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:

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.

This question is answered using the Michaelis-Menten equation:

Rearrange the equation to find the ratio of interest.

Plug in  for  and simplify.

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.

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.

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:

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.

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.

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.

The trick to this question is to notice that the  and the substrate concentration are the same. Recall that  is the substrate concentration required to reach half the maximum reaction rate. Since we are told that the substrate concentration and  are the same, we can conclude that that reaction rate of  is half the maximum reaction rate; therefore, the maximum reaction rate is .