Drug-Receptor Interaction (Affinity, Efficacy & Agonism)

# RESOURCES

## Introduction & Definitions

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

Term
Receptor Occupancy
Affinity
Efficacy
(Intrinsic Activity)
Potency
Definition
A measure of the magnitude of the drug bound to the receptor
A measure of quantity of drug needed to bind to receptors (how avidly a drug binds)
A measure of the magnitude of the effect that a drug-receptor system produces
A measure of the quantity of drug needed to produce maximal effect
Description
• 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 (Bmax)
• 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 KD - the concentration of a drug at which 50% of the available receptors are occupied
• KD best represented using an occupancy curve (receptor occupancy vs dose)
• Can be described using graded or quantal responses
• 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)
• 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 ED50 or EC50 depending upon the use of graded or quantal response
• EC50 describes the concentration of a drug that produces a specific response that is exactly halfway between baseline and maximum
• Quantal response:
• ED50 describe the dose of a drug that induces a specific response in exactly 50% of the population who take it
• EC50 / ED50 best represented using a dose-response curve (efficacy vs dose)

## Overview of Occupancy & Affinity

### What are receptors, ligands and drugs?

Receptor
Ligand
A receptor is a component of a cell that interacts selectively with a compound to initiate a biochemical change or cascade that produces the effects of the compound
A chemical messenger able to bind to a receptor. May be endogenous or exogenous (a drug)

### 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:
•
$[D] + [R] \underset{K_{on}}{\stackrel{K_{off}}{\rightleftharpoons}} [DR]$
[D] is drug
[R] is receptor
[D-R] is drug–receptor complex
Kon is rate of forward reaction (assocation rate constant)
Koff is rate of backward reaction (dissociation rate constant)

### What is the definition of receptor occupancy?

Term
Receptor Occupancy
Definition
A measure of the magnitude of the drug bound to the receptor
Description
• 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 (Bmax)
• 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:
$r= \frac{[DR]}{\text[Total Receptors]}$

### 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 (Kon)
• This is demonstrated by the equation:
$[D] \cdot [R] \cdot {K_{on}}$
• 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 (Koff)
• This is demonstrated by the equation:
$[D-R] \cdot {K_{off}}$
• The equilibrium dissociation constant kD 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:
${k_D} = {K_{off}}/{K_{on}}$

### What is the definition of affinity?

Term
Affinity
Definition
A measure of quantity of drug needed to bind to receptors (how avidly a drug binds)
Description
• 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 KD - the concentration of a drug at which 50% of the available receptors are occupied
• KD best represented using an occupancy curve (receptor occupancy vs dose)

### How can the KD be demonstrated mathematically?

• In equilibrium, the rates of drug-receptor association and dissociation will be equal
• Using equations described previously:
$Association = Dissociation$
• In equilibrium, the rates of drug-receptor association and dissociation will be equal
• Using equations described previously:
$[D] \cdot [R] \cdot {k_A}=[D-R] \cdot {k_D}$

Rearranges as:

${K_b}/{K_f} = \frac{[D]\cdot[R]}{[D-R]}$

Substituted as:

${k_D} = \frac{[D]\cdot[R]}{[D-R]}$

• 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 KD 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 KD 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 KD is equal to the concentration of the drug at this time
${K_D} = [D]$

### How is the KD defined?

• KD 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 KD used for?

• The KD 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 KD be used to help determine fractional occupancy rate?

• The previous equation representing KD can be rearranged:
$[R] = \frac{{K_D}\cdot[D-R]}{[D]}$
• This can be substituted into the equation for fractional occupancy (r) and after simplification becomes:
$r = \frac{[D]}{[D] + {K_D}}$

## 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
Description
• 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
• KD 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
• 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?

Description
• 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
• KD can be demonstrated and is a marker of the affinity of the specific drug

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

Description
• 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 KD, thus shifting the curve to the left
• A drug with decreased affinity has a higher KD, thus shifting the curve to the right

## Overview of Efficacy & Potency

### What is the definition of efficacy?

Term
Efficacy
(Intrinsic Activity)
Definition
A measure of the magnitude of the effect that a drug-receptor system produces
Description
• Can be described using graded or quantal responses
• 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:

•
Quantal 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?

Term
Potency
Definition
A measure of the quantity of drug needed to produce maximal effect
Description
• 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 ED50 or EC50 depending upon the use of graded or quantal response
• EC50 describes the concentration of a drug that produces a specific response that is exactly halfway between baseline and maximum
• Quantal response:
• ED50 describe the dose of a drug that induces a specific response in exactly 50% of the population who take it
• EC50 / ED50 best represented using a dose-response curve (efficacy vs dose)

## EC50

(Median Effective Concentration)
Quantal Response

## ED50

(Median Effective Dose)
The concentration of a drug that produces a specific response that is exactly halfway between baseline and maximum
The dose of a drug that induces a specific response in exactly 50% of the population who take it

### 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 KD = EC50
• 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
• 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 (EC50 less than KD)
• 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?

Description
• 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
• EC50 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?

Description
• 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
• ED50 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?

Description
• 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
• ED50 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?

Description
• 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 ED50, thus shifting the curve to the left
• A drug with decreased potency has a higher ED50, thus shifting the curve to the right

## TD50

(Median Toxic Dose)

## LD50

(Median Lethal Dose)
The concentration of a drug that produces a specific response that is exactly halfway between baseline and maximum
The dose of a drug that induces a specific response in exactly 50% of the population who take it

### 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:
$TI = \frac{TD_{50}}{ED_{50}}$
• 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 (TD01) to the dose that is 99% effective to the population (ED99)
$MOS = \frac{TD_{01}}{ED_{99}}$

## 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?

Type
(Full) Agonist
Partial Agonist
Antagonist
Inverse Agonist
Description
• 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
Efficacy
Efficacy = 1
0 < Efficacy < 1
Efficacy = 0
Efficacy = -1
Description
• Morphine on MOP receptors
• Buprenorphine on MOP receptors
• Atenolol on β receptors
• Flumazenil on the GABAA receptor

## Agonism Types

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

Description
• 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 ED50
• For a full agonist (A) this is always at 50% of maximal effect
• A full agonist of lower potency has a higher ED50, thus shifting the curve to the right

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

Description
• 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 ED50
• which is at 50% of partial agonists maximal effect
• Partial agonist B has an ED50 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 ED50 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?

Description
• 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?

Description
• 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?

Competitiveness
Competitive
Non-competitive
Reversibility
Reversible
Irreversible
Surmountability
Surmountable
Insurmountable
• 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?

Competitive
Non-competitive
Reversible
(Surmountable)
Irreversible
(Insurmountable)
Reversible or Irreversible
(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?

Description
• The graph is a log dose-response curve with log drug dose on the x-axis and % of maximal effect on the y-axis
• 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 ED50 for both curves

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

Description
• The graph is a log dose-response curve with log drug dose on the x-axis and % of maximal effect on the y-axis
• 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?

Description
• The graph is a log dose-response curve with log drug dose on the x-axis and % of maximal effect on the y-axis
• 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