Enzyme Kinetics

In a previous blog, we mentioned proteins are essentially micromachines that perform specialized functions necessary for life. Enzymes are one of these specialized machines, tasked with accelerating chemical reactions in order to keep up with the metabolism of an organism. In this sense, enzymes are biological catalysts, they act on a substrate to create a product. A quick example of this would be the digestive enzyme pepsin, in charge of breaking down proteins from food into smaller peptides. In this example, the substrate are the dietary proteins and the product would be the peptides. Without pepsin, the small intestine would not be able to absorb the nutrients from the ingested food.

When biochemists first started studying biochemical reactions, they found something unusual. Typical chemical reactions tend to be faster when the reactants (e.g. dietary proteins) are more concentrated, and their speed scales with concentration in a straightforward way. But this isn’t the case for the chemical reactions found in biochemistry. While biochemical reactions do get faster with an increase in reactant concentration, the increase in speed becomes lower and lower until it’s effectively nothing.

How a reaction’s speed scales with concentration of a reactant is given by the “order” of the reactant in that reaction. Reactions that move at the same rate no matter what a substrate’s concentration is are called “zero-order” reactions, and those that scale linearly with concentration are called “first-order” reactions. There are second orders, third orders, and so on, but those types of reactions are less common. Reactions generally have a set order to them that doesn’t change, but biochemical reactions can gradually “switch” between 1st and 0th-order kinetics.

Michaelis-Menten kinetics is a widely used model to figure out the order of enzyme reactions. In plain words, an enzyme E binds to the substrate S in a reversible process, forming the ES enzyme-substrate complex. After binding, however, an irreversible reaction occurs yielding the starting enzyme and the product P. The following equation represents the overall process:

The double-arrows indicate the reversible step and the single arrow is the irreversible reaction. The formula to describe the rate of these catalytic reactions in this kinematic model is the Michaelis-Menten equation:

Here, v is the rate of the reaction, Vₘₐₓ is the maximum rate, [S] is the substrate concentration, and Kₘ is the Michaelis constant, equal to the amount of substrate concentration at which v is half of Vₘₐₓ. Back to the orders of the reaction, a first-order reaction occurs when there is low substrate concentration, [S]<<Kₘ (i.e. the substrate concentration is much lower than the Michaelis constant). This allows us to approximate v as:

Meaning that the only variable is the substrate concentration. This is a linear relationship between the rate of reaction and the substrate concentration. The more substrate added, the faster the reaction… To a point.

Once the amount of substrate significantly surpasses the value of Kₘ, the reaction rate no longer keeps increasing. This relationship can be shown by approximating the original equation for the case where [S]>>Kₘ:

And the reaction rate is now constant, meaning no matter how much more substrate is added, there will be no further improvement to the time the reaction takes. This occurs when all the enzyme is bound to the substrate, represented by:

Where kcat is the catalytic rate constant and [E₀] is the enzyme concentration. A real-life example is alcohol consumption. Alcohol gets cleared by the liver in a first-order reaction… As long as there isn’t too much of it. When it reaches a high enough concentration, the liver can only get rid of it at a fixed rate. Once the alcohol (substrate) concentration reaches the limit [S]>>Kₘ, the enzymes responsible for eliminating the alcohol (called alcohol dehydrogenases) can no longer keep up with the intake. This lets alcohol accumulate in the bloodstream and leads to intoxication.

This doesn’t apply to just alcohol, but to every drug and food that we consume! Because it’s easy to overwhelm our systems, the dosages of medicines need to be tightly controlled to prevent too much of it from accumulating and causing damage. Next time you look at the dosage directions on a medication bottle, you will know that thoughtful reaction rate analysis went into them to ensure your body can handle the amount of substrate.