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Enzymatic inhibition and Lineweaver Burk plots

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Voiceover: So let's talk about inhibition and how that affects enzyme kinetics. But, first, lets review the idea that enzyme catalysis can be divided into two steps. First, the binding of enzyme to substrate, and second, the conversion of substrate to product. And using this idea you can derive the Michaelis-Menten equation, which is useful for quantitatively looking at how enzymes behave kinetically. Also remember that within that equation, we have the Km or Michaelis constant, which is defined as the substrate concentration where the speed of product formation is at one-half of its max value. So the first thing that I'm going to talk about is something called a Lineweaver-Burke plot, and how it allows us to look at the Michaelis-Menten equation in a different way. So what I'm going to do is take the Michaelis-Mentin equation, but then take the inverse of both sides of the equation, so one over everything. And that will leave us with one over V O is equal to Km over V max times S, plus S over V max times S, since I separated those two terms. Now if we cancel out the two S values, then we are left with the equation that I've just drawn out. And conveniently we can use this equation to describe a linear function. We can make one over V O our Y or dependent variable, Km over V max our coefficient m, or the slope, one over S our X, or independent variable, and then one over V max our b, or Y-intercept. We can then plot this on a graph, with our Y-axis being one over V O, and our X-axis being one over S, and if we draw out the corresponding line, the slope of our line will be equal to Km over V max, and our Y-intercept will be equal to one over V max. And we call this plot a Lineweaver-Burke plot. And it gives us another way to look into the Michaelis-Menten equation. So let's take a step away from this idea for a moment, and talk about the three types of enzyme inhibitors. So our first type of inhibitor is called the competitive inhibitor, and it works by binding to free enzyme, or E, to form EI, or enzyme inhibitor complex. And that will block the enzyme and make it unable to react with substrate to form product. So in this case the inhibitor competes with substrate for space on the enzyme. Our second type of inhibitor is called an uncompetitive inhibitor, and it works by binding to the enzyme-substrate complex to form ESI, which prevents the enzyme from turning substrate into product. Our third type of inhibitor is called a non-competitive inhibitor, which some people call a mixed inhibitor, as it can act as both a competitive or uncompetitive inhibitor, so it can either bind to free enzyme to form EI, or it can bind to the enzyme-substrate complex to form ESI, neither of which can react to form product. So now what we're going to do is take what we just learned about inhibitors and apply it to the Lineweaver-Burke plots. So I'll start with competitive inhibition, and I'll draw out these three lines on the plot, labeled one, two, and three, with line one corresponding to the enzyme acting without any inhibitor around. Line two will represent some inhibitor being present, and line three will represent even more inhibitor being present. So as you can see, as you increase the amount of inhibitor blocking the enzyme, the slope of these lines is increasing, while the Y-intercept isn't changing at all. What this means is that as you increase the concentration of an inhibitor, you're going to see an apparent increase in Km. Remember that Km is a constant, so it's only an apparent change, and that's due to the increase in the slope of the line. But since the Y-intercept isn't changing when you add a competitive inhibitor, you'll see that this competitive inhibitor has no effect on the enzyme's V max. So what that means is that competitive inhibitors will increase Km, but leave V max unchanged, meaning that if you really, really increase the concentration of substrate, you'll overcome the effects of the inhibitor as you approach the enzyme's unchanged V max. But the enzyme may not be as effective at low substrate concentrations. Next we'll talk about uncompetitive inhibition. In this case you'll notice that all three lines have the same slope, but different increasing Y-intercepts. What this means is that as you increase the concentration of inhibitor, you'll see a decrease in the apparent V max, since the Y-intercept is defined as one over V max. So since you're decreasing V max as you add more inhibitor, even if you really increase the substrate concentration, you won't be able to overcome the effects of the inhibitor. But the enzyme will still be effective at low substrate concentrations, even with the inhibitor around, since there isn't that same increase in slope. Finally, we'll take a look at non-competitive, or mixed inhibitors. And what you'll see is that this type of inhibitor, being mixed, has characteristics of both competitive and uncompetitive inhibitors. As you increase the concentration of inhibitor, there is both an increase in slope and an increase in the Y-intercept. What this means is that you'll see an apparent increase in Km, and an apparent decrease in V max. So in this case, high substrate concentrations won't completely overcome this type of inhibitor, since it lowers V max, but since there's an increase in the Km as well the enzyme will also be inhibited at low substrate concentrations. So what did we learn? Well, first we learned that we can rearrange the Michaelis-Menten equation to come up with a function for the Lineweaver-Burke plots. Second we learned about competitive, uncompetitive, and non-competitive inhibition. And third we learned that increasing substrate concentration will only be able to overcome the inhibitory effects of competitive inhibitors.