Steady-State Conditions

in this video, we're going to begin our discussion on the steady state conditions. So what's really important for you guys to know is that during a typical enzyme catalyzed reaction, the concentration of the enzyme substrate complex quickly builds up and reaches a constant value or a stable value. And so when the concentration of the enzyme substrate complex reaches this constant or the stable value we refer to this as steady state and so steady state is an incredibly important assumption that biochemist make when they're studying enzyme catalyzed reactions. And so, as we move forward in our course, we're going to talk more details about exactly what happens during the steady state conditions that biochemist tend to assume while they're studying enzyme kinetics. Now there's also another period during an enzyme catalyzed reaction referred to as the pre steady state, and so pre just means before. And so the pre steady state describes the conditions that exist before the concentration of the enzyme substrate complex reaches this stable, or this constant value that we refer to as steady state. And so in our next lesson video, we're going to talk more details about the pre steady state conditions, and then after that we'll talk about the steady state conditions. So I'll see you guys in our next video.

So in our last lesson video, we said that the pre steady state period exists before the steady state period has reached. And so in this video, we're going to talk about the pre steady state period of an enzyme catalyzed reaction. And so it's important to know is that when biochemists are studying enzyme catalyzed reactions within a laboratory setting, they Onley ad free enzyme and free substrate to the reaction mixture. But they do not add any enzyme substrate complex or any product. And so what this means is that initially, at the very, very beginning of an enzyme catalyzed reaction, the following four conditions exist just a few microseconds into the reaction. And the first is that the free substrate concentration is really, really high, and so is the free enzyme concentration. It is relatively high, not quite as high as the free substrate concentration. We already know from our previous lesson videos that the free substrate concentration is much higher than the free enzyme concentration, which is why I'm gonna Onley draw one arrow here but still relative toe other periods during the reaction. The free enzyme concentration, initially at the very beginning, is relatively high and again, since we do not add any enzyme substrate complex or any product initially to the reaction, the concentration of enzyme substrate complex, initially at the very beginning, is going to be really, really low, essentially zero, and so will the concentration of product. And so what's important to know is that as the enzyme catalyzed reaction begins and proceeds during this pre steady state period, the concentrations of all four of these substances that we mentioned above are actually going to change in their opposite directions. Which means that if the concentration start off really high, they're going to decrease and go lower over time. And if the concentration start really, really low, then they're going to increase over time. And that's exactly what we see in our plot down below, which is showing us the pre steady state period. And so notice the plot has concentration on the Y axis and the time as the reaction proceeds on the X axis and noticed that the colors of the curve correspond with the colors that we see of the substances and our reaction and up above. And so this blue curve here represents the concentration of the substrate which we can see initially starts really, really high, but decreases over time and so does the enzyme substrate complex starts relatively high and decreases over time, whereas the red curve here, which corresponds to the concentration of enzyme substrate complex, starts really, really low, and increases over time and the concentration of product also start to really low and increases over time. And so during this pre steady state period of an enzyme catalyzed reaction, the concentration of the enzyme substrate complex is going to continuously change. In fact, it's going to continuously increase as we see in our plot down below, so it continually continuously increases until ah period called steady state is reached and we're going to talk about the steady state period in our next lesson video. So I'll see you guys there.

All right. So now that we talked about the pre steady state conditions in our last lesson video in this video, we're going to talk about the steady state conditions and so steady state is literally just referring to a specific period of time during an enzyme catalyzed reaction where the concentration of enzyme substrate complex stays exactly the same. And so if the concentration of enzyme substrate complex stays exactly the same, then of course, what this means is that the rate or the velocity of the enzyme substrate complex association must be exactly equal to the rate or the velocity of the enzyme substrate complex dissociation. And so, in other words, to say the same exact thing right here. We can say that if the concentration of enzyme substrate complex remains constant or remains exactly the same then, of course, what this means is that the rate of the enzyme substrate complex association or the one for that matter is going to be exactly equal to the rate of the enzyme substrate complex dissociation, or V minus one plus V two. Now, just as a reminder down below over here recall that at the very, very beginning of an enzyme catalyzed reaction. The enzyme substrate complex here in the middle can on Lee associate or form in one way via this Ford reaction right here. And so the rate or the velocity of this Ford reaction that allows the enzyme substrate complex to associate is going to be V one and then also recall that the enzyme substrate complex here in the middle can actually disassociate in two different ways. It can disassociate backwards here to form the free substrate in the free enzyme. And the enzyme century complex could also disassociate forward to form the free enzyme in the free product. And so, really, the rate or the velocity of the enzyme substrate complex dissociation is gonna be the some of the backwards rate or the minus one, plus the rate of the four dissociation V two. And so, really, this equation that we see right here is the assumption that we can make under steady state conditions. And so, in our next lesson video, we'll see that this assumption here in this equation is very, very important. And that's because we can actually use this equation and this assumption here, uh, to derive the Michaelis constant k M and we'll be able to talk about in our next lesson video. How to rearrange this equation to derive the K M and our next lesson video. But for now, all I want you guys to know is that this equation is the most important assumption of steady state conditions. And again, it's important because we can derive. The McHale is constant K M. Now, even though we have not yet talked about the meticulous Minton enzyme kinetics equation, we are going to talk about this equation later in our course. And so what's important to note now is that this McHale is meant. An enzyme kinetics equation that we'll talk about later is actually derived under these steady state conditions that we're talking about here. And so that's another reason why steady state conditions and this equation is so important and so really noticed down below. Over here, we're just reminding you guys of the important assumption of steady state conditions, and that is that the velocity of the association of the enzyme substrate complex, or V one, is going to be exactly equal to the velocity of the dissociation of the enzyme substrate complexes, which is gonna be V minus one and V two. Now notice. Over here. We're showing you this graph where we have the concentrations on the Y axis and the time as the reaction progresses on the X axis and noticed that in the light blue background over here at the very beginning of the reaction, What we have are the pre steady state conditions which we already talked about in our last lesson video. Now notice. Over here in the yellow background, what we have are the steady state conditions, which again is just where the concentration of the enzyme substrate complex stays exactly the same. And so notice that in this yellow region the concentration of enzyme substrate complex here in red stays exactly the same. And of course, this is going to mean that the, uh, the one is gonna equal the V minus one plus V two during the steady state period. Now, notice that in this yellow region it is possible for the substrate concentration to change and it is possible for the product concentration change and again, steady state, uh, conditions is really just applying to the enzyme substrate complex. But you'll also notice that the concentration of friends I'm stays the same. But again, steady state conditions is more so referring to the concentration of enzyme substrate complex. Now, last but not least, I want you guys to notice that we have this third star over here and recall that the thirds, uh, the stars, they're going to be important later in our course when we're talking about the assumptions that we need, uh, to use the meticulous meant an enzyme kinetics equation when we cover it later in our course. But for now, the main takeaways here of the steady state conditions is that the enzyme substrate complex stays the same, and that allows us to use this equation. And that equation allows us to derive the K M. And the meticulous meant an enzyme kinetics equation. And so that concludes this video here, and we'll be able to get some practice and our next video. So I'll see you guys there

All right. So now that we've introduced steady state conditions in this video, we're going to specifically talk about how the McHale is constant or the K M can be derived under these steady state conditions. So recall from our previous lesson videos, we already mentioned that both the McHale is constant. K m as well as the McHale is meant in equation, which we haven't yet talked about. But we're going to talk about in more detail later in our course. So both the K M and the McHale is meant in equations are derived or defined under these steady state conditions, which is why steady state conditions are so important and recall from our last lesson video, we said that steady state conditions just means that the concentration of the enzyme substrate complex stays exactly the same. And of course, if the concentration of the enzyme substrate complex stays exactly the same, that means that the rate of its formation, or the rate of its association, is going to be equal to the sum of the rates of the dissociation. And that's exactly what we see down below. In this expression right here, the velocity of the association is equal to the sum of the velocities of the dissociation of the enzyme substrate complex. Now recall from our previous lesson videos that velocities reaction velocities like these can actually be expressed or rewritten as rate laws. And so if we consider the rate laws for each of these velocities, then we can go ahead and, um, put those down below. So for this rate law for the Association of the Enzyme Substrate complex, recall that the rate law says that it's gonna be equal to the rate constant, which it would be K one for this association times the concentration of the reactant, and we have to react INTs. For this association, we have the free enzyme and the free substrate so down below we can put the free enzyme as well as the free substrate. And so this represents the rate law for this reaction velocity. Now, if we write out the rate laws for the minus one, that's going to be, uh, k minus one rate constant times the reactant, which is gonna be the enzyme substrate complex. So we can put that in here and then for the K two, which is essentially going this way using this rate constant. Uh, it's rate law is gonna be k two times the enzyme substrate complex concentration. And so here notice that they both contains this enzyme substrate complex concentration. So what we can do is actually factor it out to the front, both of these out to the front. And when we do that, what we get is the concentration of the enzyme substrate complex, uh, times the some of these two rate constants. And then, of course, on the left, we still have the same exact expression. And so notice here, this is exactly where we can start to define them. Achilles constant K. M. And that's because notice that we have K minus one plus K two here. And so all we need to do is take a one and divided over under this side. So we have K minus one plus K two over K one. And so that's exactly what we see over here is that we have K minus one plus K two over K one. And of course, this is going to be equal to the McHale is constant K. M. And also noticed that we have the free enzyme times the free substrate concentration over here on the left. And then we have the enzyme substrate complex concentration so we can divide that over here so that it's below. And so what you end up getting is this same exact expression that we have right here, which is the free enzyme times, the free substrate concentration over the concentration of the enzyme substrate complex. So, again, we already talked about how the K M can be expressed in these formats and our previous lesson videos. And here we're just showing you briefly how the meticulous, constant K M can actually be derived under these steady state conditions. So it all results from making this assumption here that these velocities are going to be equal to each other in these ways. And so this here concludes our lesson, and I'll see you guys in our next video