Concentration of drug [A]

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1 Pharmacology Semester 1 page 1 of 5 PHARMACODYNAMICS 1 Receptor occupancy - mass action The interaction of a drug with a receptor is reversible due to interactions via weak bonds (not covalent). [A] + [R] k 1 k -1 [AR] [A] = Agonist concentration [R] = Receptor concentration [AR] = Agonst - receptor complex There is a limited number of receptors on a cell surface. [R T ] = [R] + [AR] [R T ] = Total concentration of receptors [R] = Concentration of unbound receptors [AR] = Concentration of bound receptors with agonist At equilibrium, the forward rate = backward rate, so that: k 1.[A][R] = k -1.[AR] Combining this with the number of receptors equation, we get an equation relating the concentration of drug to its occupancy (how much of the drug is bound to receptor). [ AR] [ A] = [ R T ] k 1 + [ A] k [AR]/[R T ] is the drug occupancy. It is the fraction of bound receptors over the total number of receptors k- 1 /k 1 is known as the equilibrium dissociation constant. It is given the symbol K A It corresponds to the concentration of drug at which half the receptors are occupied. A low value of K A means that the forward rate (formation of [AR] complexes) is greater than the backward rate (dissociation of drug from the receptor). i.e. k 1 > k -1 Hence, K A can also be considered as a measure of a drug s affinity for its receptor. Low K A means there is high affinity because the drug likes to be bound to a receptor. A low K A signifies that a lower concentration of drug is required to occupy half the receptors than another drug with a higher K A. A graph of the occupancy vs drug concentration looks like this: 1 [AR]/[R T ] K A = concentration of drug at which half the receptors are bound Concentration of drug [A] With an increasing concentration of drug, there is an increase in the fraction of receptor binding (occupancy), until we get to a point of maximum occupancy at which all the receptors are occupied. At this point, it is important to note that no response has been mentioned yet, only occupancy. Whether or not there is a response is determined by other factors. Binding of drug to receptor alone is not sufficient to say that it will cause a response!

2 Pharmacology Semester 1 page 2 of 5 To make analysis of this curve easier, we do a mathematical trick of making the x scale a logarithmic scale. By doing this, the curve is converted to a sigmoid curve. Advantages of this curve: It is linear over 20-80% of the occupancy range It is more easier to quantitative values looking off the curve It can show a much larger range of concentrations. At low concentrations, we are able to see the rapid changes that occur, while at the higher concentrations, where things are much more boring, we don t see much. Figure 1: sigmoid curve of occupancy vs concentration [AR]/[R T ] logk A log[a] As you can see from the graphs, when the concentration of drug is at K A, half the receptors are occupied. The K A remains constant for a given drug receptor combination. If you change the drug, the new drug will have a new K A value. Depending on the chemical structure of the new drug, the K A may be less (the drug has a higher affinity to the receptor) or greater (the drug has a lower affinity) than the original drug. Similarly, a change in receptor, with the drug remaining constant will alter the K A. Potency of a drug is related to the affinity. If we compare 2 different drugs acting on the same receptor, we can see that one drug has a higher affinity (lower K A ) to the receptor than the other drug. Drug 1 Drug 2 Drug 1 has higher affinity to the receptor than drug 2 K A1 K A2 The drug with the higher affinity also has a higher potency. Potency is actually concerned with the response of a drug, rather than its occupancy. When we say that a drug has high affinity, it means that more of the drug can bind to receptors at low drug concentrations. When we say that a drug has high potency, we mean that at low concentrations, the drug with higher potency will have a larger response/effect than a drug with low potency. Potency is related to EC50 rather than K A (see later). A high potency does not necessarily mean it is better therapeutically. Why? It is harder to control the dosage. Sometimes we want to regulate the dosage of a drug by deliberately trying to make it act more slowly. This is important for drugs with a small therapeutic window.

3 Pharmacology Semester 1 page 3 of 5 What we have considered so far is the binding of drug to receptor. This is only the very first part of the stimulus - response interaction. The response [A] + [R] [AR] + Transducer [AR]-Transducer In order for the drug receptor interaction to produce a response, it must interact with a transducer. The response is all dependent on the transducer. A weak transducer will result in a weaker response A strong transducer results in a stronger response What does the drug - response curve look like? The drug - response curve looks sigmoidal (if graphed against the log[a]), and it can mirror the drug - occupancy curve. However, this may not always be the case. Scenario one NB: The response curve is superimposed on the occupancy curve 100% curve curve Maximum possible response Log[A] In this case, the response curve is identical to the occupancy curve. If we have half of the receptors occupied, we would get half a response. The concentration of drug at which we see half a response is called the EC50 (the effective concentration that gives 50% response) In this case, EC50 = K A What this means is that when 100% of the receptors are occupied, we get 100% response (maximum response) In real life, we find that this is not often the case. Normally, we do not need to occupy all the receptors in order to get a maximal response. Scenario two 100% curve curve Maximum possible response ½ max response EC50 Log[A] In this situation, we can get a maximum response when only ½ the receptors are occupied. EC50 < K A This occurs because the transducer is very effective at converting the drug-receptor signal into a response.

4 1997 Pharmacology Semester 1 page 4 of 6 Since we can have a maximum response when not all of the receptors are occupied, we have the concept of receptor reserve. Therefore, we can lose some receptors (in this case up to 50%) and still get a maximum response. Scenario three: 100% curve curve Maximum possible response Submaximal response Log [A] If the transducer is weak, we will find that even when all the receptors are occupied, we still cannot get a maximum response. It is not really the transducers fault. All the transducer is doing is responding to the interaction between drug and receptor. If the binding of the drug to the receptor is not very good, the effectiveness of the transducer is thus diminished. We see this effect with the use of partial agonists. EC50 > K A The response receptor occupancy unless under special circumstances. i.e. EC50 does not always = K A Different types of agonist Drug A Drug B Drug C Log[A] Drug A is a full agonist because it can produce a maximum response Drugs B is a partial agonist because it has a range of response which is sub-maximal. They can never get a maximum response, no matter how many receptors are present. Drug C has got no response, so it termed a silent agonist. However, it may still have full occupancy of the receptors. Efficacy is a term used to describe the maximum response of a drug. Drug A has a better efficacy than drugs B and C

5 1997 Pharmacology Semester 1 page 5 of 6 Intrinsic activity is a mathematical value which determines the efficacy of a drug. It acknowledges the fact that not all agonists to a receptor produce a maximum response. α E max [A] E= EC50 + [A] E stands for response α stands for intrinsic activity When α = 1 Full agonist 0 <α < 1 Partial agonist α = 0 Silent agonist (an antagonist) The way the agonist pertubates (changes the receptor shape) the receptor affects the activity of the transducer. This can lead to a good or bad response. The transducer and its role in the response to agonist What happens if you want to stimulate a receptor in the heart to cause increased contractility but there is exactly the same receptor in the blood vessel which causes vasodilation (hence a decrease in BP). We can t stimulate both because the vasodilation would cause a reduced perfusion to a heart which is pumping harder than ever. This would cause an infarct of heart muscle due to insufficient blood supply. We can find a drug which is only specific to the heart, but this is hard because the receptors are exactly the same. In times like these, mother nature has given us a helping hand. It turns out that with the same drug, acting on the same receptor, but in different tissues, we find that the efficacy of the drug differs. of drug acting on the heart of drug acting on blood vessel Remember: Same drug + Same receptor + Different tissue = Different response compared with: Different drug + Same receptor + Same tissue = Different response In this example, the drug acting on the heart acts as a full agonist whereas the drug acting on the blood vessel is acting as a partial agonist. Because the drug and receptor are the same, only the transducer is left to blame. This is an important concept: in different tissues, there may be different transducers, and so the efficacy of the drug will be altered at different tissues. Efficiency (not efficacy) explains the drug-receptor interaction with the transducer. A good example of a drug with this property is glibenclamide (a hypoglycemic). See lecture Ion channels 1. Glibenclamine is designed to work on the β cells of the pancreas to cause insulin secretion. It also acts on vessels to cause vasoconstriction. The potency of glibenclamide on β cells is greater than it is on vessels. Hence, at low drug concentrations, glibenclamide is able to cause a response on the β cells but cannot cause a response in vessels. The vessels require a higher concentration of glibenclamide to have a response. The response to agonist depends on: The chemical property of the drug and its interaction with receptor. The affinity of the drug to the receptor may change The efficacy of the drug will change Efficacy is a measure of the maximum possible response In tissues: Variations in receptor density Does not pose as much a problem if there is receptor reserve

6 1997 Pharmacology Semester 1 page 6 of 6 Efficiency of the coupling Efficiency is the drug - receptor interaction with the transducer