Nonlinear PK, TMDD, and PBPK

Understand when standard PK breaks down and how TMDD and PBPK provide more mechanistic representations.
Tip

What you’ll build today: intuition for when linear PK assumptions fail and how TMDD and PBPK extend modeling toward mechanism and physiology.

Learning Objectives

By the end of this lesson, you will be able to:

  • Recognize nonlinear PK behavior
  • Understand the idea behind target-mediated drug disposition (TMDD)
  • Understand what PBPK models represent
  • Know when these approaches are useful

Key Ideas

So far, most PK thinking assumed:

  • linear kinetics
  • proportionality (dose ↑ → exposure ↑ proportionally)

But in many real systems:

PK can be nonlinear

This happens when processes become:

  • saturable
  • capacity-limited
  • target-driven

Why This Lesson Matters

Standard compartment models work well for many drugs.

But they can fail when:

  • binding targets affect PK
  • transporters saturate
  • physiology matters

This is where more mechanistic approaches come in.

Nonlinear PK

Nonlinear PK occurs when:

  • clearance changes with concentration
  • exposure is not proportional to dose

Example:

  • doubling dose → more than double AUC

Sources of Complexity Beyond Standard PK

When standard PK assumptions fail, the reasons may differ.

Broadly:

  • nonlinear processes → saturation, capacity limits
  • target-mediated processes → drug–target interactions
  • physiological complexity → organ-level representation

These lead to different modeling approaches.

TMDD and PBPK solve different problems.

Worked Example: Linear vs Nonlinear PK

Interpretation:

  • linear → proportional exposure increase
  • nonlinear → exposure changes disproportionately with dose

TMDD (Target-Mediated Drug Disposition)

TMDD occurs when drug–target interaction meaningfully alters pharmacokinetics.

Common in:

  • monoclonal antibodies
  • biologics

Key idea:

  • target binding affects clearance

TMDD extends standard PK by allowing the biological target itself to influence drug disposition.

Conceptual target-mediated drug disposition diagram

Figure. Conceptual structure of a TMDD model.
Free drug (\(L\)) binds to a biological target or receptor (\(R\)), forming a drug–target complex (\(RL\)). Association (\(k_{on}\)) and dissociation (\(k_{off}\)) govern binding, while complex removal can contribute to drug elimination.

Unlike standard PK:

Drug → elimination

TMDD introduces:

Drug → target binding → complex → elimination

This creates concentration-dependent clearance behavior.

Characteristic TMDD Behavior

Because target binding can become saturated, clearance may change across concentrations.

Conceptual concentration-time profile showing characteristic TMDD behavior

Figure. Conceptual concentration–time profile in TMDD.
At high concentrations, target pathways may become saturated and PK can appear approximately linear. As concentrations decrease, target-mediated processes become increasingly important, creating changing slopes and nonlinear behavior.

Typical phases:

  • A: rapid initial decline
  • B: target saturation → slower decline
  • C: mixed behavior as saturation decreases
  • D: target-mediated clearance becomes more visible

This means:

  • target may become saturated
  • clearance may change over time
  • exposure can become nonlinear

Insight

In TMDD, the drug and target interact in a way that shapes both PK and PD.

Note

At low concentrations, binding may dominate; at high concentrations, saturation may occur.

PBPK (Physiologically-Based PK)

PBPK models represent:

the body as a system of physiological compartments

They include:

  • organs (liver, kidney, etc.)
  • blood flows
  • tissue partitioning

Conceptual PBPK diagram showing organ compartments connected by arterial and venous blood.

Figure. Conceptual structure of a physiologically-based pharmacokinetic (PBPK) model.
Drug enters systemic circulation and distributes between organ compartments through arterial and venous blood flow. Each compartment represents a physiological tissue or organ: LU = lung, HT = heart, BR = brain, MU = muscle, AD = adipose tissue, SK = skin, LI = liver, BO = bone, KI = kidney, PA = pancreas, SP = spleen, ST = stomach, GU = gut, and RB = remainder of body.

Drug elimination may occur through specific organs (commonly liver and kidney). CLint denotes intrinsic clearance—the inherent ability of an eliminating organ (typically liver) to remove drug independent of blood flow limitations.

PBPK models make physiological assumptions explicit.

What PBPK Adds

Compared to standard models:

  • more mechanistic
  • more physiologically interpretable
  • more transferable across populations
  • supports extrapolation across scenarios

Expanding the Idea

PBPK is useful for:

  • predicting drug behavior in new populations
  • extrapolating across species
  • understanding physiology-driven differences

Why This Matters for Decisions

These models support:

  • dose selection for biologics
  • pediatric extrapolation
  • drug–drug interaction prediction

Strategies

  • Start with simple models
  • Move to TMDD or PBPK when needed
  • Use mechanistic models when extrapolation is required

Common Mistakes

  • Assuming linearity always holds
  • Using complex models without justification
  • Ignoring biological context

Practice Problems

  1. What causes nonlinear PK?
  2. What is TMDD?
  3. What does PBPK represent?
  1. Saturation or capacity limits
  2. PK influenced by target binding
  3. Physiological compartments and flows

Summary

Nonlinear PK, TMDD, and PBPK:

  • extend beyond simple models
  • incorporate biology and physiology
  • are used when standard assumptions break
  • Nonlinearity = dose ≠ proportional exposure
  • TMDD = target affects PK
  • PBPK = physiology-driven modeling
  • Use complexity only when needed