Enzyme Kinetics
Not all enzymes are created equal! Some are faster than others some slower. Some need a ton of substrate around to work others a lot less. In order to accurately describe enzymes and the effect, they will have on the speed of reactions (i.e. kinetics) we need to talk about an enzyme’s speed and how much substrate it needs to get there. Why? We can answer this by thinking about an analogy: baking cupcakes.
Enzyme Analogy: Cupcakes!!!
When making cupcakes there are two limiting factors that determine how quickly you can create them. The amount of cupcake batter you have and how big your ovens are. If you have room for 20 cupcakes in your oven but only enough batter to fill 8 of them you can only make 8 cupcakes at one time. Here the substrate (batter) is limiting the ability of the enzyme (oven) to fully catalyze a reaction (cupcake baking).
On the other hand, we might have 30 cupcakes worth of batter but only room for 20 cupcakes in our oven. Here our enzyme (oven) is the limiting factor in our reaction. We can’t make the remaining 10 cupcakes until we get the other baked cupcakes out of the way. When the enzyme is the limiting factor in our reaction then our enzyme is saturated. It is completely filled up and can only go as fast as it can catalyze a reaction.
Under saturating conditions, we can begin to discuss how different enzymes differ in the properties that describe them. Let’s dive right in by looking at Kcat.
Kcat
While some ovens might be super hot and cook our cupcakes really quickly others will be slow. The same is true for enzymes and scientists refer to the speed with which an enzyme can generate products as the turnover rate (Kcat). So one enzyme might have a Kcat of 2 products per second while another might have a Kcat of 40 products per second. In the same way, one oven might be able to make 20 cupcakes per 30 minutes while another might make 400 cupcakes in 30 minutes.
This means that the bigger the Kcat the faster each enzyme can catalyze a reaction.
Vmax
This also means that the number of enzymes or ovens present will determine how fast a reaction can be carried out overall. For example, if we have 20 ovens with a Kcat of 40 and 1 oven with a Kcat of 400 the slower ovens will still make more cupcakes simply because of the sheer number of ovens. The same is true for enzymes and scientists call this idea the maximal velocity (Vmax). Basically, what concentration of product can a collection of enzymes put out in a certain period of time.
[latexpage]
\[V_{max}= [E]K_{cat}\]
The higher the Vmax the faster the reaction is being catalyzed and the larger the amount of product created per unit time.
Km, Kd, and Ka
Up to this point, we have discussed many of the factors on the enzyme side of the equation, but in our analogy, the amount of substrate also matters. The analogy breaks down a bit here so we are going to leave cupcakes behind for now and talk more directly about the effect of substrate concentration.
When we discuss the effects of substrate concentration we are really talking about the affinity of the enzyme and the substrate for one another. An enzyme can’t catalyze a reaction unless the substrate is actually able to bind to the active site. Some enzymes and substrates are like super magnets and have a high affinity for one another while others are only weakly attracted.
So enzymes with a higher affinity for their substrates reach saturation faster and begin working at a faster rate. Scientists measure the affinity using several different K constants that are centered around measuring either association or dissociation. Ka not to be confused with the acid-base Ka is the association constant. While Kd is the dissociation constant and Km the Michaelis constant.
Since all K values, enzyme-related ones included, are products over reactants we don’t have to memorize what each constant stands for per se. Instead, we can focus on what they stand for.
For enzyme-substrate association, the product is the enzyme-substrate complex while the reactants are the dissociated enzymes and substrates. Therefore larger Ka values result from larger quantities of enzyme-substrate complexes and demonstrate that the enzyme and the substrate have high affinity for one another.
In contrast, Kd values are looking at the reverse reaction. Therefore the product of the dissociation is the separate enzymes and substrates and the reactants are the enzyme-substrate complex.
This means that larger Kd values indicate a larger amount of unbound substrate and enzymes. As a result higher Kd values actually indicate lower affinity.
We can think of Km as a special case of Kd. Specifically, it is the substrate concentration @ 1/2 Vmax. The smaller the Km the less substrate an enzyme needs to reach a reasonable speed. This idea is similar to what is known as the LD50 or the dose at which 50% of a group will die. For example, botulinum toxin has an LD50 of 1-3 ng/kg while the LD50 of Tylenol is >2000mg/kg. This means that we very little botulinum to kill something while we will need a lot more Tylenol to do so.
The same is true for Km values. The lower the Km value the less substrate an enzyme needs to get going while the larger the Km value the more substrate it needs to reach a reasonable speed. High-affinity enzymes end up having low Km values while low-affinity enzymes have high Km values.
Catalytic Efficiency
Putting the Vmax and Km values together we can determine the catalytic efficiency of an enzyme. In common usage, someone who is efficient can do a lot with very little. The same is true of enzymes. Enzymes with the highest catalytic efficiency can churn out tons of product with very little substrate around. This means that the bigger your Kcat the faster you are and the smaller the Km the less substrate you need to get up to speed. Putting both together the most efficient enzymes are those with the highest Kcat values and the smallest Km.
[latexpage]
\[ Catalytic \; Efficiency = \frac{K_{cat}}{K_m}\]