The proton circuit

In order to deal with the flux of H in a sarcomere it suffices to consider a pair of thin filaments of a length 4 and a thick filament interposed between them (Fig. 2). The proton flux to the Mline via the thick filament will be taken as equal to the flux of H via the pair of the thin filament to the Z disk. This means that starting with Fr = 0, no imbalance in the concentration will be created in the sarcomere and Fr can be ignored. Protons are injected in the thin filaments by the cross-bridges (CB) at different sites along their lengths. A small resistance Tcb is introduced for the path of H from the CB to the actins. The resistances r = g la and Tr = g 74 introduced for the pair of the thin filaments i.e., the gn nd 

The injection of protons in the thin filaments is due to the contacts of CB at discrete point 2, in the overlap region each causing a small flux J(. Writing r + Tr as R, Eq. (4) goes over to 

It can be seen that f 6) does not vary appreciably around the slack length. Within the range of the applicability of the expansion ( —1 0// +1) and without including the possibility of the thin filaments crossing over the region of the thick filament devoid of CB (the pseudo-H-band) Kh h gives the power output of the proton circuit (heat generation in the static case considered here) as a function of overlap. 

The same treatment can be extended to the thick filaments with (possibly) different values for r s (pertaining to S2) and R 

As discussed in Chapter 1, an accurate treatment of energy flows in a chemiosmotic system demands the use of non-equilibrium thermodynamics to relate flux to net driving force. However, since the same laws control the flow of energy in complex systems such as mitochondria and simple systems such as electrical or hydraulic circuits, the use of the latter as analogues for the proton circuit has considerable attractions to the non-mathematical bioenergeticist. 

The mitochondrial respiratory chain consists of three proton pumps which act in series with respect to the electron flow and in parallel with respect to the proton circuit (Fig. 2.2a). Two limiting states are frequently referred to for isolated mitochondria - State 4 in which the proton current is limited by the inhibition of proton re-entry through the ATP synthase (due to either actual inhibition of the synthase or to the attainment of equilibrium), and State 3 in which there is ready proton re-entry into the matrix and hence brisk respiration. The State 3 condition can be due to an induced proton leak in the membrane or to the maintenance of AG tp below that required to equilibrate with AfiH+ (by either removing ATP, or following the addition of ADP. 

Complex 1, which transfers electrons from the matrix NAD /NADH pool to the membrane-bound pool of ubiquinone/ubiquinol operates close to equilibrium such that the energy lost by the electrons (some 300 meV) is conserved in the proton electrochemical gradient. As a result, three protons can be extruded by this complex for the passage of two electrons [23]. 

Complex 111 transfers electrons from the quinone pool dissolved in the membrane to the pool of cytochrome c loosely associated with the cytosolic face of the membrane. This complex also operates with a near equilibrium between AjaH+ and the oxido-reduction span of the electrons. In contrast the final complex of the mitochondrial respiratory chain, cytochrome c oxidase, transferring electrons from cytochrome c to oxygen, operates under non-equilibrium conditions and is strictly irreversible. 

It is possible to introduce or remove electrons at the interfaces between the complexes. Thus, electrons may be added to the quinone pool from Complex II, 

---

The uptake of potassium by microorganisms has been well studied. In the case of E. coli, kinetic investigations on different strains have demonstrated the presence of three or four transport systems. The presence of inducible pathways with widely different Km values for binding K+ allows the cell to accumulate K+ to a constant level under different environments. These transport pathways include those linked to the proton circuit and an example linked to a pump and ATP hydrolysis. Thus the Kdp system is a high affinity pathway with Km = 1 mol dm-3, and involves three proteins in the inner membrane of E. coli, including a K+-stimulated membrane ATPase. The KHA (i.e. K+-H+ antiport) path is driven by proton motive force, while the low affinity system TrKA depends on both ATP and the proton motive force.80,81,82 S. cerevisiae accumulates K+ by K+/H+ exchange.83 Potassium transport may thus be used to control intracellular pH. 

This chapter is concerned with the proton circuit which in the chemiosmotic scheme links the generators and utilizers of proton electrochemical potential (A/if ) [1,2]. Since the topic has been covered extensively in a recent monograph [3], this chapter will attempt to avoid repetition by concentrating on the ionic circuitry found in association with energy conserving organelles, and no attempt will be made to discuss the structures of the black boxes of the membrane. 

The uncouplers which abolish the coupling of respiratory rate to ATP synthesis act as proton translocators, inducing net proton translocation across the membranes. In this way the proton circuit can be short-circuited , allowing the protons translocated by the generator of to cross back across the membrane without passing through the ATP synthase and producing ATP. The majority of the uncouplers are protonatable, lipophilic compounds with an extensive pi-orbital system which allows the electron of the anionic, de-protonated form to be delocalized [11]. This enhances the permeability of the anionic form in the hydrophobic membrane, and allows the proton translocators to permeate in both their neutral (protonated) and anionic (deprotonated) forms. In this way they can catalyze the net transport of protons... 

As with any other energy flow circuit, the proton circuit has inter-related potential, flow and conductance terms. These will now be considered in turn. 

After discussing the generation and quantitation of the potential term of the proton circuit, we shall now turn to the proton current, and examine the factors which control the flux of protons around the circuit. Although it is not possible to determine the proton current under steady-state conditions directly, the parameter may be calculated indirectly from the respiratory rate and the stoicheiometry of proton extrusion by the respiratory chain. It is outside the scope of this chapter to discuss the contentious issue of the proton stoicheiometries of the complexes, but the important feature is that, unless the complexities of variable stoicheiometry are invoked, respiration and proton current vary in parallel. 

When the mitochondria are allowed to produce ATP, for example by adding ADP and Pj to an incubation, the potential and current parameters of the proton circuit both change in the direction which indicates an increase in the proton conductance of the membrane due to proton re-entry through the ATP synthase. Thus, falls and this lowers the thermodynamic back pressure upon the respiratory chain, which therefore respires more rapidly. 

Fig. 2.3 also shows that the transfer of energy from the respiratory chain to the proton circuit can be extremely efficient, in that a slight thermodynamic disequilibrium results in a considerable energy flux. The actual disequilibrium between the respiratory chain and the proton electrochemical potential is even less than appears from the drop in the latter, since the redox span across the respiratory chain proton pumps also contracts [24],... 

Reversed electron transfer and the proton circuit driven by A TP hydrolysis... 

The three proton pumps of the mitochondrial respiratory chain normally function in parallel with respect to the proton circuit. It is however possible to manipulate the conditions such that the proton electrochemical potential generated by two of the pumps can be used to reverse the third proton pump (but not cytochrome oxidase). 

Fig. 2.4. Further variants of the proton circuit, a, reversed electron transfer in Complex I driven by Aft from succinate oxidation, b, reversed electron transfer in Complex I driven by Afin from ATP hydrolysis.

Coupling of the proton circuit to the transport of divalent cations... 

Since mitochondrial Ca transport is discussed in depth in Chapter 9, this section will be restrict to a brief summary of the way in which the proton circuit can be diverted into accumulating and regulating the transport of the cation, and how the permeation of weak acids is linked indirectly to net Ca transport. 

This net proton extrusion results in a net acidification of the external medium and an alkalinization of the matrix (Fig. 2.5), and should be distinguished from the steady-state cycling which occurs during the operation of the proton circuit for ATP synthesis. Clear, alkalinization of the matrix cannot continue indefinitely, and the limitation which is set is essentially thermodynamic - the respiratory chain is incapable of maintaining a proton electrochemical potential in excess of 200-230... 

Fig. 2.5. Interaction of Ca transport with the proton circuit, a, Ca uptake alone discharges the membrane potential b, Ca uptake in exchange for protons extruded by the respiratory chain generates a pH gradient c, Ca uptake together with a weak acid such as acetate does not build up a pH gradient d, Ca cycling in heart mitochondria driven by the proton circuit. R, respiratory chain C, calcium uniport NH, sodium/proton antiport NC, sodium/calcium antiport.

Is the proton circuit in equilibrium with the bulk aqueous phases on either side of the membrane ... 

In the proton circuit discussed so far in this chapter, it has been assumed that the protons, after being translocated across the membrane by the respiratory chain or... 

Fig. 2.6. Hypothetical localized variants on the proton circuit, a, fully delocalized circuit b, proton current flows along surface of membranes (note that circuit is still in equilibrium with the bulk phases) c, one leg of the proton circuit is conducted through a lateral channel insulated from the bulk phase d, both legs of the proton circuit are conducted through lateral channel insulated from the bulk phases R, respiratory chain A, ATP synthase. Note the necessity for both outward and return legs in all models.

The next stage in developing a model of localized chemiosmosis is to assume that there is a substantial resistance between the local circuit and the bulk phase [43,44]. One could devise hypothetical models in which one (Fig. 2.6c) or both (Fig. 2.6d) of the portions of the proton circuit parallel to the membrane were insulated from the bulk phases. It is important, however, to appreciate that such models still require the presence of a highly insulating phase separating the outward and return limbs of the proton circuit, with the addition of one or two further substantial resistances to protons. 

The next few years will decide whether the present anomalies in the quantitation of the proton circuit are merely due to experimental problems in the precise measurement of the parameters, or whether they will demand a wholesale revision in our understanding of the proton electrochemical coupling of respiration to ATP synthesis. In the author s opinion the evidence is not yet adequate for the second alternative, but there is a need for proponents of delocalized chemiosmosis to propose straightforward and unambiguous explanations for these phenomena. 

Active pH homeostasis Depends primarily on the potassium ion and the proton circuits. 

In the following a set of compatible values for gH> o> and s will be determined using the measured value of a = 4.8iV with the assumption that only 10% of the total power output of the proton circuit is dissipated... 

---