B7. Meaning of Kinetic Constants
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- 5103
It is important to get a "gut-level" understanding of the significance of the rate constants. Here they are:
- K_{m}: The Michaelis constant with units of molarity (M), is operationally defined as the substrate concentration at which the initial velocity is half of V_{max}. It is equal to the dissociation constant of E and S only in if E, S and ES are in rapid equilibrium. It can be thought of as an "effective" Kd in other cases.
- k_{cat}: The catalytic rate constants, with units of s^{-1} is often called the turnover number. It is a measure of how many bound substrate molecules turnover or form product in 1 second. This is evident from equation v_{0} = k_{cat}[ES]
- k_{cat}/K_{m}: Under condition when [S] << K_{m}, the Michaelis-Menten equation becomes v_{0} = (k_{cat}/K_{M})[E_{0}][S]. This really describes a biomolecular rate constant, with units of M^{-1}s^{-1}, for conversion of free substrate to product. Some enzyme have k_{cat}/K_{m} values around 10^{8}, indicating that they are diffusion controlled. That implies that the reaction is essentially done as soon as the enzyme and substrate collide. The constant kcat/Km is also referred to as the specificity constant in that it describes how well an enzyme can differentiate between two different competing substrates. (We will show this mathematically in the next chapter.)
Km values | ||
enzyme | substrate | Km (mM) |
catalase | H_{2}O_{2} | 25 |
hexokinase (brain) | ATP | 0.4 |
D-Glucose | 0.05 | |
D-Fructose | 1.5 | |
carbonic anhydrase | HCO_{3}^{-} | 9 |
chymotrypsin | glycyltyrosinylglycine | 108 |
N-benzoyltyrosinamide | 2.5 | |
b-galactosidase | D-lactose | 4.0 |
threonine dehydratase | L-Thr | 5.0 |
kcat values | ||
enzyme | substrate | k_{cat} (s^{-1}) |
catalase | H_{2}O_{2} | 40,000,000 |
carbonic anhydrase | HCO_{3}^{-} | 400,000 |
acetylcholinesterase | acetylcholine | 140,000 |
b-lactamase | benzylpenicillin | 2,000 |
fumarase | fumarate | 800 |
RecA protein (ATPase) | ATP | 0.4 |
Enzymes with kcat/Km values close to diffusion controlled (10^{8} - 10^{9} M^{-1}s^{-1}) | ||||
enzyme | substrate | kcat (s^{-1}) | Km (M) | kcat/Km (M^{-1}s^{-1}) |
acetylcholinesterase | acetylcholine | 1.4 x 10^{4} | 9 x 10^{-5} | 1.6 x 10^{8} |
carbonic anhydrase | CO_{2} | 1 x 10^{6} | 1.2 x 10^{-2} | 8.3 x 10^{7} |
HCO_{3}^{-} | 4 x 10^{5} | 2.6 x 10^{-2} | 1.5 x 10^{7} | |
catalase | H_{2}O_{2} | 4 x 10^{7} | 1.1 | 4 x 10^{7} |
crotonase | crotonyl-CoA | 5.7 x 10^{3} | 2 x 10^{-5} | 2.8 x 10^{8} |
fumarase | fumarate | 8 x 10^{2} | 5 x 10^{-6} | 1.6 x 10^{8} |
malate | 9 x 10^{2} | 2.5 x 10^{-5} | 3.6 x 10^{7} | |
triose phosphate isomeraser | glyceraldehyde-3-P | 4.3 x 10^{3} | 4.7 x 10^{-4} | 2.4 x 10^{8} |
b-lactamase | benzylpenicillin | 2.0 x 10^{3} | 2 x 10^{-4} | 1 x 10^{8} |