Enzyme Kinetics and Catalysis II

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					Enzyme Kinetics and Catalysis II

            3/24/2003
               Kinetics of Enzymes
      Enzymes follow zero order kinetics when substrate
concentrations are high. Zero order means there is no increase
   in the rate of the reaction when more substrate is added.
  Given the following breakdown of sucrose to glucose and
                          fructose
Sucrose + H20                  Glucose + Fructose
                                                                           H
                                                                 H                              H
                                        H OH                                       O
                                                                                                    OH
                                                                 HO            H       OH
                                                   H   O                                             H
                              HO                                      OH                    H
                                   HO                            H                     H
                                                                           HO
                                               H       OH

                                          H                 OH
               k1
     E  S  ES  E  P    k2

               k -1


E = Enzyme S = Substrate P = Product
ES = Enzyme-Substrate complex
k1 rate constant for the forward reaction
k-1 = rate constant for the breakdown of the ES to
substrate
k2 = rate constant for the formation of the
products
When the substrate concentration becomes large
enough to force the equilibrium to form completely
all ES the second step in the reaction becomes rate
limiting because no more ES can be made and the
enzyme-substrate complex is at its maximum value.

   d P             [ES] is the difference between the
v        k2 ES   rates of ES formation minus the
    dt               rates of its disappearance. 1


  d ES
          k1 ES  k1 ES  k2 ES
    dt
       Assumption of equilibrium
     k-1>>k2 the formation of product is so
much slower than the formation of the ES
complex. That we can assume:

               k 1 E S
          Ks      
               k1    ES 
Ks is the dissociation constant for the ES complex.
            Assumption of steady state
Transient phase where in the course of a reaction the
concentration of ES does not change



                                                   2


                                     d ES 
                                             0
                                       dt
       ET  E  ES                           3


 Combining 1 + 2 + 3

       k1 ET - ES S  k -1  k 2 ES 
 rearranging

     ES k -1  k 2  k1S  k1ET S
Divide by k1 and solve for [ES]   Where
                                        k -1  k 2
     ES   E T S             KM 
                                            k1
             K M  S
       d P              k2 ET S
 vo           k2 ES 
       dt t 0            K M  S


 vo is the initial velocity when the reaction is just starting out.


 And      Vm ax  k 2 E T            is the maximum velocity


     Vmax S                     The Michaelis - Menten
vo 
     K M  S
                                        equation
The Km is the substrate concentration where vo equals
                    one-half Vmax
   The KM widely varies among different enzymes


  The KM
                                    k 1 k 2     k2
  can be expressed as:       KM          Ks 
                                    k1 k1        k1

As Ks decreases, the affinity for the substrate
increases. The KM can be a measure for substrate
affinity if k2<k-1
There are a wide range of KM, Vmax , and efficiency
                  seen in enzymes


       But how do we analyze kinetic data?
The double reciprocal plot




1  KM      1    1
  
   V       
            S V
vo  max         max
    Lineweaver-Burk plot: slope = KM/Vmax,
  1/vo intercept is equal to 1/Vmax
  the extrapolated x intercept is equal to -1/KM
For small errors in at low [S] leads to large errors in 1/v o

                         kcat is how many reactions an
          Vm ax          enzyme can catalyze per second
k cat   
          E T             The turnover number
For Michaelis -Menton kinetics k2= kcat
When [S] << KM very little ES is formed and [E] = [E] T


              ET S  ES
and
           k2           k cat
      vo 
           KM           KM
 Kcat/KM is a measure of catalytic efficiency
         What is catalytic perfection?
                               k1k 2
When k2>>k-1 or the ratio                is maximum
                            k 1  k 2

        k cat          Or when every substrate that hits
 Then
               k1     the enzyme causes a reaction to
        KM             take place. This is catalytic
                       perfection.
 Diffusion-controlled limit- diffusion rate of a substrate
 is in the range of 108 to 109 M-1s-1. An enzyme lowers
 the transition state so there is no activation energy
 and the catalyzed rate is as fast as molecules collide.
          Reaction Mechanisms
         A: Sequential Reactions
• All substrates must combine with enzyme
  before reaction can occur
Bisubstrate reactions
Random Bisubstrate Reactions
           Ping-Pong Reactions

• Group transfer reactions
• One or more products released before all
  substrates added
     Kinetic data cannot unambiguously
      establish a reaction mechanism.




Although a phenomenological description can be
obtained the nature of the reaction intermediates
remain indeterminate and other independent
measurements are needed.
               Inhibition kinetics
There are three types of inhibition kinetics competitive,
mixed and uncompetitive.
•Competitive- Where the inhibitor competes with the
substrate.
Competitive Inhibition
KI 
     E I
      EI 
      Vm axS
vo 
     K M  S
     I 
  1  
     K 
        I 
HIV protease inhibitors
Competitive Inhibition: Lineweaver-Burke Plot
Uncompetitive Inhibition
Uncompetitive Inhibition: Lineweaver-Burke Plot
Mixed inhibition
 Mixed inhibition is when the inhibitor binds to the
 enzyme at a location distinct from the substrate
 binding site. The binding of the inhibitor will either
 alter the KM or Vmax or both.

      E I              K I 
                                  ES I
 KI 
       EI                        ESI 
       Vm axS             I 
                      1  
vo                       K 
     K M   S            I 
The effect of pH on kinetic parameters