Correspondence to: S. Györke, Department of Physiology, Texas Tech University Health Sciences Center, Lubbock, TX 79430. Fax:806-743-1512 E-mail:physg{at}ttuhsc.edu.
Released online: 15 November 1999
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Abstract |
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The local control concept of excitationcontraction coupling in the heart postulates that the activity of the sarcoplasmic reticulum ryanodine receptor channels (RyR) is controlled by Ca2+ entry through adjoining sarcolemmal single dihydropyridine receptor channels (DHPRs). One unverified premise of this hypothesis is that the RyR must be fast enough to track the brief (<0.5 ms) Ca2+ elevations accompanying single DHPR channel openings. To define the kinetic limits of effective trigger Ca2+ signals, we recorded activity of single cardiac RyRs in lipid bilayers during rapid and transient increases in Ca2+ generated by flash photolysis of DM-nitrophen. Application of such Ca2+ spikes (amplitude ~1030 µM, duration ~0.10.4 ms) resulted in activation of the RyRs with a probability that increased steeply (apparent Hill slope ~2.5) with spike amplitude. The time constants of RyR activation were 0.070.27 ms, decreasing with spike amplitude. To fit the rising portion of the open probability, a single exponential function had to be raised to a power n ~ 3. We show that these data could be adequately described with a gating scheme incorporating four sequential Ca2+-sensitive closed states between the resting and the first open states. These results provide evidence that brief Ca2+ triggers are adequate to activate the RyR, and support the possibility that RyR channels are governed by single DHPR openings. They also provide evidence for the assumption that RyR activation requires binding of multiple Ca2+ ions in accordance with the tetrameric organization of the channel protein.
Key Words: cardiac muscle, sarcoplasmic reticulum, ryanodine receptor, calcium signaling, gating model
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INTRODUCTION |
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In mammalian heart, the process of excitationcontraction (E-C)1 coupling is mediated by calcium-induced Ca2+ release (CICR,
The gating properties of the RyRs have been studied after reconstitution of the channels into lipid bilayers. All these studies have been performed under stationary Ca2+ conditions (
In the present study, we used the photolabile Ca2+ chelator DM-nitrophen (DMN) to produce brief Ca2+ elevations that mimic the waveform of Ca2+ changes associated with openings of single DHPRs. Photolysis liberates Ca2+ from the DMN-Ca complex much faster then free DMN binds Ca2+ (
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METHODS |
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Bilayer Experiments
Heavy SR microsomes were prepared from canine left ventricles by standard procedures (
Flash Photolysis Experiments
Fast changes of the Ca2+ concentration in the microenvironment of the reconstituted channel were performed by flash photolysis of DM-nitrophen (Calbiochem Corp.) as described previously (
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Modeling of RyR Gating
To simulate the RyR response to Ca2+ spikes, we used our previously published minimal gating model of RyR with one Ca2+ binding step (
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Single-channel activity in response to Ca2+ stimuli was simulated using the program SCESim (
The theoretical time course of channel open probability during and after the Ca2+ spike was calculated in Mathematica (Wolfram Research) by combining the differential equations for DMN complexation and photolysis (
The analysis of statistical significance of differences between models was performed by 2 tests, according to the procedure described by
2 were determined from the sum of squares of differences between experimental data and model prediction, and from the experimental variance. The models that did not pass the
2 test at P = 0.01 were rejected.
The apparent calcium sensitivity of peak open probability in response to a Ca2+ spike was described by a general equation (Equation 1, see
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(1) |
where KCa is apparent calcium sensitivity of the channel, and nH is the apparent Hill slope. In general, the apparent Hill slope may not necessarily correspond to the actual number (n) of Ca2+ binding sites. Specifically, nH < n when the activation path contains a Ca2+-independent closed state (as with our models of RyR), even if the binding sites are equivalent and independent.
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RESULTS |
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Generation of Rapid Ca2+ Stimuli for Activation of RyR
Single cardiac RyR channels were reconstituted at a steady state Ca2+ concentration of 20 µM. After incorporation of a single RyR, DMN (3 mM) was added to the cytoplasmic (cis) side of the channel. The free Ca2+ was titrated to 75150 nM. Identical precalibrated photolytically induced Ca2+ spikes were applied to the channel. After each UV pulse, resting conditions were reestablished by stirring the solution in the cis chamber for at least 30 s. The laser flash-induced Ca2+ spike is too fast to be directly measured by any available method, including measurements using the fastest Ca2+ indicators (on = 618 µs) to 930 µM, and then decayed with a
off = 106200 µs to a final level of 105190 nM. Ca2+ was elevated to over 5 µM for 0.10.4 ms and to over 1 µM for 0.30.7 ms. A typical example of such a Ca2+ spike is shown in Figure 1 C. The amplitude and duration of this Ca2+ stimulus is similar to that expected to occur near a RyR channel during a single brief opening of an adjacent DHPR channel (
Kinetics of RyR Response to Rapid Ca2+ Stimuli
We recorded single RyR channel activity in response to such brief free Ca2+ stimuli (Figure 2 and Table 3). The required temporal resolution was achieved by recording at a sampling rate of 100 kHz and cut-off filter setting 5 kHz. Before the flash, the channels exhibited essentially no activity. The channels responded to the Ca2+ stimulus in ~25% of the episodes. The activity evoked by DMN photolysis consisted mostly of single openings, after which the channel stayed closed until the end of the episode (Figure 2 A). To quantify the time course of channel activity, at least 32 single channel records obtained from an individual channel were combined to generate ensemble averages (Figure 2 A, bottom).
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Channel open probability transiently increased upon photolysis of DMN. The time course of activation was best fit by a single exponential association function raised to the power na (see Figure 2, legend). The rising portions of Po on expanded time scale are shown in B () along with the fits (solid lines). At 2 kHz bandwidth, the rise of Po was relatively slow (
a = 0.22 ms, na = 1.4). Expanding the bandwidth to 5 kHz resulted in a significant decrease in the rise time of Po (
a = 0.10 ms). In addition, a notable delay between the application of the laser flash and the ascent of Po became evident (na = 3). Increasing the filter cutoff frequency to 10 kHz had no further impact on the observed rate of channel activation (
a= 0.09; na = 2.8). Therefore, the temporal resolution of our measurements at 5 and 10 kHz was adequate to resolve the kinetics of RyR activation. The rising phase of Po at both 5 and 10 kHz was best fit by an exponential function with a power close to 3 (solid line), strongly suggesting that binding of several Ca2+ ions must occur before the channel can open.
To further quantify the kinetics of the channel response, we analyzed the distribution of the first latencies of channel openings induced by the laser flash (Figure 2 C). The cumulative first latency distributions () closely corresponded to the time courses of the rising phases of the respective ensemble open probabilities at each bandwidth (dashed lines). This confirms that the delay observed in the open probabilities at 5 kHz reflects channel behavior and is not merely an artifact introduced by experimental noise. Consistent with the observed time course of ensemble open probabilities, the distributions of first latencies showed no delay at 2 kHz bandwidth. At both 5 and 10 kHz, they exhibited a prominent rising phase and peaked at ~0.2 ms. The average channel open time was 1.9 ± 0.2 ms at 210 kHz. Deactivation of the channel after the Ca2+ spike had a monoexponential time course (
d = 3.2 ± 0.4 ms). It was much slower than channel activation or the decay of the Ca2+ spike and was independent of the bandwidth.
RyR Response to Transient versus Sustained Ca2+ Stimuli
Previous studies of RyR activation by photolysis of DMN (
RyR Response to Ca2+ Spikes of Different Magnitudes
To further characterize the activation of RyRs by Ca2+ spikes, we measured RyR activity in response to laser flashes of different intensities. Figure 4AC, shows channel responses to laser flashes of low, intermediate, and high intensity along with the corresponding calculated free [Ca2+] spikes in a representative experiment. In this experiment, the amplitude of the Ca2+ spike was estimated to be 9.3, 18.3, and 27.4 µM for low, intermediate, and high intensity pulses, respectively. The Ca2+ spikes decayed with time constants of 0.17, 0.18, and 0.20 ms, respectively. Ca2+ was elevated to over 5 µM for 0.13, 0.27, and 0.34 ms, and to over 1 µM for 0.4, 0.6, and 0.7 ms, respectively. As can be seen, low-intensity flashes caused channel openings only in relatively few occasions (peak Po ~ 0.06); increasing flash energy increased the probability of activation (peak Po ~ 0.25 and 0.50, respectively). Interestingly, in all cases the responses were composed of isolated openings with a similar duration. The time constants of activation, determined by fitting single exponential association function raised to the power n to the ensemble averages, progressively decreased with increasing the energy of the laser pulse (a = 0.27, 0.09, and 0.07 ms; na = 3.5, 2.5, and 2.4, respectively; Figure 5, DF). Similar results were obtained in five other experiments. These results are summarized in Figure 6 F, which plots the peak Po of the channel as a function of spike amplitude. The [Ca2+] dependence of Po could be described by Equation 1 with a KCa value of 29 ± 1 µM and an apparent Hill slope of 2.5 ± 0.2. The high values of the activation exponent and of the Hill slope further indicate that activation of the RyR channel requires binding of several calcium ions.
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Gating Mechanisms of RyR Channel during Brief Ca2+ Stimuli
To better understand the mechanisms of activation and deactivation of RyR in response to Ca2+ spikes, we performed single channel simulations using our published minimal model of RyR gating (
The excessive background activity and a lack of delay between the Ca2+ spike and RyR activation could be ascribed again to the possibility that binding of more than one Ca2+ ion is required to produce channel opening. Considering the tetrameric organization of the RyR, we extended our minimal RyR model by including four sequential Ca2+ binding steps (Figure 5 A, right; Table 2, Model 4Ca). The ensemble Po generated using the extended model showed essentially no spontaneous openings before the Ca2+ spike. After the Ca2+ spike, it exhibited a significant delay, similar to the experimentally observed behavior (Figure 5 B). Furthermore, the first latency distribution (Figure 5 C) yielded a peak near 0.25 ms, close to the experimentally observed value of 0.2 ms. These results suggest that activation of the RyR by Ca2+ spikes may indeed involve binding of multiple, perhaps as many as four, Ca2+ ions to the channel.
To further elucidate how many Ca2+ binding steps are involved in channel activation, we carried out theoretical simulations using models with different numbers of Ca2+ binding sites. We compared the abilities of the models with different numbers of Ca2+ binding sites to reproduce the experimentally observed kinetics of RyR activation. This approach is illustrated in Figure 6AE, for the experiment shown in Figure 4 and for models with one to five Ca2+ binding steps, respectively. Differences between the models were statistically analyzed by the 2 test, applied to the whole data set of six experiments. The
2 values were determined from the sum of squares of differences between experimental data and predictions of the particular model, and from the experimental variance (
2 values of 17,120, 9,821, 6,712, 4,667, and 4,711 (4,510 degrees of freedom) for models with one, two, three, four, and five Ca2+ binding sites, respectively. Models with less than four calcium binding sites have failed the
2 test at the significance level P = 0.01, while models with four and five Ca2+ binding sites passed the test and can be considered, therefore, compatible with the data. These tests strongly suggest that binding of at least four Ca2+ ions are necessary for RyR activation.
Figure 6 F shows theoretical Ca2+Po dependence curves obtained from the above series of models along with the Ca2+Po dependence curve obtained from experimental data. The apparent Hill slopes of the theoretical [Ca2+]Po relationships yielded by the models with one, two, and three Ca2+ binding steps (0.97 ± 0.15, 1.69 ± 0.02, and 2.09 ± 0.01, respectively) were significantly different from those derived from experimental data (2.5 ± 0.2) at significance levels of 0.0001, 0.001, and 0.05, respectively. Therefore, these models are not compatible with the experimental results. Models with four and five Ca2+ binding steps (apparent Hill slopes 2.6 ± 0.1 and 2.6 ± 0.1, respectively) were not significantly different from the experimental data even at P = 0.5. Therefore, the response of the RyR to Ca2+ spikes can be described by our minimal model of the RyR modified by including a total of four Ca2+ binding steps.
Theoretical Dependency of RyR Response on Amplitude-duration Characteristics of Ca2+ Stimulus
The chemistry of DMN limits flash-photolysis experiments to a rather narrow range of amplitude-duration characteristics of Ca2+ spikes. In contrast, the parameters of local Ca2+ signals associated with the activity of DHPRs vary widely. Therefore, to gain further insight into the dependence of the channel activation on the characteristics of the trigger signal, we performed simulations in response to a broad range of rectangular Ca2+ pulses using Model 4Ca with four Ca2+ binding sites described above. The properties of the Ca2+ pulse in the physiological range of durations and amplitudes had a profound effect on peak open probability of the RyR, as illustrated in Figure 7. Calcium elevations lasting <10 µs had negligible probability to open the RyR in the whole amplitude range. To increase the peak open probability from 5 to 95%, the amplitude of the calcium pulse has to be increased by ~10-fold for any pulse duration. Prolongation of the Ca2+ pulses above 1 ms was not effective in increasing peak Po of the RyR. In the high Ca2+ pulse amplitude range (>10 µM), the dependence of peak Po on pulse duration was very steep for short pulse durations (0.10.5 ms).
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DISCUSSION |
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In the present study we measured the kinetics of activation of cardiac SR Ca2+ release channels/RyRs using fast Ca2+ concentration spikes produced by photolysis of DM-nitrophen. The Ca2+ spikes mimic the profile of Ca2+ produced by openings of single DHPRs in the vicinity of the RyRs. Thus, our results show, for the first time, how single RyRs might respond to a physiological trigger signal.
Under our experimental conditions (~100 nM resting Ca2+ and 3 mM DMN), the reconstructed Ca2+ spikes were characterized by an activation time constant of ~15 µs, a duration of ~0.10.4 ms (at 5 µM Ca2+) and a peak amplitude of 1030 µM (Figure 1 C). Application of such Ca2+ pulses resulted in activation of the RyR with 550% probability, depending on spike magnitude. The activity of RyR was characterized by isolated single openings with duration of ~2 ms. It is important that in our experiments we used Cs+ instead of Ca2+ as the charge carrier. Besides improving the signal-to-noise ratio, this allowed us to determine the parameters of channel kinetics without potential side effects related to "feed-through" influences of luminal Ca2+ at the cytosolic activation and inactivation sites (
Previous studies using caged Ca2+ did not yield channel activation in response to Ca2+ spikes (
We believe that our measurements yield the true response time of the channel because channel activation displayed a distinct delay, and the kinetics of the RyR response were unaffected by increasing the filter cutoff frequency from 5 to 10 kHz. The lifetime of isolated RyR channel openings induced by Ca2+ spikes (to ~ 2 ms) was substantially longer than the average channel open time (~1 ms) reported under similar conditions at steady state (
In previous studies with photolysis of DMN and NP-EGTA, the RyRs activated rapidly, and then the Po decayed slowly, by a process termed adaptation (
The kinetics and [Ca2+] dependence of the response of the RyRs to Ca2+ spikes could be well described by our minimal model of RyR (
The existence of multiple Ca2+ binding steps in the RyR activation path is consistent with the results of analysis of closed time distributions of steady state recordings at low [Ca2+], yielding at least five closed states (
Based on our model simulations, we suggest that the response of the RyR to a Ca2+ spike includes the following steps. (a) Sequential binding of four Ca2+ ions to the channel promotes transition from closed states (RC4) to an open state (O1). The need for binding of four Ca2+ ions to open the channel accounts for the delay in channel activation, for the negligible Po at basal [Ca2+], and for the fact that spikes do not always cause channel opening. (b) After termination of the spike, Ca2+ dissociates from the channel and the channel deactivates by returning first to the closed states (C4C1) and eventually to the resting state. Transitions between states C4O2 and O1C2 are very slow (~1 s;
Our results have important ramifications for understanding CICR in vivo. It has been suggested that during E-C coupling Ca2+ entering through single L-type Ca2+ channels locally controls the activity of the Ca2+ release channels, presumably arranged into functionally independent release units (
We showed that Ca2+ spikes with an estimated amplitude of 1030 µM, which mimic single DHPR-related signals, have a 550% probability of inducing RyR activation. The results of our simulations in a wider range of amplitudes and durations of the Ca2+ elevations demonstrate that the probability of activation of a single RyR is graded with the amplitude as well as duration of the triggering Ca2+ pulse. These results are consistent with a DHPRRyR coupling arrangement that could be the subject of physiological modulation and pathological failure in the heart (
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Acknowledgements |
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We are grateful to M. Dura and A. Zahradníková, Jr., for technical assistance, and to M. Fill, A. Escobar, and R. Nathan for helpful discussions.
A. Zahradníková was supported in part by an Howard Hughes Medical Institute International Research Scholar's Award, a Fulbright Scholar's Award, and VEGA 2/5155; S. Györke by grants from the National Institutes of Health (HL 63043, HL 52620, and HL 03739-01). S. Györke is an Established Investigator of the American Heart Association.
Submitted: 25 March 1999
Revised: 20 October 1999
Accepted: 26 October 1999
CICR, calcium-induced calcium release; DHPR, dihydropyridine receptor; DMN, 1-(2-nitro-4,5-dimethoxyphenyl)-1,2-diamino-ethane-N,N,N',N'-tetraacetic acid; E-C, excitationcontraction; H, high activity; RyR, ryanodine receptor; SR, sarcoplasmic reticulum
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References |
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Bers, D.M. 1991. ExcitationContraction Coupling and Cardiac Contractile Force. Boston, MA, Kluwer Academic Publishers, pp. 258.
Bridge, J.H., Ershler, P.R., Cannell, M.B. 1999. Properties of Ca2+ sparks evoked by action potentials in mouse ventricular myocytes. J. Physiol. 518:469-478
Cannell, M.B., Cheng, H., Lederer, W.J. 1995. The control of calcium release in heart muscle. Science. 268:1045-1050[Medline].
Cannell, M.B., Soeller, C. 1997. Numerical analysis of ryanodine receptor activation by L-type channel activity in the cardiac muscle diad. Biophys. J 73:112-122[Abstract].
Chu, A., Fill, M., Stefani, E., Entman, M.L. 1993. Cytoplasmic Ca2+ does not inhibit the cardiac muscle sarcoplasmic reticulum ryanodine receptor Ca2+ channel, although Ca2+-induced Ca2+ inactivation of Ca2+ release is observed in native vesicles. J. Membr. Biol. 135:49-59[Medline].
Colquhoun, D., Hawkes, A.G. 1983. The principles of the stochastic interpretation of ion channel mechanisms. In Sakmann B., Neher E., eds. Single Channel Recording. New York, NY, Plenum Publishing Corp, 135-175.
Copello, J.A., Barg, S., Onoue, H., Fleischer, S. 1997. Heterogeneity of Ca2+ gating of skeletal muscle and cardiac ryanodine receptors. Biophys. J. 73:141-156[Abstract].
Coronado, R., Morrissette, J., Sukhareva, M., Vaughan, D.M. 1994. Structure and function of ryanodine receptors. Am. J. Physiol 266:C1485-C1504
Dettbarn, C., Györke, S., Palade, P. 1994. Many agonists induce "quantal" Ca2+ release or adaptive behavior in muscle ryanodine receptors. Mol. Pharmacol. 46:502-507[Abstract].
Ellis-Davies, G.C.R., Kaplan, J.H., Barsotti, R.J. 1996. Laser photolysis of caged Ca2+: rates of calcium release by nitrophenyl-EGTA and DM-nitrophen. Biophys. J. 70:1005-1016.
Escobar, A.L., Vélez, P., Kim, A.M., Fuentes, F., Fill, M., Vergara, J. 1997. Kinetic properties of DM-nitrophen and calcium indicators: rapid transient response to flash photolysis. Pflügers Arch. 434:615-631.
Fabiato, A., Fabiato, F. 1979. Use of chlorotetracycline fluorescence to demonstrate Ca2+-induced release of Ca2+ from the sarcoplasmic reticulum of skinned cardiac cells. Nature 281:146-148[Medline].
Gomez, A.M., Valdivia, H.H., Cheng, H., Lederer, M.R., Santana, L.F., Cannell, M.B., McCune, S.A., Altschuld, R.A., Lederer, W.J. 1997. Defective excitationcontraction coupling in experimental cardiac hypertrophy and heart failure. Science. 276:800-806
Györke, S., Fill, M. 1993. Ryanodine receptor adaptation: control mechanism of Ca2+-induced Ca2+ release in heart. Science. 260:807-809[Medline].
Györke, S., Fill, M. 1994. Ca2+-induced Ca2+ release in response to flash photolysis. Science. 263:987-988.
Györke, S., Vélez, P., Suárez-Isla, B., Fill, M. 1994. Activation of single cardiac and skeletal ryanodine receptor channels by flash photolysis of caged Ca2+. Biophys. J. 66:1879-1886[Abstract].
Lamb, G.D., Fryer, M.W., Stephenson, D.G. 1994. Ca2+-induced Ca2+ release in response to flash photolysis. Science. 263:986-988[Medline].
Landau, R.H., Páez, M.J. 1997. Computational Physics. New York, NY, John Wiley & Sons, pp. 520.
Laver, D., Curtis, B. 1996. Response of ryanodine receptor channels to Ca2+ steps produced by rapid solution exchange. Biophys. J. 71:732-741[Abstract].
Laver, D.R., Lamb, G.D. 1998. Inactivation of Ca2+ release channels (ryanodine receptors RyR1 and RyR2) with rapid steps in [Ca2+] and voltage. Biophys. J. 74:2352-2364
López-López, J., Shacklock, P., Balke, C.W., Wier, W.G. 1995. Local calcium transients triggered by single L-type calcium channel currents in cardiac cells. Science 268:1042-1045[Medline].
Naraghi, M., Neher, E. 1997. Linearized buffered Ca2+ diffusion in microdomains and its implications for calculation of [Ca2+] at the mouth of a calcium channel. J. Neurosci. 17:6961-6973
Rose, W.C., Balke, C.W., Wier, W.G., Marban, E. 1992. Macroscopic and unitary properties of physiological ion flux through L-type Ca2+ channels in guinea-pig heart cells. J. Physiol. 456:267-284[Abstract].
Rousseau, E., Meisner, G. 1989. Single cardiac sarcoplasmic reticulum Ca2+ release channel: activation by caffeine. Am. J. Physiol. 256:H328-H333
Santana, L.F., Cheng, H., Gomez, A.M., Cannell, M.B., Lederer, W.J. 1996. Relation between the sarcolemmal Ca2+ current and Ca2+ sparks and local control theories for cardiac excitationcontraction coupling. Circ. Res. 78:166-171
Schiefer, A., Meissner, G., Isenberg, G. 1995. Ca2+ activation and Ca2+ inactivation of canine reconstituted cardiac sarcoplasmic reticulum Ca2+ release channels. J. Physiol. 489:337-348[Abstract].
Shorofsky, S.R., Izu, L., Wier, W.G., Balke, C.W. 1998. Ca2+ sparks triggered by patch depolarization in rat heart cells. Circ. Res. 82:424-429
Simon, S.M., Llinás, R.R. 1985. Compartmentalization of the submembrane calcium activity during calcium influx and its significance in transmitter release. Biophys. J. 48:485-498[Abstract].
Sitsapesan, R., Montgomery, R.A., Williams, A.J. 1995. New insights into the gating mechanisms of cardiac ryanodine receptors revealed by rapid changes in ligand concentration. Circ. Res. 77:765-772
Sitsapesan, R., Williams, A.J. 1994. Gating of the native and purified cardiac SR Ca2+-release channel with monovalent cations as permeant species. Biophys. J. 67:1484-1494[Abstract].
Soeller, C., Cannell, M.B. 1997. Numerical simulation of local calcium movements during L-type calcium channel gating in the cardiac diad. Biophys. J 73:97-111[Abstract].
Stern, M.D. 1992a. Buffering of calcium in the vicinity of a channel pore. Cell Calc. 13:183-192[Medline].
Stern, M.D. 1992b. Theory of excitationcontraction coupling in cardiac muscle. Biophys. J 63:497-517[Abstract].
Stern, M.D., Lakatta, E. 1992. Excitationcontraction coupling in the heart: the state of the question. FASEB J. 6:3092-3100
Stern, M.D., Song, L.S., Cheng, H., Sham, J.S., Yang, H.T., Boheler, K.P., Ríos, E. 1999. Local control models of cardiac excitationcontraction coupling: a possible role for allosteric interactions between ryanodine receptors. J. Gen. Physiol. 113:469-489
Tripathy, A., Meissner, G. 1996. Sarcoplasmic reticulum lumenal Ca2+ has access to cytosolic activation and inactivation sites of skeletal muscle Ca2+ release channel. Biophys. J. 70:2600-2615[Abstract].
Valdivia, H., Kaplan, J.H., Ellis-Davies, G.C.R., Lederer, W.J. 1995. Rapid adaptation of cardiac ryanodine receptors: modulation by Mg2+ and phosphorylation. Science. 267:1997-2000[Medline].
Zahradníková, A., Dura, M., Györke, S. 1999a. Modal gating transitions in cardiac ryanodine receptors during increases of Ca2+ concentration produced by photolysis of caged Ca2+. Pflügers Arch. 438:283-288.
Zahradníková, A., Maco, P., Me hart, P., Zahradník, I. 1999. A novel dynamic algorithm for stochastic simulation of a group of coupled ionic channels. Biophys. J. 76:A460, b (Abstr.).
Zahradníková, A., Zahradník, I. 1995. Description of modal gating of the cardiac calcium release channel in planar lipid membranes. Biophys. J. 69:1780-1788[Abstract].
Zahradníková, A., Zahradník, I. 1996. A minimal gating model for the cardiac calcium release channel. Biophys. J. 71:2996-3012[Abstract].
Zucker, R.S. 1993. The calcium concentration clamp: spikes and reversible pulses using the photolabile chelator DM-nitrophen. Cell Calc. 14:87-100[Medline].