Physical basis of charge pairing in mitochondria.

Abstract

The postulate of charge pairing in the mitochondrial inner membrane is justified by applying a formula due to Fuoss to calculate the probability density for the distance between a positive and a negative charge. For dielectric constants 10 or less pairing is absolute, for 20 there is some tendency towards pairing, and at 78 it is nonexistent. Pairing, partner exchange or charge substitution, inhibition, and antiport uncoupling can be rationalized within this framework.In the charge pair model presently under development (1)(2)(3)(4)(5) the pairing of opposite charges is the fundamental principle by which the operation of mitochondria and of other bioenergetic systems is rationalized. This pairing has so far been treated as a postulate. Due to its fundamental significance it needs to be justified and its limitations must be explored.The distribution of all charges in and near the mitochondrial inner membrane is a problem of discouraging complexity unless some simplifying principle is recognized. The experimental techniques available in the field tend to focuson the electrons in the electron transfer chain. This point of view does not seem to lead to a successful theory. It was necessary to recognize that energy passes between two charges (6, 7), and that these charges are of-opposite sign (1). One of them can be the electron. Classification of charge separationsThere are two fields which have historically dealt with the distribution of charges from the point of view of our present interests. One is physical chemistry, as exemplified by the theory of catalysis (8), which deals with charge separations of the order of 1 A. The other one is the theory of electrolytes (9), which is valid for distances between charges larger than a few Angstroms, so that specifically quantum mechanical effects can be ignored. The medium here is characterized by a dielectric constant, which of course also means charge separation, but on a scale usually much smaller than 1 A. The charge separations of primary bioenergetic interest fall into the range of competence of the theory of electrolytes.The separation of ions in electrolytic solutions was investigated by Fuoss (9, 10). If one positions a negative ion at the center of coordinates, the probability density G(r) of finding the nearest positive ion between distances r and r + dr is G(r) = 47rr2p exp -47rp f x2e~/xdx}, In an electrolytic solution charges of both signs are free to move in three-dimensional space. The only restrictions arise from the mutual electrostatic interaction of the ions themselves and their distance of nearest approach a in Eq. [1]. This means that there is a competition between the energetic effect of the attractive Coulomb interaction favoring the nearest possible approach of opposite charges and the entropy effect favoring separations of the order of p -" due to the larger configurational volume available at larger separations. Low values of the dielectric constant make the Coulomb interaction dominant and charges tend to pair. High values of the dielec...

Charge pair model of bioenergetics: redox enzymes.

“…The charge pair model of bioenergetics (1)(2)(3)(4)(5) is based on the recognition of two basic features of bioenergetic systems: (i) separated opposite charges move in pairs, and (Hi) free energy, consisting of the interaction energy of the charges with each other and with the medium, is always at a local minimum apart from thermal fluctuations. These principles have been elaborated and fruitfully applied.…”

“…In more detail we find that the (XERedC) = 0 requirement causes the first numerator in Eq. [5] [7] .-1 and for the reduced state 0. (XU,,,) = -2( EAai -A)Xa +E0, [8] has to be added.…”