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6. Enzymes and Enzyme Kinetics

# Michaelis-Menten Equation

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#### concept

Michaelis-Menten Equation 7m
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all right, So now that we've covered the McHale is meant in assumptions. In this video, we're going to talk about The McHale is meant in equation, and so the McHale is meant in equation were commonly going to abbreviate as just the M M equation in our lesson. And so the McHale is meant in equation is just a mathematical description of the initial reaction rates or the V, not of an enzyme catalyzed reaction. And so, really, that should be no surprise to us, since we know from our previous lesson videos that biochemist mainly focus on the initial reaction rates or the V not 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 McHale is meant in equation mathematically relates the initial reaction velocity Veena to the substrate concentration, and it does that via the theoretical maximum reaction Velocity V Max and the Michaelis Constant or the K M. And so, essentially, what we're saying is that the McHale is meant in 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 meticulous meant in kinetics plot. And so again, we've seen this plot so many times before and our previous lesson videos. So we're already familiar that on the y axis we have the initial reaction rate or the V not. 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, um, actually has a name to it, and the name of the shape is actually called a rectangular hyperba. And so, essentially, what we'll see is that the McHale is meant in equation is actually describing the rectangular hyperbole a shape that we see in these enzyme kinetics plot eso often these, um, typical curves that we see in these enzyme kinetics plots. And so again, the 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 hyperba um just like a line we know has a an equation. Why equals M x plus B, a rectangular hyperba or this shape right here also has an equation. And so the equation for a rectangular hyperbole curve is actually this equation that's shown here. And so what we'll see is that the McHale is meant in equation. Really? All it does is it simply substitutes. It's substitutes, enzyme kinetics variables into this rectangular hyperbole 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 hyperbole, a equation, the same one that we have up above here. And so it's exactly the same. And so notice that, uh, the rectangular hyperbolic equation is color coded so that we can see how we can substitute enzyme kinetics variables into this equation to get our meticulous mental equation. And so the why here and the rectangular hyperbole 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 Not so you can see that we take the why and we plug it in with V Not since that's what's on the Y axis, then what we have is this a here in this A This read A is going to be our V max and the B and the denominator. The bottom here is going to be our McHale is meant in 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 could do is, uh, plug into these X is this substrate concentration over here? So we'll have substrate concentration. And so, essentially, this is our meticulous meant in 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. Asl Ong as were given the appropriate variables to solve for the missing variables. And so, uh, you can see how really the McHale is meant in equation includes all of these variables that we, uh, discussed before in our previous lesson video so we can see that the V max is included in theory, the equation. So is the k M, um, 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 McHale is meant in equation. And And our next video, I'll show you guys an example of how to utilize. Uh, this McHale is meant in equation. And so I'll see you guys in that video.
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#### example

Michaelis-Menten Equation Example 1 6m
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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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Problem

Which of the following statements about a V0 vs. [S] plot for a Michaelis-Menten enzyme is false?

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Problem

What is the ratio of [S] to Km ( [S] / K) when the V0 of an enzyme-catalyzed reaction is 80% of the Vmax?

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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?

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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:

A) [S] = 1 x 10-5 M. V0 = ___________

B) [S] = 1 x 10-2 M. V0 = ___________ 