Michaelis Menten Equation and Estimation Of Vmax and Tmax.pptx

Michaelis Menten Equation and Estimation Of Vmax and Tmax

1. PRESENTED BY: Deepak A. Thakre M.Pharm I Year Industrial Pharmacy Department Shri Sadashivrao Patil Shikshan Sanstha's SMT. KISHORITAI BHOYAR COLLEGE OF PHARMACY, KAMPTEE GUIDED BY : Dr. Jayshree B. Taksande HOD Pharmaceutics Department TOPIC : 1. The Michaelis-Menten equation & 2. Estimating Km and Vmax 1

2. If metabolism is the only pathway of elimination, the rate of metabolism or elimination is defined by the Michaelis-Menten equation. The (Non- linear) kinetics of capacity-limited or saturable processes is best described by Michaelis-Menten equation: ------- (1) Where, –dc/dt = rate of decline of drug concentration with time, Vmax = theoretical maximum rate of the process, Km = Michaelis constant , C= drug Concentration . Three situations can now be considered depending upon the values of Km and C: A] When Km = C Under this situation, the equation (1) reduces to i.e. -------(2) i.e. the rate of process is equal to one-half its maximum rate.   2

3. 3 A plot of Michaelis-Menten equation (elimination rate dC /dt versus concentration C). Initially, the rate increases linearly (first-order) with concentration, becomes mixed-order at higher concentration and then reaches maximum (Vmax) beyond which it proceeds at a constant rate (zero-order).

4. Michaelis-Menten equation is generally used to explain the kinetics of in-vitro, few enzyme catalyzed in-vivo and in-situ processes. 4

5. 5 B] Km>> C When the concentrations are low, i.e. Km> C, then Km +C is approximately equal to Km, ------------ equation .(3) The above equation is identical to the one that describes first-order elimination of a drug where Vmax/Km = KE. This means that the drug concentration in the body that results from usual dosage regimens of most drugs is well below the Km of the elimination process with certain exceptions such as phenytoin and alcohol . Because both Vmax and Km are constants, the metabolism rate is proportional to the drug concentration and is constant (i.e., first-order process).  

6. C] C>> Km When the concentrations are high, i.e. C > Km, then ------- equation (4) Equation 4 gives the zero order kinetics. Therefore, it was concluded that at high plasma concentrations, first order kinetics were not seen. The above equation is identical to the one that describes a zero-order process i.e. the rate process occurs at a constant rate Vmax and is independent of drug concentration. When given in therapeutic doses, most drugs produce plasma drug concentrations well below the Km for all carrier mediated enzyme systems affecting the pharmacokinetics of the drug. Hence most of the drugs at normal therapeutic concentrations follow 1st order rate processes. Some of the drugs like phenytoin and salicylate saturate the hepatic mixed function oxidases at higher therapeutic doses. With these drugs, elimination kinetics is 1st order at low doses and mixed at high doses and shows zero-order at very high therapeutic doses.   6

7. If a single IV bolus injection of drug D0 is given at t=0, the drug concentration, Ct in the plasma at any time may be calculated by integrated form of Eq 1 is given by ----equation (5) Where C0 is the concentration at time t=0. Alternatively the amount of the drug in the body after an IV bolus injection may be calculated by the following relationship. ------equation (6) Where Do is the amount of the drug in the body at t=0. …Equation (5) …Equation (6) Equation 6 can be used to study the decline of the drug in the body after the administration of different therapeutic doses. Here, the Km and Vmax of the drug are unknown.   7

8. By rearranging the above Equation 6, time to decline a certain amount of the dose of a drug can be calculated by the following equation -----equation (7) Equation 7 explains an inverse relationship between the time for the dose to decline to a certain amount of the drug in the body and Vmax. Actually, Km can be said as the hybrid constant in enzyme kinetics that may represents both forward as well as backward reaction. It is equivalent to the concentration of the drug in the body at ½ Vmax. The one compartment open model having capacity limited elimination pharmacokinetics effectively explains the plasma drug concentration time profiles for a number of drugs.   8

9. 9 The parameters of capacity-limited processes like metabolism, renal tubular secretion and biliary excretion can be easily defined by assuming one-compartment kinetics for the drug and that elimination involves only a single capacity-limited process. The parameters Km and Vmax can be assessed from the plasma concentration-time data collected after i.v. bolus administration of a drug with nonlinear elimination characteristics. Rewriting equation ---------equation (1) Integration of above equation followed by conversion to log base 10 yields: -------(2)   Estimating Km and Vmax

10. 10 A semilog plot of C versus t yields a curve with a terminal linear portion having slope –Vmax/2.303Km and when back extrapolated to time zero gives Y-intercept log Co .The equation that describes this line is: Fig: Semi-log plot of a drug given as i.v. bolus with nonlinear elimination and that fits one-compartment kinetics. ----equation (3)

11. 11 From equation 2 and 3 ( at low Plasma Concentration) OR For this equation Km can be obtained. Vmax can be Computed by Substituting the value of Km in the Slope value.  

12. Estimating Km and Vmax Method : Equation 1 gives the relationship of the drug biotransformation to the concentration of the drug in the body. When an experiment is performed by using different concentrations of the drug C, a series of reaction rates (V) may be calculated for each concentration. Km and Vmax can then be determined by using the special plots. Hence, V ------ equation (8) Rearranging the above equation 8, [ As Per Equation of Slope- ] -----equation (9) Above Equation 9 gives the linear equation, when 1/V is plotted against 1/C, the resultant intercept for the line is 1/Vmax and the slope is Km/Vmax Fig: Plot of 1/V against 1/C for the determination of Km and Vmax   12

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