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CALL FOR PAPERS
Special Section On Mitochondrial Modeling and Function
1Department of Bioengineering, University of California San Diego, La Jolla; 2David Geffen School of Medicine at University of California Los Angeles, California
Submitted 31 March 2006 ; accepted in final form 24 February 2007
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ABSTRACT |
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 TOP ABSTRACT GLOSSARYMETHODSRESULTSAPPENDIX AGRANTSREFERENCES |
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ATP-sensitive K+ channel; creatine and adenylate kinase reactions; phosphatidylinositol phosphates; heart; mathematical model
The epicardial, endocardial, and midmyocardial surfaces also respond differently to pharmacological agents and pathophysiological states (35, 38, 50, 51, 75, 88). The observations suggest that despite the greater susceptibility of endocardium to metabolic effects of ischemia, the electrophysiological changes evoked in epicardium are greater, and that this phenomenon may facilitate reentrant arrhythmias (35, 38, 50, 51, 72, 75). It has been demonstrated experimentally that during ATP depletion, the shortening in action potential duration is significantly greater in epicardial cells than in endocardial (35, 75). Various explanations have been offered from in vivo studies and from multicellular ventricular preparations, including effects of cavity blood (33, 54), Thebesian blood flow (30), greater capacity of the subendocardium for anaerobic metabolism (4, 40), and resistance of Purkinje fibers to the effects of hypoxia and ischemia (38). However, it is impossible to derive an understanding for the inherent regional electrophysiological cell properties from tissue preparations, which have extracellular ionic and electrotonic influences. In this contest, several reports (35, 50, 51, 75) add a further twist to the story by revealing a new role for KATP channels when ATP is depleted and these channels are activated. These reports suggest that a differential sensitivity of KATP channels to ATP among the cell subtypes might be partially responsible for the greater action potential shortening in epicardial myocytes during ischemia. To test the above hypothesis, Furukawa et al. (35) measured the effects of ATP depletion on the KATP channel activity in single cells isolated from epicardial and endocardial surfaces. They demonstrated that the reduction in intracellular ATP evoked currents through KATP channel to a greater magnitude in epicardial myocytes than in endocardial. However, the physiological basis for the site-related differential sensitivity of KATP channels to ATP remains contradictable and unclear.
The contribution of active ion transport and the physiological distinctions between ventricular epicardial, midmyocardial, and endocardial myocytes to the development of the action potential has been established in cell modeling as well (32, 45, 59, 62, 70, 73, 74, 78, 80, 87, 91). In these models the empirical functions and parameters are, in general, fitted from data obtained under normal physiological conditions when ATP is high and KATP channels are closed. However, little attention has been paid to the electrophysiological effects of anoxia (fall in [ATP]tot/[ADP]tot ratio and opening of ATP-sensitive K+ channels), acidosis (intra- and extracellular pH drop), and hyperkalemia (accumulation of extracellular K+) among the cell types, despite their obvious importance in understanding pathologies such as ischemia (10, 17, 21, 39, 63, 65, 67, 81).
In the present study we used the modeling approach to investigate the mechanisms regulating excitation-metabolic coupling in rabbit epicardial, midmyocardial, and endocardial ventricular myocytes under normal conditions and during 20 min of simulated ischemia. Here we extended the LabHEART model (74) by incorporating equations for Ca2+ and Mg2+ buffering by ATP and ADP (65) and equations describing the nucleotide regulation of several ion channels and transporters [KATP channel, L-type Ca2+ channel, Na+-K+-ATPase, sarcolemmal Ca2+-ATPase, SR Ca2+-ATPase] (20, 67). In the model, creatine and adenylate kinase (CK and AK, respectively) reactions, known to communicate the intracellular ATPases flux changes, were also included (16, 17). To simulate pHi regulation in control conditions and during ischemia, we used the approaches of Iotti et al. (43) and Shaw and Rudy (81).
In agreement with experiments of Furukawa et al. (35) and Light et al. (56), our studies revealed that in isolated membrane patches the KATP channels are activated by smallest reduction in ATP in epicardial and largest in endocardial myocytes at normal ligand (ADP, AMP, PCr, Cr), ionic (Na+, K+, Ca2+), Pi, total Mg2+, and pHi diastolic levels. Here, our analysis suggests that regional variations only in Kir6.2 half-saturation constant for ATP (kATP(4–)), but not in SUR2A half-saturation constant (kMgADP(–)), could be one of the reasons for the observed different site-related sensitivity of the channel to ATP. Thus, we concluded that in normal conditions only KATP ionophore (ATP-binding subunit) might differ among the cell types while these cells probably share common regulatory subunit (SUR2A). In agreement with experiment (41) our studies also suggest that during ischemia, the inhomogeneous accumulation of metabolites in the sarcolemma may alter in a very irregular manner the normal channel sensitivity to ATP (i.e., epicardial and endocardial kATP(4–) values) through metabolic interactions with the endogenous lipid phosphoinositide (PI) cascade. This in turn may cause differential action potential shortening among the cell subtypes. Preliminary results of this work have been presented to the Biophysical Society in abstract form (58).
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GLOSSARY |
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TOPABSTRACTGLOSSARYMETHODSRESULTSAPPENDIX AGRANTSREFERENCES |
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Volumes, Areas, and Capacity
Concentrations
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Membrane Currents, SR Fluxes, and Parameters
Dissociation, Rate, and Equilibrium Constants
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METHODS |
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TOPABSTRACTGLOSSARYMETHODSRESULTSAPPENDIX AGRANTSREFERENCES |
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Experimental data also suggest that in cardiac myocytes, ATP (as MgATP2–) and ADP (as MgADP–) drive a number of enzymes, transporters (Na+-K+-ATPase and sarcolemmal and SR Ca2+-ATPases) and channels (ATP-sensitive K+ channels, L-type Ca2+ channels) (14, 15, 43, 47, 71). In this study, to model the transporter nucleotide regulation, we modified the ATP/ADP kinetic equations of Cortassa et al. (20) for Na+-K+ pump current, sarcolemmal Ca2+ pump current, and SR Ca2+-ATPase pump current, assuming INaK, Ip(Ca), and Jup are regulated by MgATP2– and MgADP–:
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Here it is important to emphasize that model agreement with experiment will be strongly dependent on the use of realistic ligand (ATP, ADP, AMP, Pi, PCr, Cr) and extracellular and intracellular ionic (Na+, K+, Mg2+, H+) concentrations under normal conditions and during ischemia (14, 15, 43, 47, 52, 61, 77). However, experimental data for the nucleotide, PCr, Cr, Pi, and ionic concentration changes in rabbits during ischemia are limited (48, 61, 75). Thus, to be able to calculate, if experimental data were not available, the resting nucleotide, metabolite, or Mg2+ levels, we included in the model the basic reactions (ATP hydrolysis, CK and AK catalysis) known to communicate the intracellular ATPase fluxes:
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Recent studies also suggest that the exact knowledge of the apparent equilibrium constant of creatine kinase reaction (K'CK) is essential for accurate in vivo quantification of the total nucleotide, phosphate, and total Mg2+ levels (43). Therefore, in the present study, we used the model of CK reaction from Iotti et al. (43) to estimate K'CK in control conditions when diastolic [K+]i, [Na+]i, [Mg2+]i, and pHi levels are known:
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The coefficient values (a–j) describing K'CK in the pHi and pMg range 5–8 and 2–4, respectively, are shown in Table 2. Our pHi and pMg values are within that range (see Table 3, column 2). The using the accurate model for the creatine kinase reaction in normoxia was essential, because subsequently this allowed evaluating the nucleotide and free Mg2+ concentrations as well the apparent K'CK constant at 20 min of ischemia (see Table 3).
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Finally, we need to add that in this study the effects of acidosis among the cell subtypes were simulated using the approach of Shaw and Rudy (81): 1) the maximum conductance of L-type Ca2+ was reduced by 50%; and 2) the maximum conductance of INa was reduced by 25%, and its voltage-current curve was shifted to the right by 3.4 mV.
Rapid equilibrium for Ca2+ and Mg2+ buffering by ATP and ADP.
Our previous studies have demonstrated that the Eqs. 1–11 are biologically accurate but complicated computationally (65). In this article we sought to minimize the computational complexity by assuming that Ca2+ and Mg2+ buffering by ATP and ADP occur on much faster time scales than other excitation-contraction coupling processes included in the new ionic-metabolic model. Thus the following equations can be written:
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RESULTS |
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TOPABSTRACTGLOSSARYMETHODSRESULTSAPPENDIX AGRANTSREFERENCES |
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140 mM) containing 10, 25, 50, 100, 250, 500, and 1,000 µM free ATP while total intracellular Mg2+, ADP, AMP, PCr, Pi, extra- and intracellular K+, Na+, Ca2+, and pHi remained at normal diastolic levels. The data from Furukawa et al. (35) (see diamonds and triangles in Fig. 3A) suggest that the open probability of KATP channels was reduced in a dose-response fashion among the cell subtypes. Figure 3A also shows that the concentration of ATP that produced half-maximal inhibition of the channel was 23.6 µM in endocardial and 97 µM in epicardial patches. In 1999, Light et al. (56) recorded the ATP concentration-dependent relationship for KATP channel in isolated rabbit ventricle myocytes without regard to the cell location (see circles in Fig. 3B). Note that the data from Light et al. (56) show that the rabbit dose-response curve (IC50 21 µM) is quite similar to the ATP dose-response relation in cat endocardial myocytes (IC50 23.6 µM). Therefore, this was our justification for using cat data to fit the ionic-metabolic model in rabbits among the cell subtypes. Figure 3 shows our attempt to create simulations that quantitatively approximate the reported experimental data in epicardial and endocardial cat and rabbit myocytes. During this experiment, in each point on the simulated curves, the relative KATP current (IK(ATP)/IK(ATP=0)) was computed in steady state at fixed total ATP while total Mg2+ and ADP, [PCr]tot, [Cr]i, [AMP]tot, [Pi], and H+, K+, Na+, and Ca2+ diastolic concentrations were kept normal (see Table 3, column 2).
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50% that in epicardial cells (see Table 4). In addition, the results in Fig. 3A also indicate that the simulated relative currents in response to rhythmically applied pulses (1-Hz, 19–20 s) approached 1 at 0.1 µM intracellular free ATP in the three myocyte subtypes but were close to 0 at 1 mM [ATP4–]i in epicardial, at 650 µM [ATP4–]i in midmyocardial, and at 300 µM [ATP4–]i in endocardial cells.
Modeling normoxia in rabbit endocardial, midmyocardial, and epicardial ventricular myocytes.
Many experimental protocols indicate that in normal conditions the KATP channel activity is inhibited throughout the cell subtypes (see Fig. 1A) (8, 31, 35, 69, 71). To test whether our whole-cell ionic-metabolic model is able to predict that IK(ATP) current is almost inactive in healthy ventricular tissue, we calculated this current during a single beat. Graphs (see Fig. 4A) demonstrate that the channel activity in the three regions was low during the cell excitation. These results also indicate that the predicted epicardial, midmyocardial, and endocardial steady-state KATP current after 20 ms reached peaks of 0.12, 0.027, and 0.004, respectively, and that the current duration was shortest in epicardial and longest in midmyocardial myocytes. In addition, these KATP site-related currents had minimal contribution to the action potential shape when [ATP4–]i was high (390 µM) and [MgADP–]i low (67 µM) (see Fig. 4B). The channel parameter values and resting ligand and ionic concentrations used in this numerical experiment are shown in Tables 1 and 2, 4, and Table 3 (column 2).
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33 times) with [Mg2+]tot constant and the drop in pHi: 1) decreased APD90 in epicardium from 146 to 71 ms, i.e., 2 times (see solid gray and dashed black lines in Fig. 5Ba) and in endocardium from 195 to 107 ms, i.e., 1.82 times (see dotted gray and dash-dotted black lines in Fig. 5Ba); 2) did not affect the normal resting potentials; and 3) increased the steady-state outward K+ current in subepicardial cell more sensitively than in subendocardial cell (see Fig. 5B, b and c). However, it is important to stress that according to the data of Qi et al. (75), the endocardial APD90 decreased 1.32 times while the epicardial APD90 drop was much more pronounced, i.e., 2.6 times. Thus, questions arising here were the following: 1) What might be the physiological reason(s) for the observed different subendocardial and subepicardial APD90 shortening? and 2) Does our ionic-metabolic model help to explain (at least partially) this phenomenon that has puzzled people for years?
To further explore the ionic basis for the differential electrophysiological responses to ischemia at the two sites, Qi et al. (75) used specific IK(ATP) channel blockers. They demonstrated that, although the changes in steady-state outward K+ current were the sum of the changes of many K+ currents (Ito, IKp, IKr, IKs, IK1, INaK, IK(ATP)), the observed increases in the total outward K+ current among the cell types were mainly due to KATP channel opening (see Fig. 5A, b and c). However, why ischemia evoked a greater increase in the epicardial outward K+ current and a greater decrease in the epicardial APD90 remained unclear. Here, we hypothesized that ischemia may alter the normal ATP sensitivity of KATP channels among the cell subtypes in a very irregular manner, contributing to the differential response of those myocytes. To test this hypothesis we performed another set of calculations searching for new epicardial and endocardial kATP(4–), kMgADP(–), go, and gd parameter values. Surprisingly, our model predicted that in epicardial myocytes, by varying only the Kir6.2 half-maximal saturation constant (i.e., increasing kATP(4–) from 0.6 mM up to infinity), we were able to shorten the APD90 more significantly (2.43 times) (see solid black line in Fig. 5Ba). Furthermore, we searched for values of epi kATP(4–) that are reasonably close to 600 µM and that yield action potential shortening sufficiently close to the theoretical maximum. Thus, the model predicts that APD90 with kATP(4–) 8 mM is quite similar to that with kATP(4–) 
. The results also revealed that the increase in steady-state outward K+ current in subepicardial cells was significantly greater with kATP(4–) at 8 mM than predicted with kATP(4–) at 600 µM (see solid black and dashed black lines in Fig. 5Bb). Furthermore, our studies in the endocardium revealed that the normal APD90 dropped from 195 to 127 ms (1.54 times) when kATP(4–) decreased from 131 µM to zero. The simulations also showed that APD90 remained at 127 ms with kATP(4–) at 20 µM and that there was little change in APD90 with lower values of kATP(4–) (see Fig. 5Ba, dotted black line). While predicted endocardial outward K+ current was lower when calculated with the lower kATP(4–), the predicted increase in this current at 20 min ischemia was insignificant at both kATP(4–) values (131 µM or 20 µM) (see Fig. 5Bc, dotted black and dash-dotted black lines). In addition, our analysis suggests that changes in kMgADP(–), go, and gd alone (kMgADP(–) = 0.001–10, go = 0–1, gd = 0–1) do not seem to account for the experimental findings in either region (data not shown).
The predicted ionic currents and Ca2+ time courses in the myoplasm and sarcoplasmic reticulum in each of the cell subtypes during normal and ischemic action potentials (see solid and dotted lines in Fig. 5Ba) are shown in Fig. 6.
The simulations revealed that in control conditions (see gray graphs in Fig. 6, A and F–I), due to the higher K+ conductance in epicardium, the Ito, IKp, IKr, and IKs currents were enhanced, whereas the converse was true for INa current (epicardial GNa < endocardial GNa). Model results also demonstrate that under normal conditions, the differing outward K+ current densities among the tissue sublayers (see gray graphs in Fig. 5B, b and c) had a differential effect on the epicardial and endocardial ICa, INaCa, INaK, IK1, Ip(Ca), ICa,b, INa,b, [Ca2+]i, and [Ca2+]SR time courses (see gray graphs in Fig. 6, B–D and J–O). Finally, Fig. 6E shows that in normoxia the KATP channel activity was low in both regions.
At 20 min simulated ischemia, the epicardial and endocardial INa values were reduced due to the effects of acidosis (see Fig. 6A). The combined effects of acidosis and anoxia had a significant influence on ICa peak and duration throughout the cell subtypes (see Fig. 6B). Anoxia also resulted in activation of IK(ATP) current that was much more pronounced in epicardial myocytes (Fig. 6E). Our analysis also suggests that changes in [MgATP2–]i and [MgADP–]i most significantly affected the SR Ca2+-ATPase pump activities that in turn depleted the SR Ca2+ content and decreased the myoplasmic Ca2+ peaks in both cell subtypes (see Fig. 6, N and O). In addition, the ischemic changes in global [Ca2+]i concentration affected the efficiency of the Na+/Ca2+ exchanger (see Fig. 6C). Figure 6D shows that in both regions, the anoxic changes in MgATP2– and MgADP– significantly shortened INaK duration, increased the rest current, and decreased INaK peak while not significantly affecting Ip(Ca) time course (see Fig. 6K). The results in Fig. 6 also indicate that the changes in the ligand, [Na+]o, [Mg2+]i, pHi, and [Pi] levels and the drop in K'CK value (1.8 times) at 20 min of simulated ischemia had marked effects on Ito, IKp, IKr, IKs, IK1, ICa,b, and INa,b time courses throughout the cell subtypes. The model predictions for reduced SR content, decreased systolic Ca2+ peak, and activated IK(ATP) current during ischemia are in qualitative agreement with experiment (15, 44, 46).
DISCUSSION
Regional ionic-metabolic models in rabbit ventricular myocytes. In 2001, we extended the model of Winslow et al. (87) in dog ventricular myocytes to investigate how Ca2+ and Mg2+ buffering and transport by ATP and ADP regulate cardiac excitation-contraction coupling (65, 87) and how the fall in [ATP]tot/[ADP]tot ratio may affect the intracellular Ca2+, Mg2+, Na+, and K+ concentrations, the free and bound ATP and ADP diastolic and systolic levels, and the ionic currents in the myoplasm, submembrane space, and sarcoplasmic reticulum. The important limitation of this model was that the KATP current, known to be inactive in healthy ventricular tissue and increasingly outward with decreasing levels of ATP, was not included. For this reason recently, using a model approach aimed at simulating the underlying molecular nature of the KATP channel rather than taking a phenomenological approach, we formulated a new model for IK(ATP) regulation by intracellular free ATP and MgADP and incorporated this model into our whole-cell dog ionic-metabolic model (67). The updated model was able to reproduce quantitatively or qualitatively a sequence of events that corresponds well with published experimental data under normal conditions and during ischemia (2, 55, 69). However, we need to acknowledge that both models (65, 67) have limitations: 1) over a longer time period (t > 15 s) these models failed to achieve steady state; 2) the effects of acidosis on the ionic currents and concentrations were not included; 3) some unrealistic ligand ([ATP]tot, [ADP]tot) and extra- and intracellular ionic concentrations (Na+, K+, Mg2+, Ca2+) under normal conditions and for the duration of ischemia were used. To overcome the above limitations, in this article we extended the LabHEART model in rabbits (74), which is reasonably stable over a long time period, by incorporating equations for Ca2+ and Mg2+ buffering by ATP and ADP, and for the nucleotide regulation of KATP and L-type Ca2+ channels. Here, to further investigate and better understand how the changes in ATP and ADP during ischemia regulate the complex cellular dynamics, we updated the flux equations from Michailova et al. (65) for SERCA2a, Ip(Ca), and INaK ATPases. For this purpose, we modified the Cortassa et al. (20) ATP/ADP kinetic equations for these cytosolic ATP-consuming transporters, assuming dependence on MgATP2– and MgADP–. In addition, because we could not find experimental data for [CaATP2–]i, [ADP3–]i, [MgADP–]i, [CaADP–]i, [AMP]tot, [Cr]i, [phosphate], or total Mg2+ levels in normoxia, we included in the model expressions for total adenine, creatine, and phosphate, and CK and AK equilibrium reactions (16, 17), which allowed us to calculate these model parameters. To maximize the advantages of biophysically based modeling while minimizing computational complexity, we assumed also that Ca2+ and Mg2+ are buffered by ATP and ADP on much faster time scales than other excitation-contraction coupling processes. Finally, we used the approaches of Shaw and Rudy (81) and Iotti et al. (43) to simulate the pHi regulation in normoxia and during ischemia. To further test the assumptions that Michailova et al. (67) made about the kinetic mechanisms of nucleotide actions on the KATP channel subunits, we investigated the mechanisms regulating excitation-metabolic coupling in cardiac cells of epicardial, endocardial, and midmyocardial origin. Every attempt has been made to create simulations that quantitatively or qualitatively approximate published experimental data in normoxia or during 20 min of simulated ischemia in rabbit ventricular myocytes (35, 56, 75).
However, it is important to acknowledge that our new ionic-metabolic model also has limitations. The most important one is that this common-pool model is based on the assumption that the major factors affecting ionic channels and pumps (Ca2+, Na+, H+, ATP, ADP) are spatially uniform while recent studies suggest large Ca2+, Na+, H+, ATP, and ADP nonuniformity within the cell (11, 13, 14, 15, 16, 45, 47, 65, 66, 73, 76, 77, 79, 80, 84, 85, 87). This is probably true for the PIP levels also instead of assuming uniformity. However, we could not find experimental data suggesting PIP nonuniformity in the cell membrane or throughout the tissue regions. In addition, the assumption of CK in equilibrium imposes an unnecessary limitation, masking the real mechanism of metabolic regulation of respiration (77). Therefore, in our whole-cell model 1) the KATP channel is regulated by the cytosolic free ATP4– and MgADP– and not by the local link between the channel and neighboring mitochondria via the adenylate kinase energy transfer (1, 16, 79), and 2) the effects of local ligand and ionic concentration changes on Na+-K+- and Ca2+-ATPases were not studied (25, 68, 77). Other model limitations are: 1) the complex regulation of KATP channel by phosphoinositide, kinases and phosphatases is excessively simplified (89); 2) H+ binding to troponin C was not included (14, 17); 3) the normal diastolic [ATP4–]i, [CaATP2–]i, [MgATP2–]i, [ADP3–]i, [CaADP–]i, or [MgADP–]i are probably overestimated because some Mg2+, Na+, K+, and acidic forms of ATP and ADP have not been taken into account (see Ref. 43):
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Modeling KATP channel heterogeneity in excised membrane patches and normal intact cells. One problem has puzzled investigators for years: Why does the KATP channel gradually inactivate in MgATP-free solution when the integrity of the cell is disrupted by the excited patch method of voltage-clamp? Recently, a solution to the puzzle has been suggested (9, 12, 24, 26, 27, 42, 60, 82). It has been demonstrated that this phenomenon (known as channel run-down) is induced by wash out of phospholipids, including phosphatidylinositol-4,5-bisphosphates (PIP2) or phosphatidylinositol-4-phosphates (PIP) and is accompanied by a marked increase in the ATP sensitivity of the channel (12, 27, 37). Thus, it has been assumed that in vivo, MgATP2– might serve as a substrate maintaining the membrane concentrations of PIPs critical for channel activation. On the basis of these findings, a molecular/physical model describing how the channel activity might be regulated by the PIPs has been proposed (9, 22, 23, 26). This model suggests that the membrane-incorporated PIPs can bind to the positive charges in the cytoplasmic region of the channel's Kir6.2 subunits, stabilizing the open state of the channel and antagonizing the inhibitory effect of ATP. However, important questions still remain to be answered: What is the resting concentration of PIPs in the cell membrane and is it sufficient to account for the difference in the ATP sensitivity of the channel between the normal intact cell and excited patch? Why are KATP channels activated by a smaller reduction in intracellular ATP in epicardial cells than in endocardial cells in the excited patches?
In this paper, we used the model approach to address some of these questions. Our first goal was to estimate as accurately as possible the normal K'CK value, taking into account realistic intracellular ionic concentrations (Na+, K+, Mg2+, H+) reported in rabbit myocytes in control conditions (43, 74, 75). Here, we need to mention that we calculated normal K'CK as follows: 1) assuming pHi 7.1, not 7.4 (as reported in the study of Qi et al., Ref. 75), because the former value was the most widely reported (14, 15, 48); and 2) using a value of 1 mM for free normal Mg2+ because this value is reported in the experiment by Qi et al. (75) and is widely cited (1, 16, 17, 19, 80, 84, 86). Furthermore, we assumed that K'CK at [K+]i of 150 mM (see Ref. 43), which we used in our simulations, is approximately equal to K'CK at [K+]i of 145 mM, the value widely reported in normal rabbit myocytes (14, 15, 74, 80). Our studies revealed that the predicted normoxic [ATP]tot, [ADP]tot, [ATP4–]i, and [MgATP2–]i concentrations are comparable to experimentally measured values when pHi was 7.1, [Mg2+]i was 1 mM, and [K+]i was 150 mM (see Table 3, column 2).
An interesting theoretical result was that the model predictions were in a good agreement with experiment for intact epicardial, endocardial, and midmyocardial cells (15, 35, 77) despite use of kATP(4–), kMgADP–, gd, and go values estimated in isolated patches. The simulations demonstrated that KATP channel activity was inhibited in the endocardial patch at free ATP concentration of 390 µM and that the predicted endocardial KATP current was approximately zero in normal conditions. Although there was some channel activity in the epicardial and midmyocardial membrane patches in normal conditions, the KATP currents in all three populations of myocytes had minimal contributions to the normal action potential configuration when [ATP4–]i was 390 µM. In addition, our model predictions in normoxia were in good qualitative agreement with the experimental data of Qi et al. (75), suggesting shorter action potential duration and greater relative increase of the outward K+ current in the subepicardial myocytes and no differences in the epi and endo resting potentials. However, these model predictions presented a new question: how could we solve or explain the apparent dilemma that both in normal intact cells (where no alterations in normal MgATP2– and membrane PIPs levels occur) and in excited patches (where the gradual loss of PIPs has been suggested in the MgATP2– free solution), our model predictions were in good quantitative agreement with experiment (35, 75)? The answer is that in this study, in agreement with the experiment of Furukawa et al. (35) in excited patches, we estimated the KATP channel parameters (kATP(4–), kMgADP(–), gd, go) in the different cell types assuming [MgATP2–]i 
0 (4.49 mM). In addition, we concluded that our KATP model may still lack important channel structure or function details to account for the channel run-down, including how [MgATP2–]i directly regulates the KATP channel activity.
Another interesting model prediction, which was in good agreement with experimental data of Furukawa et al. (35) and Light et al. (56), was that in isolated membrane patches, KATP channels are activated by a smaller reduction in free ATP in epicardial and larger in endocardial cells at normal resting ligand (ADP, AMP, PCr, Cr), ionic (Na+, K+, Ca2+), Pi, total Mg2+, and pHi levels. Here, we found that variations only in the Kir6.2 half-saturation constant (kATP(4–)) among the isolated membrane cell patches, and not in SUR2A half-saturation constant (kMgADP(–)) or in the relative channels conductance (gd, go), are able to quantitatively fit these measurements (35, 56). Therefore, we concluded that only the KATP ionophore (i.e., Kir6.2 subunit) and not the regulatory subunit (i.e., SUR2A) differs among the cell subtypes. However, this new result yielded a new question: what could be the physiological reason(s) for the predicted regional differences in the KATP channel ionophore? Could it be differences in Kir6.2 subunit structure or some other mechanism regulating the channel function? Note that in the model, we assume that PIP levels are equal and spatially uniform and that there is not the inhomogeneous accumulation of metabolites throughout the regions in normoxia. New experiments should be suggested to test above hypotheses and the correctness of our model predictions. In addition, we need to emphasize that because the data in control conditions from Qi et al. (75) were incomplete, we did not attempt to reproduce these data quantitatively (see Table 5).
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The advantage of this model is its ability to examine and predict how the fall of [ATP]tot/[ADP]tot ratio regulates action potential development, outward K+ current, myoplasmic and SR Ca2+ transients, IK(ATP), and many other ionic currents in the different cell subtypes. To estimate as accurately as possible the initial ligand, [Pi], and [Mg2+]i concentrations at 20 min of ischemia, we searched the literature for such data measured in rabbits, and when such data could not be found, we calculated some values with the model (see Table 3, column 4). Note that Table 3 shows that predicted free Mg2+ concentration (2.24 mM) is comparable with the experimentally reported value (2–6 mM) (15). Here we simulated the effects of 20 min ischemia assuming [K+]i, [Na+]i, [Ca2+]i, [Ca2+]SR, and [Ca2+]o at normal diastolic levels. The main reasons for this were as follows: 1) in the experiment of Qi et al. (75), [Na+]o decreased by 20 mM; however, the changes in diastolic [K+]i, [Na+]i, [Ca2+]i, [Ca2+]SR, and [Ca2+]o levels were not reported; and 2) by assuming normal [K+]i while increasing [Na+]i up to 50 mM (see the fourth table in Iotti et al., Ref. 43), the predicted ischemic epicardial and endocardial action potentials were quite different in shape compared with those shown in the article by Qi et al. (75) (data not shown). To calculate K'CK, and total ADP and AMP ischemic values, we used Eqs. 15–19. In addition, we assumed K
K
because changes in the apparent KAK constant during ischemia are not reported (79).
Our study clearly demonstrates that models, including the individual components that retain details of underlying molecular processes regulating the channel kinetics, are of great importance in better understanding and explaining the electrical and contractile functions of the cell. Thus, our whole-cell model predicts that in endocardial myocytes at 20 min ischemia, the APD90 decreased 1.82 times when kATP(4–) was at the normal level of 131 µM. Note that in the experiment by Qi et al. (75), the reported decrease in the endo APD90 was 1.32 times. In addition, experiment suggests that in epicardial myocytes at 20 min ischemia, the APD90 decreased 2.6 times while the predicted APD90 drop in the epicardium was 2 times when kATP(4–) was at the normal value of 600 µM. For this reason we searched for new epicardial and endocardial kATP(4–), kMgADP(–), gd, and go parameter values. Surprisingly, the model predicted again that by varying only the Kir6.2 half-maximal saturation constant (i.e., increasing epi kATP(4–) from 600 µM to 8 mM and decreasing endocardial kATP(4–) from 131 µM to 20 µM), the degree of APD90 shortening during ischemia could more closely approximate the experiment, with epicardial APD90 shortening by 2.43 times and endocardial APD90 shortening by 1.54 times. The analysis also suggests that the changes in kMgADP(–), gd, and go alone (kMgADP(–) = 0.001–10, go = 0–1, gd = 0–1) did not account for the experimental findings in either myocyte layer at 20 min ischemia (data not shown). In addition, results revealed that the increase in outward epicardial K+ current was now significantly greater than that predicted with kATP(4–) 600 µM while endocardial outward K+ current decreased slightly when kATP(4–) was 20 µM (75). However, these new findings yielded a new question: What could be the physiological reason for the predicted dramatic changes in epicardial and endocardial kATP(4–) values during ischemia? A reasonable explanation has been suggested by Haruna et al. (41). They demonstrated experimentally that during ischemia, L-palmitoylcarnitine (a fatty acid metabolite) accumulates in the sarcolemma, deranging in a very irregular manner the membrane lipid environment, including the endogenous PI cascade (PIP2, PIP). Thus, we hypothesize here that during ischemia the inhomogeneous accumulation of the metabolites in the different tissue sublayers may alter differently the normal epicardial and endocardial ATP sensitivity of the KATP channel (i.e., kATP(4–) values) via the interactions with the membrane lipid environment (or PIPs) that in turn may cause differential transmural action potential shortening. New experiments must be performed to test the correctness of this hypothesis.
However, it is important to stress that 1) in epicardium the experiment suggest 2.6 times APD90 decrease during ischemia while the model predicted 2.43 times decrease at kATP(4–) of 8 mM; 2) in endocardium, APD90 dropped 1.54 times at kATP(4–) of 20 µM while the experiment suggests a decrease of 1.32 times; and 3) the predicted increases in the endocardial outward K+ current were insignificant at both kATP(4–) of 131 or 20 µM. Possible reasons for these differences might be that our KATP model may be incomplete or that during ischemia there are some other factors not yet included in our whole-cell model, such as intracellular acidosis (21), the activation of KATP channels by arachidonic acids (15, 49), or the regional variations in the other ionic currents during ischemia (53, 75), which might additionally affect the outward K+ current and subsequently the regional action potential configuration. Furthermore, because the data from Qi et al. (75) at 20 min of ischemia were also incomplete, in this study we did not attempt to reproduce quantitatively these data (see Table 6).
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Conclusion
In the present study we developed a detailed biochemical model that connects Ca2+ signaling and cell electrophysiology with the main interactions between the phosphorylated species (ATP, ADP, AMP, PCr, Cr, Pi) and the cytosolic Lewis acids (Na+, K+, Mg2+, H+). This comprehensive ionic-metabolic model was able to reproduce qualitatively a sequence of events in the epicardium, midmyocardium, and endocardium that corresponds well with experimental data under normal conditions and during 20 min of simulated ischemia. New and more precise experiments must be performed to test the model predictions. This model provides a good basis for further investigation of how cell electrophysiology and cytosolic metabolism might regulate the ATP consumption by ATPases and contraction, the cell respiration and glycolysis, and the progressive changes during ischemia across the different cell subtypes of the myocardium.
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APPENDIX A |
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TOPABSTRACTGLOSSARYMETHODSRESULTSAPPENDIX AGRANTSREFERENCES |
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 | (32) |
 | (33) |
 | (34) |
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GRANTS |
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TOPABSTRACTGLOSSARYMETHODSRESULTSAPPENDIX AGRANTSREFERENCES |
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
* A. Michailova and W. Lorentz are equal contributors to this paper. 
1 See Glossary for the notations of parameters used throughout the study.
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REFERENCES |
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TOPABSTRACTGLOSSARYMETHODSRESULTSAPPENDIX AGRANTSREFERENCES |
|---|
2. Agus ZA, Kelepouris E, Dukes I, Morad M. Cytosolic magnesium modulates calcium channel activity in mammalian ventricular cells. Am J Physiol Cell Physiol 256: C425–C455, 1989.
3. Akar FG, Yan GX, Antzelevitch C, Rosenbaum DS. Unique topographic distribution of M cells underlies reentrant mechanism of torsade de pointes in the long-QT syndrome. Circulation 105: 1247–1253, 2002.
4. Allison TB, Holsinger JW. Transmural metabolic gradients in normal dogs left ventricle: effect of right atrial pacing. Am J Physiol Heart Circ Physiol 233: H217–H221, 1977.
5. Antzelevitch C, Sicouri S, Litovski HL, Lukas A, Krishman SC, Diego JM, Gintant GA, Liu DW. Heterogeneity within the ventricular wall: Electrophysiology and pharmacology of epicardial, endocardial, and M cells. Circ Res 69: 1427–1449, 1991.
6. Antzelevitch C. Modulation of transmural repolarization. Ann NY Acad Sci 1047: 314–323, 2005.[CrossRef][Web of Science][Medline]
7. Anyukhovsky EP, Sosunov EA, Rosen MR. Regional differences in electrophysiological properties of epicardium, mid-myocardium, and endocardium: in vitro and in vivo correlations. Circulation 94: 1981–1988, 1996.
8. Ashcroft FM, Gribble FM. Correlating structure and function in ATP-sensitive K+ channels. Trends Neurosci 21: 288–294, 1998.[CrossRef][Web of Science][Medline]
9. Ashcroft FM. Ion channels: exciting times for PIP2. Science 282: 1059–1060, 1998.
10. Aslandi OV, Clayton RH, Lambert JL, Holden AV. Dynamic and cellular electrophysiological mechanisms of ECG changes during ischaemia. J Theor Biol 237: 369–381, 2005.[CrossRef][Web of Science][Medline]
11. Balaban RS. Cardiac energy metabolism homeostasis: role of cytosolic calcium. J Mol Cell Cardiol 34: 1259–1271, 2002.[CrossRef][Web of Science][Medline]
12. Baukrowitz T, Schulte U, Oliver D, Herlitze S, Krauter T, Tucker S, Ruppersberg JP, Fakler B. PIP2 and PIP as determinants for ATP inhibition of KATP channels. Science 282: 1141–1144, 1998.
13. Baylor SM, Hollingworth S. Model of sarcomeric Ca2+ movements, including ATP Ca2+ binding and diffusion, during activation of frog skeletal muscle. J Gen Physiol 112: 297–316, 1998.
14. Bers DM. Excitation-contraction Coupling and Cardiac Contractile Force. Dordrecht, Boston, London, Kluwer, 2001.
15. Carmeliet E. Cardiac ionic currents and acute ischemia: from channels to arrhythmias. Physiol Rev 79: 917–1017, 1999.
16. Carasco AJ, Dzeja PP, Alekseev AE, Pucar D, Zingman LV, Abraham MR, Hodgson D, Bienengraeber M, Puceat M, Janssen E, Wieringa B, Terzic A. Adenylate kinase phosphotransfer communicates cellular energetic signals to ATP-sensitive potassium channels. Proc Natl Acad Sci USA 98: 7623–7628, 2001.
17. Ch'en FFT, Vaughan-Jones RD, Clarke K, Noble D. Modelling myocardial ischaemia and reperfusion. Prog Biophys Mol Biol 69: 515–538, 1998.[CrossRef][Web of Science][Medline]
18. Cordeiro JM, Greene L, Heilmann C, Antzelevitch D, Antzelevitch C. Transmural heterogeneity of calcium activity and mechanical function in the canine left ventricle. Am J Physiol Heart Circ Physiol 286: H1471–H1479, 2004.
19. Corkey B, Duszynski J, Rich T, Matschinsky B, Williamson J. Regulation of free and bound magnesium in rat hepatocytes and isolated mitochondria. J Biol Chem 261: 2567–2574, 1986.
20. Cortassa S, Aon MA, O'Rourke B, Jacques R, Tseng HJ, Marban E, Winslow R. A computational model integrating electrophysiology, contraction and mitochondrial bioenergetics in ventricular myocyte. Biophys J 91: 1564–1589, 2006.[CrossRef][Web of Science][Medline]
21. Crampin EJ, Smith NP. A dynamic model of excitation-contraction coupling during acidosis in cardiac ventricular myocytes. Biophys J 90: 3074–3090, 2006.[CrossRef][Web of Science][Medline]
22. Cukras CA, Jeliazkova I, Nichols CG. Structural and functional determinants of conserved lipid interaction domains of inward rectifying Kir6.2 channels. J Gen Physiol 119: 581–591, 2002.
23. Cukras CA, Jeliazkova I, Nichols CG. The role of NH2-terminal positive charges in the activity of inward rectifier KATP channels. J Gen Physiol 120: 437–446, 2002.
24. Deutsch N, Matsuoka S, Weiss JN. Surface charge and properties of cardiac ATP-sensitive K+ channels. J Gen Physiol 104: 773–800, 1994.
25. Dzeja PP, Zeleznikar RJ, Goldberg ND. Adenylate kinase: kinetic behavior in intact cells indicates it is integral to multiple cellular processes. Mol Cell Biochem 184: 169–182, 1998.[CrossRef][Web of Science][Medline]
26. Enkvetchakul D, Jeliazkova I, Nichols CG. Direct modulation of Kir channel gating by membrane phosphatidylinositol 4,5-bisphosphate. J Biol Chem 280:35785–35788, 2005.
27. Fan Z, Makielski JC. Anionic phospholipids activate ATP-sensitive potassium channels. J Biol Chem 9: 5388–5395, 1997.
28. Fedida D, Giles WR. Regional variations in action potentials and transient outward current in myocytes isolated from rabbit left ventricle. J Physiol 442: 191–209, 1991.
29. Findlay I. ATP4– and ATP·Mg inhibit the ATP-sensitive K+ channel of rat ventricular myocytes. Pflugers Arch 412: 37–41, 1988.[Web of Science][Medline]
30. Fixler DE, Wheeler M, Huffines D. Extent of myocardial flow from luminal collateral circulation. J Appl Physiol 37: 282–285, 1974.
31. Flagg TP, Nichols CG. Sarcolemmal KATP channels: what do we really know? J Mol Cell Cardiol 39: 61–70, 2005.[CrossRef][Web of Science][Medline]
32. Flaim SN, Giles WR, McCulloch AD. Contribution of sustained INa and IKv43 to transmural heterogeneity of early repolarization and arrhythmogenesis in canine left ventricular myocytes. Am J Physiol Heart Circ Physiol 291: H2617–H2629, 2006.
33. Friedman PL, Stewart JR, Fenoglio JJ, Wit AL. Survival of sub-endocardial Purkinje fibers after extensive myocardial infraction in dogs: In vitro and in vivo correlations. Circ Res 33: 597–611, 1973.
34. Furukawa T, Myerburg RJ, Furukawa N, Bassett AL, Kimura S. Differences in transient outward current of feline endocardial and epicardial myocytes. Circ Res 67: 1287–1291, 1990.
35. Furukawa T, Kimura S, Furukawa N, Bassett AL, Myerburg RJ. Role of cardiac ATP-regulated potassium channels in differential responses of endocardial and epicardial cells to ischemia. Circ Res 68: 1693–1702, 1991.
36. Furukawa T, Kimura Sh Furukawa N, Bassett AL, Myerburg RJ. Potassium rectifier currents differ in myocytes of endocardial and epicardial origin. Circ Res 70: 91–103, 1992.
37. Furukawa T, Yamane T, Terai T, Katayama Y, Hiraoka M. Functional linkage of the cardiac ATP-sensitive K+ channel to the actin cytoskeleton. Pflugers Arch 431: 504–512, 1996.[Web of Science][Medline]
38. Gilmore RF, Zipes DP. Different electrophysiological responses of canine endocardium and epicardium to combined hyperkalemia, hypoxia, and acidosis. Circ Res 46: 814–825, 1980.
39. Gima K, Rudy Y. Ionic Current basis of electrocardiographic waveforms: A model study. Circ Res 90: 889–896, 2002.
40. Griggs MD. Blood flow and metabolism in different layers of the left ventricle. Physiologist 22: 36–40, 1979.[Medline]
41. Haruna T, Horie M, Takano M, Kono Y, Yoshida H, Otani H, Kubota T, Ninomiya T, Akao M, Sasayama S. Alteration of the membrane lipid environment by L-palmitoylcarnitine modulates KATP channels in guinea-pig ventricular myocytes. Pflugers Arch 441: 200–207, 2000.[CrossRef][Web of Science][Medline]
42. Huang Ch-L, Feng S, Hilgemann DW. Direct activation of inward rectified potassium channels by PIP2 and its stabilization by G
. Nature 391: 803–806, 1998.[CrossRef][Medline]
43. Iotti S, Frassineti C, Sabatini A, Vacca A, Barbiroli B. Quantitative mathematical expressions for accurate in vivo assessment of cytosolic [ADP] and 
G of ATP hydrolysis in the human brain and skeletal muscle. Biochim Biophys Acta 1708: 164–177, 2005.[Medline]
44. Isenberg G, Han S, Schiefer A, Wendt-Gallitelli MF. Changes in mitochondrial calcium concentration during the cardiac contraction cycle. Cardiovasc Res 27: 1800–1809, 1993.
45. Jafri MS, Rice JJ, Winslow RL. Cardiac Ca2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys J 74: 1149–1168, 1998.[Web of Science][Medline]
46. Kaplan P, Hendrikx M, Mattheussen M, Mubagwa K, Flameng W. Effect of ischemia and reperfusion on sarcoplasmic reticulum calcium uptake. Circ Res 71: 1123–1130, 1992.
47. Kagacin ME, Kargacin GJ. Predicted changes in concentrations of free and bound ATP and ADP during intracellular Ca2+ signaling. Am J Physiol Cell Physiol 42: C1416–C1426, 1997.
48. Kawabata HK, Sugiyama K, Katori R. Effect of acetylsalicylic acid on metabolism and contractility in the ischemic reperfused heart. Jpn Circ 60: 961–971, 1996.[CrossRef]
49. Kim D, Clapham DE. Potassium channels in cardiac cells activated by arachidonic acid and phospholipids. Science 224: 1174–1179, 1989.
50. Kimura Sh Basset AL, Kohya T, Kozlovskis PL, Myerburg RJ. Simultaneous recording of action potentials from endocardium and epicardium during ischemia in the isolated cat ventricle: relation of temporal electrophysiological heterogeneities to arrhythmias. Circ 74: 401–409, 1986.
51. Kimura Sh Basset AL, Furukawa T, Cuevas J, Myerburg RJ. Electrophysiological properties and responses to simulated ischemia in cat ventricular myocytes of endocardial and epicardial origin. Circ Res 66: 469–477, 1990.
52. Kushmerick MJ. Multiple equilibria of cations with metabolites in muscle bioenergetics. Am J Physiol Cell Physiol 272: C1739–C1747, 1997.
53. Lai-Hua X, Scott AJ, Ribalet JB, Weiss JN. Activation of inwardly rectifying potassium (Kir) channels by phosphatidylinosita-4,5-bisphophate (PIP2): Interaction with other regulatory ligands. Prog Biophys Mol Biol 2006. (in press).
54. Lazzara R, El-Sherif N, Scherlag BJ. Electrophysiological properties of canine Purkinje tissue. Circ Res 33: 722–734, 1973.
55. Lederer WJ, Nichols CG. Nucleotide modulation of the activity of rat heart ATP-sensitive K+ channels in isolated membrane patches. J Physiol 419: 193–211, 1989.
56. Light PE, Cordeiro JM, French RJ. Identification and properties of ATP-sensitive potassium channels in myocytes from rabbit Purkinje fibers. Cardiovasc Res 44: 356–369, 1999.
57. Liu DW, Gintant GA, Antzelevitch Ch. Ionic bases for electrophysiological distinctions among epicardial, mid-myocardial, and endocardial myocytes from the free wall of the canine left ventricle. Circ Res 72: 671–687, 1993.
58. Lorentz W, Healy S, McCulloch AD, Michailova A. Modeling transmural heterogeneity in rabbit ventricular myocytes during ischemia. Biophys J 2006 (Abstract).
59. Luo CH, Rudy Y. A model of the cardiac ventricular action potential, depolarization, repolarization and their interaction. Circ Res 68: 1501–1526, 1991.
60. MacGregor GG, Dong Ke Vanoys CG, Tang LQ, Giebisch G, Hebert SC. Nucleotides and phospholipids compete for binding to the C terminus of KATP channels. PANS 99: 2726–2731, 2002.[CrossRef]
61. Matherne GP, Headrick JP, Berr S, Berne RM. Metabolic and functional responses of immature and mature rabbit hearts to hypoperfusion, ischemia, and reperfusion. Am J Physiol Heart Circ Physiol 264: H2141–H2153, 1993.
62. Matsuoka S, Sarai N, Kuratomi S, Ono K, Noma A. Role of individual ionic current systems in ventricular cells hypothesized by a model study. Jap J Physiol 53: 105–123, 2003.[CrossRef][Web of Science][Medline]
63. Matsuoka S, Sarai N, Jo H, Noma A. Simulation of ATP metabolism in cardiac excitation-contraction coupling. Prog Biophys Mol Biol 85: 279–299, 2004.[CrossRef][Web of Science][Medline]
64. McIntosh MA, Cobbe SM, Smith GL. Heterogeneous changes in action potential and intracellular Ca2+ in left ventricular myocyte sub-types from rabbits with heart failure. Cardiovasc Res 45: 397–409, 2000.
65. Michailova AP, McCulloch AD. Model study of ATP and ADP buffering, transport of Ca2+ and Mg2+, and regulation of ion pumps in ventricular myocyte. Biophys J 81: 614–629, 2001.[Web of Science][Medline]
66. Michailova A, DelPrincipe F, Egger M, Niggli E. Spatiotemporal features of Ca2+ signaling, buffering and diffusion in atrial myocytes with inhibited sarcoplasmic reticulum. Biophys J 83: 3134- 3151, 2002.[Web of Science][Medline]
67. Michailova A, Saucerman J, Belik ME, McCulloch A. Modeling regulation of cardiac KATP and L-type Ca2+ currents by ATP, ADP and Mg2+. Biophys J 88: 2234–2249, 2005.[CrossRef][Web of Science][Medline]
68. Neely JR, Denton RM, England PJ, Randle PJ. The effects of increased heart work on the tricarboxylate cycle and its interactions with glycolysis in the perfused rat heart. Biochem J 128: 147–159, 1972.[Web of Science][Medline]
69. Nichols CG, Ripoll C, Lederer WJ. ATP-sensitive potassium channel modulation of the guinea pig ventricular action potential and contraction. Circ Res 68: 280–287, 1991.
70. Noble D. Cardiac action and pacemaker potentials based on the Hodgkin-Huxley equations. Nature 188: 495–497, 1960.[Medline]
71. Noma A. ATP-regulated K+ channels in cardiac muscle. Nature 305: 147–148, 1983.[CrossRef][Medline]
72. Okumura K, Horio Y, Matsuyama K, Araki S. Alterations in electrophysiological properties during canine myocardial ischemia: variation with location in the ischemic zone in vivo. Jpn Circ J 47: 661–670, 1983.[Medline]
73. Pandit SV, Clark RB, Giles WR, Demir SS. A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes. Biophys J 81: 3029–3051, 2001.[Web of Science][Medline]
74. Puglisi JL, Bers DM. LabHEART: an interactive computer model of rabbit ventricular myocyte ion channels and Ca transport. Am J Physiol Cell Physiol 281: C2049–C2060, 2001.
75. Qi XY, Shi WB, Wang HH, Zhang ZX, Xu YQ. A study on the electrophysiological heterogeneity of rabbit ventricular myocytes- the effect of ischemia on action potentials and potassium currents. Acta Physiol Sinica 52: 360–364, 2000.[Medline]
76. Saks VA, Kuznetsov A, Andrienko T, Usson Y, Appaix F, Guerrero K, Kaambre T, Sikk P, Lemba M, Vendelin M. Heterogeneity of ADP diffusion and regulation of respiration in cardiac cells. Biophys J 84: 3436–3456, 2003.[Web of Science][Medline]
77. Saks VA, Dzeja P, Schattner U, Vendelin M, Terzic A, Wallimann T. Cardiac system bioenergetics: metabolic basis of the Frank-Starling law. J Physiol 571: 253–273, 2006.
78. Saucerman JJ, Healy SN, Belik ME, Puglisi JL, McCulloch AD. Proarrhythmic consequences of a KCNQ1 AKAP-binding domain mutation: Computational models of whole cells and heterogeneous tissue. Circ Res 95: 1216–1224, 2004.
79. Selivanov VA, Alekseev AE, Hodgson DM, Dzeja P, Terzic A. Nucleotide-gated KATP channels integrated with creatine and adenylate kinases: amplification, tuning and sensing of energetic signals in the compartmentalized cellular environment.Mol Cell Biochem 256–257: 243–256, 2004.[CrossRef]
80. Shannon T, Wang F, Puglisi J, Weber Ch, Bers DB. A mathematical treatment of integrated Ca dynamic within the ventricular myocyte. Biophys J 87: 3351–3371, 2004.[CrossRef][Web of Science][Medline]
81. Shaw RM, Rudy Y. Electrophysiologic effects of acute myocardial ischaemia: a theoretical study of altered cell excitability and action potential duration. Cardiovasc Res 35: 256–272, 1997.
82. Shyng SL, Nichols CG. Membrane phospholipid control of nucleotide sensitivity of KATP channels. Science 282: 1138–1141, 1998.
83. Sicouri S, Antzelevitch C. A subpopulation of cells with unique electrophysiological properties in the deep subepicardium of the canine ventricle: the M cell. Circ Res 68: 1729–1741, 1991.
84. Vaughan-Jones RD, Peercy BE, Keener JP, Spitzer KW. Intrinsic H+ ion mobility in the rabbit ventricular myocyte. J Physiol541. 1: 139–158, 2002.
85. Vendelin M, Emire M, Seppet E, Peet N, Andrienko T, Lemba M, Engelbrecht J, Seppet EK, Saks V. Intracellular diffusion of adenosine phosphates is locally restricted in cardiac muscle. Mol Cell Biochem 256–257: 229–241, 2004.
86. Wang M, Tashiro M, Berlin J. Regulation of L-type calcium current by intracellular magnesium in rat cardiac myocytes. J Physiol 555: 383–396, 2003.[CrossRef][Web of Science][Medline]
87. Winslow RL, Rice J, Jafri J, Marban E, O'Rourke B. Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure. II. Model studies. Circ Res 84: 571–586, 1999.
88. Wolk R, Kane KA, Cobbe SM, Hicks MN. Regional electrophysiological effects of hypokalaemia, hypomagnesaemia and hyponatraemia in isolated rabbit hearts in normal and ischemic conditions. Cardiovasc Res 40: 492–501, 1998.
89. Xie LH, Takano M, Kakei M, Okumura Midori, Noma A. Wortmannin, an inhibitor of phosphatidylinositol kinases, blocks the MgATP-dependent recovery of Kir6.2/SUR2A channels. J Physiol 514: 655–665, 1999.
90. Yamashita T, Nakajima T, Hazama H, Hamada E, Murakawa Y, Sawada K, Omata M. Regional differences in transient outward current density and inhomogeneities of repolarization in rabbit right atrium. Circ 92: 3061–3069, 1995.
91. Zhang H, Holden AV, Kodama I, Honjo H, Lei M, Varghese T, Boyett MR. Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node. Am J Physiol Heart Circ Physiol 279: H397–H421, 2000.
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