Michaelis-Menten Equation - Video Tutorials & Practice Problems
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Michaelis-Menten Equation
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Video transcript
Alright. So now that we've covered the Michaelis Menten assumptions, in this video, we're gonna talk about the Michaelis Menten equation. And so the Michaelis Menten equation, we're commonly going to abbreviate as just the m m equation in our lesson. And so the Michaelis Menten equation is just a mathematical description of the initial reaction rates or the V naught of an enzyme catalyzed reaction. And so really that should be no surprise to us since we know from our previous lesson videos that biochemists mainly focus on the initial reaction rates or the V naught of enzyme catalyzed reaction. And so now we're talking about an equation that allows us to calculate these initial reaction rates. And so really, the, Michaelis Menten equation mathematically relates the initial reaction velocity v naught to the substrate concentration, and it does that via the theoretical maximum reaction velocity v max and the Michaelis constant or the kilometers. And so, essentially, what we're saying is that the Michaelis Menten equation mathematically relates all of these enzyme kinetics variables that we already talked about in our previous lesson videos, and we'll be able to see that down below in our example on the left hand side. Now, if we take a quick look at our example down below, at this plot that we have on the right, notice that this is our enzyme kinetics plot, which is also commonly known as just a Michaelis Menten kinetics plot. And so, again, we've seen this plot so many times before in our previous lesson videos. So we're already familiar that on the y axis we have the initial reaction rate or the v naught, and on the x axis we have the substrate concentration. And, of course, we know that it's typical for enzymes to show this curve that we see here on this plot. Now, what you may not have known is that the shape of the curve that we see here is, actually has a name to it, and the name of the shape is actually called a rectangular hyperbola. And so essentially what we'll see is that the, Michaelis Menten equation is actually describing the rectangular hyperbola shape shape that we see in these, enzyme, kinetics plot, so often, these typical curves that we see in these enzyme kinetics plots. And so, again, the enzyme enzyme kinetics plot that we see down below plots the initial reaction velocity on the y axis, and it plots the substrate concentration on the x axis. And so, what you'll notice is that the rectangular hyperbola, just like a line, we know has an equation, y equals mx+b. A rectangular hyperbola, or this shape right here also has an equation. And so the equation for a rectangular hyperbola curve is actually this equation that's shown here. And so what we'll see is that the Michaelis Menten equation, really all it does is it simply substitutes, it substitutes enzyme kinetics variables into this rectangular hyperbolic equation that we see up above. So all we do is we take enzyme kinetics variables and we plug them in to this equation that we see here. So to see what I mean, let's take a look at our image down below on the left hand side here. And so notice on the left, what we have is the rectangular hyperbola equation, the same one that we have up above here and so it's exactly color coded so that we can see how we can substitute enzyme color coded so that we can see how we can substitute enzyme kinetics variables into this equation to get our Michaelis Menten equation. And so the y here and the rectangular hyperbola equation is going to be what we have on the y axis of our enzyme kinetics plot. And what we have on the y axis is our initial reaction rate v naught. So you can see that we take the y and we plug it in with v naught, since that's what's on the y axis. Then what we have, is this a here and this a, this red a is going to be our v max. And the b in the denominator, the bottom here, is going to be our Michaelis Menten k m. And so what can help us remember that is if we take a look at our enzyme kinetics plot, notice that the v max is towards the top of our plot, whereas the k m is on the x axis towards the bottom of our plot. So you can see k m is on the bottom and the v max is on the top of our plot. So that's what helps us remember to substitute these variables, accordingly. And then of course, we know that the x is going to be exactly what we have on the x axis which is the substrate concentration. And so essentially what we can do is, plug into these x's the substrate concentration over here. So we'll have substrate concentration. And so essentially, this is our Michaelis Menten equation. And moving forward in our course, we're going to be able to use this equation to solve for the initial reaction velocity and for other variables as well, as long as we're given, the appropriate, variables to solve for the missing variables. And so, you can see how really the Michaelis Menten equation includes all of these, variables that we, discussed before in our previous lesson video. So we can see that the v max is, included in the equation. So is the k m down below. And we have the substrate concentration included in the equation as well as the initial reaction velocity. And so this concludes our lesson on the introduction to the Michaelis Menten equation. And in our next video, I'll show you guys an example of how to utilize, this Michaelis Menten equation. And so I'll see you guys in that video.
2
example
Michaelis-Menten Equation Example 1
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6m
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Video transcript
All right. So now that we formally introduced the Michaelis Menten equation in our last lesson video, in this video, I'm going to show you guys how to the Michaelis Menten equation in a 2 part example problem. And so this example problem wants us to consider the following enzyme kinetics data down below for the enzyme catalyzed reaction shown right here, where we have substrate a being converted into product b. And so looking at this enzyme kinetics data down below, notice in the first column on the left hand side, what we have is the concentration of our substrate a in units of micromoles. And in the second column on the right, what we have is the v naught or the initial reaction velocity of the enzyme catalyzed reaction in units of micromoles moles per minute. And so looking at part a, it's asking us what is the Michaelis constant or the Kilometers of the enzyme. And so what we need to recall from our previous lesson videos is that the kilometers can be defined as, notice that the kilometers can be defined as the exact substrate concentration when the initial reaction velocity is exactly equal to half of the v max. And so notice that we are given the initial reaction velocity, velocity, in our data over here, but we're not directly given the v max. And so what we need to do is use this data on the right to help us it starts really, really low and it steadily increases, and then the increases get greater and greater and greater to a point where the concentrations are so great that the initial reaction velocity doesn't even change. And so this is suggesting that the substrate concentrations are so high that it's completely saturating the enzyme. And recall from our previous lesson videos that when an enzyme is completely saturated with substrate, the initial reaction velocity can approach the v max. And so what we're saying is that these initial reaction velocities of 80 must be approaching and getting really close to the v max. And so we can pretty much say that our v max is equal to a value of 80 micro moles per minute. And so now that we have our v max, if we want to get half the v max, then all we need to do is take half of the value of the v max, and half of our v max, which is 80, is going to be 40, of course. And notice that 40 actually shows up here in our data. And so, this is a velocity that's equivalent to half of the v max. And notice that the substrate concentration, when the initial reaction velocity is half the v max, is going to be the k m. And so this substrate concentration here of 50 micromoles corresponds with half of the v max. And so we can say that this substrate concentration micromolar 50 micromolar is our k m, and that is the answer to part a. Now, moving on to part b, it's asking what is the value of the v naught or the initial reaction velocity when the concentration of substrate a is equal to 43, and we'll assume the units are micromolar. And so in order to solve this, we're going to need to utilize our Michaelis Menten equation or the equation, which is provided down below in this box here. And so, we want to solve for the initial reaction velocity, so all we need to do is plug in all of these other values here and calculate it using our calculator. So let's go on and do that. So we have the initial reaction velocity v naught, is equal to the vmax here, and the vmax we previously identified as being 80 micromoles per minute, and so we're going to multiply this by the concentration of our substrate, which is given to us as 43 micromolar. So we'll go ahead and multiply molar, so we can put that in down below. And then this is molar, so we can put that in down below. And then this is going to be added to the substrate concentration again, which we know is 43 micromolar, given to us as 43 micromolar. And so all we need to do is plug all of this into our calculator. So if you do 80 micromoles per minute times 43 micromoles, and take that answer and divide it by 50 micromole plus 43 micromoles, you'll get the answer, which is approximately equal to 36 point 99, which rounds off to about 37, and the units of the initial reaction velocity are gonna equal the units of the initial reaction velocity that we have in our chart, so it's gonna be micromoles per minute. And so this here is the answer that we are looking for, so 37 micromoles per minute. And so we can say that when the initial, or when the concentration of our substrate is equal to 43 micromolar, the initial reaction velocity will be 37 micromoles per minute. And so we could have kind of, checked to look at our data over here to see if our answer makes sense. And so notice that a concentration of 43 micromolar is just below the concentration of 50 micromolar, just a little bit smaller. And so we expect that the velocity that corresponds with 43 is just going to be a little bit smaller than the velocity that corresponds with 50. And so when we see that this 40 here, we can see that our velocity is in the right ballpark. So we know that our answer is in the right ballpark. And so, also what this example shows us is that as long as we have 3 out of the 4 total variables that are present in our Machias Menton equation, then we can solve for that 4th and missing variable. And so that shows us the power of the Michaelis Menten equation, and we'll be able to continue to utilize it as we move forward in our next video. So I'll see you guys there.
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Problem
Problem
A) Suppose the [S] = 10 Km. Use the Michaelis-Menten equation to determine what percentage of the Vmax will be equal to the value of V 0.
B) Now suppose the [S] = 20 Km. Use the Michaelis-Menten equation to determine what percentage of the Vmax will be equal to the value of V 0. What conclusion can be made from these calculations?
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4
Problem
Problem
Which of the following statements about a V0 vs. [S] plot for a Michaelis-Menten enzyme is false?
A
As [S] increases, V0 also increases.
B
At very high [S], the curve becomes a horizontal line that intersects the y-axis at Km.
C
Km is the [S] at which V0 = ½ Vmax.
D
The shape of the curve is a hyperbola.
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Problem
Problem
What is the ratio of [S] to Km ( [S] / Km ) when the V0 of an enzyme-catalyzed reaction is 80% of the Vmax?
A
1.
B
2.
C
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D
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E
5.
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Problem
Problem
An enzyme-catalyzed reaction was carried out with a [substrate] initially 1000 times greater than the Km for that enzyme. After 9 minutes, 1% of the total substrate was converted into 12 μmoles of product. If in a separate experiment, one-third as much enzyme and twice as much substrate had been combined, how long would it take for the same amount of product (12 μmoles) to be formed?
A
1.5 min.
B
13.5 min.
C
27 min.
D
3 min.
E
6 min.
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Problem
Problem
An enzyme catalyzes a reaction at a velocity of 10 μmol/min when all enzyme active sites are occupied with substrate. The Km for this substrate is 1 x 10-5 M. Assume that Michaelis-Menten kinetics are followed, calculate the initial reaction velocity (V0) when: