last time 3/4/08. increase (i) concentration increase slope intercept remains unchanged
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Last Time 3/4/08
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Increase (I) concentration increase slope intercept remains unchanged.
rS Vmax S
KM 1I
KI
S
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Uncompetitive Inhibition
Inhibition only has affinity for enzyme-substrate complex
Developing the rate law
(1)
(2)
E Sk1 k2
E Skcat P
IE Sk4 k5
I E S
rP rS kcat E S
rES 0 k1 E S k2 E S kcat E S k4 I E S k5 I E S
rIES 0
k4 I E S k5 I E S
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Adding (1) and (2)
k1 E S k2 E S kcat E S 0
E S k1 E S k2 kcat
E S KM
I E S k4
k5
I E S I E S
KI
I E S KIKM
KI k5
k4
rp kcat E S kcat E S
KM
From (2)
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Total enzyme
E t E E S I E S
E 1S
KM
I S
KIKM
rp kcatE t S
KM 1S
KM
I S
KIKM
rS rP Vmax S
KM S 1I
KI
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rS rP Vmax S
KM S 1I
KI
1
rS
1
Vmax S KM S 1
I KI
KM
Vmax
1
S
1
Vmax
1I
KI
Slope remains the same but intercept changes as inhibitor concentration is increased
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Lecture16 Thursday 3/6/08
Enzyme Kinetics
Noncompetive Inhibition
Bioreactors
Monod Equation
Yield Coeficients
Washout
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Bioreactors
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D=vo / V
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Noncompetitive, Bioreactors
More uncompetitive inhibition
S
mI
I
S
I
ISm
SSP
CV
k
V
kC
r
kC
Ck
CVrr
11
1
1
maxmax
max
Only intercept changes
SC
1
Sr
1
Increasing I
No I
Lineweaver-Burk
Noncompetitive inhibition (Mixed)
Both slope and intercept change
SC
1
Sr
1
Increasing I
No I
E + S E·S P
E·I + S E·S·I
+I +I-I -I
I
I
S
m
I
I
S
I
ISm
SS
k
C
CV
k
k
C
Vr
kC
Ck
CVr
11
111
1
maxmax
max
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Bioreactors
Cells + substrate → product + more cells
Cell growth can be modeled with enzyme equations since all cell reactors are enzyme catalyzed
Lag phase
Exponential growth phase
stationary phase Death
phase
Algorithm
1) Mass balance (later)
2) Rates
**
max
max
1
equation) monad(
P
n
P
POBS
OBSCSS
Sg
SS
SCg
CC
Ck
kCCk
Cr
Ck
CCr
sometimes
Product concentration at which all metabolism ceases (93 g/L for wine production, n = ½)
Substrate is used to form both products and cell maintenance
(rate of substrate disappearance for maintenanceCsm mCr
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3) Stoichiometry – yield coefficients
CDD
CgCSSgCPP
CP
SCCSSC
Ckr
mCryrryr
y
yyy
//
/
///
formed cells new of mass
formedproduct of mass
1
consumed substrate mass
formed cells of mass
1) Mass balance
Parameters:
(product)
)(substrate
rate)(dilution 1
(cells) 0
0
000
0
0
PPP
SSSS
SSSS
dgCC
dgCC
rDCdt
dC
rCCDdt
dC
VrCvCvdt
dCV
V
vDrrDC
dt
dC
VrrCvdt
dCV
2) Rates
CDD
CgCSS
gCPP
n
P
POBS
OBSCSS
Sg
Ckr
mCryr
ryr
C
CK
KCCk
Cr
/
/
*
max
1
VDVvCvmCvm
CDmyykknC
PpC
SCPCSDSP
, , ,
, , , , , , , , ,
000
0//*
max