Drug-Receptor Interaction (Affinity, Efficacy & Agonism)

# RESOURCES

### Guidelines

### Review Articles

## Introduction & Definitions

### What are the key factors that characterise the interaction of a drug with a receptor?

(Intrinsic Activity)

- Usually described using 'fractional occupancy' rate:
- Value between 0 - 1 is given depending on the fraction of receptors bound to the drug
- The value of 1 represents maximal saturation of binding sites (B
_{max})

- Fractional occupancy forms the y-axis in an occupancy curve (receptor occupancy vs dose)

- Drugs of high affinity bind to a critical number of receptors at low concentration compared with drugs of low affinity which require a high concentration to bind to a critical number of receptors
- Affinity of a drug is described by it's K
_{D}- the concentration of a drug at which 50% of the available receptors are occupied - K
_{D}best represented using an occupancy curve (receptor occupancy vs dose)

- Can be described using graded or quantal responses
- Graded response
- Value between 0 - 100% given depending on the effect on a particular system
- The value of 100% represents maximal effect of a drug-receptor complex (E
_{max}) irrespective of drug concentration

- Quantal response:
- Value between 0 - 100% is given depending on the proportion of a specific population in which effect is produced
- Efficacy forms the y-axis in a dose-response curve (efficacy vs dose)

- Drugs of high potency produce an effect bind at low concentration compared with drugs of low potency which require a high concentration to bind to a critical number of receptors
- Potency of a drug is described by it's ED
_{50}or EC_{50}depending upon the use of graded or quantal response - Graded response:
- EC
_{50}describes the concentration of a drug that produces a specific response that is exactly halfway between baseline and maximum

- EC
- Quantal response:
- ED
_{50}describe the dose of a drug that induces a specific response in exactly 50% of the population who take it

- ED
- EC
_{50}/ ED_{50}best represented using a dose-response curve (efficacy vs dose)

## Overview of Occupancy & Affinity

### What are receptors, ligands and drugs?

### How is drug receptor-drug interaction modelled and explained mathematically?

- Drug-receptor interaction is explained by the ‘law of mass action’:
- Proposes that the rate of binding is directly proportional to the product of the concentrations of the reactants

- Can be demonstrated by the equation:

[R] is receptor

[D-R] is drug–receptor complex

K

_{on}is rate of forward reaction (assocation rate constant)

K

_{off}is rate of backward reaction (dissociation rate constant)

### What is the definition of receptor occupancy?

- Usually described using 'fractional occupancy' rate:
- Value between 0 - 1 is given depending on the fraction of receptors bound to the drug
- The value of 1 represents maximal saturation of binding sites (B
_{max})

- Fractional occupancy forms the y-axis in an occupancy curve (receptor occupancy vs dose)

### What is fractional occupancy?

- Fractional occupancy (r) is a way of describing the degree of receptor occupancy
- It is equal to the number of occupied receptor sites divided by the total receptor binding sites and can be demonstrated by the following:

### Which factors determine receptor occupancy?

- Binding occurs when ligand and receptor collide (due to diffusion) with the correct orientation and sufficient energy:
- The rate of binding is a product of the concentration of drug, concentration of receptor and the rate of association (K
_{on}) - This is demonstrated by the equation:

- The rate of binding is a product of the concentration of drug, concentration of receptor and the rate of association (K

- Once binding has occurred, the ligand and receptor remain bound together for a random amount of time
- The rate of unbinding is a product of the concentration of drug-receptor complexes and the rate of dissociation (K
_{off}) - This is demonstrated by the equation:

- The rate of unbinding is a product of the concentration of drug-receptor complexes and the rate of dissociation (K

- The equilibrium dissociation constant k
_{D}describes the relationship between the association and dissociation rate and thus the strength of drug-receptor binding- It is a physical constant unique to each drug-receptor complex:

### What is the definition of affinity?

- Drugs of high affinity bind to a critical number of receptors at low concentration compared with rugs of low affinity which require a high concentration to bind to a critical number of receptors
- Affinity of a drug is described by it's K
_{D}- the concentration of a drug at which 50% of the available receptors are occupied - K
_{D}best represented using an occupancy curve (receptor occupancy vs dose)

### How can the K_{D} be demonstrated mathematically?

- In equilibrium, the rates of drug-receptor association and dissociation will be equal
- Using equations described previously:

- In equilibrium, the rates of drug-receptor association and dissociation will be equal
- Using equations described previously:

Rearranges as:

Substituted as:

- If a drug has a high affinity:
- The DR form will be favoured at equilibrium, hence the value of [D][R] will be small and that of [DR] will be high
- Therefore, the value of K
_{D}will be small

- If a drug has low affinity :
- The D and R form will be favoured, hence the value of [D-R] will be low
- Therefore, the value of K
_{D}will be large

- The above equation can be considered at the point when a drug occupies exactly 50% of receptors in equilibrium (r=0.5)
- At this point, the number of free receptors [R] will equal that of occupied receptors [DR]
- Therefore, these cancel each other out, demonstrating that K
_{D}is equal to the concentration of the drug at this time

### How is the K_{D} defined?

- K
_{D}is the uquilibrium dissociation constant describing the relationship between association and dissociation rates - It can also be described as:
The drug concentration at which 50% of the maximum receptor population is occupied, usually expressed in units of mmol/L

### What is the K_{D} used for?

- The K
_{D}is a physiochemical constant – it the same for a given receptor and drug combination in any tissue, in any species - It can therefore be used:
- To quantitatively compare the affinity of different drugs on the same receptor
- To identify an unknown receptor

### How can the K_{D} be used to help determine fractional occupancy rate?

- The previous equation representing K
_{D}can be rearranged:

- This can be substituted into the equation for fractional occupancy (r) and after simplification becomes:

## Binding Curves

### How is the relationship between concentration and receptor occupancy graphically displayed?

- Displayed using a binding curve which plots:
- Concentration of the drug on the x-axis
- Fractional occupancy on the y-axis

- Can be used to determine the KD of a drug-receptor system

- The x-axis is labelled with drug concentration (mmol/L). It is linear in nature
- The y-axis is labelled with fractional occupancy with a value 0-1
- The curve is a rectangular hyperbola passing through the origin and demonstrates how fractional occupancy varies with concentration of drug
- K
_{D}can be demonstrated and is a marker of the affinity of the specific drug

### Why is a semi-log plot of the binding curve used?

- It is now customary to use a semi-log curve to demonstrate fractional occupancy vs. dose:
- Drug concentration / dose plotted on a logarithmic scale
- Produces a sigmoidal curve

- Has the advantages of:
- Better assessment of the effects of low doses and for a wide range of doses on the same plot
- Easier comparison of different drugs on the same plot

### How is a log binding curve graphically displayed?

- The x-axis is labelled with drug concentration (mmol/L). It is logarithmic in nature with each point 10x greater than the previous
- The y-axis is labelled with fractional occupancy with a value 0-1
- The curve sigmoid in shape with a linear middle portion and demonstrates how fractional occupancy varies with concentration of drug
- K
_{D}can be demonstrated and is a marker of the affinity of the specific drug

### How does the log binding curve change with differing affinity?

- The graph is a log binding curve with x-axis as drug concentration (mmol/L) in a logarithmic nature, and the y-axis as fractional occupancy
- The curves for each drug are sigmoid in nature
- A drug with increased affinity has a lower K
_{D}, thus shifting the curve to the left - A drug with decreased affinity has a higher K
_{D}, thus shifting the curve to the right

## Overview of Efficacy & Potency

### What is the definition of efficacy?

(Intrinsic Activity)

- Can be described using graded or quantal responses
- Graded response
- Value between 0 - 100% given depending on the effect on a particular system
- The value of 100% represents maximal effect of a drug-receptor complex (Emax) irrespective of drug concentration

- Quantal response:
- Value between 0 - 100% is given depending on the proportion of a specific population in which effect is produced
- Efficacy forms the y-axis in a dose-response curve (efficacy vs dose)

### How can efficacy and potency be measured?

Can be measured by assessing graded or quantum response:

- Measures the efficacy of a receptor-effector in a particular system (e.g. tissue, animal or patient)
- Measures effect on a continuous scale
- Used to plot drug concentration vs. response on a graded dose-response curve
- Examples of graded response include: effect of GTN on arterial pressure, streptomycin on protein synthesis etc.

- Measures the efficacy of a receptor-effector in a population, where the effect is binary on each individual (present or absent)
- Measures effect on a percentile scale, describing the size of population in which the effect is seen
- Used to plot drug dose vs outcome occurrence on a quantal dose-response curve
- Examples include: effect of aspirin in reducing MI occurrence etc.

### What is the definition of potency?

- Drugs of high potency produce an effect bind at low concentration compared with drugs of low potency which require a high concentration to bind to a critical number of receptors
- Potency of a drug is described by it's ED
_{50}or EC_{50}depending upon the use of graded or quantal response - Graded response:
- EC
_{50}describes the concentration of a drug that produces a specific response that is exactly halfway between baseline and maximum

- EC
- Quantal response:
- ED
_{50}describe the dose of a drug that induces a specific response in exactly 50% of the population who take it

- ED
- EC
_{50}/ ED_{50}best represented using a dose-response curve (efficacy vs dose)

### Which terms can be used to describe potency and how are they defined?

*Graded Response*

## EC_{50}

(Median Effective Concentration)*Quantal Response*

## ED_{50}

(Median Effective Dose)### What is the relationship between occupancy, efficacy, affinity and potency?

- Classical receptor theory suggests that the response seen will be proportional to the percentage of receptors occupied
- In this situation when the relationship between receptor occupancy and response is linear
- Occupancy is directly proportional to efficacy
- Affinity is directly proportional to potency, with K
_{D}= EC_{50}

- If a simple dose-occupancy curve for a full agonist is plotted on the same axes as a dose–response curve they would be identical

- In this situation when the relationship between receptor occupancy and response is linear
- However, this relationship usually does not bear true:
**Receptor Reserves:**- It is often the case that only 5–10% occupancy is needed to produce a full response
- Indicates that ∼90% of receptors are not needed to elicit a maximum response and hence form the receptor reserve
- Results in dose-response response lying to left of the binding curve in full agonist (EC
_{50}less than K_{D})

**Partial agonism:**- Implied that at a full response can be produced with full receptor occupancy
- For a partial agonist, even at 100% occupancy a full response (similar to the full agonist) cannot be produced
- Spare receptors are not pooled or hidden; they are simply surplus to requirements

## Dose-Response Curve

### What is a graded dose-response curve and how is it plotted?

- The x-axis is labelled with drug concentration (mmol/L). It is linear in nature
- The y-axis is labelled % of maximum response
- The curve is a rectangular hyperbola passing through the origin and demonstrates how fractional occupancy varies with concentration of drug
- The graph is identical to a binding curve except for the y-axis
- EC
_{50}can be demonstrated and is a marker of the potency of the specific drug

### What is a quantal dose-response curve and how is it plotted?

- The x-axis is labelled with drug dose (mg). It is linear in nature
- The y-axis is labelled % of population
- The curve is a rectangular hyperbola passing through the origin and demonstrates how fractional occupancy varies with concentration of drug
- The graph is again identical to a binding curve except for the y-axis
- ED
_{50}can be demonstrated and is a marker of the potency of the specific drug

### Why is a log dose-response curve used and how is it plotted?

- The x-axis is labelled with drug dose (mg). It is logarithmic in nature with each point 10x greater than the previous
- The y-axis is labelled with % of population responding
- The curve sigmoid in shape with a linear middle portion and demonstrates how fractional occupancy varies with concentration of drug
- The graph is identical to a log binding curve except for the axis labels
- ED
_{50}can be demonstrated and is a marker of the potency of the specific drug

### How does the log dose-response curve change with different potency of drugs?

- The graph is a log dose-response curve with x-axis as drug dose (mg) in a logarithmic nature, and the y-axis as % of population responding
- The curves for each drug are sigmoid in nature
- A drug with increased potency has a lower ED
_{50}, thus shifting the curve to the left - A drug with decreased potency has a higher ED
_{50}, thus shifting the curve to the right

## Therapeutic Index

### Besides the ED50 / EC50 which other markers of a drug’s potency can be described?

## TD_{50}

(Median Toxic Dose)## LD_{50}

(Median Lethal Dose)### What is the therapeutic index?

- The therapeutic index is the ratio of the dose that produced toxicity to the dose that produces a clinically desired effect:

- It is a statement of the relative safety of a drug – the larger the TI, the safer the drug
- In animal models, the LD50 may be used instead of the TD50 when calculating the therapeutic index

### How is therapeutic index determined?

- Therapeutic index is determined from quantal dose curves
- Both the concentrations of drugs producing desired and toxic clinical effects are plotted and ED50 / TD50 determined

### What is the margin of safety?

- Because of differences in slopes and threshold doses, low doses of a drug may be effective but at higher concentrations cause toxicity in specific parts of the population without being effective

- The Margin of Safety (MOS) is used as a marker of drug safety to overcome limitations with the therapeutic index (demonstrated in the above graph)
- It uses the ratio of the toxic dose of a drug to 1% of the population (TD
_{01}) to the dose that is 99% effective to the population (ED_{99})

## Overview of Agonism

### What is drug agonism?

The phenomena of a drug to selectively bind to a specific receptor and trigger a response

### What types of agonism can drugs exhibit towards a receptor?

- Has affinity for receptors
- Able to produce a maximal response

- Has affinity for receptors
- Produces a sub-maximal response

- Has affinity for receptors
- Produces no effect of its own
- Presence inhibits the action of other agonists at that receptor

- Has affinity for receptors
- Produces the opposite effect to the endogenous agonist

- Morphine on MOP receptors

- Buprenorphine on MOP receptors

- Atenolol on β receptors

- Flumazenil on the GABA
_{A}receptor

## Agonism Types

### How can the response to a full agonist be demonstrated on a log dose-response curve?

- The graph is a log dose-response curve with log drug dose on the x-axis and % of maximal effect on the y-axis
- The curve sigmoid in shape
- The height of the curve is the maximal effect which for a full agonist is 100%
- The curve always passes through the ED
_{50} - For a full agonist (A) this is always at 50% of maximal effect
- A full agonist of lower potency has a higher ED
_{50}, thus shifting the curve to the right

### How can the response to a partial agonist be demonstrated on a log dose-response curve?

- The graph is a log dose-response curve with log drug dose on the x-axis and % of maximal effect on the y-axis
- The curve sigmoid in shape
- The height of the curve is the maximal effect which for a partial agonist is lower than 100%
- The curve always passes through the ED
_{50} - which is at 50% of partial agonists maximal effect
- Partial agonist B has an ED
_{50}which is the same dose as full agonist A and thus they have equal potency despite exhibiting a lower maximal effect - Partial agonist C has an ED
_{50}which is the same dose as full agonist A and thus they have equal potency despite exhibiting a lower maximal effecthigher than both drugs A&B and thus is less potent

### How can the response to an antagonist be demonstrated on a log dose-response curve?

- The graph is a log dose-response curve with log drug dose on the x-axis and % of maximal effect on the y-axis
- An antagonist displays no effect regardless of the concentration and thus follows a horizontal linear path at 0% effect

### How can the response to an inverse agonist be demonstrated on a log dose-response curve?

- The graph is a log dose-response curve with log drug dose on the x-axis
- However, the y-axis shows % response of maximal response and is drawn to show both a poitive and negative response
- The curve of an antagonist is sigmoid in shape and is a reflection of the curve of a full agonist

## Antagonism Types

### What is an antagonist?

A drug that reduces the action of another drug, generally an agonist

- Antagonists can act by a number of different mechanisms:
*Pharmacological antagonism:*Interaction at the same receptor macromolecule as the agonist*Chemical antagonism:*Combination with the substance being antagonized*Functional antagonism:*Disruption to effect occurring at cellular sites distinct from the receptor mediating the agonist response

### What is a functional antagonist?

- Describes disruption to the agonist effect occurring at cellular sites distinct from the receptor mediating the response
- Can include mechanisms such as:
*Indirect antagonism:*competition for the binding site of an intermediate macromolecule that links the binding of the administered agonist to the effect observed*Physiological antagonism:*drug exerts an opposite physiological effect to that of the original agonist, usually through different receptors

### Which characteristics can be used to describe a pharmacological antagonist?

- The antagonist and agonist compete for the same binding site
- Reduces the number of free receptor sites for agonist binding

- The antagonist binds to a separate site on the receptor to the agonist
- Can act to change the shape of the agonist binding site (allosteric modulation) or prevent receptor activation without effect on agonist binding

- Antagonist forms only short-lasting combinations with the receptor

- Antagonist form a stable covalent bond with the receptor

- The effect of the antagonist can be overcome by increasing concentrations of the agonist

- The maximum effect of the agonist is reduced by the antagonist and cannot be overcome by increasing concentrations

### What are the main forms of pharmacological antagonists?

(Surmountable)

(Insurmountable)

(Insurmountable)

- The agonist and antagonist compete for the same binding site
- Only short-lasting combinations with the receptor are formed, so that equilibrium between agonist, antagonist, and receptors is reached
- Antagonism is surmountable as increased concentrations of agonist can outcompete the antagonist

- The agonist and antagonist compete for the same binding site
- A stable covalent bond with the receptor is formed
- Antagonism becomes insurmountable at higher concentrations when no spare receptors remain as this cannot be overcome by increased concentrations of agonist to 'outcompete'

- The antagonist binds to a different site on the than the agonist
- Antagonism is insurmountable as the agonist action is prevented when receptors are bound by the antagonist and cannot be overcome by increased concentrations
- Binding can be short lived (reversible) or permanent (irreversible) but the antagonism is insurmountable with either

### How can the effect of the addition of a competitive reversible antagonist be demonstrated on a dose-response curve?

- A standard sigmoid curve represents a full agonist alone
- A second curve to the right of the first curve can be drawn to show the effect of the addition of a competitive reversible inhibitor
- The curve sits to the right due to decreased potency of the agonist in the presence of the antagonist
- This can be demonstrated by plotting the ED
_{50}for both curves

### How can the effect of the addition of a competitive irreversible antagonist be demonstrated on a dose-response curve?

- A standard sigmoid curve represents a full agonist alone
- At low doses a competitive irreversible antagonist is surmountable at high concentrations but at the expense of decreased potency of the agonist - represented by a curve to the right of the first curve
- At high doses the antagonistic effects become insurmountable despiute increasing agonist concentrations - represented by a curve to the right represeting reduced potency, and with a lower height representing reduced maximal effect

### How can the effect of the addition of a non-competitive antagonist be demonstrated on a dose-response curve?

- A standard sigmoid curve represents a full agonist alone
- A non-competitive antagonist prevents antagonist binding and the effect is insurmountable
- This results in decreased potency and decreased maximal effect of the agonist - the curve is shifted down and to the right
- The curve is similar in shape to the effects of a partial agonist alone

# Author

**The Guidewire**

Trainee in ICM & Anaesthesia

# Reviewer

**The Guidewire**

Trainee in ICM & Anaesthesia