Basics of enzyme kinetics graphs

How to read enzyme kinetics graphs (and how they're made). Km and Vmax. Competitive and noncompetitive inhibitors.

Wstęp

Let’s imagine that you’re in the market for a sports car. What might you want to know about your various options (Ferrari, Porsche, Jaguar, etc.) to decide which one is best? One obvious factor would be how fast the car can go when you floor it. But you might also want more fine-grained information on car’s performance, such as how quickly it can accelerate from 0 to 60 mph. In other words, instead of just knowing its maximum speed, you’d also want to know the kinetics of how the car reaches that speed.
Biochemists tend to feel similarly about the enzymes they study. They want to know as much as possible about an enzyme’s effects on reaction rate, not just how fast the enzyme can go in a flat-out scenario.
As a matter of fact, you can tell a remarkable amount about how an enzyme works, and about how it interacts with other molecules such as inhibitors, simply by measuring how quickly it catalyzes a reaction under a series of different conditions. The information from these experiments is often presented in the form of graphs, so we’ll spend a little time here discussing how the graphs are made (and how to read them to get the most out of them).

Basic enzyme kinetics graphs

Graphs like the one shown below (graphing reaction rate as a function of substrate concentration) are often used to display information about enzyme kinetics. They provide a lot of useful information, but they can also be pretty confusing the first time you see them. Here, we’ll walk step by step through the process of making, and interpreting, one of these graphs.
Imagine that you have your favorite enzyme in a test tube, and you want to know more about how it behaves under different conditions. So, you run a series of trials in which you take different concentrations of substrate - say, 0 M, 0.2 M, 0.4 M, 0.6 M, 0.8 M, and 1.0 M - and find the rate of reaction (that is, how fast your substrate is turned into product) when you add enzyme in each case. Of course, you have to be careful to add the same concentration of enzyme to each reaction, so that you are comparing apples to apples.
How do you determine the rate of reaction? Well, what you actually want is the initial rate of reaction, when you’ve just combined the enzyme and substrate and the enzyme is catalyzing the reaction as fast as it can at that particular substrate concentration (because the reaction rate will eventually slow to zero as the substrate is used up). So, you would measure the amount of product made per unit time right at the beginning of the reaction, when the product concentration is increasing linearly. This value, the amount of product produced per unit time at the start of the reaction, is called the initial velocity, or V0V_0, for that concentration.
Now, let’s say you’ve found your V0V_0 values for all your concentrations of interest. You can then plot each substrate concentration its V0V_0 as an (X, Y) pair. Once you’ve plotted all your (X, Y) pairs for different concentrations, you can connect the dots with a best-fit curve to get a graph. For many types of enzymes, the graph you get will resemble the purple line shown above: the V0V_0 values will increase rapidly at low substrate concentrations, then level off to a flat plateau at high substrate concentrations.
This plateau occurs because the enzyme is saturated, meaning that all available enzyme molecules are already tied up processing substrates. Any additional substrate molecules will simply have to wait around until another enzyme becomes available, so the rate of reaction (amount of product produced per unit time) is limited by the concentration of enzyme. This maximum rate of reaction is characteristic of a particular enzyme at a particular concentration and is known as the maximum velocity, or VmaxV_{max}. VmaxV_{max} is the Y-value (initial rate of reaction value) at which the graph above plateaus.
The substrate concentration that gives you a rate that is halfway to VmaxV_{max} is called the KmK_m, and is a useful measure of how quickly reaction rate increases with substrate concentration. KmK_m is also a measure of an enzyme's affinity for (tendency to bind to) its substrate. A lower KmK_m corresponds to a higher affinity for the substrate, while a higher KmK_m corresponds to a lower affinity for the substrate. Unlike VmaxV_{max}, which depends on enzyme concentration, KmK_m is always the same for a particular enzyme characterizing a given reaction (although the "apparent," or experimentally measured, KmK_m can be altered by inhibitors, as discussed below).

Enzyme kinetics graphs and inhibitors

Now, what about inhibitors? We discussed two types of inhibitors, competitive and noncompetitive, in the article on enzyme regulation.
  • Competitive inhibitors impair reaction progress by binding to an enzyme, often at the active site, and preventing the real substrate from binding. At any given time, only the competitive inhibitor or the substrate can be bound to the enzyme (not both). That is, the inhibitor and substrate compete for the enzyme. Competitive inhibition acts by decreasing the number of enzyme molecules available to bind the substrate.
  • Noncompetitive inhibitors don’t prevent the substrate from binding to the enzyme. In fact, the inhibitor and substrate don't affect one another's binding to the enzyme at all. However, when the inhibitor is bound, the enzyme cannot catalyze its reaction to produce a product. Thus, noncompetitive inhibition acts by reducing the number of functional enzyme molecules that can carry out a reaction.
If we wanted to show the effects of these inhibitors on a graph like the one above, we could repeat our whole experiment two more times: once with a certain amount of competitive inhibitor added to each test reaction, and once with a certain amount of noncompetitive inhibitor added instead. We would get results as follows:
  • With a competitive inhibitor, the reaction can eventually reach its normal VmaxV_{max}, but it takes a higher concentration of substrate to get it there. In other words, VmaxV_{max} is unchanged, but the apparent KmK_m is higher. Why must more substrate be added in order to reach VmaxV_{max}? The extra substrate makes the substrate molecules abundant enough to consistently “beat” the inhibitor molecules to the enzyme.
  • With a noncompetitive inhibitor, the reaction can never reach its normal VmaxV_{max}, regardless of how much substrate we add. A subset of the enzyme molecules will always be “poisoned” by the inhibitor, so the effective concentration of enzyme (which determines VmaxV_{max}) is reduced. However, the reaction reaches half of its new VmaxV_{max} at the same substrate concentration, so KmK_m is unchanged. The unchanged KmK_m reflects that the inhibitor doesn't affect binding of enzyme to substrate, just lowers the concentration of usable enzyme.

Michaelis-Menten and allosteric enzymes

Many enzymes act similarly to the hypothetical enzyme in the example above, producing parabolic curves when reaction rate is graphed as a function of substrate concentration. Enzymes that display this behavior can often be described by an equation relating substrate concentration, initial velocity, KmK_m, and VmaxV_{max}, known as the Michaelis-Menten equation. Enzymes whose kinetics obey this equation are called Michaelis-Menten enzymes. If you want a more detailed look at the Michaelis-Menten equation and the model underlying it, you may want to check out the Michaelis-Menten videos in the MCAT section.
Michaelis-Menten enzymes are different from allosteric enzymes (discussed in the main article on enzyme regulation). Allosteric enzymes typically have multiple active sites and often display cooperativity, meaning that the binding of a substrate at one active site increases the ability of the other active sites to bind and process substrates.
Cooperative enzymes are more sensitive in their response to changes in substrate concentrations than other enzymes and display a “switch-like” transition from low to high reaction rate as substrate concentration increases. This corresponds to a velocity vs. substrate curve that is S-shaped, as shown above.
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