📒 Michailova 2005

Modeling regulation of cardiac KATP and L-type Ca2+ currents by ATP, ADP, and Mg1



  • Pathological changes of intracellular free and bound Mg2+, ATP, and ADP concentrations occur during ischemia, and reperfusion and the concentrations of these metabolites have been shown to affect the availability and activity of ATP-sensitive K+ and L-type Ca2+ channels and consequently cell excitability and contractility
  • the goals of this study were
    1. to formulate a new model for cardiac KATP current regulation by intracellular free ATP and MgADP that takes into account the octameric channel stoichiometry
    2. to formulate a new reduced-order model of the L-type Ca2+ channel
  • The new model reproduces experimental data on the ATP dependence of KATP channel activity in the presence of normal ADP and Mg2+ and the effects of stimulated KATP current on cell excitability and contractility

Mathematical model

  • whole-cell ionic-metabolic model is described in Michailova (2001), extenden from 1999 Winslow model
  • the role of ATP and ADP as Ca2+ and Mg2+ buffers
  • in our current whole-cell model the NKA current is not MgATP dependent

Modeling KATP channel availability

  • there are four Kir6.2 sites that bind ATP independently with equal affinity, but that binding of only one molecule of ATP is sufficient to close the channel
  • channel activation by ADP requires the presence of Mg2+ (MgADP). simultaneous binding of two MgADP molecules to one SUR2A subunit is required to increase the channel open probability

$$ \begin{aligned} I_{KATP} &= g_{KATP} (V-E_K) \cr g_{KATP} &= G_{KATP}f_{KATP}([K^+]_o / 5.4)^0.24 \cr f_{ATP} &= M(K_{ATP}, [ATP]_i)^4 \cr f_{MgADP}^\prime &= M([MgADP], K_{MgADP})^2 \cr c_{MgADP} &= 1 - f_{MgADP}^\prime \cr f_{MgADP} &= 1 - c_{MgADP}^4 \cr f_{KATP} &= P_0f_{ATP}(1 - f_{MgADP}) + P_df_{ATP}f_{MgADP} \end{aligned} $$

MgATP regulation in a reduced-order model of the L-type Ca2+ channel

  • Here we sought to formulate a simplified model of the L-type Ca2+ channel, which retains the properties of the more detailed equation M34 Markov model yet reduces the complexity
    1. the four channel subunits gate independently of one another
    2. voltage-independent activation gating occurs independently of the voltage-dependent conformational changes in the subunits
    3. voltage-dependent inactivation occurs independently of activation and Ca2+-dependent inactivation
    4. transitions between normal and Ca2+-inactivated modes occur much more slowly than voltage-dependent gating within a mode $$ \begin{aligned} \frac{d v}{d t}&=\alpha(1-v)-\beta v \cr \frac{d w}{d t}&=\alpha^{\prime}(1-w)-\beta^{\prime} w \cr x&=\frac{f}{f+g} \cr \frac{d y}{d t}&=\left(y-y_{\infty}\right) / \tau_{\mathrm{y}} \cr \frac{d z}{d t}&=v_{\omega}(1-z)-v_{\gamma} z \cr v_{\omega}&=\omega \sum_{i=0}^{4} b^{-i} w^{i}(1-w)^{4-i} \cr v_{\gamma}&=\gamma\left[\sum_{i=0}^{4} a^{i} v^{i}(1-v)^{4-i}-a^{4} v^{4} x\right] \cr P_{\mathrm{rom}}&=v^{4} y z \frac{f}{f+g} \cr f_{Ca} &= H([MgATP]_ss, K_{MgATPss}, 2.6) \cr K_{MgATPss} &= 1.4 mM \end{aligned} $$


Effects of ATP on IK(ATP) and ICa currents, contractile activity, and action potential

  • KATP = 0.6mM, KMgADP = 0.4mM, G_KATP = 0.05 mS/ΞF, P0 = 0.08, PD = 0.8
  • Simulations are generated in response to 1-Hz pulse and model outputs at the tenth stimulus are shown only. ADP_tot 200ΞM, Mg_tot 4.84mM, K_o 4mM, Na_o 138mM, Ca_o 2mM.
Dependence of KATP channel activity on ADP in the presence of Mg2+

Absolute levels of ATP and ADP regulate cardiac EC coupling independently of ATP/ADP ratio

Effects of cytosolic Mg2+ on cardiac EC coupling

Metabolic inhibition

  • During ischemia
    1. average cytosolic ATP remains in the millimolar range (normoxia ∞ 6.8 mM; 40-s ischemia ∞ 5.4 mM; 10-min ischemia ∞ 4.6 mM
    2. free cytosolic ADP increases from 15 to 30 or 99 ΞM after 40-s or 10-min ischemia
    3. total Mg2+ dose not change whereas normal Mg2+ increases (normal free Mg2+ ∞ 2mM)


KATP channel model

  • there are four sites that bind ATP but only a single ATP molecule needs to bind to cause channel closure
  • simultaneous binding of two MgADP molecules to one of SUR2A subunit is required to increase channel open probability
  • there are two populations of sarcolemmal KATP channels open.
  • Hopkins model: one site specifically binds two MgADP molecules and increases channel opening. The other site binds either one molecule ATP or ADP and decreases channel opening
  • the gating kinetics of the single KATP channel is not included into our ionic-metabolic model yet

Cardiac KATP and L-type Ca2+ currents, cytosolic Mg2+, adenine nucleotide phosphates, and EC coupling

  • the enhanced KATP current and markedly shortened current and AP-potential durations, were due to decreased free diastolic ATP and increased diastolic MgADP level
  • its ability to simulate the modulation of ATP sensitivity of KATP channel by ADP in the presence of Mg2+. When free ADP is > 500 ΞM, channel inhibition is observed.
  • Despite of the fact that Mg2+ is the most abundant divalent cation in the cell, little is known about intracellular Mg2+ homeostasis and mechanisms controlling [Mg2+]i. Assumption: total Mg2+ content is kept constant at the level necessary for enzyme and channel function
  • Changes in Mg(0.2–1.8 mM) with total ATP and ADP normal, may have pronounced effect on IKATP. Increase in Mg => shortening of action potential duration (also in experiment)


  1. Michailova A, Saucerman J, Belik ME, McCulloch AD. Modeling regulation of cardiac KATP and L-type Ca2+ currents by ATP, ADP, and Mg2+. Biophys J. 2005;88(3):2234-49. PMC1305273 ↩︎