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**Enzyme kinetics -- Michaelis Menten kinetics**

Two approaches: Rapid equilibrium approach Quasi steady state approach Assumptions: Total enzyme concentration remains constant during the reaction Amount of enzyme is very small compared to amount of substrate The product concentration is so low that the product inhibition is negligible.

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where k1= forward rate constant for formation of ES complex k2= backward rate constant for formation of ES complex k3= rate constant for formation of product P

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**some notations…….. e = concentration of enzyme**

s = concentration of substrate p = concentration of product (es) = concentration of enzyme substrate complex t = time v = reaction rate or velocity

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**Michaelis Menten kinetics --Rapid equilibrium approach**

It is assumed that ES complex is established very rapidly (since this equilibrium step is only the formation of weak interaction between E & S) The product releasing step (k3) is very slow…….which determines the rate The rate of reverse reaction of the second step is negligible

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**The equilibrium constant**

The rate of product formation, (mol/ l.s) The total enzyme concentration 1 2 3

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**Get an expression for (es) in known quantities……**

Sub. eqn (1) in (3)

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**Now sub. the value of (es) in eqn 2.**

Michaelis Menten Equation 5

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**Three special cases…….. Case I (s=KM) Therefore……..**

is a function of enzyme concentration only A low value of means that the enzyme has high affinity for the substrate Three special cases…….. Case I (s=KM) Case II (s>>KM) Case III (s<<KM)

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**Case I (s=KM) Eqn. (5) =>**

So when s=KM, the rate of reaction is one half of its maximal value. i.e. at which 50% of enzyme active sites are occupied by substrate

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Case II (s>>KM) Eqn. (5) => ZERO ORDER

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**Case III (s<<KM)**

Eqn. (5) => FIRST ORDER

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**Michaelis Menten kinetics --Quasi steady state approach**

This approach is assumed that the change in the intermediate (transition complex) concentration with respect to time is negligible. (pseudo steady state/quasi steady state)--- Briggs-Haldane approach i.e.

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1 1 1

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By p.s.s assumption, Eqn 4==>

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We know,

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**sub the value of (es) in (1)**

Michaelis Menten Equation

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**Means that ‘S’ is costant…..which is not correct**

Controversy of Equilibrium approach: by Equilibrium approach, Means that ‘S’ is costant…..which is not correct

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**This has been rectified by PSS approach…..**

by PSS assumption

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**Life of a man…… Before marriage…. After finding a girl…..**

SPIDERMAN After finding a girl….. SUPERMAN After engagement…. GENTLEMAN After marriage…… WATCHMAN After 10 yrs….. DOBERMAN

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© 2014 Carl Lund, all rights reserved A First Course on Kinetics and Reaction Engineering Class 9.

© 2014 Carl Lund, all rights reserved A First Course on Kinetics and Reaction Engineering Class 9.

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