Nonequilibrium linear behavior of biological systems. Existence of enzyme-mediated multidimensional inflection points

The linear phenomenological equations of nonequilibrium thermodynamics are limited theoretically to near equilibrium although a number of biological systems have been shown to exhibit a "linear" relationship between steady-state flows and conjugate thermodynamic forces outside the range of equilibrium. We have found a multidimensional inflection point which can exist well outside the range of equilibrium around with enzyme-catalyzed reactions exhibit "linear" behavior between the logarithm of reactant concentrations and enzyme catalyzed flows. A set of sufficient conditions has been derived which can be applied to any enzyme mechanism to determine whether a multidimensional inflection point exists. The conditions do not appear overly restrictive and may be satisfied by a large variety of coupled enzyme reactions. It is thus possible that the linearity observed in some biological systems may be explained in terms of enzyme operating near this multidimensional point.