Affinity and Concentration Response Curves

Goals of Drug Treatment:

Drugs are developed to modify biological functions in ways that improve health.

• Cure disease

  • e.g. antibiotics and antivirals.

• Alleviate symptoms

  • e.g. painkillers and medications like salbutamol for asthma.

• Prevent disease or complications

  • e.g. insulin prevents DKA and statins lower cardiovascular risk.

Drug-Receptor Interactions:

A receptor is a protein target that binds a drug (ligand).

• Affinity = ability to bind to receptor.

• Efficacy = ability, once bound, to activate the receptor and trigger a response.

Drug Classes:

• Agonists - high affinity and high efficacy, so produce a response.

• Partial Agonists - bind receptors but produce only partial activation, even at full occupancy (such as buprenorphine at μ-opioid receptors).

• Antagonists - high affinity, zero efficacy, so block a receptor without activating it (such as propranolol at β-adrenoceptors).

• Inverse Agonists - bind and reduce basal receptor activity below resting level (e.g. some β-blockers at β₂AR).

Law of Mass Action:

Drug-receptor binding is reversible and follows equilibrium rules:

                    D + R ⇌ DR

The forward binding rate has equation:

• Rate = k_on[D][R]

The reverse dissociation rate has equation:

• Rate = k_off[DR]

At equilibrium:

• k_on[D][R] = k_off[DR]

This is the foundation of pharmacological binding theory.

The Dissociation Constant (K_D):

The Dissociation Constant is defined as K_D = k_off  /  k_on.

• It is the equilibrium dissociation constant.

  • A measure of drug affinity.

    • Low K_D = high affinity.

    • High K_D = low affinity.

  • It is the concentration of drug at which 50% of receptors are occupied.

• A higher affinity means that a lower dose is required, and there is longer therapeutic action.

Receptor Occupancy:

Fractional occupancy (α) is given by: α = [D] / [D] + K_D.

• The proportion of receptors that are occupied (bound) by a drug at a given concentration.

• If [D] = K_D, then α = 0.5.

It is also important to note that occupancy is not response, which also depends on efficacy and receptor reserve. 

Binding Kinetics:

KD is useful, but isn’t the whole story.

• k_on is how quickly a drug binds.

• k_off is how quickly a drug dissociates.

Residence time (average time a drug is bound to a receptor before dissociating) is 1 / k_off.

Measuring Affinity - Radioligand Binding Studies:

Radioligands are radioactively labelled drugs that bind receptors.

• Radiolabel drug (e.g. with tritium (³H)).

• Mix with receptor preparation.

• Allow binding to equilibrium.

• Separate bound vs free ligand (filtration/centrifugation).

• Count radioactivity.

Specific vs Non-Specific Binding

• Specific + Non-Specific Binding = Total Binding

• Non-Specific Binding = radioligand sticking to membranes, filters etc.

• Measure by adding excess unlabelled drugs.

  • This displaces radioligands from receptors, leaving only non-specific binding.

Saturation and Competition Analysis:

Saturation Binding

• Varying concentration of radioligand.

• Curve approaches a plateau at B_max (total receptor number).

• KD found at [radioligand] that gives 50% of B_max.

Competition Binding

• Keep the radioligand concentration constant.

  • Add increasing concentrations of an unlabelled competitor drug.

  • The competitor displaces the radioligand from the receptor in a concentration-dependent manner.

• In a competition binding experiment, you plot % radioligand bound (y-axis) against log[competitor] (x-axis).

  • As the competitor concentration increases, it displaces more radioligand from receptors.

  • The resulting sigmoid (“S-shaped”) displacement curve shows the degree of displacement.

• IC₅₀ is the concentration of unlabeled competitor drug that displaces 50% of the specifically bound radioligand.

• True Affinity (Ki) is calculated using the Cheng-Prusoff equation: $K_i = \frac{IC_{50}}{1 + \frac{[L]}{K_D}}$

Modern Binding Assays:

• Non-radioactive probes (i.e. fluorescent or luminescent etc.).

• Allows real-time binding studies in living cells.

• Safer and more versatile than radioactive assays.

  • Example: fluorescent ligand binding to Neuropeptide Y receptors.

Limitations of K_D:

• KD does not tell you:

  • Whether the drug activates a receptor (efficacy).

  • How selective the drug is for one receptor over another.

  • Its pharmacokinetics (absorption, metabolism, clearance).

  • Its clinical effect size (which depends on tissue receptor density, spare receptors, signalling pathway etc.).

Why isn’t K_D enough?

• Affinity (KD) tells us how strongly a drug binds to its target.

  • However, binding alone doesn’t tell us what the drug does.

    • A ligand can be an antagonist, agonist or an inhibitor.

• Therefore, we need functional bioassays to measure the actual response a drug produces, not just the binding.

Concept of Bioassays:

A bioassay is any experiment that measures the functional response or potency of a drug.

• Cellular - measures second messenger production (e.g. cAMP at β-adrenoceptors).

• Tissue - contraction of isolated cardiac muscle strips.

• Organ - rate and force of isolated heart beats.

• Whole System - blood pressure changes in a live animal.

Advantages vs Disadvantages:

• Simple Bioassays (e.g. cell lines, recombinant receptors):

  • ✔ Receptor is well-defined.

  • ❌ May be artificial - cell behaviour might not reflect true physiology.

• Complex Bioassays (e.g. organ and system level):

  • ✔ Closer to “real” physiology.

  • ❌ Multiple types of receptor, so response may be a composite.

Concentration Basics:

• Concentration = amount of drug (moles) per unit volume (litres).

  • Units: M (molar).

• Drug responses typically vary over 1000-fold differences.

  • For clarity, pharmacologists plot concentration logarithmically.

    • Each step is a 10-fold step.

Concentration-Response Curves (CRCs):

Concentration-Response Curves show the relationship between drug concentration and response. It typically follows a sigmoid curve when plotted logarithmically.

• R_max = maximum response a drug can produce in that system.

  • Reflects the efficacy of the drug.

• EC₅₀ = concentration that produces 50% of R_max.

  • Reflects the potency of the drug.

    • A low EC₅₀ means there is a high potency.
         → Potency depends not only on affinity, but also on receptor density and amplification.

EC₅₀ shows how much drug is needed, and R_max shows the maximum response it can have.

Comparing Agonists:

• Full Agonist - achieves the system’s maximum possible response.

  • E.g. formoterol at β₂ receptors in airway smooth muscle.

• Partial Agonist - cannot achieve full response even at 100% receptor occupancy.

  • E.g. salbutamol (lower efficacy than adrenaline).

Partial Agonists in Therapy:

Partial agonists have clinical advantages that full agonists do not have:

• Lower maximal effect, which may lead to reduced side effects.

• Less likely to cause receptor desensitisation or tolerance.

Interpreting CRCs - The Limitations:

• Does a lower R_max always mean partial agonism?

  • Yes. It can indicate partial agonism, but not always.

    • Low receptor expression or downstream signalling bottlenecks can also reduce the R_max.

• Is EC₅₀ the same as K_D?

  • No. Agonist EC₅₀ is often lower than K_D due to signal amplification and receptor reserve.

Signal Amplification and Receptor Reserve:

One activated receptor can trigger thousands of signalling events (second messengers, ion fluxes, gene expression etc.).

• This amplification means:

  • Not all receptors need to be occupied to achieve maximal response.

  • The system appears more sensitive, i.e. EC₅₀ < K_D.

Receptor Reserve

• The “spare receptors” in a system that aren’t needed for maximum response.

  • It explains why potency is not the same as affinity.