Video

# What is the dissociation constant KD?

Published on July 25th, 2019

What is the dissociation constant KD?

How do I calculate KD?

And where can I find it on the binding affinity curve?

All these questions can be answered in this series of short and handy videos listed below, check back regularly since we are always updating this page.

## Part 1 – What is the dissociation constant and how to calculate KD? ### Video Transcript: Part 1 – What is the Dissociation constant and how to calculate KD?

Slide 1: Hello, and welcome to part one of this KD video series. In this video, I will go over what the dissociation constant KD is and how it is derived. But before we get into that, I want to take you through some of the fundamental details the underlying KD.

Slide 2: So in a biochemical reaction, equilibrium is the state in which the proteins, ligands and protein ligand complexes are at a point where there is no observable change in the properties of the system. A common misconception is that there is no longer protein ligand complexes being formed and dissociated. This is not the case. Once equilibrium has been reached, it means that there is the same number of complexes forming and dissociating at any given time. One way to think of this is imagining a person running in place on a treadmill.

The person is traveling forward at, say, ten miles per hour and the treadmill belt is traveling at the same speed, but in the opposite direction. Both the treadmill and the person are constantly in motion, but because they are traveling in different directions, there is no net movement.

Slide 3: If we look at defining the dissociation constant, KD, we must first define the protein ligand interaction equilibrium. This equilibrium represents a dynamic relationship between the unbound protein, its respective ligand and the protein ligand complex in a given system.

It should be noted that the ligand could also be another protein or something else, such as a small molecule. Protein ligand binding can be represented by the equation on this line. Here he represents a protein, L is a ligand that combines the protein, and PL is the protein ligand complex.

As this is an equilibrium, not all the ligands are bound to the protein. Some of them are bound and some of them are free in the system.

Slide 4: Here is the same equation again. But now we are going to describe the two directions that govern the equilibrium of the reaction. kon is a rate constant. The value of which stays the same for a given pair of proteins and ligands, kon describes the rate at which the forward reaction is taking place so that a protein ligand complex is formed.

This rate is dependent on the concentration of the proteins and ligands and is measured in per moles per second (M-1s-1). On the other hand, the koff describes the rate of the backwards reaction depicting the rate at which the complex dissociates into separate proteins and ligands. This rate is independent of the concentrations of the free protein and ligands in the system, and it is measured in per seconds (s-1).

Slide 5: So what is KD? KD is the dissociation constant and is the concentration of ligand, which half the ligand binding sites on the protein are occupied in the system equilibrium. It is calculated by dividing the koff value by the kon value. It is also equal to the product of the concentrations of the ligand and protein divided by the concentration of the protein ligand complex once equilibrium is reached.

The units for KD are measured in molar. This might seem confusing at first. But if we look at the equation above as a set of units, then it becomes clear the smaller the KD, the more affinity to proteins have for each other.

Slide 6: So now let’s take a look at KA the association constant. Having now described the forward and backward rate, constants and KD, it is time to look at the association constant. KA. KA is the opposite of KD and is calculated by dividing the kon by the koff.

Because of this equation, it’s units are measured as per molar, which is why scientists prefer to work with KD since molar is easier to work with.

Slide 7: KD is an equilibrium description and is not representative of the concentrations of proteins and ligands in any given system. This is something to always bear in mind. In the following three examples I’m about to go through, the code for the system will always remain at three. So in the first example, there are eight proteins and three ligands that are in the system with the KD of three.

That means there will always be six free proteins, one free ligand and two protein ligand complexes at any moment in time. If we look at a system where there is six ligands and six proteins to meet a KD of three, there will always have to be three proteins ligands and protein ligand complexes at any given time.

The final example is a reverse of the first so that there are three proteins and ligands, this time here to meet the KD. They will always have to be one free protein, six free ligands and two protein ligand complexes at any given time.

Slide 8: Thank you for watching. A second video that will cover how to generate a binding curve and derive the KD from the graph is also available. The link is in the description below. For more educational content regarding the dissociation constant.

Feel free to visit our website. The link is also in the description. If you’ve enjoyed this video, please like and subscribe for more content. Thanks again and have a great day.

## Part 2 – How to create a binding curve and derive KD from it? ### Video Transcript: Part 2 – How to create a binding curve and derive KD from it?

Slide 1: Hello and welcome to part two of this KD video series. If you haven’t seen part one, I encourage you to check it out. It goes over what the dissociation constant KD is and how it is derived. This information is vital in order to understand what we will be covering in this video.

Slide 2: Essentially, we will be covering the fundamentals of what a binding curve is and how it is generated. Following on from this, we will take a look at what makes an inaccurate binding curve and how to avoid making these.

Slide 3: So let’s take a look at the science behind a binding curve, in order to generate a binding curve for a given protein ligand pair, a titration experiment is carried out. In this example, one of the protein ligand pair is held at constant concentration.

In this case, the ligand, while the protein concentration is changed or titrated, the signal of the system is measured by either an increase or decrease of a quantifiable signal. For example, a change in the light absorbance or fluorescence.

Slide 4: From this experiment, the data is then plotted onto a graph. This is a fraction bound plot. Here, the fraction of the ligand bound to the protein is plotted against the total concentration of the protein at the beginning of this titration, there is only ligand.

As protein is added to the system, the proportion of ligand bound to protein increases until saturation when all of the ligand in the system is bound to the protein. The concentration at which half the ligand is bound is the KD value.

Slide 5: When choosing concentrations of protein and ligand, your concentration of ligand should be relatively small. However, your concentration range of proteins should span one order of magnitude above and below the KD. It is for this reason that the plots you create should be logarithmic rather than linear, because as you can see in this slide, the detail tends to get lost in the linear plots. It becomes nearly impossible to accurately determine the KD in most cases.

Slide 6: So let’s say we want to create a binding affinity curve, but we don’t know what the KD is for a protein interaction. For this curve we’re going to plot the concentrations of protein that amount to one 50th, all the way up to 200 times, the KD value. By going below and above one order of magnitude of KD, we are able to plot a clear binding curve and determine the KD.

In the following set of binding curves, the committee for each curve is higher than the total ligand concentration, which is listed at the top of the graph. As you can see, the binding curves here, while not necessarily reaching plateau, are clearly distinguishable from one another.

In other words, the KD value for the binding curve where the KD is ten micron is clearly different to the binding curve, where the KD is one micro molar.

Slide 7: So in this set of binding curves, the KD values for each of them are lower than the total ligand concentration. In other words, the protein concentration we’re plotting is far lower than that of the KD. In this sort of binding curves, the KD values for each binding curve are lower than the total ligand concentration. So where the curves represent a protein interaction with a KD of 0.1 micro molar or point not one micro molar, the curves are very close together. Since these curves are so close and hard to distinguish, the graph presumes that the KD values must be close together when we know in reality they are not. This illustrates why we should always use the lowest concentration of label species to ensure you get good discrimination for KD values.

Slide 8: Thank you for watching. If you have any questions, you might want to check out part one of this video series where we cover the basics of what KD is and how to calculate it. For more educational content regarding the dissociation constant KD, please check out our web site. The link for this is also in the description. If you have enjoyed this video, please like and subscribe for more content. Thanks again and have a great day.