Phosphate potential

A quantitative description of oxidative phosphorylation within the cellular environment can be obtained on the basis of nonequilibrium thermodynamics. For this we consider the simple and purely phenomenological scheme depicted in Fig. 1. The input potential X0 applied to the converter is the redox potential of the respiratory substrates produced in intermediary metabolism. The input flow J0 conjugate to the input force X0 is the net rate of oxygen consumption. The input potential is converted into the output potential Xp which is the phosphate potential Xp = -[AG hoS -I- RT ln(ATP/ADP P,)]. The output flow Jp conjugate to the output force Xp is the net rate of ATP synthesis. The ATP produced by the converter is used to drive the ATP-utilizing reactions in the cell which are summarized by the load conductance L,. Since the net flows of ATP are large in comparison to the total adenine nucleotide pool to be turned over in the cell, the flow Jp is essentially conservative. 

After these general comments let us further test the idea of thermodynamic buffering on an experimental basis by repeating the above experiment but this time in the presence of an inhibitor of adenylate kinase, namely, diadenosine pentaphosphate. As is depicted in Fig. 6b the buffering effect of the adenylate kinase is abolished by inhibiting this enzyme and it becomes now possible to drive the system beyond the state of optimal efficiency by increasing the hexokinase concentration in the medium. Note that it was not possible to measure points closer to level flow than the ones shown in the figure. This is due to technical reasons. At the lowest phosphate potentials the ATP/ADP ratios where of the order... 

Finally, we might wish to observe thermodynamic buffering at work in an intact cell in a fluctuating environment. Unfortunately there is no experimental technique available at present which would permit a continuous measurement of the phosphate potential in the cytosol of a living cell. Therefore, we are left with the only possibility to give such a demonstration by a numerical computer simulation. 

Based on the analyses of the trace contaminants conducted on the wheat millfeed-derived products, numerous potential problem components were identified, relative to catalyst activity (3). These components (shown in Table 1) include sulfate (potential for metal sulfide formation) calcium, magnesium, and phosphate (potential for catalyst pore plugging by insoluble salt precipitation) sodium or potassium (alkali attack on the catalyst support) organic nitrogen components, such as amino acids (thiol... 

Stucki (1980, 1984) applied the linear nonequilibrium thermodynamics theory to oxidative phosphorylation within the practical range of phosphate potentials. The nonvanishing cross-phenomenological coefficients Ly(i v /) reflect the coupling effect. This approach enables one to assess the oxidative phosphorylation with H+pumps as a process driven by respiration by assuming the steady-state transport of ions. A set of representative linear phenomenological relations are given by... 

Assuming that oxidation drives the phosphorylation process, thenA) < 0 andX2 > 0, and J U2 is the conventional P/O ratio, while X IX2 is the ratio of phosphate potential to the applied redox potential. The following relations are from Stucki (1980). At static head (sh), analogous to an open circuited cell, the net rate of ATP vanishes, and the rate of oxygen consumption and the force (the phosphate potential) are expressed in terms of a as follows... 

This equation shows that the energy needed at the static head is a quadratic function of the phosphate potential. 

At level flow (If), analogous to a short-circuited cell, the phosphate potential vanishes. Hence, no net work is performed by the mitochondria, and we have... 

This equation shows the maximal P/O ratio measurable in mitochondria at a zero phosphate potential. Equation (11.97) also indicates that at level flow, the flow ratio does not yield the phenomenological stoichiometry Z but approaches this value within a factor of q. Therefore, if the degree of coupling q is known, it is then possible to calculate Z from the P/O measurements in a closed-circuited cell. 

Obviously, in state 3, the phosphate potential is not zero, however, for values of q approaching unity, the dependence of the flow ratio on the force ratio is weak, according to Eq. (11.92). Therefore, state 3 is only an approximation of the level flow at values of q close to unity, and the dissipation function to maintain a level flow is given by... 

Assuming that the ATP-utilizing processes are driven by the phosphate potential, X3=Xh and a linear relation between the net rate of ATP utilization and A, we have... 

Michaelis-Menten equation shows that the enzyme reactions in certain regions can be approximated by linear kinetics. Stucki (1984) demonstrated that variation of the phosphate potential at constant oxidation potential yields linear flow-force relationships in the mitochondria. Through linear flow-force relationships, cells may optimize their free energy production and utilization by lowering their entropy production and hence exergy losses at stationary states. 

The matrix of the phenomenological coefficients must be positive definite for example, for a two-flow system, we have L0 > 0, Ip >0, and Z/.p Z,pZpo > 0.1,0 shows the influence of substrate availability on oxygen consumption (flow), and Ip is the feedback of the phosphate potential on ATP production (flow). The cross-coupling coefficient Iop shows the phosphate influence on oxygen flow, while Zpo shows the substrate dependency of ATP production. Experiments show that Onsagers s reciprocal relations hold for oxidative phosphorylation, and we have Iop = Zpo. 

Here, JL is the net rate of ATP consumed and A is the driving force. If we assume that the ATP-utilizing process is driven by the phosphate potential Xp, and JL is linearly related to Xp, then we have JL = LXp. Here, L is a phenomenological conductance coefficient. The dissipation caused by the load is. /LA p = LX2, and the total exergy loss becomes... 

This shows a measure for the efficiency gain in linear mode operation. The efficiency in linear modes depends on only q (Eq. (11.149)), while the efficiency in nonlinear modes depends on input force X0 besides q. In nonlinear regions, the efficiency decreases at high values of input force, and the force ratio at optimum operation xoptnl is shifted towards the level flow where x = 0. In oxidative phosphorylation, the input force is the redox potential of the oxidizable substrates and the output force is the phosphate potential. If these two forces are balanced, the system operates close to reversible equilibrium. Experiments show that in mitochondria, q < 1, and the input force is well above 50RT. For a fully coupled system in the nonlinear region of a single force, the phosphate potential Xp would be very small. However, a dissipative structure can only be maintained with a considerable Xp. On the other hand, in the linear mode of operation, optimum force ratio xopt does not depend on the input force (Eq. (11.163)). 

Within the framework of the theory of dissipative structures, thermodynamic buffering represents a new bioenergetics regulatory principle for the maintenance of a nonequilibrium conditions. Due to the ATP production in oxidative phosphorylation, the phosphate potential is shifted far from equilibrium. Since hydrolysis of ATP drives many processes in the cell, the shift inXp to far from equilibrium results in a shift of all the other potentials into the far from equilibrium regime. 

Perhaps it is the Na cycle that is responsible for the effect observed by Michel and Oesterhelt[109] (see also [110]) who reported that the protonophorous uncoupler abolishes A/Ih+ at much lower concentrations than those affecting the phosphate potential. 

Aue WP, Roufosse AH, Gitmcher MJ, Griffin RG (1984) Solid-state phosphorus-31 nuclear magnetic resonance studies of synthetic solid phases of calcium phosphate potential models of hone mineral. Biochemistry 23 6110-6114... 

Fig. 21.10. The concentration of ADP (or the phosphate potential -[ATP]/[ADP][PJ) controls the rate of oxygen consumption. (1) ADP is phosphorylated to ATP by ATP synthase. (2) The release of the ATP requires proton flow through ATP synthase into the matrix. (3) The use of protons from the intermembrane space for ATP synthesis decreases the proton gradient. (4) As a result, the electron transport chain pumps more protons, and oxygen is reduced to H2O. (5) As NADH donates electrons to the electron transport chain, NAD" is regenerated and returns to the TCA cycle or other NADH-producing pathways.

The difference in extramitochondrial and intramitochondrial ATP/ADP ratio is observed not only in isolated mitochondria but also in intact cells [44-46]. It allows the symbiosis of the intra- and extramitochondrial ATP systems which have to operate at different phosphate potentials (40). 

According to Holian et al. [53], however, respiration in tightly coupled mitochondria is controlled by the extramitochondrial ATP/ADP XP ratio (the phosphate potential) rather than by ATP/ADP. Since Pj is not involved in ADP transport it was concluded that ADP transport could not be rate-limiting. However, since under flux conditions both Pj and ADP have to enter to allow exit of ATP, it will be impossible to uncouple the effect of P, and adenine nucleotide transport. This... 

Van der Meer et al. [59] have described the regulation of mitochondrial respiration on the basis of the principles of irreversible thermodynamics. According to these authors, and thus in contrast to the view of Holian et al. [53], the entire system of oxidative phosphorylation in the hepatocyte is displaced from equilibrium. They observed a linear relationship between the rate of oxygen consumption and the affinity of the entire oxidative pho.sphorylation system, a term which includes the cytosolic phosphate potential, the mitochondrial NADH/NAD ratio and the partial pressure of oxygen. They concluded that the adenine nucleotide translocator may be a rate-limiting step in cellular oxidative phosphorylation. 

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