" 95="" at="" confidence="" considered="" level.="" o:p="" significant="" the="">0>
Drugs and solutions
Isoproterenol
Hydrochloride (247.72 mw), dobutamine HCl (337.85 mw) and metoprolol tartrate
(Lopressor) (684.82 mw) were all purchased by Gwathmey, Inc. They were used as
the following solutions: Iso = isoproterenol solution (1mg 50cc-1),
Dob = dobutamine solution (1mg cc-1), Met = metoprolol solution (1mg
10cc-1), which were combined in the ratios (g kg-1min-1)
of 1:85 for the Iso/Met solution and 1:1.6 for the Dob/Met solution. These and
all other drugs or solutions were of the highest grade commercially available.
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