The Rate-Limiting Step RLS Approximation

Consider a reversible isomerization reaction catalyzed by an enzyme E. The reaction will be represented as 

In the biochemical literature, a reactant fiequently is referred to as a substrate. The symbol S is used in the above reaction, in deference to this tradition. This reaction mightrepresent, for example, the reversible isomerization of glucose to fructose, which is central to the process for producing ttie sweetener known as high-fructose com syrup. Glucose and fructose contain approximately the same number of calories. However, fructose is about five times sweeter to the taste. Therefore, high-fiuctose com syrup is widely used as a sweetener in, e.g., soft drinks. 

Let s assume that the overall reaction proceeds according to the sequence of elementary reactions 

In this sequence, E represents the free enzyme, E-S represents an enzyme that is bound to a molecule of substrate (an enzyme-substrate complex), and E-P represents an enzyme that is bound to a molecule of product (an enzyme-product complex). Reactions (5-H), (5-1), and (5-J) must be written as reversible because the overall reaction is reversible. If any one of the reactions leading from reactants to products were irreversible, there would be no pathway leading from the products back to the reactants, and the overall reaction would not be able to proceed in the reverse direction, i.e., it would be irreversible. 

The sequence of elementary reactions shown above is closed, and there are three active centers E, E--S, and E-P. 

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This picture leads to a tool, called the rate-limiting step (RLS) approximation, that is very useful in chemical kinetics. The figure suggests that Reactions 1 (5-H) and 3 (5-J) are essentially in chemical equilibrium because the rates of the forward and reverse reactions are almost equal. The equilibrium expressions for these fast reactions then can be used to solve for the concentrations of the active centers, instead of using the more cumbersome SSA. The rate of the overall reaction can be written in terms of the slow reaction, which is referred to as the rate-limiting step (or rate-determining step or rate-controlling step). 

The rate-limiting step (RLS) approximation also can be used to derive the form of the rate equation. The RLS Approximation is based on the assumption that a single RLS exists, and diat it has been identified correedy. The RLS approximation contains all of the assumptions of the SSA, and is less general than the SSA. 

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