5. Characterisation of agonist-receptor interaction. Occupancy, affinity, dose-response curve, potency, efficacy

Last updated on January 18, 2019 at 13:56

Summary
  • Occupancy shows the fraction of the total number of receptors in the tissue that is occupied by the drug. It’s determined by the constant p.
  • A drug’s affinity to its receptor is determined by the constant Kd. When Kd is low is the affinity high. A high affinity is always good and has no drawbacks.
  • Efficacy is a measure of how “effective” the drug is. It measures how severe symptoms or how big an effect the drug can induce in the tissue. The drug’s intrinsic activity determines its efficacy. Intrinsic activity (IA) ranges between 0 and 1.
  • Potency is a measure of how much of a drug you need to get the desired effect. It’s measured by the constant ED50. The lower the ED50, the more potent the drug is. It increases with higher affinity and higher intrinsic efficacy.
  • Receptor reserve shows how many receptors in the tissue that are not occupied by the drug even when the drug has reached its maximum effect.
  • Intrinsic efficacy is measured by the constant ε, and “sums up” the intrinsic activity and receptor reserve. A higher intrinsic efficacy is always good.

This topic is theory-heavy so hold on tight.

In this topic we study the agonist-receptor interaction, that is, what determines how an agonist affects the receptor and how can we differentiate different agonists.

A = Agonist, R = receptor, AR = agonist bound to the receptor, AR* = the activated receptor. Effect and response are used interchangeably.

This figure is scary. The A is the agonist, while the R is the receptor. In order for anything to happen, the agonist must bind to the receptor to form AR. This binding is not permanent, meaning that there is an equilibrium between the number of free agonists (A) and receptors (R) and bound agonist-receptors (AR), which is why the arrow goes both ways. After A has bound R, the receptor will become activated (AR*). When the receptor is activated, it will cause an effect.

As we can see on the figure, the relationship between the agonist concentration and how many agonists are actually bound to a receptor (AR) is called the concentration-occupancy relationship. The relationship between how agonists bound to the receptor cause their effect is called the occupancy-response relationship. The sum of these two relationships, the relationship between the agonist concentration and the resulting tissue effect is called the concentration-response relationship. We’ll discuss the three separately.

Concentration-occupancy relationship
L = Ligand, R = Receptor, LR = ligand bound to the receptor, c = concentration of ligand, NT = total number of receptors, NL = number of receptors that have bound the ligand.

This is the same equation as in the previous figure, however we use ligand instead of agonist in this case because this relationship doesn’t only count for agonists, but for antagonists as well. For our use case we can think of the ligand as a drug.

Now, we’re interested in knowing the answer to the following question: How does the concentration of the drug affect how many receptors are actually bound by the drug? We want to know this because it turns out that when we apply drugs to tissues, the drugs don’t occupy all the receptors. Then, what determines how many drug molecules will bind to the receptors?

This equation is called the Hill-Langmuir equation. p = the fraction of the total number of receptors that have bound the ligand. NL = Number of receptors that have bound the ligand, NT = Total number of receptors, c = drug concentration, Kd is a constant.

We’re interested in finding out what parameters determines how big is the fraction of receptor that have bound a ligand. Like, what determines if only 50% of the receptors are occupied by a ligand, or 75%, or 100%? The fraction (p) of occupied receptors can be calculated by calculating NL/NT. We call this p for occupancy. Mathematical magic concludes that this fraction (p) is equal to c/(c+Kd). Kd is a constant that is characteristic for a single drug. Each drug has its own Kd. The Hill-Langmuir equation therefore tells us that the fraction of occupied receptors (p) is determined only by the concentration of the drug and a drug constant. Makes sense, right?

Mathematics show that the constant Kd is the concentration that the drug must be given in in order to occupy exactly 50% of the available receptors. That means that if a drug has a Kd of 0.24M, then this drug must be given in a concentration of 0.24M in order to occupy half of the receptors in the given tissue.

This graph shows what the Hill-Langmuir equation looks like if you plot it. The x axis is the logarithm of the concentration of the drug (meaning that this is a logarithmic scale), while the y axis is the percentage of all receptors that are occupied by a ligand.

From the graph, we can see that any drug can occupy 100% of the receptors as long as the concentration is high enough. Likewise, when the drug concentration sinks, the occupancy sinks along this sigmoidal curve.

Kd characterizes the drugs tendency to bind the receptor, also called the affinity. The lower the Kd, the higher the affinity, meaning that they are inversely correlated. A high affinity is always good, because when the drug has a high affinity then a lower concentration of the drug is needed for it to occupy the desired fraction of receptors.

Concentration-response relationship

It’s easy to determine the concentration-response relationship. In humans, we do it like this:

Let’s say that we want to determine the concentration-response relationship of a new vasodilator. We determine a satisfactory clinical effect, like “the blood pressure of the patient decreased by 10 mmHg or more”, and then give the drug to many patients. First, we give it at a very low concentration. At a low concentration, the drug is unlikely to give the desired clinical effect in many of the patients, however we write it down if some of them do. Then, we increase the dose slightly, then do it again and repeat. As the dose increases, the fraction of patients that reach the desired effect will increase, until at one point, the drug concentration is so high that every single patient have reduced their blood pressure by 10 mmHg.

Then, we plot the data into a graph. It’s going to look like this:

A drug-response curve. The x-axis is the drug dose while the y-axis is the fraction of patients that reached the target clinical effect at a specific concentration

We’re going to introduce three new terms: efficacy, intrinsic activity and potency.

Efficacy (pronounced effikacy) can be though of as effectiveness. It shows how big the effect of the drug has the potential to be, if the concentration is high enough. It is determined by the drug’s intrinsic activity (IA). IA of a drug ranges between 0 and 1 and shows how big the effect of the drug is, compared to the largest effect achievable in the tissue by any drug. Efficacy determines how severe symptoms can be treated with the drug. Let’s look at an example.

We have a group of patients with cancer-related pain, which is very severe. We divide the group into two and give one group paracetamol for the pain and the other group morphine. It’s pretty certain that no matter the dose of paracetamol it will never be enough to treat the pain the patients have, however the morphine probably will. This is because paracetamol has a lower efficacy than morphine in this case; paracetamol just isn’t effective enough as a painkiller to treat such severe pains.

Potency is the measure of how large of a dose of a drug is needed to achieve the desired effect. It’s determined by a constant called ED50 (or EC50, they mean the same in this context). This constant determines the concentration of the drug needed to achieve 50% of the maximum possible effect of the drug. This means that more potent drugs need a lower concentration to reach the same effect as a similar but less potent drug. When ED50 is low, the drug is potent.

A concentration-response curve. The axes are the same as in the previous figure. The four curves A, B, C and D show the concentration-response relationship of four different drugs. The EC50 of them can be seen. Drugs A, B and C are agonists. D is an antagonist, which is why it doesn’t give a response no matter the dose.

In the curve above, four different drugs can be seen. The figure shows that the curves’ position along the x-axis shows their potency, while their height shows their efficacy. Drug A is the most potent, followed by drug B and lastly drug C. Drug A and B have the same efficacy, while drug C has a lower efficacy.

In this example, drug A and B are full agonists, because drug A and B can reach 100% of the achievable effect in the tissue, while drug C can only reach about 50%, meaning it is a partial agonist. Drug A and B will therefore have intrinsic activity = 1 (= 100%), while drug C has IA = 0.5 (= 50%). All drugs that have a lower than 100% efficacy are partial agonists, meaning they can’t’ give the maximum possible effect of the tissue.

A high potency is always a good thing, because when a drug is very potent it can be given in a low dose, which can reduce non-receptor mediated side effects. Efficacy is a different story however, as it depends on what we need. Think back to the painkiller example: we wouldn’t use morphine to treat a headache!

The last thing we must talk about in this case is the margin of safety. Looking back to the concentration-response curves we need to take a look at their slopes, that is, how steep the curve is around the middle. When a curve is very steep, it means that a small increase in dose will give a larger effect, while if the curve is gentle (not steep), then a small increase in dose won’t give a much larger effect. This means that drugs with gentler slopes are safer, as the drug dosage can be varied somewhat without a large change in effect.

Occupancy-response relationship

Recall that the Kd constant shows the drug concentration where half the receptors are occupied by the drug, and that the ED50 constant shows the drug concentration where half of the possible effect is reached. Intuition may say that they should be equal, but they’re not. EC50 is always smaller than (or equal to) Kd, meaning that the drug concentration needed to give 50% effect is lower than the concentration needed to saturate 50% of the receptors. The same also goes for 100%: the drug concentration needed to give 100% effect is lower than the concentration needed to occupy 100% of the receptors. What does this mean?

It means that when we give a drug in the concentration that gives 100% effect, there are many receptors that are not occupied by the drug! We introduce a term called receptor reserve, defined as the fraction of receptors that are apparently not needed for the maximal effect. Receptor reserve can be found by plotting a drug’s effect against its occupancy, like this:

A, B, C, D and E are different drugs. Details about them are in the table.

Here we have plotted the occupancy-response relationship of five different drugs. From this graph, we can determine the drugs’ efficacy (their intrinsic activity, IA) and their receptor reserve. The IA is where the highest point of the graph is on the y-axis. To find the receptor reserve, we need to see at what occupancy the drug can achieve 100% effect. Drug A reaches 100% effect at around 20% occupancy. That means that 100-20=80% of the receptors are available, meaning that for drug A, the receptor reserve is 80%. Drug B achieves 100% with around 60% occupancy, meaning that it has a receptor reserve of around 40%. C achieves 100% effect with 100% occupancy, meaning that it has no receptor reserve. D and E never even reach 100% effect, so they have no receptor reserve. However, we can see that their efficacy is below 100%, so they’re both partial agonists.

There are two mechanisms that can explain the receptor reserve:

  • High signal amplification in the receptor, so even if not all receptors are activated will the response still be 100%
  • High receptor density, meaning that there are so many receptors that some are left unbound after 100% effect has been reached
  • High intrinsic efficacy

We introduce yet another term: intrinsic efficacy (not to be confused with intrinsic activity). The symbol of intrinsic efficacy is ε (epsilon). On occupancy-response relationship graphs, the intrinsic efficacy increases upwards and to the left. On the previous graph, the intrinsic efficacy of the five drugs are different. A has the highest, then B, C, D and E has the lowest.

A higher intrinsic efficacy is a good thing, because drugs with higher intrinsic efficacy have higher receptor reserves and higher intrinsic activity. Intrinsic efficacy can be used to differentiate the usefulness of different full agonists.


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4. Basic mechanisms of drug actions

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6. Significance of signal transduction mechanisms in the effects of drugs. Tachyphylaxis and tolerance to drugs

2 thoughts on “5. Characterisation of agonist-receptor interaction. Occupancy, affinity, dose-response curve, potency, efficacy”

  1. Commendable effort is recognised for these notes; however I must emphasise that the layout on this topic is very misleading. Please revise this topic and re-write to demonstrate the various pharmacological jargon to the lay man who would be misinformed otherwise.

    1. I agree that the layout isn’t optimal and I’m sure you’ll find more topics that have the same problem. The layout somewhat follows the layout of the lecture or seminars they’re based on.

      I will not rewrite it as I’m not sure I could do it better if I tried and I don’t want to use valuable time on that. I have already simplified it compared to the original seminar and in my opinion have I not left out anything that would be important. The topic isn’t written for laymen anyway.

      If you have any more specific points you would want improved then could I take a look.

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