# Graphical Estimation of Kd from P:L Binding Plot

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Back to protein function in biochemistry. My name is kevin toh cough make sure to to like this video and subscribe to the channel for future videos and notifications. All so were going to have a several discussions.
Are several videos relating to a concept called k. D. Alright.
K. D. Is equilibrium.
Constant. Theres lots of things. That you can get out of this with respect to protein binding.
So we know proteins can bind ligands. All right much in the same. Way.
Enzymes can bind substrates. Were specifically looking here at non enzymatic proteins. So in general so something like myoglobin which binds oxygen.
Its not catalyzing. A reaction is just binding. It.
So. This is what we call a binding curve alright on the y axis. We have this variable called theta.
What theta is is its the percentage of protein that have bound ligand another way of looking at it and ill write it like this its the because if you have a ton of proteins. They all have some number of binding sites for the ligand and theta is also the percentage. The percentage of binding sites occupied by the ligand okay whatever that ligand happens to be.
Okay so if theta was 05 or this is 50 one is also a hundred. Percent if theta was 05. That means 50 of all available binding sites are occupied by the ligand and fifty percent or not.
If theta was thirty percent then thirty percent of those available. Binding sites are occupied by the ligand and seventy percent or what we call free. Okay theyre free binding sites.
They dont have anything bound. And you can actually plot through various concentrations of ligand. What happens the percentage of those binding sites that become occupied that turns out that that relationship is actually not linear.
Its actually hyperbolic okay alright. So we have two curves here alright. So one way to look at this is you have some protein.
And this one will call this is the binding curve for ligon. One. This is the binding curve for ligand two we want to ultimately figure out what the kd is for both of these ligands.
So this protein. Whatever. It is will have some kd for ligand one itll have some kd for ligon.
Too. If youre if you need more detail on what kd is go back and watch one of the previous videos. We go into it details on what that is lets talk about how you estimate kd from a binding curve.
The way that you do this graphically is you start at 50. Its always at 50 never at 60 never at 100 never at. 30 its always 50 or where this is 05.
So what you do to estimate kd for that particular ligand and proteins you start at 50 and you go over horizontally to wherever to until basically that horizontal line hits. The curve of interest. Im going to do the blue.
One first once it hits the curve you go directly down this point. Where it hits the x axis that concentration thats the kd. So its just an estimate.
Because its certainly not math based and ultimately. Its sort of youre. Eyeballing.

It but im going to say that looks like about 175. So im going to say the kd for this first one. Kd.
1 is about 175. And whatever the units of this. Concentration are you use those so this is.
Micromolar so. Kd. 1 is 175 micro molar.
Okay now what i want to do is i want to do the same thing. I want to do it for the second binding curve okay. This one below it so what im going to do is the same thing on it start at 50 and go over to where this line hits.
The second curve alright oops. Let me redo that goes over to where it hits the second curve alright. Now.
Im going to go from that point and go straight down. And this point where it hits the x axis or verdict or horizontal axis look at that concentration. And that is the kd so im looking at this lets just estimate as three point one that looks about right so the kd2 for the second curve or the second ligand is approximately 31.
And since the units here are micromolar for concentration. The kd is also in units of micro molar. Okay so another typical question that you can see on some exam is theyll give you binding curves and say estimate graphically.
The kds for each one. Then you determine. Which ligand binds more strongly to the protein.
The rule for kd is this when you have a lower kd that indicates tighter or stronger binding when you have a higher kd that indicates what we call weaker binding okay so if i want to find the one the ligand that binds most strongly to this protein. I want to find the one with the lower kd. It turns out thats this kd one.
So were going to say this one right here has stronger or tighter binding. Thats the type more tightly bound ligand at a particular concentration. Okay.
Theres another way to kind of interpret. This and is to do this kind of backwards so what you do is you just pick a generic concentration. All right im going to pick lets just say five to make it easy.
Because its pretty resolute there so im going to pick five and im going to determine. Which one binds more strongly so start at five and now what ill do is im going to go up and im going to completely bisect both of those curves. Then what im going to do is im going to go over to where that curve hits each or where that line hits each curve and then go over to the vertical axis okay.
So let me do that and let me do it on this one too okay. So what im saying is that at at a ligand concentration of five micromolar at the same concentration ligand to the second curve is im going to estimate that about point. Maybe.
07 ligand to theta is equal to. 07 and for. Ligand one theta is equal to about 09.
What was thea theta was the percentage of available binding sites occupied by the ligand will notice here for the same concentration ligand. One has a higher proposed a higher percentage of binding sites. So wouldnt that likely indicate that ligand.
One was a tighter binder and it would because at the same concentration ligand. One. Occupies a higher percentage of binding sites.
That means. It. Binds.
Tighter ligand. Two occupies a lower percentage of available binding sites. And so its a weaker binder.
So those are two ways to figure this out. But generally when they ask a question like this with these two binding curves. Theyre going to actually ask you to estimate the kd and then compare the kds to determine.
Which one is the tighter binder. But you can actually if they ask you which one binds more tightly you can use either one of these graphical methods alright. So i hope this video made a little bit of sense and after this were going to go into other types of practice problems that involve more of calculations of kd and other things from a formula that were going to look at in the next video thanks for watching this make sure to like the video and subscribe to the channel.
Thank you .