| A Biophysically Based Mathematical Model of Unitary Potential Activity in Interstitial Cells of Cajal Biophysical Journal, Volume 95, Issue 1, 1 July 2008, Pages 88-104 R.A. Faville, A.J. Pullan, K.M Sanders and N.P. Smith Abstract Unitary potential (UP) depolarizations are the basic intracellular events responsible for pacemaker activity in interstitial cells of Cajal (ICCs), and are generated at intracellular sites termed “pacemaker units”. In this study, we present a mathematical model of the transmembrane ion flows and intracellular Ca dynamics from a single ICC pacemaker unit acting at near-resting membrane potential. This model quantitatively formalizes the framework of a novel ICC pacemaking mechanism that has recently been proposed. Model simulations produce spontaneously rhythmic UP depolarizations with an amplitude of ∼3mV at a frequency of 0.05Hz. The model predicts that the main inward currents, carried by a Ca-inhibited nonselective cation conductance, are activated by depletion of sub-plasma-membrane [Ca] caused by sarcoendoplasmic reticulum calcium ATPase Ca sequestration. Furthermore, pacemaker activity predicted by our model persists under simulated voltage clamp and is independent of [IP] oscillations. The model presented here provides a basis to quantitatively analyze UP depolarizations and the biophysical mechanisms underlying their production. Abstract | Full Text | PDF (631 kb) |
| Stoichiometry of the Cardiac Na/Ca Exchanger NCX1.1 Measured in Transfected HEK Cells Biophysical Journal, Volume 82, Issue 4, 1 April 2002, Pages 1943-1952 Hui Dong, Jeremy Dunn and Jonathan Lytton Abstract The stoichiometry with which the Na/Ca exchanger, NCX1, binds and transports Na and Ca has dramatic consequences for ionic homeostasis and cellular function of heart mycocytes and brain neurons, where the exchanger is highly expressed. Previous studies have examined this question using native NCX1 in its endogenous environment. We describe here whole-cell voltage clamp studies using recombinant rat heart NCX1.1 expressed heterologously in HEK-293 cells. This system provides the advantages of a high level of NCX1 protein expression, very low background ion transport levels, and excellent control over clamped voltage and ionic composition. Using ionic conditions that allowed bi-directional currents, voltage ramps were employed to determine the reversal potential for NCX1.1-mediated currents. Analysis of the relation between reversal potential and external [Na] or [Ca], under a variety of intracellular conditions, yielded coupling ratios for Na of 1.9–2.3 ions per net charge and for Ca of 0.45±0.03 ions per net charge. These data are consistent with a stoichiometry for the NCX1.1 protein of 4 Na to 1 Ca to 2 charges moved per transport cycle. Abstract | Full Text | PDF (254 kb) |
| A Mathematical Treatment of Integrated Ca Dynamics within the Ventricular Myocyte Biophysical Journal, Volume 87, Issue 5, 1 November 2004, Pages 3351-3371 Thomas R. Shannon, Fei Wang, José Puglisi, Christopher Weber and Donald M. Bers Abstract We have developed a detailed mathematical model for Ca handling and ionic currents in the rabbit ventricular myocyte. The objective was to develop a model that: 1), accurately reflects Ca-dependent Ca release; 2), uses realistic parameters, particularly those that concern Ca transport from the cytosol; 3), comes to steady state; 4), simulates basic excitation-contraction coupling phenomena; and 5), runs on a normal desktop computer. The model includes the following novel features: 1), the addition of a subsarcolemmal compartment to the other two commonly formulated cytosolic compartments (junctional and bulk) because ion channels in the membrane sense ion concentrations that differ from bulk; 2), the use of realistic cytosolic Ca buffering parameters; 3), a reversible sarcoplasmic reticulum (SR) Ca pump; 4), a scheme for Na-Ca exchange transport that is [Na] dependent and allosterically regulated by [Ca]; and 5), a practical model of SR Ca release including both inactivation/adaptation and SR Ca load dependence. The data describe normal electrical activity and Ca handling characteristics of the cardiac myocyte and the SR Ca load dependence of these processes. The model includes a realistic balance of Ca removal mechanisms (e.g., SR Ca pump versus Na-Ca exchange), and the phenomena of rest decay and frequency-dependent inotropy. A particular emphasis is placed upon reproducing the nonlinear dependence of gain and fractional SR Ca release upon SR Ca load. We conclude that this model is more robust than many previously existing models and reproduces many experimental results using parameters based largely on experimental measurements in myocytes. Abstract | Full Text | PDF (578 kb) |
Copyright © 2008 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 94, Issue 7, L54-L56, 1 April 2008
doi:10.1529/biophysj.107.127878
Biophysical Letters
Eric A. Sobie*, Mark B. Cannell† and John H.B. Bridge‡,
, 
* Department of Pharmacology & Systems Therapeutics, Mount Sinai School of Medicine, New York, New York
† Department of Physiology, University of Auckland, Auckland, New Zealand
‡ Nora Eccles Harrison Cardiovascular Research and Training Institute, University of Utah, Salt Lake City, Utah
Address reprint requests and inquiries to John H. B. Bridge, Tel.: 801-581-8183.Contraction in cardiac muscle cells results from an increase in intracellular Ca2+ concentration ([Ca2+]i) from a diastolic level of roughly 100nM to a peak of ∼1μM. The source of most of this Ca2+ is release from the sarcoplasmic reticulum (SR), which occurs as a collection of microscopic release events known as Ca2+ sparks 1. Ca2+ sparks have been shown to be triggered primarily by Ca2+ ions crossing the cell membrane through L-type Ca2+ channels 2.
As the heart cell relaxes, the electrogenic Na+-Ca2+ exchanger (NCX) removes Ca2+ from the cell. This protein imports three Na+ ions for every Ca2+ ion that exits 3. Depending on cellular transmembrane potential (Vm) and the relative concentrations of Na+ and Ca2+ inside and outside the cell, NCX can also work in “reverse mode,” in which Ca2+ is imported and Na+ is extruded. The issue of whether Ca2+ entry via this pathway can contribute to the trigger for Ca2+ release has remained controversial because of apparently contradictory data from different groups. On the one hand, blockade Ca2+ entry due to other pathways has led to the conclusion that Ca2+ entry via NCX is ineffective at triggering release 4,5,6. On the other hand, some investigators have demonstrated dramatically increased Ca2+ release at positive potentials when internal Na+ is present compared with when it is absent 7,8,9. Because NCX is presumably working in reverse mode under these conditions, this extra release has been ascribed to the actions of the exchanger.
One possible confounding factor in these experiments is the SR Ca2+ load, which strongly influences the quantity of Ca2+ released 10. Because changes in intracellular [Na+] affect the balance of Ca2+ across the cell membrane, measurements of SR Ca2+ release with and without reverse-mode NCX might be performed at different SR Ca2+ loads. To avoid this potential complication, we measured the Vm dependence of Ca2+ flux crossing the cell membrane with SR release disabled. Our results, which indicate that reverse mode NCX can augment the transmembrane Ca2+ flux substantially, suggest a resolution to the apparently contradictory results obtained in previous studies.
Experiments were performed on isolated rabbit ventricular myocytes incubated with ryanodine and thapsigargin (1 μM each) to prevent SR Ca2+ release. Cells were voltage-clamped in whole-cell mode and loaded with fluo-3. The pipette solution contained 120mM Cs+ to block most outward K+ currents and either 10mM or 0mM Na+. Cells were held at −80mV, a slow ramp (500ms) to −50mV was applied to inactivate Na+ current, and then cells were depolarized to a range of test potentials. Confocal line scan recordings of fluorescence (F) were made concurrently. This protocol therefore allowed simultaneous measurement of L-type Ca2+ current (ICa) and the total transmembrane flux of Ca2+, assessed by increases in fluorescence (ΔF/F0).
Examples of patch-clamp and line-scan recordings are shown in Fig. 1. A depolarization to 0mV (top left) induced both a large inward ICa and a sizable ΔF/F0. A depolarization to +50mV (top right) caused a much smaller current, but still a substantial ΔF/F0. This probably occurred because Ca2+ was also entering via reverse mode NCX at this potential.
We used two methods to assess the relative contributions of these pathways. First, we added nifedipine (40μM) to block L-type Ca2+ current. ΔF/F0 was essentially zero at 0mV (bottom left), a potential below the NCX reversal potential under these conditions (+27mV). At +50mV, an increase in F was observed (bottom right); however, this was much less than that seen with both inward NCX and ICa present. We also integrated the ICa recorded at 0mV and scaled the result to approximate the ΔF/F0 time course at that Vm. When ICa at +50mV was integrated, and the same scaling factor was applied, the estimated ΔF/F0 due to ICa was only 51% of the total increase observed (top right; red trace). Thus, the Ca2+ trigger flux at +50mV under control conditions is much greater than a simple sum of fluxes due to ICa and reverse-mode NCX measured in the absence of ICa.
Fig. 2 shows summary data from experiments such as that shown in Fig. 1. Peak ICa and trigger flux, approximated as the maximal rate of rise of F (dF/dtmax; see Supplementary Material, Fig. S1 ), before and after adding nifedipine, are plotted together on a normalized scale for comparison. Peak ICa and dF/dtmax match one another below +20mV, but the latter is greater at more positive Vm, consistent with Ca2+ entry via reverse mode NCX at these potentials. We considered whether imperfect selectivity of the L-type Ca2+ channel, by underestimating Ca2+ entry via ICa at potentials such as +50mV, could cause the divergence between the two curves. Even after correcting for this, however, the trigger flux at +50mV assessed by dF/dtmax is still ∼2.5 times the calculated Ca2+ influx through ICa (see Supplementary Material Fig. S2 ).
To verify that NCX contributed to the surprisingly large trigger flux observed at positive Vm, we performed additional experiments with 0mM Na+ in the patch pipette. Fig. 3 compares dF/dtmax measured with 0mM [Na+] (black squares) and 10mM [Na+] (red circles). Plots are normalized for comparison. At Vm >+20mV, dF/dtmax is relatively much larger with [Na+] in the pipette, confirming that reverse-mode NCX augments the trigger flux at these voltages. It is striking that the flux of Ca2+ at +50mV in the presence of internal [Na+] is more than twice that measured in its absence.
Overall, these results suggest that the Ca2+ “trigger flux” at positive Vm is much greater than that estimated from a simple summation of the fluxes through ICa and reverse mode NCX measured in the absence of ICa. The most likely explanation for this finding is that Ca2+ entering through L-type channels activates the catalytic Ca2+-binding site on NCX 11,12, thereby causing an increase of Ca2+ influx on the exchanger. Indeed, early studies on the function of cardiac NCX suggested that this could be the case 13. Reverse-mode NCX after L-type channel block is less than in control conditions because this catalysis does not occur, and, consistent with this idea, large differences in Ca2+ fluxes tend to shrink at very positive Vm (e.g., +80mV), probably because smaller ICa leads to a reduction in NCX catalysis. This hypothesis therefore provides an explanation for the contradictory results mentioned earlier. More important, the data presented suggest that NCX may contribute substantially to Ca2+ entry at Vm corresponding to the early action potential plateau.
These results are similar to observations recently made by Viatchenko-Karpinski et al. in rat myocytes 14. These authors, however, only observed nonlinear summation of ICa and reverse mode NCX after β-adrenergic stimulation. The fact that we observe such an augmentation of the trigger flux under control conditions is consistent with the greater NCX currents recorded in larger mammals and suggests that NCX may have a larger role in triggering Ca2+ release in such species. This species difference also suggests that experiments such as those performed here may provide insight into spatial relationships between L-type Ca2+ channels and Na+-Ca2+ exchangers under a range of conditions.
Supported by the National Institutes of Health grants No. HL076230 and No. HL62690.
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