Steady-State Conditions - Video Tutorials & Practice Problems
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Steady State Conditions
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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 biochemists make when they're studying enzyme catalyzed reactions. And so as we move forward in our course, we're going to to talk more details about exactly what happens during the steady state conditions that biochemists, 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 gonna 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.
2
concept
Steady-State Conditions
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3m
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So in our last lesson video, we said that the pre steady state period exists before the steady state period is reached. And so in this video, we're going to talk about the pre steady state period of an enzyme catalyzed reaction. And so what's important to know is that when biochemists are studying enzyme catalyzed reactions within a laboratory setting, they only add 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 only draw one arrow here. But still relative to 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 0, 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 4 of these substances that we mentioned above are actually going to change in their opposite directions, which means that if the concentrations start off really high, they're going to decrease and go lower over time. And if the concentrations 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 notice that the colors of the curve correspond with the colors that we see of the substances in 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 starts 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 a 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.
3
concept
Steady-State Conditions
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6m
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Video transcript
Alright. 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 v one for that matter is going to be exactly equal to the rate of the enzyme substrate complex dissociation or v minus 1 plus v 2. 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 only associate or form in one way via this forward reaction right here. And so the rate or the velocity of this forward 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 dissociate in 2 different ways. It can dissociate backwards here to form the free substrate and the free enzyme, and the enzyme substrate complex, could also dissociate forward to form the free enzyme and the free product. And so, really, the rate or the the velocity of the enzyme substrate complex dissociation is gonna be the sum of the backwards rate, or v minus 1, plus the rate of this, forward dissociation, v 2. 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, to derive the Michaelis constant Kilometers And we'll be able to talk about in our next lesson video, how to rearrange this equation to derive the Kilometers in 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 Michaelis constant kilometers. Now even though we have not yet talked about the Michaelis Menten 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 Michaelis Menten 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 notice 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 complex, which is gonna be v-one and v two. Now, notice over here we're showing you this graph where we have on the y axis and the time as the reaction progresses on the x axis. And notice that in the light blue background over here at the very 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, v one is gonna equal to the, v minus 1 plus v 2, during this 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 to change. And again, steady state, conditions is really just applying to the enzyme substrate complex. But you'll also notice that the concentration of free enzyme 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, the stars are going to be important later in our course when we're talking about the assumptions that we need, to use the Michaelis Menten 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 Kilometers and the Michaelis Menten Enzyme Kinetics Equation. And so that concludes this video here and we'll be able to get some practice in our next video. So, I'll see you guys there.
4
Problem
Problem
True or false: A reaction system at steady-state must also be at equilibrium.
A
True
B
False
5
concept
Steady-State Conditions
Video duration:
4m
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Video transcript
Alright. So now that we've introduced steady state conditions, in this video, we're going to specifically talk about how the Machias constant or the Kilometers can be derived under these steady state conditions. So recall from our previous lesson videos, we already mentioned that both the Michaelis constant kilometers, as well as the Michaelis Menten 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 Kilometers and the Michaelis Menten equation 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, 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 reactants. And we have 2 reactants 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 v minus 1, that's going to be, k minus 1 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, 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, times the sum 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 the Macalus constant k m. And that's because notice that we have k minus 1 plus k 2 here. And so all we need to do is take k one and divide it over under this side. So we have k minus 1 plus k 2 over k 1. And so that's exactly what we see over here, is that we have k minus 1, plus k 2 over k 1. And of course, this is gonna be equal to the Michaelis constant k m. And also notice 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's 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 in our previous lesson videos, and here, we're just showing you briefly how the Machlis constant kilometers 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.
6
Problem
Problem
Draw the curves that show the appropriate relationships between the variables in each of the plots below for a simple enzyme-catalyzed reaction that follows Michaelis-Menten kinetics.