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PK-PD Primer Homework

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PK-Pharmacology Primer

Instructions for the PK problems:

Please answer the questions below as best as you can by examining the outcomes of the pharmacokinetic models provided in the Excel file “CLRE-238 SP21 PK-PD Homework.xlxs.” In many cases, you will need to find the requested value of parameters by trial and error, changing some of the values in bold red in the worksheets and looking at the resulting plots. You do not need to perform any calculations. All the answers are very short. Do not be intimidated by the Excel worksheets; this is a lot easier than it appears at first glance.

General comment: Because you are expected to obtain your answers by visually examining the pharmacokinetic plots in the associated Excel file, your quantitative answers will be graded as correct if they were reasonably close to the exact answer. There is no requirement to be precise.

Problem A:

The antibiotic genericomycin (not a real one) is administered by iv bolus to hospitalized patients. The antibiotic has an elimination half-life of 4.0 h in people. Previous experience has shown that to be effective at reducing the bacterial burden its plasma concentration must equal or higher than 5 µg/ml (Ceff).

Question 1: Using the “Intravenous” tab of the Excel file, determine the duration of action of the following iv bolus doses and enter the values in the table below.

Hint: You can eyeball the time values from the chart or read them from the list of Cp vs time for the Plot (blue numbers)

Answer 1:

Dose
(mg)

Duration of Action
(h)

140

4

280

8

560

12

1120

16

Question 2: What is the effect of doubling the dose on the duration of action?
Answer 2: it adds the duration of action by 4 hours

Question 3: What would be the necessary iv bolus dose to establish plasma concentration 5 µg/ml at 24 h? Is this dose realistic? Assume genericomycin costs $10/mg.
Answer 3:

Problem B:

You have created a new company, NovoAntibiot, Inc. with the intention of creating a new antibiotic with much better properties than genericomycin. Your clinical advisors suggest that the new antibiotic should be administered by iv bolus once a day with a dose of at most 560 mg per person (your new therapeutic product profile).

Question 4: What elimination half-life should you design in your new antibiotic to achieve a plasma concentration of at least 5 µg/ml 24 h after a 560 mg iv bolus dose?
Answer 4: 40

Welcome to drug discovery! After working for 2 years and spending $15 M from your Angel and series A investors you were unable to increase the half-life of your new antibiotics. All of them still have halflives around 4 h. But you got lucky, some of your new compounds have higher potency. Drug candidate NABT 813, is much more potent than genericomycin. In vitro experiments and animal models suggest that the minimum effective concentration (Ceff) in humans will be 1 µg/ml.

Question 5: What iv bolus dose of NABT 813 will treat the patients for 24h if its elimination half-life is 4.0 h and its Ceff is 1 µg/ml? Is it realistic? (compare with your Answer 3 above).)
Answer 5: 140mg

Problem C

Unfortunately, your new antibiotic NABT 813 decreased the number and body weight of rat pups in formal GLP repro-tox studies in rats. The compound cannot be used in women who might not know whether they are pregnant at the time they are admitted to the hospital with a systemic infection. This is a crushing blow and your investors abandon you. The new drug discovery program is terminated.

However, your PK consultant suggests that you might be able to formulate genericomycin for subcutaneous administration by creating an insoluble salt and adding some excipients that will retard its absorption, allowing (perhaps) once a day dosing. Your intellectual property attorney states that you might be able to obtain patent protection for the new formulation if you demonstrate substantial advantages over the generic iv formulation. You apply for and get an SBIR grant to demonstrate proof of (PK) concept.

Question 6: In the “Subcutaneous” tab of the Excel file, set the elimination half-life of genericomycin to 4.0 h, its Ceff at 5 µg/ml, and its dose to 280 mg. Examine the effect of changing the absorption half-life of genericomycin from your new formulations by replacing the value of t1/2 (abs) and complete the table below.

Answer 6:

t1/2 abs (h)

Tmax (h)

Cmax (µg/ml)

0.05

0.25

18

1

2.5

13

3

5

8.5

6

7

5.9

10

9

4.2

Hint: You can eyeball the above values from the chart or read them from the list of Cp vs time for the Plots (blue numbers). No need to be very precise.

Question 7: Why does the PK profile for absorption with a very short half-life (0.05 h) look like the iv bolus profile? (This never happens in real life….)
Answer 7: Clearance is more rapid and half-lives are shorter

Question 8: What is the effect of increasing the absorption half-life on Tmax and Cmax?
Answer 8: increasing tmax increases absorption while increasing cmax decreases absorption

Question 9: Is there any value of absorption half-life that will allow you to have plasma concentration higher or equal to Ceff at 24 h when dosing sc 280 mg?
Answer 9: yes

Question 10: What is the duration of action of genericomycin at a dose of 280 mg if it is administered in the formulation with absorption half-life of 10 hours?
Answer 10: 4.3

Problem X (bonus):

Your microbiology consultant tells you that an analogue of genericomycin with longer elimination halflife was developed in the Soviet Union in the 1960’s, but it never reached the West and was forgotten. Its name was bolshoimitsina and had an elimination half-life in humans of 7.8 h, and Ceff also 5 µg/ml. You obtain a sample of bolshoimitsina via a website vendor in Bulgaria and find that it also has a sc absorption half-life of 10.0 h in your preferred formulation.

Question 11: What sc dose of formulated bolshoimitsina will provide a plasma concentration equal to Ceff 5 µg/ml at 24 h?
Answer 11: 9.43mg

Question 12: At the dose of bolshoimitsina you found in Answer 11, when does the drug start having its effect in the patient?
Answer 12: 0.5hrs

PK-Pharmacology Primer

Homework with Answers

Student Name:

Instructions for the Pharmacology problems:

Please extract the requested information from the papers provided. You do not need to read the papers in detail. This is an exercise in identifying the required information quickly while checking its validity. Your answers will be very short, a value (with units!) or a few words.

Problem P:

Look at the provided paper by Busnelli et al., “Selective and Potent Agonists and Antagonists for Investigating the Role of Mouse Oxytocin Receptors”, and answer the following questions:

Question 31: What was the Ki value for compound “LVA” at the mOTR (mouse oxytocin receptor)?
Answer 31:

Question 32: Does LVA have higher or lower affinity than “OT” (oxytocin) for the mOTR?
Answer 32:

Look in Materials and Methods, section on Ligand Binding Assays.
Question 33: How were the Ki values obtained: Schild analysis or from IC50 values?
Answer 33:

Question 34: What compound was the radioligand for measuring binding to the mOTR, and at what concentration was used?
Answer 34:

Question 35: What was the Kd value for the radioligand at the mOTR?
Answer 35:

Look in the main body of the paper.

Question 36: Which figure shows the competition binding experiments for compound “OTA1”?
Answer 36:

Question 37: Looking at said figure, would you say that OTA1 has higher affinity for the mV1aR (mouse vasopressin type 1a receptor) than for the mOTR?
Answer 37:

Problem Q:

Look at the provided paper by Ichinose et al., “Development of a Highly Potent Analogue and a Long-Acting Analogue of Oxytocin for the Treatment of Social Impairment-Like Behaviors”, and answer the following questions:

Question 38: What was the EC50 at the hOTR (human oxytocin receptor) of compound 4?
Answer 38:

Question 39: What was the efficacy of compound 4?
Answer 39:

Question 40: Of the new compounds prepared in this paper (Compounds 1 to 6), which one was more potent at the hOTR? Which one was the most potent at the hV1aR?
Answer 40:

Look in Results and Discussion, section on Agonist-Induced Increase in Intracellular Ca2+ Concentrations.

Question 41: Which second messenger was measured to determine receptor activation?
Answer 41:

Look at Table 2, data on Ki at the hOTR and EC50 at the hOTR

Question 42: Would you suspect that there might be considerable “receptor reserve” for activation of the hOTR by OT? What about carbetocin?
Answer 42:

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