This document discusses saturation kinetics and nonlinear pharmacokinetics. It explains that drug clearance follows first-order kinetics at low concentrations but can become saturated and shift to zero-order kinetics at high concentrations due to limited enzyme capacity. This nonlinear behavior is described by Michaelis-Menten kinetics. A few drugs like phenytoin exhibit saturation kinetics in the therapeutic range, making their dosing more complex due to changing half-lives with concentration. Understanding saturation and nonlinear pharmacokinetics is important for safely dosing drugs that exhibit these behaviors.

1. SATURATION KINETICS
PREPARED AND PRESENTED BY
MOHAMMED MUZAMMIL
1ST YEAR MPHARM
DEPARTMENT OF PHARMACOLOGY
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2. INTRODUCTION
• What is kinetics ? It is the the branch of chemistry or biochemistry concerned with measuring and studying
the rates of reactions.
• First order elimination kinetics: a constant proportion (eg. a percentage) of drug is eliminated per unit
time
• Zero order elimination kinetics: a constant amount (eg. so many milligrams) of drug is eliminated per
unit time
• First order kinetics is a concentration-dependent process (i.e. the higher the concentration, the faster the
clearance), whereas zero order elimination rate is independent of concentration.
• Michaelis-Menten kinetics describes enzymatic reactions where a maximum rate of reaction is reached
when drug concentration achieves 100% enzyme saturation.
• Non-linear elimination kinetics is the term which describes drig clearance by Michaelis-
Menten processes, where a drug at low concentration is cleared by first-order kinetics and at high
concentrations by zero order kinetics (eg. phenytoin or ethanol).
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3. Vmax AND Km VALUE
• The rate of reaction when the enzyme is saturated with substrate is the
maximum rate of reaction, Vmax.
The relationship between rate of reaction and concentration of substrate
depends on the affinity of the enzyme for its substrate. This is usually
expressed as the Km (Michaelis constant) of the enzyme, an inverse
measure of affinity.
For practical purposes, Km is the concentration of substrate which
permits the enzyme to achieve half Vmax. An enzyme with a high Km
has a low affinity for its substrate, and requires a greater concentration of
substrate to achieve Vmax.
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4. FIRST ORDER ELIMINATION
KINETICS• First-order kinetics... is where a constant fraction of drug in the body is
eliminated per unit of time“
• This is a logarithmic function. All enzymes and clearance mechanisms are
working at well below their maximum capacity, and the rate of drug
elimination is directly proportional to drug concentration.
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5. • The drug concentration halves predictably according to fixed time intervals.
When you plot this on a semi-logarithmic scale, the relationship of
concentration and time is linear.
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6. • If you plot the relationship of concentration vs. elimination rate, the same
sort of linear relationship is seen:
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7. ZERO-ORDER ELIMINATION
KINETICS• In chemistry, when doubling the concentration of
reagents(ENZYMES) has no effect on the reaction rate, the increase in rate
is by a factor of 0 (i.e. 20). This is zero-order kinetics. The relationship of
concentration to reaction rate can therefore be plotted as a boring straight
line:
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8. • In the realm of pharmacokinetics, "reaction rate" is elimination of the drug, by
whatever clearance mechanisms (some of which might actually involve
reactions).
• Generally speaking first-order kinetics can describe clearance which is driven
by diffusion; diffusion rate is directly proportional to drug concentration. If
there is a functionally inexhaustible amount of metabolic enzymes available,
the reaction will also be first order (i.e. the more substrate you throw at the
system, the harder the system will work).
• However, if there is some limit on how much enzyme activity there can be,
then the system is said to be saturable, i.e. it is possible to saturate the enzymes
to a point where increases in concentration can no longer produce increases in
enzyme activity. This gives rise to non-linear elimination kinetics, known by
the uninformatively eponymous term "Michaelis-Menten elimination".
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9. MICHAELIS-MENTEN
ELIMINATION KINETICS
• Named after Leonor Michaelis and Maud Menten, this model of enzyme
kinetics describes the relationship between the concentration and the rate of
enzyme-mediated reaction. In short, at low concentrations, the more
substrate you give the faster the reaction rate.
• At high concentrations, the rate of reaction remains the same because all
the enzyme molecules are "busy", i.e. the system is saturated.
• This concept can be described by the unimaginatively named Michaelis-
Menten equation, which relates the rate (velocity, V) of a reaction to the
concentration of the substrate (lets call it "drug").
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10. • A maximum rate of reaction is reached when drug concentration achieves
100% enzyme saturation. Beyond this concentration, clearance will be
zero-order.
• The maximum rate of reaction in this instance is called Vmax (i.e. maximum
velocity). The concentration required to achieve 50% of this maximum
reaction rate is called Km, where K presumably stands
for Konzentration because everything in science was named by the
Germans.
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11. • The graph of the enzymatic reaction rate to drug concentration looks a little
like this:
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12. • Thus, when the patient is receiving regular doses of the drug, if the
concentration is already high then relatively small changes in the dose will
produce a disproportionately large change in drug concentration.
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13. • This has relevance to clinical pharmacology. Drugs which have a
therapeutic concentration range in the steep part of this curve are said to
have a narrow therapeutic range (i.e. the effective dose is not too far off the
toxic dose).
• If relatively large changes in dose produce relatively small changes in the
concentration , toxic levels will be difficult to achieve and the drug is said
to have a broad therapeutic index.
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14. SATURATION KINETICS
• Also called as Nonlinear Pharmacokinetics Most of the rate processes
discussed in this course, except for the infusion process, follow first order
kinetics.
• For a few drugs it is observed that the elimination of the drug appears to be
zero order at high concentrations and first order at low concentrations.
• That is 'concentration' or 'dose' dependent kinetics are observed. At higher
doses, which produce higher plasma concentrations, zero order kinetics
are observed, whereas at lower doses the kinetics are linear or first order.
• This occurs especially with drugs which are extensively metabolized.
• A typical characteristic of enzymatic reactions and active transport is a
limitation on the capacity of the process.
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15. • There is only so much enzyme present in the liver, and therefore there is a
maximum rate at which metabolism can occur.
• A further limitation in the rate of metabolism can be the limited availability
of a co-substance or co-factor required in the enzymatic process.
• This might be a limit in the amount of available glucuronide or glycine, for
example.
• Drug concentrations in the blood can increase rapidly once an elimination
process is saturated.
• This nonlinear pharmacokinetic behavior is also termed dose-dependent
pharmacokinetics.
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16. • A number of drugs demonstrate saturation or capacity-limited metabolism
in humans.
• Examples of these saturable metabolic processes include:
• – glycine conjugation of salicylate.
• –sulfate conjugation of salicylamide.
• –acetylation of p-aminobenzoic acid.
• –The elimination of phenytoin.
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17. • Drugs that demonstrate saturation kinetics usually show the following
characteristics:
• 1)Elimination of drug does not follow simple first-order kinetics—that is,
elimination kinetics are nonlinear.
• 2)The elimination half-life changes as dose is increased. Usually, the
elimination half-life increases with increased dose due to saturation of an
enzyme system. However, the elimination half-life might decrease due to
"self"-induction of liver biotransformation enzymes, as is observed for
carbamazepine.
• 3)The area under the curve (AUC) is not proportional to the amount of
bioavailable drug.
• 4)The saturation of capacity-limited processes may be affected by other
drugs that require the same enzyme or carrier-mediated system (ie,
competition effects).
• 5)The composition and/or ratio of the metabolites of a drug may be affected
by a change in the dose.
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18. • When a large dose is given, a curve is obtained with an initial slow
elimination phase followed by a much more rapid elimination at lower
blood concentrations (curve A).
• With a small dose of the drug, apparent first-order kinetics are observed,
because no saturation kinetics occur (curve B).
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19. • If the pharmacokinetic data were estimated only from the blood levels
described by curve B, then a two fold increase in the dose would give the
blood profile presented in curve C, which considerably underestimates the
drug concentration as well as the duration of action.
• In order to determine whether a drug is following dose-dependent kinetics,
the drug is given at various dosage levels and a plasma level–time curve is
obtained for each dose.
• The curves should exhibit parallel slopes if the drug follows dose-
independent kinetics. Alternatively, a plot of the areas under the plasma
level–time curves at various doses should be linear.
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20. SATURABLE ENZYMATIC
ELIMINATION PROCESSES
• The elimination of drug by a saturable enzymatic process is described by
Michaelis–Menten kinetics.
• If Cp is the concentration of drug in the plasma, then:
• Where:
• –Vmax is the maximum elimination rate.
• –KM is the Michaelis constant that reflects the capacity of the enzyme
system.
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21. • When the drug concentration Cp is large in relation to KM (Cp >> Km),
saturation of the enzymes occurs and the value for KM is negligible.
• The rate of elimination proceeds at a fixed or constant rate equal to Vmax.
Thus, elimination of drug becomes a zero-order process and Eq. becomes:
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22. • When the drug concentration Cp is small in relation to the KM, the rate of
drug elimination becomes a first-order process.
• Where: k' is a first-order rate constant
• When given in therapeutic doses, most drugs produce plasma drug
concentrations well below KM for all carrier-mediated enzyme systems
affecting the pharmacokinetics of the drug.
• Therefore, most drugs at normal therapeutic concentrations follow first-
order rate processes.
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23. • Only a few drugs, such as salicylate and phenytoin, tend to saturate the
hepatic mixed-function oxidases at higher therapeutic doses.
• With these drugs, elimination kinetics are first-order with very small
doses, mixed order at higher doses, and may approach zero-order with
very high therapeutic doses.
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24. NONLINEAR PHARMACOKINETICS
• As the concentration increases we would expect the clearance to decrease.
• Calculations based on an assumption of constant clearance, such as the
calculation of AUC are no longer valid.
• A simple increasing of dose becomes an adventure.
• No longer can we increase the dose by some fraction, for example 25%,
and expect the concentration to increase by the same fraction. The
calculations are more complex and must be done carefully.
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25. • When we talked about linear kinetics we talked about the time it takes to
get to steady state concentrations. With linear kinetics this time was
independent of concentration and could be calculated as 3, 4 or 5 half-lives.
• With non-linear kinetics, this time will increase with concentration just as
this psuedo half-life increases with concentration.
• The relationship between elimination half-life and drug concentration is
shown in Equation 10.16. The elimination half-life is dependent on the
Michaelis–Menten parameters and concentration
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26. • The presence of saturation kinetics can be quite important when high doses
of certain drugs are given, or in case of over-dose.
• In the case of high dose administration the effective elimination rate
constant is reduced and the drug will accumulate excessively if saturation
kinetics are not understood.
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27. NONLINEAR PHARMACOKINETICS
(PHENYTOIN)
• Phenytoin is an example of a drug which commonly has a Km value within
or below the therapeutic range.
• –The average Km value is about 4 mg/L.
• –The normally effective plasma concentrations for phenytoin are between
10 and 20 mg/L.
• Therefore it is quite possible for patients to be overdosed due to drug
accumulation.
• At low concentration the apparent half-life is about 12 hours, whereas at
higher concentration it may well be much greater than 24 hours.
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28. • Dosing every 12 hours, the normal half-life, can rapidly lead to dangerous
accumulation.
• At concentrations above 20 mg/L elimination maybe very slow in some
patients. Dropping for example from 25 to 23 mg/L in 24 hours, whereas
normally you would expect it to drop from -25> -12.5> 6 mg/L in 24 hours.
• Typical Vm values are 300 to 700 mg/day. These are the maximum
amounts of drug which can be eliminated by these patients per day. Giving
doses approaching these values or higher would cause very dangerous
accumulation of drug.
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