Introduction to Pharmacodynamics��Novartis-Academia Hackathon

Andrew Stein, PhD

Associate Director Pharmacometrics

Cambridge, MA August 2019

Pharmacometrics

Pharmacometrics

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

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Pharmacometrics

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 http://holford.fmhs.auckland.ac.nz/Teaching/pharmacometrics/advanced.php

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Pharmacometrics

Pharmacodynamics

What the drug does to the body

Pharmacometrics

The “PKPD” pathway of drug effect

5

Oral Dose

Elimination

from body

Pharmacokinetics (PK):

How body affects drug

Pharmacodynamics (PD):

How drug affects body

Should children and adults receive the same dose?

What does is needed to shrink a tumor without causing severe neutropenia

Drug Concentration

Measurement

Pharmacometrics

Main targets for drugs

6

Pharmacometrics

Cell

7

wikipedia

Pharmacometrics

Receptor – Signal Transduction

8

Ligand

Receptor

Binding

Conformation

Change

Signaling

Pharmacometrics

Drug can block binding and inhibit signaling (antagonist)

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Receptor

Binding

Conformation

Change

Signaling

Ligand

Drug 1

Drug 2

Pharmacometrics

Drug can enhance signaling�(agonist)

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Receptor

Binding

Conformation

Change

Signaling

Drug

Pharmacometrics

Receptor - Ion channel

Cell membrane receptors allow the outside of the cell to communicate with the inside of the cell

From Peter Bonate

Pharmacometrics

Drug can keep an ion channel open or closed

From Peter Bonate

Pharmacometrics

Enzyme kinetics

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Substrate

Enzyme

Complex

Enzyme

Products

Pharmacometrics

Drug interference with enzyme

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Substrate

Enzyme

Complex

Enzyme

Products

Pharmacometrics

Classical Binding Theory

15

k_off

​

k_on

Pharmacometrics

The dissociation constant gives the equilibrium drug concentration

16

k_on

​

k_off

dissociation constant

The dissociation constant tells you how tightly the drug binds

Pharmacometrics

We want a formula for what fraction of the target is free.

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k_on

​

k_off

Given a starting drug concentration,

what is percent of free target: R/R_tot?

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Pharmacometrics

Solving for free target

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Pharmacometrics

Solving for target occupancy

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When R_tot >> K_d

If target is a receptor, this is called receptor occupancy (RO)

Pharmacometrics

Receptor occupancy data

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15

50

K_d = 15 ng/ml (≈ 40 nM)

where 50% is bound

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 331.2 (2009): 470-484.

Pharmacometrics

Receptor occupancy in linear and log space

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Linear Space

Log Space

Kd = 15 ng/ml

Pharmacometrics

Receptor occupancy type curves describes a lot of data

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Pharmacometrics

Emax model – positive effect

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Pharmacometrics

Imax model – negative effect�(I = inhibition)�

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Pharmacometrics

Adding in a steepness factor

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Rowland and Tozer

- Linear Space

- Log Space

Pharmacometrics

Pharmacokinetics and Pharmacodynamics��Putting it all together

Pharmacometrics

The “PKPD” pathway of drug effect

Oral Dose

Elimination

from body

Pharmacokinetics (PK):

How body affects drug

Pharmacodynamics (PD):

How drug affects body

Drug Concentration

Measurement

Pharmacometrics

Overview – Drug effect/response

• Immediate

​

• Delayed
• Distributional

​

​

• Cumulative
• Tumor shrinkage
• Bone remodeling

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28 | Presentation Title | Presenter Name | Date | Subject | Business Use Only

Pharmacometrics

Immediate Effect

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C

Dose

k₁₀

Terminal

Half-Life = 6 h

Doubling dose prolongs effect by 1 half-life

Pharmacometrics

Delayed Effect (distributional)

• Measuring drug concentration in tissue is difficult
• But it takes time for drug to distribute to tissue

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C

Dose

C_eff

k₁₀

k_eff

Effect compartment is “empirical”

We don’t track the mass of drug moving from central to effect compartment

Pharmacometrics

Thiopentone Time Course�(anaesthesia drug)

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Change in EEG frequency

From Nick Holford

Pharmacometrics

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

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C

Dose

k₁₀

E

Pharmacometrics

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

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C

Dose

k₁₀

E

Pharmacometrics

Cumulative Effect Equations�(Indirect Response)

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C

Dose

k₁₀

E

Pharmacometrics

Effect steady states for indircet response equation

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When C=0

At large concentrations,

Pharmacometrics

Solution for very large concentration

36

Pharmacometrics

Cumulative Effect

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Terminal

Half-Life = 6 h

C

Dose

k₁₀

E

Doubling dose prolongs effect by 1 half-life

Pharmacometrics

Cumulative Effect

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C

Dose

k₁₀

E

Pharmacometrics

Overview – Drug effect/response

• Immediate

​

​

• Delayed
• Distributional

​

• Cumulative
• Tumor shrinkage
• Bone remodeling

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k₁₀

Pharmacometrics

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

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Pharmacometrics

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

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Pharmacometrics

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)

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Pharmacometrics

Bonus Topics

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Pharmacometrics

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Examples:

Anesthetics

Codeine

Cancer chemotherapy

Counterclockwise hysteresis

Source: S Kern lecture

Reasons:

Biophase

Pro-drug

Indirect effect

Pharmacometrics

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Clockwise hysteresis

Source: S Kern lecture

Examples:

Chronic activator/blocker

Antibiotics

Morphine (?)

Reasons:

Tolerance

Learning

Antagonistic metabolite

Pharmacometrics