At the beginning of the 20th century, the two scientists Michaelis and Menten developed a concept that made it easier to describe the enzyme kinetics – i.e. how fast an enzyme-controlled reaction takes place. To perpetuate their names in history, they called it «Michaelis-Menten kinetics».
Although the equation they formulated is only a very simplified representation, it can still be used to describe the reaction rate of most enzyme reactions.
Basics of the Michaelis Menten equation
What is an enzyme anyway?
A enzyme is a special protein that accelerates or catalyzes biochemical reactions so that they don’t last so long. So an enzyme is a biocatalyst.
And what is meant by an enzymatic controlled reaction?
In an enzymatically controlled reaction, enzymes catalyze a biochemical reaction that produces a product from a substrate.
They do this by reversibly binding to and merging with the substrate enzyme-substrate complex form. In the catalytic center of the enzyme, the substrate is now converted into a product. This product separates from the enzyme, leaving the product and enzyme at the end of the reaction.
The Michaelis-Menten equation describes the dependence of the conversion rate of the enzyme on the substrate concentration and can thus predict the rate of an ongoing reaction. It is always assumed that the enzyme concentration remains constant and the reaction rate therefore only depends on the substrate concentration.
So if you’re running an enzyme reaction in your home lab and want to know if you have time to go to the movies with your friends in between, the Michaelis-Menten equation is for you.
Prerequisites for the Michaelis-Menten kinetics
Since the Michaelis-Menten equation is only a simplification, certain prerequisites must be met in order to use it correctly:
- A substrate and an enzyme always form an enzyme-substrate complex. An enzyme cannot bind several substrates at the same time or vice versa.
- The reaction is in steady state. Put simply, this means that the concentration of the enzyme-substrate complex remains constant over time. So all the substrates present bind immediately, at the beginning of the reaction, to all the enzymes present.
- The product and the enzyme do not form their own complex. The affinity of the enzyme for the product is therefore zero and the product cannot take any enzymes away from the substrate.
- The balance is on the side of the product. There are more than enough substrates (excess substrate) and the reaction is not slowed down by a lack of substrate.
- At the same time, the formation of the product is the rate-limiting step in the reaction, not the formation of the enzyme-substrate complex. That is, the product forming step is the slowest step.
If all these requirements are met, you can work with the Michaelis-Menten equation without any problems.
What does the Michaelis-Menten equation look like?
The Michaelis-Menten equation is structured as follows:
Here is the explanation of the individual components:
- is the initial rate of the reaction. In other words, the speed at which there is still no product but the maximum substrate concentration.
- is the maximum speed that the reaction can reach. It is reached when all enzymes are each occupied with a substrate. From here on, the amount of substrate no longer influences the reaction speed, because all the enzymes are already occupied and the state of saturation is reached. Only when more enzymes are added, which could then bind substrate again, would the speed increase.
- is the amount of substrate available in the reaction.
- is the Michaelis-Menten constant. At their value, exactly half of all enzymes involved in the reaction are occupied with a substrate.
However, there are a few participants in this equation that are not dependent on substrate concentration. These are and . The two are enzyme properties and enzyme constants, respectively.
is actually not a real one Enzyme constant, as it depends on the specified enzyme concentration. however, is a true enzyme constant that applies to any enzyme, regardless of the concentration of enzymes or substrates.
Michaelis-Menten constant
The Michaelis-Menten constant, also called, is a measure of an enzyme’s affinity for its substrate.
It is the substrate concentration at which exactly half of the enzymes are occupied by a substrate and the reaction proceeds at half the maximum rate.
So you could also say:
It is also the point at which the Michaelis-Menten diagram is half saturated.
- If the value is large, one needs a lot of substrate to reach the half-maximal rate, since the enzyme affinity for the substrate is very low.
- On the other hand, if the value is small, you need very little substrate to reach the half-maximal speed, since the enzyme has a very high affinity. That is, the enzyme binds very tightly to the substrate.
If an enzyme could interact with multiple substrates, each substrate has its own . is given in moles per liter (mol/l).
not only a purely theoretical meaning, but in reality the substrate concentration for many enzymes is around . An exception to this observation are the key enzymes.
key enzymes are enzymes that sit at very important points in biochemical reactions. They can often be found, for example, at the beginning of important reaction steps or at important branching points.
An example of a key enzyme would be the phosphofructokinase-1 in glycolysis.
Mathematical derivation
If you like to deal with mathematical backgrounds, you could also derive the Michaelis-Menten constant from the simple reaction scheme of an enzyme reaction.
This simple representation assumes that the reaction is in steady state.
That steady state refers to the state of a chemical reaction in which enough substrate is being added and enough product is being removed at all times so that the reaction can proceed at a constant rate. It doesn’t stop and doesn’t slow down.
This scheme is already known. The rate constants have now been added.
Enzyme (E) and substrate (S) form the enzyme-substrate complex at a constant rate.
At the same time, this complex can also break down into its individual parts with speed. must be less than , otherwise the reaction would proceed in the wrong direction (ie not in the direction of the product).
Thereafter, the substrate is converted into the product at the speed.
The Michaelis-Menten constant now consists of the three rate constants and .
So:
Michaelis-Menten diagram
If you now want to plot the Michaelis-Menten equation, you get the Michaelis-Menten diagram. The velocity (v) is entered on the y-axis and the substrate concentration (S) on the x-axis.
The diagram shows the rate of the chemical reaction at a specific substrate concentration.
Since the amount of enzyme always remains constant, at some point the reaction rate can no longer be increased, no matter how much substrate is added, since all enzymes are eventually saturated.
So the chart represents a saturation curve going against. Mathematically, you can also do one hyperbole to name.
Figure 1: Michaelis-Menten diagram
- If the curve is flat, the reaction will be slower. So the value is relatively high and more substrate is needed to make the reaction run faster.
- If the curve is steep, the reaction proceeds relatively quickly. The value is relatively low and therefore a low substrate concentration is required for the reaction to proceed quickly.
The Michaelis-Menten diagram can also be divided into three phases:
1st phase: First-order reaction
In the beginning there is still a very low concentration of substrate, so any substrate present will easily find an enzyme in the large amount. In simple terms, one can say that the reaction rate only depends on the substrate concentration.
2nd phase: transitional phase
At an intermediate substrate concentration, the first substrates start to compete for the enzymes. It is becoming increasingly difficult to find an enzyme in the crowd because more and more enzymes are already occupied.
3rd phase: zero-order reaction
The closer you get, the less influence the substrate concentration has on the reaction speed, since the enzymes are all saturated slowly. When the substrate is fully saturated, the reaction proceeds at maximum speed (). The reaction speed is therefore not dependent on any concentration, but runs at maximum speed.
Now you know the Michaelis-Menten equation and you know how and where to apply it. If you are still interested in the topic of enzymes, please have a look at our other articles, for example on the key-lock principle.
Michaelis Menten Equation – The Most Important
- The Michaelis-Menten equation can be used to calculate the rate of enzymatically controlled reactions.
- The rate of the enzyme reaction depends (assuming a constant enzyme concentration) on the substrate concentration.
- We can derive the Michaelis-Menten equation mathematically from the dynamic equilibrium.
- The Michaelis-Menten constant describes the affinity of an enzyme to its substrate.
- The Michaelis-Menten plot is the graphical representation of our equation and is a saturation curve.