  In this paper, we perform a complete analysis of the kinetic behavior of the
general modifier mechanism of Botts and Morales in both equilibrium steady
states and non-equilibrium steady states (NESS). Enlightened by the
non-equilibrium theory of Markov chains, we introduce the net flux into
discussion and acquire an expression of product rate in NESS, which has clear
biophysical significance. Up till now, it is a general belief that being an
activator or an inhibitor is an intrinsic property of the modifier. However, we
reveal that this traditional point of view is based on the equilibrium
assumption. A modifier may no longer be an overall activator or inhibitor when
the reaction system is not in equilibrium. Based on the regulation of enzyme
activity by the modifier concentration, we classify the kinetic behavior of the
modifier into three categories, which are named hyperbolic behavior,
bell-shaped behavior, and switching behavior, respectively. We show that the
switching phenomenon, in which a modifier may convert between an activator and
an inhibitor when the modifier concentration varies, occurs only in NESS.
Effects of drugs on the Pgp ATPase activity, where drugs may convert from
activators to inhibitors with the increase of the drug concentration, are taken
as a typical example to demonstrate the occurrence of the switching phenomenon.
