go from starting material to product, and the denominator consists of a sum of terms describing each of the states in which the catalyst exists (and 1 corresponds to the free catalyst). For the simplest case where one substrate goes to one product through a single intermediate: = In the slightly more complex situation where two substrates bind in sequence followed by product release: = In the case of the simple pre-equilibrium conditions described above, the catalyst resting state is either entirely or partially (depending on the magnitude of the equilibrium constant) the substrate bound complex. Saturation kinetics Saturation conditions can be viewed as a special case of pre-equilibrium conditions. At the concentration of substrate examined, formation of the catalyst-substrate complex is rapid and essentially irreversible. The catalyst resting state consists entirely of the bound complex, and [A] is no longer present in the rate law; changing [A] will have no effect on reaction rate because the catalyst is already completely bound and reacting as rapidly as k2 allows. The simplest case of saturation kinetics is the well-studied Michaelis-Menten model for enzyme kinetics. Changes in catalyst resting state While a reaction may exhibit one set of kinetic behavior at early conversion, that behavior may change due to: changes in catalyst resting state influenced by changing substrate concentrations multiple or changing mechanisms influenced by substrate or product concentrations catalyst activation (an initiation period) product inhibition irreversible (or reversible) catalyst death In the case of saturation kinetics described above, provided that [A] is not present in a large excess relative to [B], saturation conditions will only apply at the beginning of the reaction. As the substrate is consumed, the concentration decreases and eventually [A] is no longer sufficient to completely overwhelm [Cat]. This is manifested by a gradual change in rate from 0-order to some higher (i.e. 1st, 2nd, etc.) order in [A]. This can also be described as a change in catalyst resting state from the bound form to the unbound form over the course of the reaction. In addition to simply slowing the reaction, a change in catalyst resting state over the course of the reaction may result in competing paths or processes. Multiple mechanisms may be present to access the product, in which case the order in catalyst or substrate may change depending on the conditions or point in the reaction. A particularly useful probe for changes in reaction