Question

A receptor has a \(K_{\mathrm{d}}\) for its ligand of \(50 \mathrm{nM}\). This receptor a. has a higher affinity for its ligand than does a receptor with a \(K_{d}\) of \(100 \mathrm{nM}\) b. has a higher affinity for its ligand than does a receptor with a \(K_{\mathrm{d}}\) of \(10 \mathrm{nM}\) c. is mostly bound by its ligand when the ligand concentration is \(100 \mathrm{nM}\). d. must be an intracellular receptor. e. both a and \(c\) are true of this ligand.

Short answer

Options a, c and e are true. Options b and d are false.

Step-by-step solution

Affinity comparison with \(K_{d} = 100 nM\) receptor

The statement in part a is saying that the given receptor with a \(K_{d} = 50 nM\) has a higher affinity than a receptor with a \(K_{d} = 100 nM\). Since lower \(K_d\) values mean greater affinity, it can be concluded that our receptor indeed has a higher affinity than a receptor with a \(K_{d} = 100 nM\). Thus, option a is true.

Affinity comparison with \(K_{d} = 10 nM\) receptor

The statement in part b is saying that the receptor with a \(K_{d} = 50 nM\) has a higher affinity than a receptor with a \(K_{d} = 10 nM\). Again, considering that lower \(K_d\) values indicate a higher affinity, it can be concluded that our receptor actually has a lower affinity than a receptor with a \(K_{d} = 10 nM\). Thus, option b is false.

Verification of ligand binding at \(100 nM\)

In part c, it is mentioned that the receptor is mostly bound by its ligand when the ligand concentration is \(100 nM\). Since the \(K_d\) is \(50 nM\), at concentrations of ligand greater than \(50 nM\), it is safe to say that most receptors will indeed be bound by the ligand. Hence, option c is true.

Checking location of receptor

Statement d suggests that the given receptor must be an intracellular receptor based solely on its \(K_d\) value. This statement is incorrect because the \(K_d\) value alone does not provide information about the location of the receptor. Therefore, option d is false.

Verification of multiple statements

In part e, it is stated that both options a and c are true. Given the analysis and verification in Steps 1 and 3, it can be concluded that option e is true since both options a and c are indeed correct.

Key concepts

Receptor Affinity

Receptor affinity is a crucial concept in understanding ligand-receptor interactions. It refers to the strength with which a ligand binds to its receptor. This is an essential measure because:

• High affinity means that a ligand can effectively bind to its receptor even at lower concentrations.
• Low affinity indicates that higher concentrations of the ligand are needed for effective binding.

A receptor with a dissociation constant ( \( K_d \) ) of \( 50 \mathrm{nM} \) has a greater affinity compared to one with a \( K_d \) of \( 100 \mathrm{nM} \) because the ligand can more readily bind to the receptor. Lower \( K_d \) values correspond to higher affinity, which is a key reason in differentiating binding strengths among different receptors.
Understanding receptor affinity helps in predicting how effectively drugs or hormones can modulate receptor function, providing insight into their potential effectiveness and interactions.

Dissociation Constant \(K_d\)

The dissociation constant ( \( K_d \) ) is a quantitative measure of a receptor's affinity for its ligand. It represents the concentration of ligand at which half of the receptors are occupied. Mathematically, \[ K_d = \frac{[R][L]}{[RL]} \]where \([R]\) is the concentration of free receptors, \([L]\) is the concentration of free ligand, and \([RL]\) is the concentration of bound receptor-ligand complexes.
A low \( K_d \) value indicates high affinity, meaning the ligand binds tightly and effectively to the receptor. For example, with a \( K_d \) of \( 50 \mathrm{nM} \) , the ligand binds more effectively than it would with a \( K_d \) of \( 100 \mathrm{nM} \). As ligand concentration increases beyond the \( K_d \), more receptors become occupied, which in turn often leads to a physiological effect.
The \( K_d \) is a critical parameter for drug development, as it aids in the assessment of potential drug efficacy by estimating required dosages for desired effects.

Intracellular Receptors

Unlike surface receptors, intracellular receptors are located inside the cell, often in the cytoplasm or nucleus. These receptors tend to bind ligands that are small and hydrophobic, allowing them to pass through the cell membrane. It is important to note:

• Common ligands include steroid hormones, thyroid hormones, and certain vitamins.
• These ligands usually lead to long-lasting effects by altering gene transcription.

Although the original exercise included an option that identified the receptor as intracellular based solely on its \( K_d \), this is misleading. The \( K_d \) value does not specify where the receptor is located within the cell or whether it is on the cell surface or intracellular. Therefore, a more comprehensive understanding is needed to categorize a receptor as intracellular, focusing on the ligand type and cellular location rather than just \( K_d \).Understanding the role and function of intracellular receptors provides insights into gene regulation and development of therapies targeting chronic diseases or hormonal imbalances.