# Km and kcat relationship advice

The Michaelis-Menten equation can then be rewritten as V= Kcat [Enzyme] [S] / ( Km + [S]). Kcat is equal to K2, and it measures the number of substrate. Skip the theory and go straight to: How to determine Km and Vmax reaction with a single substrate shows a linear relationship between the rate of formation of. I'm trying to check the substrate specificity of an enzyme and calculated the Vmax and Km for each substrate. In enzyme kinetics (Michaelis-Menten model), is Vmax dependent on the enzyme concentration? Does Km (Michaelis constant) vary with enzyme concentration?.

An enzyme with a low Km relative to the physiological concentration of substrate, as shown above, is normally saturated with substrate, and will act at a more or less constant rate, regardless of variations in the concentration of substrate within the physiological range.

An enzyme with a high Km relative to the physiological concentration of substrate, as shown above, is not normally saturated with substrate, and its activity will vary as the concentration of substrate varies, so that the rate of formation of product will depend on the availability of substrate.

If two enzymes, in different pathways, compete for the same substrate, then knowing the values of Km and Vmax for both enzymes permits prediction of the metabolic fate of the substrate and the relative amount that will flow through each pathway under various conditions. In order to determine the amount of an enzyme present in a sample of tissue, it is obviously essential to ensure that the limiting factor is the activity of the enzyme itself, and not the amount of substrate available.

This means that the concentration of substrate must be high enough to ensure that the enzyme is acting at Vmax. In practice, it is usual to use a concentration of substrate about 10 - fold higher than the Km in order to determine the activity of an enzyme in a sample. If an enzyme is to be used to determine the concentration of substrate in a sample e.

The relationship is defined by the Michaelis-Menten equation: A number of ways of re-arranging the Michaelis-Menten equation have been devised to obtain linear relationships which permit more precise fitting to the experimental points, and estimation of the values of Km and Vmax.

There are advantages and disadvantages associated with all three main methods of linearising the data. The Lineweaver-Burk double reciprocal plot rearranges the Michaelis-Menten equation as: These are the points at which the precision of determining the rate of reaction is lowest, because the smallest amount of product has been formed.

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The Eadie-Hofstee plot rearranges the Michaelis-Menten equation as: However, it has the disadvantage that v, which is a dependent variable, is used on both axes, and hence errors in measuring the rate of reaction are multiplied, resulting in lower precision of the estimates of Km and Vmax The Hanes plot rearranges the Michaelis-Menten equation as: An equation with a high Km indicates that the enzyme does not bind as efficiently with the substrate, and Vmax will only be reached if the substrate concentration is high enough to saturate the enzyme.

As the concentration of substrates increases at constant enzyme concentration, the active sites on the protein will be occupied as the reaction is proceeding. When all the active sites have been occupied, the reaction is complete, which means that the enzyme is at its maximum capacity and increasing the concentration of substrate will not increase the rate of turnover. Here is an analogy which helps to understand this concept easier.

Vmax is equal to the product of the catalyst rate constant kcat and the concentration of the enzyme. Kcat is equal to K2, and it measures the number of substrate molecules "turned over" by enzyme per second. The reciprocal of Kcat is then the time required by an enzyme to "turn over" a substrate molecule.

Catalytic Efficiency of Enzymes (kcat/Km)

The higher the Kcat is, the more substrates get turned over in one second. Km is the concentration of substrates when the reaction reaches half of Vmax. A small Km indicates high affinity since it means the reaction can reach half of Vmax in a small number of substrate concentration.

## Structural Biochemistry/Enzyme/Michaelis and Menten Equation

This small Km will approach Vmax more quickly than high Km value. The enzyme efficiency can be increased as Kcat has high turnover and a small number of Km.

Taking the reciprocal of both side of the Michaelis-Menten equation gives: To determined the values of KM and Vmax. The double-reciprocal of Michaels-Menten equation could be used.