Alright Ninja Nerds, so we're going to continue. If you remember in the last video we talked about competitive inhibition, non-competitive inhibition, uncompetitive inhibition, and suicide inhibition. And then we talked about the Michaelis-Menten equation and we derived that in the first video.
In this video we're going to take all of those concepts and put it together and apply that to this graph right here. If you notice this is what's called a rectangular hyperbola. This is the Michaelis-Menten curve, right?
So this is going to give us a little bit of information about the Michaelis-Menten equation that we derived. This one over here, we'll talk about that one afterwards, this is a linear form. So in other words, it's the inverse function of the Michaelis-Manton equation. I'll show you what I mean by that when we get to this one.
But this is called the Line-Weaver-Burke plot. Just another way of looking at the concept of enzyme kinetics here. Okay, so let's go ahead and look at this graph here. So first off, let's get our axes straight. So on the x-axis, this is the substrate concentration.
as it increases. over time, right? So on the x-axis is our substrate concentration.
On the y-axis is the velocity, okay? We can put v naught as your initial velocity, but according to the Michaelis-Menten equation, based on that, we can say that the actual effect of the velocity is directly proportional to the substrate concentration, except for one thing, and I'll explain that as we go along. So, what happens in this reaction is you're taking the enzyme, right?
You're reacting with the substrate. As the enzyme begins to react with the substrate, it begins to form enzyme-substrate complex. So what we see within the beginning of this is that when we take and we monitor the velocity of this reaction going up in the y-axis, substrate concentration on the x-axis, as the enzyme begins to react with the substrate, it progresses in a linear fashion. Now if this is progressing in a linear fashion, This right here is following.
first order kinetics. So again, this component right here, if I were to kind of encircle it like this, this linear part of the graph right here, all to right here, this whole component right here is following a linear fashion that as you increase the substrate concentration, the velocity of the rate of the reaction increases proportionally. That's following first order kinetics.
So this one is, this part of the graph is following first Order kinetics. Okay? All right. But then what happens is as the enzyme begins to react with the substrate and it just continues to keep reacting with the enzyme, as the enzyme continues to react with the substrate, as the substrate concentration increases, you'll notice that it begins to plateau and level off.
And no matter how much more substrate you add, the velocity of the reaction doesn't change. This point right here, let's actually highlight this one in red. So this point here in which you notice this plateau point, or this point where it's not changing, no matter how much substrate you add, the velocity of the reaction isn't changing.
This is following zero-order kinetics. Because zero-order kinetics, for example, what do I mean by first-order kinetics? First order kinetics just means that I'm saying here that the rate of this reaction is equal to K times the concentration, let's just say that it's of the substrate, let's just say substrate, raised to the 1, right?
Zero order kinetics just means that the rate is equal to the K, the constant. Because no matter how much substrate concentration you add, you can put it like this. If you want substrate raised to the zero, but anything raised to the zero is one. So with the fact of this, substrate concentration has no effect on the rate. First order, as the substrate concentration increases, the rate increases proportionally.
All right, so now that we've gone over that, let's talk about a couple more terms here. What do we call this point here, which we said in which the enzyme is completely bound to substrate, no matter how much more substrate you add beyond this point? the velocity doesn't change, it kind of stays level. That point right here, if I was to follow it all the way from here, let's say I followed it from here, make like this little horizontal line here, that all that point right there is referred to as Vmax or maximum velocity.
It's the point, right? So if I were to come over here, this would be its maximum velocity. This is the point at which no matter how much more substrate you add to the enzyme, okay, there's no free enzyme left in other words. All of the free enzyme is bound to the substrate, it's completely saturated no matter how much more substrate you add, it's not going to do anything because all of the enzymes are completely occupied with substrate and they're at their max velocity. Alright, but if I come to a point at which I have to Vmax, so let's look here and I have this point, so it kind of falls right around about here.
So I'm going to come here now. Let me come about right here and then I'm going to come down here. This point right here, I'm going to erase this and move this over a little bit guys, this first order kinetic. So again, this increase right here as it's going up, this right here, I'll circle it right there, this is first order kinetics.
So first order kinetics. Alrighty, anyway and again what would that be? Rate is equal to K times the concentration of the substrate because it's proportional.
At this point right here, if you remember, when I'm at half the maximum velocity, what did we say that the substrate concentration is equal to? The Km. Okay? So at this point right here, in which we're at half the maximum velocity, because this right here, if you kind of look, it's about half the maximum velocity.
I follow it down here. It's at substrate concentration, but what is substrate concentration equal to at that point? It's equal to the Km.
So this point right here I can say is my Km at what? Half my maximum velocity. Let me get this out of the way so it's not so cluttered in here, guys. So we have some more room in here. So again, what would this point right here be?
This point right here would be half Vmax. All right. Now that we've got that concept done, Now let's apply what we've talked about with competitive inhibition, non-competitive inhibition, uncompetitive inhibition in this graph. So now that we know that, we can get rid of first order kinetics and we can get rid of the zero order because we're going to need room to explain. this next concept.
So competitive inhibition, I'm going to do that one in black. What happened with competitive inhibition? If you remember, what did we have to do?
We had to increase the substrate concentration, which increased our Km, right? But it didn't affect Vmax. So what would that look like?
If KM increases, where's KM? It's right here. What's KM equal to?
Half Vmax, substrate. So it's increasing, so in other words, it's going this way. So but what happens?
Vmax doesn't change. So I can say that I could start here now, this new KM point, and I'm gonna come here and move up, but eventually I will reach Vmax. Okay? Not the most beautiful graph here, but again, this would help you with that concept here.
So again, I would come here. and I would move over, I could actually move this point over here at about half, and if you'll notice here, that would give me that point there. Not the most beautiful graph.
Let me fix it up a little bit here. Fix it up just a little. Let's bring this point from here down, and we'll come this way.
A little better, still not the most beautiful graph, but again, this is that new KM or that increased KM from competitive inhibition. So it reaches Vmax, but the KM increases. Okay? So they came at this... point will increase.
Alright and if we come down here that's our KM. Alright now that we've gotten that one this is our competitive inhibition. I'll put CI up here.
Competitive inhibition. So what we notice, we'll notice a kind of a shift to the right from normal. So this would be a shift to the right from the normal point of the curve.
And I can kind of bring this one just a little bit over here to make it a little bit nicer. That's a little better. Okay, that's a little better.
Alright, now let's move on to the next one. Next one is non-competitive inhibition. Non-competitive inhibition, we said it didn't affect the Km. So it didn't affect the equilibrium of our reactions.
Okay, so it didn't affect Km. So Km stayed the same, but they never could reach Vmax. So I'm going to do that one in red. I'm going to do that one in red.
So again, Km should stay the same. So it should still start here, but look what happens. here as it rises, it rises, it rises look what happens it never reaches the maximum velocity. Okay so if you look here at this red line the Km stays the same but as it starts rising and rising and rising if you notice no matter how much substrate you add it will not reach Vmax.
This is non-competitive inhibition okay and this black one is competitive inhibition Okay, so again Km should stay the same but Vmax should decrease on this one. What was the last one? The last one was uncompetitive inhibition.
Let's do that one in orange. What do we say happened with uncompetitive inhibition? We said the Km on that one decreased. So if it decreased, which way would it go? It would shift to the left over here.
So if it shifts over here to the left, we're going to notice this decrease in Km, right? What else happens? We also know that it decreases the Vmax.
They never reach their true Vmax. So if you'll notice here, what's going to happen? It's going to start Moving up, but then look, it also never reaches the maximum velocity. And again, what will this one be?
This will be uncompetitive inhibition. All right, guys, so let's do a quick recap. of this again.
So again, when we said normal Km is going to, you know, half Vmax is equal to the substrate concentration. So it's going to, it's kind of the normal activity of the enzyme substrate reaction, right? And again, as the enzyme is reacting with the substrate, it produces a first order, you know, order kinetics, right? Where it's increasing linearly.
Then after the enzyme is completely balanced substrate and almost no matter how much substrate you add, it won't change the velocity it reaches. Vmax, which is zero order kinetics. Alright, we said that that would be our Vmax point when it's completely saturated, when all the enzyme is saturated with substrate.
And so we said that half the Vmax, it's equal to the Km, which is equal to substrate concentration. Then what do we say? When we apply the inhibitors into this concept, competitive inhibitors decrease the, I'm sorry, increase the Km.
Competitive inhibitors increase the Km. Well, if it increases the Km, where's the Km going to shift? it's going to shift over here to the right.
If it shifts over here to the right but it doesn't affect Vmax, what will the graph look like? It'll look like this, right? But eventually, again, what will happen? These two lines, we could say, will at some point in time come together, right? So it'll eventually be able to reach Vmax.
That's competitive inhibition. Non-competitive inhibition, we said, doesn't affect the Km, but decreases the Vmax. So it'll start here at the normal Km. But then look what happens.
As you begin to add substrate to the enzyme, no matter how much substrate you add, you'll never be able to reach maximum velocity. So it never reaches this point where these two lines come together. Okay, the last one was uncompetitive inhibition, which was the one in blue, right? And we said that uncompetitive decreases both the Km and the Vmax.
So if you decrease the Km, it shifts over here to the left. And then it'll again go up. But look, no matter how much substrate you add, you'll never be able to reach the point of maximum velocity.
It never merges with that line there. So you'll see it below the Vmax. Okay, that takes care of that concept.
Now what we're going to do is... We're going to apply what we just did here over here to the Lineweaver-Burke plot. But before I do the Lineweaver-Burke plot, we have to understand how the Michaelis-Menten equation can be applied to the Lineweaver-Burke plot.
So let's do that really quickly over here. All right. So let's write out the Michaelis-Menten equation.
So again, it is V naught is equal to V max times substrate concentration over Km plus substrate concentration. All I'm going to do for this graph is I'm going to take the inverse. I'm going to flip it. So this is normally V0 over 1 if you want to think about it. If I flip it, it would be 1 over V0.
And I'm going to flip this whole equation here. And that equals Km plus substrate concentration over Vmax times substrate concentration. All I literally did was just flip this equation. Now what I'm going to do is I'm going to separate it into Y equals Mx plus B form.
So I can get kind of a nice linear slope here instead of a rectangular hyperbola. So how do I do that? Well, this is our y.
If I notice, Km plus S is all over the same denominator. So I can split Km over this denominator and S over this denominator. Let's do that.
So 1 over V0 is equal to Km over Vmax times substrate concentration, right, same denominator, plus substrate concentration over Vmax times substrate concentration. What does this look like afterwards? Well, substrate concentration cancels out. And then what does it look like?
1 over V0 is my y equals, I can split this up into m and x, I'll show you. So I'll put Km over Vmax, that is my slope, my m. Then I'll separate 1 over substrate concentration, right?
because I can say over here if I put one over substrate concentration, that's going to be my X. Axis there, plus, look, substrates cancel out. So I have 1 over Vmax, and that is my y-intercept. So that gives me my y equals mx plus b. Let's go ahead and plot that then.
So what do we see on the y-axis? This will be 1 over V naught. Let's write that down. 1 over V naught is going to be this axis here.
What will we see on the x-axis? We'll see 1 over substrate. So I'll put 1 over substrate. Let me go ahead and erase this out of the way here. Okay, so what do we get here?
We have on the x-axis, I have 1 over substrate concentration. Okay, what's my slope? My slope here for this normal line is Km over Vmax. Okay, what else? And then my y-intercept where it crosses the y-axis, that point right there is my 1 over Vmax.
So this is 1 over V. Okay, cool. And then over here, I can actually say this point right here is called 1 over, negative 1 over Km. And that's my X intercept there.
Okay? Now. Now let's go back off of everything we have with competitive, non-competitive, uncompetitive.
What did we say was the problem with competitive inhibition? So competitive inhibition was the one we're going to look at here. Competitive inhibition we said it did what? It did what to the Km? It increased the Km but didn't affect the Vmax.
What about non-competitive inhibition? Non-competitive inhibition did what? Well, it doesn't reach Vmax, but it doesn't affect the Km. So it decreases Vmax, but no effect on Km.
And then uncompetitive inhibition did what? It decreased the Vmax, but it also decreased the Km. So it decreases Km and decreases Vmax. Okay, let's see how these affect these normal formulas that we have.
Let's start with competitive inhibition, and let's do that one in purple. Let's start with that one first. So Km. Where in here do we see Km? Well, I see it right here.
So what happens if normally Km is like this, right? So let's say it's just some number. But then I take that number and I increase it.
Well, what's going to happen when I take 1 over a larger number? It decreases. So in other words, this x-intercept will shift over here to the right. So that's where my new x-intercept is going to be.
I'm going to mark that point right there for right now. Does it affect my y-intercept? No. So it should still cross through the normal y-intercept.
What else happens? My slope. Km is a part of my slope.
But if I increase Km, what happens to the slope? It also increases. So if I were to do this, it should come straight up. So let me go ahead and do that then. It would come like this, right?
It's not going to be the perfect graph, but it's going to look like that. And what's this going to be? This is going to be my competitive inhibitor. Okay?
Now let's do the next one, which is the non-competitive inhibitor. Let's do that one in green. Non-competitive inhibitor does what to the Vmax?
It decreases the Vmax. Well, where's the Vmax? Right there.
I don't see it anywhere else over here except for right there. Well, what happens if you, let's say that this is some number, and I decrease that number below normal, right? So one over a smaller number produces a bigger number. So in other words, the Vmax is going to rise a little bit. So it might come like right here, right?
But it doesn't affect the Km. So the Km should still kind of follow the same point here. What else though? What else did I do to the Vmax? I decreased my Vmax.
So if I decrease the Vmax, what do I do to my slope then? If I put a lower number underneath that number, some number divided by a lower number increases the slope. So I'll also have an increased slope.
So it'll start right here. same point like this guy right here, still cross that KM point, but it's going to go through a different Vmax and it's going to be high. So let's say I start like right here. I'm going to come at this point here.
I'm still going to cross that point, but I'm going to rise through this point here and then come up like that, right? So let me move this guy over here, this purple one. So again, it would look something like this here. And again, this green one right here is going to non-competitive inhibitor.
This purple one here is going to be competitive inhibitor. And what was the last one? The last one was uncompetitive inhibitor.
I'm going to do this last one in orange. Uncompetitive inhibitor does what to the Km? It decreases the Km. Well what will it do to that point?
One over a smaller number does what? Increases it, right? So it's going to shift more than one.
this way. Okay, what else will happen? It also decreases the Vmax. If you decrease the Vmax it rises up more. Right, okay, so I know it's going to be like this so far.
I know it's also going to rise. What else do I know? Well look here, this is where it gets funky. My KM decreases and my Vmax decreases.
So if you think about it, it's not really going to have some definitive effect on the slope. So the slope, it'll kind of in other words, almost be parallel. So let's bring this guy over a little bit more to where we can try to make this as parallel as possible. So what would this look like here?
If I were to move this guy up, it would move almost parallel to this black line. okay and it would look a little bit like that okay and this is our uncompetitive inhibitor and what's the one in black so that we have unspecifically we know what that one is this is no inhibitor okay so So this is non-competitive inhibitor, this is competitive inhibitor, uncompetitive inhibitor, and no inhibitor. All right, so again, one more time and we'll finish up here. Competitive inhibitor, Km increases.
So where will we see that effect? We would see it here on the x-intercept. If you increase this bottom denominator, what's going to happen?
It's going to make a smaller overall number. It's going to shift it to the right. It's also going to do what to the Km? It's going to increase the Km. And if you increase the cam, you have a more steep slope.
So you'll notice that point there. Non-competitive inhibitor decreases the Vmax. If you decrease this number, it's going to make a larger overall number, which brings that Vmax up, that green point there.
What else did it do? It decreases the Vmax here, which increases the slope, so you'll have a more steep slope, and that's our non-competitive inhibitor. Then the uncompetitive inhibitor, it decreases the Km and the Vmax. Well, it affects our x-intercept, it affects our y-intercept, but it doesn't really affect the slope. So this line should almost be moving parallel with the no inhibitor line.
Okay and that's what we would see with our line weaver burke plot with respect to competitive inhibition, non-competitive inhibition, uncompetitive inhibition, and no inhibition.