Drug-Receptor Interaction (Affinity, Efficacy & Agonism)

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
  • 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)
  • 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
  • Graded 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
  • 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?

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
    • 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:

    •  
    Graded 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
    • Graded 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)

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

    Graded Response

    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

      Therapeutic Index

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

        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