12. First and Zero-Order Kinetics

Question 1

What are first-order kinetics?

Answer 1

> In first-order kinetics a
constant proportion of the drug

is eliminated from the body
per unit time,

e.g. 50% per hour and
therefore clearance
and half-life can be used

to describe elimination kinetics.

> The rate of elimination varies
and is directly proportional
to the concentration of
drug in the body at that time.

This produces an exponential decay curve
and is due to non-saturatable enzymes
being involved in drug elimination..

> The majority of drugs display 
first-order kinetics because the body
contains more enzymes than needed 
to metabolise the 
clinically effective dose.

Question 2

What are zero-order kinetics?

examples

Answer 2

> In zero-order kinetics a
constant amount of drug
is eliminated from the body
per unit time,

e.g. 
10 mg per hour 
and therefore 
clearance an half-life 
cannot be used to 
describe elimination kinetics.

> The rate of elimination is constant
and changing the quantity of
drug available for metabolism
does not alter the rate of the reaction.

This produces a
linear graph because the enzymes
involved in drug
elimination become saturated.

> Ethanol,
 phenytoin, 
aspirin, 
theophylline and 
thiopentone display
zero-order kinetics

Question 3

Why is this important clinically?

Answer 3

> The therapeutic dose of some drugs
is close to the plasma concentration
at which the metabolic enzymes
become saturated.

Once saturated, 
a small increase in dosing 
or plasma drug concentration 
will result in greatly increased 
availability of the drug.

> If the drug has serious side effects,
these too could become more
pronounced.

A common example of this is seen 
with alcohol intoxication,
where consuming more than 1 unit/hour
will lead to enzyme saturation,
and the person concerned will become ‘drunk’.

Question 4

What are Michaelis–Menten

kinetics?

Answer 4

> These describe the kinetics
of the body’s enzymes

and are used

to predict the rate of reaction

between an
enzyme (E) and
substrate (S) to
form a product (P).

S + E ⇌ ES ⇌ P

> In terms of drug elimination,
represents the enzymes
involved in drug metabolism

and S represents the
plasma concentration of the drug

Question 5

Michaelis–Menten equation:

Answer 5

VMax [S]
V = ________

    Km + [S] 

Where:

V velocity (or rate) of reaction

Vmax maximal rate of reaction

[S] substrate (or drug) concentration

Km Michaelis constant,
which is the substrate concentration
at which V = ½ Vmax

> At low substrate concentrations: 
V ∝ [S] − it obeys first-order kinetics
and as the substrate concentration 
increases so does 
the rate of the reaction.

> At high substrate concentrations: 
V ∝ Vmax − 
it obeys zero-order kinetics
because the enzymes become 
saturated and the 
rate of reaction cannot
increase any further.

Question 6

Graph Michaelis menten

Answer 6

Fig. 12.3 Michaelis-Menten graph - velocity of reaction [V] over substrate concentration [S]