Degree of coupling

Two stationary states in the coupled processes can be identified as the level flow where A = 0, and the static head where J, = 0. Examples of the static head are open-circuited fuel cells and active transport in a cell membrane, while examples of the level flow are short-circuited fuel cells and salt and water transport in kidneys. 

Equation (7.66) shows that the ratio of flows 17 varies with the ratio of forces A. As the quantity LU]/(LqiILu)U2 approaches zero, each flow becomes independent, and we have the ratio of flows approaching rj - (Lqq/Lu)A. If L q/(LqqL )V2 approaches to 1, then the two flows are not associated with the forces, and the ratio of flows approaches a fixed value when rj - (LqqILx ])V2. This is the case where the matrix of the phenomenological coefficients becomes singular. The ratio 

Equation (7.69) indicates that for the known values of z and A, the ratio of flows is determined by the degree of coupling q. With complete coupling, A is equal to z and q becomes +1 or -1. The value of A may be negative when the chemical potential may a have negative value due to the nonideality of the mixture. In nonideal systems, the change 

5 COUPLING IN LIQUID MIXTURES 7.5.1 Coupling in Binary Liquid Mixtures 

For a binary fluid at mechanical equilibrium and for diffusion based on the mass-average velocity, we can now establish a set of phenomenological equations (Eqs. 7.6 and 7.7) with nonvanishing cross coefficients, and hence represent the coupled heat and mass flows 

---

DR. MARSHALL NEWTON (Brookhaven National Laboratory) The Landau-Zener theory in the weak-coupling regime may be derived by perturbation theory, as Dr. Sutin mentioned earlier. The complete derivation is much more general than the perturbation theory, and allows one to include an arbitrary degree of coupling. Thus, one can go continuously from nonadiabatic to the adiabatic limits. 

However, the efficiency is clearly not a constant it depends on how the system is operated (i.e., on the ratio of the forces AjlJA). Thus when A/x+ is zero ( level flow ), the efficiency is zero. Similarly, when Ajxt assumes such a value that J is brought to a halt ( static head, also known as state 4 in oxidative phosphorylation), the efficiency is also zero. Between these two limiting states the efficiency passes through a maximum. The value of rjmax depends on a single parameter, the degree of coupling q [Kedem and Caplan, Trans. Faraday Soc., 61, 1897 (1965)] ... 

Fig. 3. Dependence of efficiency on the force ratio. Plot of equation (5) for values of the degree of coupling indicated in the figure.

This necessary and sufficient condition called conductance matching of oxidative phosphorylation relates the ratio of load and phosphorylation conductance to the degree of coupling.1 Thus, for any given degree of coupling and value of the conductance of phosphorylation, we can exactly... 

Let us first consider the problem of an appropriate degree of coupling of oxidative phosphorylation in the cell. The solution to this question depends entirely on what output function is to be optimized. We might for example require a maximal net flow of ATP at optimal efficiency (Jp) opt. As is evident from Fig. 4 there is a unique degree of coupling qf, which corresponds to the maximum of this output function (see also Table I). Such a low value of the degree of coupling has never been experi-... 

TABLE I. Physiologically Meaningful Values of the Degree of Coupling ... 

Figure 4 shows that the economic net rate of ATP synthesis (VPT))opt as well as the economic output power (JpXpTi)opt at optimal efficiency both assume a maximum at the unique values of the economic degrees of coupling qfc and qep, respectively (Table I). 

On these theoretical curves two sets of experimental data are inserted the cytosolic adenine nucleotide concentrations measured in livers from fed rats (F) and starved rats (H).5 In the livers of the fed rats the degree of coupling is astonishingly close to cfif (Table I). These livers have been regarded to be in a metabolic resting state. 7 Hence, for the metabolic resting state, the maximization of the economic output power seems to be of importance. In contrast, in the livers from starved rats the degree... 

Fig. 5. Steady-state cytosolic adenine nucleotide concentrations. Plot of equations (10)-(14) as a function of the degree of coupling in the interval qe(0.9,l). Values of the parameters AGj hos = 8.5 kcal/mole, AGak = 0.15 kcal/mole, Pj = 0.008 M, Xa = 50 kcal/mole, Z = 3, 0 = l. Inserted points experimental values from perfused livers.5 Normalized plots with 2=1.

Fig. 13. Dependence of optimal force ratio on input force. The force ratio jrop, for optimal efficiency states in the previous figures were plotted as a function of A o for the values of the degrees of coupling indicated in the figure. Normalized by b = c (l + l) and -y = 1.

---