Reciprocity or near-reciprocity of highly coupled enzymatic processes at the multidimensional inflection point

It has recently been demonstrated that coupled enzymatic processes may possess, for a particular choice of the state variables, multidimensional inflection points in thermodynamic force-flow space. The conditions for reciprocity in the linear region near such a reference state, which may be far from equilibrium, are of considerable interest. It is shown by examining the associated Hill diagrams that all cycles in which a given pair of forces act contribute a corresponding pair of symmetrical terms to the Jacobian matrix characterizing perturbations about this stationary state. To the extent that these cycles dominate--i.e., to the extent that the system is highly coupled--reciprocity or near-reciprocity will be obeyed. This would be expected to be the case in most biological systems.