©1997 Gale Rhodes
Department of Chemistry
University of Southern Maine
Portland, Maine 04104-9300
Revised 2006/10/23
For all types of inhibition, the rate law for a Michaelis-Menten enzyme is
where "app" means the new or "apparent" value of Km and/or Vmax in the presence of I, the inhibitor.
The fraction of enzyme molecules bound to I can be expressed as a saturation fraction:
where Ki is the dissociation constant for the enzyme-inhibitor complex (EI). Therefore, the fraction of enzyme molecules that are free of I (and behaving normally) is
If Km and/or Vmax are affected by inhibition, they are increased or decreased in proportion to the fraction of enzyme molecules that are free of inhibitor. So Kmapp and Vmaxapp can be expressed in terms of (1-Yi) and the normal values of Km or Vmax , as shown in the table below, which also shows how to compute Ki for each type of inhibition.
|
Type of Inhibition |
|
|
|
|
Competitive |
|
|
|
|
Uncompetitive |
|
|
|
|
Noncompetitive (pure) |
|
|
|
|
Noncompetitive (mixed)* |
|
|
|
1) Can you derive the expressions in column 4 from the appropriate corresponding entries in columns 2 or 3?
2) CHALLENGE: For mixed inihibition,
the table shows you how to compute Ki from Vmax (in
the absence of inhibitor) and Vmaxapp (in the
presence of inhibitor).
Can you derive a formula for determining
Ki' from Km and
Kmapp?
* In mixed noncompetitive inhibition, Yi is the saturation fraction for EI, and Yi' is the saturation fraction for ESI. Yi is governed by Ki, and Yi' is governed by Ki'. If Ki = Ki', the inhibition is pure noncompetitive, because Yi = Yi', and Kmapp = Km.
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