# What is the Binding Constant?

Instructor: Laura Foist

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

The binding constant is an important concept to understand when studying ligand-molecule complexes. We'll learn what the binding constant is, how to calculate it, and what changes in the binding constants means.

## Ligands

When hemoglobin comes to the lungs it needs to get filled up with oxygen, so it needs to be tightly bound to oxygen. But when hemoglobin gets to the muscles it needs to let go of that oxygen, so it needs to be loosely bound to oxygen. So hemoglobin needs to be tightly bound to oxygen at times, but other times it needs to bind loosely to oxygen. If this didn't occur then we would suffocate quickly. How tightly a ligand and molecule are bound together is called the binding constant.

Let's review a few terms. Ligand simply means the compounds which is being bound, and it gets bound to a receptor molecule. In terms of hemoglobin, the hemoglobin molecule would be the receptor molecule and the oxygen would be the ligand.

## Binding Constant Equation

When talking about binding constants we will use L to refer to the ligand, R to refer to the binding molecule, and LR to refer to the ligand-molecule complex. We present the reaction that occurs like this:

The arrow points in both directions because the ligand and receptor molecule can bind together or the ligand-molecule complex could become unbound forming free ligands and molecules again.

So the speed, or rate, by which the ligand and receptor molecule becomes a ligand-molecule complex is called the on-rate constant. The speed, or rate, at which the ligand-molecule complex breaks down into free ligands and receptor molecules is called the off-rate constant.

Now the binding constant is equal to the ratio of on-rate to off-rate:

Take a look at this. As you can see, the binding constant equals rate on divided by rate off which equals concentration of ligand-receptor complex divided by concentration of ligand times concentration of receptor.

## Example

Now let's go back and take a look at hemoglobin. In the lungs, we have a high concentration of the ligand (oxygen), and in the lungs, nearly all of the hemoglobin is filled up with oxygen, so there's a very low amount of free receptor molecules, but a high level of ligand-molecule complex.

Let's say that the concentration of oxygen is 0.6, the concentration of hemoglobin (without oxygen attached) is 0.02, and the concentration of hemoglobin-oxygen complex is 0.98.

The binding constant can now be calculated as follows:

So in the lungs the binding constant of hemoglobin is 81.7.

Now let's move to the muscles. The level of oxygen has gone way down, and almost all of the hemoglobin has released its oxygen. So let's say that we have an oxygen concentration of 0.1, a free hemoglobin concentration of 0.77, and an oxygen-hemoglobin complex concentration of 0.33. The binding constant can now be calculated as follows:

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