Biochemistry Enzymes VII: Km & Kcat

Hello and welcome back to Educator.com, and welcome back to Biochemistry.0000

Today's lesson, we are going to be talking about the Michaelis-Menten constant and this new constant that we are going to introduce called K_cat.0004

This particular lesson is really, really, very, very important.0016

I am not suggesting that the other lessons are not important, but in the biochemistry course, this quantitative study of kinetics is usually, sort of, a daunting thing for the kids.0020

There is just a lot of symbols floating around; there is a lot of mechanisms, a lot of reactions.0035

You have enzyme substrate product, enzyme substrate, enzyme substrate pro...all kinds of things.0040

So, it tends to get really, really confusing.0047

What I wanted to do is I wanted to come back; we have already discussed the Michaelis-Menten kinetics.0051

We have the Michaelis-Menten equation; I wanted to go back and talk about what K_m actually means.0056

I want to talk about how it is used in biochemistry, whether that usage is actually justified or not.0062

I just wanted to spend some more time with it- that is it.0070

I just want you to be as comfortable as possible because these things do come up a lot - well, of course, they come up a lot - in the literature, and it is the one area that I think kids are the most...that it alienates them the most easily.0074

It is really not that bad; a lot of it is actually quite intuitive.0089

You just need to, sort of, get past a lot of the symbolism.0093

In any case, let's just jump right on in, and hopefully, we can help you to get a better understanding of what all of these different things mean.0097

Let's see what we can do; OK, let's go ahead and start off with the Michaelis-Menten equation.0104

Again, let's recall the MM - you know what, I am just going to...the Michaelis-Menten equation.0109

It said v₀ is equal to V_max x the substrate concentration over something called K_m plus the substrate concentration.0125

Basically, what this equation does is it relates the speed, the velocity, the rate of the reaction, how fast it is going, in either moles per second or molarity per second as a function of substrate concentration, which is really, really, very, very convenient.0138

It is a beautiful, beautiful equation; now, this V_max, we saw already that if you are given a particular enzyme, you can keep adding substrate, keep adding substrate.0154

You are going to increase the rate, but at some point, all of the enzyme molecules are going to be completely saturated with substrate.0163

All of the binding sites are taken over; now, enzyme can only go so fast.0171

So, no matter how much more substrate you add, you are not going to make it go any faster.0176

From your perspective, what you see - or actually I will draw it on here - is this thing that looks like this.0181

It ends up maxing out at some speed; there is some upper limit to how fast an enzyme can go.0188

You cannot push it any further than it will go if you have a certain amount of enzyme.0193

Now, it is true; you can add more enzyme, but that is experimental conditions.0198

The body does not just add more enzyme; the body needs to keep its enzyme concentration reasonably low because enzymes are not used up in a reaction.0202

It needs to keep them low and constant; it does not just add enzyme whenever it wants to speed it up.0213

It is substrate concentration that changes; V_max is just an upper limit on how fast the reaction will go.0217

This K_m, as it turns out, is remember, it is the concentration at which the speed it 1/2 of the maximum speed.0224

I did not draw it very well here; let me raise this one a little bit, so something like that.0237

That will be V_max; that is some upper limit that the speed is going to approach.0242

K_m is a constant, but it has units of concentration because you remember, it is concentration of substrate that is on the X axis and its rate, its speed that is on the Y axis.0247

So, this K_m is the concentration of substrate that I need that will make the enzyme operate at half of its maximum velocity.0262

Half is just a good number- not too low, not too high, right in the middle.0275

That is what K_m is, so this is the Michaelis-Menten equation.0280

Now, recall also from the derivation because we did do the derivation, recall that this was derived from the following postulated 2-step process.0284

Michaelis and Menten, they postulated this particular process- a 2-step process.0312

They said that you had enzyme plus substrate.0321

There is an equilibrium that exists between that and the complex enzyme substrate once it is attached, and then, that breaks down into enzyme plus product.0325

Now, there is some k₁, which is the rate constant for the forward reaction.0334

There is some k_-1 for the breakdown of enzyme substrate back to enzyme and substrate, and then, there is k₂, which is the rate constant for the breakdown of the enzyme substrate complex into enzyme and product.0339

They postulated that this was the slow step; this was very important.0353

They postulated that this was the slow step- the rate-determining step.0358

So, when we say slow, we mean rate-determining; I will go ahead and write that down here: the slow step, the rate-determining step.0363

Because again, your reaction is only going to go as fast as your slowest.0372

OK, now, OK, let's see if we can do this.0378

Now, K_m is the amount of substrate concentration that will put your enzyme at half velocity.0384

Well, K_m is often interpreted as a numerical measure of an enzyme's affinity for its substrate.0392

You will often see K_m as interpreted as some numerical measure of an enzyme's affinity for its substrate.0438

I am going to show you why it is interpreted that way, and then, I am going to discuss why you have to be careful with that particular interpretation.0448

For the most part, it is not going to be a problem, as far as the problems that you do in your book or the things that you discuss in class, but it is very, very important not to just automatically assume that some K_m value that you are given or that you read off in some reference book for an enzyme is a measure of the affinity of that enzyme for its substrate.0455

I am going to discuss why it is interpreted that way; let's start off there.0478

Here is why.0483

OK, now, in the derivation of the Michaelis-Menten equation, if you want to go back a couple of lessons, the K_m was this.0488

It was a combination of the rate constants k₁, k₂ and k_-1.0502

It was k₂ + k_-1/k₁.0506

That was the K_m; the actual definition of K_m is this.0514

Our interpretation this way makes more sense intuitively because we have a graph that represents it, but this is the actual definition.0518

It is actually a combination of the rate constants of a given process.0527

In this case, you have a 1, 2, 3; you have a 3-step.0531

There is one this way, one this way, one that way; it is a combination of those rate constants.0535

Now, if k₂ - let me write this a little bit better - is, in fact, rate-limiting, in other words, if that k₂ step is really the slow step as what was postulated, then, k₂ is a lot less than k_-2.0540

It is just a slow step; the rate constant is very, very low, very, very small compared to k₁, this thing.0574

This is small compared to this.0583

Well, because k₂ is so much less than k₁, we can actually ignore it in the numerator.0592

So, K_m becomes K_m = k_-1/k₁.0598

This is what the K_m actually becomes under these conditions.0610

OK, now, let's investigate this; what does this mean?0615

When we have the rate constant in the reverse direction, divided by the rate constant in the forward direction, that is the K_m under conditions that we have postulated where k₂ really is the slow step and can be ignored in the actual definition of K_m.0622

Well, here is what it means.0634

Let's go back to our equilibrium.0638

We have enzyme plus substrate in equilibrium with enzyme substrate.0642

This is k₁; this is k_-1.0648