1. Introduction to Pharmacodynamics Novartis-Academia Hackathon
Pharmacometrics
Introduction to Pharmacodynamics Novartis-Academia Hackathon
Andrew Stein, PhD
Associate Director Pharmacometrics
Cambridge, MA August 2019

2. Overview
Target Audience: people with a quantitative background that are new to pharmacometrics.
Simple differential equations will be used
Topics covered
Key mathematical results for pharmacodynamic models
Introduction and motivation for the Emax model
Introduction to immediate and delayed effect PKPD models

3. Acknowledgements (Based on material from)
Rowland, M., Tozer, T. N. Clinical pharmacokinetics and pharmacodynamics: concepts and applications 
Peter Bonate, Astellas
Richard Brundage, U Minnesota
Leon Aarons, U Manchester
Jean-Louis Steimer, Novartis
Martin Fink, Novartis
Nick Holford, U Auckland metrics/advanced.php

4. What the drug does to the body
Pharmacodynamics
What the drug does to the body

5. The “PKPD” pathway of drug effect
Absorbed by intestines into blood
Distribute from blood into tissue
Binds target in tissue
Effects
Oral Dose
Drug Concentration
Measurement
Elimination
from body
Pharmacokinetics (PK):
How body affects drug
Pharmacodynamics (PD):
How drug affects body
What does is needed to shrink a tumor without causing severe neutropenia
Should children and adults receive the same dose?

6. Main targets for drugs Receptors Enzymes Soluble agents
Signal Transduction
Ion Channels
Enzymes
Soluble agents
Cytokines

7. Cell
wikipedia

8. Receptor – Signal Transduction
Binding
Conformation
Change
Signaling
Ligand
Receptor

9. Drug can block binding and inhibit signaling (antagonist)
Conformation
Change
Signaling
Ligand
Drug 2
Drug 1
Receptor

10. Drug can enhance signaling (agonist)
Binding
Conformation
Change
Signaling
Drug
Receptor

11. Receptor - Ion channel
Cell membrane receptors allow the outside of the cell to communicate with the inside of the cell
From Peter Bonate

12. Drug can keep an ion channel open or closed
From Peter Bonate

13. Enzyme kinetics
Substrate
Products
Enzyme
Complex
Enzyme

14. Drug interference with enzyme
Substrate
Products
Enzyme
Complex
Enzyme

15. Classical Binding Theory
koff
kon
Drug
(C)
Complex
(CR) +
Target
(R)
𝑑(𝐶𝑅) 𝑑𝑡 = 𝑘 𝑜𝑛 𝐶·𝑅− 𝑘 𝑜𝑓𝑓 (𝐶𝑅)

16. The dissociation constant gives the equilibrium drug concentration
kon
koff
Drug
(C)
Complex
(CR) +
Target
(R)
0= 𝑑(𝐶𝑅) 𝑑𝑡 = 𝑘 𝑜𝑛 𝐶·𝑅− 𝑘 𝑜𝑓𝑓 𝐶𝑅
𝑘 𝑜𝑛 𝐶·𝑅= 𝑘 𝑜𝑓𝑓 𝐶𝑅
𝐶·𝑅 (𝐶𝑅) = 𝑘 𝑜𝑓𝑓 𝑘 𝑜𝑛 = 𝐾 𝑑
dissociation constant
The dissociation constant tells you how tightly the drug binds

17. We want a formula for what fraction of the target is free.
kon
koff
Drug
(C)
Complex
(CR) +
Target
(R)
Total drug: 𝐶 𝑡𝑜𝑡 =𝐶+ 𝐶𝑅
Total target: 𝑅 𝑡𝑜𝑡 =𝑅+ 𝐶𝑅
Dissociation Constant: 𝐶 𝑅 = K d 𝐶𝑅
Given a starting drug concentration,
what is percent of free target: R/Rtot?

18. Solving for free target
Total drug: 𝐶 𝑡𝑜𝑡 =𝐶+ 𝐶𝑅
Total target: 𝑅 𝑡𝑜𝑡 =𝑅+ 𝐶𝑅
Dissociation Constant: 𝐶 𝑅 = 𝐾 𝑑 𝐶𝑅
𝐶 𝑅 = 𝐾 𝑑 𝑅 𝑡𝑜𝑡 −𝑅
𝐶 𝑅 = 𝐾 𝑑 𝑅 𝑡𝑜𝑡 − 𝐾 𝑑 𝑅
𝐶+ 𝐾 𝑑 𝑅 = 𝐾 𝑑 𝑅 𝑡𝑜𝑡
𝑅 𝑅 𝑡𝑜𝑡 = 𝐾 𝑑 𝐶+ 𝐾 𝑑

19. Solving for target occupancy
𝑅 𝑅 𝑡𝑜𝑡 ≈ 𝐾 𝑑 𝐶+ 𝐾 𝑑
Total target: 𝑅 𝑡𝑜𝑡 =𝑅+ 𝐶𝑅
𝑅 𝑡𝑜𝑡 𝑅 𝑡𝑜𝑡 = 𝑅 𝑅 𝑡𝑜𝑡 + 𝐶𝑅 𝑅 𝑡𝑜𝑡 =1
𝐶𝑅 𝑅 𝑡𝑜𝑡 =1− 𝑅 𝑅 𝑡𝑜𝑡
𝐶𝑅 𝑅 𝑡𝑜𝑡 =1 − 𝐾 𝑑 𝐶+ 𝐾 𝑑
𝐶𝑅 𝑅 𝑡𝑜𝑡 = 𝐶 𝐶+ 𝐾 𝑑
If target is a receptor, this is called receptor occupancy (RO)
𝑅𝑂= 𝐶𝑅 𝑅 𝑡𝑜𝑡 ≈ 𝐶 𝑡𝑜𝑡 𝐶 𝑡𝑜𝑡 + 𝐾 𝑑
When Rtot >> Kd

20. Receptor occupancy data
𝑅𝑂= 𝐶 𝑡𝑜𝑡 𝐶 𝑡𝑜𝑡 + 𝐾 𝑑 50
Kd = 15 ng/ml (≈ 40 nM)
where 50% is bound 15
Atack, John R., et al. "In vitro and in vivo properties of 3-tert-butyl-7-(5-methylisoxazol-3-yl)-2-(1-methyl-1H-1, 2, 4-triazol-5-ylmethoxy)-pyrazolo [1, 5-d]-[1, 2, 4] triazine (MRK-016), a GABAA receptor α5 subtype-selective inverse agonist." Journal of Pharmacology and Experimental Therapeutics (2009):

21. Receptor occupancy in linear and log space
Linear Space
Log Space
𝑅𝑂= 𝐶 𝑡𝑜𝑡 𝐶 𝑡𝑜𝑡 + 𝐾 𝑑
Kd = 15 ng/ml

22. Receptor occupancy type curves describes a lot of data
Propafol effect on heart rate
Rowland and Tozer, Fig 3-6
Keytruda effect on IL-2 stimulation
Elassaiss‐Schaap, J., et al. "Using model‐based “learn and confirm” to reveal the pharmacokinetics‐pharmacodynamics relationship of pembrolizumab in the KEYNOTE‐001 Trial." CPT: pharmacometrics & systems pharmacology 6.1 (2017):
Atkinson, Hartley C., Amanda L. Potts, and Brian J. Anderson. "Potential cardiovascular adverse events when phenylephrine is combined with paracetamol: simulation and narrative review." European journal of clinical pharmacology 71.8 (2015):
Phenylepherine effect on blood pressure

23. Emax model – positive effect
Maximal effect
EC50
Concentration that produces 50% of the maximal effect

24. Imax model – negative effect (I = inhibition)
Maximal
Inhibitory
effect
IC50
Concentration that produces 50% of the maximal inhibitory effect 24

25. Adding in a steepness factor
Effect= 𝐶 𝛾 𝐶 𝛾 + 𝐸𝐶 50 𝛾
- Linear Space
- Log Space
The classical Emax model is for gamma equals to 1
Please note that the x-axis on the LEFT plot is a linear scale  therefore “sigmoidicity” (e.g. between 2 and 5 for the Ketamine data))
Rowland and Tozer

26. Pharmacokinetics and Pharmacodynamics Putting it all together

27. The “PKPD” pathway of drug effect
Absorbed by intestines into blood
Distribute from blood into tissue
Binds target in tissue
Effects
Oral Dose
Drug Concentration
Measurement
Elimination
from body
Pharmacokinetics (PK):
How body affects drug
Pharmacodynamics (PD):
How drug affects body

28. Overview – Drug effect/response
Immediate
Delayed
Distributional
Cumulative
Tumor shrinkage
Bone remodeling
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29. C Immediate Effect Eff= 𝐸 𝑚𝑎𝑥 ·𝐶 𝐸 𝐶 50 +𝐶 Dose k10 Terminal
Half-Life = 6 h 6h
Doubling dose prolongs effect by 1 half-life

30. Delayed Effect (distributional)
Measuring drug concentration in tissue is difficult
But it takes time for drug to distribute to tissue
keff C
Ceff
Eff= 𝐸 𝑚𝑎𝑥 · 𝐶 eff 𝐸 𝐶 50 + 𝐶 eff
Dose
k10
𝑑𝐶 𝑑𝑡 =− 𝑘 10 ·𝐶
Effect compartment is “empirical”
We don’t track the mass of drug moving from central to effect compartment
𝑑 𝐶 eff 𝑑𝑡 =− 𝑘 eff ·( 𝐶 eff −𝐶)
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31. Thiopentone Time Course (anaesthesia drug)
Change in EEG frequency
From Nick Holford

32. Cumulative Effect (Indirect Response)
Drug impacts the “rate of change” of the effect
Synthesis or degradation of a protein
Growing/shrinking tumor
Could be a stimulatory or inhibitory effect
k in = 𝑘 in0 ± 𝐸 𝑚𝑎𝑥 ·𝐶 𝐸 𝐶 50 +𝐶 C E
Dose
k10
k out
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33. Cumulative Effect (Indirect Response)
Drug impacts the “rate of change” of the effect
Synthesis or degradation of a protein
Growing/shrinking tumor
Could be a stimulatory or inhibitory effect on either the input or the output rate
k in C E
Dose
k out = 𝑘 out0 1± 𝐸 𝑚𝑎𝑥 ·𝐶 𝐸 𝐶 50 +𝐶
k10
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34. Cumulative Effect Equations (Indirect Response)
k in = 𝑘 in 𝐸 𝑚𝑎𝑥 ·𝐶 𝐸 𝐶 50 +𝐶 C E
Dose
k10
k out
𝑑𝐶 𝑑𝑡 =− 𝑘 10 ·𝐶
𝑑𝐸 𝑑𝑡 = 𝑘 in 𝐸 𝑚𝑎𝑥 ·𝐶 𝐸 𝐶 50 +𝐶 −𝑘 out 𝐸
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35. Effect steady states for indircet response equation
𝑑𝐸 𝑑𝑡 = 𝑘 in 𝐸 𝑚𝑎𝑥 ·𝐶 𝐸 𝐶 50 +𝐶 −𝑘 out 𝐸
When C=0
At large concentrations,
𝑑𝐸 𝑑𝑡 = 𝑘 in0 −𝑘 out 𝐸=0
𝑑𝐸 𝑑𝑡 = 𝑘 in0 1+ 𝐸 𝑚𝑎𝑥 −𝑘 out 𝐸=0
𝐸 0 = 𝑘 in0 𝑘 out
𝐸 𝑠𝑠,𝑚𝑎𝑥 = 𝑘 in0 (1+ 𝐸 𝑚𝑎𝑥 ) 𝑘 out

36. Solution for very large concentration
𝑑𝐸 𝑑𝑡 ≈ 𝑘 in0 1+ 𝐸 𝑚𝑎𝑥 −𝑘 out 𝐸
𝐸 0 = 𝑘 in0 𝑘 out
𝐸 𝑠𝑠,𝑚𝑎𝑥 = 𝑘 in0 1+ 𝐸 𝑚𝑎𝑥 𝑘 out
𝐸 𝑡 = 𝐸 𝑠𝑠,𝑚𝑎𝑥 + 𝐸 0 − 𝐸 𝑠𝑠,𝑚𝑎𝑥 𝑒 − 𝑘 𝑜𝑢𝑡 𝑡

37. C E Cumulative Effect k in = 𝑘 in0 1+ 𝐸 𝑚𝑎𝑥 ·𝐶 𝐸 𝐶 50 +𝐶 Dose k10
k out
Terminal
Half-Life = 6 h
∞ mg 6h
Doubling dose prolongs effect by 1 half-life

38. C E Cumulative Effect k in = 𝑘 in0 1+ 𝐸 𝑚𝑎𝑥 ·𝐶 𝐸 𝐶 50 +𝐶 Dose k10
k out
𝑘 𝑖𝑛0 =100%/h
𝑘 𝑜𝑢𝑡 =1/h
𝐸 𝑚𝑎𝑥 =4
𝐸 𝐶 50 =0.1 mg/L
𝐸 0 = 𝑘 in0 𝑘 out = 100%/h 1/h =100%
𝑘 𝑖𝑛,𝑚𝑎𝑥 = 𝑘 in0 1+ 𝐸 𝑚𝑎𝑥
=100%/ℎ 1+4 =500%
𝐸 𝑠𝑠,𝑚𝑎𝑥 = 𝑘 in,𝑚𝑎𝑥 𝑘 out = 500%/ℎ 1/ℎ =500%

39. Overview – Drug effect/response
Dose
k10
Eff= 𝐸 𝑚𝑎𝑥 ·𝐶 𝐸 𝐶 50 +𝐶
Immediate
Delayed
Distributional
Cumulative
Tumor shrinkage
Bone remodeling C
Dose
Ceff
keff
Eff= 𝐸 𝑚𝑎𝑥 · 𝐶 eff 𝐸 𝐶 50 + 𝐶 eff
k10 C
Dose
k10 E
kout
k in = 𝑘 in0 ± 𝐸 𝑚𝑎𝑥 ·𝐶 𝐸 𝐶 50 +𝐶
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40. More complex models may be needed in some scenarios
PD response changes with time. Examples include:
Tolerance, where first dose has larger effect than subsequent doses.
Cases where PD affects the PK
When a drug shrinks a tumor, but the tumor is also eliminating the drug.
When a drug that affects kidney function is also cleared by the kidney
When patient health generally affects clearance (e.g. checkpoint inhibitors)
Data is rich enough and biology is well enough understood that more mechanism can be built into model

41. Key Lessons The Emax model is very useful for describing response
Emax = maximum effect
EC50 = concentration of 50% effect
γ = steepness of effect
Model is inspired by physiology, but parameters do not always have direct physiological meaning
Doubling dose of drug in general prolongs duration of effect by one half-life

42. Where to learn more Pharmacology and Pharmacokinetics
Rowland and Tozer, Clinical Pharmacokinetics and Pharmacodynamics (book)
Pharmacometrics (Modeling)
Gabrielsson and Weiner, Pharmacokinetic and Pharmacodynamic Data Analysis (book)
Bonate, Pharmacokinetic-Pharmacodynamic Modeling and Simulation (book)

43. Bonus Topics

44. Counterclockwise hysteresis
Reasons:
Biophase
Pro-drug
Indirect effect
Examples:
Anesthetics
Codeine
Cancer chemotherapy
Source: S Kern lecture
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45. Clockwise hysteresis Reasons: Tolerance Learning
Antagonistic metabolite
Examples:
Chronic activator/blocker
Antibiotics
Morphine (?)
Source: S Kern lecture
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