Analysis of functional coupling: mitochondrial creatine kinase and adenine nucleotide translocase

Abstract

The mechanism of functional coupling between mitochondrial creatine kinase (MiCK) and adenine nucleotide translocase (ANT) in isolated heart mitochondria is analyzed. Two alternative mechanisms are studied: 1), dynamic compartmentation of ATP and ADP, which assumes the differences in concentrations of the substrates between intermembrane space and surrounding solution due to some diffusion restriction and 2), direct transfer of the substrates between MiCK and ANT. The mathematical models based on these possible mechanisms were composed and simulation results were compared with the available experimental data. The first model, based on a dynamic compartmentation mechanism, was not sufficient to reproduce the measured values of apparent dissociation constants of MiCK reaction coupled to oxidative phosphorylation. The second model, which assumes the direct transfer of substrates between MiCK and ANT, is shown to be in good agreement with experiments--i.e., the second model reproduced the measured constants and the estimated ADP flux, entering mitochondria after the MiCK reaction. This model is thermodynamically consistent, utilizing the free energy profiles of reactions. The analysis revealed the minimal changes in the free energy profile of the MiCK-ANT interaction required to reproduce the experimental data. A possible free energy profile of the coupled MiCK-ANT system is presented.

FIGURE 1

Scheme of interaction between mitochondrial creatine kinase (MiCK) and adenine nucleotide translocase (ANT). The interaction between the proteins is considered as a sum of two interaction modes: ATP and ADP are transferred through solution (subplot A) or directly channeled between the proteins (subplot B). In the model based on dynamic compartmentation hypothesis, only the interaction through solution is considered. When direct channeling between MiCK and ANT is assumed, both modes are taken into account. (Subplot A) In the first mode of MiCK-ANT interaction, ATP after transport from matrix to intermembrane space by ANT (link between ANTx.ATP and ANTi.ATP in the scheme) is released to solution. Next, the released ATP participates in MiCK reaction according to the random Bi-Bi mechanism with fast equilibrium between all states of MiCK. ADP produced by MiCK reaction is released into solution by MiCK and picked up by ANT for transport to mitochondrial matrix (link between ANTi.ADP and ANTx.ATP in the scheme). (Subplot B) In direct transfer mode, ATP is transferred from ANT to MiCK without leaving two-protein complex to solution. Since MiCK has only one binding site for ATP and ADP, such transfer is possible only if this site is free, i.e., MiCK is either free (CK) or has only Cr or PCr bound (CK.Cr and CK.PCr). In the scheme, we grouped the states of MiCK according to whether ATP or ADP is bound to enzyme or not (open boxes in the scheme with three states of MiCK in each group). During direct transfer of ATP from ANT to MiCK, MiCK is transferred from states CK, CK.Cr, and CK.PCr to states CK.MgATP, CK.Cr.MgATP, and CK.PCr.MgATP, respectively. In the scheme, this transfer is shown as a link between ANTi.ATP and two corresponding groups of MiCK states. Next, after MiCK reaction (link between states CK.Cr.MgATP and CK.PCr.MgADP in the scheme), ADP is transferred directly to ANT. Note, that MiCK operates with Mg-bound ATP and ADP and ANT requires Mg-free ATP and ADP forms. Thus, during direct transfer between MiCK and ANT, Mg is either bound or released, as shown in the scheme.

FIGURE 2

Calculated apparent dissociation constants of MiCK reaction as functions of ATPase activity (ν_ATPase) in the solution in the presence of oxidative phosphorylation. Coupling between MiCK and oxidative phosphorylation was modeled according to the dynamic compartmentation hypothesis. ATPase activity is presented relative to maximal MiCK activity, in percents. Subplots A, B, C, and D correspond to apparent K_a, K_ia, K_cr, and K_icr, respectively. The simulation results (solid lines) obtained with the model are compared with the measured values of apparent dissociation constants, indicated by the average measured value (dashed line) and shaded area corresponding to the measured average ± standard deviation (SD) (data from Jacobus and Saks, 1982). In the calculations, maximal activity of ANT was taken equal to that of MiCK; ATP and ADP exchange constants D_ATP and D_ADP were 10⁻⁹ s⁻¹ and 10⁻¹ s⁻¹, respectively. Note that with the increase of ATPase activity in the solution, apparent dissociation constants of ATP from ternary and binary complexes with MiCK (K_a and K_ia, respectively) are reduced considerably.

FIGURE 3

Calculated apparent dissociation constants K_a and K_ia of the MiCK reaction in the presence of oxidative phosphorylation. Coupling between MiCK and oxidative phosphorylation was modeled according to the dynamic compartmentation hypothesis. Here, apparent dissociation constants K_a and K_ia (represented by small dots in the figure) were computed in case of different combinations of the values of ATPase activity in the solution ν_ATPase and exchange constants D_ATP and D_ADP. In the figure, the measured values are shown (open circles) in the right upper corner (no oxidative phosphorylation) and in the left lower corner (with oxidative phosphorylation). When using the kinetic constants of ANT transport as given in Table 1, all combinations of computed K_a and K_ia are aligned along the line with index 1 (indexes are shown within larger open circles in the figure). By increasing the maximal activity of ANT by 10 or 100 times, this line can be shifted to the left (lines with indexes 2 and 3, respectively). When instead of increasing the maximal activity of ANT, the apparent dissociation constant K_g is increased, the line shifts to the right (line with index 4). Note that regardless of the values used of ANT kinetic constants, all computed combinations of K_a and K_ia were considerably adrift from the measured values of these constants in the presence of oxidative phosphorylation. Experimental data from Jacobus and Saks (1982).

FIGURE 4

Analysis of the direction of the MiCK reaction in the presence of oxidative phosphorylation. In this contour plot, the rates of the MiCK reaction, relative to the maximal rate of the MiCK reaction in the direction of PCr synthesis, are depicted by different shades and iso-lines. Numbers on the iso-lines show the value of reaction rates; positive values correspond to PCr synthesis. The shades correspond to the values of MiCK reaction rate, changing gradually from white (maximal rate, PCr synthesis) to dark gray (minimal rate, ATP synthesis). Concentrations in solution were kept at the following values: 2 mM PCr, 0.12 mM ATP, 0.05 mM ADP, and 5 mM Pi. According to Saks et al. (1985), the direction of MiCK reaction depends on whether MiCK is coupled to oxidative respiration or not (Saks et al., 1975). Namely, whereas coupling of MiCK to oxidative phosphorylation favors the synthesis of PCr by MiCK (positive reaction rates on the figure), noncoupled MiCK reaction is driven toward the breakdown of PCr (negative reaction rates on the figure). D_ATP and D_ADP are exchange constants that characterize the exchange of ATP and ADP between the compartment and the solution (both constants are given in s⁻¹). Note that at smaller values of D_ATP and D_ADP, the MiCK reaction direction predicted by the model is in correspondence with the measurements (reaction rate is positive).

FIGURE 5

In this contour plot, the relative decrease in respiration rate after addition of the external ADP-trapping system into the solution containing isolated respiring mitochondria in the presence of oxidative phosphorylation is shown. The decrease v/v₀, where v₀ and v are the respiration rate before and after pyruvate kinase and phosphoenolpyruvate (PK+PEP) addition, is depicted by different shades and iso-lines. Numbers on the iso-lines show the value of v/v₀, shades change gradually from white (v/v₀ = 1, no drop in respiration) to dark gray (v/v₀ = 0, respiration completely inhibited). Initial conditions in the solution: 0.33 mM ATP, 0 mM ADP and PCr, 33 mM Cr, 5 mM Mg²⁺, 10 mM Pi, and 2.5 mM PEP. In the calculations, the activity of PK+PEP system was taken to be infinite compared to that of MiCK. According to Gellerich and Saks (1982), PK+PEP system is able to decrease the rate of respiration by ∼60% at maximum, i.e., the decrease v/v₀ is ∼0.4. D_ATP and D_ADP are exchange constants that characterize the exchange of ATP and ADP between the compartment and the solution (both constants are given in s⁻¹). In these simulations, ATPase activity in the solution was taken to be equal to 0.1% of the maximal activity of MiCK. Varying ATPase activity did not alter the results qualitatively. Note that the region in D_ATP–D_ADP plane corresponding to the measured drop in respiration rate is rather limited (see area around v/v₀ = 0.4 in the figure).

FIGURE 6

Calculated apparent dissociation constants K_a and K_ia of the MiCK reaction in the presence of oxidative phosphorylation. Coupling between MiCK and oxidative phosphorylation was modeled assuming direct transfer of metabolites between ANT and MiCK. Apparent dissociation constants K_a and K_ia (represented by small dots in the figure) are computed for different combinations of the free energies of the MiCK-ANT complex states and the free energies of transition. In the figure, the measured values are shown by open circles in the right upper corner (no oxidative phosphorylation) and in the left lower corner (with oxidative phosphorylation). Note that the range of computed K_a–K_ia combinations covers the area near the measured values of these constants in the presence of oxidative phosphorylation. Experimental data from Jacobus and Saks (1982).

FIGURE 7

Computed MiCK reaction rate as a function of ATP with (subplot A) and without (subplot B) oxidative phosphorylation. Coupling between MiCK and oxidative phosphorylation was modeled assuming direct transfer of metabolites between ANT and MiCK. (Subplot A) Experimental data (black dots) was reproduced by model with five different parameter sets. The parameter sets are indexed (see Table 3); correspondence between line-type and the index is shown in the legend. In this subplot, the MiCK reaction rate is shown for ATP titrations in the presence of three different combinations of Cr and PCr concentrations, which are indicated in the figure in mM. Note that all used parameter sets fit experimental data quite well, with parameter set 3 somewhat underestimating the reaction rate. (Subplot B) Computed MiCK rate with inhibited oxidative phosphorylation is in correspondence with the experimental data (black dots). The same parameter sets were used as in subplot A. Experimental MiCK rate used in both subplots was estimated on the basis of apparent MiCK reaction kinetic constants reported in Jacobus and Saks (1982).

FIGURE 8

Inhibition of respiration rate by a concurrent enzyme system, 60 IU/ml pyruvate kinase and phosphoenolpyruvate (PEP). The respiration was stimulated by the addition of 0.33 mM of ADP in the presence of 33 mM Cr. In the figure, the respiration rate after addition of PK+PEP (V) is normalized by the respiration rate obtained before PK+PEP addition (V_ADP), as shown in the y-axis label (V₀ corresponds to the respiration rate without added ADP). The simulation results (bars) are compared with the measured drop in VO₂, indicated by the average measured VO₂ (dashed line). The parameter sets are indexed (Table 3). Note that results obtained with all parameter sets used are close to the measurements. Experimental data is from Gellerich and Saks (1982).

FIGURE 9

Competition between ADP supplied by MiCK reaction and ADP from solution. The amount of ADP retransported to mitochondria after MiCK reaction, without mixing with ADP in the intermembrane space, is shown at different levels of ADP concentration in surrounding solution. Simulation results obtained for the five parameter sets (see legend at upper right for parameter set index) are close to the measured data (black dots). Experimental data from Barbour et al. (1984).

FIGURE 10

The free energy profile of the MiCK reaction in the absence (subplot A) or presence (subplot B) of oxidative phosphorylation. Note that the free energies of the states are shown relative to different initial states in these schemes: MiCK without any substrates bound and with MgATP²⁻ and Cr in solution (uncoupled case); MiCK-ANT complex without any bound substrates, ANT directed toward the intermembrane space, and with Mg²⁺, Mg-free ATP⁴⁻, and Cr in solution (coupled case). Such difference in selection of initial states of reactions is due to the difference in the forms of ATP binding to MiCK and ANT: MiCK binds MgATP²⁻ and ANT binds Mg-free ATP⁴⁻. (Subplot A) The relative free energies of MiCK states are estimated from measured kinetic constants. Here, MgATP and MgADP are denoted as T and D, respectively. Note that the free energy change during reaction is clear from the difference in free energies after (CK+D+PCr) and before (CK+T+Cr) the reaction. The differences in maximal rates of forward and backward MiCK reactions can be explained by the differences in the free energies of CK.T.Cr and CK.D.PCr (Eqs. 21–22). (Subplot B) Partial free energy profile of the MiCK reaction coupled to ANT. The free energies of the coupled system (boxes with solid border) are compared with the free energies of uncoupled MiCK and ANT (boxes with dashed border). In the first column, three states of two-protein complexes are shown with ATP (T in the scheme) attached to ANT directed to intermembrane space (Ni). The total free energy of the MiCK-ANT complex depends on the state of the coupled MiCK, as shown in the first column. ATP, attached to ANT, is either released to solution (second column) or transferred from ANT to MiCK (third column). After the MiCK reaction, ADP (D in the scheme) is transferred to ANT (last column) and then either released to solution (fourth column) or transported to mitochondrial matrix (not shown). This profile corresponds to the parameter set 4 (see Table 3). In the scheme, all reactions that are in the pathway leading to synthesis of PCr after the transfer of ATP from ANT to MiCK are shown by thick lines. Note that there are several simplifications made to keep the profile as simple as possible. First, the free energies changes indicated in the profile are induced by differences of the free energies of the complex states as well as changes in solution due to binding and release of the substrates and magnesium. However, in the scheme, only release and binding of ATP and ADP are indicated. Second, possible binding of ATP and ATP by ANT during the MiCK reaction is not indicated in this profile.