Structural Biochemistry/Enzyme/Kcat/Km

k_cat,k_{d and} K_M == k_cat,k_d and K_M are terms helpful in the description of an enzyme that follows the Michaelis-Menten kinetics.

• k_cat is a constant that describes the turnover rate of an enzyme-substrate complex to product and enzyme. It is also the rate of catalyst with a particular substrate.
  

K_d is dissociation constant. which describe how affinite two reactants are in a reaction. The following reaction is an example to show dissociation constant:

                                k1

                     A + B      ↔   AB 

                                k-1

Where A and B are the two reactant, AB is the formed complex, k_-1 is the reverse constant rate, and k₁ is the forward constant rate. The dissociation constant is defined as: k_d=k_-1/k₁.
The smaller the dissociation constant is, the better two reactants can combine. Since the affinity of enzyme with substrate determines how favorable the reaction can form enzyme-substrate complex, k_d is often studied in Michaelis-Menten equation.

• K_M is the Michaelis constant that describes the amount of substrate needed for the enzyme to obtain half of its maximum rate of reaction.
  

Deriving from Michaelis-Menten equation: k_M=(k_-1+k_cat)/k₁
Since K_M, which is also referred as Michaelis constant, is an important constant to study the ability of catalysis reaction of enzyme with specific substrate. k_M can be separated into two parts:
a.k_d
The first step of catalysis kinetic is the binding between substrate and enzyme, which is also the rate determine step in the reaction. the better enzyme bind to substrate, the smaller k_dis, thus the smaller k_M is.
b.k_cat
The second step of catalysis kinetic is the forming of product. The larger k_cat is, the more favorable the reaction towards product, and the larger k_M is.
There seems to be a contradiction between k_d and k_cat in the Michelis constant equation: the better enzyme to the specific substrate, the smaller k_d is, and the larger k_cat is. However, what determine the performance of catalysis reaction is dissociation constant k_d, because the first step of the reaction--binding is the rate determine step, forming enzyme-substrate complex is the essential step to form product, thus k_d is the major factor to determine k_M
Together they show an enzymes preference for different substrates.
k_cat/K_M results in the rate constant that measures catalytic efficiency. This measure of efficiency is helpful in determining whether the rate is limited by the creation of product or the amount of substrate in the environment.
In situations where k_-1 (the rate at which substrate unbinds from the enzyme) is much greater than k₂ (the rate at which substrate converts to product), if the rate of efficiency is:

• HIGH, k_cat is much larger than K_M, and the enzyme complex converts a greater proportion of the substrate it binds into product. This increased conversion can be seen in one of two ways -- either substrate binds more firmly to the enzyme, a consequence of relatively low K_M, or a greater proportion of the substrate that is bound is converted before it dissociates, due to a large turnover rate k_cat.
• LOW, k_cat is much smaller than K_M, and the complex converts a lesser proportion of the substrate it binds into product.
  

k_cat/K_M measures the catalytic efficiency, though, only when the substrate concentration is much lower than the K_M. Looking at the enzyme/substrate catalytic reaction equation,

E+S↔ES->E+P

with the rate going towards ES being k₁, the rate going back towards E+S being k_-1, and the rate going towards product formation (E+P) being k₂ or k_cat, it is evident from

k_cat/K_M=[k_cat/(k_-1 + k_cat)]k₁

that even if k_cat is much greater than k_-1 (much product is forming) and there is great efficiency, the equation will still be limited by k₁, which is the rate of ES formation. This tells us that k_cat/K_M has a limit placed on efficiency in that it cannot be faster than the diffusion controlled encounter of an enzyme and its substrate (k1). Therefore, enzymes that have high k_cat/K_M ratios have essentially attained kinetic perfection because they have come very close to reaching complete efficiency only being limited by the rate at which they encounter the substrate in solution.

In cases near the limit, there may be attractive electrostatic forces on the enzyme that entice the substrate to the active site, known as Circe effects. Diffusion in solution can be partly overcome by confining substrates and products in the limited volume of a multienzyme complex. Some series of enzymes are associated into organized assemblies so that the product of one enzyme is rapidly found by the next enzyme.

References

Berg, Jeremy M. 2007. Biochemistry. Sixth Ed. New York: W.H. Freeman.