Saturation kinetics

saturation kinetics or non linear kinetics which will help you to study over dosing and excretion rate of a drug

1. SATURATION KINETICS PREPARED AND PRESENTED BY MOHAMMED MUZAMMIL 1 ST YEAR MPHARM DEPARTMENT OF PHARMACOLOGY 06-Apr-19 srinivas college of pharmacy 1

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).  06-Apr-19 srinivas college of pharmacy 2

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 . 06-Apr-19 srinivas college of pharmacy 3

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.  06-Apr-19 srinivas college of pharmacy 4

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.  06-Apr-19 srinivas college of pharmacy 5

6. If you plot the relationship of concentration vs. elimination rate, the same sort of linear relationship is seen: 06-Apr-19 srinivas college of pharmacy 6

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. 2 ). This is zero-order kinetics. The relationship of concentration to reaction rate can therefore be plotted as a boring straight line : 06-Apr-19 srinivas college of pharmacy 7

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". 06-Apr-19 srinivas college of pharmacy 8

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"). 06-Apr-19 srinivas college of pharmacy 9

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 V max  (i.e. maximum velocity). The concentration required to achieve 50% of this maximum reaction rate is called K m , where K presumably stands for  Konzentration  because everything in science was named by the Germans. 06-Apr-19 srinivas college of pharmacy 10

11. The graph of the enzymatic reaction rate to drug concentration looks a little like this : 06-Apr-19 srinivas college of pharmacy 11

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 . 06-Apr-19 srinivas college of pharmacy 12

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.  06-Apr-19 srinivas college of pharmacy 13

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. 06-Apr-19 srinivas college of pharmacy 14

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. 06-Apr-19 srinivas college of pharmacy 15

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. 06-Apr-19 srinivas college of pharmacy 16

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. 06-Apr-19 srinivas college of pharmacy 17

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 ). 06-Apr-19 srinivas college of pharmacy 18

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. 06-Apr-19 srinivas college of pharmacy 19

20. SATURABLE ENZYMATIC ELIMINATION PROCESSES The elimination of drug by a saturable enzymatic process is described by Michaelis – Menten kinetics . If C p is the concentration of drug in the plasma, then : Where: – V max is the maximum elimination rate. – K M is the Michaelis constant that reflects the capacity of the enzyme system. 06-Apr-19 srinivas college of pharmacy 20

21. When the drug concentration C p is large in relation to K M ( C p >> K m), saturation of the enzymes occurs and the value for K M is negligible. The rate of elimination proceeds at a fixed or constant rate equal to V max . Thus, elimination of drug becomes a zero-order process and Eq. becomes: 06-Apr-19 srinivas college of pharmacy 21

22. When the drug concentration C p is small in relation to the K M, 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 K M for all carrier-mediated enzyme systems affecting the pharmacokinetics of the drug. Therefore , most drugs at normal therapeutic concentrations follow first-order rate processes. 06-Apr-19 srinivas college of pharmacy 22

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 . 06-Apr-19 srinivas college of pharmacy 23

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. 06-Apr-19 srinivas college of pharmacy 24

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 06-Apr-19 srinivas college of pharmacy 25

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 . 06-Apr-19 srinivas college of pharmacy 26

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. 06-Apr-19 srinivas college of pharmacy 27

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. 06-Apr-19 srinivas college of pharmacy 28