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Effects of Mg2+, pH and PCr on cardiac excitation-metabolic coupling

Magnesium Research. Volume 21, Numéro 1, 16-28, march 2008, original article

DOI : 10.1684/mrh.2008.0126

Summary

Auteur(s) : Anushka Michailova, Andrew D McCulloch , Department of Bioengineering, PFBH 241, University of California San Diego, USA.

Illustrations

ARTICLE

Auteur(s) : Anushka Michailova, Andrew D McCulloch

Department of Bioengineering, PFBH 241, University of California San Diego, USA

In cardiac myocytes the intracellular ionic and metabolic concentrations within physiological limits are highly regulated and magnesium (Mg²⁺), hydrogen (H⁺) and phosphocreatine (PCr) are no exceptions. Magnesium is known to stabilize the macromolecule structure and to participate as an essential cofactor in many enzymatic reactions [1-4]. Cytosolic Mg²⁺ is strongly buffered and free Mg²⁺ ([Mg²⁺]_i) appears to be between 0.2-1.8 mM [5-8]. Small changes in [Mg²⁺]_i may significantly affect the activity of ion channels and transporters and consequently cell excitability, contractility and bioenergetics [7-10]. Magnesium transporters in the plasma membrane have not yet been purified or cloned. In summary, experimental studies suggest that Mg²⁺ enters the cell along the concentration gradient via selective Mg²⁺ channels [11, 12] and is extruded out of the cell via the Na⁺/Mg²⁺ exchanger [2-4, 13, 14].

Intracellular H⁺ (pH_i) is also an important modulator of the electrical and contractile properties of cardiac cells [15, 16]. Changes in pH_i may have significant kinetic and thermodynamic effects on biochemical reactions [17-21]. Intracellular H⁺ is strongly buffered and four H⁺ sarcolemmal transporters are known: sodium-bicarbonate co-transporter (NBC) and sodium-hydrogen exchange (NHE) are acid extruders increasing pH_i, while chloride-hydroxide exchange (CHE) and bicarbonate-chloride exchange (anion exchanger, AE) are acid loaders [15].

The rate of mitochondrial oxidative phosphorylation in muscle cells depends on both the oxygen and substrate supplies, and on the mechanisms regulating the energy consuming systems, such as, contractile machinery and ion pumps, and channels involved in excitation-contraction coupling [22-24]. Under conditions of sufficient oxygen and substrate supply, the later mechanisms become the most important in determining the rate at which mitochondria will respire to match the energy supply with its demand. The creatine/phosphocreatine system is an important component in this intracellular energy transfer and metabolic signaling network [25]. Experimental data suggest that PCr provides a buffer, or capacitance, for the chemical potential of ATP during contraction that minimizes changes in total ATP concentration ([ATP]_tot) and especially in total ADP ([ADP]_tot) during a period of increased ATPase activity [26-28]. Thus under physiological conditions, significant changes in the level of ATP dose do not occur but the levels of total phosphocreatine ([PCr]_tot) (in mM range) and in [ADP]_tot (in μM range) do vary [26]. Intracellular PCr is also strongly buffered [18]. However, it is important to acknowledge that little is yet known about how the changes in intracellular Mg²⁺, pH_i or [PCr]_tot alone or simultaneous changes in [Mg²⁺]_i, pH_i and [PCr]_tot regulate cell excitability, contractility and bioenergetics in normoxia or pathology.

In this study we used a modeling approach to investigate further these complex interactions. In agreement with experiments our studies revealed that: (1) the fall in free cytosolic Mg²⁺ prolongs the action potential duration; (2) during the normal cardiac cycle a pH_i decrease accompanied by a free Mg²⁺ increase tends to counteract an [ADP]_tot increase due to [PCr]_tot depletion.

Materials and methods

Excitation-metabolic model in rabbit ventricular myocytes

In 2007 we developed a detailed biophysical model [29] that connected Ca²⁺ signaling and cell electrophysiology with the main interactions between phosphorylated species (ATP, ADP, AMP, PCr, Cr, P_i) and cytosolic Lewis acids (Na⁺, K⁺, Mg²⁺, H⁺) (figure 1). In that article, we extended the LabHEART ionic model in rabbits [30] to incorporate equations for Ca²⁺ and Mg²⁺ buffering by ATP and ADP [31] and equations describing the nucleotide regulation of several ion channels and transporters (K_ATP channel, L-type Ca²⁺ channel, Na⁺/K⁺ ATPase, sarcolemmal Ca²⁺-ATPase, SR Ca²⁺ -ATPase) [32, 33]. The creatine and adenylate kinase reactions, known to communicate the intracellular ATPases flux changes, were also included (figure 1) [24, 34].

In the present study, to examine these complex mechanisms and interactions further, we extended the Michailova et al. model [29] to include the Iotti et al. [18] mathematical expressions for ΔG⁰ and ΔG of MgATP^2- hydrolysis and apparent equilibrium constant of the CK reaction (eqs. 1–4, table 1).where: a₁–a₉, b₁–b₁₂ and c₁–c₁₀ are coefficients, x is pHi, y is pMg_i = –log[Mg²⁺]_i, z is [PCr]_tot.

Unless otherwise specified in the figure legends or in the text, the standard set of parameters used in the calculations is listed in the tables 1 and 2. All initial conditions and values of the parameters that are not included in the present paper correspond to those used in Michailova et al. [29].
Table 1 The Iotti et al. [18] Gibbs free energy and K_CK coefficients values at [Na⁺]_i 10 mM, [K⁺]_i 150 mM, pH_i 5-8, [Mg²⁺]_i 0.1-10 mM.

		K_CK
a₁ = - 74.071	b₁ = - 80.605	c₁ = - 0.621
a₂ = 21.3814	b₂ = 7.423	c₂ = 3.2245
a₃ = - 13.723	b₃ = - 7.652	c₃ = - 0.9316
a₄ = - 2.4018	b₄ = - 1.0014	c₄ = - 0.5517
a₅ = 2.1238	b₅ = 0.86547	c₅ = 0.1347
a₆ = 1.3501	b₆ = 0.038867	c₆ = - 0.0341
a₇ = 0.24662	b₇ = 1.417	c₇ = 0.0175
a₈ = - 0.867	b₈ = - 0.05439	c₈ = 0.03869
a₉ = 0.44423	b₉ = 0.03573	c₉ = - 0.1098
	b₁₀ = - 0.75623 e-3	c₁₀ = 0.07188
b₁₁ = - 0.0205 e-3
b₁₂ = - 0.19564

Table 2 Metabolite and ionic concentrations, Gibbs free energy and equilibrium CK and AK constants in normal rabbit myocytes.

Definition	Symbol	Value	Reference No
Total adenine	[Adenine]	5 mM	[23]
Total phosphate	[Phosphate]	35.79 mM	Estimated
Total creatine	[Creatine]	25.2 mM	[37]
Total ATP	[ATP]_tot	4.91 mM^a	[29]
Free ATP	[ATP^4-]_i	0.39 mM^a	[29]
Mg²⁺-bound ATP	[MgATP^2-]_i	4.52 mM^a	[29]
Ca²⁺-bound ATP	[CaATP^2-]_i	0.00024 mM	Estimated
Total ADP	[ADP]_tot	0.085 mM^a	[24]
Free ADP	[ADP^3-]_i	0.034 mM	Estimated
Mg²⁺-bound ADP	[MgADP^-]_i	0.05 mM	Estimated
Ca²⁺-bound ADP	[CaADP^-]_i	0.0000026 mM	Estimated
Total AMP	[AMP]_tot	0.0015 mM	Estimated
Free phosphate	[P_i]	2.78 mM	[29]
Total phosphocreatine	[PCr]_tot	18.1 mM	[37]
Free creatine	[Cr]_i	7.1 mM	Estimated
Total Mg²⁺	[Mg²⁺]_tot	5.57 mM	Estimated
Free Mg²⁺	[Mg²⁺]_i	1 mM	[29]
Intracellular H⁺	pH_i	7	[29]
Intracellular Na⁺	[Na⁺]_i	10 mM	[22]
Intracellular K⁺	[K⁺]_i	150 mM	[40]
ΔG⁰ of MgATP^2- hydrolysis		- 32.88 kJ/mol^a	[22]
ΔG of MgATP^2- hydrolysis		- 53.965 kJ/mol^a	[47]
Apparent equilibrium constant of CK reaction	K_CK	22.777	Estimated
Apparent equilibrium constant of AK reaction	K_AK	1	[29]

^aComputed parameter values comparable with experimentally measured.

Results

Free and bound metabolite concentrations, Gibbs free energy and K_CK constants under normal conditions

Our previous studies on the cardiac metabolism [29, 31, 33, 35] have clearly demonstrated that the model agreement with the experiment will be strongly dependent on the use of realistic physiological ligand (ATP, ADP, AMP, P_i, PCr, Cr) and ionic (Na⁺, K⁺, Mg²⁺, H⁺) concentrations. However, experimental data for the total nucleotide, [Cr]_i, and total phosphate and Mg²⁺ concentrations in normal rabbit cells are limited or contradictable [36-38]. For this reason we used the model to estimate above parameter values (table 2). Table 2 also demonstrates that the predicted [ATP]_tot, [ATP^4-]_i, [MgATP^2-]_i, [ADP]_tot, and in control conditions are comparable to those measured experimentally in rabbit ventricular myocytes.

Effects of Mg²⁺ on cardiac excitation-metabolic coupling

Here we present the results of several simulations showing that [Mg²⁺]_i decrease from 1.8 to 0.2 mM (corresponding to the pMg_i range of 2.74-3.7) notably inhibited the global I_KATP current, slightly prolonged the action potential duration (APD₉₀) and negligibly affected global I_Ca and I_NaK time courses (figure 2A). Figure 2A also demonstrates that additionally increasing [Mg²⁺]_i up to 5 mM (pMg_i 2.3) further enhanced the I_KATP peak and shortened APD₉₀, I_Ca and I_NaK current durations. Furthermore, simulations with the model revealed that global [Ca²⁺]_i, [Ca²⁺]_SR, [Na⁺]_i and [K⁺]_i transients and global I_Na, I_Na,b, I_NaCa, I_p(Ca), I_Ca,b, I_Kr, I_Ks, I_to, I_K₁, I_Kp currents remained essentially unchanged when [Mg²⁺]_i decreased from 5 mM to 0.2 mM (data not shown).

In contrast to the predicted insignificant effects of Mg²⁺ on the cell excitability, the changes in [Mg²⁺]_i significantly affected total nucleotide and Mg²⁺ concentrations, P_i, and K_CK constants (figure 2B). Here results indicate that increasing pMg_i from 2.74 to 3.7 increased [AMP]_tot ~ 78 fold and [ADP]_tot ~8.5 fold while K_CK and [Mg²⁺]_tot decreased ~9.2 and ~1.9 fold. Figure 2B also demonstrates that the predicted changes in P_i, and [ATP]_tot were less significant (between 1.1-1.2 fold) while remained essentially unchanged.

Effects of H⁺ on cardiac excitation-metabolic coupling

Figures 3A and B show the predicted variations in ionic currents, action potential shape and cell bioenergetics with pH_i increasing from 5 to 7.4 (corresponding to [H⁺]_i drop from 10 μM to 0.04 μM). These results suggest that the [H⁺]_i drop (in contrast to the [Mg²⁺]_i drop) increased the I_KATP current, slightly shortened APD₉₀ while the I_Ca and I_NaK remained essentially unchanged (figure 3A and inset).

Our studies also revealed that a further pH_i increase (up to 8) had a more pronounced effect on I_KATP, I_Ca, I_NaK and APD₉₀ (figure 3A). In addition, calculations demonstrated that the pH_i increase had a negligible effect on [Ca²⁺]_i, [Ca²⁺]_SR [Na⁺]_i and [K⁺]_i transients and global I_Na, I_Na,b, I_NaCa, I_p(Ca), I_Ca,b, I_Kr, I_Ks, I_to, I_K₁, I_Kp currents (data not shown). An interesting model prediction is that both pH_i and pMg_i increases, in contrast to their opposite effects on cell excitability, had similar effects on the cell bioenergetics, [Mg²⁺]_tot, [ATP]_tot, [ADP]_tot, [AMP]_tot, P_i, and K_CK constant figures 2 and 3). Thus when pH_i increased from 6 to 8 , P_i, [ADP]_tot and [AMP]_tot increased approximately 1.07, 1.3, 46.7 and 2556 fold respectively (figure 3B). Figure 3B also shows that the pH_i increase decreased ~1.2 fold, K_CK ~54.5 fold, [Mg²⁺]_tot ~1.05 fold and [ATP]_tot ~1.17 fold.

Effects of PCr on cardiac excitation-metabolic coupling

The results in figure 4A show that a [PCr]_tot drop (similarly to [H⁺]_i drop) sensitively increased the I_KATP current, shortened I_Ca and I_NaK durations and APD₉₀. Simulations also revealed that the changes in [Ca²⁺]_i, [Ca²⁺]_SR, [Na⁺]_i and [K⁺]_i and I_Na, I_Na,b, I_NaCa, I_p(Ca), I_Ca,b, I_Kr, I_Ks, I_to, I_K₁, I_Kp were less significant even with a 75% [PCr]_tot depletion (data not shown). Furthermore the model predicts that the [PCr]_tot drop (similarly to the [H⁺]_i or [Mg²⁺]_i drop) increased [AMP]_tot, [ADP]_tot, P_i, and while [Mg²⁺]_tot and [ATP]_tot decreased (figure 4B). Note here figure 4B also demonstrates that and K_CK remained unchanged, since Iotti et al. [18] found that [PCr]_tot is a variable mainly influencing (eqs. 2–4).

Simultaneous changes in Mg²⁺, pH and PCr during normal cardiac cycle

It has been reported that in normal skeletal muscle cells the depletion of [PCr]_tot is accompanied by a simultaneous pH_i decrease and [Mg²⁺]_i increase (or pMg_i drop) during exercise [17, 18]. In this study we also tested how the reported simultaneous changes in [PCr]_tot, [H⁺]_i and [Mg²⁺]_i in skeletal cells (we could not find data in cardiac myocytes) would affect the normal cardiac cycle and bioenergetics. The results in figure 5 (black lines) demonstrate that 50% [PCr]_tot depletion, pHi drop (from 7 to 6.5) and pMg_i drop (from 3 to 2.74) increased the I_KATP peak ~2.4 times but this current increase had negligible effects on APD₉₀, I_Ca and I_NaK currents. Our studies also revealed that all other ionic concentrations and currents remained essentially unchanged (data not shown).

The predicted total nucleotide and Mg²⁺ concentrations, P_i, Gibbs free energy and K_CK constant changes are shown in table 3. These results suggest that above simultaneous changes in [PC]_tot, pH_i and [Mg²⁺]_i most significantly affected the K_CK value and free P_i level, while the changes in , , [ATP]_tot, [AMP]_tot and [Mg²]_tot were less significant. An interesting model prediction is that the K_CK increase resulted in a decrease of [ADP]_tot, thus suggesting that both the pH_i and free Mg²⁺ changes occurring during the normal contractile cycle tend to counteract the ADP increase due to [PCr]_tot depletion.
Table 3 Estimated Gibbs free energy, K_CK, [Mg²⁺]_tot, [P_i] and metabolite levels at normal Na⁺ and K⁺ levels and relative changes in [PCr]_tot, pH_i and [Mg²⁺]_i.

	[PCr]_tot 18.1 mM	[PCr]_tot 9.05 mM
	pH_i 7	pH_i 6.5
	pMg_i 3	pMg_i 2.74
	- 53.965 kJ/mol	- 51.7837
	- 32.88 kJ/mol	- 30.8431
K_CK	22.777	104.8144
[ATP]_tot	4.91 mM	4.9149
[ADP]_tot	0.085 mM	0.083679
[AMP]_tot	0.0015 mM	0.0014247
[Mg²⁺]_tot	5.57 mM	6.549
[P_i]	2.78 mM	11.829

Discussion

To understand the cardiac cell cycle requires an integral comprehension of how cell excitation, contraction and energetics interact. Over the last 10 years many comprehensive ionic-metabolic models have been developed to encompass new understandings gained from interaction between experimental and modeling studies [6, 15, 16, 25, 29, 31-35, 39-52]. These models have had considerable success in elucidating the mechanisms underlying mitochondrial metabolism, pH_i regulation of excitation-contraction coupling and some electrophysiological effects of acute myocardial ischemia. However, how the changes in metabolite and ionic concentrations regulate action potential genesis, cytosolic and mitochondrial metabolisms in control or pathological conditions still remain poorly understood.

In this study to further investigate these complex interactions and processes we extended the Michailova et al. ionic-metabolic model in rabbits [29] to include the Iotti et al. [18] mathematical expressions for ΔG⁰ and ΔG of MgATP^2- hydrolysis and the apparent equilibrium constant of the CK reaction. We examined how the changes in cytosolic Mg²⁺, H⁺ and PCr regulate cell excitability and bioenergetics. In agreement with experiment [9] our studies demonstrated that the fall in free cytosolic Mg²⁺ (from 5 mM to 0.2 mM) systematically prolongs action potential duration. The results also revealed that the predicted APD₉₀ increase was mainly due to K_ATP current inactivation while all other currents and ionic concentrations remained essentially unaffected. We concluded that this multi-component whole-cell model: (1) correctly predicts [Mg²⁺]_i effects on APD₉₀ in a wide region in contrast to our previous model [35] where no variations in APD₉₀ were found in [Mg²⁺]_i range 0.2-1 mM; (2) the predicted small [Mg²⁺]_i electrophysiological effects, in contrast to the experimentally observed [9], are probably due to the fact that many important Mg²⁺ regulations (such as Mg²⁺ effects on L-type Ca²⁺ channel, SR Ca²⁺ release and uptake or cell contractility) and Mg²⁺ transporters (Na⁺/Mg²⁺ exchanger, selective sarcolemmal or mitochondrial Mg²⁺ channels) are not included into our model yet [2-4, 11-14, 53-57].

An interesting model prediction is that a [H⁺]_i fall (in contrast to a [Mg²⁺]_i fall) systematically shortened APD₉₀ but again no significant changes in ADP₉₀ were found. Furthermore, the results demonstrated that the pH_i alterations affected the K_ATP current more sensitively. However, in contrast to experimental observations [15, 49], all other currents and ionic concentrations remained essentially unchanged. We concluded that the predicted negligible modulator pH_i effects on the cell excitability and contractility are probably because important acid loaders (CHE, AE) and extruders (NBC, NHE) or pH_i effects on ion channels and pumps (RyRs, SERCA pump, Na⁺/Ca²⁺ exchanger, L-type Ca²⁺ current) and force development are not included into our current model yet [15, 23, 34, 42, 55].

In this study, we also used the model to examine what may happen in aerobic heart cells with normal CK activity when [PCr]_tot is depleted but free Mg²⁺ and pH_i remain normal (1 mM [Mg²⁺]_i, 7 pH_i). Our simulations revealed that the [PCr]_tot decrease sensitively increased the I_KATP current and shortened APD₉₀, I_Ca and I_NaK durations. No significant changes were found in any other currents and ionic concentrations even with a 75% [PCr]_tot drop. New experiments need to be performed to test our model predictions. We could not find experimental data in the literature suggesting how [PCr]_tot deletion alone may affect cardiac cell electrical properties.

Finally, we investigated how the simultaneous changes in free Mg²⁺, pH_i and [PCr]_tot (as reported in normal skeletal muscle during exercise [18], i.e. 50% [PCr]_tot depletion, pHi drop from 7 to 6.5, pMg_i drop from 3 to 2.74) may affect the normal cardiac cycle. The calculations demonstrated that the I_KATP peak increase (~ 2.4 fold) had insignificant effect on APD₉₀. We concluded that under physiological conditions the [PCr]_tot depletion, accompanied by a free Mg²⁺ increase and pH_i decrease, is probably unable to affect the normal ionic current and pump functions and consequently the action potential genesis [18, 24]. New experiments need to be performed to estimate accurately the ligand (ATP, ADP, AMP) and PCr, Cr, P_i at different Na⁺, K⁺, Mg²⁺, H⁺ concentrations in rabbit heart cells [18].

This comprehensive ionic-metabolic model provided also a unique opportunity for the first time to investigate theoretically how the changes in pH_i, free Mg²⁺ and [PCr]_tot may affect the whole-cell bioenergetics. Our computations reveled that (in contrast to predicted insignificant [Mg²⁺]_i and pH_i electrical effects) the pMg_i and pH_i alterations may have a pronounced effect on [AMP]_tot, [ADP]_tot and K_CK control values. In addition, results demonstrated that [PCr]_tot depletion also significantly may affect [AMP]_tot and [ADP]_tot control levels while K_CK and remained unchanged [18]. The free Mg²⁺, pHi and [PCr]_tot effects on P_i, [Mg²⁺]_tot and [ATP]_tot were less pronounced. No significant changes in were found in pMg_i and pH_i ranges 2.7-3.6 and 6-8, respectively. The pMg_i increase had negligible effect on while the pH_i increase and [PCr]_tot depletion (18 mM - 4 mM) increased approximately 1.07 and 1.1 fold respectively. In summary, our analysis suggests that when pMg_i, pH_i and [PCr]_tot varied: (1) the predicted sensitive changes in I_KATP current were primarily due to the variations in [MgADP]_i control level because of the [ADP]_tot changes; (2) the predicted small changes in I_Ca, I_NaK and all other currents and concentrations were since no significant variations in [MgATP]_i respectively in [ATP]_tot and [Mg²⁺]_tot were found.

In this study, we also used our model to investigate how the simultaneous changes in pH_i, [Mg²⁺]_i and [PCr]_tot may affect the whole-cell bioenergetics. The simulations revealed that during normal cardiac cycle the pH_i decrease accompanied by a free Mg²⁺ increase most significantly increased the control K_CK value (~ 4.6 fold). This K_CK increase resulted in [ADP]_tot decrease thus suggesting that the changes in both pH_i and free Mg²⁺ tend to counteract the [ADP]_tot increase due to [PCr]_tot depletion. In addition, the results demonstrated that under the above conditions: (1) [P_i] sensitively increased (~4.25 fold) while total ATP, Mg²⁺ and AMP remained essentially unchanged; and (2) and increased by ~ 2.01 kJ/mol and ~ 2.18 kJ/mol respectively.

Conclusion

Further experimental and theoretical work is needed to better understand the Mg²⁺, pH and PCr homeostasis and the mechanisms underlying Mg²⁺, pH and PCr effects on cell excitation, contraction and energetics. The present study has raised a number of interesting possibilities concerning the ways in which Mg²⁺, pH and PCr changes could fine-tune the cardiac regulatory processes.

Acknowledgments

This work was supported by National Biomedical Computational Resource (NIH grant P41 RR08605) and NSF grant (BES – 0506252).

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