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Biophys J, August 1999, p. 808-816, Vol. 77, No. 2
*Department of Physiology and Biophysics, Case Western Reserve University, Cleveland, Ohio 44106 USA; #Department of Physiology, University of Maryland, Baltimore, Maryland 21201 USA; and §Department of Pharmacology, University of Tokyo, Tokyo 113, Japan
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ABSTRACT |
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To study the function and regulation of the cardiac ryanodine receptor (RyR2) Ca2+ release channel, we expressed the RyR2 proteins in a Chinese hamster ovary (CHO) cell line, and assayed its function by single channel current recording and confocal imaging of intracellular Ca2+ ([Ca2+]i). The 16-kb cDNA encoding the full-length RyR2 was introduced into CHO cells using lipofectAmine and electroporation methods. Incorporation of microsomal membrane vesicles isolated from these transfected cells into lipid bilayer membrane resulted in single Ca2+ release channel activities similar to those of the native Ca2+ release channels from rabbit cardiac muscle SR membranes, both in terms of gating kinetics, conductance, and ryanodine modification. The expressed RyR2 channels were found to exhibit more frequent transitions to subconductance states than the native RyR2 channels and RyR1 expressed in CHO cells. Caffeine, an exogenous activator of RyR, induced release of [Ca2+]i from these cells. Confocal imaging of cells expressing RyR2 did not detect spontaneous or caffeine-induced local Ca2+ release events (i.e., "Ca2+ sparks") typically seen in cardiac muscle. Our data show that the RyR2 expressed in CHO cells forms functional Ca2+ release channels. Furthermore, the lack of localized Ca2+ release events in these cells suggests that Ca2+ sparks observed in cardiac muscle may involve cooperative gating of a group of Ca2+ release channels and/or their interaction with muscle-specific proteins.
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INTRODUCTION |
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In cardiac muscle, excitation-contraction
(E-C) coupling involves entry of extracellular Ca2+
through voltage-sensitive Ca2+ channels, which in turn
triggers release of Ca2+ from the sarcoplasmic reticulum
(SR), via a Ca2+-induced Ca2+ release (CICR)
mechanism. This phenomenon is mediated by ryanodine receptor (RyR)
which functions as Ca2+ release channel (Fleischer and
Inui, 1989
; McPherson and Campbell, 1993
; Sutko and Airey, 1996
). RyR
is a single polypeptide of ~560 kDa, and exists in a homotetrameric
structure with at least two functional domains: a carboxyl-terminal
hydrophobic domain containing the conduction pore of the
Ca2+ release channel (Takeshima et al., 1989
; Zorzato et
al., 1990
; Bhat et al., 1997b
), and a large amino-terminal cytoplasmic
domain referred to as the "foot structure" (Block et al., 1988
; Lai
et al., 1989
; Sorrentino and Volpe, 1993
; Franzini-Armstrong and Jorgensen, 1994
). The cardiac (RyR2) and skeletal (RyR1)
Ca2+ release channels are encoded by different genes, and
share a high degree (~66%) of amino acid sequence identity,
especially in the carboxyl-terminal region, which contains several
putative transmembrane segments (Takeshima et al., 1989
; Zorzato et
al., 1990
; Nakai et al., 1990
; Otsu et al., 1990
; Wagenknecht et al., 1989
; Takeshima, 1993
). The carboxyl-terminal region of the protein also contains putative binding site(s) for Ca2+ and
ryanodine (Callaway et al., 1994
; Witcher et al., 1994
). In recent
studies, we have successfully used a heterologous expression system to
study the structure-function relationship of the skeletal Ca2+ release channel (Bhat et al., 1997a
-c
). Full-length
RyR1 expressed in Chinese hamster ovary (CHO) cells exhibits single
channel properties similar to those of RyR from skeletal muscle SR. The
carboxyl-terminal ~20% of the RyR1 (RyR-C) was found to contain
structures sufficient to form a functional Ca2+ release
channel (Bhat et al., 1997b
). The amino-terminal foot structure appears
to participate in the ion-conduction, Ca2+-dependent
regulation, and caffeine-induced activation of the Ca2+
release channel (Bhat et al., 1997a
-c
).
Compared with RyR1, it has been difficult to study the
structure-function relationship of RyR2. First, the cDNA for RyR2 is intrinsically unstable, which frequently undergoes large deletions and/or recombination during its propagation in Escherichia
coli strains making the DNA preparation difficult. Second, it is
not easy to select stable mammalian cell clones expressing RyR2
proteins. Nakai et al. (1990)
expressed and indirectly studied the
function of the RyR2 channel in Xenopus oocytes by measuring
Ca2+-dependent chloride current in response to stimulation
with caffeine. Caffeine-induced Ca2+ release as well as
Ca2+-dependent [3H]ryanodine binding were
studied by Imagawa et al. (1992)
in CHO cells expressing RyR2. But, no
single channel studies with expressed RyR2 have been reported thus far.
In the present study, we have successfully overcome the problem of RyR2
cDNA instability in E. coli cells and expressed the
full-length RyR2 protein in CHO cells. The Ca2+ release
channel activity of the expressed RyR2 was studied using single channel
current measurements and by intracellular Ca2+ imaging in
single cells using laser scanning confocal microscopy. The single
channel properties of RyR2 expressed in CHO cells were similar to those
of native Ca2+ release channels from the rabbit cardiac
muscle SR. RyR2 channels expressed in CHO cells were found to exhibit
multiple conductance states more frequently than the native
Ca2+ release channels from the cardiac muscle SR. Caffeine,
an exogenous activator of RyR, induced release of
[Ca2+]i from cells expressing RyR2. Confocal
imaging of single CHO cells expressing RyR2 did not detect any
spontaneous or caffeine-induced local Ca2+ release events
(viz., "Ca2+ sparks") typically seen in cardiac muscle cells.
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MATERIALS AND METHODS |
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Cells and expression system
The entire cDNA sequence (~16.5 kb) of the rabbit cardiac
muscle RyR was cloned into the pHRRS1 expression vector and the transcription occurs under the control of the SV40 promoter (Nakai et
al., 1990
). This DNA was transformed into a competent HB101 strain of
E. coli cells and grown in LB medium at 30°C. The bacteria were harvested for DNA isolation mid-to-late in the logarithmic period
of growth. CHO cells were grown at 37°C and 5% CO2 in
Ham's F-12 medium supplemented with 10% fetal bovine serum, 100 U/ml penicillin, and 100 µg/ml streptomycin. The expression plasmids were
introduced into the cells (60-70% confluent) using lipofectAmine reagent (Life Technologies, Inc., Gaithersburg, MD) following manufacturer's instructions, or by electroporation methods (Imagawa et
al., 1992
). Stable transfectant cells were selected with G418 (0.5 mg/ml, Calbiochem, La Jolla, CA) ~48 h after transfection. The level
of RyR2 protein expression was tested using Western blot analysis.
Western blot analyses
Control and transfected CHO cells were harvested and washed
twice with ice-cold PBS and lysed with ice-cold modified RIPA buffer
(150 mM NaCl, 50 mM Tris-Cl, pH 8.0, 1 mM EGTA, 1% Triton X-100, 1%
sodium deoxycholate) in the presence of protease inhibitors (0.5 mM
Pefabloc, 1 µM pepstatin, 1 µM leupeptin, 1 µg/ml aprotinin, and
1 mM benzamidine). The proteins in the whole cell lysate were mixed
with the 2X sample buffer (200 mM Tris-Cl, pH 6.7, 9% SDS, 6%
-mercaptoethanol, 15% glycerol, 0.01% bromophenol blue) and separated on a 3-12% linear gradient SDS-PAGE gel after heating the
samples at 37°C for ~15 min. The proteins were then transferred to
a polyvinylidene difluoride (PVDF) membrane and blotted with C3-33
monoclonal antibody raised against the RyR2 protein (Affinity BioReagents, Golden, CO), and horseradish peroxidase-linked secondary antibody. The proteins were visualized using the enhanced
chemiluminescence detection system (Amersham Corp., Piscataway, NJ).
Confocal imaging of intracellular [Ca2+]
Single rat cardiac ventricular cells were obtained from
two-month-old Sprague-Dawley rats by an enzymatic technique described in detail previously (Lopez-Lopez et al., 1995
). Both cardiac myocytes
and CHO cells expressing RyR2 were loaded with the Ca2+
indicator Fluo-3 by incubation for 30 min or longer in Tyrode's solution to which 10 µM Fluo-3 AM was added (Molecular Probes Inc.,
Eugene, OR). Recordings of [Ca2+] were made in normal
Tyrode's solution (composition in mM: NaCl, 140; dextrose, 10; Hepes,
10; KCl, 4.0; MgCl2, 1; CaCl2, 1; pH adjusted
to 7.3-7.4 with NaOH) at room temperature, as described (Bhat et al.,
1997c
). For "x-y" or "full-frame" imaging of calcium in the CHO
cells a Bio-Rad MRC 600 confocal microscope (Bio-Rad Laboratories,
Inc., Hercules, CA) was used. Fluo-3 fluorescence line-scan
images were acquired with the homemade confocal microscope attached to
the camera port of a Nikon Diaphot inverted microscope equipped with a
60× plan-apo oil-immersion objective (numerical aperture 1.4), with a
resolution of 3 ms per scan line (Parker et al., 1997
). The
fluorescence is expressed as normalized increases in fluorescence
compared to "resting" level (F/F0).
Isolation of SR membranes from rabbit cardiac muscle
Junctional SR membranes were isolated from rabbit cardiac muscle
following the procedure similar to that used to prepare the skeletal
muscle SR membranes (Ma et al., 1995
). Briefly, cardiac muscle tissues
were homogenized in 100 mM NaCl, 2 mM EDTA, 0.1 mM EGTA, and 5 mM
Tris-Maleate (pH 6.8). Microsome vesicles obtained after sequential
centrifugation at 2600 × g and 35,000 × g were loaded onto discontinuous sucrose gradients. The
junctional SR membranes were recovered from the 40-45% region of the
gradients. The junctional SR membrane vesicles were stored at
75°C
at a concentration of 3-5 mg protein/ml; 1-3 µl of the vesicles
were used for recording of single channel currents in the lipid bilayer.
Isolation of microsomal membrane vesicles from CHO cells
Microsomal membrane vesicles were isolated from transfected CHO
cells as described (Bhat et al., 1997b
). Briefly, the cells were
homogenized on ice in hypotonic lysis buffer (10 mM Hepes-Tris, pH 7.4, 1 mM EDTA) containing protease inhibitors (0.5 mM Pefabloc-SC, 1 µM
pepstatin, 1 µM leupeptin, 1 µg/ml aprotinin, and 1 mM benzamidine) using nitrogen cavitation (300 Psi for 15 min on ice) and with 10 strokes in a tight-fitting Dounce homogenizer, followed by 15 strokes
after addition of an equal volume of sucrose buffer (500 mM sucrose, 10 mM Hepes-Tris, pH 7.4, 1 mM EDTA). Microsome vesicles were collected by
centrifugation of post-nuclear supernatant (10,000 × g, 15 min) at 100,000 × g for 45 min at
4°C. The pellet was resuspended in a buffer containing 250 mM
sucrose, 10 mM Hepes-Tris, pH 7.2. The membrane vesicles were stored at
a protein concentration of 2-6 mg/ml at
75°C until use. Usually,
1-3 µl of microsomal membrane vesicles was used for reconstitution
of Ca2+ release channels in the lipid bilayer system.
Reconstitution of Ca2+ release channels in lipid bilayer membrane
Lipid bilayer membranes were formed across an aperture of ~200
µm diameter using the Muller-Rudin method with a mixture of phosphatidylethanolamine/phosphatidylserine/cholesterol (6:6:1); the
lipids were dissolved in decane at a concentration of 40 mg/ml. Incorporation of the Ca2+ release channel in bilayer was
achieved by addition of membrane vesicles containing RyR2 proteins to
the cis solution, under a concentration gradient of 200 mM
(cis)/50 mM (trans) cesium gluconate. After
incorporation of a single Ca2+ release channel, the
concentration of cesium gluconate in the trans solution was
adjusted to 200 mM. The pH in both cis and trans
solutions was maintained throughout the experiment at 7.4 with 10 mM
Hepes-Tris. The free Ca2+ concentration in both solutions
was buffered with 1 mM EGTA, and measured using a
Ca2+-sensitive electrode (Orion, Boston, MA). Orientation
of the Ca2+ release channel in the lipid bilayer, usually
in the cis-cytoplasmic trans-luminal SR manner,
was determined by the sensitivity of the channel to cytoplasmic
Ca2+ (Bhat et al., 1997b
). To maintain stability of the
bilayer membrane and channel activity, designed pulse protocols were
used to measure currents through the single Ca2+ release
channels. The bilayer membrane was kept at a holding potential of 0 mV,
and pulsed to different test potentials of 0.5-1-s durations.
Single channel currents were recorded with an Axopatch 200A patch clamp
unit (Axon Instruments, Inc., Foster City, CA). Data acquisition and
pulse generation were performed with a 486 computer and 1200 Digidata
A/D-D/A convertor (Axon Instruments). The currents were sampled at 0.05 ms/point and filtered at 1 kHz through an 8-pole Bessel filter. Single
channel data analyses were performed with the pClamp program.
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RESULTS AND DISCUSSION |
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Expression of full-length cardiac RyR in CHO cells
The expression vector pHRRS1 contains the cDNA sequence (~16.5
kb) encoding the full-length RyR2 protein. One of the commonly encountered difficulties in working with large DNA molecules such as
pHRRS1 (total size ~24 kb) is their tendency to be unstable in that
the cDNA undergoes spontaneous deletions and/or rearrangements during
plasmid propagation. This phenomenon appears to be specific for RyR2
cDNA since we encountered no such problems with the RyR1 cDNA (Bhat et
al., 1997a
-c
). We have optimized the procedure to overcome this
problem and to stabilize the DNA sequence by growing the host bacterial
strain (HB101) at a lower temperature (30°C) and by harvesting the
cells for plasmid DNA isolation before the culture grows to saturation.
Of the several bacterial strains tested (such as DH5
, JM109, SURE,
HB101), we found HB101 to be efficient for stable propagation of RyR2
cDNA. A similar technique has been used to reduce the probability of
instability of retroviral DNA clones that are otherwise unstable
(Kanahan et al., 1991
; Joshi and Jeang, 1993
).
CHO cells were transfected with pHRRS1 using the cationic lipid
lipofectAmine as described by the manufacturer, or using
electroporation as described (Imagawa et al., 1992
). Transfected cells
were isolated ~48 h after transfection, and the expression of RyR2
protein was assayed by Western blot analysis (Fig.
1). CHO cells transfected with pHRRS1
expressed a protein of high Mr (~560 kDa,
lane 7) that is identical to RyR2 from rabbit cardiac muscle
SR (lane 4). These proteins were detected with a monoclonal
antibody (C3-33) raised against canine cardiac ryanodine receptor, and
this antibody also recognizes RyR1 from skeletal muscle SR as well as
that expressed in CHO cells (lanes 2 and 3). No protein was
recognized by the C3-33 antibody in untransfected CHO cells (lane
1), indicating that CHO cells do not contain any detectable levels
of endogenous RyR1 and RyR2.
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To isolate stable clones expressing RyR2, CHO cells expressing RyR2 were cultured by limiting dilution in media containing G418 (0.5 mg/ml). Of the 28 clones analyzed, two (clones C-26 and C-53) were found to express proteins of significantly lower molecular mass than the native RyR2 (Fig. 1, lane 4) or RyR2 transiently expressed in CHO cells (lane 7), and both these proteins were recognized by the monoclonal antibody C3-33 (Fig. 1, lanes 5 and 6). This suggests that the RyR2 cDNA has undergone deletions and/or rearrangements in these stable CHO clones, similar to its instability in bacterial host cells as described above. This result raises the need for caution in the expression of functional RyR2 proteins in heterologous systems. While the reason for this phenomenon is not clearly understood, in this study we have used transiently transfected CHO cells expressing only the high molecular weight (~560 K) RyR2 for functional analysis.
The function of RyR2 expressed in CHO cells was studied by measuring
the changes in intracellular Ca2+
([Ca2+]i) in response to stimulation with
caffeine, which is an activator of the Ca2+ release channel
(Fig. 2). Application of 10 mM caffeine
to CHO cells expressing RyR2 resulted in an increase of
[Ca2+]i in a reversible manner in two of the
four cells shown in Fig. 2 A (cells 1 and 2). No
changes in [Ca2+]i were observed in
untransfected CHO cells (not shown). The absence of caffeine response
in cells 3 and 4 in Fig. 2 A is likely due to the lack of
RyR2 expression in these cells. The ability of caffeine to induce
Ca2+ release suggests that RyR2 expressed in CHO cells is
capable of functioning as Ca2+ release channels (Imagawa et
al., 1992
).
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Comparison of single channel properties of RyR1 and RyR2 expressed in CHO cells
The Ca2+ release channel functions of native and
expressed RyR2 were further studied by using the lipid bilayer
reconstitution system. Functional channel activity could be
measured by incorporating the microsomal membrane vesicles from
CHO cells expressing RyR2 into lipid bilayer using cesium gluconate as
current carrier (Bhat et al., 1997b
). The single channel currents
through expressed RyR2 exhibited fast kinetics of transition between
open and closed states (Fig. 3). These
properties are comparable to those of the native RyR2 Ca2+
release channel currents recorded using SR membrane vesicles from
rabbit cardiac muscle (see Fig. 4
A). The RyR2 channels are activated by micromolar
concentrations of [Ca2+] in the cis
(cytoplasmic) solution. As shown in Fig. 3 B, chelation of
[Ca2+] in the cytoplasmic solution from 220 µM to 240 nM and 80 nM gradually decreased the channel open probability
(Po = 21.47 ± 3.48%, 220 µM;
Po = 1.60 ± 0.36%, 240 nM;
Po = 0.70 ± 0.10%, 80 nM), leading
to complete inhibition of the channel activity at [Ca2+] = 32 nM. This is similar to the Ca2+-dependent activation
of recombinant RyR1 channels expressed in CHO cells (Bhat et al.,
1997a
-c
). Furthermore, the channels formed by the expressed RyR2 are
sensitive to modification by ryanodine in that the channel conductance
is reduced by ~50% and the open lifetime of the channels is
increased dramatically (Fig. 3 A, bottom four traces).
Open-time histogram analyses of native and expressed RyR2 channels
revealed two similar time constants, i.e.,
01 = 0.65 ms and 0.44 ms, and
02 = 2.63 ms and 2.19 ms
for native and expressed RyR2 channels, respectively (Fig.
4 B).
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We have previously described the functional properties of RyR1
expressed in CHO cells (Bhat et al., 1997a
-c
). Comparison of the
single channel properties of full-length RyR1 and RyR2 expressed in CHO
cells is illustrated in Fig. 5. Both RyR1
and RyR2 channels exhibit distinct subconductance states
(O1 through O4). However, the RyR2 expressed in
CHO cells stays open more frequently at lower conductance levels (i.e.,
O1 and O3) with rare transitions to half and
full conductance levels (i.e., O2 and O4) (Fig.
5 A). This is in contrast to RyR1 channels expressed in CHO
cells, which mostly open to full conductance state (i.e.,
O4) when activated (Fig. 5 B). The
O4 state occurs in the majority of the experiments with the
RyR1 channels (~63%, 30 of 48 experiments), whereas O3 is the major conductance state occurring with the RyR2 channels (~80%, 23 of 29 experiments), with only brief transitions to the O4 state. The mean variance analysis of the amplitude
histogram for RyR2 channels expressed in CHO cells is presented in Fig. 6, which illustrates the presence of a
major peak corresponding to the O3 state with minor peaks
at O1 and O4 states (Ma and Zhao, 1994
). At +50
mV, the RyR2 channels exhibit a mean outward (cytoplasm
lumen)
current amplitude of 14.90 ± 0.68 pA (n = 24),
which corresponds to the O3 conductance level. By contrast,
the major outward current amplitude for RyR1 was 20.23 ± 1.29 pA
(n = 48, Bhat et al., 1997b
), which corresponds to the
O4 conductance level, and this is similar to the native
RyR1 channels from rabbit skeletal muscle SR (Bhat et al., 1997b
). The
analysis of the current-voltage relationship of the RyR2 channels is
presented in Fig. 7. Under the recording
conditions of symmetrical 200 mM cesium gluconate, three distinct
conductance states could be measured (O1 = ~100 pS,
O3 = ~290 pS, and O4 = ~401 pS)
(Fig. 7).
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The difference in the distribution of the conductance states between
RyR2 and RyR1 may reflect the differences in the pore properties of
these channels. This may happen because of the differences in the
channel structure itself and/or differential interaction with the
regulatory proteins. While the RyR1 channel opens to the full
conductance state in >60% of the experiments, the RyR2 channel
exhibits full conductance state in only <20% of the experiments. Furthermore, the RyR2 channels appear to be unstable, as they always
exhibit frequent transitions to subconductance states of O1
and O3 (see Fig. 5 A). Subconductance states are
characteristic features of the Ca2+ release channels from
both skeletal and cardiac muscles, which likely reflect the oligomeric
structure of the RyR protein complex, although the molecular
mechanism(s) is largely unknown. FK506 binding proteins (FKBP) have
been shown to associate and regulate the function of the
Ca2+ release channels (Marks, 1996
). While FKBP12
specifically associates with RyR1, RyR2 preferentially interacts with
FKBP12.6 (Jayaraman et al., 1992
; Timerman et al., 1994
, 1996
). These
proteins are known to regulate the function of RyRs by stabilizing the
conductance state(s) of the Ca2+ release channels
(Brillantes et al., 1994
; Ma et al., 1995
; Ahern et al., 1997
), and the
RyR channels depleted of FKBP12 have been shown to exhibit
subconductance states (Ahern et al., 1997
; Shou et al., 1998
). While we
do not know whether CHO cells express any endogenous FKBP12 or
FKBP12.6, it will be interesting to examine the properties of RyR2
channels in CHO cells co-transfected with these regulatory proteins.
Lack of Ca2+ sparks in CHO cells expressing RyR2
In cardiac muscle cells, spontaneous local increases in
intracellular Ca2+, termed Ca2+ sparks, have
been observed which occur spontaneously (Fig.
8 A top, panel a; Cheng et
al., 1993
), and in response to activation of voltage-gated
Ca2+ channels (Cannell et al., 1994
, 1995
;
Lopez-Lopez et al., 1994
, 1995
). Stimulation of cardiac myocytes with
caffeine increases the frequency of Ca2+ sparks (Fig. 8
A top, panel b) leading up to a global increase in the
intracellular Ca2+ (Fig. 8 A top, panel c).
Similar elementary Ca2+ release events, although smaller in
size than the cardiac Ca2+ sparks, have also been recorded
in skeletal muscle cells (Tsugorka et al., 1995
). However, it is not
known whether a single or a group of Ca2+ release channels
acting in concert constitute the "Ca2+ release units"
underlying the local Ca2+ transients in muscle cells. We
tested for the presence of spontaneous changes in intracellular
Ca2+ in CHO cells expressing RyR2 (Fig. 8 B).
Under resting conditions (Fig. 8 B top, panel a), or in
response to stimulation with caffeine (Fig. 8 B top, panel
b) no spontaneous local Ca2+ transients were evident
in the line-scan images of CHO cells expressing RyR2, although caffeine
was capable of inducing Ca2+ release in these cells (Fig. 8
B top, panel c, and bottom).
|
The lack of local Ca2+ transients in CHO cells expressing
RyR2 is similar to our recent results where CHO cells expressing RyR1 also did not exhibit spontaneous or caffeine-activated signals typical
of Ca2+ sparks (Bhat et al., 1997c
). These results suggest
that ryanodine receptors by themselves are not sufficient to support
elementary Ca2+ release events, although they are capable
of functioning as Ca2+ release channels both in vivo
(caffeine-induced Ca2+ release, Fig. 2) and in vitro
(single channel experiments, Figs. 3-5). The absence of
muscle-specific spatial environment in CHO cells may not support local
cooperative opening of expressed Ca2+ release channels
which is believed to be responsible for the origin of Ca2+
sparks. The absence in heterologous expression systems of
muscle-specific accessory protein(s) (as discussed above) that interact
with RyR to constitute a "local Ca2+ release unit" may
also contribute to the lack of spontaneous or caffeine-induced
Ca2+ sparks in CHO cells. The activity of both skeletal and
cardiac Ca2+ release channels is controlled by both
cytoplasmic and luminal Ca2+ (Sitsapesan and Williams,
1997
). Furthermore, in cardiac myocytes the fractional SR
Ca2+ release and the frequency and amplitude of Ca
2+ sparks are increased by an increase in the SR
Ca2+ content (Bassani et al., 1995
; Lukyanenko et al.,
1996
). Although the Ca2+ content of the intracellular
stores of CHO cells is not known, it may not mimic that of muscle cells
to support spontaneous opening of the expressed RyR channels.
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ACKNOWLEDGMENTS |
|---|
We thank Dr. Stephen W. Jones for his generous help with the mean variance analysis.
This work was supported by an American Heart Association (Northeast Ohio Affiliate) post-doctoral fellowship (to M.B.B.), an Established Investigatorship from the American Heart Association (to J.M.), and National Institutes of Health Grant AG15556 (to J.M.).
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FOOTNOTES |
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Received for publication 30 July 1998 and in final form 26 April 1999.
Address reprint requests to Dr. Jianjie Ma, Department of Physiology and Biophysics, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH 44106. Tel.: 216-368-2684; Fax: 216-368-5586; E-mail: jxm63{at}po.cwru.edu.
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REFERENCES |
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Biophys J, August 1999, p. 808-816, Vol. 77, No. 2
© 1999 by the Biophysical Society 0006-3495/99/08/808/09 $2.00
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