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


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

DOI : 10.1684/mrh.2008.0126

Summary  

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

Summary : A tight coupling between ionic currents, intracellular Ca2+ homeostasis, cytosolic [ADP] and ΔG of ATP hydrolysis underlies the regulation of cardiac cell function. As more experimental detail on the biochemistry and biophysics of these complex processes and their interactions accumulates, the intuitive interpretation of the new findings becomes increasingly impractical. For this reason we developed detailed biophysical model that couples Ca2+ signaling, cell electrophysiology and bioenergetics with the main interactions between phosphorylated species (ATP, ADP, AMP, PCr, Cr, Pi) and Lewis cytosolic acids (Na+, K+, Mg2+, H+). The results indicate that the increase in free cytosolic Mg2+ (0.2-5 mM) systematically shortens the action potential duration. The analysis suggests that that under physiological conditions a pH decrease accompanied by a free Mg2+ increase tends to counteract an [ADP] increase due to PCr depletion. The model reproduces qualitatively a sequence of events that correlates well with the experimental data.

Keywords : Mg2, pH, PCr, ΔG of ATP hydrolysis, creatine kinase reaction, cardiac cell, mathematical model

Pictures

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+ (pHi) is also an important modulator of the electrical and contractile properties of cardiac cells [15, 16]. Changes in pHi 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 pHi, 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+, pHi or [PCr]tot alone or simultaneous changes in [Mg2+]i, pHi 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 pHi 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, Pi) 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 (KATP 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 MgATP2- 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 pMgi = –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 KCK coefficients values at [Na+]i 10 mM, [K+]i 150 mM, pHi 5-8, [Mg2+]i 0.1-10 mM.

KCK

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 mMa

[29]

Free ATP

[ATP4-]i

0.39 mMa

[29]

Mg2+-bound ATP

[MgATP2-]i

4.52 mMa

[29]

Ca2+-bound ATP

[CaATP2-]i

0.00024 mM

Estimated

Total ADP

[ADP]tot

0.085 mMa

[24]

Free ADP

[ADP3-]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

[Pi]

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+

pHi

7

[29]

Intracellular Na+

[Na+]i

10 mM

[22]

Intracellular K+

[K+]i

150 mM

[40]

ΔG0 of MgATP2- hydrolysis

- 32.88 kJ/mola

[22]

ΔG of MgATP2- hydrolysis

- 53.965 kJ/mola

[47]

Apparent equilibrium constant of CK reaction

KCK

22.777

Estimated

Apparent equilibrium constant of AK reaction

KAK

1

[29]

aComputed parameter values comparable with experimentally measured.

Results

Free and bound metabolite concentrations, Gibbs free energy and KCK 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, Pi, 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, [ATP4-]i, [MgATP2-]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 pMgi range of 2.74-3.7) notably inhibited the global IKATP current, slightly prolonged the action potential duration (APD90) and negligibly affected global ICa and INaK time courses (figure 2A). Figure 2A also demonstrates that additionally increasing [Mg2+]i up to 5 mM (pMgi 2.3) further enhanced the IKATP peak and shortened APD90, ICa and INaK current durations. Furthermore, simulations with the model revealed that global [Ca2+]i, [Ca2+]SR, [Na+]i and [K+]i transients and global INa, INa,b, INaCa, Ip(Ca), ICa,b, IKr, IKs, Ito, IK1, IKp 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, Pi, and KCK constants (figure 2B). Here results indicate that increasing pMgi from 2.74 to 3.7 increased [AMP]tot ~ 78 fold and [ADP]tot ~8.5 fold while KCK and [Mg2+]tot decreased ~9.2 and ~1.9 fold. Figure 2B also demonstrates that the predicted changes in Pi, 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 pHi 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 IKATP current, slightly shortened APD90 while the ICa and INaK remained essentially unchanged (figure 3A and inset).

Our studies also revealed that a further pHi increase (up to 8) had a more pronounced effect on IKATP, ICa, INaK and APD90 (figure 3A). In addition, calculations demonstrated that the pHi increase had a negligible effect on [Ca2+]i, [Ca2+]SR [Na+]i and [K+]i transients and global INa, INa,b, INaCa, Ip(Ca), ICa,b, IKr, IKs, Ito, IK1, IKp currents (data not shown). An interesting model prediction is that both pHi and pMgi 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, Pi, and KCK constant figures 2 and 3). Thus when pHi increased from 6 to 8 , Pi, [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 pHi increase decreased ~1.2 fold, KCK ~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 IKATP current, shortened ICa and INaK durations and APD90. Simulations also revealed that the changes in [Ca2+]i, [Ca2+]SR, [Na+]i and [K+]i and INa, INa,b, INaCa, Ip(Ca), ICa,b, IKr, IKs, Ito, IK1, IKp 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, Pi, and while [Mg2+]tot and [ATP]tot decreased (figure 4B). Note here figure 4B also demonstrates that and KCK 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 pHi decrease and [Mg2+]i increase (or pMgi 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 pMgi drop (from 3 to 2.74) increased the IKATP peak ~2.4 times but this current increase had negligible effects on APD90, ICa and INaK 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, Pi, Gibbs free energy and KCK constant changes are shown in table 3. These results suggest that above simultaneous changes in [PC]tot, pHi and [Mg2+]i most significantly affected the KCK value and free Pi level, while the changes in , , [ATP]tot, [AMP]tot and [Mg2]tot were less significant. An interesting model prediction is that the KCK increase resulted in a decrease of [ADP]tot, thus suggesting that both the pHi 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, KCK, [Mg2+]tot, [Pi] and metabolite levels at normal Na+ and K+ levels and relative changes in [PCr]tot, pHi and [Mg2+]i.

[PCr]tot 18.1 mM

[PCr]tot 9.05 mM

pHi 7

pHi 6.5

pMgi 3

pMgi 2.74

- 53.965 kJ/mol

- 51.7837

- 32.88 kJ/mol

- 30.8431

KCK

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

[Pi]

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, pHi 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 MgATP2- 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 KATP 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 pHi alterations affected the KATP 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 pHi effects on the cell excitability and contractility are probably because important acid loaders (CHE, AE) and extruders (NBC, NHE) or pHi 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 pHi remain normal (1 mM [Mg2+]i, 7 pHi). Our simulations revealed that the [PCr]tot decrease sensitively increased the IKATP current and shortened APD90, ICa and INaK 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+, pHi 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, pMgi drop from 3 to 2.74) may affect the normal cardiac cycle. The calculations demonstrated that the IKATP 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 pHi 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, Pi 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 pHi, free Mg2+ and [PCr]tot may affect the whole-cell bioenergetics. Our computations reveled that (in contrast to predicted insignificant [Mg2+]i and pHi electrical effects) the pMgi and pHi alterations may have a pronounced effect on [AMP]tot, [ADP]tot and KCK control values. In addition, results demonstrated that [PCr]tot depletion also significantly may affect [AMP]tot and [ADP]tot control levels while KCK and remained unchanged [18]. The free Mg2+, pHi and [PCr]tot effects on Pi, [Mg2+]tot and [ATP]tot were less pronounced. No significant changes in were found in pMgi and pHi ranges 2.7-3.6 and 6-8, respectively. The pMgi increase had negligible effect on while the pHi 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 pMgi, pHi and [PCr]tot varied: (1) the predicted sensitive changes in IKATP current were primarily due to the variations in [MgADP]i control level because of the [ADP]tot changes; (2) the predicted small changes in ICa, INaK 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 pHi, [Mg2+]i and [PCr]tot may affect the whole-cell bioenergetics. The simulations revealed that during normal cardiac cycle the pHi decrease accompanied by a free Mg2+ increase most significantly increased the control KCK value (~ 4.6 fold). This KCK increase resulted in [ADP]tot decrease thus suggesting that the changes in both pHi 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) [Pi] 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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