MBB 323

1
MBB 323

• Lecture 30
• Enzymes (Chapter 8)

2
Michaelis-Menten equation

• This approximation results in the
  Michaelis-Menten equation derived from
• AE lt-gt EA -gt P E
• (k1, k-1) k2
• Equation 1 VP k2 CEA
• Equation 2 CEA k1 CA CEinitial /(k1CA k-1
  k2),
• Equation 2 into equation 1 gives
• VP k2 k1 CA CEinitial /(k1CA k-1 k2),
• k2 CA CEinitial /(CA (k-1 k2)/ k1),
• The M-M equation
• VP VMax CA /(CA Km), with VMax k2
  CEinitial,Km (k-1 k2)/ k1
• We could define f(cat) VP /VMax in analogy to
  the f used in binding calculations. f(cat) 0 for
  no velocity and 1 for max velocity
• f(cat) CA /(CA Km), note the similarity
  with the binding calculation on slide 4 of
  this lecture.
• f(cat) 1/2 when CA Km

3
Michaelis-Menten equation

• This approximation results in the
  Michaelis-Menten equation derived from
• AE lt-gt EA -gt P E
• (k1, k-1) k2
• The M-M equation
• VP VMax CA /(CA Km), with VMax k2
  CEinitial,Km (k-1 k2)/ k1
• Define
• kcat VMax /CEinitial
• This is the maximum rate at which an enzyme can
  convert substrate into product (see overhead).

4
Michaelis-Menten equation

• The M-M equation at low substrate concentrations
  (p408), can be further approximated as
• VP VMax CA /(CA Km), in the limit CA tends
  to zero.
• VMax CA /Km,
• At high substrate concentration the equation also
  reduces to
• VP VMax CA /(CA Km), in the limit CA tends to
  infinity.
• VMax,
• Study p413-414 to understand how more complicated
  situations can also reduce to the M-M form when
  only working with steady-state kinetics.
• -This means that relaxation techniques are
  required to understand more complicated kinetic
  schemes.

5
Competitive Inhibition

• The M-M situation consider in the presence of a
  compound I that can bind to the enzyme but not
  react (p416-418).
• 1. A E lt-gt EA -gt P E
• (k1, k-1) k2
• 2. I E lt-gt EI
• KI
• We can write using KI CECI/CEI
• that the total amount of enzyme (which is
  conserved) is
• CEinitial CE CEA CEI
• CEinitial CE CEA CECI /KI
• CE (1CI /KI) CEA
• CE (CEinitial - CEA)/(1CI /KI) See slide 10
  lecture 29 and page 407-408.
• The net effect is to change to a new K(I)m Km
  (1CI /KI),
• This equation makes sense, K(0)m Km, also since
  the inhibition is competitive the maximum
  velocity of the reaction is unaffected even at
  high concentrations of the inhibitor (see
  overhead).

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Noncompetitive Inhibition

• A number of general and important classes which
  we will not treat in detail.
• Irreversible (i.e. covalent or suicide)
  modification of active site residues.
• -Glyceraldehyde-3-phosphate dehydrogenase (1 mM
  in the cell, substrate is lt 100 mM).
• (Aldehyde to acyl phosphate using NAD -gt NADH)
• -Enzyme is inhibited by sulfhydryl reactive
  compounds (iodoacetly derivatives).
• -Provides evidence of mechanism (thioester
  linkage of substrate to enzyme as intermediate
  step).
• Allosteric effects
• 2. Reversible binding, but not at the active
  site
• 3. Reversible binding, to the enzyme-substrate
  complex.