in this video, we're going to begin talking about the maximum reaction velocity or the V max oven enzyme. So already from our previous lesson videos, we've mentioned the V max a good handful of time. So we already kind of know that the V Max is just the maximum reaction velocity of an enzyme. But really, the V max is more than just that, And the V max is actually better defined as the theoretical maximum reaction velocity of an enzyme that can Onley occur at infinitely large substrate concentrations graphically and by infinitely large substrate concentrations. What we really mean are substrate concentrations that are so large that the substrate is completely saturating all of the active sites that are available on all of the available enzymes. And so, by theoretical, maximum reaction velocity. What we mean is that the reaction velocities of enzyme catalyzed reactions can Onley approach the V max or get really, really close to the V max. But the V Max can actually never be attained by any enzyme, and so that's why it's better suited as the theoretical maximum velocity now recall from our previous lesson videos on the initial velocity of an enzyme catalyzed reaction that the initial velocity or the V not is actually a reactions. Best chance at approaching the maximum velocity v max. And that's partially why biochemist tend to focus on measuring the initial velocity of enzyme catalyzed reactions. Now, in our typical enzyme kinetics plot, the V Max acts as a horizontal as, um, tote toe limit the reaction velocity. And so let's take a look down below at our image to clear some of this up. Now notice. Over here on the left, what we have is an enzyme kinetics plot where we have the initial reaction rate, or the V not on the Y axis, and we have the substrate concentration on the X axis. And of course, we've got our typical curve that we said we tend to see for so many different enzymes. And so notice that at low substrate concentrations, we have a pretty low initial reaction rate at medium substrate concentrations. We tend to have a medium initial reaction rate. However, at really, really high substrate concentrations noticed that our initial reaction rate begins to approach this horizontal Assam tote line right here, which which actually indicates the maximal reaction velocity or the V max of our enzyme. And so if we take a look and zoom in on each of these different images here we get this image that we see here on the right. And so, uh, notice that if we look at low substrate concentrations and zoom in on low substrate concentrations over here we have the substrate in this pink little dot and then we have the enzyme in these orange Aziz brownish structures here, and so notice that at low substrate concentrations, most of the enzymes are actually not occupied. Their active sites are empty, and we only have a very little bit of enzymes that are actually occupied and forming the enzyme substrate complex. And so what this means is that at low substrate concentrations, we're going to have a low initial reaction rate. Now, if we increase the concentration just a little bit so that we have medium substrate concentration notice that if we zoom in on that, that we have still, uh, some enzymes are not occupied with substrate. And even though we have mawr enzymes that are forming the enzyme substrate complex, uh, not all of them are forming the enzyme substrate complex, and for that reason we just have a medium amount of initial reaction rate. Now notice that when we increase the substrate concentration toe a point where it's really, really high, we will get this box right here that has high substrate concentrations. And so notice all of these pink little dots that we see that represent our substrate. It's really, really high concentration. And when our concentration is high enough to the point where the enzyme is actually saturated with the substrate, that is a point where all of the enzyme that is present is forming the enzyme substrate complex. And so what we can say is that the total amount of enzyme here notice E. T. Is the total amount of enzyme is going to be equal to the the concentration of the enzyme substrate complex. And so when this becomes true, then the enzyme is capable of approaching its V max. It's maximal reaction velocity. And so this here concludes our introduction to the V max and the maximum reaction velocity. And as we move forward in our course, we're going to be able to continue to utilize all of these different concepts that we've learned here. So I'll see you guys in our next video

all right. So now that we've covered a little bit about the V max oven enzyme in this video, we're going to talk about a different way to express the V max. And that is by expressing the V max with a rate law. Now we know from our previous lesson videos on rate laws that the rate law is just an alternative way to express the reaction rate or the reaction velocity. And because the V max is a reaction velocity, then we kind of should have already known that the V Max could be expressed with a rate law. And so what we need to recall from our previous lesson video is that the V max or the maximum reaction velocity can Onley occur at saturating substrate concentrations where all of the available enzyme active sites are 100% full or 100% occupied with substrate? And so what that means is that under saturating substrate concentrations, all of the available enzymes or E T, will be associated with substrate to form the enzyme substrate complex. So what we can say is that under saturating substrate concentrations, the total concentration of enzyme will equal the concentration of enzyme substrate complex. And so what's really important to note is that the V max and the total enzyme concentration relationship eyes actually expressed via substituting variables into the rate law that were already familiar with from our previous lesson videos. And that is the rate law of the product formation step. And so notice down below. In our image, we have broken it up into two different sections. We have this section over here on the left, which is essentially review information from our previous lesson videos. No new information over there, And, uh, this image over here on the right is the new information that we're introducing in this video. And so just to do some review from our previous lesson, videos recall that the reaction rate or the reaction velocity, uh, including the initial reaction velocity, can commonly be expressed as the change in the product concentration over the change in time and initially during a typical enzyme catalyzed reaction. This is how it can be expressed. And so we know initially there's Onley, one rate constant that actually affects the change in the product concentration as we see up above, and that rate constant that affects the change in product concentration directly is K two. And so, if we focus on drawing or writing the rate law for this product formation step here, uh, it's going to include the rate law that includes this rate constant. And so we already know that the rate law for the product formation step, uh, is just going to be the initial reaction velocity V nod, which is equal to the rate constant for the product formation step, which is K two times the reactant for this particular reaction arrow. And the reactant for this arrow is actually the enzyme substrate complex. And so we know that it's gonna be, uh, raised to the power of the order reaction order. But because we assume that this is going to be a simple reaction, we know that the coefficient of one is going to equal the reaction order. And so it's just one. So essentially, this here is the rate law for the product formation step And again, this is all review information from our previous lesson videos. No new information here. So if you don't remember much about all of these rate laws, be sure to go back and check out our rate law videos and those topics. Now, over here on the right, we're gonna cover the new information that we're introducing here. And that is that we can actually variable do variable substitution into this rate law right here in order to get the rate law for the V max. And so what we need to recall is that under saturating substrate concentrations, we know that the initial reaction velocity V not can actually approach the maximum reaction Velocity v max, and so they're gonna be approximately equal to each other under saturating substrate concentrations. And what we also need to know is that also under saturating substrate concentrations, the total concentration of enzyme E T is going to equal the concentration of enzyme substrate complex. Just like what we said up above here. And so, essentially, by substituting these variables here into the rate law down below, we can actually get the rate law for the V Max. And so if we essentially take this v not here and we substitute it with the V Max, then we can put the V max right here in this position. And if we take the enzyme substrate complex concentration and substitute that with the total enzyme substitute concentration. Then we can place it in here. And so the rate constant is still going to be K two. And so, essentially, what we're saying is that this right here is the rate constant for the V max. And so this is an alternative way to express the V Max. And so later, in our course, we're gonna talk about different ways to be able to calculate the V max, um, and different types of practice problems. But for now, all I want you guys to realize is that through understanding that under saturating substrate concentrations, these variables will be equal to each other. We can actually get the rate law, um, for the V Max and express the V max with a rate law. And so that concludes our lesson on how V Max can be expressed with a rate law. And I'll see you guys in our next video

So it's also important to note that the theoretical maximal reaction velocity or the V max is actually directly impacted by the total enzyme concentration. And so the greater the total enzyme concentration is, the greater the V Max will be. And so, before we actually get to our example down below, I want to point out that we should have already known this from our previous lesson video on the rate law. And so recall that the V Max rate law is expressed right here and again. We covered this in our last lesson video, and we can clearly see that the total enzyme concentration will be directly impacting the V max of the reaction. And so the greater this total enzyme concentration is, the greater the V Max will be. And so if we take a look at our example down below to analyze the graph and get, um, or visual way of what this looks like notice here in this graph, what we have is an enzyme kinetics plot where we have the initial reaction rates, or the V not on the y axis, and we have the substrate concentration on the X axis and notice that we have two different curves here we have this red curve right here and then we have this green curve up here. And so notice that this green curve actually has double the total concentration of enzymes in comparison to the red curve and noticed that because it has double the total concentration, the theoretical maximum reaction velocity or the V max is also being doubled, since the total enzyme concentration is also doubled. And so we can see that by increasing the total enzyme concentration. That will also increase not only the initial reaction velocity but also the maximal reaction velocity v max. And so that's important to note. As we move forward in our course and when we're trying to compare the V max of different enzyme catalyzed reactions, we need to make sure that the total enzyme concentration was the same. Otherwise, we're not really comparing the two maximal reaction velocities fairly and so that's again important to note as we move forward through our course and that concludes our lesson and I'll see you guys in our next video