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6|	
  Enzymes	
  
© 2013 W. H. Freeman and Company
Catalysis	
  
• Think of sugar:
Our bodies use it to give energy within
seconds (converting it to CO2 + H2O)
But a bag of sugar can be on the shelve for
years even though the process is very
thermodynamically favorable
• The difference is catalysis
What	
  are	
  Enzymes?	
  
• Biological catalysts
•  Highly specialized proteins or RNA
•  Extraordinary catalytic power
•  High degree of specificity
•  Accelerate chemical reactions tremendously
•  Function in aqueous solutions under very mild
conditions of temperature and pH
•  Very few non-biological molecules have all these
properties
What	
  are	
  Enzymes?	
  
• Enzymes	
  are	
  catalysts	
  
•  Increase	
  reac0on	
  rates	
  without	
  being	
  used	
  up	
  
• Most	
  enzymes	
  are	
  globular	
  proteins	
  	
  
•  However,	
  some	
  RNA	
  (ribozymes	
  and	
  ribosomal	
  RNA)	
  also	
  
catalyze	
  reac0ons	
  
• Study	
  of	
  enzyma0c	
  processes	
  is	
  the	
  oldest	
  field	
  of	
  
biochemistry,	
  da0ng	
  back	
  to	
  late	
  1700s	
  
• Study	
  of	
  enzymes	
  has	
  dominated	
  biochemistry	
  in	
  the	
  
past	
  and	
  con0nues	
  to	
  do	
  so	
  
What	
  are	
  Enzymes?	
  
• Some enzymes need other chemical groups
•  Cofactors – either one or more inorganic ions
•  Coenzymes – complex organic or metalloorganic
molecules
•  Some enzymes require both
•  Prosthetic group – a coenzyme or cofactor that is
very tightly (or covalently) bound to an enzyme
•  Holoenzyme – a complete active enzyme with its
bound cofactor or coenzyme
•  Apoprotein – the protein part of a holoenzyme
What	
  are	
  Enzymes?	
  
•  Enzyme classification
•  Common names (DNA polymerase,
urease; pepsin; lysozyme, etc.)
•  6 classes each with subclasses
What	
  are	
  Enzymes?	
  
Group Reaction catalyzed Typical reaction
Enzyme example(s)
with trivial name
EC 1
Oxidoreductases
To catalyze oxidation/reduction reactions;
transfer of H and O atoms or electrons from
one substance to another
AH + B → A + BH (reduced)
A + O → AO (oxidized)
Dehydrogenase, oxidase
EC 2
Transferases
Transfer of a functional group from one
substance to another. The group may be
methyl-, acyl-, amino- or phosphate group
AB + C → A + BC Transaminase, kinase
EC 3
Hydrolases
Formation of two products from a substrate
by hydrolysis
AB + H2O → AOH + BH
Lipase, amylase,
peptidase
EC 4
Lyases
Non-hydrolytic addition or removal of groups
from substrates. C-C, C-N, C-O or C-S bonds
may be cleaved
RCOCOOH → RCOH + CO2 
or [X-A-B-Y] → [A=B + X-Y]
Decarboxylase
EC 5
Isomerases
Intramolecule rearrangement, i.e.
isomerization changes within a single
molecule
AB → BA Isomerase, mutase
EC 6
Ligases
Join together two molecules by synthesis of
new C-O, C-S, C-N or C-C bonds with
simultaneous breakdown of ATP
X + Y+ ATP → XY + ADP + Pi Synthetase
Example:	
  
•  ATP + D-glucose à ADP + D-glucose 6-phosphate
• Formal name: ATP:glucose phosphotransferase
• Common name: hexokinase
• E.C. number (enzyme commission): 2.7.1.1
2 à class name (transferases)
7 à subclass (phosphotransferases)
1 à phosphotransferase with –OH as acceptor
1 à D-glucose is the phosphoryl group acceptor
Why	
  biocatalysis	
  over	
  inorganic	
  catalysts?	
  
•  Greater	
  reac0on	
  specificity:	
  avoids	
  side	
  products	
  
•  Milder	
  reac0on	
  condi0ons:	
  conducive	
  to	
  condi0ons	
  in	
  	
  cells	
  
•  Higher	
  reac0on	
  rates:	
  in	
  a	
  biologically	
  useful	
  0meframe	
  
•  Capacity	
  for	
  regula0on:	
  control	
  of	
  biological	
  pathways	
  
COO
OH
O COO
COO
O COO
NH2
OOC
COO
O
OH
OH
COO
NH2
COO
-
-
-
-
-
-
-
-
Chorismate
mutase
•  Metabolites	
  have	
  many	
  
poten0al	
  pathways	
  of	
  
decomposi0on	
  	
  
	
  
	
  
•  Enzymes	
  make	
  the	
  
desired	
  one	
  most	
  
favorable	
  
Enzyma@c	
  Substrate	
  Selec@vity	
  
No	
  binding	
  
OOC NH3
H
OOC NH3
H
H
NH
H
OH
OH
H
OH
CH3
OOC NH3
H
OH
-
-
-
+
+
+
	
  	
  	
  Binding	
  but	
  no	
  reac0on	
  
Example:	
  Phenylalanine	
  hydroxylase	
  
6.2	
  How	
  Enzymes	
  Work	
  
• Recall:
• Active site
• Substrate
Binding of a substrate
to an enzyme
at the active site
(chemotrypsin)
Enzymes	
  affect	
  reac@on	
  rates	
  not	
  equilibria	
  
•  A simple enzyme reaction:
E + S ßà ES ßà EP ßà E + P
–  The function of a catalyst is to increase the
rate of the reaction.
–  Catalysts do not affect the equilibrium
–  Reaction coordinate diagram
Reaction coordinate diagram. The free energy of the system is plotted
against the progress of the reaction S → P.
Starting points for forward or
reverse reactions
–ve (eq. favors P)
Position  direction of
eq. is not affected by
ANY catalyst
Activation
energy
Enzymes	
  affect	
  reac@on	
  rates	
  not	
  equilibria	
  
•  A favorable equilibrium does not mean the S à P
conversion would be detectable
•  The rate of the reaction depends on the energy
barrier (the activation energy):
- a higher activation energy à slower reaction
•  Rates of reactions can be increased with:
- increasing temperature
- increasing pressure
- the addition of catalysts
Reaction coordinate diagram comparing enzyme-catalyzed and
uncatalyzed reactions
ΔGB
Reac@on	
  rates	
  	
  equilibria	
  have	
  precise	
  
thermodynamic	
  defini@ons	
  
S ßà P
•  K’eq = [P] / [S] (equilibrium
constant)
and ΔG’o = –RT ln K’eq
•  A large –ve free-energy change à a favorable
reaction equilibrium (but does not mean the
reaction will proceed at a high rate!)
•  The rate of any reaction depends on [reactant]
and k (rate constant)
•  V = k[S] (1st order reaction)
units of k (s–1)
•  V = k[S1][S2] (2nd order reaction)
units of k (M–1s–1)
Transi@on	
  State	
  Theory	
  
•  Slow reactions face significant activation
barriers that must be surmounted during the
reaction
k =
kBT
h
⎛
⎝
⎞
⎠
exp
−ΔG≠
RT
⎛
⎝
⎜ ⎞
⎠
⎟
– transition state theory is applicable for catalysis
– rate constants and free energies can be related
– Enzymes increase reaction rates (k) by
decreasing ΔG‡
kB: Boltzmann const.
h: Planck’s const.
k is inversely proportional to ΔG ‡ and exponential
è a lower activation energy means a faster rate
How	
  do	
  enzymes	
  lower	
  ΔG≠?
Enzymes	
  organize	
  reac0ve	
  groups	
  into	
  close	
  
proximity	
  and	
  proper	
  orienta0on	
  
• Uncatalyzed	
  bimolecular	
  reac0ons	
  	
  
	
  two	
  free	
  reactants	
  →	
  single	
  restricted	
  transi0on	
  state	
  	
  
	
  conversion	
  is	
  entropically	
  unfavorable	
  
• 	
  Uncatalyzed	
  unimolecular	
  reac0ons	
  	
  
	
  flexible	
  reactant	
  →	
  rigid	
  transi0on	
  state	
  conversion	
  is	
  	
  
	
  entropically	
  unfavorable	
  for	
  flexible	
  reactants	
  
• 	
  Catalyzed	
  reac0ons	
  
	
  Enzyme	
  uses	
  the	
  binding	
  energy	
  of	
  substrates	
  to	
  organize	
  	
  
	
  the	
  reactants	
  to	
  a	
  fairly	
  rigid	
  ES	
  complex	
  
	
  Entropy	
  cost	
  is	
  paid	
  during	
  binding	
  
	
  Rigid	
  reactant	
  complex	
  →	
  transi0on	
  state	
  conversion	
  is	
  entropically	
  OK	
  
	
  Weak	
  interac0ons	
  are	
  op0mized	
  in	
  the	
  TS	
  (ac0ve	
  sites	
  are	
  
	
   	
  complementary	
  to	
  TS)	
  	
  
Support	
  for	
  the	
  Proximity	
  Model	
  
The	
  rate	
  of	
  anhydride	
  forma0on	
  from	
  esters	
  and	
  carboxylates	
  
shows	
  a	
  strong	
  dependence	
  on	
  proximity	
  of	
  two	
  reac0ve	
  groups	
  
(work	
  by	
  Thomas	
  C.	
  Bruice’s	
  group).	
  
How	
  to	
  Lower	
  ΔG≠
Enzymes	
  bind	
  transi0on	
  states	
  best	
  
•  The	
  idea	
  was	
  proposed	
  by	
  Linus	
  Pauling	
  in	
  1946	
  
–  Enzyme	
  ac0ve	
  sites	
  are	
  complimentary	
  to	
  the	
  transi0on	
  
state	
  of	
  the	
  reac0on	
  
–  Enzymes	
  bind	
  transi@on	
  states	
  beer	
  than	
  substrates	
  
–  Stronger/addi0onal	
  interac0ons	
  with	
  the	
  transi0on	
  
state	
  as	
  compared	
  to	
  the	
  ground	
  state	
  lower	
  the	
  
ac0va0on	
  barrier	
  
Weak	
  interac@ons	
  are	
  op@mized	
  in	
  TS	
  
•  “Lock and key” model – substrate fits the
enzyme like a key in a lock
•  This hypothesis can be misleading in terms of
enzymatic reactions
•  An enzyme completely complementary to its
substrate is a very poor enzyme!
Illustra@on	
  of	
  TS	
  Stabiliza@on	
  Idea	
  
Imaginary	
  S@ckase
Rate	
  Enhancement	
  by	
  Enzymes	
  
Specific	
  cataly@c	
  groups	
  contribute	
  
to	
  catalysis	
  
•  When a substrate binds to an enzyme, catalytic
functional groups which are place in proper
positions help in the breaking and making
bonds by many mechanisms:
Cataly@c	
  Mechanisms	
  
– acid-­‐base	
  catalysis:	
  give	
  and	
  take	
  protons	
  
– covalent	
  catalysis:	
  change	
  reac0on	
  paths	
  
– metal	
  ion	
  catalysis:	
  use	
  redox	
  cofactors,	
  pKa	
  shi_ers	
  
– electrosta0c	
  catalysis:	
  preferen0al	
  interac0ons	
  with	
  TS	
  	
  
Acid-­‐base	
  Catalysis:	
  	
  
Chemical	
  Example	
  
Consider ester hydrolysis:
R
O CH3
O
R
O
CH3
O
OH H
+
R
O
OH
+ H-OH + + CH3OH
Water is a poor nucleophile, and methanol is a
poor leaving group
Aqueous hydrolysis can be catalyzed either by
acids or by bases
Enzymes can do acid and base catalysis simultaneously
How a catalyst stabilizes unfavorable charge development during
amide hydrolysis
(specific acid
catalysis)
(general acid
catalysis)
Not involved in
enzyme catalysis
In active sites, many aa
side chains can act as H+
donors or acceptors
Amino	
  Acids	
  in	
  	
  
General	
  Acid-­‐Base	
  Catalysis	
  
Covalent	
  Catalysis	
  
•  A	
  transient	
  covalent	
  bond	
  between	
  the	
  enzyme	
  and	
  
the	
  substrate	
  
•  Changes	
  the	
  reac0on	
  Pathway	
  
	
  
–  Uncatalyzed:	
  	
  	
  	
  
–  Catalyzed:	
  
•  Requires	
  a	
  nucleophile	
  on	
  the	
  enzyme	
  
–  Can	
  be	
  a	
  reac0ve	
  serine,	
  thiolate,	
  amine,	
  or	
  
carboxylate	
  
BAB—A
OH2
+→
B:XABX—A:XB—A
OH2
++→+→+
• The anhydride hydrolysis
reaction is catalyzed by
pyridine, a better nucleophile
than water (pKa=5.5).
• Hydrolysis is accelerated
because of charge loss in the
transition state makes pyridine
a good leaving group.
• The new reaction has a new
pathway which lowers the
activation energy
Covalent	
  Catalysis:	
  Chemical	
  Example	
  
CH3
O
O
CH3
O
N
CH3
O
O
N CH3
O
O
H H
N CH3
O
OH
N
CH3
O
O
H
+
..
fast
-
+ +
..
+
-
-+
..
CH3
O
O
CH3
O
CH3
O
O
CH3
O
O
H
+
- -+
H2O
slow + 2
Metal-­‐ion	
  Catalysis	
  
•  Weak bonding between metal and substrate
(similar to binding energy of substrate to
enzyme)
•  Redox reactions (metal ions can change their
oxidation state reversibly)
•  ~ 1/3 of all known enzymes need one or more
metal ions for catalysis 	
  
6.3	
  Enzyme	
  Kine@cs	
  
•  Kinetics is the study of the rate at which
compounds react
•  Rate of enzymatic reaction is affected by
– Enzyme
– Substrate
– Effectors
– Temperature
– Etc.
How	
  to	
  Do	
  Kine@c	
  Measurements	
  
Experiment:	
  
1)  Mix	
  enzyme	
  +	
  substrate	
  
2)  Record	
  rate	
  of	
  substrate	
  disappearance/product	
  forma0on	
  as	
  a	
  func0on	
  of	
  0me	
  
(the	
  velocity	
  of	
  reac0on)	
  
3)  Plot	
  ini0al	
  velocity	
  versus	
  substrate	
  concentra0on.	
  
4)  Change	
  substrate	
  concentra0on	
  and	
  repeat	
  
A tangent to each curve
taken at t = 0 defines
the initial velocity, V0,
of each reaction.
The rate of an enzyme-catalyzed reaction declines as
substrate is converted to product.
Effect	
  of	
  [S]	
  on	
  reac@on	
  rate	
  
• 	
  The	
  rela0onship	
  between	
  [S]	
  and	
  V0	
  is	
  similar	
  for	
  
most	
  enzymes	
  (rectangular	
  hyperbola)	
  
• 	
  Mathema0cally	
  expressed	
  by	
  Michaelis-­‐Menten	
  
equa0on:	
  	
  	
  
• Devia0ons	
  due	
  to:	
  
– 	
  limita0on	
  of	
  measurements	
  
– 	
  substrate	
  inhibi0on	
  
– 	
  substrate	
  prep	
  contains	
  inhibitors	
  
– 	
  enzyme	
  prep	
  contains	
  inhibitors	
  
][
][max
0
SK
SV
V
m +
=
Effect	
  of	
  Substrate	
  Concentra@on	
  
V0 approaches but never reaches Vmax
(Michaelis constant)
[S]  [E]
Satura@on	
  Kine@cs:	
  	
  
At	
  high	
  [S]	
  velocity	
  does	
  not	
  depend	
  on	
  
[S]	
  
At high [S], [S]  Km
the Km becomes insignificant è V0 = Vmax
At low [S], Km  [S], [S] becomes 
insignificantè V0 = Vmax[S]/Km
(V0 is linear with [S]).
Determina@on	
  of	
  Kine@c	
  Parameters	
  
Nonlinear	
  Michaelis-­‐Menten	
  plot	
  should	
  be	
  used	
  to	
  
calculate	
  parameters	
  Km	
  and	
  Vmax.	
  
	
  
Linearized	
  double-­‐reciprocal	
  (Lineweaver-­‐Burk)	
  plot	
  
is	
  good	
  for	
  analysis	
  of	
  two-­‐substrate	
  data	
  or	
  
inhibi0on.	
  	
  
	
  
Lineweaver-­‐Burk	
  Plot:	
  
Linearized,	
  Double-­‐Reciprocal	
  
][
][1
max0 SV
SK
V
m +
=
Deriva@on	
  of	
  Enzyme	
  Kine@cs	
  Equa@ons	
  
•  Simplest Model Mechanism: E + S → ES → E + P
–  One reactant, one product, no inhibitors
•  Total	
  enzyme	
  concentra0on	
  is	
  constant	
  
–  Mass	
  balance	
  equa0on	
  for	
  enzyme:	
  Et	
  =	
  [E]	
  +	
  [ES]	
  
–  It	
  is	
  also	
  implicitly	
  assumed	
  that:	
  St	
  =	
  [S]	
  +	
  [ES]	
  ≈	
  [S]	
  
•  Steady	
  state	
  assump@on	
  (ini0ally	
  [ES]	
  is	
  constant!)	
  
•  What	
  is	
  the	
  observed	
  rate?	
  
–  Rate	
  of	
  product	
  forma0on	
  	
  
←
k2
k–1
k1
0ESofbreakdownofrateESofformationofrate
][
=−=
dt
ESd
][20 ESk
dt
dP
V ==
Some	
  useful	
  equa@ons	
  
–  The	
  term:	
  (k–1	
  +	
  k2)/k1	
  is	
  Michaelis	
  constant	
  (Km)	
  for	
  a	
  
two-­‐step	
  reac0on	
  
–  The	
  maximum	
  velocity	
  of	
  an	
  enzyme	
  (Vmax)	
  for	
  a	
  two-­‐step	
  
reac0on	
  occurs	
  when	
  the	
  enzyme	
  is	
  fully	
  saturated	
  with	
  
substrate	
  (i.e.	
  when	
  Et	
  =	
  [ES])	
  è	
  Vmax	
  =	
  k2[Et]	
  
–  Km	
  and	
  Vmax	
  depend	
  on	
  the	
  reac0on	
  mechanisms	
  (2-­‐step,	
  
3-­‐step,	
  etc.)	
  à	
  more	
  appropriately	
  we	
  use	
  the	
  general	
  
rate	
  constant	
  (kcat,	
  turnover	
  number)	
  which	
  describes	
  the	
  
rate	
  limi@ng	
  step	
  of	
  the	
  reac0on	
  (for	
  the	
  previous	
  
example	
  kcat	
  =	
  k2)	
  	
  
	
  
–  kcat	
  is	
  equivalent	
  to	
  the	
  number	
  of	
  substrate	
  molecules	
  
converted	
  to	
  product	
  in	
  a	
  given	
  unit	
  of	
  0me	
  on	
  a	
  single	
  
enzyme	
  when	
  enzyme	
  is	
  saturated	
  with	
  substrate	
  
Carry	
  out	
  the	
  algebra	
  
•  The	
  final	
  form	
  in	
  case	
  of	
  a	
  single	
  substrate	
  is	
  
•  The	
  values	
  of	
  Km	
  and	
  kcat	
  together	
  are	
  useful	
  to	
  evaluate	
  
the	
  kine/c	
  efficiency	
  of	
  enzymes	
  
	
  *	
  Two	
  enzymes	
  catalyzing	
  different	
  reac0ons	
  may	
  have	
  
the	
  same	
  kcat	
  but	
  the	
  uncatalyzed	
  reac0on	
  rates	
  can	
  be	
  
different	
  è	
  the	
  rate	
  enhancement	
  rate	
  will	
  be	
  different	
  
	
  *	
  Specificity	
  constant	
  is	
  kcat/Km	
  (used	
  to	
  compare	
  the	
  
cataly0c	
  efficiencies	
  of	
  different	
  enzymes	
  or	
  the	
  turnover	
  
of	
  different	
  substrates	
  by	
  the	
  same	
  enzyme)	
  
	
  *	
  When	
  [S]	
  	
  Km…	
  What	
  happens	
  to	
  the	
  rate	
  equa0on?	
  	
  
Second	
  order	
  reac/on,	
  how?	
  	
  
][
]][[
0
SK
SEk
V
m
tcat
+
=
Enzyme	
  efficiency	
  is	
  limited	
  by	
  diffusion:	
  
kcat/KM	
  
•  Can	
  gain	
  efficiency	
  by	
  having	
  high	
  velocity	
  or	
  affinity	
  
for	
  substrate	
  
–  Catalase	
  vs.	
  acetylcholinesterase	
  
Km for an enzyme tends to be similar to its
substrate’s cellular concentration
Two-­‐Substrate	
  Reac@ons	
  
• The	
  rate	
  of	
  a	
  bisubstrate	
  reac0on	
  can	
  also	
  be	
  analyzed	
  by	
  
Michaelis-­‐Menten	
  kine0cs.	
  Enzymes	
  catalyzing	
  
polysubstrate	
  reac0ons	
  have	
  Km	
  for	
  each	
  of	
  their	
  
substrates	
  
• Kine0c	
  mechanism:	
  the	
  order	
  of	
  binding	
  of	
  substrates	
  
and	
  release	
  of	
  products	
  
• When	
  two	
  or	
  more	
  reactants	
  are	
  involved,	
  enzyme	
  
kine0cs	
  allows	
  to	
  dis0nguish	
  between	
  different	
  kine0c	
  
mechanisms	
  
–  	
  Sequen(al	
  mechanism	
  (involving	
  a	
  ternary	
  complex)	
  
–  	
  Ping-­‐Pong	
  (double	
  displacement)	
  mechanism	
  
ternary complex
Cleland Diagram
S1 S2
S2 S1
E
ES1
ES2
(ES1S2 ↔ EP1P2)
P1 P2
P2 P1
EP2
EP1
E
Cleland Diagram
S1 S2
E ES1 (ES1S2 ↔ EP1P2) E
P1 P2
P2 P1
EP2
EP1
S1 S2
E ES1 (ES1S2 ↔ EP1P2) E
P1 P2
EP2
OR
Cleland Diagram
S1
E (ES1↔E’P1) E’ (E’S2 ↔ EP2) E
P1 S2 P2
Sequen@al	
  Kine@c	
  Mechanism	
  
•  We	
  cannot	
  easily	
  dis0nguish	
  random	
  from	
  ordered	
  
•  Lineweaver-­‐Burk:	
  lines	
  intersect	
  
Ping-­‐Pong	
  Kine@c	
  Mechanism	
  
Lineweaver-­‐Burk:	
  lines	
  are	
  parallel	
  
Enzyme	
  Inhibi@on	
  
Inhibitors	
  are	
  compounds	
  that	
  decrease	
  enzyme’s	
  ac0vity	
  
	
  
• 	
  Irreversible	
  inhibitors	
  (inac0vators)	
  react	
  with	
  the	
  enzyme	
  
•  One	
  inhibitor	
  molecule	
  can	
  permanently	
  shut	
  off	
  one	
  enzyme	
  molecule	
  
•  They	
  are	
  o_en	
  powerful	
  toxins	
  but	
  also	
  may	
  be	
  used	
  as	
  drugs	
  
• 	
  Reversible	
  inhibitors	
  bind	
  to	
  and	
  can	
  dissociate	
  from	
  the	
  enzyme	
  
•  They	
  are	
  o_en	
  structural	
  analogs	
  of	
  substrates	
  or	
  products	
  
•  They	
  are	
  o_en	
  used	
  as	
  drugs	
  to	
  slow	
  down	
  a	
  specific	
  enzyme	
  
• 	
  Reversible	
  inhibitor	
  can	
  bind:	
  	
  
•  to	
  the	
  free	
  enzyme	
  and	
  prevent	
  the	
  binding	
  of	
  the	
  substrate	
  
•  to	
  the	
  enzyme-­‐substrate	
  complex	
  and	
  prevent	
  the	
  reac0on	
  
•  Competes	
  with	
  substrate	
  for	
  binding	
  	
  
–  Binds	
  ac0ve	
  site	
  
–  Does	
  not	
  affect	
  catalysis	
  
–  many	
  compe00ve	
  inhibitors	
  are	
  similar	
  in	
  
structure	
  to	
  the	
  substrate,	
  and	
  combine	
  with	
  the	
  
enzyme	
  to	
  form	
  an	
  EI	
  complex	
  
•  No	
  change	
  in	
  Vmax;	
  apparent	
  increase	
  in	
  Km	
  
•  Lineweaver-­‐Burk:	
  lines	
  intersect	
  at	
  the	
  y-­‐axis	
  
at	
  –1/Vmax	
  	
  
Compe@@ve	
  Inhibi@on	
  
Compe@@ve	
  Inhibi@on	
  
α = 1 + [I]/KI
KI = [E][I]/[EI]
αKm (the apparent Km) is
the Km measured in the
presence of an inhibitor
When [S]  [I] à
reaction shows normal Vmax
because the substrate
competes out the
inhibitor
No effect of the
competitive inhibitor on
Vmax
Compe@@ve	
  Inhibi@on	
  
Uncompe@@ve	
  Inhibi@on	
  
•  Only	
  binds	
  to	
  ES	
  complex	
  	
  
•  Does	
  not	
  affect	
  substrate	
  binding	
  
•  Inhibits	
  cataly0c	
  func0on	
  
•  Decrease	
  in	
  Vmax;	
  apparent	
  decrease	
  in	
  Km	
  
•  No	
  change	
  in	
  Km/Vmax	
  
•  Lineweaver-­‐Burk:	
  lines	
  are	
  parallel	
  
Uncompe@@ve	
  Inhibi@on	
  
α’ = 1 + [I]/KI
K’I = [ES][I]/[ESI]
At high [S], V0 à Vmax/α’
Therefore, an uncompetitive
inhibitor lowers the measured
Vmax
Km also decreases because 
[S] required to reach 
½ Vmax is reduced by 
the factor α’
Uncompe@@ve	
  Inhibi@on	
  
Mixed	
  Inhibi@on	
  
• Binds	
  enzyme	
  with	
  or	
  without	
  substrate	
  
―  Binds	
  to	
  regulatory	
  site	
  
―  Inhibits	
  both	
  substrate	
  binding	
  and	
  catalysis	
  
• Decrease	
  in	
  Vmax;	
  apparent	
  change	
  in	
  Km	
  
• Lineweaver-­‐Burk:	
  lines	
  intersect	
  le_	
  from	
  the	
  y-­‐axis	
  
• Noncompe00ve	
  inhibitors	
  are	
  mixed	
  inhibitors	
  such	
  
that	
  there	
  is	
  no	
  change	
  in	
  Km	
  	
  
Mixed	
  Inhibi@on	
  
Mixed	
  Inhibi@on	
  
A	
  special	
  case	
  
•  Noncompetitve inhibitors: a special (rare)
case of mixed inhibitors when α and α’ are
equal
•  x-intercept is –1/Km (no effect on Km with
increasing [I])
•  Vmax is lowered with increasing [I]	
  
1
Km
–
V0 =
Vmax [S]
αKm + α’[S]
When α = 1 à uncompetitive
When α’ = 1 à competitive
When α’ = α ≠ 1à noncompetitive
Enzyme	
  ac@vity	
  depends	
  on	
  pH	
  
• Enzymes	
  have	
  op0mum	
  pH	
  ranges	
  at	
  
which	
  their	
  ac0vity	
  is	
  maximal:	
  
–  Ac0vity	
  decreases	
  at	
  higher	
  or	
  lower	
  pH	
  values	
  
–  Due	
  to	
  the	
  physical	
  and	
  chemical	
  proper0es	
  of	
  
amino	
  acids	
  and	
  their	
  side	
  
chains	
  
6.5	
  Regulatory	
  Enzymes	
  
• Each cellular metabolism pathway has one or
more regulatory enzymes (enzymes that have a
greater effect on the rate of the overall sequence)
• They show increased or decreased activities in
response to certain signals (function as switches)
• Generally, the first enzyme in a pathway is a
regulatory enzyme (not always true!)
Regulatory	
  Enzymes	
  
• Classes of regulatory enzymes:
v allosteric enzymes (affected by reversible
noncovalent binding of allosteric modulators)
v nonallosteric/covalent enzymes (affected by
reversible covalent modification)
v regulatory protein binding enzymes
(stimulated or inhibited by the binding of separate
regulatory proteins)
v proteolytically activated enzymes (activated
by the removal of some segments of their
polypeptide sequence by proteolytic cleavage)
Allosteric	
  Enzymes	
  
• Allosteric enzymes function through reversible,
noncovalent binding of regulatory compounds
(allosteric modulators, aka allosteric effectors)
• Modulators can be stimulatory or inhibitory
• Sometimes, the regulatory site and the catalytic
site are in different subunits
• Recall: homotropic and heterotropic enzymes
• Conformational change from an inactive T state
to an active R state and vice versa
(C) catalytic (R) regulatory subunits
• Not to be confused
with uncompetitive
or mixed
inhibitors…
• Those inhibitors
are kinetically
distinct and they do
not necessarily
induce
conformational
changes
Allosteric	
  Enzymes	
  
• Allosteric enzymes are generally larger and more
complex than nonallosteric enzymes with more
subunits
• Aspartate transcarbamoylase (ATCase) catalyzes an
early step in pyrimidine nucleotide biosynthesis
• Allosteric enzyme, composed of 6 catalytic subunits
(organized as 2 trimeric complexes) and 6 regulatory
subunits (organized as 3 dimeric complexes)
• Catalytic subunits function cooperatively
• Regulatory subunits have binding sites for ATP (+ve
regulator) and CTP (–ve regulator)
ATCase	
  
• CTP is an end product of the pathway, negative feedback
• ATP signifies energy abundance à need for growth à need for RNA
transcription and DNA replication à need for new nucleotides
Regulated	
  Steps	
  Are	
  Catalyzed	
  by	
  
Allosteric	
  Enzymes	
  
• Feedback inhibition – regulatory enzymes are
specifically inhibited by the end product of the
pathway whenever the concentration of the end
product exceeds the cell’s requirements
• Heterotropic allosteric inhibition
Threonine dehydratase (E1) is
specifically inhibited allosterically
by L-isoleucine, the end product of
the sequence, but not by any of the
four intermediates (A to D).
Ile does not binds to the active site
but to a regulatory site on the
enzyme.
The binding is reversible: if
[Ile]↓à rate of Thr dehydration ↑
Kine@c	
  Proper@es	
  of	
  Allosteric	
  Enzymes	
  
Diverge	
  from	
  Michaelis-­‐Menten	
  
Behavior	
  
• For some allosteric enzymes, plots of V0 vs [S] give
sigmoid (not hyperbolic) saturation curves
• In a sigmoid curve, the [S] that gives ½ Vmax is K0.5
• Homotropic allosteric enzymes are multisubunit
proteins. The same binding site on each subunit
serves as both an active and regulatory site
• Heterotropic allosteric enzymes, an activator causes
the curve to be more hyperbolic (also ↓in K0.5; no
change in Vmax) and an inhibitor produces a more
sigmoid curve (↑ in K0.5; no change in Vmax)
The sigmoid curve of a homotropic enzyme, in which the substrate also
serves as a positive (stimulatory) modulator, or activator
Small change in [S] leads to a
large change in activity
Noncovalent	
  Modifica@on:	
  
Allosteric	
  Regulators	
  
The	
  kine0cs	
  of	
  allosteric	
  regulators	
  differ	
  from	
  
Michaelis-­‐Menten	
  kine0cs.	
  
	
  
A less common type of modulation, in which Vmax is changed and K0.5 is
nearly constant.
Some	
  Enzymes	
  Are	
  Regulated	
  by	
  
Reversible	
  Covalent	
  Modifica@on	
  
• Over 500 different kinds of covalent modifications
are found in proteins
• Covalent bonds form (reversibly) between
regulatory molecules and aa residues in proteins
• When an aa residue is modified, a new aa with
changed properties has effectively been introduced in
the enzyme (for instance, Ser-OH can be
phosphorylated to Ser-O-PO3
– changing the
properties à conformation à function, etc.)
Some	
  Reversible	
  Covalent	
  Modifica@ons	
  
Example	
  on	
  Protein	
  Phosphoryla@on	
  
• Protein kinases – add phosphate groups on
specific aa residues of other proteins
• Protein phosphatases – remove phosphate
groups from phosphorylated proteins
• Glucosen + Pi à glucosen-1 + glucose 1-phosphate
(Glycogen)
glycogen
phosphorylase
The less active form of the enzyme, phosphorylase b, specific
Ser residues, one on each subunit, are not phosphorylated.
In the more active form of the enzyme, phosphorylase a, specific
Ser residues, one on each subunit, are phosphorylated.
Phosphorylase b and phosphorylase a can be interconverted.
Phosphorylase b can be converted (activated) to phosphorylase a
by the action of phosphorylase kinase.
Phosphorylase a is converted to the less active phosphorylase b by
enzymatic loss of these phosphoryl groups, promoted by
phosphoprotein phosphatase 1 (PP1).
• The activity of both forms of the enzyme is allosterically
regulated by an activator (AMP) and by inhibitors (glucose
6-phosphate and ATP) that bind to separate sites on the
enzyme
• The activities of phosphorylase kinase and PP1 are also
regulated via a short pathway that responds to the
hormones glucagon and epinephrine
 
•  When	
  blood	
  sugar	
  levels	
  are	
  low,	
  the	
  pancreas	
  and	
  adrenal	
  glands	
  
secrete	
  glucagon	
  and	
  epinephrine.	
  	
  
•  Epinephrine	
  binds	
  to	
  its	
  receptor	
  in	
  muscle	
  and	
  some	
  other	
  
0ssues,	
  and	
  ac0vates	
  the	
  enzyme	
  adenylyl	
  cyclase.	
  	
  
•  Glucagon	
  plays	
  a	
  similar	
  role,	
  binding	
  to	
  receptors	
  in	
  the	
  liver.	
  	
  
•  This	
  leads	
  to	
  the	
  synthesis	
  of	
  high	
  levels	
  of	
  cAMP,	
  ac0va0ng	
  the	
  
enzyme	
  cAMP-­‐dependent	
  protein	
  kinase	
  (PKA).	
  	
  
•  PKA	
  phosphorylates	
  several	
  target	
  proteins,	
  among	
  them	
  
phosphorylase	
  kinase	
  and	
  phosphoprotein	
  phosphatase	
  inhibitor	
  
1	
  (PPI-­‐1).	
  	
  
•  The	
  phosphorylated	
  phosphorylase	
  kinase	
  is	
  ac0vated	
  and	
  in	
  turn	
  
phosphorylates	
  and	
  ac0vates	
  glycogen	
  phosphorylase.	
  	
  
•  At	
  the	
  same	
  0me,	
  the	
  phosphorylated	
  PPI-­‐1	
  interacts	
  with	
  and	
  
inhibits	
  PP1.	
  	
  
•  PPI-­‐1	
  also	
  keeps	
  itself	
  ac0ve	
  (phosphorylated)	
  by	
  inhibi0ng	
  
phosphoprotein	
  phosphatase	
  2B	
  (PP2B),	
  the	
  enzyme	
  that	
  
dephosphorylates	
  (inac0vates)	
  it.	
  	
  
•  In	
  this	
  way,	
  the	
  equilibrium	
  between	
  the	
  a	
  and	
  b	
  forms	
  of	
  
glycogen	
  phosphorylase	
  is	
  shi_ed	
  decisively	
  toward	
  the	
  more	
  
ac0ve	
  glycogen	
  phosphorylase	
  a	
  

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Chapter6 enzymes

  • 1. 6|  Enzymes   © 2013 W. H. Freeman and Company
  • 2. Catalysis   • Think of sugar: Our bodies use it to give energy within seconds (converting it to CO2 + H2O) But a bag of sugar can be on the shelve for years even though the process is very thermodynamically favorable • The difference is catalysis
  • 3. What  are  Enzymes?   • Biological catalysts •  Highly specialized proteins or RNA •  Extraordinary catalytic power •  High degree of specificity •  Accelerate chemical reactions tremendously •  Function in aqueous solutions under very mild conditions of temperature and pH •  Very few non-biological molecules have all these properties
  • 4. What  are  Enzymes?   • Enzymes  are  catalysts   •  Increase  reac0on  rates  without  being  used  up   • Most  enzymes  are  globular  proteins     •  However,  some  RNA  (ribozymes  and  ribosomal  RNA)  also   catalyze  reac0ons   • Study  of  enzyma0c  processes  is  the  oldest  field  of   biochemistry,  da0ng  back  to  late  1700s   • Study  of  enzymes  has  dominated  biochemistry  in  the   past  and  con0nues  to  do  so  
  • 5. What  are  Enzymes?   • Some enzymes need other chemical groups •  Cofactors – either one or more inorganic ions •  Coenzymes – complex organic or metalloorganic molecules •  Some enzymes require both •  Prosthetic group – a coenzyme or cofactor that is very tightly (or covalently) bound to an enzyme •  Holoenzyme – a complete active enzyme with its bound cofactor or coenzyme •  Apoprotein – the protein part of a holoenzyme
  • 6. What  are  Enzymes?   •  Enzyme classification •  Common names (DNA polymerase, urease; pepsin; lysozyme, etc.) •  6 classes each with subclasses
  • 7. What  are  Enzymes?   Group Reaction catalyzed Typical reaction Enzyme example(s) with trivial name EC 1 Oxidoreductases To catalyze oxidation/reduction reactions; transfer of H and O atoms or electrons from one substance to another AH + B → A + BH (reduced) A + O → AO (oxidized) Dehydrogenase, oxidase EC 2 Transferases Transfer of a functional group from one substance to another. The group may be methyl-, acyl-, amino- or phosphate group AB + C → A + BC Transaminase, kinase EC 3 Hydrolases Formation of two products from a substrate by hydrolysis AB + H2O → AOH + BH Lipase, amylase, peptidase EC 4 Lyases Non-hydrolytic addition or removal of groups from substrates. C-C, C-N, C-O or C-S bonds may be cleaved RCOCOOH → RCOH + CO2 or [X-A-B-Y] → [A=B + X-Y] Decarboxylase EC 5 Isomerases Intramolecule rearrangement, i.e. isomerization changes within a single molecule AB → BA Isomerase, mutase EC 6 Ligases Join together two molecules by synthesis of new C-O, C-S, C-N or C-C bonds with simultaneous breakdown of ATP X + Y+ ATP → XY + ADP + Pi Synthetase
  • 8. Example:   •  ATP + D-glucose à ADP + D-glucose 6-phosphate • Formal name: ATP:glucose phosphotransferase • Common name: hexokinase • E.C. number (enzyme commission): 2.7.1.1 2 à class name (transferases) 7 à subclass (phosphotransferases) 1 à phosphotransferase with –OH as acceptor 1 à D-glucose is the phosphoryl group acceptor
  • 9. Why  biocatalysis  over  inorganic  catalysts?   •  Greater  reac0on  specificity:  avoids  side  products   •  Milder  reac0on  condi0ons:  conducive  to  condi0ons  in    cells   •  Higher  reac0on  rates:  in  a  biologically  useful  0meframe   •  Capacity  for  regula0on:  control  of  biological  pathways   COO OH O COO COO O COO NH2 OOC COO O OH OH COO NH2 COO - - - - - - - - Chorismate mutase •  Metabolites  have  many   poten0al  pathways  of   decomposi0on         •  Enzymes  make  the   desired  one  most   favorable  
  • 10. Enzyma@c  Substrate  Selec@vity   No  binding   OOC NH3 H OOC NH3 H H NH H OH OH H OH CH3 OOC NH3 H OH - - - + + +      Binding  but  no  reac0on   Example:  Phenylalanine  hydroxylase  
  • 11. 6.2  How  Enzymes  Work   • Recall: • Active site • Substrate Binding of a substrate to an enzyme at the active site (chemotrypsin)
  • 12. Enzymes  affect  reac@on  rates  not  equilibria   •  A simple enzyme reaction: E + S ßà ES ßà EP ßà E + P –  The function of a catalyst is to increase the rate of the reaction. –  Catalysts do not affect the equilibrium –  Reaction coordinate diagram
  • 13. Reaction coordinate diagram. The free energy of the system is plotted against the progress of the reaction S → P. Starting points for forward or reverse reactions –ve (eq. favors P) Position direction of eq. is not affected by ANY catalyst Activation energy
  • 14. Enzymes  affect  reac@on  rates  not  equilibria   •  A favorable equilibrium does not mean the S à P conversion would be detectable •  The rate of the reaction depends on the energy barrier (the activation energy): - a higher activation energy à slower reaction •  Rates of reactions can be increased with: - increasing temperature - increasing pressure - the addition of catalysts
  • 15. Reaction coordinate diagram comparing enzyme-catalyzed and uncatalyzed reactions ΔGB
  • 16. Reac@on  rates    equilibria  have  precise   thermodynamic  defini@ons   S ßà P •  K’eq = [P] / [S] (equilibrium constant) and ΔG’o = –RT ln K’eq •  A large –ve free-energy change à a favorable reaction equilibrium (but does not mean the reaction will proceed at a high rate!) •  The rate of any reaction depends on [reactant] and k (rate constant) •  V = k[S] (1st order reaction) units of k (s–1) •  V = k[S1][S2] (2nd order reaction) units of k (M–1s–1)
  • 17. Transi@on  State  Theory   •  Slow reactions face significant activation barriers that must be surmounted during the reaction k = kBT h ⎛ ⎝ ⎞ ⎠ exp −ΔG≠ RT ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ – transition state theory is applicable for catalysis – rate constants and free energies can be related – Enzymes increase reaction rates (k) by decreasing ΔG‡ kB: Boltzmann const. h: Planck’s const. k is inversely proportional to ΔG ‡ and exponential è a lower activation energy means a faster rate
  • 18. How  do  enzymes  lower  ΔG≠? Enzymes  organize  reac0ve  groups  into  close   proximity  and  proper  orienta0on   • Uncatalyzed  bimolecular  reac0ons      two  free  reactants  →  single  restricted  transi0on  state      conversion  is  entropically  unfavorable   •   Uncatalyzed  unimolecular  reac0ons      flexible  reactant  →  rigid  transi0on  state  conversion  is      entropically  unfavorable  for  flexible  reactants   •   Catalyzed  reac0ons    Enzyme  uses  the  binding  energy  of  substrates  to  organize      the  reactants  to  a  fairly  rigid  ES  complex    Entropy  cost  is  paid  during  binding    Rigid  reactant  complex  →  transi0on  state  conversion  is  entropically  OK    Weak  interac0ons  are  op0mized  in  the  TS  (ac0ve  sites  are      complementary  to  TS)    
  • 19. Support  for  the  Proximity  Model   The  rate  of  anhydride  forma0on  from  esters  and  carboxylates   shows  a  strong  dependence  on  proximity  of  two  reac0ve  groups   (work  by  Thomas  C.  Bruice’s  group).  
  • 20. How  to  Lower  ΔG≠ Enzymes  bind  transi0on  states  best   •  The  idea  was  proposed  by  Linus  Pauling  in  1946   –  Enzyme  ac0ve  sites  are  complimentary  to  the  transi0on   state  of  the  reac0on   –  Enzymes  bind  transi@on  states  beer  than  substrates   –  Stronger/addi0onal  interac0ons  with  the  transi0on   state  as  compared  to  the  ground  state  lower  the   ac0va0on  barrier  
  • 21. Weak  interac@ons  are  op@mized  in  TS   •  “Lock and key” model – substrate fits the enzyme like a key in a lock •  This hypothesis can be misleading in terms of enzymatic reactions •  An enzyme completely complementary to its substrate is a very poor enzyme!
  • 22. Illustra@on  of  TS  Stabiliza@on  Idea   Imaginary  S@ckase
  • 23. Rate  Enhancement  by  Enzymes  
  • 24. Specific  cataly@c  groups  contribute   to  catalysis   •  When a substrate binds to an enzyme, catalytic functional groups which are place in proper positions help in the breaking and making bonds by many mechanisms:
  • 25. Cataly@c  Mechanisms   – acid-­‐base  catalysis:  give  and  take  protons   – covalent  catalysis:  change  reac0on  paths   – metal  ion  catalysis:  use  redox  cofactors,  pKa  shi_ers   – electrosta0c  catalysis:  preferen0al  interac0ons  with  TS    
  • 26. Acid-­‐base  Catalysis:     Chemical  Example   Consider ester hydrolysis: R O CH3 O R O CH3 O OH H + R O OH + H-OH + + CH3OH Water is a poor nucleophile, and methanol is a poor leaving group Aqueous hydrolysis can be catalyzed either by acids or by bases Enzymes can do acid and base catalysis simultaneously
  • 27. How a catalyst stabilizes unfavorable charge development during amide hydrolysis
  • 28. (specific acid catalysis) (general acid catalysis) Not involved in enzyme catalysis In active sites, many aa side chains can act as H+ donors or acceptors
  • 29.
  • 30. Amino  Acids  in     General  Acid-­‐Base  Catalysis  
  • 31. Covalent  Catalysis   •  A  transient  covalent  bond  between  the  enzyme  and   the  substrate   •  Changes  the  reac0on  Pathway     –  Uncatalyzed:         –  Catalyzed:   •  Requires  a  nucleophile  on  the  enzyme   –  Can  be  a  reac0ve  serine,  thiolate,  amine,  or   carboxylate   BAB—A OH2 +→ B:XABX—A:XB—A OH2 ++→+→+
  • 32. • The anhydride hydrolysis reaction is catalyzed by pyridine, a better nucleophile than water (pKa=5.5). • Hydrolysis is accelerated because of charge loss in the transition state makes pyridine a good leaving group. • The new reaction has a new pathway which lowers the activation energy Covalent  Catalysis:  Chemical  Example   CH3 O O CH3 O N CH3 O O N CH3 O O H H N CH3 O OH N CH3 O O H + .. fast - + + .. + - -+ .. CH3 O O CH3 O CH3 O O CH3 O O H + - -+ H2O slow + 2
  • 33. Metal-­‐ion  Catalysis   •  Weak bonding between metal and substrate (similar to binding energy of substrate to enzyme) •  Redox reactions (metal ions can change their oxidation state reversibly) •  ~ 1/3 of all known enzymes need one or more metal ions for catalysis  
  • 34. 6.3  Enzyme  Kine@cs   •  Kinetics is the study of the rate at which compounds react •  Rate of enzymatic reaction is affected by – Enzyme – Substrate – Effectors – Temperature – Etc.
  • 35.
  • 36. How  to  Do  Kine@c  Measurements   Experiment:   1)  Mix  enzyme  +  substrate   2)  Record  rate  of  substrate  disappearance/product  forma0on  as  a  func0on  of  0me   (the  velocity  of  reac0on)   3)  Plot  ini0al  velocity  versus  substrate  concentra0on.   4)  Change  substrate  concentra0on  and  repeat   A tangent to each curve taken at t = 0 defines the initial velocity, V0, of each reaction. The rate of an enzyme-catalyzed reaction declines as substrate is converted to product.
  • 37. Effect  of  [S]  on  reac@on  rate   •   The  rela0onship  between  [S]  and  V0  is  similar  for   most  enzymes  (rectangular  hyperbola)   •   Mathema0cally  expressed  by  Michaelis-­‐Menten   equa0on:       • Devia0ons  due  to:   –   limita0on  of  measurements   –   substrate  inhibi0on   –   substrate  prep  contains  inhibitors   –   enzyme  prep  contains  inhibitors   ][ ][max 0 SK SV V m + =
  • 38. Effect  of  Substrate  Concentra@on   V0 approaches but never reaches Vmax (Michaelis constant) [S] [E]
  • 39. Satura@on  Kine@cs:     At  high  [S]  velocity  does  not  depend  on   [S]   At high [S], [S] Km the Km becomes insignificant è V0 = Vmax At low [S], Km [S], [S] becomes insignificantè V0 = Vmax[S]/Km (V0 is linear with [S]).
  • 40. Determina@on  of  Kine@c  Parameters   Nonlinear  Michaelis-­‐Menten  plot  should  be  used  to   calculate  parameters  Km  and  Vmax.     Linearized  double-­‐reciprocal  (Lineweaver-­‐Burk)  plot   is  good  for  analysis  of  two-­‐substrate  data  or   inhibi0on.      
  • 41. Lineweaver-­‐Burk  Plot:   Linearized,  Double-­‐Reciprocal   ][ ][1 max0 SV SK V m + =
  • 42. Deriva@on  of  Enzyme  Kine@cs  Equa@ons   •  Simplest Model Mechanism: E + S → ES → E + P –  One reactant, one product, no inhibitors •  Total  enzyme  concentra0on  is  constant   –  Mass  balance  equa0on  for  enzyme:  Et  =  [E]  +  [ES]   –  It  is  also  implicitly  assumed  that:  St  =  [S]  +  [ES]  ≈  [S]   •  Steady  state  assump@on  (ini0ally  [ES]  is  constant!)   •  What  is  the  observed  rate?   –  Rate  of  product  forma0on     ← k2 k–1 k1 0ESofbreakdownofrateESofformationofrate ][ =−= dt ESd ][20 ESk dt dP V ==
  • 43. Some  useful  equa@ons   –  The  term:  (k–1  +  k2)/k1  is  Michaelis  constant  (Km)  for  a   two-­‐step  reac0on   –  The  maximum  velocity  of  an  enzyme  (Vmax)  for  a  two-­‐step   reac0on  occurs  when  the  enzyme  is  fully  saturated  with   substrate  (i.e.  when  Et  =  [ES])  è  Vmax  =  k2[Et]   –  Km  and  Vmax  depend  on  the  reac0on  mechanisms  (2-­‐step,   3-­‐step,  etc.)  à  more  appropriately  we  use  the  general   rate  constant  (kcat,  turnover  number)  which  describes  the   rate  limi@ng  step  of  the  reac0on  (for  the  previous   example  kcat  =  k2)       –  kcat  is  equivalent  to  the  number  of  substrate  molecules   converted  to  product  in  a  given  unit  of  0me  on  a  single   enzyme  when  enzyme  is  saturated  with  substrate  
  • 44. Carry  out  the  algebra   •  The  final  form  in  case  of  a  single  substrate  is   •  The  values  of  Km  and  kcat  together  are  useful  to  evaluate   the  kine/c  efficiency  of  enzymes    *  Two  enzymes  catalyzing  different  reac0ons  may  have   the  same  kcat  but  the  uncatalyzed  reac0on  rates  can  be   different  è  the  rate  enhancement  rate  will  be  different    *  Specificity  constant  is  kcat/Km  (used  to  compare  the   cataly0c  efficiencies  of  different  enzymes  or  the  turnover   of  different  substrates  by  the  same  enzyme)    *  When  [S]    Km…  What  happens  to  the  rate  equa0on?     Second  order  reac/on,  how?     ][ ]][[ 0 SK SEk V m tcat + =
  • 45. Enzyme  efficiency  is  limited  by  diffusion:   kcat/KM   •  Can  gain  efficiency  by  having  high  velocity  or  affinity   for  substrate   –  Catalase  vs.  acetylcholinesterase   Km for an enzyme tends to be similar to its substrate’s cellular concentration
  • 46. Two-­‐Substrate  Reac@ons   • The  rate  of  a  bisubstrate  reac0on  can  also  be  analyzed  by   Michaelis-­‐Menten  kine0cs.  Enzymes  catalyzing   polysubstrate  reac0ons  have  Km  for  each  of  their   substrates   • Kine0c  mechanism:  the  order  of  binding  of  substrates   and  release  of  products   • When  two  or  more  reactants  are  involved,  enzyme   kine0cs  allows  to  dis0nguish  between  different  kine0c   mechanisms   –   Sequen(al  mechanism  (involving  a  ternary  complex)   –   Ping-­‐Pong  (double  displacement)  mechanism  
  • 48. Cleland Diagram S1 S2 S2 S1 E ES1 ES2 (ES1S2 ↔ EP1P2) P1 P2 P2 P1 EP2 EP1 E
  • 49. Cleland Diagram S1 S2 E ES1 (ES1S2 ↔ EP1P2) E P1 P2 P2 P1 EP2 EP1 S1 S2 E ES1 (ES1S2 ↔ EP1P2) E P1 P2 EP2 OR
  • 50. Cleland Diagram S1 E (ES1↔E’P1) E’ (E’S2 ↔ EP2) E P1 S2 P2
  • 51. Sequen@al  Kine@c  Mechanism   •  We  cannot  easily  dis0nguish  random  from  ordered   •  Lineweaver-­‐Burk:  lines  intersect  
  • 52. Ping-­‐Pong  Kine@c  Mechanism   Lineweaver-­‐Burk:  lines  are  parallel  
  • 53. Enzyme  Inhibi@on   Inhibitors  are  compounds  that  decrease  enzyme’s  ac0vity     •   Irreversible  inhibitors  (inac0vators)  react  with  the  enzyme   •  One  inhibitor  molecule  can  permanently  shut  off  one  enzyme  molecule   •  They  are  o_en  powerful  toxins  but  also  may  be  used  as  drugs   •   Reversible  inhibitors  bind  to  and  can  dissociate  from  the  enzyme   •  They  are  o_en  structural  analogs  of  substrates  or  products   •  They  are  o_en  used  as  drugs  to  slow  down  a  specific  enzyme   •   Reversible  inhibitor  can  bind:     •  to  the  free  enzyme  and  prevent  the  binding  of  the  substrate   •  to  the  enzyme-­‐substrate  complex  and  prevent  the  reac0on  
  • 54. •  Competes  with  substrate  for  binding     –  Binds  ac0ve  site   –  Does  not  affect  catalysis   –  many  compe00ve  inhibitors  are  similar  in   structure  to  the  substrate,  and  combine  with  the   enzyme  to  form  an  EI  complex   •  No  change  in  Vmax;  apparent  increase  in  Km   •  Lineweaver-­‐Burk:  lines  intersect  at  the  y-­‐axis   at  –1/Vmax     Compe@@ve  Inhibi@on  
  • 56. α = 1 + [I]/KI KI = [E][I]/[EI] αKm (the apparent Km) is the Km measured in the presence of an inhibitor When [S] [I] à reaction shows normal Vmax because the substrate competes out the inhibitor No effect of the competitive inhibitor on Vmax
  • 58. Uncompe@@ve  Inhibi@on   •  Only  binds  to  ES  complex     •  Does  not  affect  substrate  binding   •  Inhibits  cataly0c  func0on   •  Decrease  in  Vmax;  apparent  decrease  in  Km   •  No  change  in  Km/Vmax   •  Lineweaver-­‐Burk:  lines  are  parallel  
  • 60. α’ = 1 + [I]/KI K’I = [ES][I]/[ESI] At high [S], V0 à Vmax/α’ Therefore, an uncompetitive inhibitor lowers the measured Vmax Km also decreases because [S] required to reach ½ Vmax is reduced by the factor α’ Uncompe@@ve  Inhibi@on  
  • 61. Mixed  Inhibi@on   • Binds  enzyme  with  or  without  substrate   ―  Binds  to  regulatory  site   ―  Inhibits  both  substrate  binding  and  catalysis   • Decrease  in  Vmax;  apparent  change  in  Km   • Lineweaver-­‐Burk:  lines  intersect  le_  from  the  y-­‐axis   • Noncompe00ve  inhibitors  are  mixed  inhibitors  such   that  there  is  no  change  in  Km    
  • 64. A  special  case   •  Noncompetitve inhibitors: a special (rare) case of mixed inhibitors when α and α’ are equal •  x-intercept is –1/Km (no effect on Km with increasing [I]) •  Vmax is lowered with increasing [I]  
  • 66. V0 = Vmax [S] αKm + α’[S] When α = 1 à uncompetitive When α’ = 1 à competitive When α’ = α ≠ 1à noncompetitive
  • 67. Enzyme  ac@vity  depends  on  pH   • Enzymes  have  op0mum  pH  ranges  at   which  their  ac0vity  is  maximal:   –  Ac0vity  decreases  at  higher  or  lower  pH  values   –  Due  to  the  physical  and  chemical  proper0es  of   amino  acids  and  their  side   chains  
  • 68. 6.5  Regulatory  Enzymes   • Each cellular metabolism pathway has one or more regulatory enzymes (enzymes that have a greater effect on the rate of the overall sequence) • They show increased or decreased activities in response to certain signals (function as switches) • Generally, the first enzyme in a pathway is a regulatory enzyme (not always true!)
  • 69. Regulatory  Enzymes   • Classes of regulatory enzymes: v allosteric enzymes (affected by reversible noncovalent binding of allosteric modulators) v nonallosteric/covalent enzymes (affected by reversible covalent modification) v regulatory protein binding enzymes (stimulated or inhibited by the binding of separate regulatory proteins) v proteolytically activated enzymes (activated by the removal of some segments of their polypeptide sequence by proteolytic cleavage)
  • 70. Allosteric  Enzymes   • Allosteric enzymes function through reversible, noncovalent binding of regulatory compounds (allosteric modulators, aka allosteric effectors) • Modulators can be stimulatory or inhibitory • Sometimes, the regulatory site and the catalytic site are in different subunits • Recall: homotropic and heterotropic enzymes • Conformational change from an inactive T state to an active R state and vice versa
  • 71. (C) catalytic (R) regulatory subunits • Not to be confused with uncompetitive or mixed inhibitors… • Those inhibitors are kinetically distinct and they do not necessarily induce conformational changes
  • 72. Allosteric  Enzymes   • Allosteric enzymes are generally larger and more complex than nonallosteric enzymes with more subunits • Aspartate transcarbamoylase (ATCase) catalyzes an early step in pyrimidine nucleotide biosynthesis • Allosteric enzyme, composed of 6 catalytic subunits (organized as 2 trimeric complexes) and 6 regulatory subunits (organized as 3 dimeric complexes) • Catalytic subunits function cooperatively • Regulatory subunits have binding sites for ATP (+ve regulator) and CTP (–ve regulator)
  • 73. ATCase   • CTP is an end product of the pathway, negative feedback • ATP signifies energy abundance à need for growth à need for RNA transcription and DNA replication à need for new nucleotides
  • 74. Regulated  Steps  Are  Catalyzed  by   Allosteric  Enzymes   • Feedback inhibition – regulatory enzymes are specifically inhibited by the end product of the pathway whenever the concentration of the end product exceeds the cell’s requirements • Heterotropic allosteric inhibition
  • 75. Threonine dehydratase (E1) is specifically inhibited allosterically by L-isoleucine, the end product of the sequence, but not by any of the four intermediates (A to D). Ile does not binds to the active site but to a regulatory site on the enzyme. The binding is reversible: if [Ile]↓à rate of Thr dehydration ↑
  • 76. Kine@c  Proper@es  of  Allosteric  Enzymes   Diverge  from  Michaelis-­‐Menten   Behavior   • For some allosteric enzymes, plots of V0 vs [S] give sigmoid (not hyperbolic) saturation curves • In a sigmoid curve, the [S] that gives ½ Vmax is K0.5 • Homotropic allosteric enzymes are multisubunit proteins. The same binding site on each subunit serves as both an active and regulatory site • Heterotropic allosteric enzymes, an activator causes the curve to be more hyperbolic (also ↓in K0.5; no change in Vmax) and an inhibitor produces a more sigmoid curve (↑ in K0.5; no change in Vmax)
  • 77. The sigmoid curve of a homotropic enzyme, in which the substrate also serves as a positive (stimulatory) modulator, or activator Small change in [S] leads to a large change in activity
  • 78. Noncovalent  Modifica@on:   Allosteric  Regulators   The  kine0cs  of  allosteric  regulators  differ  from   Michaelis-­‐Menten  kine0cs.    
  • 79. A less common type of modulation, in which Vmax is changed and K0.5 is nearly constant.
  • 80. Some  Enzymes  Are  Regulated  by   Reversible  Covalent  Modifica@on   • Over 500 different kinds of covalent modifications are found in proteins • Covalent bonds form (reversibly) between regulatory molecules and aa residues in proteins • When an aa residue is modified, a new aa with changed properties has effectively been introduced in the enzyme (for instance, Ser-OH can be phosphorylated to Ser-O-PO3 – changing the properties à conformation à function, etc.)
  • 81. Some  Reversible  Covalent  Modifica@ons  
  • 82. Example  on  Protein  Phosphoryla@on   • Protein kinases – add phosphate groups on specific aa residues of other proteins • Protein phosphatases – remove phosphate groups from phosphorylated proteins • Glucosen + Pi à glucosen-1 + glucose 1-phosphate (Glycogen) glycogen phosphorylase
  • 83. The less active form of the enzyme, phosphorylase b, specific Ser residues, one on each subunit, are not phosphorylated.
  • 84. In the more active form of the enzyme, phosphorylase a, specific Ser residues, one on each subunit, are phosphorylated.
  • 85. Phosphorylase b and phosphorylase a can be interconverted.
  • 86. Phosphorylase b can be converted (activated) to phosphorylase a by the action of phosphorylase kinase.
  • 87. Phosphorylase a is converted to the less active phosphorylase b by enzymatic loss of these phosphoryl groups, promoted by phosphoprotein phosphatase 1 (PP1).
  • 88. • The activity of both forms of the enzyme is allosterically regulated by an activator (AMP) and by inhibitors (glucose 6-phosphate and ATP) that bind to separate sites on the enzyme • The activities of phosphorylase kinase and PP1 are also regulated via a short pathway that responds to the hormones glucagon and epinephrine
  • 89.   •  When  blood  sugar  levels  are  low,  the  pancreas  and  adrenal  glands   secrete  glucagon  and  epinephrine.     •  Epinephrine  binds  to  its  receptor  in  muscle  and  some  other   0ssues,  and  ac0vates  the  enzyme  adenylyl  cyclase.     •  Glucagon  plays  a  similar  role,  binding  to  receptors  in  the  liver.     •  This  leads  to  the  synthesis  of  high  levels  of  cAMP,  ac0va0ng  the   enzyme  cAMP-­‐dependent  protein  kinase  (PKA).     •  PKA  phosphorylates  several  target  proteins,  among  them   phosphorylase  kinase  and  phosphoprotein  phosphatase  inhibitor   1  (PPI-­‐1).     •  The  phosphorylated  phosphorylase  kinase  is  ac0vated  and  in  turn   phosphorylates  and  ac0vates  glycogen  phosphorylase.     •  At  the  same  0me,  the  phosphorylated  PPI-­‐1  interacts  with  and   inhibits  PP1.     •  PPI-­‐1  also  keeps  itself  ac0ve  (phosphorylated)  by  inhibi0ng   phosphoprotein  phosphatase  2B  (PP2B),  the  enzyme  that   dephosphorylates  (inac0vates)  it.     •  In  this  way,  the  equilibrium  between  the  a  and  b  forms  of   glycogen  phosphorylase  is  shi_ed  decisively  toward  the  more   ac0ve  glycogen  phosphorylase  a