Biochemistry Enzymes III: Kinetics

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

Today, we are going to start talking about enzyme kinetics.0004

Kinetics is just a fancy word for rate of a reaction, how fast does this reaction go.0009

Kinetics is, sort of, the beginning of our understanding of mechanism.0016

With biochemistry, with all of chemistry, our ultimate goal is to understand the mechanism, how something goes from one thing to another, in the case of an enzyme, how an enzyme takes a particular substrate and how it converts it to product.0022

Each individual little step, every single electron, where it goes, every single atom, every single hydrogen ion that is transferred from here to there- that is our ultimate goal because if we understand the mechanism, then we know how to control it.0038

We know how to fiddle with it, how to do whatever we want to it because we understand how it works.0050

Kinetics is, sort of, the first step of understanding that mechanism.0057

It is the oldest approach to understanding mechanism, and it is still very, very, very important.0062

Let's jump in and see what we can do; now, we are going to deal with the quantitative aspects of kinetics, and I am going to go through a derivation of the Michaelis-Menten equation.0069

Hopefully, it will not be too bad; ultimately, we are not going to be concerned with the derivation.0082

Your teacher will let you know about the extent to which you need to know the derivation or not the derivation, but we will go through it.0086

It is the final form of the equation and how the enzyme behaves; that is what is important.0093

It is more of a global understanding; let's see what we can do.0098

OK, now, as we said, the fundamental approach - let's see here - to studying a mechanism is to determine the rate of an enzyme-catalyzed reaction/rxn and more importantly and how this rate actually changes with changes in substrate concentration.0102

In other words, if I start with a certain amount of enzyme that will hold constant and if I add a certain amount of substrate to this enzyme solution and if I measure how fast these substrate molecules are being turned over into product, that gives me a rate.0175

It will often be expressed in terms of, let's say, millimoles or micromoles per minute or perhaps in molarity, millimolar or micromolar per minute or per second.0195

A rate is some change in some value per unit time.0205

That is what a rate is, how fast something is happening; well, if I start with a different initial concentration, does that change the rate?0209

As it turns out, the answer is yes.0216

Ultimately, substrate concentration controls how fast or how slow an enzyme-catalyzed reaction is going to go.0220

Now, it is never always this simple.0227

With normal chemical reaction, it is not even that simple; you can just imagine how complex it can become in the case of an enzyme-catalyzed reaction where you have, maybe, more than 1 substrate, where you have multiple steps in a mechanism, not just 1 or 2 but perhaps 7 or 8 before the enzyme releases the product.0231

Again, we are going to be making some simplifying assumptions to make it tractable, so that we can actually deal with it, but ultimately, it is about how the substrate concentration affects how fast an enzyme-catalyzed reaction can go.0250

OK, let's see what we have.0266

Now, since the substrate concentration will denote it like that, S with a bracket.0270

Concentration - you remember from chemistry - always has brackets, and those brackets are normally in moles per liter.0277

In the case of biochemistry, it will usually be millimolarity, occasionally micromolarity because you are talking about pretty small amount, at least as far as the enzyme is concerned, and often the substrate is well.0283

Since S changes, as the reaction proceeds, we simplify matters by measuring initial rates.0296

And you remember or you should remember, at least, or I hope you remember initial rates from general chemistry when you were doing the kinetics portion, although I do understand that the kinetics portion of general chemistry is generally that portion of chemistry that one would like to forget.0326

That is the one that seems to leave the mind the quickest because it was so very odd compared to the other concepts because it was heavily mathematical.0339

In any case, as you know, you put a substrate in with an enzyme, the substrate concentration actually changes.0347

So, as an experimenter, how can one...and since the substrate concentration is changing, how can I actually try different substrate concentrations to get some, sort of, a relationship between substrate concentration and speed of the reaction?0355

Well, if we measure how fast the reaction is going in the beginning, right when we put the substrate and the enzyme together, let's say, within the first 30 seconds or, at most, the first minute, we never want to let it go past that.0370

Well, during that timeframe, because the substrate concentration in general is usually going to be so much more than the enzyme concentration - right - enzyme, well, is not used up in a reaction, so the enzyme concentration is very small.0383

One enzyme molecule can handle millions of substrate molecules.0398

Because that is the case, in the first part of a reaction, the first 30 seconds, the first minute, maybe the first minute and a half, the substrate concentration does not really change all that much, especially since the substrate concentration is so much bigger than the enzyme concentration.0401

So, for all practical purposes, the substrate concentration that I start the experiment with, it is going to be held constant.0417

If I start with 10 millimoles or 20 millimoles or 30 millimoles, even though substrate is being used up, compared to the 20 millimoles, 30 millimoles, 40 millimoles, that I start off with, it is going to be completely negligible.0425

Now, we can actually do that; even though substrate concentration changes with an enzyme-catalyzed reaction because of the difference, because there is so much substrate, I can pretend that it does not really change.0440

Now, I can actually run my experiment; I can actually collect some data.0450

Since S changes to the reaction when we simplify matters by measuring initial rates of reaction, how fast the reaction is going at the beginning before other complications start to slow the reaction down.0456

Now, as we said, since the concentration of S is so much greater than the concentration of enzyme during the first minute or 2, the substrate concentration is essentially constant.0470

OK, now, what this does is this allows us to choose various initial concentrations - like I said, 10, 20, 40, 80, 160, however - then, plot the rate of reaction that we measure as a function of these different initial concentrations.0510

In other words, what we are saying is that the rate - I will call it initial velocity, so we will use the symbolism that is pretty common, well, actually, you know what, let me go ahead and just write it as rate first, and I will go ahead and use the symbolism - is going to be some function of S.0568

In other words, you are going to have S on the X axis.0590

OK, that is going to be your independent variable, and the rate is going to be your dependent variable.0594

That is going to be your Y axis.0598

Rate or speed of the reaction, we will often symbolize with v₀, initial velocity.0602

Sort of, this is 0 making reference to that fact that we are dealing with an initial rate.0608

v₀ is equal to some function of the substrate concentration.0613

Different substrate concentrations, different values, and you end up getting this curve.0620

Well, when we do this, when we actually run the experiment, we get the following.0625

We take some enzyme; we start with different substrate concentrations.0631

Let's say we run 10 different initial concentrations, we get 10 data points.0636

We measure the speed at the beginning of the reaction.0640

We get the following graph.0645

We get something that looks like this, so let's take a look at this- very, very, very important graphical representation.0650

This is a plot of substrate concentration on the X axis and reaction rate on the Y axis.0657

Do not worry about what the V_max, half V_max and K_m mean right now.0664

We will get to that in a minute when we talk about this Michaelis-Menten equation that we want to deal with.0668

OK, if I start with an initial concentration of a substrate concentration of 0, well, nothing is going to happen.0673

As I increase my initial substrate concentration, I am going to measure a rate.0682

I try another initial concentration, I am going to measure an initial rate.0688

Another experiment, another concentration, I measure another rate; I do this several times.0693

In this case, it looks like 1, 2, 3, 4, 5, 6, 7, 8, 9, 9 experiments.0698

You can do as many as you like; obviously, the more that you do, the better data you get.0703

When I connect all of those dots, I get this thing.0707

This is a very, very, very characteristic enzyme behavior- reaction rate versus substrate concentration.0712

Let's just talk a little bit about what is happening here just qualitatively; let's get a sense of what is happening.0722

You notice in the beginning almost this...well, that is OK.0728

At low concentrations of substrate, what happens is you have basically almost a straight line here - right - of 2 about right here?0735

For very, very low concentrations, what you have is, sort of, a linear behavior, in other words, just something that is like the rate equals some constant times the concentration of S.0745

That is just some line - that is it - a linear relationship, but as the substrate concentration increases, notice that the speed actually starts to slow down.0760

You might ask yourself, well why is that, why does it slow down?0772

Well, think about it; it actually makes sense.0775

You only have so much enzyme; you keep adding substrate.0778

You keep adding substrate; you keep adding substrate.0781

At some point, you have added so much substrate; around this point, you have added so much substrate that, now, the enzyme is completely tied up with substrate.0784

In other words, it is bound to the substrate; it is converting it to product.0795

The minute it releases that product, yes, it is a free enzyme again, but immediately, another substrate binds to it.0798

So, for all practical purposes, at some point, you have tied up all of the enzymes that can turn molecules over, that can turn substrates over.0804

It does not matter how much more substrate you add; you can keep adding substrate.0813

You are not going to make the reaction go any faster because there is only so much enzyme there that can react, that can actually do the job.0816

That is why you see this tapering off behavior, and you know intuitively that at some point, you are just going to keep adding so much substrate- that is it.0824

There is only so fast that the enzyme is going to turn these substrates over.0835

That is what this is here; this is an upper limit on the speed of the enzyme.0840