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Hill Coefficient: MCAT Test Prep (Simple)

June 2, 2022
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The Hill Coefficient DefinedHow Is the Hill Coefficient Calculated?Applying the Hill Coefficient to the MCAT

”Akhil

Reviewed by:

Akhil Katakam

Third-Year Medical Student, Lewis Katz School of Medicine at Temple University

Reviewed: 6/2/22

Studying for the MCAT and wondering what the Hill coefficient is and how it relates to enzymes? Read on to learn everything you should know about the Hill coefficient for the MCAT.

Enzymes are protein catalysts responsible for increasing the rate of chemical reactions in our cells. These reactions allow our bodies to carry out essential functions such as digestion, breathing, destroying toxins, and more. Enzyme deficiencies can lead to the underproduction of necessary biological compounds, underlying various health issues.

Hopefully, the above paragraph convinced you of the importance of enzyme knowledge as an aspiring doctor and why the MCAT will heavily test you on them. This includes your understanding of the Hill coefficient and its relation to different types of enzymes. Read on to learn what you should know about the Hill coefficient for the MCAT.

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The Hill Coefficient Defined

First, let’s cover some basic terminology. To start the process of speeding up a chemical reaction, enzymes bind to reactant molecules called substrates. These substrates bind to an enzyme’s active site or binding site. Once bound, the enzyme will catalyze a chemical reaction. 

Once the reaction is finished, the enzymes release molecular product(s). This process is summarized below: 

Infographic outlining the Hill Coefficient chemical reaction process

Many enzymes have more than one binding site, allowing them to bind to multiple substrates. However, different enzymes have different affinities for binding to more than one substrate. In other words, the binding of one substrate to one binding site can impact the binding of a second substrate. 

The Hill coefficient for the MCAT is a unitless measure of this cooperativityof substrate binding sites. The three types of cooperative binding and their associated Hill coefficients are summarized below:

Table outlining the three types of cooperative binding and their associated Hill coefficients

Formulated by Archibald Hill in the early 1900s, the Hill coefficient was initially used to characterize the binding of oxygen to hemoglobin, which is a protein molecule in our red blood cells that transports oxygen. 

A hemoglobin molecule contains four binding sites that each bind to one oxygen molecule. Hemoglobin has a Hill coefficient of 2.8, meaning that the binding of oxygen at one binding site causes a conformational change in the other sites that increases their likelihood of also binding to oxygen.

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How Is the Hill Coefficient Calculated?

The Hill coefficient for the MCAT can be found in the Hill equation, a version of which is below:

Infographic outlining the Hill equation

Where Θ is the fraction of the binding sites occupied by a substrate

[S] is the total substrate concentration 

n is the Hill coefficient

Kd is the dissociation constant

This Hill Equation can be used to model the different types of cooperative binding with the Hill coefficient, n, as the slope. Positive cooperativity (green) takes on a characteristic sigmoidal curve.

Graph outlining how the Hill Equation can be used to model the different types of cooperative binding with the Hill coefficient, n, as the slope. Positive cooperativity (green) takes on a characteristic sigmoidal curve.

Note that cooperativity can also be graphed by plotting reaction velocity against substrate concentration.

Applying the Hill Coefficient to the MCAT

Be prepared to define what the Hill coefficient is and to recall the information summarized in the above table for the MCAT. For instance, a question may assess whether you know that a Hill coefficient of 2.0 corresponds to positive cooperativity.

You should also be able to recognize the curves associated with the different types of cooperativity, per the graph above.

The MCAT will most likely not test you on the Hill equation, so don’t worry about that too much. Understanding it generally, however, can help you grasp the above graph. 

Reviewing what the Hill coefficient was first used for (to measure the cooperativity of hemoglobin) is a great place to start in understanding the Hill coefficient. Of course, enzyme practice questions are also a classic study strategy you should be using to assess your understanding.

It’s important to note that there is more about enzymes on the MCAT than just the Hill coefficient and cooperativity. This includes questions on activation energy, types of enzymes, the Michaelis-Menten equation, and more.

Final Thoughts

Given their biological importance, expect that you’ll encounter quite a few questions on enzymes on the MCAT. Some of these questions will assess your understanding of enzymes that display cooperative behavior, which is measured by the Hill coefficient. 

Like with any MCAT section, pace yourself and focus on understanding the “why” behind what you’re learning instead of just the “what.” Don’t get too bogged down by the details but make sure you understand the logic behind the Hill coefficient for the MCAT.

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