Lecture 2: Drug-Receptor I

Key Definitions in Pharmacology

• Ligand: A molecule that binds to a specific receptor site on another molecule. This binding interaction may or may not trigger a biological response.

• Affinity: The tendency for a drug to bind to a receptor. Drugs categorized as having high potency generally possess a high affinity for their respective receptors.

• Efficacy: The tendency for a drug, once bound to a receptor, to activate that receptor and induce a signaling response.

  • Agonists: Possess significant efficacy, meaning they both bind to and activate the receptor.

  • Antagonists: In the simplest case, antagonists have zero efficacy; they bind to the receptor but do not activate it.

The Quantitative Basis of Drug Affinity

Drug-receptor interactions are typically reversible and involve the interaction of two molecules. This relationship is defined by the following rates:

• Forward Rate of Reaction: This is a second-order reaction because it depends on the concentration of two types of molecules: the drug molecule and the receptor. As the concentration of either increases, the reaction is pushed forward to create more product. It is expressed as:     $k_{+1}[A] \times [R]$

• Reverse Rate of Reaction: This is a first-order reaction because it only depends on the concentration of the drug-receptor complex. It is expressed as:     $k_{-1}[AR]$

• Equilibrium: At equilibrium, the forward rate equals the reverse rate:     $k_{+1}[A_{eq}] \times [R_{eq}] = k_{-1}[A_{eq}R_{eq}]$

• The Dissociation Constant ($K_D$): This constant defines the affinity of a drug for a receptor. It is the ratio of the reverse rate constant to the forward rate constant:     $K_D = \frac{k_{-1}}{k_{+1}} = \frac{[A_{eq}] \times [R_{eq}]}{[A_{eq}R_{eq}]}$

Understanding Receptor Occupancy

Occupancy refers to the proportion of receptors occupied by a drug and is governed by affinity.

• Occupancy Formula:     $\text{Occupancy} = \frac{\text{number of receptors occupied}}{\text{total number of receptors}}$

• Occupancy Range: The value of occupancy varies between $0$ (no drug present) and $1$ (all receptors are occupied).

• Relationship with $K_D$: $K_D$ is equivalent to the concentration of drug required to occupy $50\%$ of receptors at equilibrium.

  • A low $K_D$ indicates high affinity (less drug is needed to occupy half the receptors).

  • A high $K_D$ indicates low affinity (more drug is needed to occupy half the receptors).

Experimental Approaches to Measuring Drug Affinity

There are several laboratory techniques used to determine how well a drug binds to its target:

• Radioligand Binding Assays: A radiolabeled drug is incubated with receptor-containing tissue or cells. The amount of radiolabel bound to the receptors is then measured.

• Fluorescence Polarization Assays (FPAs): Using a fluorescently labeled drug, researchers measure its rotational freedom. Binding to a receptor decreases this freedom, leading to increased polarization of emitted fluorescence.

• Surface Plasmon Resonance (SPR): This technique measures changes in the refractive index of a surface when molecules bind to it.

• Isothermal Titration Calorimetry (ITC): This measures the heat released or absorbed during a binding interaction.

• Computational Modelling: Uses mathematical and molecular simulations to predict drug-receptor interactions based on molecular structures.

Practical Considerations for Radioligand Binding Assays

1. Source of Receptors and Incubation

• Tissue/Cells: Selected to contain the specific recognition sites (receptors). Preparations include isolated membranes, tissue slices, synaptosomes, cultured cells, or purified receptors (e.g., from specific brain regions or immortalized cell lines).

• Incubation Conditions: Must preserve the integrity of the ligand and receptor.

  • Additives: Protease inhibitors protect peptides; antioxidants (e.g., ascorbic acid) protect ligands like catecholamines from oxidation.

  • Temperature: Usually kept low, ranging from room temperature down to $0^{\circ}C$.

2. The Radioligand Characteristics

• Biological Activity: The ligand must remain active to ensure binding correlates with pharmacological action.

• Purity: The ligand must be extremely pure chemically.

• Stability: Degradation is prevented using free-radical scavengers (e.g., ethanol), storage at low temperatures (avoiding freezing), dark bottles to avoid light, and antioxidants.

• Labeling: Must achieve high specific activity to allow for very low "tracer" concentrations.

3. Choice of Radio-Labels

• Tritium ($^3H$):

  • Advantages: Product is indistinguishable from the native compound; high specific activity (> 80\,Ci\,mmol^{-1}); good stability; long half-life (~$12.5\,\text{years}$).

  • Disadvantages: Requires specialized labs; labeling is expensive and difficult.

• Iodine-125 ($^{125}I$):

  • Advantages: Can be incorporated into compounds with an aromatic hydroxyl group (e.g., tyrosine in peptides); extremely high specific activity (> 2000\,Ci\,mmol^{-1}); easy and cheap to produce.

  • Disadvantages: More readily degraded; can reduce biological activity (not functionally invisible); short half-life ($67\,\text{days}$).

4. Separating Bound from Free Ligand

Separation is usually achieved via filtration or centrifugation. Soluble receptors require techniques like dialysis, column chromatography, or precipitation. The speed of separation must be compatible with the affinity to prevent dissociation:

• $K_D = 10^{-12}\,M$: Allowable separation time of $1-2\,\text{days}$.

• $K_D = 10^{-11}\,M$: Allowable separation time of $3\,\text{hours}$.

• $K_D = 10^{-10}\,M$: Allowable separation time of $17\,\text{minutes}$.

• $K_D = 10^{-9}\,M$: Allowable separation time of $1.7\,\text{minutes}$.

• $K_D = 10^{-8}\,M$: Allowable separation time of $10\,\text{seconds}$.

• $K_D = 10^{-7}\,M$: Allowable separation time of $0.1\,\text{seconds}$.

• $K_D = 10^{-6}\,M$: Allowable separation time of $0.01\,\text{seconds}$.

Non-Specific Binding (NSB)

Ligands may bind to non-receptor targets such as glass, plastic, filter paper, or other lipids and proteins in the preparation.

• Reduction: Binding to glass/filters is reduced using anti-absorbants like albumin or collagen (for peptides) or o-catechol (for catecholamines).

• Measurement: Determined by adding an excess of non-radioactive drug. The non-radioactive drug displaces the specific bound radioactive drug, but the non-specific bound radioactivity remains.

Data Analysis: Binding Curves and Equations

• Specific Binding Calculation:     $\text{Specific Binding} = \text{Total Bound} - \text{Non-Specific Binding}$

• Plotting: Data is usually plotted on a semi-logarithmic scale. Specific binding shows "saturation" as receptors become filled, while non-specific binding typically does not.

• The Langmuir/Scatchard Equation: Describes the relationship between occupancy, affinity, and drug concentration:     $\text{Specific Bound} = \frac{B_{max} \times [X_a]}{[X_a] + K_D}$

  • $B_{max}$: The binding capacity, often expressed in $fmoles\,mg^{-1}$ of protein.

  • $[X_a]$: Concentration of the ligand.

Competition Assays

Ligands may compete for the same receptor site. In a competition assay, increasing concentrations of an unlabelled ligand are added to a fixed concentration of a labelled ligand.

• Displacement: As the concentration of the unlabelled inhibitor increases, the percentage of bound labelled ligand decreases as it is displaced.

• Inhibition Constant ($K_i$): The concentration of inhibitor required to displace $50\%$ of the bound radioligand.

• Equivalence: When the inhibitor competes for the same site as the ligand, $K_i \approx K_D$.

• Example: Naloxone competitively displaces $^3H$-DAMGO (an enkephalin analogue) from mu-opioid receptors.

Questions & Discussion

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Test Your Understanding Questions:

• Which of three ligands (a, b, or c) has the highest affinity for a receptor if their $K_D$ values are different? (Ligand with the lowest $K_D$ concentration for $50\%$ occupancy).

• What can be learned about muscarinic receptors in sympathetic ganglia versus sublingual glands using selective and non-selective ligands?

• Which opiate has the highest affinity for the mu opioid receptor based on displacement of $^3H$-DAMGO?