| Model of Intracellular Calcium Cycling in Ventricular Myocytes Biophysical Journal, Volume 85, Issue 6, 1 December 2003, Pages 3666-3686 Y. Shiferaw, M.A. Watanabe, A. Garfinkel, J.N. Weiss and A. Karma Abstract We present a mathematical model of calcium cycling that takes into account the spatially localized nature of release events that correspond to experimentally observed calcium sparks. This model naturally incorporates graded release by making the rate at which calcium sparks are recruited proportional to the whole cell L-type calcium current, with the total release of calcium from the sarcoplasmic reticulum (SR) being just the sum of local releases. The dynamics of calcium cycling is studied by pacing the model with a clamped action potential waveform. Experimentally observed calcium alternans are obtained at high pacing rates. The results show that the underlying mechanism for this phenomenon is a steep nonlinear dependence of the calcium released from the SR on the diastolic SR calcium concentration (SR load) and/or the diastolic calcium level in the cytosol, where the dependence on diastolic calcium is due to calcium-induced inactivation of the L-type calcium current. In addition, the results reveal that the calcium dynamics can become chaotic even though the voltage pacing is periodic. We reduce the equations of the model to a two-dimensional discrete map that relates the SR and cytosolic concentrations at one beat and the previous beat. From this map, we obtain a condition for the onset of calcium alternans in terms of the slopes of the release-versus-SR load and release-versus-diastolic-calcium curves. From an analysis of this map, we also obtain an understanding of the origin of chaotic dynamics. Abstract | Full Text | PDF (299 kb) |
| A Rabbit Ventricular Action Potential Model Replicating Cardiac Dynamics at Rapid Heart Rates Biophysical Journal, Volume 94, Issue 2, 15 January 2008, Pages 392-410 Aman Mahajan, Yohannes Shiferaw, Daisuke Sato, Ali Baher, Riccardo Olcese, Lai-Hua Xie, Ming-Jim Yang, Peng-Sheng Chen, Juan G. Restrepo, Alain Karma, Alan Garfinkel, Zhilin Qu and James N. Weiss Abstract Mathematical modeling of the cardiac action potential has proven to be a powerful tool for illuminating various aspects of cardiac function, including cardiac arrhythmias. However, no currently available detailed action potential model accurately reproduces the dynamics of the cardiac action potential and intracellular calcium (Ca) cycling at rapid heart rates relevant to ventricular tachycardia and fibrillation. The aim of this study was to develop such a model. Using an existing rabbit ventricular action potential model, we modified the L-type calcium (Ca) current () and Ca cycling formulations based on new experimental patch-clamp data obtained in isolated rabbit ventricular myocytes, using the perforated patch configuration at 35–37°C. Incorporating a minimal seven-state Markovian model of that reproduced Ca- and voltage-dependent kinetics in combination with our previously published dynamic Ca cycling model, the new model replicates experimentally observed action potential duration and Ca transient alternans at rapid heart rates, and accurately reproduces experimental action potential duration restitution curves obtained by either dynamic or S1S2 pacing. Abstract | Full Text | PDF (662 kb) |
| Action Potential Morphology Influences Intracellular Calcium Handling Stability and the Occurrence of Alternans Biophysical Journal, Volume 90, Issue 2, 15 January 2006, Pages 672-680 Peter N. Jordan and David J. Christini Abstract Instability in the intracellular Ca handling system leading to Ca alternans is hypothesized to be an underlying cause of electrical alternans. The highly coupled nature of membrane voltage and Ca regulation suggests that there should be reciprocal effects of membrane voltage on the stability of the Ca handling system. We investigated such effects using a mathematical model of the cardiac intracellular Ca handling system. We found that the morphology of the action potential has a significant effect on the stability of the Ca handling system at any given pacing rate, with small changes in action potential morphology resulting in a transition from stable nonalternating Ca transients to stable alternating Ca transients. This bifurcation occurs as the alternans eigenvalue of the system changes from absolute value <1 to absolute value >1. These results suggest that the stability of the intracellular Ca handling system and the occurrence of Ca alternans are not dictated solely by the Ca handling system itself, but are also modulated to a significant degree by membrane voltage (through its influence on sarcolemmal Ca currents) and, therefore, by all ionic currents that affect membrane voltage. Abstract | Full Text | PDF (271 kb) |
Copyright © 2006 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 90, Issue 1, 381-389, 1 January 2006
doi:10.1529/biophysj.105.069013
Electrophysiology
F. Brette*,
,
, L. Sallé† and C.H. Orchard*
* Department of Physiology, Medical Sciences Building, University of Bristol, Bristol, United Kingdom
† Laboratoire de Physiologie Cellulaire, EA3212, Université de Caen, 14032 Caen, France
Address reprint requests to Dr. Fabien Brette, Dept. of Physiology, Medical Sciences Bldg., University of Bristol, Bristol, UK. Tel.: 44-117-331-7585; Fax: 44-117-331-7585.During the cardiac action potential (AP), Ca influx via individual L-type Ca channels activates a cluster of adjacent sarcoplasmic reticulum (SR) Ca release channels (ryanodine receptors; RyRs); the consequent systolic Ca transient is the spatial and temporal sum of such local Ca releases 1,2. It is now generally accepted that L-type Ca current (ICa) is the major trigger for SR Ca release 3,4,5, and that alternative pathways (Na/Ca exchange, T-type Ca current) are weak triggers under physiological conditions 6,7. The rise of intracellular Ca leads to contraction of the cardiomyocyte; relaxation is brought about by Ca extrusion from the cell and resequestration into intracellular stores, via Ca ATPases and Na/Ca exchange 8. ICa also helps to load the SR with Ca for subsequent release 9: the contribution of the late phase of ICa to SR Ca loading has been demonstrated using action potential waveforms in voltage clamp experiments on guinea-pig ventricular myocytes 10, and the substantial role of ICa in SR Ca loading has been demonstrated in previous work from Eisner's laboratory (reviewed in 11). Ca is thus both a second messenger (above) and a charge carrier: ICa is a depolarizing current and therefore determines the shape of the action potential.
Although ICa is present on the sarcolemma of cardiac myocytes, it has become increasingly clear that it is not uniformly distributed on the cardiac cell membrane. The sarcolemma of mammalian ventricular myocytes contains invaginations called transverse (T)-tubules (see 12 for review). T-tubules occur perpendicularly to the longitudinal axis of the cell at intervals of ∼1.8–2μm 13,14. They are located at the Z-lines and have a mean diameter of ∼250nm 14,15. Several studies have shown that ICa is located predominantly in the T-tubules in ventricular myocytes (see 12 for review). For example, immunocytochemistry has shown that in ventricular cells staining of L-type Ca channels occurs primarily at the T-tubules in rabbit 16, guinea-pig 17, and rat 18 myocytes. These data are supported by work investigating the functional localization of ICa: we have developed a technique to disrupt the T-tubules of rat ventricular myocytes (detubulation) 19. After osmotic shock, the T-tubules seal off within the cell and hence are physically and electrically uncoupled from cell surface membrane 20. By comparing currents from detubulated and control myocytes it is possible to estimate the proportion of current within the T-tubules. We have found ∼80% of ICa within the T-tubules 21. This concentration of ICa at the T-tubules (and its colocalization with RyRs) allows spatial and temporal synchronization of Ca release throughout the cell, ensuring rapid and synchronous contraction 20,22,23. Although we have previously characterized the role of ICa at the T-tubules and cell surface in triggering SR Ca release 21, they are no quantitative data about Ca entry at the two sites. Furthermore, no information is available on the role of T-tubules in shaping the AP.
In this study, we have therefore investigated the role of the T-tubules in determining action potential configuration. We have also examined Ca entry in control and detubulated myocytes under voltage clamp using square and action potential waveforms, to quantify Ca entry at the T-tubule and surface membranes.
Male Wistar rats (250–300g) were killed humanely by cervical dislocation after stunning, and the heart rapidly removed, in accordance with the United Kingdom Home Office Guidance on the Operation of the Animals (Scientific Procedures) Act of 1986. The heart was mounted on a Langendorff apparatus and perfused retrogradely with a HEPES-based isolation solution containing (in mmol/L): 130 NaCl, 5.4 KCl, 0.4 NaH2PO4, 1.4 MgCl2, 0.75 CaCl2, 10 HEPES, 10 glucose, 20 taurine, and 10 creatine (pH 7.3 with NaOH). When the coronary circulation had cleared of blood, perfusion was continued with Ca-free isolation solution (in which CaCl2 was replaced with 0.1 mmol/L EGTA) for 5min, followed by perfusion for a further 7–10min with isolation solution containing 0.8 mg/ml collagenase (type I; Worthington Biochemical, Lakewood, NJ), and 0.08 mg/ml protease (type XIV; Sigma, St. Louis, MO). The ventricles were then excised from the heart, minced, and gently shaken at 37°C in collagenase-containing isolation solution supplemented with 1% bovine serum albumin. Cells were filtered from this solution at 5min intervals and resuspended in isolation solution containing 0.75 mmol/L Ca.
Detubulation was induced by osmotic shock as described previously 19. Briefly, 1.5 mol/L formamide was added to the cell suspension for 15–20min, before returning the cells to the standard solution. Detubulation occurs because of the osmotic shock produced by formamide withdrawal.
Myocytes were studied in a chamber mounted on the stage of an inverted microscope (Nikon Diaphot, Tokyo, Japan). Cells were initially superfused with a normal physiological salt solution containing (in mmol/L): 113 NaCl, 5 KCl, 1 MgSO4, 1 CaCl2, 1 Na2HPO4, 20 Na acetate, 10 glucose, 10 HEPES, and 5 U/L insulin, pH set to 7.4 with NaOH. All experiments were performed at room temperature (22–25°C).
Membrane potential and currents were recorded using the whole-cell configuration of the patch clamp technique 24. An Axopatch 200B (Axon Instruments, Union City, CA) amplifier was used, controlled by a Pentium PC connected via a Digidata 1322A A/D converter (Axon Instruments), which was also used for data acquisition and analysis using pClamp software (Axon Instruments). Signals were filtered at 2–10kHz using an 8-pole Bessel low pass filter before digitization at 10–20kHz and storage. Patch pipettes resistance was typically 1.5–2.5 MΩ when filled with intracellular solution (below).
Action potentials were evoked by 2.5ms subthreshold current steps. Trains of pulses were applied at 0.1Hz. The bath solution was the normal physiological salt solution described above. The pipette solution contained (in mmol/L): 130 K-glutamate, 9 KCl, 10 NaCl, 0.5 MgCl2, 5 Mg-ATP, 0.5 EGTA, 10 HEPES, 0.4 GTPTris, set to pH 7.2 with CsOH.
ICa was measured using Na- and K-free external and internal solutions to avoid contamination by overlapping ionic currents, and to allow us to use a physiological holding potential 21. The external solution contained (in mmol/L): 5 4AP, 130 TEACl, 0.5 MgCl2, 10 HEPES, 10 Glucose, 1 CaCl2, pH set to 7.4 using TEAOH. The pipette solution contained (in mmol/L): 110 CsCl, 20 TEACl, 0.5 MgCl2, 5 Mg-ATP, 5 EGTA, 10 HEPES, 0.4 GTPTris, set to pH 7.2 with CsOH. At least 5min was allowed for cell dialysis by the pipette solution before experiments were initiated. Cell membrane capacitance was measured by integrating the capacitance current recorded during a 10-mV hyperpolarizing pulse from −80mV. Cell capacitance and series resistance were compensated (> 80%) so that the maximum voltage error was <3.5mV. ICa was elicited by either a rectangular step (150-ms pulse to 0mV from a holding potential of −80mV) or a representative action potential waveform. The action potential waveforms were the average of the APs recorded in the current clamp experiments in control and detubulated myocytes (n=10 of each cell type, see Figure 1A). Trains of depolarizing pulses were applied at 0.1Hz.
Action potential amplitude was measured as the difference between the overshoot and the resting membrane potential. Membrane potentials were corrected by −11mV to compensate for liquid junction potentials between the external and pipette solutions. APD was measured as the duration from the overshoot to three different percentages of repolarization (25: APD25; 50: APD50; 90: APD90).
ICa was measured as the difference between the peak inward current and the current at the end of the depolarizing pulse. Currents are expressed as current density (pA/pF). Time to peak ICa was measured from the start of the depolarizing pulse. Because the decay of ICa varied between cell types and experimental conditions, the kinetics of inactivation of ICa were characterized by the time required for the current to decay to 0.37 of the peak amplitude (T0.37) 21. ICa was also analyzed by integrating ICa during the test pulse to obtain total Ca influx during the pulse. Ca entry is expressed as charge density (fC/pF) and as cytosolic [Ca] using estimates of surface to volume ratios for control and detubulated cardiac myocytes 25.
All solutions were prepared using ultrapure water supplied by a Milli-Q system (Millipore, Watford, UK). All solution constituents were reagent grade and purchased from Sigma (St. Louis, MO).
Data are presented as mean±SE. Statistical analysis was performed using SigmaStat software. A two-tailed unpaired t-test was used to compare data from control and formamide treated cells, after confirmation of normal distribution and equal variance. Friedman Repeated Measures Analysis of Variance on Ranks and Student-Newman-Keuls Method were used to test the effect of multiple voltage waveforms within the same group of cells. P<0.05 was taken as significant.
Figure 1A shows action potentials elicited by brief current pulses at 0.1Hz in control and detubulated ventricular myocytes. Each trace shows the mean of the APs recorded from 10 control (left) and 10 detubulated (right) myocytes; these mean APs were used as representative action potentials for subsequent voltage clamp studies. The principal effect of detubulation was to shorten the action potential, shown by a significant reduction of APD25, APD50, and APD90 (Table 1). In contrast, resting membrane potential and action potential amplitude were unchanged (−81.2±0.9mV vs. −81.0±1.2mV; NS, and 114±4mV vs. 108±3mV; NS; n=10 myocytes of each type, Table 1). Figure 1B shows the detubulated/control ratios for these variables, showing that the effect of detubulation appears most marked for APD50, the point at which ICa contributes most to the action potential 26. To investigate this further, we recorded ICa using action potential waveforms in voltage clamp experiments on control and detubulated myocytes.
| Table 1 Action potential characteristics of control and detubulated myocytes |
| Controls | Detubulated | |||
|---|---|---|---|---|
| Resting potential (mV) | −81.2±0.9 | −81.0±1.2 | ||
| Amplitude (mV) | 114±4 | 108±3 | ||
| APD25 (ms) | 11.9±2.1 | 6.7±0.9* | ||
| APD50 (ms) | 31.6±5.8 | 13.5±1.7* | ||
| APD90 (ms) | 61.0±9.8 | 30.7±3.4* | ||
| Values are mean±SE from 10 cells in each type; APD, action potential duration. |
| * P<0.05. |
ICa was elicited at 0.1Hz in each cell type using three different voltage command waveforms: a square pulse, the control action potential, and the detubulated action potential (Fig. 2, top panel).
Typical results for control myocytes are shown in the middle panel of Fig. 2. Peak ICa was slightly, but significantly, smaller when the control AP waveform was used, compared to the square pulse and detubulated AP waveform (Figure 3A). However the major effects were on ICa kinetics: time to peak ICa was significantly longer when using AP waveforms, compared to the square pulse, and this was more marked for control than detubulated AP waveforms (13.8±1ms vs. 10.9±0.2ms, n=12, P<0.05, Figure 3B). Part of the longer time to peak can be explained by the longer time to maximum depolarization when using AP waveforms (indicated by the longer capacitance transients, see Fig. 2). The kinetics of inactivation were also markedly different: during the square pulse, the decay of ICa was biphasic because of fast Ca-dependent inactivation and slower voltage dependent inactivation 27. However biphasic inactivation was absent when using AP waveforms. Inactivation (monitored as T0.37, see Methods) was also slightly faster when using control AP waveform compared to square pulse and significantly faster when using detubulated AP waveform (Figure 3C).
The lower panel of Fig. 2 shows typical results for a detubulated myocyte. Detubulation resulted in a significant decrease in cell capacitance (by 28.5%; 186±11pF in 14 control cells vs. 133±8pF in 13 detubulated cells, P<0.05). Peak ICa also decreased, because ICa is concentrated at the T-tubules, consistent with previous work 21: peak ICa density was significantly smaller than control myocytes for all voltage waveforms (Figure 3A). In contrast, the time to peak was not significantly different from control myocytes (Figure 3B). T0.37 was longer than in control myocytes when using a square pulse (Figure 3C), as described previously 21 but surprisingly, T0.37 was similar in control and detubulated myocytes when using the AP waveforms (Figure 3C). These data show that a large proportion of Ca influx occurs across the T-tubule membrane, and that Ca influx depends on the voltage waveform used; these data were used, therefore, to quantify Ca entry across the T-tubule and surface membranes when using different waveforms.
ICa was integrated, and the integral normalized to cell capacitance, to quantify Ca entry. Figure 4A shows that Ca influx was significantly smaller in detubulated cells than in control cells when using a given waveform, but was larger during square pulse stimulation, compared to AP waveforms, in both cell types. Figure 4B shows the ratio of Ca entry/peak ICa density, showing that a given peak ICa produced more Ca influx in detubulated myocytes than in control myocytes during a square pulse, but that this difference was absent when using AP waveforms. The ratio of net entry of positive charge when using the detubulated AP for detubulated myocytes versus control AP for a control myocyte was 0.421 (8.3±1.4 pC vs. 23.5±4.2 pC, n=13 and 12, respectively). This is similar to the ratio of APD50 for detubulated versus control myocytes (0.427, Figure 1B). Thus the reduction in Ca entry after detubulation is compatible with the reduction in APD shown in Fig. 1, and with the idea that the role of the T-tubules in shaping AP configuration is mainly due to the localization of ICa is these invaginations. Conversely, AP waveform can influence ICa, and therefore Ca entry. We examined this by calculating the ratio of Ca entry during different voltage waveforms (Figure 4C). The ratio of Ca entry is reduced when using AP waveforms (either control or detubulated) compared to square pulse, although AP voltage waveform (control versus detubulated) has little effect upon Ca entry in either cell type, as the ratio is ∼1 (Figure 4C, right). This suggests that reduction of APD has little effect upon Ca entry via ICa, therefore the decrease in Ca entry after detubulation is mainly due to a decrease in ICa rather than a decrease in APD.
The main findings of this study are summarized in Table 2. Ca fluxes and ICa in the T-tubules were calculated as the difference in whole-cell Ca entry between control and detubulated myocytes. These Ca fluxes and ICa were divided by the difference in membrane capacitance between control and detubulated cells, to derive the Ca flux and ICa density in the T-tubules. The data from detubulated myocytes have been corrected by 10% to account for the presence of nondetubulated myocytes 25.
| Table 2 Distribution of mean cell capacitance, ICa, and Ca entry in the external sarcolemma and T-tubules |
| Surface area (pF) | ICa SP (pA/pF) | Ca entry SP (fC/pF) | Ca entry AP (fC/pF) | |||
|---|---|---|---|---|---|---|
| Total SL (control cells) | 186 | 10.3 | 215 | 108 | ||
| External SL (detubulated cells)* | 127 | 3.8 | 149 | 55 | ||
| T-tubules (calculated) | 59 | 24.3 | 357 | 222 | ||
| % in T-tubules | 32 | 75 | 53 | 65 | ||
| Density T-tub/ext SL | 6.4 | 2.4 | 4 | |||
| SP, square pulse; AP, action potential; SL, sarcolemma. |
| * These values have corrected by 10% for the presence of nondetubulated myocytes. |
In rat ventricular myocytes, Ca entry is greater when using the square voltage waveform than when using the AP waveform (Table 2). Ca entry at the T-tubules represents 53% and 65% of total during a square pulse and AP waveform, respectively. These values are less than the percentage of ICa at the T-tubules (75%).
These Ca influx measurements were further converted to changes in [Ca]. Integrated fluxes were converted to molar quantity (by dividing by zF) and normalized to cell volume. Surface/volume ratios (5.1 and 3.4 pF/pL in control and detubulated myocytes from our recent study 25) give a volume of 36.4±2.2 pL for control (n=14) and 39.22±2.3 pL for detubulated myocytes (n=13); these values are not significantly different. Fig. 5 shows the results of these calculations with [Ca] in μmol/L cytosol (assuming the fraction of nonmitochondrial cell volume to be 0.65L cytosol/L cell 28). Ca influx at the T-tubules is 1.3 times that at the cell surface (4.9 vs. 3.8μmol/L cytosol, respectively) during a square pulse. In contrast, during an AP, Ca entry at the T-tubules is 2.2 times that at the cell surface (3.0 vs. 1.4μmol/L cytosol, respectively, calculated by the difference between average of control and detubulated AP; Figure 5A–C). The percentage of Ca influx at the T-tubules is also smaller that the percentage of ICa density (Table 2).
We also estimated the junctional Ca flux at the two sites. In rat ventricular myocytes, 7.7% of the surface sarcolemma, and 48% of the T-tubules, is junctional 29. Assuming that 1μF represents 1cm230, we calculated that junctions represent 978μm2 at the cell surface and 2832μm2 in the T-tubules (Table 3). Thus Ca influx per μm2 of junction is 2.2 higher at the cell surface than in the T-tubules (3.89 vs. 1.73 nmol/L cytosol/μm2, respectively) during a square pulse, and 1.3 times higher during an AP (1.43 vs. 1.06 nmol/L cytosol/μm2, respectively; Table 3). To investigate whether the greater Ca entry per μm2 of cell surface, compared to the T-tubules, is due to a difference in the number of Ca channels at each junction, we estimated the total number of Ca channels, using the equation N=ICa/(iCa×p), where N is the number of functional channels, ICa is the whole cell Ca current (data from Table 2 converted to pA), iCa is the unitary current (0.2 pA, see Discussion), and p is the probability of channel opening (0.05, see Discussion). From these values, we estimate that 191,600 functional Ca channels are present in rat myocytes, with 48,200 channels at the cell surface and 143,400 at the T-tubules (Table 4). Expressed as Ca channel density, this gives 10.3, 3.8, and 24.3 Ca channels/μm2 at the total sarcolemma, cell surface, and T-tubules, respectively. These values are in the range observed by others in cardiac preparations (see 31 and 32 for review). We next estimated the number of junctions in the myocyte. Data from electron microscopy have shown that in rat ventricular myocytes a typical junction consists of 267 feet (ryanodine receptors), each separated by 29nm, with a minimum distance between junctions of 414nm 33; this give a minimum mean area of 0.788μm2 for each junction plus its surrounding membrane. This enables us to calculate the (maximum) total number of junctions as 4832, and hence, from junctional surface area at the two sites (Table 3) that 1240 junctions are present at the cell surface and 3592 at the T-tubules (Table 4). Given that 90% of Ca channels are junctional 18, we estimate that a typical junction in rat ventricular myocytes contains ∼35 Ca channels at both the cell surface and T-tubules (Table 4).
| Table 3 Junctional Ca entry at the surface sarcolemma and T-tubules |
| External SL | T-tubules | |||
|---|---|---|---|---|
| Total surface area (pF) | 127 | 59 | ||
| Junctional surface area (μm2)* | 978 | 2832 | ||
| Ca entry SP (μM) | 3.8 | 4.9 | ||
| Ca entry AP (μM) | 1.4 | 3.0 | ||
| Ca entry per μm2 junction (nM) SP | 3.89 | 1.73 | ||
| Ca entry per μm2 junction (nM) AP | 1.43 | 1.06 | ||
| SP, square pulse; AP, action potential; SL, sarcolemma. |
| * These values have been calculated assuming that junctional sarcolemma forms 7.7% of the surface SL and 48% of the t-tubule membrane 29. |
| Table 4 Number of Ca channels per junction at the surface sarcolemma and T-tubules |
| Total SL | External SL | T-tubules | |||
|---|---|---|---|---|---|
| Number of Ca channels* | 191,600 | 48,200 | 143,400 | ||
| Number of junctions† | 4832 | 1240 | 3592 | ||
| Ca channels per junction‡ | 35.7 | 35.0 | 35.9 | ||
| SL, sarcolemma. |
| * These values have been calculated assuming that at 0mV, the unitary current is 0.2 pA and probability of channel opening is 0.05 (see text for details). † These values have been calculated assuming that a typical rat junction is formed by 267 ryanodine receptors and the minimum distance between junctions is 414nm 33. ‡ These values have been calculated assuming that 90% of Ca channels are junctional 18. |
This study provides the first quantitative description of Ca entry at the T-tubules and cell surface of cardiac ventricular myocytes.
The method used to detubulate rat ventricular myocytes has been described and validated previously 19,20. Notably, this procedure has no effect on cell capacitance, ICa or the AP in atrial myocytes, which lack T-tubules 20. This method enables investigation of the physiological function of surface and T-tubule membranes in rat ventricular myocytes. Using this technique, we have shown previously that L-type Ca current, Na/Ca exchange and Na-K pump currents are located predominantly in the T-tubules 21,25. In contrast, K currents are evenly distributed between the surface sarcolemma and T-tubules 34. We have also shown that the T-tubules are essential for spatial and temporal synchronization of Ca release throughout the cell 20,23,35.
We chose to use Na- and K-free experimental solutions to record ICa because this enabled us to use a physiological resting potential (near −80mV for step and AP waveforms) without contamination by other currents, such as Na current, Na/Ca exchanger current, and K currents, allowing us to quantify Ca entry via ICa only. The use of a physiological holding potential is important since depolarized holding potentials (e.g., −40mV) are closer to the activation threshold of ICa and can therefore interfere with Ca channel availability and gating (see 32 for review). However, we might have slightly underestimated Ca entry because of the lack of Na/Ca exchange activity, although Ca entry via this route in cardiac myocytes is small compared to ICa8. Inclusion of a low concentration of a slow Ca buffer (5 mmol/L EGTA) in the pipette solution allows Ca in the bulk cytosol to be “clamped” (indicated by the absence of cell contraction) while permitting Ca in the dyadic space to change 27. Therefore, Ca entry via ICa measured in this study is close to Ca entry during normal excitation-contraction coupling.
The main effect of loss of the T-tubules was to decrease APD. This shortening is unlikely to be due to differences in K currents because they are evenly distributed between surface membrane and T-tubules 34, consistent with the absence of changes in the resting membrane potential (mainly due to IK1 in cardiac myocytes, 31). Reduction of APD is also unlikely to be due to a change in Na current because: i), Na current causes only a small entry of positive charge because it is very brief 36; and ii), AP amplitude, which is mainly due to Na current, is the same in control and detubulated myocytes, compatible with uniform distribution of Na current at the cell surface 23. It is therefore more likely that the decrease in APD is due to less ICa and Na/Ca exchange current, which carry positive charge into the cell and are concentrated at the T-tubules 21,25. Given the results from this study, it is expected that the AP in the T-tubules of cardiac myocytes will be longer than at the cell surface. Calculation from APD50 in detubulated (surface membrane) and control (total membrane) myocytes gives a value of 73.8ms for APD50 in the T-tubules (30% of membrane), ∼5.5 times longer than at the cell surface. This challenging speculation of course requires experimental confirmation, but to date no electrophysiological technique has enabled recording of electrical activity of the T-tubules only. The action potential is shaped by ionic currents; conversely the form of the action potential influences ionic currents. This study shows that a shorter action potential enhances the magnitude and reduces the time to peak and T0.37 of ICa (Fig. 3). This is similar to previous work showing that rapid early repolarization of the AP is crucial in shaping ICa37,38.
Our data show that Ca entry during a square pulse is larger than during an AP waveform (Fig. 4). This is consistent with a previous report in rat ventricular myocytes using a similar approach 39, and highlights the caution required when interpreting results obtained using square pulses to calculate Ca flux. Our calculated Ca entry is similar to previous work using an AP waveform in rat myocytes (∼120 fC/pF 40; ∼4μmol/L cytosol 41). In contrast, Yuan et al. 39 found values that are somewhat higher than observed in this study (∼14μmol/L cytosol), but this may be due to higher external [Ca] and lower Ca-dependent inactivation. It is unlikely that the temperature used to perform our experiments (room temperature) altered the quantification of Ca entry because temperature (25°C vs. 35°C) has been shown to alter ICa kinetics but not total ICa flux in rabbit ventricular myocytes 42.
We found that Ca entry at the T-tubules is larger than at surface sarcolemma, although not to the extent of ICa density (∼75%). This can be explained by reduced Ca-dependent inactivation of the Ca channels present at the cell surface 21, which will prolong ICa. However, this difference in Ca-dependent inactivation of ICa at the T-tubules and cell surface was less marked during the AP waveform (Figure 3C).
Interestingly, Ca entry after detubulation is reduced by ∼60%, a value close to the density of Na/Ca exchanger present in the T-tubules (63%, 25). Since Ca entry via ICa is extruded by the Na+/Ca2+ exchanger during a normal Ca cycle in cardiac myocyte 11, this can explain how SR Ca2+ load remains constant after detubulation 19,23,35. The relative difference between ICa density and Ca entry at the T-tubule and surface membranes (Table 2) also suggests a different role for ICa at the two sites: the large, rapidly inactivating ICa in the T-tubules will form an effective trigger for SR Ca release 9, whereas the more slowly inactivating ICa, and relatively large Ca entry (for the density of ICa) at the cell surface will be effective in loading the SR with Ca2+ that can be released in response to a subsequent stimulus 9,43.
This work suggests that Ca entry per μm2 of junctional membrane is greater at the cell surface than in the T-tubules (Table 3). When normalized to the number of junctions present (Table 4), calculated from available electron microscopy data 33, the data suggest that Ca entry is 1.13 nmol/L cytosol/junction at the cell surface versus 0.85 nmol/L cytosol/junction at the T-tubules during an action potential. However our calculation of the number of junctions may be overestimated because, to the best of our knowledge, there is currently no information about the mean distance between junctions but only the minimum distance between them 33. Similarly, our calculation of the number of Ca channels is speculative, since it depends critically on iCa (the unitary current) and p (the probability of channel opening). Experimental values are quite disparate, ranging from 0.15 to 0.4 pA for iCa and 0.015 to 0.08 for p (at 0mV, e.g., see 44,45,46,47,48 and for review 31); this probably reflects differences in species and experimental conditions between studies. We have therefore used midrange values which are classically used for computer modeling of cardiac excitation-contraction coupling (iCa=0.2 pA and p=0.05, see 49,50. These values give us a total Ca channel number (Table 4) that is within the range observed experimentally by others (from 28,000 48 to 300,000 47). It is also important to note that we used similar parameters for cell surface and T-tubule Ca channels and this might not be the case, although no experimental data from single Ca channel recording at the T-tubules are available. We estimated that ∼35 Ca channels are present at each junction in rat ventricular myocytes (independent of the subcellular location of the junction). This is somewhat higher than described by Bers (10–25 Ca channels, 31), although rat ventricular myocytes tend to have more feet (or ryanodine receptors, 267 33) per junction than other species (e.g., 60 in dog, 128 in mouse; see 33). Thus our values give a ryanodine receptor/Ca channel ratio of ∼7, which is in the range of other species (4–10; see 31). These considerations therefore suggest that a similar number of Ca channels are present at each junction at the cell surface and T-tubules. Thus it appears likely that greater Ca entry/Ca channel at the cell surface, rather than a greater number of Ca channels, accounts for the differential Ca influx at the two sites (Table 3).
This differential Ca entry might also have implications for the gain of SR Ca release; however previous work has suggested that the gain of SR Ca release is similar at the surface and T-tubule membranes 21, so that the different Ca dependent inactivation at the two sites (above) is unlikely to be due to differences in local Ca release. The extensive T-tubule system therefore allows synchronous Ca release within the cell (see above). Ca entry at the cell surface provides Ca2+ for the SR which can then diffuse within the SR to be available for subsequent release at the T-tubules. This requires further investigation, although it has been recently shown that Ca diffuses very quickly within the SR 51,52. Such balance between Ca entry at the cell surface and T-tubules might also be important during development and in pathological conditions in which T-tubule density changes (see 12 for review); it has, for example, been reported to decrease during heart failure 53,54,55.
In conclusion, our study provides the first evidence that the T-tubules are a key site for the regulation of action potential duration in ventricular cardiac myocytes. Our data also provide the first direct measurements of T-tubular Ca influx, which are consistent with the idea that cardiac excitation-contraction coupling largely takes place at the T-tubule dyadic clefts. The quantification of local Ca entry within the T-tubules and at junctional membrane may also have important implications for modeling cardiac cell function and for understanding cellular Ca cycling and suggests that the key role of Ca entry may be different at the T-tubule and surface membranes.
This work was supported by The Wellcome Trust. F.B. is a Wellcome Trust fellow.
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