What is measurable/reported (e.g. in BRENDA)?
Enzyme Kinetics
i.e. characterization by assay in the test tube
(typically with purified protein and through
monitoring of emerging product)
saturation
conditions
[S] >> [E]
Stryer Fig. 8.12 Determining initial velocity
steady-state
assumption
Michaelis-Menten Kinetics (slides need a few minor corrections!)
k2
k1
a.k.a. kcat
E + S !ES"E+P
k-1
v=
d[P]
dt
(k-2 is negligible until products
start to build up)
= k2[ES]
Steady state conditions--[ES] remains
relatively constant over the course of
the rxn until S starts running out.
d[ES]
dt
=0
k1[E][S] = k-1[ES] + k2[ES] = (k-1 + k2)[ES]
Define a new constant: [E][S]/[ES] = (k-1 + k2)/ k1= KM
KM[ES] = [S][E]
[E] = [E]T -[ES] KM[ES] = [E]T[S]-[ES][S]
[ES](KM + [S]) = [E]T[S]
[E]T[S]
[ES] = ------------------KM + [S]
k2[E]T[S]
v = -----------------KM + [S]
vmax[S]
v = ----------------KM + [S]
vmax
v = ---2
And [ES] = v/k2
Define vmax=k2[E]T
Michaelis-Menten equation
at [S] = KM
Determining kcat and KM from
“intial rate” data
[S]
vo
5
10
20
50
100
200
22
39
65
102
120
135
Vmax = 150-160??
Vo
150
Km = ???
100
50
0
0
100
200
300
[S]
Vo
a
Vmax = 150-160??
150
100
50
0
Km = ???
0
100
200
300
LineweaverBurk plot
Vmax = 164 µM/min
1/Vo
[S]
y = 0.1961x + 0.0061
R2 = 0.9995
0.06
0.04
0.02
0
0
Km = 32.2 µM
0.1
0.2
1/[S]
0.3
VVP Fig. 12-4
LineweaverBurk plot
competitive inhibition
KM increases; Vmax unchanged
+ inhibitor
Vmax
no inhibitor
1/Vo
100
Vo
75
50
+ inhibitor
25
0
0
10
KM
[S]
20
no inhibitor
1/[S]
30
-1/KM
competitive inhibition
VVP Fig. 12-7
modifying
factor #
mixed and uncompetitive inhibition
Vmax decreases
uncompetitive inhibition
(rare)
VVP Fig.12-8
mixed competitive inhibition
(a.k.a. non-competitive inhibition if KI ! K’I)
VVP Fig. 12-9
Summary of simple inhibition models
Inhibitor
binds at
Effect on
Vmax
Effect on KM other
competitive
Active site
None
Apparent
KM
increases
uncompetitive
Allosteric
site after S
binds
decreases
Apparent
KM
decreases
noncompetitive
(or “mixed”)
Allosteric
site (to E or
ES)
decreases
varies
Overcome
inhibition at
high [S]
noncompetitive
is special case:
no KM change
Catalytic Mechanism Determination
1) kinetic analysis
- what is the kinetic “signature”?
- mode of inhibition revealed
- determine rates for individual steps
- does order of addition matter? (sequential vs. Ping-Pong)
2) active site modification (irreversible inhibitors)
- derivatize protein; identify the modified sidechain(s)
3) structure determination (e.g. RNase A, lysozyme,
serine proteases)
Some Peroxidases use heme prosthetic groups
(e.g. cytochrome c peroxidase uses heme b
EC 1.11.1.5, PDB 2CYP)
(Fe is 2+/II
or 3+/III
or 4) +/IV
or 6+/VI)
(metal co-ordination
= donated bonds!)
(hemoglobin/myoglobin;
cytochrome c peroxidase)
_ _
His-N
His-N
His-N
- | O-O|-
_ _
- | O-OH
Enzymatic redox cycles typically
involve two redox reactions
“intended”
reaction
cofactor is
recycled
(two ways shown)
Interesting:
In cytochrome c
peroxidase, the radical
seems to be forming on
a tryptophan (could
also be in the heme system)
radical •
(- charge symbolizes
that system is one edeficient)
Are these residues
conserved? (e.g. in PIRSF
family around PDB:2CYP)
(http://chem-faculty.ucsd.edu/kraut/projects.html)
Indications for this come
largely from a crystal structure
of a dioxygen (O2) complex
Many important reaction
steps are proton transfer
(rather than e--transfer)
Indolyl cation radical on
Trp51 seems to be stabilized
by the enzyme (much less
labile than in solution - up
to 4h half-life!)
(Vit: Niacin)
NAD+ / NADH
NADP+ / NADPH
add 2H+ + 2elose 1H+
(Vit: Riboflavin)
FAD / FADH2
FMN / FMNH2
add 2H+ + 2e-
Redoxcoenzymes
Also: Other folate/THF-derivatives
Note in closing:
Controversy regarding precise
mechansim(s) of redox reactions
(e.g. using NAD+/NADH)
• direct (bio-)hydride transfer (i.e. H- “ion”)
• direct electron transfer (via free radical = 1e-)
• intermediates enabling transfer via covalent bond
… though as bioinformaticians we don’t
care all that much :-)