Draw the curves that show the appropriate relationships betwee...

Question

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.

Graphs showing enzyme-catalyzed reaction dynamics over time for [P], [ES], [S], and V0.

Accepted Answer

Alright. So this practice problem wants us to draw the curves that show the appropriate relationships between the variables in each of the 4 plots below for a simple enzyme catalyzed reaction that follows Michaelis Menten Kinetics. Now, we have not yet talked about Michaelis Menten Kinetics, but we are a little later in our course. But we do know from our last lesson video on steady state conditions that Michaelis Menten Kinetics and the equation that's associated with it are derived under steady state conditions, and because we're somewhat familiar with steady state conditions, and we've seen a good handful of these plots before in our previous lesson videos, we still should be able to solve this problem. And so what we need to recall is that when biochemists are studying an enzyme catalyzed reaction in a lab, they only add free enzyme and free substrate to the reaction mixture. And essentially, they do not add any enzyme substrate complex or any product. So at the very very beginning of an enzyme catalyzed reaction, we can say that the product concentration is really, it's gonna be 0. And so when we're looking at this first plot over here looking at the product concentration on the y axis and the time as the reaction progresses on the x axis, we know that really, really early on in the reaction the product concentration is going to be 0. So, we can say that at time 0 the product concentration will be 0. So we know we're going to start down here at this corner for this plot. And then over time we know that the product concentration is going to increase and it's going to continuously increase until it reaches its equilibrium concentration. So at this point up here where it becomes horizontal, we know that the product has reached equilibrium. So we can write here, equilibrium has been reached. And really, this is the answer to this first plot right here, this curve that we've drawn. And that's it. So we can move on to our next plot. Now again, we know that, when biochemists are studying that enzyme catalyzed reaction, they only add the free enzyme and the free substrate, and, they do not add any enzyme substrate complex. So the enzyme substrate complex at the very, very beginning of a reaction is pretty much going to be 0 because the reaction hasn't really had a chance to get going yet. And so we can say that on this plot here where we have the enzyme substrate complex concentration on the y axis and the time as the reaction progresses on the x axis, we know that at the very beginning of time of, very beginning of the enzyme catalyzed reaction at time 0, the enzyme substrate complex concentration will be 0. So, we know that we're also starting down here. Now, we also know that the concentration of free enzyme is going to be much smaller than the concentration of the substrate. And so what that means is that the concentration of the enzyme substrate complex is limited by how much enzymes there is. And since there's not that much enzyme in comparison to the substrate, we know that the enzyme substrate complex is going to, have relatively low concentration. Now, we know that, from our previous lesson videos on pre steady state conditions, before the enzyme substrate complex gets to steady state and becomes stable, it has to increase and so it's actually rapidly going to increase. And then what's gonna happen is it's going to become stable and it's going to, reach steady state. And so, essentially, this is the curve that we're looking for for the enzyme substrate complex. And so, what we can say is that this period here, as it's increasing, is the pre steady state, and then this period here where it's constant is going to be the steady state. And so that is pretty much it for this curve, and we can move on to our next plot. So now, down below, notice what we have is the substrate concentration on the y axis and the time as the reaction progresses on the x axis. And of course, we know that at the very, very beginning of the, reaction, the substrate concentration is going to be really, really high because remember, the biochemist just added the substrate, so it hasn't had much of a chance to convert into product. So the substrate concentration is still going to be really, really high. So we know that at the very beginning of time here, we're going to start pretty high on this axis, somewhere up here. And then over time, we know that the substrate concentration is going to decrease, not necessarily all the way down to 0 because we know that enzymes only help the substrate concentrations get to their equilibrium concentrations. And the equilibrium concentration does not necessarily mean it's gonna go all the way down to 0. So, we know that it's going to, stabilize right at its equilibrium concentration. And so when it reaches this flat point over here we know that equilibrium has been reached just like what we saw up above with the product concentration. Just like what we saw up above here, with the product concentration. Equilibrium is reached when it gets flat. And so now, that is it for that, plot. So now we can move on to our final plot here. And in this plot what we have is the initial reaction rate on the y axis and the substrate concentration this time on the x axis. So notice that we do not have time. All of the other plots we had time on the x axis, whereas in this plot here we have the substrate concentration. So, when we're thinking of 0 here we can't be thinking at the beginning of time, so we're not gonna really be thinking of it in the same way that we thought about the other three plots. So, essentially we're gonna be thinking of it in a different way because we're we have different axes and different variables. And so we know that this is really our our typical enzyme kinetics plot and the typical curve here is for it to go up and then for it to curve across like this. Now when it curves across at this point, the reason that it becomes horizontal is not because equilibrium is reached because remember, equilibrium, it takes time, it takes some time, to reach equilibrium, but the initial velocity that we're plotting is at the very, very beginning of the reaction, so, it's not occurring over time, so we can't say that equilibrium has been reached over here. And so, instead the reason that it's, becoming flat is because, the substrate concentration has gotten so high that, the enzyme, we can say that the enzyme is saturated and, the enzyme is specifically saturated with substrate. And so that's the reason why, our line, becomes horizontal here. And so essentially, these are the 4 curves that we're looking to create for this problem, and that concludes this practice problem. So I'll see you guys in our next video.

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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.

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