# Biochemistry : Michaelis-Menten Equation

## Example Questions

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### Example Question #1 : Michaelis Menten Equation

For a given enzyme catalyzed reaction, the Michaelis constant is 0.6mM and the substrate concentration is 1.0mM. What is the fractional saturation of the enzyme under these conditions?

Explanation:

The fractional saturation of an enzyme is defined as the amount of enzyme that is bound to substrate divided by the total amount of enzyme. To calculate the fractional saturation, we'll need to use the Michaelis-Menton equation:

In addition, we'll need to define the rate and maximum rate in terms of enzyme concentrations:

From the above equations, we can calculate the fractional saturation of the enzyme:

### Example Question #1 : Michaelis Menten Equation

Which of the following is true about the Michaelis constant for any given enzyme?

It increases as the enzyme’s specificity for the substrate decreases

It is equal to

None of the other answers are true

It increases as the enzyme’s affinity for the substrate decreases

It is independent of the type of substrate

It increases as the enzyme’s affinity for the substrate decreases

Explanation:

The Michaelis constant, , is not equal to , but is rather the substrate concentration when the reaction rate is .  is an inverse measure of a substrate’s affinity for the enzyme. So as the affinity decreases,  increases. Enzyme specificity is measured by a different constant, , the specificity constant. Although  and specificity are in an inversely proportional relationship,  does not necessarily increase as specificity decreases; rather, , also known as the catalytic constant, could decrease proportionally for a given enzyme. The Michaelis constant, being a measure of affinity, is going to differ for different types of substrates, depending on their shape and other features that influence their ability to bind to an enzyme.

### Example Question #1 : Michaelis Menten Equation

What is the ratio of  when  ?

Cannot be determined

Explanation:

This question is answered using the Michaelis-Menten equation:

Rearrange the equation to find the ratio of interest.

Plug in  for  and simplify.

### Example Question #1 : Michaelis Menten Equation

What does Michaelis-Menten model assume?

No intermediate is formed

enzyme, substrate, and enzyme-substrate complex are in equilibrium

Enzyme-substrate complex decomposes to product only

There are no enzyme catalyzed reactions

The rate limiting step may not be present

enzyme, substrate, and enzyme-substrate complex are in equilibrium

Explanation:

In this model, an intermediate is formed when the substrate binds to an enzyme.  The intermediate decomposes to an enzyme and a product, not just the product alone. The model requires enzyme-catalyzed reactions that include a rate limiting step of the enzyme-substrate complex breaking down into the enzyme and product.

### Example Question #5 : Michaelis Menten Equation

Given an enzyme with  of 0.5mM. at what substrate concentration will the velocity of the enzyme reach   of the

Explanation:

To solve this, we need the solve for  in the Michaelis-Menten equation:

We know the following information:

Plug in these numbers and solve for substrate concentration.

### Example Question #2 : Michaelis Menten Equation

Suppose that an enzyme mixture contains an enzyme with a michaelis constant of . If the substrate concentration in this mixture is , what is the fractional saturation of this enzyme mixture?

Explanation:

This question is asking us to determine the fractional saturation of a solution containing enzyme and substrate. Let's start by considering what we have, and what we are trying to solve for.

We know that the substrate concentration is  and we also know that this enzyme has a Michaelis constant of .

Also, let's consider what fractional saturation is. Fractional saturation refers to the proportion of enzyme molecules in a solution that are bound to substrate. This value can range from  (all enzymes are not bound to substrate) to  (all enzymes are bound to, or saturated with, substrate).

So, we are looking to calculate the number of enzyme-substrate complexes divided by the total amount of enzyme in solution, which we can express as . We can also relate these terms by the following equations.

Dividing these equation by each other, we obtain:

Furthermore, we can relate these terms by considering the Michaelis-Menten equation:

Or, written another way:

And combining everything we have done so far, we have:

And plugging in values, we can solve:

### Example Question #7 : Michaelis Menten Equation

Which of the following is false about the Michaelis-Menten equation?

The maximum rate of reaction is reached as the substrate concentration increases indefinitely.

Velocity is proportional to the turnover number.

Velocity is proportional to substrate concentration.

Velocity is proportional to enzyme concentration.

Velocity is inversely proportional to enzyme concentration.

Velocity is inversely proportional to enzyme concentration.

Explanation:

The Michaelis-Menten equation can be expressed as:

The velocity is therefore proportional to the enzyme concentration , not inversely so.  is also referred to as the turnover number. As the substrate concentration  keeps increasing, then we end up with a steady state in which all the enzyme is bound. At this point, the maximum velocity, , has been reached.

### Example Question #1 : Michaelis Menten Equation

An enzyme with a  value of  has a reaction rate of  at a substrate concentration of . What is the maximum reaction rate that this enzyme can achieve when it is saturated with substrate?

Explanation:

For this question, we're provided with the michaelis constant for an enzyme, as well as the reaction rate for that enzyme at a particular substrate concentration. We're asked to determine the maximum possible reaction rate that this enzyme can achieve when it is saturated with substrate.

To solve this problem, we'll need to use the michaelis-menten equation, which is expressed as follows.

Then, we can rearrange the equation above in order to isolate the  term.

Now, we can plug in the values given to us in the question stem in order to solve for our answer.

### Example Question #2 : Michaelis Menten Equation

Which of the following will increase the reaction rate of an enzymatic reaction?

II. Increasing the substrate concentration

III. Decreasing the affinity of substrate to the enzyme

I only

I and III

I and II

II only

II only

Explanation:

Reaction rate of an enzymatic reaction can be calculated using the Michaelis-Menten equation.

where  is the reaction rate, is the maximum reaction rate,  is the substrate concentration and  is the Michaelis constant.

Recall that adding a competitive inhibitor will increase the  but will not alter the . From the equation, we can see that increasing  will decrease the reaction rate; therefore, adding a competitive inhibitor will decrease reaction rate.

Substrate concentration is found in both the numerator and denominator of the equation; however, the substrate concentration is multiplied in the numerator whereas it is added in the denominator. This means that increasing substrate concentration will increase the numerator more than the denominator; therefore, increasing substrate concentration will increase reaction rate.

Affinity between enzyme and substrate is determined by . This constant is defined as the substrate concentration required to reach half the . Lowering  suggests that a lower substrate concentration is needed to reach the same half  (lower substrate concentration is needed because the affinity between enzyme and substrate increases and a more efficient reaction is carried out). This implies that lowering  increases the affinity between substrate and enzyme; therefore,  and affinity are inversely related. Decreasing the affinity will increase the  and, subsequently, decrease reaction rate.

### Example Question #3 : Michaelis Menten Equation

What is the maximum reaction rate if adding  of substrate produces a reaction rate of ?