From Ф1I = – Ф2II, and Lc1I(A1I)2 = -Lc2II(A2II)2, LIc1 = – LIIc2 is obtained. That is, the partial conductances of two coupled reactions in series are opposite and equal, if under conditions of steady state cycling the magnitudes of the output force of reaction I and the input force of reaction II are equal. Ф1I = -Ф2II can also be expressed in terms of the steady state flux of cycling and of resistances Rc1I = 1/Lc1I, and Rc2II = 1/Lc2II, yielding Rc1IJ2 + Rc2IIJ2 = 0. It follows that at steady state cycling between two coupled reactions, the sum of the resistances in that cycle must vanish,
Inhibitors,research,lifescience,medical i.e., that the steady state flux through a cycle between two coupled reactions always occurs at zero overall resistance. Cycling is driven solely by A2I + A1II(A1II negative). Because both reactions are coupled, Inhibitors,research,lifescience,medical the conductance (resistance) of the whole cycling process is brought about by both partial (in series) conductances associated with the input and load affinity, respectively. In oxidative phosphorylation (OP), as described in detail in , a proton cycle is
generated over the inner Inhibitors,research,lifescience,medical mitochondrial membrane. At steady state, coupled outward proton pumping by redox (NADred and FADred) reactions of the respiratory chain (JNA and JFA) equals the back flow of a given fraction (QH) of protons through ATP synthase (JSY) and ATP/ADP learn more exchange (JAE) plus H/Pi symport (JPi). Both partial conductances, , and (5) are opposite and equal. For the first reaction (index R) , and Inhibitors,research,lifescience,medical for the second , with vR = vs+1 (total coupling; ARo = affinity of JNA plus JFA; vR = vs+1 = 4protons/extent of reaction). The remaining fraction of protons (QrH) flows back (driven by) through several parallel conductances given by the proton
leak flux, JPL, mitochondrial Na+/Ca2+ exchange (with Na+/H+ contracted to H+/Ca2+ exchange), 2JHCE, and the malate-aspartate shuttle, JMS. The partial conductance of this residual proton efflux and the sum of conductances of back flowing fluxes, are also of opposite equality. Analogously, partial conductances of ATP cycling Inhibitors,research,lifescience,medical through the potentials of mitochondrial ATP (ATPm) production plus ATP transport (contracted to A1I), and of cytosolic ATP splitting (A2II) can be formulated. Opposite equality of partial conductances is also fulfilled for this cycle (the above results were old obtained by using the simulation SIMGlOx from reference ). For a further illustration, an analytically solvable example is given in the Appendix section. Simple electric circuits consisting of one battery connected to an outer conductance, or of two batteries in series, are analysed. These examples show very clearly the behavior of coupled in series reactions. Further evidence of such an equality of conductances comes from the known fact that for a coupled reaction with an attached load, conductance matching (LLd = Lc) is needed to achieve a maximal power output .