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Seminar on

    MICHAELIS MENTEN
        KINETICS
            PRESENTED BY
     MOHAMMED MUNAWAR ALI
     (M.PHARM. 1 ST SEMESTER)
     DEPT. OF PHARMACEUTICS
      ST. PETER’S INSTITUTE OF
    PHARMACEUTICAL SCIENCES,
VIDYANAGAR, HANAMKONDA. 506001.
AFFILIATED TO KAKATIYA UNIVERSITY
C ONTENTS
   Introduction
   Some pharmacokinetic aspects of Michaelis-Menten equation.
   In vivo estimation of Km and Vm
   Estimation of pharmacokinetic parameters concerned
   Other Non-linear Processes
   Problems in quantifying non-linear kinetics
   Conclusion
   References



                                                                 2
I NTRODUCTION
 Linear kinetics, wherein the change in plasma
  concentration of drug due to absorption, distribution,
  binding, metabolism or excretion is proportional to its
  dose whether administered as single or multiple doses.
 Drug biotransformation, renal tubular secretion, and
  biliary secretion usually require enzyme or carrier
  systems. These systems are relatively specific with
  respect to substrate and have finite capacities, such
  processes are called capacity limited process; commonly
  called non-linear pharmacokinetics.
                                                      3
 The pharmacokinetics of such drugs which follow non-
  linear are said to be dose dependent, mixed order or
  capacity limited process.
 The kinetics of capacity limited process are best
  explained by Michaelis-Menten equation, given as



   This equation is derived from the following scheme.

                                     E = conc. of enzyme
         K-1        K                C = conc. of drug
E+C      K1
               EC       2
                            E+M      EC= conc. of enzyme-drug complex
                                     M = conc. of metabolite
                                     K2 and K-1 = first order rate constants
                                     K1 = second order rate constant    4
Table-1
Causes of non linearity                                     Examples
                                        Absorption
Saturable transport in gut wall                             Riboflavin
Drug comparatively insoluble                                Griseofulvin

Saturablegut wall or hepatic metabolism on first pass       Salicylamide, propranolol

Pharmacologic effect on GI motility                         Metoclopramide, chloroquine
Saturable gastric or GI decomposition                       Some penicillins
                                       Distribution
Saturable plasma protein binding                            Phenylbutazone, salicylates
Saturable tissue binding                                    Naproxen
Saturable transport into or out of tissues                  methotrexate
                                     Renal elimination
Active secretion                                            Penicillin G
Active reabsorption                                         Ascorbic acid
Change in urine pH                                          Salicylic acid
Saturable plasma protein binding                            Salicylic acid
Nephrotoxic effect at higher doses                          Amino glycosides
Diuretic effect                                             Theophylline, alcohol
                                  Extra renal elimination
Capacity limited metabolism                                 Phenytoin, theophylline
Enzyme saturation or co-factor limitation                   Salicylic acid, alcohol
Saturable biliary secretion                                 Tetracycline, indomethacin
Enzyme induction                                            Carbamazepine
Hepatotoxic at higher doses                                 Acetaminophen
Saturable plasmaproteinbinding                              Phenylbutazone
                                                                                          5
Altered hepatic blood flow                                  Propranolol
Metabolite inhibition.                                      Diazepam
SOME PHARMACOKINETIC
ASPECTS

   Three conditions are considered here where the
    michaelis-menten equation alter depending.

   i) when Km=C
         -dC/dt= Vm/2
   ii) when Km>>> C
         -dC/dt= (Vm/Km)C
   iii) when Km<<< C
          -dC/dt= Vm            Fig 1
                                                                         6
                                Source: Milo Gibaldi, Pharmacokinetics
In vivo ESTIMATION OF K m AND V m
   When drug is administered via IV injection, eliminated by single capacity
    limited process.

   Solving the equation we get,



   Modified form of which is,



   Conversion to common logarithmic form
    and solving for log C,
                                                 Fig 2.
                                                 Source: Milo Gibaldi, Pharamacokinetics



                                                                                      7
   Lineweaver-Burk equation

   Hanes-woolf plot

   Woolf-Augustinsson-Hofstee equation

   Direct method




                                                                           8
                                 Fig 3.
                                 Source: Milo Gibaldi, Pharamacokinetics
   Considering the drug elimination involving one capacity limited process and
    one or more first order processes, the rate of elimination is represented as,

                                     Km<<<C




        Km>>>C                                   Plot -d ln C/dt Vs 1/C
                                                  where slope is Vm. To get
                                                 Km the eq. is considered at
                                                 lower concentration.




                                                                               9
Fig 3.                                    Fig 4.
Source: Milo Gibaldi, Pharamacokinetics   Source: Milo Gibaldi, Pharamacokinetics




                                                                                10
USAGE OF URINE DATA

                                 K’

                           V’m                          kmu
                                  K’m


 V’m is maximum rate of metabolite,
K’ & kmu are first order rate constants,
K’m is michaelis-menten’s constant,
Cm is plasma drug conc. at midpoint of
collection interval.




                                           Fig 5.                                    11
                                           Source: Milo Gibaldi, Pharamacokinetics
ESTIMATION OF
PHARMACOKINETIC PARAMETERS
CONCERNED
   Clearance(ClS), Half-life (t1/2) and Volume of distribution.
   In linear kinetics,

   While in non-linear kinetics,                or




                                                                   12
   For the case where linear pathways of elimination in parallel with a
    non-linear process,




                                                                  13
OTHER NON-LINEAR PROCESSES

I. CHRONOPHARMACOKINETICS
   It refers to temporal changes in rate processes like absorption and
    elimination which may be either cyclical or noncyclical.
   aminoglycoside


II. ENZYME INDUCTION
   Repeated doses of Carbamazepine induces the enzymes
    responsible for its elimination.


                                                                   14
III. PROTEIN BINDING

 Plasma level- time profiles
  of two drugs A and B where
   A is 90% protein bound and
  B does not bind with plasma
  protein.
Ex: Valproic acid.




                                Fig 6.
                                Source: Leon Shargel, Applied biopharmaceutics
                                 Pharamacokinetics


                                                                        15
PROBLEMS IN QUANTIFYING NON-LINEAR
PHARMACOKINETICS
 Estimation of Km and Vm assuming multi compartment would
  be more approporiate rather than considering a one
  compartment model.
 One more problem encounters when a drug is eliminated via
  more than one capacity limited processes.[Sedmen et al.] No
  problem in Km, when it is in factor of 3.
 Drugs which effect the hepatic blood flow in turn effecting the
  rate of elimination. The mechanism by which these act are
  altering the cardiac outflow.



                                                               16
CONCLUSION
 Non linear pharmacokinetics is dose dependent and
  does not occur significantly at lower doses of drug.
 Probable reasons to occur may be attributed to change
  in physiologic system or saturation or protein binding
  or enzyme induction.
 Though the level of complexity increases when it is
  applied more realistic, assuming the process in a
  single    compartment      several    pharmacokinetic
  parameters are estimated concerned.

                                                      17
REFERENCES
   G. Levy. Pharmacokinetics of salicylate elimination in man. J.
    Pharm. Sci. 54:959 (1965).
   K. Arnold and N. Gerber. The rate of decline of
    diphenylhydantoin in human plasma. Clin. Pharmacol. Ther.
    11: 121 (1970).
   N. Gerber and J. G. Wagner. Explanation of dose-dependent
    decline of diphenylhydantoin plasma levels by fitting to the
    integrated form of Michaelis-Menten equation. Res. Commun.
    Chem. Pathol. Pharmacol. 3: 455 (1972).
   L. Martis and R. H. Levy. Bioavailability calculations for
    drugs showing simultaneous first -order and capacity-limited
    elimination kinetics. J. Pharmacokinet. Biopharm. 1: 283
                                                                 18
    (1973) .
   T. Tsuchiya and G. Levy. Relationship between dose and plateau
    levels of drugs eliminated by parallel first-order and capacity-
    limited kinetics. J. Pharm. Sci. 61:541(1972).
   W. H. Pitlick and R. H. Levy. Time-dependent kinetics: I.
    Exponential autoinduction of carbamazepine in monkeys. J. Pharm.
    Sci. 66:647 (1977).
BIBILIOGRAPHY
   Milo Gibaldi and Donald Perrier. Pharmacokinetics. Second
    edition. Volume 15. Marcel Dekker INC. 272-289 (2006).
   Leon Shargel, Susanna Wu-Pong and Andrew B.C Yu. Non-linear
    Pharmacokinetics. Applied Biopharmaceutics and
    Pharmacokinetics. Fifth edition. The McGraw-Hill Companies,
    INC. 240-242 (2007)

                                                               19
20

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Michaelis-menten kinetics

  • 1. Seminar on MICHAELIS MENTEN KINETICS PRESENTED BY MOHAMMED MUNAWAR ALI (M.PHARM. 1 ST SEMESTER) DEPT. OF PHARMACEUTICS ST. PETER’S INSTITUTE OF PHARMACEUTICAL SCIENCES, VIDYANAGAR, HANAMKONDA. 506001. AFFILIATED TO KAKATIYA UNIVERSITY
  • 2. C ONTENTS  Introduction  Some pharmacokinetic aspects of Michaelis-Menten equation.  In vivo estimation of Km and Vm  Estimation of pharmacokinetic parameters concerned  Other Non-linear Processes  Problems in quantifying non-linear kinetics  Conclusion  References 2
  • 3. I NTRODUCTION  Linear kinetics, wherein the change in plasma concentration of drug due to absorption, distribution, binding, metabolism or excretion is proportional to its dose whether administered as single or multiple doses.  Drug biotransformation, renal tubular secretion, and biliary secretion usually require enzyme or carrier systems. These systems are relatively specific with respect to substrate and have finite capacities, such processes are called capacity limited process; commonly called non-linear pharmacokinetics. 3
  • 4.  The pharmacokinetics of such drugs which follow non- linear are said to be dose dependent, mixed order or capacity limited process.  The kinetics of capacity limited process are best explained by Michaelis-Menten equation, given as  This equation is derived from the following scheme.  E = conc. of enzyme K-1 K  C = conc. of drug E+C K1 EC 2 E+M  EC= conc. of enzyme-drug complex  M = conc. of metabolite  K2 and K-1 = first order rate constants  K1 = second order rate constant 4
  • 5. Table-1 Causes of non linearity Examples Absorption Saturable transport in gut wall Riboflavin Drug comparatively insoluble Griseofulvin Saturablegut wall or hepatic metabolism on first pass Salicylamide, propranolol Pharmacologic effect on GI motility Metoclopramide, chloroquine Saturable gastric or GI decomposition Some penicillins Distribution Saturable plasma protein binding Phenylbutazone, salicylates Saturable tissue binding Naproxen Saturable transport into or out of tissues methotrexate Renal elimination Active secretion Penicillin G Active reabsorption Ascorbic acid Change in urine pH Salicylic acid Saturable plasma protein binding Salicylic acid Nephrotoxic effect at higher doses Amino glycosides Diuretic effect Theophylline, alcohol Extra renal elimination Capacity limited metabolism Phenytoin, theophylline Enzyme saturation or co-factor limitation Salicylic acid, alcohol Saturable biliary secretion Tetracycline, indomethacin Enzyme induction Carbamazepine Hepatotoxic at higher doses Acetaminophen Saturable plasmaproteinbinding Phenylbutazone 5 Altered hepatic blood flow Propranolol Metabolite inhibition. Diazepam
  • 6. SOME PHARMACOKINETIC ASPECTS  Three conditions are considered here where the michaelis-menten equation alter depending.  i) when Km=C -dC/dt= Vm/2  ii) when Km>>> C -dC/dt= (Vm/Km)C  iii) when Km<<< C -dC/dt= Vm Fig 1 6 Source: Milo Gibaldi, Pharmacokinetics
  • 7. In vivo ESTIMATION OF K m AND V m  When drug is administered via IV injection, eliminated by single capacity limited process.  Solving the equation we get,  Modified form of which is,  Conversion to common logarithmic form and solving for log C, Fig 2. Source: Milo Gibaldi, Pharamacokinetics 7
  • 8. Lineweaver-Burk equation  Hanes-woolf plot  Woolf-Augustinsson-Hofstee equation  Direct method 8 Fig 3. Source: Milo Gibaldi, Pharamacokinetics
  • 9. Considering the drug elimination involving one capacity limited process and one or more first order processes, the rate of elimination is represented as, Km<<<C Km>>>C Plot -d ln C/dt Vs 1/C where slope is Vm. To get Km the eq. is considered at lower concentration. 9
  • 10. Fig 3. Fig 4. Source: Milo Gibaldi, Pharamacokinetics Source: Milo Gibaldi, Pharamacokinetics 10
  • 11. USAGE OF URINE DATA K’ V’m kmu K’m V’m is maximum rate of metabolite, K’ & kmu are first order rate constants, K’m is michaelis-menten’s constant, Cm is plasma drug conc. at midpoint of collection interval. Fig 5. 11 Source: Milo Gibaldi, Pharamacokinetics
  • 12. ESTIMATION OF PHARMACOKINETIC PARAMETERS CONCERNED  Clearance(ClS), Half-life (t1/2) and Volume of distribution.  In linear kinetics,  While in non-linear kinetics, or 12
  • 13. For the case where linear pathways of elimination in parallel with a non-linear process, 13
  • 14. OTHER NON-LINEAR PROCESSES I. CHRONOPHARMACOKINETICS  It refers to temporal changes in rate processes like absorption and elimination which may be either cyclical or noncyclical.  aminoglycoside II. ENZYME INDUCTION  Repeated doses of Carbamazepine induces the enzymes responsible for its elimination. 14
  • 15. III. PROTEIN BINDING  Plasma level- time profiles of two drugs A and B where A is 90% protein bound and B does not bind with plasma protein. Ex: Valproic acid. Fig 6. Source: Leon Shargel, Applied biopharmaceutics Pharamacokinetics 15
  • 16. PROBLEMS IN QUANTIFYING NON-LINEAR PHARMACOKINETICS  Estimation of Km and Vm assuming multi compartment would be more approporiate rather than considering a one compartment model.  One more problem encounters when a drug is eliminated via more than one capacity limited processes.[Sedmen et al.] No problem in Km, when it is in factor of 3.  Drugs which effect the hepatic blood flow in turn effecting the rate of elimination. The mechanism by which these act are altering the cardiac outflow. 16
  • 17. CONCLUSION  Non linear pharmacokinetics is dose dependent and does not occur significantly at lower doses of drug.  Probable reasons to occur may be attributed to change in physiologic system or saturation or protein binding or enzyme induction.  Though the level of complexity increases when it is applied more realistic, assuming the process in a single compartment several pharmacokinetic parameters are estimated concerned. 17
  • 18. REFERENCES  G. Levy. Pharmacokinetics of salicylate elimination in man. J. Pharm. Sci. 54:959 (1965).  K. Arnold and N. Gerber. The rate of decline of diphenylhydantoin in human plasma. Clin. Pharmacol. Ther. 11: 121 (1970).  N. Gerber and J. G. Wagner. Explanation of dose-dependent decline of diphenylhydantoin plasma levels by fitting to the integrated form of Michaelis-Menten equation. Res. Commun. Chem. Pathol. Pharmacol. 3: 455 (1972).  L. Martis and R. H. Levy. Bioavailability calculations for drugs showing simultaneous first -order and capacity-limited elimination kinetics. J. Pharmacokinet. Biopharm. 1: 283 18 (1973) .
  • 19. T. Tsuchiya and G. Levy. Relationship between dose and plateau levels of drugs eliminated by parallel first-order and capacity- limited kinetics. J. Pharm. Sci. 61:541(1972).  W. H. Pitlick and R. H. Levy. Time-dependent kinetics: I. Exponential autoinduction of carbamazepine in monkeys. J. Pharm. Sci. 66:647 (1977). BIBILIOGRAPHY  Milo Gibaldi and Donald Perrier. Pharmacokinetics. Second edition. Volume 15. Marcel Dekker INC. 272-289 (2006).  Leon Shargel, Susanna Wu-Pong and Andrew B.C Yu. Non-linear Pharmacokinetics. Applied Biopharmaceutics and Pharmacokinetics. Fifth edition. The McGraw-Hill Companies, INC. 240-242 (2007) 19
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