Theoretical evaluation of a possible nature of the outer membrane potential of mitochondria

Abstract

A possibility of generation of the outer membrane potential in mitochondria has been suggested earlier in the literature, but the potential has not been directly measured yet. Even its nature, metabolic impact and a possible range of magnitudes are not clear, and require further theoretical and experimental analysis. Here, using simple mathematical model, we evaluated a possible contribution of the Donnan and metabolically derived potentials to the outer membrane potential, concluding that the superposition of both is most probable; exclusively Donnan origin of the potential is doubtful because unrealistically high concentrations of charged macromolecules are needed for maintaining its relatively high levels. Regardless of the mechanism(s) of generation, the maximal possible potential seems to be less than 30 mV because significant osmotic gradients, created at higher values, increase the probability of the outer membrane rupture. New experimental approaches for direct or indirect determination of true value of the outer membrane potential are suggested here to avoid a possible interference of the surface electrical potential of the inner membrane, which may change as a result of the extrusion of matrix protons under energization of mitochondria.

Appendix: mathematical description of the liposomal model for generation of the Donnan and metabolically derived potentials

Let us assume that the liposome is placed in a medium of infinitely large volume composed of 125 mM K⁺, 105 mM Cl⁻, 10 mM S⁻ and 10 mM P⁻ (Fig. 1). The rate of an irreversible reaction of conversion of S⁻ into P⁻, catalyzed by a liposomal enzyme E and characterized by simple first order Michaelis–Menten kinetics, may be described as

$$ v = \frac{{v_{m} [S^{ - } ]_{i} }} {{K_{m} + [S^{ - } ]_{i} }}, $$

(5)

where v _m is the maximum rate, which can be varied to simulate various metabolic activities, and K _m is the Michaelis–Menten constant. For all calculations, K _m = 2 mM.

The steady-state fluxes of the ions S⁻ and P⁻ across the membrane due to the difference in their concentrations in the external medium and in generated membrane potential may be expressed by the Goldman equation:

$$ J_{{\text{S}}} = P_{{\text{S}}} \frac{{\Delta \psi F}} {{RT}} \times \frac{{[S^{ - } ]_{i} - [S^{ - } ]_{0} {\text{e}}^{{\frac{{\Delta \psi F}} {{RT}}}} }} {{1 - {\text{e}}^{{\frac{{\Delta \psi F}} {{RT}}}} }} , $$

(6)

$$ J_{{\text{P}}} = P_{{\text{P}}} \frac{{\Delta \psi F}} {{RT}} \times \frac{{[P^{ - } ]_{i} - [P^{ - } ]_{0} {\text{e}}^{{\frac{{\Delta \psi F}} {{RT}}}} }} {{1 - {\text{e}}^{{\frac{{\Delta \psi F}} {{RT}}}} }} , $$

(7)

where P _S is the membrane permeability coefficient for S⁻, P _P is the permeability coefficient for P⁻, F is the Faraday constant, Δψ is the membrane potential, R is the gas constant and T = 310 K.

At steady state, the rate v of conversion of S⁻ into P⁻ (Eq. 5), and the fluxes of S⁻ and P⁻ (Eqs. 6, 7) across the membrane must be equal (Lemeshko and Lemeshko 2000):

$$ J_{{\text{S}}} = - J_{{\text{P}}} $$

(8)

$$ J_{{\text{S}}} = v. $$

(9)

The liposome also contains macromolecules with the charge 10⁻ (polyanion) or 10⁺ (polycation) at the concentration [M ^z] _i , thus the electro-neutrality principle for the liposomal space is described as

$$ [{\text{K}}^{ + } ]_{i} - [{\text{Cl}}^{ - } ]_{i} - [{\text{S}}^{ - } ]_{i} - [{\text{P}}^{ - } ]_{i} + z[M^{z} ]_{i} = 0, $$

(10)

where z is the valence of a macromolecule.

Assuming that the liposomal membrane is highly permeability for K⁺ and Cl⁻, electrochemical equilibriums for these ions can be presented by Nernst equations:

$$ \Delta \psi = - {\left( {RT/F} \right)}\ln {\left( {[K^{ + } ]_{i} /[K^{ + } ]_{0} } \right)}, $$

(11)

$$ \Delta \psi = {\left( {RT/F} \right)}\ln {\left( {[{\text{Cl}}^{ - } ]_{i} /[{\text{Cl}}^{ - } ]_{0} } \right)}. $$

(12)

Solving the system of Eqs. 5–12 allows for estimating the values of the DP potential (if v _m = 0), or the MDP (if [M^z] _i  = 0), or the superposition of both.