WEBVTT chemistry/biochemistry/hovasapian 00:00:00.000 --> 00:00:04.000 Hello and welcome back to Educator.com; welcome back to Biochemistry. 00:00:04.000 --> 00:00:12.000 Today, we are going to continue our discussion using this thing called the Michaelis-Menten equation that we introduced in the last lesson. 00:00:12.000 --> 00:00:22.000 We introduced this idea of the velocity max and this thing called the Km, the Michaelis-Menten constant- very, very important. 00:00:22.000 --> 00:00:42.000 In this lesson, what I am going to do is give you an alternate version of that, where instead of estimating Vmax and estimating the Km like we did in the previous lesson, we are going to develop an actual analytical method, where we actually come up with some really, really exact values for this. 00:00:42.000 --> 00:00:46.000 Let's just jump right on in; it is actually quite simple. 00:00:46.000 --> 00:00:52.000 OK, let's go ahead and start off with our Michaelis-Menten equation again. 00:00:52.000 --> 00:00:54.000 That is fine; I guess I can stick with black. 00:00:54.000 --> 00:01:10.000 It is not a problem; we said that rate of the reaction, the speed at which it is going, is going to equal some maximum velocity times this substrate concentration over this Michaelis-Menten constant plus the substrate concentration. 00:01:10.000 --> 00:01:14.000 This is our initial equation; well, let's do something to this equation. 00:01:14.000 --> 00:01:18.000 Let's actually reciprocate their left side and the right side. 00:01:18.000 --> 00:01:23.000 Let's just flip it and then, manipulate it algebraically to see what we might get. 00:01:23.000 --> 00:01:28.000 When you do that - excuse me - you end up with the following. 00:01:28.000 --> 00:01:40.000 You end up with 1/v0 = Km + S/Vmax - excuse me - x S. 00:01:40.000 --> 00:01:44.000 Now, we have everything under 1 denominator; there is only a single term of the denominator. 00:01:44.000 --> 00:02:12.000 Let's separate those out and see what happens; you end up with 1/v0 = Km/Vmax x S + S/Vmax x S. 00:02:12.000 --> 00:02:16.000 These Ss cancel; let me rearrange this. 00:02:16.000 --> 00:02:22.000 This term right here is the same as Km/Vmax x 1/S. 00:02:22.000 --> 00:02:40.000 I end up with 1/v0 = Km/Vmax x - let me put that in parentheses - 1/S + 1/Vmax. 00:02:40.000 --> 00:02:45.000 This equation, it is called the double reciprocal equation. 00:02:45.000 --> 00:03:00.000 Double reciprocal because I took the reciprocal of the left and the right, also called the Lineweaver-Burk equation. 00:03:00.000 --> 00:03:04.000 That is what is important; notice the form of this. 00:03:04.000 --> 00:03:11.000 This is Y = mx + B, and this is the equation for line. 00:03:11.000 --> 00:03:19.000 Y is 1/v0; M the slope, is Km/Vmax. 00:03:19.000 --> 00:03:27.000 1/s is the independent variable, and 1/Vmax, that is the Y intercept. 00:03:27.000 --> 00:03:34.000 Here is what you do; when you are given rate-concentration data like the previous lesson. 00:03:34.000 --> 00:03:40.000 What you do is you create 2 new columns; you take the reciprocal of the substrate concentrations that you used. 00:03:40.000 --> 00:03:52.000 That is going to be another column; those are going to be your X axis, and you take the reciprocal of the velocity values that you have got, and that is going to be your other column. 00:03:52.000 --> 00:03:57.000 That is going to be your Y axis; you are going to plot this out. 00:03:57.000 --> 00:04:08.000 When you plot this out, here is what you are going to get. 00:04:08.000 --> 00:04:12.000 On this axis, we have our 1/S. 00:04:12.000 --> 00:04:16.000 On this axis, we have 1/v0. 00:04:16.000 --> 00:04:27.000 When you plot this out, the 1/v0 versus the 1/S, you are going to end up with a line, some straight line like that. 00:04:27.000 --> 00:04:38.000 Here is what is great; the Y intercept, well, that is equal to...let me actually rewrite the equation here again, so we see it. 00:04:38.000 --> 00:04:50.000 We had 1/v0 = Km/Vmax x 1/S + 1/Vmax. 00:04:50.000 --> 00:04:56.000 Well, this Y intercept because it is 1/v0, it is not v0 versus S anymore. 00:04:56.000 --> 00:05:00.000 It is 1/v0 versus 1/S. 00:05:00.000 --> 00:05:09.000 You get a straight line; where it hits the Y axis, that is equal to 1/Vmax. 00:05:09.000 --> 00:05:13.000 You literally read this number; you said it equalled to Vmax. 00:05:13.000 --> 00:05:14.000 You switched the 2; you solved for Vmax. 00:05:14.000 --> 00:05:18.000 It is an analytical way of finding Vmax. 00:05:18.000 --> 00:05:29.000 Where it hits the X axis here, this is equal to -1/Km. 00:05:29.000 --> 00:05:38.000 The slope of this equation is equal to Km/Vmax. 00:05:38.000 --> 00:05:41.000 That is the slope; that is the Y intercept. 00:05:41.000 --> 00:05:46.000 We have an analytical method based on rate-concentration data. 00:05:46.000 --> 00:05:50.000 Create 2 new columns of data: 1 over concentration, 1 over velocity. 00:05:50.000 --> 00:05:54.000 Graph that; take the 2 intercepts. 00:05:54.000 --> 00:05:59.000 Solve for Vmax, and solve for Km; now, we have a precise way. 00:05:59.000 --> 00:06:08.000 We do not have to, anymore, estimate where the Vmax is going to be and then, take half of that and then, find the Km. 00:06:08.000 --> 00:06:14.000 Now, we have a nice analytical procedure for finding Vmax and Km- that is it. 00:06:14.000 --> 00:07:35.000 That is all that is happening here; again, when given data that includes substrate concentration and various initial rates, in other words, when you are given substrate initial rate data, when you are given data that includes substrate concentrations and various initial rates, we form new data, and the new data we form is 1 over those substrate concentration and 1 over the initial rates and then, plot this. 00:07:35.000 --> 00:07:40.000 From the plot, we calculate Vmax and Km- pretty standard when dealing with a new enzyme. 00:07:40.000 --> 00:07:58.000 You have purified a new enzyme; one of the first things you do is you run these initial rate experiments, and you find its Km, and you find its maximum velocity under a certain set of conditions and for that particular substrate- that is it. 00:07:58.000 --> 00:08:01.000 That is it; it is literally that simple. 00:08:01.000 --> 00:08:08.000 Let's go ahead and do an example; let's see what we have got. 00:08:08.000 --> 00:08:15.000 Carboxypeptidase is a digestive enzyme of the pancreas, and its activity was monitored under several initial substrate concentrations. 00:08:15.000 --> 00:08:20.000 The data is as follows. 00:08:20.000 --> 00:08:33.000 In this particular case, the substrate concentration happens to be in millimoles per liter, 0.1, 2, 10, 20, 40, 60, 120, 1000, 2000. 00:08:33.000 --> 00:08:38.000 The initial velocities that were measured are here, millimoles per liter per minute. 00:08:38.000 --> 00:08:48.000 And again, it is a rate; it is the rate at which the concentration is changing initial rate- 0.2, 5, 4.8, 19, all of these numbers here. 00:08:48.000 --> 00:08:52.000 Well, given concentration rate data, we create 2 new columns. 00:08:52.000 --> 00:09:00.000 We take 1/S, 1 over these; that is this column here, and then, we take 1/V, 1 over all of these. 00:09:00.000 --> 00:09:04.000 That is this column here; notice what is different, though. 00:09:04.000 --> 00:09:08.000 Excuse me; 1 over these numbers, these numbers are going to start to get very, very small. 00:09:08.000 --> 00:09:22.000 What I have done is instead of writing them as, let's say for example 10.5, 0.05, 0.025, I have went ahead, and I have multiplied them by 10^-3. 00:09:22.000 --> 00:09:30.000 Notice here, that is why I have this x 10^-3; this is actually 100 x 10^-3, 25 x 10^-3. 00:09:30.000 --> 00:09:35.000 I did this in order to make my graph a little easier to deal with. 00:09:35.000 --> 00:09:42.000 I do not want to graph 0.1, 0.5, 0.025, 0.010, 0.005. 00:09:42.000 --> 00:09:46.000 I am just scaling the graph; that is all I am doing. 00:09:46.000 --> 00:09:50.000 When you read the information off the graphs, be very, very careful. 00:09:50.000 --> 00:09:55.000 Make sure you actually include that number, and you will see what we deal with in just a minute. 00:09:55.000 --> 00:10:00.000 Again, for the 1/S, and this, I have gone ahead and expressed these as 10^-3. 00:10:00.000 --> 00:10:04.000 For example, this value is actually 50 x 10^-3. 00:10:04.000 --> 00:10:10.000 This one is 12.8 x 10^-3 or 0.0128. 00:10:10.000 --> 00:10:14.000 12.8 is easier to graph than 0.0128. 00:10:14.000 --> 00:10:18.000 That is the only reason we are doing this to make it convenient for ourselves. 00:10:18.000 --> 00:10:27.000 What we are going to be doing is we are going to be graphing this now on the X axis; this on the Y axis, we are going to draw our best line, and we are going to read off the Y intercept and the X intercept. 00:10:27.000 --> 00:10:34.000 We are going to solve for Vmax and Km- very, very nice, the beautiful, beautiful thing. 00:10:34.000 --> 00:10:38.000 OK, let's see what we have got here. 00:10:38.000 --> 00:10:44.000 OK, let's go ahead and draw our graph; let me go ahead and actually do this in black. 00:10:44.000 --> 00:10:48.000 What you are going to end up with is something that looks like this. 00:10:48.000 --> 00:11:00.000 I am not going to make it 2; OK, we have got 10, 20 and 30. 00:11:00.000 --> 00:11:08.000 OK, we have got 10, 20, 30, 40 and 50. 00:11:08.000 --> 00:11:14.000 When we go ahead and plot all of this, we are going to end up with some line that looks like this. 00:11:14.000 --> 00:11:21.000 Let me go ahead and mark this point, and let me mark this point. 00:11:21.000 --> 00:11:37.000 I am going to have something like here and then, a 10 maybe here and then, a 20 like there and there and then there. 00:11:37.000 --> 00:11:40.000 We are going to end up with some lines; what we do is we end up doing it best fit. 00:11:40.000 --> 00:11:44.000 You do not connect the dots; you are doing the best fit line. 00:11:44.000 --> 00:11:48.000 It is not going to be exactly a straight line, but it is actually going to be pretty close surprisingly. 00:11:48.000 --> 00:12:04.000 You are going to end up with something that looks like...I know it does not look like a straight line, but well, you know what, let me try to make this a little bit better. 00:12:04.000 --> 00:12:10.000 You are going to end up with something that is like...let me not put a point there. 00:12:10.000 --> 00:12:19.000 Let me not put a point there just yet; let me go ahead and do some values like there and there. 00:12:19.000 --> 00:12:32.000 What you are going to end up with is the following; erase these...maybe something that looks like that. 00:12:32.000 --> 00:12:38.000 You graphed it; you have a best fit line, and then, you have that point; and you have that point. 00:12:38.000 --> 00:12:42.000 Now, let's go ahead and just read them off. 00:12:42.000 --> 00:12:45.000 This is 10; this is 20. 00:12:45.000 --> 00:12:51.000 This is 30; this is 10, 20, 30, 40 and 50. 00:12:51.000 --> 00:12:56.000 Recall, this is 1/S, and recall, this is x 10^-3. 00:12:56.000 --> 00:13:06.000 This is the 1/v0 axis, and recall, this is x 10^-3. 00:13:06.000 --> 00:13:16.000 So, when I read this one off right here...I will do this one down here, and I will actually do it in blue. 00:13:16.000 --> 00:13:20.000 The Y intercept, that was the Vmax. 00:13:20.000 --> 00:13:23.000 We have 1/Vmax is equal to...and when you read it off the graph, it ends up being 6.1 x 10^-3. 00:13:23.000 --> 00:13:38.000 You just read it right off the graph: 6.1 x 10^-3. 00:13:38.000 --> 00:13:47.000 When you solve this, you get a Vmax is equal to, of course, 1/6.1 x 10^-3. 00:13:47.000 --> 00:14:02.000 It is going to equal 164 mmol - I will do the molarity that way - per minute- that is it. 00:14:02.000 --> 00:14:10.000 This is our Vmax, an analytical way of coming, 164 mmol/min. 00:14:10.000 --> 00:14:14.000 That is the fastest that this enzyme is going to go under these conditions. 00:14:14.000 --> 00:14:24.000 Now, we will go ahead and do this one; this is -1/Km, and remember, again, it is x 10^-3. 00:14:24.000 --> 00:14:35.000 When you read this one, you are going to get...when you read it right off the graph, it is going to be -15.5 x 10^-3. 00:14:35.000 --> 00:14:51.000 When you solve this, you end up with the following; you end up with a Km equal to 64.5mmol/L- that is it. 00:14:51.000 --> 00:15:06.000 The Km has units of concentration because remember what we said: Km is the concentration of substrate at which the speed of enzyme turnover is 1/2 the maximum velocity. 00:15:06.000 --> 00:15:25.000 So, when the substrate concentration is 64.5mmol/L under these conditions, the speed of the reaction, that is going to be somewhere in the neighborhood of 82mm/L/min- that is it. 00:15:25.000 --> 00:15:32.000 This is an analytical way of finding the Km and the Vmax- that is it. 00:15:32.000 --> 00:15:37.000 That is what this Lineweaver-Burk plots do; you can use the rate concentration data if you want. 00:15:37.000 --> 00:15:45.000 Estimate Vmax, read it off the graph, or you can do something a little bit more analytical and make a Lineweaver-Burk plot. 00:15:45.000 --> 00:15:57.000 These Lineweaver-Burk plots are actually going to play a very, very important role when we talk about enzyme inhibition in the next lesson- very, very important analytical tool. 00:15:57.000 --> 00:16:05.000 One caveat, as we said, we have a purified enzyme; one of the first things we do is find the Km and find the Vmax for the particular enzyme. 00:16:05.000 --> 00:17:04.000 Now, it is very, very important - I will just leave you with this - to remember that Km and Vmax give very little information about the actual individual steps in a reaction, in other words, what is happening at the molecular level. 00:17:04.000 --> 00:17:21.000 I will say not in a reaction, and we know this, but in an enzyme catalyzed reaction, but it is a place to start. 00:17:21.000 --> 00:17:25.000 And again, sometimes, all you need is a place to start. 00:17:25.000 --> 00:17:34.000 When we talk about kinetics, the Michaelis-Menten kinetics, steady state kinetics where all of this is coming from, this Km and this Vmax, understand that these are kinetic data. 00:17:34.000 --> 00:17:38.000 These are kinetic parameters; what that means is they talk. 00:17:38.000 --> 00:17:39.000 They relate to rate; that is what kinetics is. 00:17:39.000 --> 00:17:49.000 It is how fast something is going, or in the case of Km, how much substrate will allow me half the maximum velocity. 00:17:49.000 --> 00:17:53.000 Again, velocity still plays a role in this. 00:17:53.000 --> 00:17:56.000 This does not really tell me anything much more than that. 00:17:56.000 --> 00:18:01.000 It is more historical for all practical purposes, I mean, still one of the things that you are going to do. 00:18:01.000 --> 00:18:05.000 I am not saying that it does not give you information; of course, it gives you information. 00:18:05.000 --> 00:18:10.000 And again, it is a place to start, but ultimately what we are concerned with is mechanism. 00:18:10.000 --> 00:18:21.000 Mechanism is the individual steps- what is happening at the atomic/molecular level between an enzyme and a substrate that converts a substrate to a product. 00:18:21.000 --> 00:18:26.000 The Km and the Vmax do not give you much information; they are just a place to start. 00:18:26.000 --> 00:18:34.000 Do not think that you are missing something, that if you have a certain Km or if you have a certain Vmax, that is necessarily going to tell you something about the mechanism. 00:18:34.000 --> 00:18:51.000 It is not; there are lots of experimental tools and lots of other things that need to be done that allow us to find out what is happening individually in a given active site of a given enzyme with a given amino acid sequence. 00:18:51.000 --> 00:19:01.000 There are other things that we do; this information does not give us information about those steps, and ultimately, it is those steps that we want to consider. 00:19:01.000 --> 00:19:08.000 But again, this is part of biochemistry; it is part of the normal routine that people go through on a daily basis in laboratories. 00:19:08.000 --> 00:19:11.000 You are going to have to know something about it. 00:19:11.000 --> 00:19:19.000 That is all, but do not feel that you are missing anything; do not try to extrapolate any other information other than what is given. 00:19:19.000 --> 00:19:46.000 This is all that it is, no more and no less, and it is all based on those 2 assumptions- the steady state assumption, that the breakdown of the enzyme substrate complex and the formation of the enzyme substrate complex happen at the same rate; and, of course, ultimately, this is based on Michaelis and Menten simplifying assumption that this thing happens in 2 steps, and the second step, the breakdown of the enzyme substrate is the slowest step. 00:19:46.000 --> 00:19:50.000 We need to know where these things come from. 00:19:50.000 --> 00:19:55.000 We want to see the forest from the trees; I cannot reiterate this enough. 00:19:55.000 --> 00:20:05.000 The Km and the Vmax are just kinetic parameters; they do not tell you anything about how the substrate turns into product in the active site. 00:20:05.000 --> 00:20:10.000 Other things are used to extract that information. 00:20:10.000 --> 00:20:30.000 We will be looking at mechanisms, of course, individually in a couple of lessons, and, of course, when we talk about metabolic pathways, we are definitely going to be talking about enzyme mechanisms - which proton is being transferred, which amino acid is involved in the catalytic mechanism, things like that - but these do not give you that information directly. 00:20:30.000 --> 00:20:34.000 OK, thank you for joining us here at Educator.com. 00:20:34.000 --> 00:20:37.000 We will see you next time for discussion of enzyme inhibition; take care, bye-bye.