Enzyme Kinetics

1
Enzyme Kinetics

• Chapter 8

2
Kinetics

• Study of rxn rates, changes with changes in
  experimental conditions
• Simplest rxn S ltgt P
• Rate measd by V velocity (M/sec)
• Depends on k, S

3
Michaelis-Menten

• Genl theory rxn rate w/ enzymatic catalysis
• Add E, ES to rxn
• E S ltgt ES ltgt E P
• Assume little reverse rxn E P ? ES
• So E S ltgt ES ? E P
• Assign rate constants k1, k-1, k2

4

• Assume Vo condition S gtgtgt E
• Since S used up during rxn, cant be limiting
• Assume
• All E goes to ES
• Assume fixed amt enzyme
• If all E ? ES, will see max rate of P formed
• At steady state, rate formn ES rate breakdown
  ES

5
Experl findings

• As incr S, V incrs linearly up to some max V
• At max V, little V incr regardless of S added

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Fig. 8-11
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M-M relates E, S, P ? experly provable
variables

• New constant KM (k2 k-1) / k1
• M-M eqn
• Vo (Vmax S) / (KM S)
• Quantitative relationship between
• Initial velocity
• Max rate of rxn
• Initial S

8
Experl definition of KM

• At ½ Vmax (substitute ½ Vmax for Vo)
• Divide by Vmax
• Solve for KM
• KM S
• So when Vo ½ Vmax , KM S

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Fig. 8-12
10
Difficult to determine variables from M-M plot

• Hard to measure small changes in V
• Use double reciprocal plot ? straight line
• Lineweaver-Burk (Box 8-1)

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Box 8-1
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KM (Table 8-6)

• S at which ½ enz active sites filled
• Related to rate constants
• In living cells, value close to S for that E
• Commonly enz active sites NOT saturated w/ S
• May describe affinity of E for S ONLY if k-1 gtgtgt
  k2
• Right half of rxn equation negligible
• KM k-1 / k1
• Describes rate formn, breakdown of ES
• Here, KM value indicates strength of binding E-S
• In real life, system is more complex

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Table 8-6
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Other kinetics variables (Table 8-7)

• Turnover
• S molecules converted ? P by 1 enz molecule per
  unit time
• Use when enz is fully satd w/ S
• Equals k2
• Can calc from Vmax if know ET

15
Other kinetics variables (contd)

• kcat
• Max catalytic rate for E when S saturating
• Equivalent to k of rate limiting step
• For M-M ( E S ltgt ES ltgt E P ),
  kcat k2
• Can be complex
• Book turnover

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Table 8-7
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Comparisons of catalytic
abilities

• Optimum KM, kcat values for each E
• Use ratio to compare catalytic efficiencies
• Max efficiency at kcat / KM 108 109 M-1 sec-1
• Velocity limited by E encounters w/ S
• Called Diffusion Controlled Limit

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Table 8-8
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Kinetics when gt 1 substrate

• Random order E can accept either S1 or S2 first
• Ordered mechanism E must accept S1 first,
  before S2 can bind
• Double displacement (or ping-pong) S1 must bind
  and P1 must be released before S2 can bind and P2
  is released

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Fig. 8-13
21
Fig. 8-13 (contd)
22
Inhibition

• Used by cell to control catalysis in metabolic
  pathways
• Used to alter catalysis by drugs, toxins
• Used as tools to study mechanisms
• Irreversible
• Reversible
• Includes competitive, noncompetitive,
  uncompetitive

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Irreversible inhibition

• Inhibitor binds tightly to enz
• Dissociates slowly or not at all
• Book example DIFP
• Includes suicide substrate inhibitors

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Fig. 8-16
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Reversible inhibition

• Inhibitor may bind at active site or some distal
  site
• Binding is reversible
• Temporarily inhibits E, S binding or proper rxn
• Can calculate KI
• Competitive
• Appear as S
• Bind active site
• So compete w/ S for active site
• Overcome w/ incrd S
• Affects KM, not Vmax

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Fig. 8-15
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Reversible inhibition (contd)

• Noncompetitive (Mixed)
• When S bound or not
• Bind at site away from active site
• Causes conforml change in E
• E inactivated when I bound
• Decrd E avail for binding S, rxn catalysis
• Not overcome w/ incrd S
• Affects both KM, Vmax
• Common when S1 S2

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Fig. 8-15 (contd)
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Reversible inhibition (contd)

• Uncompetitive
• Binds only when S already bound (so ES complex)
• Bind at site away from active site
• Causes conforml change, E inactivated
• Not overcome w/ incrd S
• Affects both KM, Vmax
• Common when S1 S2

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Fig. 8-15 (contd)
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Effect of pH on catalysis

• Optimum pH where maximal activity
• Aas impt to catalysis must maintain particular
  ionization
• Aas in other parts of enz impt to maintain
  folding, structure must also maintain partic.
  ionization
• Can predict impt aas by activity changes at
  different pHs (use pKa info)

32
Fig. 8-17