(3A) Non-Linear Pharmacokinetics

What drugs have Nonlinear behavior

• Phenytoin (Dilantin)

• Alcohol

LINEAR PK

Processes =

constant

Means:

• Same mechanism regardless of dose

LINEAR PK

KEY IDEA:

Dose ↑ → concentration ↑ proportionally

INTERMITTENT INFUSION SHORTCUT

If SAME:

• Dosing interval

• Infusion time

• Concentration type

👉 Then:

• Can use simple proportion

If NOT same:

• Must do:

  • Step-by-step PK math

I THINK WE WILL HAVE QUESTION ON INTERMITTENT INFUSION

NONLINEAR PK DEFINITION

• Processes:

• NOT constant

• Change with:

  • Dose

  • Concentration

NONLINEAR PK

MAIN CAUSE

Saturation of enzymes/proteins

OTHER CAUSES

• Change in urine pH

• Altered hepatic blood flow

• Disease states

👉 Not always enzyme-based

HOW NONLINEAR HAPPENS

At low dose:

At high dose:

At low dose:

• Plenty of enzyme

• Normal metabolism

At high dose:

• Enzyme gets saturated

• Drug cannot be metabolized properly

👉 System changes

💡 CONCEPT: NOT ONLY METABOLISM

Can also affect:

• Absorption

• Distribution

• Excretion

Linear behavior

• Dose ↑ → concentration ↑ proportionally

• Half-life constant

• Clearance constant

Nonlinear behavior

• No predictable relationship ❌

• Can see:

  • Huge increase (↑↑ concentration)

  • Plateau (no increase)

• have no dose-proportionally

• involve one or more zero-order process

• Drug-drug interactions ↑

• Cannot use superposition ❌

• No single population parameter

HALF-LIFE CHANGES

• Can:

• Increase (drug accumulates)

• Decrease (less absorption or faster removal)

👉 Depends on cause

DOSE PROPORTIONALITY

• Linear →

• Nonlinear →

• Linear → proportional

• Nonlinear → lost proportionality ✅⭐

ZERO-ORDER PROCESS

• Occurs when:

System is saturated

Constant rate (not dependent on concentration)

CONCEPT: POPULATION VALUES

• Instead of one value:

  • You may see:

Ranges

Natural (saturable) drug metabolism - STARTS FROM HERE

• Michaelis-Menten kinetics

  • Originally developed:

• NOT for drugs

• From test tube dye reactions

👉 Later applied to:

• Drug metabolism

MICHAELIS-MENTEN KINETICS

We have:

• E = enzyme

• S = drug (substrate)

MICHAELIS-MENTEN KINETICS

PROCESS

Step 1:

• Enzyme + Drug → bind
  → form:
  👉 Enzyme-substrate complex (ES)

---

Step 2:

• Binding is reversible

  • Can bind and unbind

👉 Represented by:

• K₁ (forward)

• K₋₁ (backward)

---

Step 3:

• Complex → metabolized
  → produces:

  • Metabolite (product)

  • Enzyme regenerated

MICHAELIS-MENTEN KINETICS

IMPORTANT

Once metabolite forms:

• ❌ Cannot go back to original drug

MICHAELIS-MENTEN KINETICS

RATE CONSTANTS

• K₂ = rate of metabolism

• Also represents:
  👉 Maximum rate (Vmax concept later)

MICHAELIS-MENTEN KINETICS

Enzyme is:

• Released after reaction

• Can be reused again

WHERE MICHAELIS-MENTEN KINETICS CAME FROM?

• Developed in:

  • Controlled lab environment

• Conditions:

  • Fixed enzyme

  • Fixed drug

  • Clean system

WHEN MICHAELIS-MENTEN FAILS

1. Enzyme concentration changes

• Reaction changes enzyme amount

---

2. Body changes enzyme production

• Upregulation

• Downregulation

👉 Very common in drugs

---

3. Drug can be regenerated Example: Phase II reactions

• Drug + something (e.g., sugar)

WHEN MICHAELIS-MENTEN FAILS

example

• Estrogen:

  • Gets conjugated (sugar added)

  • Gut bacteria remove sugar

  • Drug becomes active again

  • Gets reabsorbed

👉 This breaks model ❌

KEY PARAMETERS of Michaelis–Menten model - overview

• Km = capacity

• Vmax = speed

Vmax

• Maximum rate of metabolism

• Fastest body can metabolize drug

👉 Cannot go faster than this

Km

• Concentration threshold

• Point where system is:

  • Getting saturated

INTERPRETATION

• If concentration > Km:

• If concentration < Km:

• If concentration > Km:

  • System ≈ saturated

  • Working near Vmax

  • zero-order (constant rate)

• If concentration < Km:

  • System NOT saturated

  • Has extra capacity

  • pseudo-first-order

TWO SCENARIOS in Michaelis–Menten model?

CASE 1: UNSATURATED (LOW CONC)

CASE 2: SATURATED (HIGH CONC)

CASE 1: UNSATURATED (LOW CONC) - equation you use

CASE 2: SATURATED (HIGH CONC) - equation you use

Michaelis–Menten model

GRAPH THINKING

At any point:

• Look at concentration (Ct)

👉 Ask:

• Is it:

  • Above Km?

  • Below Km?