You measure V₀ of an enzyme at 6 different [S] &...

Question

You measure V₀ of an enzyme at 6 different [S] & plot the data on a Lineweaver-Burk plot. You then determine the line of best fit to the data to visualize the x & y intercepts. Calculate the V_max & K_m of the enzyme. Hint: pay close attention to the indicated units.

Lineweaver-Burk plot showing enzyme kinetics with Vmax and Km calculations.

Accepted Answer

Alright. So this practice problem says you measure the initial reaction velocity or the v naught of an enzyme at 6 different substrate concentrations, and then you plot that data onto the Lineweaver Burk plot shown down below. And so notice that with the Lineweaver Burk plot, again, it has the reciprocal of the initial reaction velocity on the y axis and the reciprocal of the substrate concentration on the x axis. And so, we can tell that we've plot we've plotted 6 different experimental data points in our plot below because we have these 6 experimental data point circles in red down below. And so the problem continues to tell us that you then determine the line of best fit to this data. So this line right here is the line of best fit that best fits the experimental data points that are shown. And, the reason that we do that is to visualize the x and the y intercept. So notice that the, y intercept is equal to 3 times 10 to the 7th, and the x intercept is equal to negative 5 times 10 to the 4th. And so, it wants us to calculate the v max and the cam of the enzyme from this information, and it gives us the hint to pay close attention to the indicated units. And so, again, we know that we're going to be calculating the v max. And so in order to calculate the v max, we're gonna need to pay close attention to the y intercept, and the y intercept is where our line crosses the y axis. So that's gonna be right at this particular point here, which is associated with the value 3 times 10 to the 7th. And so, essentially what we can say is the y intercept on a Lineweaver Burk plot, we know is going to be a reciprocal just like the x axis and the y axis are also reciprocals. So it's going to be one over something, and that something is going to be associated with the y axis. So because the y axis is associated with a reaction velocity, so is the y intercept, and it's actually going to be the reciprocal of the theoretical maximal reaction velocity v max. And so, we just said that this value here is associated with the value 3 times 10 to the 7th. And so, this is the value of the y intercept, not the value of the vmax itself. And so, we need to set our y intercept equal to 3 times 10 to the 7th. And then that allows us to calculate for this v max. So we can calculate the v max by moving it up to this side by multiplying both sides of the equation by v max, And then after we do that, we can divide both sides of the equation by 3 times 10 to the 7th. And when you do that, you'll get that the v max is equal to 1 over 3 times 10 to the 7th. And so if you type that into your calculator, 1 divided by 3 times 10 to the 7th, you'll get an answer of 3.33 times 10 to the negative 8th. And the units of the v max are gonna be the same as the units of the initial reaction velocity, v naught, which is units of molarity per minute. So we can put that here. So what we need to notice next is that the answer here, wants us to, indicate the answer in units of nanomolar per minute, not molarity per minute. And so we need to convert the molarity into nanomolar so that they match each other. And so in order to do that, what we can do is take our 3.33 times 10 to the negative 8, the same number here, and, we can say that this is in units of molarity, and we wanna convert it to nano molar. So we know that we want molarity to be here, so we can say that in 1 molar, that will allow the molarity to cancel out. We can say that there are 10 to the 9th nanomolar. And so nano here means to the 9th, 10 to 9th. And so, if you take your calculators and you do 3.33 times 10 to the negative 8th, times 10 to 9th, you'll get the answer of 33.3 times 10 to, or just 33.3, nanomolar, per minute. And so now that we have our v max and units of nanomolar per minute, we can go ahead and plug that value into our answer below. And so, the answer is going to be 33.3 nanomolar per minute for the v max. So now that we've done that, we can do the same with the k m, which we know is instead, associated with the x intercept instead of the y intercept. And the x intercept is gonna be where our line crosses the x axis. So it's going to be right at this particular point right here, which we can see is associated with this value negative 5 times 10 to the 4th. So we can say over here that our x intercept on a Lineweaver Burk plot, just like everything else is essentially reciprocals, so is the x intercept. It's going to be a reciprocal, so it's going to be one over something, and that something is going to be associated with what's on the x axis, which is a substrate concentration. And we know that the kilometers is an exact substrate concentration that allows the initial reaction velocity to be half of the v max. And so, next what we need to recall is that the x intercept always falls into this negative region here of our Lineweaver Burk plot. So notice that the values of the x intercept are always negative. And so, what that means is we need to remember to include the negative sign here with the one. And so, the x intercept on a line we were Burke plot is the negative reciprocal of the kilometers. And, we just said that the x intercept is associated with this value, negative 5 times 10 to the 4th. So we can set it equal to that. And so now we can solve for the value of our Kilometers, our Michaelis constant. We can do that by moving it up to this side of the equation by multiplying both sides of the equation by the Kilometers. And then after we do that, we can divide both sides of the equation by negative 5 times 10 to the 4th. And when we do that, what we'll get is that the Kilometers all by itself is equal to negative one over negative five times 10 to the 4th. And so if you take your calculator and you do negative one divided by negative five times 10 to the 4th, you'll get an answer of 2 times 10 to the negative 5th. And the units are gonna be the same units that are associated with the substrate concentration on the bottom, which are just molarity. And so we can put that here as well, molarity. And so, notice that our k m, we want in the units of micromolar, not in the units of molar. And so, what we need to do is convert these units. So we can take our 2 times 10 to the negative 5th molar, and we can say that in one molarity, there are 10 to the 6 micromolars. And so, that allows our units of molarity to cancel out. And so if we take our calculator and we do 2 times 10 to the negative 5th times 10 to the 6 here, we'll get an answer of 20 micromolar. And so now that our answer of micromolar, matches, the units that we need, we can say that our kilometers our k m is just 20 micromolar. And so, these here are the answers to our practice problem, and that concludes this practice. So I'll see you guys in our next video.

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You measure V₀ of an enzyme at 6 different [S] & plot the data on a Lineweaver-Burk plot. You then determine the line of best fit to the data to visualize the x & y intercepts. Calculate the V_max & K_m of the enzyme. Hint: pay close attention to the indicated units.

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You measure V₀ of an enzyme at 6 different [S] & plot the data on a Lineweaver-Burk plot. You then determine the line of best fit to the data to visualize the x & y intercepts. Calculate the V_max & K_m of the enzyme. Hint: pay close attention to the indicated units.