# Physical Chemistry : Michaelis-Menton Analysis

## Example Questions

### Example Question #1 : Michaelis Menton Analysis

Which of the following is true regarding the Michaelis constant?

It is the substrate concentration at which the reaction rate is half of maximum

It is the enzyme concentration at which the reaction rate is half of maximum

It is the substrate concentration at which the reaction rate is at maximum

It is the enzyme concentration at which the reaction rate is at maximum

It is the substrate concentration at which the reaction rate is half of maximum

Explanation:

Michaelis constant, or , is defined as the concentration of substrate at which the reaction rate is half the maximum (). It is a useful measure of how much substrate is needed for reaction to proceed rapidly. A reaction with a high Michaelis constant will need lots of substrate to reach high reaction rates whereas a reaction with low Michaelis constant will need small amounts of substrate to reach high reaction rates.

### Example Question #2 : Michaelis Menton Analysis

Which of the following will have the greatest increase in reaction rate?

Increasing the substrate concentration by a factor of 2

Increasing the maximum velocity by a factor of 2

Increasing the Michaelis constant by a factor of 2

Decreasing the substrate concentration by a factor of 2

Increasing the maximum velocity by a factor of 2

Explanation:

Reaction rate, according to Michaelis-Menten model is as follows.

where  is reaction rate,  is maximum reaction rate,  is substrate concentration, and  is the Michaelis constant. If we analyze the given options, we will observe that the greatest increase in  occurs when  is doubled (increased by a factor of 2). Increasing substrate concentration by a factor of 2 will have nearly the same effect; however, since  is also found in the denominator it will only slightly contribute to an increase in .

Note that the units for  is molarity,  is molarity, and  is . Solving for  will give us units of .

### Example Question #3 : Michaelis Menton Analysis

Consider the following reaction parameters.

Substrate concentration =

Michaelis constant =

What can you conclude about the reaction rate?

The reaction rate is

The reaction rate cannot be determined from the given information

The reaction rate is

The reaction rate is

The reaction rate is

Explanation:

To solve this problem we need to use the Michaelis-Menten equation.

where  is reaction rate,  is maximum reaction rate,  is substrate concentration, and  is the Michaelis constant. If we plug in the given values we get a reaction rate of

Note that the Michaelis-Menten equation implies that the  will never exceed . Regardless of how high the substrate concentration is, the reaction rate will approach  but will never equal or exceed it. You can try this by substituting very high values for substrate concentration. The  will get very close to 0.2 () but will never equal or exceed it.

### Example Question #4 : Michaelis Menton Analysis

The Michaelis-Menten model implies that __________ the Michaelis constant will __________ the reaction rate.

decreasing . . . not change

increasing . . . decrease

decreasing . . . decrease

increasing . . . not change

increasing . . . decrease

Explanation:

The Michaelis-Menten equation is as follows.

Where  is reaction rate,  is maximum reaction rate,  is substrate concentration, and  is the Michaelis constant. Since the Michaelis constant, , is in the denominator, the reaction rate is inversely proportional to the Michaelis constant; therefore, increasing the Michaelis constant will decrease the reaction rate.