lecture 15
DESCRIPTION
Lecture 15. Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place. Lecture 15 – Tuesday 3/12/2013. Enzymatic Reactions Michealis-Menten Kinetics Lineweaver -Burk Plot - PowerPoint PPT PresentationTRANSCRIPT
Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of
chemical reactions and the design of the reactors in which they take place.
Lecture 15
Lecture 15 – Tuesday 3/12/2013Enzymatic Reactions
Michealis-Menten KineticsLineweaver-Burk PlotEnzyme Inhibition
CompetitiveUncompetitiveNon-Competitive
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3
Active Intermediates and PSSH
Review Last Lecture
4
Active Intermediates and PSSH
Review Last Lecture
1.In the PSSH, we set the rate of formation of the active intermediates equal to zero. If the active intermediate A* is involved in m different reactions, we set it to:
2. The azomethane (AZO) decomposition mechanism is
By applying the PSSH to AZO*, we show the rate law, which exhibits first-order dependence with respect to AZO at high AZO concentrations and second-order dependence with respect to AZO at low AZO concentrations.
01
*.*
m
iiAnetA rr
)('1)( 2
2 AZOkAZOkrN
Enzymes
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Michaelis-Menten KineticsEnzymes are protein-like substances with catalytic properties.
Enzyme Unease [From Biochemistry, 3/E by Stryer, copywrited 1988 by Lubert Stryer. Used with
permission of W.H. Freeman and Company.]
Enzymes
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Enzymes provide a pathway for the substrate to proceed at a faster rate. The substrate, S, reacts to form a product P.
A given enzyme can only catalyze only one reaction. Example, Urea is decomposed by the enzyme urease.
E S
SlowS P
Fast
Enzymes - Urease
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A given enzyme can only catalyze only one reaction. Urea is decomposed by the enzyme urease, as shown below.
UREASECONH2UREASECONHNH 23OH
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EPES OH2
SESE 1k SESE 2k
EPWSE 3k
The corresponding mechanism is:
Enzymes - Michaelis-Menten Kinetics
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WSEkrP 3
SEWkSEkSEkr SE 3210
WkkSk
EE t
32
11
WkkSEkSE
32
1
SEEEt
Enzymes - Michaelis-Menten Kinetics
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SKSEk
SkWkkSEWkWSEkr
M
V
tcat
K
t
k
P
M
cat
max
1
32
33
SKSVWSEkr
mP
max3
Enzymes - Michaelis-Menten Kinetics
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Turnover Number: kcatNumber of substrate molecules (moles) converted to product in a given time (s) on a single enzyme molecule (molecules/molecule/time)
For the reaction:
40,000,000 molecules of H2O2 converted to product per second on a single enzyme molecule.
H2O2 + E →H2O + O + Ekcat
Vmax=k
catEt
Enzymes - Michaelis-Menten Kinetics
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(Michaelis-Menten plot)Solving:
KM=S1/2
therefore KM is the concentration at which the rate is half the maximum rate.
Vmax
-rs
S1/2 CS
Michaelis-Menten Equation
SKSVrr
M
maxSP
2/1M
2/1maxmax
SKSV
2V
Enzymes - Michaelis-Menten Kinetics
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S1
VK
V1
r1
max
M
maxS
Inverting yields:
Lineweaver-Burk Plot
slope = KM/Vmax
1/Vmax
1/S
1/-rS
Types of Enzyme Inhibition
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)inactive( EIIE
Competitive
)inactive( SEIISE
Uncompetitive
)inactive( SEIISE
)inactive( SEISEI
Non-competitive
Competitive Inhibition
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Competitive Inhibition
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2
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k
kk
PESESE
SE3P CkrIEIE
IEIE EPSESESE SESE
1) Mechanisms:
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4
k
k
)inactive(IEI E
2) Rate Laws:
SE3SE2ES1SE CkCkCCk0r
4
5I
I
EIEI k
kK KCCC
m
ES
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ES1SE K
CCkkCCkC
m
ES3P K
CCkr
EI5EI4EI CkCCk0r
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Competitive Inhibition
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Competitive Inhibition
I
I
m
S
EtotEEISEEEtot
KC
KC1
CC CCCC
SI
I
max
m
maxS C1
KC1
Vk
V1
r1
I
mISm
SEtot3P
KKCCK
CCkr
I
ImS
SmaxS
KC1KC
CVr
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Competitive InhibitionFrom before (no competition):
S
M
S CVK
Vr111
maxmax
Intercept does not change, slope increases as inhibitor concentration increases
max
slopeVKM
max
1InterceptV
Sr1
SC1
No Inhibition
Competitive
Increasing CI
Competitive
SI
IM
S CKC
VK
Vr1111
maxmax
Uncompetitive Inhibition
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Uncompetitive Inhibition
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PSESE 3
2
1k
k
k
SEkrr catSP
Inhibition only has affinity for enzyme-substrate complex
Developing the rate law:
SEIkSEIkSEkSEkSEkr catSE 54210 (1)
0r SEI SEIkSEIk 54 (2)
)inactive(SEISEI5
4
k
k
Adding (1) and (2)
Mcat
cat
KSE
kkSEkSE
SEkSEkSEk
2
1
21 0
M
catcatp
I
MII
KSEkSEkr
kkK
KKSEI
KSEISEI
kkSEI
4
5
5
4
From (2)
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Uncompetitive Inhibition
MIMM
tcatp
MIM
t
KKSI
KSK
SEkr
KKSI
KSE
SEISEEE
1
1
Total enzyme
IM
PS
KISK
SVrr1
max
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Uncompetitive Inhibition
Slope remains the same but intercept changes as inhibitor concentration is increased
Lineweaver-Burk Plot for uncompetitive inhibition23
I
M
S
IM
S
KI
VSVK
r
KISK
SVr
1111
111
maxmax
max
Uncompetitive Inhibition
Non-competitive Inhibition
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Non-competitive Inhibition
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Both slope and intercept changes
SC1
Sr1
Increasing I
No Inhibition
E + S E·S P + E
(inactive)I.E + S I.E.S (inactive)
+I +I-I -I
I
I
S
M
I
I
S
I
ISM
SS
kC
CVk
kC
Vr
kCCk
CVr
11111
1
maxmax
max
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Summary: Types of Enzyme Inhibition
Lineweaver–Burk plots for three types of enzyme inhibition.
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End of Lecture 15