Pharmacology Quiz: Receptor Agonists And Antagonists
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Receptor Agonists And AntagonistsQuestion 1 of 20

During an anaphylactic reaction, histamine released from mast cells causes bronchoconstriction by activating H1 receptors on bronchial smooth muscle. A physician administers epinephrine, which causes potent bronchodilation by activating beta-2 adrenergic receptors on the same muscle tissue. How is the interaction between histamine and epinephrine in the bronchioles best classified?

Competitive antagonism at the H1 receptor
Functional (physiological) antagonism
Negative allosteric modulation of the H1 receptor
Chemical antagonism in the bloodstream
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Pharmacology Quiz

Pharmacology Quiz: Receptor Agonists And Antagonists

Practice Receptor Agonists And Antagonists in Pharmacology with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

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This quiz focuses on Receptor Agonists And Antagonists, giving you a quick way to practice the rules, question types, and explanations that matter most for Pharmacology.

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Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

During an anaphylactic reaction, histamine released from mast cells causes bronchoconstriction by activating H1 receptors on bronchial smooth muscle. A physician administers epinephrine, which causes potent bronchodilation by activating beta-2 adrenergic receptors on the same muscle tissue. How is the interaction between histamine and epinephrine in the bronchioles best classified?

  1. Competitive antagonism at the H1 receptor
  2. Functional (physiological) antagonism (correct answer)
  3. Negative allosteric modulation of the H1 receptor
  4. Chemical antagonism in the bloodstream
Explanation: Functional or physiological antagonism occurs when two agonists bind to two separate receptor types and produce opposing physiological effects. Histamine (via H1 receptors) and epinephrine (via beta-2 receptors) have opposite effects on bronchial smooth muscle tone. They are antagonizing each other's effects at the tissue level, not by interacting at the same receptor.

Question 2

A specific receptor has a dissociation constant (Kd) of 5 nM for its agonist (Drug A) and an inhibition constant (Ki) of 5 nM for a competitive antagonist (Drug B). If this receptor is incubated in a solution containing 5 nM of Drug A and 10 nM of Drug B, what is the approximate fractional occupancy of the receptor by the agonist?

  1. 50%
  2. 33%
  3. 25% (correct answer)
  4. 20%
Explanation: Fractional occupancy by an agonist in the presence of a competitive antagonist can be calculated using the formula: Occupancy = ([A]/Kd) / (1 + [A]/Kd + [B]/Ki). Given [A] = 5 nM, Kd = 5 nM, [B] = 10 nM, and Ki = 5 nM. First, calculate the concentration/constant ratios: [A]/Kd = 5/5 = 1. [B]/Ki = 10/5 = 2. Now, substitute these values into the formula: Occupancy = 1 / (1 + 1 + 2) = 1 / 4. Therefore, the fractional occupancy by the agonist is 0.25, or 25%.

Question 3

A patient with opioid use disorder is maintained on a stable, high dose of methadone (a full mu-opioid agonist). The patient is then administered buprenorphine, a drug with high affinity for the mu-opioid receptor but lower intrinsic activity than methadone. Which of the following outcomes is most likely?

  1. A synergistic increase in opioid effect, leading to severe respiratory depression.
  2. No significant change in the patient's state, as both drugs are opioids acting on the same receptor.
  3. Precipitation of an opioid withdrawal syndrome and a reduction in the level of analgesia. (correct answer)
  4. A complete and rapid reversal of all opioid effects, similar to that caused by naloxone.
Explanation: Buprenorphine is a partial agonist at the mu-opioid receptor. In a patient physically dependent on a full agonist like methadone, buprenorphine's high affinity allows it to displace methadone from the receptors. Because buprenorphine has lower intrinsic activity, this displacement leads to a net decrease in receptor stimulation, which can precipitate a withdrawal syndrome and reduce the analgesic effect.

Question 4

A study investigates the effect of an irreversible antagonist, Drug Z, on the response to a full agonist in a smooth muscle preparation. At a low concentration of Drug Z, the agonist's dose-response curve shifts to the right without a change in the maximal response (Emax). However, at a higher concentration of Drug Z, the Emax is significantly reduced. Which of the following best explains this observation?

  1. Drug Z exhibits mixed antagonism, acting competitively at low concentrations and non-competitively at high concentrations.
  2. The agonist has a low intrinsic activity, requiring high receptor occupancy for a maximal response.
  3. The receptor system possesses spare receptors, allowing a maximal response even when a fraction of receptors is inactivated. (correct answer)
  4. The tissue is developing tachyphylaxis to the agonist in the presence of the higher concentration of Drug Z.
Explanation: This phenomenon is the classic demonstration of spare receptors (or a receptor reserve). A maximal response can be achieved without occupying all available receptors. When a low concentration of an irreversible antagonist inactivates a fraction of the receptors, there are still enough 'spare' receptors left to elicit a maximal response, although a higher concentration of agonist is required (rightward shift). Once the antagonist concentration is high enough to inactivate receptors beyond the spare capacity, the maximal achievable response (Emax) decreases.

Question 5

A patient has a genetic disorder caused by a constitutively active G-protein coupled receptor, which leads to excessive hormone production independent of the endogenous ligand. Which type of therapeutic agent would be most effective at specifically reducing the receptor's basal signaling?

  1. A neutral antagonist to block the ligand binding site.
  2. A partial agonist to compete with any residual endogenous ligand.
  3. An inverse agonist that preferentially binds to the inactive receptor state. (correct answer)
  4. An irreversible antagonist to permanently inactivate the entire receptor pool.
Explanation: The core problem is the receptor's constitutive (ligand-independent) activity. A neutral antagonist (A) would only block a ligand and would not affect this basal activity. A partial agonist (B) would still provide some stimulation. An inverse agonist (C) is uniquely suited for this situation because it binds to the inactive receptor conformation and reduces basal signaling. An irreversible antagonist (D) would inactivate receptors it binds to, but it would not affect the signaling from receptors that are already in the active state.

Question 6

In a Schild analysis to characterize a new antagonist, a pharmacologist generates dose-response curves for an agonist in the presence of several fixed concentrations of the antagonist. A plot of log(dose ratio - 1) versus log[Antagonist] yields a straight line with a slope of approximately 1. The x-intercept of this line provides what important pharmacological parameter?

  1. The Emax of the agonist.
  2. The intrinsic activity of the antagonist.
  3. The number of spare receptors in the tissue.
  4. The pA2 value, which reflects the antagonist's affinity. (correct answer)
Explanation: Schild analysis is a fundamental tool in pharmacology for characterizing competitive antagonists. When you encounter questions about Schild plots, focus on what the key components tell you about antagonist behavior and binding affinity. In Schild analysis, you measure how much more agonist is needed to produce the same response when an antagonist is present. The "dose ratio" represents this shift - if you need 10 times more agonist, the dose ratio is 10. The Schild plot graphs log⁡(dose ratio−1)\log(\text{dose ratio} - 1) versus log⁡[Antagonist]\log[\text{Antagonist}]. For a competitive antagonist, this yields a straight line with slope = 1. The x-intercept of this line occurs when log⁡(dose ratio−1)=0\log(\text{dose ratio} - 1) = 0, meaning the dose ratio equals 2. At this point, you need exactly twice as much agonist to overcome the antagonist. This x-intercept value is the pA₂ - the negative logarithm of the antagonist concentration that doubles the agonist dose needed. The pA₂ directly reflects the antagonist's binding affinity: higher pA₂ means higher affinity. This makes D correct. Choice A is wrong because Emax (maximum response) comes from dose-response curves, not Schild analysis. Choice B is incorrect because competitive antagonists have zero intrinsic activity by definition - they block receptors without activating them. Choice C is wrong because spare receptors affect response sensitivity but aren't determined by Schild analysis. Remember: pA₂ = antagonist affinity. When you see Schild analysis questions, the x-intercept always relates to how tightly the antagonist binds to its target receptor.

Question 7

A clinical trial for a new hypnotic drug reports a therapeutic index (TI) calculated from population data as TD50/ED50. The ED50 is the dose at which 50% of patients experience sleep, and the TD50 is the dose at which 50% of patients experience a specific adverse effect. If a reversible competitive antagonist for the hypnotic's receptor is co-administered, how would this most likely affect the quantal dose-response curves and the TI?

  1. Both the ED50 and TD50 values will increase, resulting in an unpredictable change to the TI. (correct answer)
  2. The maximal effect for both therapeutic and toxic responses will be reduced, decreasing the TI.
  3. Both the ED50 and TD50 values will decrease, resulting in an unpredictable change to the TI.
  4. Only the ED50 value will increase, leading to a definite decrease in the TI.
Explanation: A reversible competitive antagonist requires a higher dose of the agonist to achieve a given effect. In quantal (population) dose-response curves, this causes a rightward shift, increasing both the ED50 and TD50. Since the TI is the ratio of these two values (TD50/ED50), and both values are increasing, the net effect on the ratio is not predictable without knowing the exact magnitude of the shift for each curve. They often shift in a parallel fashion, which would leave the TI relatively unchanged, but this is not guaranteed.

Question 8

A cell line expresses beta-adrenergic receptors. When stimulated with the full agonist isoproterenol, cAMP production reaches a maximum of 100 units. A second drug, pindolol, is a partial agonist that produces a maximal response of 40 units when administered alone. If the cells are treated with a saturating concentration of isoproterenol, and then a high concentration of pindolol is added, what will be the expected final level of cAMP production?

  1. The response will remain at 100 units as the full agonist is already at a saturating concentration.
  2. The response will increase to 140 units due to the additive effects of both drugs.
  3. The response will decrease to approximately 40 units as pindolol displaces isoproterenol. (correct answer)
  4. The response will decrease to 0 units as pindolol will antagonize the constitutive activity.
Explanation: A partial agonist competes with a full agonist for the same receptor binding site. When a high concentration of a partial agonist (pindolol) is added in the presence of a full agonist (isoproterenol), the partial agonist will displace the full agonist from the receptors. The resulting response of the system will be determined by the intrinsic activity of the partial agonist, which is 40 units. Therefore, the response will decrease from 100 units to 40 units.

Question 9

Drug M is a novel compound that reduces the therapeutic effect of an endogenous agonist. Binding studies reveal that Drug M binds to a site on the receptor distinct from the agonist's binding site. Further analysis shows that Drug M does not alter the agonist's binding affinity (Kd) but reduces the maximal response (Emax) that the agonist can achieve. Drug M is best classified as a:

  1. Competitive antagonist.
  2. Negative allosteric modulator affecting efficacy. (correct answer)
  3. Negative allosteric modulator affecting affinity.
  4. Irreversible orthosteric antagonist.
Explanation: The key features described are: (1) binding to a different (allosteric) site, (2) not changing agonist affinity (Kd), and (3) reducing the maximal response (Emax). This profile precisely defines a negative allosteric modulator that acts by reducing the efficacy of the agonist (the ability of the agonist-bound receptor to signal), rather than by altering its binding affinity.

Question 10

A cell line expresses beta-adrenergic receptors. When stimulated with the full agonist isoproterenol, cAMP production reaches a maximum of 100 units. A second drug, pindolol, is a partial agonist that produces a maximal response of 40 units when administered alone. If the cells are treated with a saturating concentration of isoproterenol, and then a high concentration of pindolol is added, what will be the expected final level of cAMP production?

  1. The response will remain at 100 units as the full agonist is already at a saturating concentration.
  2. The response will increase to 140 units due to the additive effects of both drugs.
  3. The response will decrease to approximately 40 units as pindolol displaces isoproterenol. (correct answer)
  4. The response will decrease to 0 units as pindolol will antagonize the constitutive activity.
Explanation: A partial agonist competes with a full agonist for the same receptor binding site. When a high concentration of a partial agonist (pindolol) is added in the presence of a full agonist (isoproterenol), the partial agonist will displace the full agonist from the receptors. The resulting response of the system will be determined by the intrinsic activity of the partial agonist, which is 40 units. Therefore, the response will decrease from 100 units to 40 units.

Question 11

A patient has a genetic disorder caused by a constitutively active G-protein coupled receptor, which leads to excessive hormone production independent of the endogenous ligand. Which type of therapeutic agent would be most effective at specifically reducing the receptor's basal signaling?

  1. A neutral antagonist to block the ligand binding site.
  2. A partial agonist to compete with any residual endogenous ligand.
  3. An inverse agonist that preferentially binds to the inactive receptor state. (correct answer)
  4. An irreversible antagonist to permanently inactivate the entire receptor pool.
Explanation: The core problem is the receptor's constitutive (ligand-independent) activity. A neutral antagonist (A) would only block a ligand and would not affect this basal activity. A partial agonist (B) would still provide some stimulation. An inverse agonist (C) is uniquely suited for this situation because it binds to the inactive receptor conformation and reduces basal signaling. An irreversible antagonist (D) would inactivate receptors it binds to, but it would not affect the signaling from receptors that are already in the active state.

Question 12

A new analgesic is selected for development because it provides effective pain relief but has a significantly lower maximal effect on respiratory depression compared to morphine, even at very high doses. This 'ceiling effect' on the major adverse outcome reduces the risk of fatal overdose. This compound is most likely acting as a:

  1. Non-competitive antagonist at the mu-opioid receptor.
  2. Full agonist with very low potency at the mu-opioid receptor.
  3. Competitive antagonist with a short half-life.
  4. Partial agonist at the mu-opioid receptor. (correct answer)
Explanation: When you encounter questions about drugs with "ceiling effects" on adverse outcomes while maintaining therapeutic benefits, you're dealing with receptor pharmacology concepts, specifically the difference between full and partial agonists. This analgesic demonstrates the classic profile of a partial agonist at the mu-opioid receptor. Partial agonists have intrinsic activity that's less than 100%, meaning they can only activate receptors to a submaximal level regardless of dose or concentration. This creates a "ceiling effect" where increasing the dose beyond a certain point produces no additional pharmacological response. For respiratory depression - the most dangerous opioid side effect - this ceiling provides a crucial safety margin, as the drug physically cannot depress breathing beyond a certain threshold even in overdose situations. Option A is incorrect because non-competitive antagonists block receptors and wouldn't provide analgesic effects. Option B misses the mark - a full agonist with low potency would still cause maximal respiratory depression at high enough doses, just requiring more drug to get there. The ceiling effect described can't be explained by potency alone. Option C describes a competitive antagonist, which would block rather than activate opioid receptors, eliminating analgesic properties entirely. Remember this pattern: when you see "ceiling effect" combined with maintained therapeutic benefit but reduced adverse effects, think partial agonist. This mechanism explains drugs like buprenorphine, which provides effective pain relief and opioid substitution therapy while having inherent overdose protection due to its partial agonist properties at mu-opioid receptors.

Question 13

A newly discovered G-protein coupled receptor (GPCR) is found to have a gain-of-function mutation, causing a high level of constitutive activity and downstream signaling even in the absence of its endogenous ligand. To develop a therapeutic agent for a disease caused by this hyperactivity, researchers are looking for a compound that will reduce this signaling by directly targeting the receptor. Which of the following describes the most appropriate pharmacological agent?

  1. A competitive antagonist that binds to the orthosteric site with high affinity.
  2. An inverse agonist that stabilizes the inactive conformation of the receptor. (correct answer)
  3. A partial agonist with very low intrinsic activity and high potency.
  4. A negative allosteric modulator that only binds when the endogenous ligand is present.
Explanation: The disease is caused by constitutive (ligand-independent) receptor activity. An inverse agonist is the only class of drug that can reduce this basal signaling by binding to and stabilizing the inactive receptor conformation (R), thereby shifting the equilibrium away from the constitutively active state (R*). A competitive antagonist would block an endogenous ligand but have no effect on constitutive activity. A partial agonist would still be an agonist. An allosteric modulator dependent on ligand binding would be ineffective.

Question 14

A patient with opioid use disorder is maintained on a stable, high dose of methadone (a full mu-opioid agonist). The patient is then administered buprenorphine, a drug with high affinity for the mu-opioid receptor but lower intrinsic activity than methadone. Which of the following outcomes is most likely?

  1. A synergistic increase in opioid effect, leading to severe respiratory depression.
  2. No significant change in the patient's state, as both drugs are opioids acting on the same receptor.
  3. Precipitation of an opioid withdrawal syndrome and a reduction in the level of analgesia. (correct answer)
  4. A complete and rapid reversal of all opioid effects, similar to that caused by naloxone.
Explanation: Buprenorphine is a partial agonist at the mu-opioid receptor. In a patient physically dependent on a full agonist like methadone, buprenorphine's high affinity allows it to displace methadone from the receptors. Because buprenorphine has lower intrinsic activity, this displacement leads to a net decrease in receptor stimulation, which can precipitate a withdrawal syndrome and reduce the analgesic effect.

Question 15

Drug M is a novel compound that reduces the therapeutic effect of an endogenous agonist. Binding studies reveal that Drug M binds to a site on the receptor distinct from the agonist's binding site. Further analysis shows that Drug M does not alter the agonist's binding affinity (Kd) but reduces the maximal response (Emax) that the agonist can achieve. Drug M is best classified as a:

  1. Competitive antagonist.
  2. Negative allosteric modulator affecting efficacy. (correct answer)
  3. Negative allosteric modulator affecting affinity.
  4. Irreversible orthosteric antagonist.
Explanation: The key features described are: (1) binding to a different (allosteric) site, (2) not changing agonist affinity (Kd), and (3) reducing the maximal response (Emax). This profile precisely defines a negative allosteric modulator that acts by reducing the efficacy of the agonist (the ability of the agonist-bound receptor to signal), rather than by altering its binding affinity.

Question 16

A full agonist's effect is measured in an in vitro system. The experiment is then repeated in the presence of both a reversible competitive antagonist (Drug X) and a non-competitive antagonist (Drug Y). What change to the agonist's dose-response curve is expected compared to the curve of the agonist alone?

  1. The curve will shift to the right, and the maximal effect will be reduced. (correct answer)
  2. The curve will shift to the left, and the maximal effect will be increased.
  3. The maximal effect will be reduced, with no change in the agonist's apparent EC50.
  4. The curve will shift to the right, with no change in the maximal effect.
Explanation: This scenario involves the combined effects of two different types of antagonists. The reversible competitive antagonist (Drug X) competes with the agonist for the binding site, which increases the apparent EC50 and shifts the dose-response curve to the right. The non-competitive antagonist (Drug Y) reduces the total number of functional receptors, which decreases the maximal possible response (Emax). The combination of these two effects results in a curve that is both shifted to the right and has a depressed maximum.

Question 17

A patient who has received an overdose of the anticoagulant heparin is administered protamine sulfate. Protamine, a highly positively charged protein, binds directly to the highly negatively charged heparin molecule, forming a stable, inactive complex. This interaction, which neutralizes heparin's effect, is best described as:

  1. Pharmacological antagonism
  2. Physiological antagonism
  3. Non-competitive antagonism
  4. Chemical antagonism (correct answer)
Explanation: When you encounter questions about drug interactions and antagonism, focus on the mechanism by which one substance counteracts another. The key is identifying whether the interaction occurs at receptors, through opposing physiological pathways, or through direct molecular binding. In this scenario, protamine sulfate works through chemical antagonism (D). The mechanism is straightforward: protamine's positive charges directly bind to heparin's negative charges, forming an inactive complex that removes heparin from circulation. This is a direct chemical neutralization reaction, not an interaction involving receptors or competing pathways. Let's examine why the other options don't fit. Pharmacological antagonism (A) occurs when two drugs compete for the same receptor binding site, like naloxone blocking opioid receptors. Here, protamine doesn't compete with heparin for any receptor. Physiological antagonism (B) happens when two drugs produce opposite effects through different pathways, such as epinephrine countering histamine's effects during anaphylaxis. Protamine doesn't produce an opposite effect; it eliminates heparin entirely. Non-competitive antagonism (C) involves a drug binding to an allosteric site and changing receptor conformation, preventing the agonist from working effectively. Again, no receptors are involved in the protamine-heparin interaction. Remember this pattern: when you see direct molecular binding that neutralizes a drug's activity (especially involving opposite charges or chemical reactions), think chemical antagonism. Look for keywords like "binds directly," "forms complex," or "neutralizes" to identify this mechanism.

Question 18

In a Schild analysis to characterize a new antagonist, a pharmacologist generates dose-response curves for an agonist in the presence of several fixed concentrations of the antagonist. A plot of log(dose ratio - 1) versus log[Antagonist] yields a straight line with a slope of approximately 1. The x-intercept of this line provides what important pharmacological parameter?

  1. The Emax of the agonist.
  2. The intrinsic activity of the antagonist.
  3. The number of spare receptors in the tissue.
  4. The pA2 value, which reflects the antagonist's affinity. (correct answer)
Explanation: Schild analysis is a fundamental tool in pharmacology for characterizing competitive antagonists. When you encounter questions about Schild plots, focus on what the key components tell you about antagonist behavior and binding affinity. In Schild analysis, you measure how much more agonist is needed to produce the same response when an antagonist is present. The "dose ratio" represents this shift - if you need 10 times more agonist, the dose ratio is 10. The Schild plot graphs log⁡(dose ratio−1)\log(\text{dose ratio} - 1) versus log⁡[Antagonist]\log[\text{Antagonist}]. For a competitive antagonist, this yields a straight line with slope = 1. The x-intercept of this line occurs when log⁡(dose ratio−1)=0\log(\text{dose ratio} - 1) = 0, meaning the dose ratio equals 2. At this point, you need exactly twice as much agonist to overcome the antagonist. This x-intercept value is the pA₂ - the negative logarithm of the antagonist concentration that doubles the agonist dose needed. The pA₂ directly reflects the antagonist's binding affinity: higher pA₂ means higher affinity. This makes D correct. Choice A is wrong because Emax (maximum response) comes from dose-response curves, not Schild analysis. Choice B is incorrect because competitive antagonists have zero intrinsic activity by definition - they block receptors without activating them. Choice C is wrong because spare receptors affect response sensitivity but aren't determined by Schild analysis. Remember: pA₂ = antagonist affinity. When you see Schild analysis questions, the x-intercept always relates to how tightly the antagonist binds to its target receptor.

Question 19

A new analgesic is selected for development because it provides effective pain relief but has a significantly lower maximal effect on respiratory depression compared to morphine, even at very high doses. This 'ceiling effect' on the major adverse outcome reduces the risk of fatal overdose. This compound is most likely acting as a:

  1. Non-competitive antagonist at the mu-opioid receptor.
  2. Full agonist with very low potency at the mu-opioid receptor.
  3. Competitive antagonist with a short half-life.
  4. Partial agonist at the mu-opioid receptor. (correct answer)
Explanation: When you encounter questions about drugs with "ceiling effects" on adverse outcomes while maintaining therapeutic benefits, you're dealing with receptor pharmacology concepts, specifically the difference between full and partial agonists. This analgesic demonstrates the classic profile of a partial agonist at the mu-opioid receptor. Partial agonists have intrinsic activity that's less than 100%, meaning they can only activate receptors to a submaximal level regardless of dose or concentration. This creates a "ceiling effect" where increasing the dose beyond a certain point produces no additional pharmacological response. For respiratory depression - the most dangerous opioid side effect - this ceiling provides a crucial safety margin, as the drug physically cannot depress breathing beyond a certain threshold even in overdose situations. Option A is incorrect because non-competitive antagonists block receptors and wouldn't provide analgesic effects. Option B misses the mark - a full agonist with low potency would still cause maximal respiratory depression at high enough doses, just requiring more drug to get there. The ceiling effect described can't be explained by potency alone. Option C describes a competitive antagonist, which would block rather than activate opioid receptors, eliminating analgesic properties entirely. Remember this pattern: when you see "ceiling effect" combined with maintained therapeutic benefit but reduced adverse effects, think partial agonist. This mechanism explains drugs like buprenorphine, which provides effective pain relief and opioid substitution therapy while having inherent overdose protection due to its partial agonist properties at mu-opioid receptors.

Question 20

A specific receptor has a dissociation constant (Kd) of 5 nM for its agonist (Drug A) and an inhibition constant (Ki) of 5 nM for a competitive antagonist (Drug B). If this receptor is incubated in a solution containing 5 nM of Drug A and 10 nM of Drug B, what is the approximate fractional occupancy of the receptor by the agonist?

  1. 50%
  2. 33%
  3. 25% (correct answer)
  4. 20%
Explanation: Fractional occupancy by an agonist in the presence of a competitive antagonist can be calculated using the formula: Occupancy = ([A]/Kd) / (1 + [A]/Kd + [B]/Ki). Given [A] = 5 nM, Kd = 5 nM, [B] = 10 nM, and Ki = 5 nM. First, calculate the concentration/constant ratios: [A]/Kd = 5/5 = 1. [B]/Ki = 10/5 = 2. Now, substitute these values into the formula: Occupancy = 1 / (1 + 1 + 2) = 1 / 4. Therefore, the fractional occupancy by the agonist is 0.25, or 25%.