From the Department of Medicine, University of North
Carolina, Chapel Hill, North Carolina 27599 and Departments of
§ Surgery, ¶ Cell Biology, and
Medicine, §§ Howard
Hughes Medical Institute, Duke University, Durham, North Carolina
27710
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ABSTRACT |
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We studied the effect of alterations in the level
of myocardial -adrenergic receptor kinase (
ARK1) in two types of
genetically altered mice. The first group is heterozygous for
ARK1
gene ablation,
ARK1(+/
), and the second is not only heterozygous
for
ARK1 gene ablation but is also transgenic for cardiac-specific
overexpression of a
ARK1 COOH-terminal inhibitor peptide,
ARK1(+/
)/
ARKct. In contrast to the embryonic lethal phenotype
of the homozygous
ARK1 knockout (Jaber, M., Koch, W. J.,
Rockman, H. A., Smith, B., Bond, R. A., Sulik, K., Ross, J.,
Jr., Lefkowitz, R. J., Caron, M. G., and Giros, B. (1996)
Proc. Natl. Acad. Sci. U. S. A. 93, 12974-12979),
ARK1(+/
) mice develop normally. Cardiac catheterization was
performed in mice and showed a stepwise increase in contractile function in the
ARK1(+/
) and
ARK1(+/
)/
ARKct mice with the greatest level observed in the
ARK1(+/
)/
ARKct animals.
Contractile parameters were measured in adult myocytes isolated from
both groups of gene-targeted animals. A significantly greater increase in percent cell shortening and rate of cell shortening following isoproterenol stimulation was observed in the
ARK1(+/
) and
ARK1(+/
)/
ARKct myocytes compared with wild-type cells,
indicating a progressive increase in intrinsic contractility. These
data demonstrate that contractile function can be modulated by the
level of
ARK1 activity. This has important implications in disease
states such as heart failure (in which
ARK1 activity is increased)
and suggests that
ARK1 should be considered as a therapeutic
target in this situation. Even partial inhibition of
ARK1
activity enhances
-adrenergic receptor signaling leading to improved
functional catecholamine responsiveness.
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INTRODUCTION |
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One of the most important mechanisms for rapidly regulating
-adrenergic receptor (
AR)1 function is
agonist-stimulated receptor
phosphorylation by G protein-coupled receptor kinases (GRKs) resulting
in decreased sensitivity to further catecholamine stimulation (1). GRKs phosphorylate only agonist-occupied receptors leading to homologous desensitization (1, 2). The
-adrenergic receptor kinase (
ARK1) is
a member of a family of at least 6 GRKs, which phosphorylate and
regulate a wide variety of receptors that couple to heterotrimeric G
proteins (3, 4). When
ARs or other G protein-coupled receptors are
activated by agonist, heterotrimeric G proteins dissociate into
G
and G
subunits, and the
G
subunit complex, which is membrane anchored by a
lipid group (geranylgeranyl), can target
ARK1 to the membrane
through a direct physical interaction that facilitates phosphorylation
of activated receptors (5, 6).
Using a transgenic based strategy for cardiac-specific overexpression
of either ARK1 or a peptide inhibitor of
ARK1 (
ARKct), we have
recently shown that in vivo, myocardial
1-adrenergic and angiotensin II receptors are targets
for
ARK1 mediated desensitization (7, 8). The
ARK1 inhibitor
utilized is a peptide containing the carboxyl-terminal 194 amino acids
of
ARK1, which competes with endogenous
ARK1 for
G
binding (7). Evidence suggesting a fundamental role
for
ARK1 in cardiac development was provided by gene-targeted mice
in which the
ARK1 gene was ablated by homologous recombination (9).
Knockout mice, homozygous for the
ARK1 deletion, died during
mid-gestation with no viable
ARK1(
/
) embryos observed past E15.5
(9). Histologic analysis revealed hypoplasia of ventricular myocardium
with disorganized trabeculation. Furthermore, in vivo
embryonic cardiac function demonstrated significantly impaired left
ventricular (LV) ejection fraction compared with wild-type hearts,
showing that
ARK1 is required for normal cardiac development (9). In
contrast to the complete knock out,
ARK1(+/
) heterozygous animals
have no obvious developmental abnormalities despite an approximate 50% reduction in the level of
ARK1 protein and GRK activity (9).
In a variety of human and experimental conditions, prominent AR
desensitization in response to catecholamine stimulation has recently
been shown to be associated with heightened levels of
ARK1 (10-13).
In chronic human heart failure, reduced agonist-stimulated adenylyl
cyclase activity due to both diminished receptor number and impaired
receptor function is a predominant feature (14). In end-stage human
heart failure, these changes in
AR function were shown to be
associated with elevated mRNA levels and activity for
ARK1 (10,
15). Results from transgenic mice that overexpress
ARK1 and GRK5 (7,
8) demonstrate how the up-regulation of these molecules in heart
failure could markedly alter
AR function by enhancing receptor
desensitization. Furthermore, chronic treatment with either the
AR
antagonist bisoprolol in the pig (16) or carvedilol in the
mouse2 (a potent therapeutic
agent in human heart failure, see Ref. 18), substantially decreased the
level of
ARK1 activity. The most compelling evidence demonstrating
the importance of
ARK1 in heart failure comes from a recent
study whereby transgenic mice with cardiac-restricted overexpression of
the
ARKct were mated into a genetic model of murine heart failure
achieved through ablation of the MLP gene (19). Overexpression of the
ARK1 inhibitor reversed the heightened
AR desensitization in the
MLP knockout mice and completely normalized cardiac function. These
data strongly implicate abnormal
AR-G protein coupling in the
pathogenesis of the failing heart (19). Taken together, these studies
indicate the potential for a therapeutic strategy that aims to modulate the activity level of myocardial
ARK1 in disease states. Decreasing the level of myocardial
ARK1 in established heart failure is a novel
approach to improving impaired
AR receptor function and potentially
alter the pathogenesis in this disease.
In the present study, we sought to test the hypothesis that the level
of cardiac ARK1 activity regulates myocardial contractile function
in vivo. To test these hypotheses, we used a strategy that
utilized mouse genetics to create varying levels of
ARK1 activity in
the heart, coupled with a physiological assessment of contractile
function in the absence and presence of catecholamine stimulation.
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MATERIALS AND METHODS |
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Experimental Animals--
The gene-targeted mice used for this
study were 1) heterozygous for targeted disruption of the ARK1 gene
(9), and 2) offspring generated by cross breeding transgenic mice with
cardiac-specific overexpression of a
ARK1 inhibitor (
ARKct, shown
previously to have enhanced basal contractility) (7) with the
ARK1(+/
) to yield the double gene-targeted line
ARK1(+/
)/
ARKct. Offspring were genotyped by Southern blot
analysis on DNA extracted from tail biopsies. Mice of either sex, 4-6
months of age were used and compared with wild-type litter mates. The
animals in this study were handled according to approved protocols and
the animal welfare regulations of the University of North Carolina at
Chapel Hill and Duke University.
Hemodynamic Evaluation in Intact Anesthetized Mice-- Mice were anesthetized with a mixture of ketamine (100 mg/kg) and xylazine (2.5 mg/kg) and analyzed as described previously (8). Briefly, after endotracheal intubation, mice were connected to a rodent ventilator. Following bilateral vagotomy, the chest was opened and a 1.8-French high fidelity micromanometer catheter (Millar Instruments) was inserted into the left atrium, advanced through the mitral valve, and secured in the LV. Hemodynamic measurements were recorded at baseline and 45-60 seconds after injection of incremental doses of isoproterenol. Doses of isoproterenol were specifically chosen to maximize the contractile response but limit the increase in heart rate. Experiments were then terminated, hearts were rapidly excised, with individual chambers separated, weighed, and frozen in liquid N2 for later biochemical analysis. Ten sequential beats were averaged for each measurement.
Myocyte Isolation-- Adult myocytes were isolated as described previously (20, 21). Following anesthesia, the heart was excised and the aorta was cannulated with a 20-gauge needle then mounted on the perfusion apparatus. The perfusion solution was composed of Joklik's minimum essential medium containing (in mM) 113 NaCl, 4.7 KCL, 0.6 KH2PO2, 0.6 Na2PO4, 1.2 MgSO4, 0.5 MgCl2, 10 HEPES, 20 D-glucose, 30 taurine, 2.0 carnitine, 2.0 creatine, and 20 µM Ca2+ at pH 7.4. The aorta was perfused for 2-3 min, then 150 units/ml of type-II collagenase (Worthington) was added and perfused for 15 min. The temperature of perfusate was maintained at 34 °C and all solutions were continuously bubbled with 95% 02, 5% CO2. LV tissue was separated from the great vessels, atria and right ventricle, minced, and allowed to digest in perfusate for 15 min. The digested heart was filtered through 200 µm nylon mesh, placed in a conical tube, and spun at 100 rpm to allow viable myocytes to settle. Serial washes were used to remove nonviable myocytes and digestive enzymes until the concentration of Ca2+ was gradually increased to 1.8 mM in Joklik's minimal essential medium. The operator was blinded to the genotype of the animals.
Evaluation of Myocyte Function--
Myocytes were placed in a
0.5-ml chamber with 1.8 mM Ca2+ Tyrode's
solution at room temperature. Myocytes were visualized with a Nikon
inverted microscope with a solid state CCD camera attached and
displayed on a video monitor. Two platinum electrodes placed in the
bathing fluid were connected to a stimulator to field stimulate the
myocytes with a pulse duration of 5 ms and a frequency of 0.5 Hz.
Myocyte cell edges were enhanced and processed with a video edge
motion detection system (Crescent Electronics) at a sampling rate of
240 Hz. Recordings were performed under basal conditions and then 1-2
min after isoproterenol (107 M)
administration. Calibrated myocyte lengths were converted from analog
to digital on-line (MacLab) and stored on computer. All myocytes were
studied within 1-2 h after myocyte isolation. Data from 5-8
consecutive contractions were averaged. Contractile parameters measured
were: percent cell shortening (%CS) (calculated as percent
change in myocyte length from rest (Lmax) to
minimum length (Lmin)), rate of shortening
(
dL/dt) and rate of relengthening (+dL/dt). 7-15 myocytes from each heart were
studied.
GRK Activity by Rhodopsin Phosphorylation--
Myocardial
extracts were prepared by homogenization of excised hearts in ice-cold
lysis buffer (2 ml) (25 mM Tris-Cl (pH 7.5), 5 mM EDTA, 5 mM EGTA, 10 µg/ml leupeptin, 20 µg/ml aprotinin, and 1 mM phenylmethylsulfonyl fluoride)
and centrifuged at 48,000 × g for 30 min. The
supernatants that contain soluble kinases were concentrated using a
Centricon-10 (Amicon) microconcentrator. Protein concentration was
determined by the Bradford method. Concentrated cytosolic extracts (200 µg of protein) were incubated with rhodopsin-enriched rod outer
segment membranes in reaction buffer (75 µl) containing 10 mM MgCl2, 20 mM Tris-Cl, 2 mM EDTA, 5 mM EGTA, and 0.1 mM ATP (containing [-32P]ATP) as described (9). Reactions
were carried out in the absence and presence of purified
G
(
20 pmol) to maximally activate
ARK (9).
After incubating in white light for 15 min at room temperature,
reactions were quenched with ice-cold lysis buffer (300 µl) and
centrifuged for 15 min at 13,000 × g. Sedimented proteins were resuspended in 20 µl of protein-gel loading dye and
electrophoresed through 12% SDS-polyacrylamide gels. Phosphorylated rhodopsin was visualized by autoradiography of dried polyacrylamide gels and quantified using a Molecular Dynamics PhosphorImager.
Statistical Analysis--
Results are expressed as mean
value ± S.E. To examine the effect of isoproterenol on changes in
hemodynamic parameters between wild-type controls and the two
gene-targeted groups (ARK1(+/
) and
ARK1(+/
)/
ARKct), a 3 × 4 repeated measures
analysis of variance (ANOVA) was used. To test for statistical
difference in isolated cell contractile parameters and adenylyl cyclase
activity, a one factor ANOVA was used. Post hoc analysis with regard to differences in mean values between groups was conducted with either a
Newman-Keuls or Duncan test. A Student's t test with
Bonferroni correction for 3 comparisons was used to test for
statistical difference in the chamber weight parameters.
p < 0.05 was considered significant.
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RESULTS |
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To determine whether altered levels of ARK1 influence
myocardial growth in the adult mouse, left ventricular weight
normalized for body weight (LV/BW) and tibia length was compared in
wild type (n = 26),
ARK1(+/
) (n = 19), and
ARK1(+/
)/
ARKct (n = 9) gene-targeted
mice. No significant difference was observed for any of the measured
variables between the three groups (LV/BW; wild type 3.5 ± 0.1,
ARK1(+/
) 3.7 ± 0.1,
ARK1(+/
)/
ARKct 3.6 ± 0.2, mg/g, p = not significant). In contrast to the
embryonic lethal phenotype of the homozygous
ARK1 knockout, the
heterozygote mice developed normally and attained a similar body weight
as wild-type adults. Similarly, we previously had not observed any differences in heart weight in the animals overexpressing the
ARKct
alone compared with wild type controls (7).
To assess the levels of myocardial ARK activity in the different
gene-targeted mice, we prepared soluble myocardial extracts and carried
out in vitro GRK phosphorylation assays using rhodopsin as a
G protein-coupled receptor substrate. To address whether the
ARKct
is functional, we added purified G
to the reactions.
As shown in Fig. 1,
G
-stimulated
ARK activity is decreased in a
stepwise fashion with the
ARK1(+/
)/
ARKct animals having only
25% of the wild-type myocardial
ARK activity. Myocardial
extracts from the
ARK1(+/
) animals had 50% of the wild-type
activity, which correlates to the 50% decrease in
ARK1 protein we
have previously described (9). This significant decrease in myocardial
ARK1 activity in the double gene-targeted mice could also be
demonstrated when expressing the data as fold-stimulation of
G
over basal rhodopsin phosphorylation activity
(
G
). In
ARK1(±)/
ARKct animals,
G
only stimulated activity by 2.24 ± 0.30-fold (n = 5) compared with 4.48 ± 0.93-fold
(n = 6) for the wild-type animals (p < 0.05). Extracts from
ARK1(+/
) hearts had similar values to
wild-type (3.75 ± 0.88-fold, n = 6). Because of
the dependence of the
ARKct activity on G
, as
expected, in vitro
ARK activity in the absence of
G
was equivalent between
ARK1(+/
) extracts and
ARK1(+/
)/
ARKct extracts, which was
50% of wild-type
activity (data not shown).
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We have previously reported that overexpression of the ARKct in
transgenic mice leads to a significant enhancement of myocardial
AR
signaling and myocardial contractility in vivo under basal conditions and in response to catecholamine infusion (7). To determine
whether the level of
ARK1 modulates catecholamine responsiveness in vivo, cardiac catheterization was performed in intact
anesthetized mice before and after infusion of isoproterenol (Fig.
2). Although the isovolumic phase measure
of myocardial contractility, LV
dP/dtmax, was not increased in
the
ARK1(+/
) at baseline compared to wild type, it was
significantly enhanced in the
ARK1(+/
)/
ARKct mice. Contractile
function was further and significantly augmented in the two
gene-targeted groups in response to isoproterenol with the greatest
level observed in the
ARK1(+/
)/
ARKct (Fig.
2A). Enhanced myocardial relaxation, as assessed by LV
dP/dtmin was particularly evident in
the
ARK1(+/
)/
ARKct animals but not in the
ARK1(+/
) at
baseline (Fig. 2B). As shown in Fig. 2, C and
D, LV systolic pressure and heart rate were increased in the gene-targeted animals at baseline, which was further potentiated with
isoproterenol stimulation. This is particularly apparent for changes in
heart rate (Fig. 2D).
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Heart rate is a powerful determinant of myocardial contractility and
can have important influences on LV
dP/dtmax (22). To illustrate this
point, the data has been plotted for the three groups showing the
relationship between LV dP/dtmax and
heart rate at baseline (Fig.
3A) and with maximal
isoproterenol (Fig. 3B). In general, the animals with the
highest heart rate also had the greatest LV
dP/dtmax. Taken together these data
demonstrate that the level of ARK1 activity exerts tight control
over the inotropic and chronotropic response to catecholamine
stimulation in the heart in vivo.
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Since both loading conditions (LV end-diastolic pressure) and heart
rate influence the in vivo measurement of myocardial
contractility as measured by LV
dP/dtmax (22, 23), studies were
performed on adult myocardial cells isolated from both of the
gene-targeted mouse strains. To determine whether a decrease in the
level of ARK1 would affect myocyte contractility in the absence of
potential confounding influences such as heart rate and mechanical
loading, freshly isolated single adult myocytes were obtained from
normal,
ARK1(+/
), and
ARK1(+/
)/
ARKct)
gene-targeted mice followed by an assessment of the contractile
properties.
Measurements of contractile parameters in unloaded isolated adult
cells were made in the absence and presence of isoproterenol (107 M) at a constant paced stimulation of
0.5 Hz. Adult myocytes isolated from wild-type hearts responded to
isoproterenol stimulation with a 12% increase from baseline in %CS
and the rate of shortening (
dL/dt) without a
change in diastolic cell length (Fig. 4
and Table I). In contrast, adult myocytes
isolated from
ARK1(+/
) heterozygote animals showed an 18%
increase in
dL/dt, whereas myocytes from
ARK1(+/
)/
ARKct hearts showed an even greater increase in
dL/dt (29%) following isoproterenol
administration (Table I and Fig. 4). Similarly, %CS under baseline and
isoproterenol conditions was progressively higher in myocytes isolated
from the two gene-targeted mouse lines compared with wild-type cells (Table I). Overall cells isolated from
ARK1(+/
) and
ARK1(+/
)/
ARKct mice had a significantly greater, and stepwise,
increase in contractile parameters with isoproterenol compared
with wild-type litter mates (Table I). These data complement the
in vivo assessment of contractile function and show that
intrinsic myocyte contractility can be directly influenced by the level
of
ARK1.
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DISCUSSION |
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The present study demonstrates that 1) ARK1(+/
) mice that are
heterozygote for ablation of the
ARK1 gene and have a 50% reduction
in the level of
ARK1 in the heart develop normally, 2) the level of
chronotropy and inotropy in vivo can be modulated by the
level of
ARK1 expression, and 3) contractile function can be further
enhanced through in vivo
ARK1 inhibition by competing for
G
binding and endogenous
ARK1 translocation and activation.
Complete disruption of the ARK1 gene in mice leads to a lethal
phenotype with no
ARK1(
/
) embryos surviving beyond gestational day 15.5 (9). The finding that mice that are heterozygous for the
ARK1 deletion have no developmental abnormalities and develop into
normal adults, suggests that there is a threshold level for
ARK1
that allows for normal cardiac development. Although the
ARK1(+/
)
mice grow into normal adults, the functional consequence of reduced
ARK1 levels is a phenotype of decreased desensitization in the heart
as shown by the enhanced contractile response to isoproterenol
stimulation (Fig. 2).
ARK1 requires a membrane-targeting event prior to receptor
phosphorylation that occurs through the interaction of membrane anchored G
subunits and the carboxyl terminus of
ARK1 (5). Preventing
ARK1 translocation by competing for
G
binding in transgenic mice overexpressing a peptide
inhibitor (
ARKct) results in an in vivo phenotype of
enhanced basal and agonist-stimulated contractility due to decreased
receptor desensitization (7). The mating of these two gene-targeted
mice (
ARK1(+/
) and
ARKct overexpression) results in a further
enhancement of contractility and relaxation (Fig. 2). These data
suggest that both the level of
ARK1 expression and the active
process of translocation and activation of
ARK1, determine the
degree of
AR desensitization and subsequent receptor-G protein
coupling.
The isovolumic phase index (LV
dP/dtmax) is a sensitive measure of
contractility. However, the level of contractility is significantly influenced by heart rate and loading conditions in particular, preload
(23). In this regard, it has recently been shown that there is a linear
relationship between heart rate and LV
dP/dtmax (22). In the present study
we show that the significantly enhanced contractile performance of mice
with altered levels of ARK1, as measured by LV
dP/dtmax, is also associated with a
modest increase in heart rate. To address this issue, we specifically
assessed contractile parameters in single adult ventricular myocytes
isolated from both the
ARK1(+/
) and
ARK1(+/
)/
ARKct
gene-targeted mice to determine whether the in vivo
phenotype in these animals can be attributed to an intrinsic increase
in myocyte contractility. The effect of heart rate on contractile
function was eliminated by pacing cells at 0.5 Hz. As shown in Table I,
a significant augmentation of contractile parameters occurred following
AR stimulation in the
ARK1(+/
) cells, which was further
enhanced in the
ARK1(+/
)/
ARKct cells. Although as a group the
cells isolated from the
ARK1(+/
)/
ARKct hearts were smaller than
the other cells it did not seem to affect indices of contraction, but
may have had some influence on the rate of relengthening
(+dL/dt). These data show that
ARK1 can
directly influence contractility at a cellular level and confirm the
in vivo data showing that reduced
ARK1 levels leads to
enhanced catecholamine responsiveness. These results are also
consistent with a recent study on contractile function in single adult
myocytes isolated from transgenic mice that overexpress either
ARK1
or the
ARKct, which showed that the presence of the
ARKct
resulted in an enhanced contractile response to
AR stimulation
compared with control cells (24).
We have previously shown that adenoviral-mediated gene transfer of the
ARKct can restore
AR signaling in failing myocytes isolated from
chronically paced rabbits (25). In that in vitro study we
showed that the biochemical defects in
AR signaling in isolated
failing myocytes could be reversed by gene transfer of the
ARKct
(25). In this study, we extend those findings by showing that in
vivo contractile function and isoproterenol responsiveness in the
intact animal is related to the level of
ARK1. Furthermore, we not
only demonstrate that an inhibitor of
ARK1 (
ARKct) can affect
cellular contractility but also that the contractile state of the
myocyte can be directly influenced by the level of
ARK1
expression.
There is increasing evidence that elevated levels of ARK1 contribute
to impaired catecholamine responsiveness observed in disease states of
cardiac hypertrophy and heart failure (26). Elevated levels of
ARK1
have been shown to be present in heart extracts from human end-stage
heart failure (15) and in circulating lymphocytes from patients with
mild to moderate essential hypertension (11). An essential role for
ARK1 leading to impaired catecholamine responsiveness has been shown
in various animal models of cardiac disease including cardiac
hypertrophy (12) and myocardial ischemia (13). In this regard it is
worthwhile to note that the use of angiotensin-converting enzyme
inhibitors (17) in experimental heart failure was associated with a
reduction in myocardial
ARK1 activity. Furthermore in a mouse model
of pressure overload hypertrophy, impaired
AR signaling that occurs
with the development of modest myocardial hypertrophy, could be
completely reversed in the presence of the
ARK inhibitor (
ARKct)
(12). In this study, we show that not only is
ARK1 a critical
modulator of in vivo cardiac function (7), but the level of
ARK1 activity is important and can directly influence the degree to
which the
AR-signaling pathway is activated. This has important
implications in disease states of increased
ARK activity when
considering
ARK1 as a therapeutic target, since even partial
inhibition of
ARK1 function will effectively enhance
AR signaling
leading to improved catecholamine responsiveness. This study is of
particular significance given our recent data showing the dramatic
beneficial effect of overexpression of a
ARK inhibitor in a mouse
model of heart failure (19).
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ACKNOWLEDGEMENTS |
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We gratefully acknowledge the expert help
from Dr. Lan Mao in the microsurgical techniques in the mouse, Kyle
Shotwell for technical assistance with ARK activity
assays, Mark Griswold with isolated cell measurements, and Susan Suter
and Sandy Duncan for maintenance of the mouse colonies.
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FOOTNOTES |
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* This work was supported in part by National Institutes of Health Grants HL 56687 (to H. A. R.), HL 16037 (to R. J. L.), and NS 19576 (to M. G. C.).The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Present address: CNRS U-5541, University Bordeaux II, 146 rue
Leo Saignat, 33076 Bordeaux Cedex, France.
** Present address: Unite INSERM 288, CHU Pitie-Salpetriere, Paris, France.
¶¶ To whom correspondence should be addressed: Dept. of Surgery, Duke University Medical Center, Box 2606, Room 472 MSRB, Durham, NC 27710. Tel.: 919-684-3007; Fax: 919-684-5714; E-mail: koch0002{at}mc.duke.edu.
1
The abbreviations used are: AR,
-adrenergic receptor; GRK, G protein-coupled receptor kinase;
ARK,
AR kinase; LV, left ventricular; ANOVA, analysis of
variance; BW, body weight; %CS, percent cell shortening;
dL/dt, rate of shortening;
+dL/dt, rate of relengthening.
2 G. Iaccarino, E. D. Tomhave, R. J. Lefkowitz, and W. J. Koch, submitted.
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REFERENCES |
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