Shifting Lineweaver-Burk Plots - Video Tutorials & Practice Problems
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Shifting Lineweaver-Burk Plots
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In this video, we're going to talk even more details about a Lineweaver Burk plot, specifically how to shift the line on a Lineweaver Burk plot. So recall from our previous lesson videos that the Line Weaver Burke equation resembles the equation of a line. And so what this means is that we can take the equation of a line, which is y equals mx+b, and substitute in enzyme kinetics variables to get the Lineweaver Burk equation. And so when it comes down to it, what actually defines a line are 2 different factors. The first factor that defines a line is the slope of the line or the m variable in the equation of the line, or the Kilometers over the Vmax ratio in the Lineweaver Burk equation. And the second factor that defines a line is actually the y intercept of the line, which is the variable b in the equation of the line and the reciprocal of the vmax in the Lineweaver Burk equation. And so if we start off with just talking about the slope of the line, recall from your previous courses that when the slope of the line is equal to 0, that means that the line is going to be completely horizontal. It's going to be a completely horizontal line when the slope is equal to 0. And as we begin to increase the slope, as we begin to increase the value of the slope, that will make the line become, a steeper line. So that will make the line steeper. And so if we take a look at this lineweaver burk plot that we have down below, notice that this horizontal red line that we see here, as we set up above, horizontal lines will have a slope or, that is going to be equal to 0. So we know that the slope of this red line, or the m value, is going to be equal to 0. And also, as we said up above, if we increase the value of the slope, that's going to make the line steeper. So notice that this green line right here is much steeper and so that means that its slope must be greater than the value 0. And so, essentially what you'll notice is that the slope is also going to be equal to the rise over the run. And so if we wanted to determine the slope of this green line right here, all we would need to do is start at any point on the line and figure out how much do we need to rise or how much do we need to go up and how much do we need to go, to the right or how much do we need to run horizontally in order to, get back to a point on our line. And so, if we start at this point, we can see that we need to go up 1 unit and to the right one unit in order to get to a point on our line, which means that the rise is going to be 1 and the run will also be 1, and of course one over 1 is just 1. And so that means that the slope of this line is just going to be 1. And so, what we can see is that a line that has a slope of 0 is going to be horizontal and if we increase the value of the slope, then we're just going to get ourselves a steeper line, as we see here. Now, if we were to increase the value of the slope to 2, then here we would have a steeper line, and if we were to increase the value of the slope to 3, then we would have an even steeper line. So you can see the effect that increasing the slope will have on the steepness of the line. Now moving on to the y intercept, the y intercept b, increasing the value of the y intercept is actually going to elevate, it's going to elevate the position that the line intersects the y axis. So remember that the y intercept is going to be the value of y when it crosses the, y enters, the y axis, which is going to be this horizontal axis. So now notice looking at this, Lineweaver Burk plot here in the middle, we have a horizontal line, so we already know that horizontal lines are going to have a slope equal to 0. So we can go ahead and say that the slope is equal to 0 here. However, notice that this horizontal line is crossing the y axis at a different position than the horizontal line that we had over here. Notice that the horizontal line on the left is crossing the y axis specifically at, the value of 1. However, over here on the right, this horizontal line is crossing the y axis at a different position at a value of 2. And so what this shows is that, if we increase the value of the y intercept b, that's going to elevate the position of where the line is going to intersect the y axis. And so essentially when it comes to shifting the line on a Lineweaver Burk plot, all we need to consider is the slope of the line and the y intercept of the line. Now, the last point that I want to make, that's important about shifting the lines of a Lineweaver Burk plot is that the slope of a line on a Lineweaver Burk plot, which is of course going to be, the m which is going to be the ratio of the cam over the v max. So we can say that the slope, which is Kilometers over v max cannot actually be 0 or have a negative value. So essentially what this means is that for, Lineweaver Burk plots, we're never going to see a Lineweaver Burk plot where we have a slope of 0. So we're never going to see horizontal lines like this, and we're also never going to see a, a slope that has a negative value. So we're never going to see lines that go like this in this direction and decrease from the left to the right. So what we can say is that the slope, which is the Kilometers of the Vmax, is never going to be negative and it's never going to be 0. It's always gonna have some kind of value. And so, essentially we will always expect the lines of our Lineweaver Burk plot to have a positive value and have a positive slope. And so that makes it a little bit easier to interpret as well and it takes away a lot less factors that we need to worry about. And so, this concludes our lesson on shifting Lineweaver Burk plots by using the slope of the line and the y intercept of a line. And in our next lesson video, we're going to talk about how to quickly look and visualize a Lineweaver Burk plot and analyze the Kilometers and the vmax. So I'll see you guys in that lesson video.
2
concept
Shifting Lineweaver-Burk Plots
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7m
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Video transcript
In this video, we're gonna talk about how to glance at lines on a Lineweaver Burk plot and quickly visualize whether there have been increases or decreases to the Kilometers and or the v max. And so this will be a skill that will be especially useful to you guys once we start talking about enzyme inhibitors later in our course. Now, I also wanna point out that in this video, you might get a little bit confused because we're gonna talk about some counterintuitive stuff. But if you do get confused, hang on tight because in our next example video, I'm gonna show you guys an example of how to apply this counter intuitive stuff, so hopefully things will start clicking and it'll make a lot more sense to you guys after our next example video. And so let's go on and get started here. So first, I want you guys to recall from our previous lesson videos that a Lineweaver Burk plot is also known as a double reciprocal plot because it plots reciprocals on the x and the y axis. On the x axis, it plots the reciprocal of the substrate concentration, and on the y axis, it plots the reciprocal of the initial reaction velocity or v naught. And so because both the x and the y axes in a Lineweaver Burk plot are actually reciprocals, essentially one over the substrate concentration, and one over the initial reaction velocity v naught, then we can say that the substrate concentration and the initial reaction velocity themselves will actually increase towards 0. That's right. I said increase, not decrease towards 0, And that is a little bit counterintuitive. So let's take a look at our image down below to begin clearing up some of this counterintuitive stuff. And so in this line we revert plot down below, we're first going to focus only on the x axis, and we're going to kind of ignore the y axis for a little while. So, notice that the x axis plots the reciprocal of the substrate concentration, and normally on either side of this 0 on the x axis, we expect the magnitude on the right side of the x axis to increase towards the right in that direction. And on the left side of the 0 on the x axis, we expect the magnitude to increase towards the left. And really with a Lineweaver Burk plot, it's the same exact deal, except we need to remember that the Lineweaver Burk plot is again plotting substrate concentration. And so when we're considering the entire reciprocal as a whole, it's true that the magnitude of the reciprocal will increase towards the right of the 0, and it will increase towards the left of the 0. However, if we're not considering the entire reciprocal as a whole and instead we're only considering part of the reciprocal or just the substrate concentration, then we can say that the substrate concentration itself will increase in the opposite direction towards the 0 marker. And so instead of increasing outwards from the 0 in opposite directions, it's actually going to increase towards the 0. And so that's exactly what these arrows here are showing us that the substrate concentration itself, when we're only considering the substrate concentration, it will actually increase towards this 0 marker. And the same thing over here on the right, on the left hand side. It will increase. So substrate concentration increasing towards the 0 marker. And so the 0 marker here is really acting as the infinity marker for the substrate concentration itself, and that's why we have that the substrate concentration is equal to infinity at this 0 marker here. And so, also what's associated with the x axis is, of course, the x intercept, which we know from our previous lesson videos is the negative reciprocal of the kilometers. And so just be, just like the substrate concentration increases towards 0, we can also say that the Kilometers is also going to increase towards 0. And so, also on this side, the kilometers would also increase towards 0 as well. And so, recall that lines on a Lineweaver Burk plot are always gonna have a positive slope like this. So we're never gonna have a negative slope where the x intercept actually has a positive value. And so what that means is, really, we don't need to even think about the Kilometers ever being on this side of the 0. So the Kilometers is never gonna land on this side of the 0, it's always gonna land over here. So really we don't need to consider the Kilometers over here, and really we don't even need to consider this substrate concentration line over here because, again, we're never going to have lines that land the x intercept on this side of the 0, on the x axis. And so now moving on to the next axis, the y axis here that goes vertically, notice that the y axis also plots the reciprocal. And so, it's true that when we're initial reaction velocity as a whole, and we're only considering the initial reaction velocity, it's actually going to increase in the opposite direction towards the zero mark again. And so that's why we have, indicated down below that the initial reaction velocity is increasing downwards in this fashion towards the zero mark. And so the zero mark also acts as the infinity mark for the initial reaction velocity on a Lineweaver Burk plot. And so, this also applies, recall that the y axis here is associated with the y intercept, which is the reciprocal of the v max, which means that the v max itself in the bottom is going to increase towards 0, just like the Kilometers on the x axis increases towards 0 as well. And so, essentially what I want you guys to note here is that the y intercept of our line, which is, b in the equation of a line, and one over v max in our Lineweaver Burk equation, will occur graphically at infinite substrate concentrations, And here we have the infinity marker. And so really what we can see here is that the Lineweaver Burk plot, or the double reciprocal plot, really just allows us to visualize a law that we already knew from our previous lesson videos, and that is that the initial reaction velocity will approach the v max when the substrate concentration approaches infinite substrate concentrations. And so by remembering that this zero mark here acts as an infinity marker for the substrate concentration, for the initial reaction velocity, and for the v max and the kilometers, then hopefully moving forward, that'll help you guys to quickly visualize increases and or decreases to the k m and v max. And so again, if you're a little bit confused on these difficult and counterintuitive concepts, hang on tight because in our next example video, I'll show you guys how to apply these counterintuitive concepts. So I'll see you guys there.
3
example
Shifting Lineweaver-Burk Plots Example 1
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4m
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Video transcript
Alright. So now that we have an idea from our previous lesson video that both the Kilometers and the v max of an enzyme will actually increase towards the 0 marker on a Lineweaver Burk plot. In this video, we get to apply that counterintuitive idea in an example, And so let's start And so let's start with the line weaver burke plot over here on the left first. And so notice that we actually have two lines on this line weaver burke plot, one for enzyme a in light blue and one for enzyme b in black. And so starting with the kilometers here, we need to recall from our previous lesson videos that the kilometers is associated with the x intercept of the lines on a Lineweaver Burk plot. And so recall that the x intercept is where the lines cross the x axis. And so for enzyme b in black, the x intercept is right here, and for enzyme a in light blue, the x intercept is right here. And so what we need to recall from our previous lesson video is that the 0 marker here acts as an infinity marker for the substrate concentration as well as for the Kilometers, and it acts as an infinity marker for the initial reaction velocity as well as for the vmax. And so because the x intercept of enzyme a is closer to the infinity marker, that means that the k m of enzyme a is actually going to be greater than the k m of enzyme b, which is, further away from the infinity marker. And so what that means is that we can say that enzyme a has a greater kilometers than enzyme b since it's closer to this infinity marker here. And so down below, we can indicate that the kilometers of enzyme a is actually greater than the kilometers of enzyme b. And so now moving on to the v max, recall that the v max is associated with the y intercept of the Lineweaver Burk plot. And so, the y intercept is where the lines cross the y axis, and so notice that both of these lines actually cross the y axis at the same exact point, so they have the same value of the y intercept, which means that both enzymes actually have the same v max. And so we can say that the v max of enzyme a is exactly equal to the v max of enzyme b. And so that actually concludes our answers for the first line weaver Burk plot. So now let's move on to the Lineweaver Burk plot on the right. And again, we have 2 different lines, one for enzyme c in orange, and one for enzyme d here in purple. And so this time looking at the kilometers, recall that it's associated with the x intercept which is where the lines cross the x axis, and notice that they both cross the x axis here at the same exact point, which is indicating that the Kilometers of both of these enzymes is exactly the same. So we can say that the Kilometers of enzyme c is exactly equal to the Kilometers of enzyme D. And so now moving on to the v max, which is again associated with the y intercept, we need to recall that the y intercept is where the lines cross the y axis. And so for enzyme c, the y intercept is up here, and for enzyme d, the y intercept is right here. And so because the y intercept for enzyme d is closer to to 0, which again acts as the infinity marker, we can say that the v max for enzyme D is actually going to be greater than the v max for enzyme C, which is further away from the infinity marker. And so we can say that the v max of enzyme c is actually going to be smaller than the v max of enzyme d, which is greater and closer to this infinity marker. And so this here concludes our example on how to apply the counterintuitive, plots for Lineweaver Burk plots and double reciprocal plots, and we'll be able to apply these counterintuitive ideas in our practice problems. So I'll see you guys there.
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Problem
Problem
Use the plot below. The Km of both enzymes for their substrate is:
A
4 M
B
2 M
C
1 M
D
0.5 M
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Problem
Problem
Suppose a company develops two enzymes that degrade highly toxic compounds to non-toxic compounds. Your task is to degrade the greatest amount of toxic compound in the shortest amount of time.
A) Which enzyme is better to use when [S] = 0.167 mM? ____________
B) Which enzyme is better to use at saturating [S]? ____________
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Problem
Problem
Considering the Lineweaver-Burk plot below, which of the following enzymes would be better to use (converts more substrate to product) when the [S] = 0.001 M?