A simple enzymatic reaction is a substrate (S) binding to an enzyme (E) and forming an enzyme-substrate complex (ES). This is followed by an irreversible step to form the product (P). The rate constant k23 is also known as kcat, which is typically the first-order irreversible step in the formation of the product (Fig. 5.1).
b Mechanism-based inhibition k12 k23 k„„. E + S ES-23 Intermediate-cat E + P
Figure 5.1. (a) Overall conversion of substrate (S) to product (P) by enzyme (E). k12 is a rate constant for the formation of enzyme-substrate complete (ES) and k21 is a rate constant for the reverse direction. k23 (or kcat) is the rate constant for the formation of the product, which is considered irreversible. (b) Overall conversion of a suicide substrate (S) to inactivate the enzymes.
Assuming that the formation of the ES complex is fast relative to the rate of formation of P, the kinetics for this reaction, also known as Michaelis-Menten kinetics, is described as:
inact v = reaction velocity.
Vmax — maximum reaction velocity (at saturation) and equals ^23 x [E].
Km — The Michaelis-Menten constant and is defined as the substrate concentration at half Vmax and equals (k21+k23)/k12 (Table 5.1).
Table 5.1. Linear transformations of the Michaelis-Menten equation for the diagnostics of enzyme kinetics
Equation y-axis Slope x-intercept y-intercept
Km Vmax 1
v Vmax V
Km Vma x-axis k is a reaction rate constant and K is an equilibrium constant.
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