Use the Lineweaver-Burk plot to help you calculate the V_m...

Question

Use the Lineweaver-Burk plot to help you calculate the V_max, k_cat, K_m and specificity constant for the enzyme.

Assume the [E]_T = 2.9 nM. Hint: Pay close attention to units.

V_max = ___________.

k_cat = ___________.

K_m = ___________.

k_cat / K_m = ___________.

Accepted Answer

Alright. So this practice problem wants us to use the Lineweaver Burk plot to help you calculate the v max, the kcat, the kilometers, and the specificity constant for the enzyme. And so it wants us to assume that the total enzyme concentration is equal to 2.9 nanomolar, and it gives us this hint to pay very close attention to the units. And so we can provide the answers to this problem in these spaces that are provided. And so what we need to recall from problem in these spaces that are provided. And so what we need to recall from our previous lesson videos is that a Lineweaver Burk plot is also known as a double reciprocal plot, because it plots the reciprocal of the initial reaction velocity on the y axis, and it also plots the reciprocal of the substrate concentration on the x axis. And of course, a line Weaver Burke plot will allow us to form a line from our data, and the intercepts of this line, specifically the x and the y intercepts, are going to reveal critical information about the enzyme. And so recall that the y intercept is going to be exactly where the line of our data crosses the y axis, so that's going to be right at this particular point here. And recall that the y intercept on a Lineweaver Burk plot is also going to be a reciprocal. It's going to be the reciprocal of a velocity since the velocity is on the y axis, so it's actually gonna be the reciprocal of the maximum velocity v max. And so we can see here that the max. And so we can see here that the numbers on the y axis are increasing incrementally by 5 here, so we know that this must be associated with 5, so the y intercept is equal to 5. So all we need to do to calculate for the v max is to solve for the v max here. So we can move the v max up to this side by multiplying both sides of this equation here by v max. And so when we do that what we get is, we get that 5, times the v max here on the right and that's gonna be equal to 1. And then, essentially we can continue to solve for the v max, so we can divide both sides of the equation by 5. So when we do that, what we get is v max is equal to 1 over 5, which is of a quart which is of course equal to 0 point 2, and, the v max, the maximum reaction velocity is gonna have the same units as the initial, reaction velocity, which is in units of micromolar, per second here. And so, what we can say here is that the units are in units of micromolar per second. And so, okay, now that we've got the v max, we can go ahead and plug that in up here, so it's going to be 0.2 micromolar per second. Alright, so now we can go on and move on to the x intercept here, and so recall that the x intercept is going to be where our line here crosses the x axis, so that is going to be right here at this particular point. And recall that the x intercept is also going to be a reciprocal, except it's going to be a reciprocal of something that's associated with a substrate concentration, which would be the k m. It's gonna be the reciprocal of the k m, 1 over k m. However, we need to recall that because the x intercept always falls into this negative region here of our Lineweaver Burk plot, that our reciprocal here is actually going to be negative. And so the x intercept is actually equal to the negative reciprocal of the k m. And so, here we can see that the x intercept is equal to a value of negative 2, so we can set this equal to negative 2. And then of course, all we need to do is solve for the k m, so we can move it up to this side by multiplying both sides of the equation by k m. And so what we end up getting is that negative 2 times kilometers on the right is equal to negative 1. And then of course, when we continue to isolate for the kilometers, so, we can get rid of the negative 2 here by dividing both sides of the equation by negative 2. So then when we do that, what we get is the k m is equal to negative 1, over negative 2, which is of course equal to just 0.5 and, because k m is an exact substrate concentration that allows us to get, the initial concentration that allows us to get, the initial reaction velocity to half v max, we can say that the Kilometers is gonna have unit of a concentration. So it's gonna have the same units of concentration here, and so because the units of concentration are micromolar, then we're gonna also have micromolar for our k m. And so we can say that our k m up here is going to be 0.5 micromolar. Alright. So now what we can do is calculate the kcat. So, recall that the kcat, which we will do over here, is equal to the ratio of the vmax over the, total enzyme concentration or the e, t here. And so we just solved for the vmax, so we know that we can plug that in. And here we're given the e t, so that is in 2.9 nanomolars. But what we need to do is make sure that all of the units match each other and correspond with each other before we plug them into this expression. So notice that the v max has units of micromolar, whereas the enzyme concentration here has units of nanomolar. So let's convert these nanomolar. So let's convert these units of nanomolar into micromolar, so that we can plug it into our expression. And so, if we take the, do that down here, so if we take the total enzyme concentration, which is equal to 2.9 nanomolars, and, essentially we convert this into micromolar, we can say that there are 1,000 nanomolar and 1 micromolar. And so, essentially, what we need to do is we can see that these units cancel here, and so if you take your calculator and you do 2.9 divided by 1,000, you'll get the answer of 0.0029, and of course the only units that are left are units of micromolar. And so, now that we have our total enzyme concentration, matching the units in our v max, we can go ahead and plug into this expression here. So the v max is going to be 0.2 micromolar per second, and then, over the total enzyme concentration, which is 0.0029, 0.0029 micromolar. And so, if you take your calculator and you do 0.2 divided by 0.0029, then you'll get the answer of about 68.97, which is approximately equal to 69. And so, notice that the units of micromolar here are going to cancel, and all we're left with are, one over seconds here, so that's just essentially inverse seconds, so seconds inverse. And so this is going to be our k cat, 69 inverse seconds. So we can go ahead and plug that in up above here, 69 inverse seconds. And so now that we have both the k cat value and the k m value, we can get our specificity constant, which is the ratio of the k cat over the k m. So all we need to do is take this value of k cat and divide it by the value of the k m. And so, if we do that, if we take our kcat, so our kcat over our k m, ratio is gonna be equal to 69 inverse seconds over, the k m, which is 0.5 micromolar, 0.5 micromolar. What we're gonna get is our answer, which comes out to 138, and the units are going to be inverse seconds, as well as micro inverse micro molar since micro molar is in the bottom here. So we're gonna have inverse micro molar as well. And so this is going to be the answer for our specificity constant here, kcat over k m. So, we can say that the kcat over k m is gonna be equal to 138 inverse seconds, and inverse micromolar. And so, essentially this here concludes our answer. We were able to determine all of these different, variables here. And, so that concludes this practice, and I'll see you guys in our next video.

Struggling with Biochemistry?

Use the Lineweaver-Burk plot to help you calculate the V_max, k_cat, K_m and specificity constant for the enzyme.
Assume the [E]_T = 2.9 nM. Hint: Pay close attention to units.

V_max = ___________.
k_cat = ___________.
K_m = ___________.
k_cat / K_m = ___________.

Watch next

Specificity Constant practice set

Struggling with Biochemistry?

Use the Lineweaver-Burk plot to help you calculate the Vmax, kcat, Km and specificity constant for the enzyme.Assume the [E]T = 2.9 nM. Hint: Pay close attention to units. Vmax = ___________. kcat = ___________. Km = ___________.kcat / Km = ___________.

Watch next

Specificity Constant practice set

Use the Lineweaver-Burk plot to help you calculate the V_max, k_cat, K_m and specificity constant for the enzyme.
Assume the [E]_T = 2.9 nM. Hint: Pay close attention to units.

V_max = ___________.
k_cat = ___________.
K_m = ___________.
k_cat / K_m = ___________.