A biophysical model of the mitochondrial ATP-Mg/P(i) carrier

Abstract

Mitochondrial adenine nucleotide (AdN) content is regulated through the Ca(2+)-activated, electroneutral ATP-Mg/P(i) carrier (APC). The APC is a protein in the mitochondrial carrier super family that localizes to the inner mitochondrial membrane (IMM). It is known to modulate a number of processes that depend on mitochondrial AdN content, such as gluconeogenesis, protein synthesis, and citrulline synthesis. Despite this critical role, a kinetic model of the underlying mechanism has not been developed and validated. Here, a biophysical model of the APC is developed that is thermodynamically balanced and accurately reproduces a number of reported data sets from isolated rat liver and rat kidney mitochondria. The model is based on an ordered bi-bi mechanism for heteroexchange of ATP and P(i) and includes homoexchanges of ATP and P(i) to explain both the initial rate and time course data on ATP and P(i) transport via the APC. The model invokes seven kinetic parameters regarding the APC mechanism and three parameters related to matrix pH regulation by external P(i). These parameters are estimated based on 19 independent data curves; the estimated parameters are validated using six additional data curves. The model takes into account the effects of pH, Mg(2+), and Ca(2+) on ATP and P(i) transport via the APC, and supports the conclusion that the pH gradient across the IMM serves as the primary driving force for AdN uptake or efflux. Moreover, computer simulations demonstrate that extramatrix Ca(2+) modulates the turnover rate of the APC and not the binding affinity of ATP, as previously suggested.

Figure 1

Proposed kinetic mechanism of ATP (MgATP²⁻) and P_i (HPO₄²⁻) exchange via the ATP-Mg/P_i carrier (APC). The mechanism is ordered bi-bi for heteroexchange and random bi-bi for homoexchange of ATP and P_i. It is assumed that the APC has two binding sites: one exposed to the external side and the other to the matrix side. Once both the binding sites are occupied, the APC undergoes conformational change to translocate the bound substrates. E1 is the unbound state of the APC to which either of the external substrates can bind first for homoexchanges, but only external ATP can bind first for heteroexchange. E2 state is analogous to E1 with the exception that matrix substrate can bind first. K_T and K_P represent the binding affinity of the APC for ATP and P_i, respectively; k_E is the rate of futile exchange between the unbound states E1 and E2, k_T is the translocation rate when ATP is exchanged for P_i, and k_H is the translocation rate for homoexchanges. Here, T_x and P_x represent matrix ATP and P_i, whereas T_e and P_e represent external ATP and P_i.

Figure 2

Model simulations of initial tracer (ATP) efflux rates from the experiments of Hagen et al. (3) conducted in isolated rat kidney mitochondria. Experimental conditions are as in Table 1, except for the titration of reagents in panels A–D. (A) ATP efflux rate with increasing matrix [ATP] in presence (solid line; [ATP]_e = 1 mM) and absence (broken line; [ATP]_e = 0 mM) of ATP in the incubation medium. (B) Effect of increasing external [ATP] over ATP efflux rate. (C) Effect of external [P_i] on ATP efflux rate in the absence of [ATP]_e. (D) ATP efflux rate as a function of increasing external [Ca²⁺] in the incubation medium.

Figure 3

Model simulations of initial tracer (ATP) influx rates from the experiments of Hagen et al. (3). (A) Effect of increasing external [ATP] on ATP influx rate. (B) ATP influx rate as a function of increasing external [Ca²⁺]. (C) ATP influx rate as a function of increasing [Mg²⁺] in the incubation medium.

Figure 4

Model simulations of initial tracer (ATP) efflux rates from the experiments of Austin and Aprille (6) conducted in isolated rat liver mitochondria. Experimental conditions are as in Table 1, except for the titration of reagents in panels A–C. (A) ATP efflux rate as a function of matrix [ATP] with [ATP]_e = 2 mM (solid line), [ATP]_e = 1 mM (broken line), and [ATP]_e = 0.5 mM (dotted line). (Arrow) Decrease in external [ATP] (from 2 mM to 0.5 mM). (B) Effect of external [ATP] on ATP efflux rate. (C) ATP efflux rate as a function of external [P_i] with (solid line; [ATP]_e = 2 mM) and without (broken line; [ATP]_e = 0 mM) [ATP] in the incubation medium. Note that [ATP]_e was reported to be 1 mM for plot C, which doesn’t seem to be consistent with the efflux rates at [ATP]_e = 1 mM from plot B; [ATP]_e = 2 mM seems to be more probable, and thus is used for parameter estimation.

Figure 5

Model simulations of initial tracer (ATP) influx rates from the experiments of Austin and Aprille (6) and Nosek et al. (10). (A) Effect of external [ATP] on ATP influx rate with incubation medium containing 2 μM Ca²⁺ (solid line) and 1 μM Ca²⁺ (broken line). (B) ATP influx rate as a function of external [P_i] with increasing [ATP] in the incubation medium: [ATP]_e = 1 mM (dotted line), [ATP]_e = 2 mM (broken line), and [ATP]_e = 4 mM (solid line).

Figure 6

Model simulations of matrix AdN content time course data from the experiments of Austin and Aprille (20). The matrix AdN time course is governed by Eq. 16 and includes the experimentally measured residual matrix AdN content (see text for detail). For simulating the matrix AdN content time course, matrix pH was set at 7.8 based on a ΔpH of 0.4, determined by Joyal and Aprille (5) under the same experimental conditions. In these experiments, isolated rat liver mitochondria were incubated with different external ATP and the net change in matrix AdN content was measured.