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8/13/2019 MFA Examples
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MFASome further examples
Lactic acid bacteriaExample 5.6 Important example!
Lactic acid bacteria are often grown on complex
media rich in amino acids, which provide the carbon
skeleton for biomass synthesis.The catabolic
pathways can therefore be analyzed decoupled from
the anabolic pathways.
There is virtually no drain of precursors in the EMP
pathway, which therefore can be regarded as a linear
pathway.
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Lactic acid bacteria
Glucose
NADH
Pyruvate
CO2
ATP
Lactate
Acet yl-
CoA
FormateNADH
Acetyl-P
Acetate
Acetaldehyde
Ethanol
NADH
ATP
NADH
NADH
v1v2
v4
v3
v5 v6
In general we know that
6
5
4
3
2
1
200111
111100
001111
100000
010000
001000
000100
000010
000005.0
0
0
0
v
v
v
v
v
v
r
r
r
r
r
r
NADH
AcCoA
PYR
e
a
f
c
l
g
But we cannot solve the problem using rf, ra and re as measured rates
T r
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(Or in C-moles)
6
5
4
3
2
1
1003333.03333.03333.0116667.06667.000
001111
003333.0000
100000
010000
0003333.000
000010
000001
00
0
v
v
v
v
v
v
r
r
r
r
r
r
NADHAcCoA
PYR
f
e
a
c
l
g
T r
6
5
4
3
2
1
200111
111100
001111
100000
010000001000
000100
000010
000005.0
0
0
0
v
v
v
v
v
v
r
rr
r
r
r
NADH
AcCoA
PYR
e
a
f
c
l
g
Assume instead that glucose,lactate and formate are measured
Move rows
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The new matrix T becomes
6
5
4
3
2
1
200111111100
001111
001000
000010
000005.0
000100
100000
010000
00
0
v
v
v
v
v
v
r
r
r
r
r
r
NADHAcCoA
PYR
f
l
g
c
e
a
flg
f
f
flg
l
g
f
l
g
rrr
r
r
rrr
r
r
r
r
r
v
v
v
v
v
v
5.02
5.0
2
2
0
0
0
200111
111100
001111
001000
000010
000005.01
6
5
4
3
2
1
Interestingly, the rate of formation of acetate (5) and formate (4)are stoichiometrically directly coupled. Therefore, one cannot
include both of these rates as measured rates, since they are not
independent. (Try it!)
Solving for the fluxes one gets
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A net surplus of NADH results from synthesis of amino acids
E. Albers, Ph.D. thesis, 2000
NADH formation (mmol NADH/mol glucose)
without GOGAT activity with GOGAT activity
Type of cultivation Type of cultivation
Source of NADH batch chemostatD=0.1 h
-1chemostatD=0.4 h
-1batch chemostat
D=0.1 h-1
chemostatD=0.4 h
-1
Amino acids
a
192-228 172-201 221-257 94-228 81-201 105-257Nucleic acids 8-12 9-12 15-21 5-12 5-12 9-21
Organic acids 28-40 26-37 50-83 28-40 26-37 50-83
Total est imated
NADH formation
228-280 207-249 287-362 127-280 112-249 164-362
Experimental
glycerol formation
(various refs)
210 172 217 210 172 217
There are also other sources of net NADH formation, but protein
synthesis is the most important
E. Albers, Ph.D. thesis, 2000
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Glycerol formation in yeast
DHAP G-3-P Glycerol
NAD+NADH
Regeneration of NAD+ is accomplished by glycerol formation
Stoichiometry
03/13/2:5
03/13/1O:4
03/13/13/2:3
03/13/1:2
042.215.012.012.1:1
25.023/4
382
25.033/4
3/42
212.06.074.12
COOCHOCH
ATPNADH-O-CHCH
CONADHOCHOCH
ATPNADHOCHOCH
ATPNADHCONOCHOCH
/
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The stoichiometric matrix
-1.12 1 0 0 0.12 0 0.15 -2.42 0
-1 0 0 0 0 0 0.333 0.333 1
0 0 0 0.667 0.333 0 -0.333 0 -1
-1 0 0 0 0 1 -0.333 -0.333 0
0 0 0.667 0 0.333 0 0 0 -1
=
s x acet eth CO2 glyc NADH ATP pyr
-1.12 -1 0 -1 0
1 0 0 0 0
0 0 0 0 0.667
0 0 0.667 0 0
0.12 0 0.333 0 0.333
0 0 0 1 0
0.15 0.333 -0.333 -0.333 0
-2.42 0.333 0 -0.333 0
0 1 -1 0 -1
T =
T2
T1
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0.3937 -0.1311 0 -0.3937 0.1311
2.8611 0.047244 0 0.14187 0.95276
3.0385 -1.0118 -3.003 -0.035469 1.0118
0 1 0 0 0
-0.177341.0591 3.003 0.17734 -1.0591
T2-1 =
glycc
glyc
glycc
glycc
glycc
rr
r
rr
rr
rr
0591.11773.0
0118.10385.3
0472.08611.2
13.03937.0
02
02
02
02
5
4
3
2
1
mc rTTTr1
211
What about calculated net formation rates?
Fluxes
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-1.1200 -1.0000 0 -1.0000 0
1.0000 0 0 0 0
0 0 0 0 0.6670
0 0 0.6670 0 0
T1 =
-3.3021 -0.9004 0 0.2991 -1.0996
0.3937 -0.1311 0 -0.3937 0.1311
-0.1183 0.7064 2.0030 0.1183 -0.7064
2.0267 -0.6749 -2.0030 -0.0237 0.6749
T1* T2-1 =
glycc
glycc
glycc
glycc
e
a
x
s
rr
rr
rrrr
r
r
rr
6749.00267.2
7064.01183.0
13.03937.09004.03.3021-
02
02
02
02
Perhaps difficult to see but re is in fact proportional to rx
The stoichiometric matrix - rearranged
=
s xacet eth CO2 glyc NADH ATPpyr
0 0 0.12 0 -1.12 1 0.15 -2.42 0
0 0 0 0 -1 0 0.333 0.333 10 0.667 0.333 0 0 0 -0.333 0 -1
0 0 0 1 -1 0 -0.333 -0.333 0
0.667 0 0.333 0 0 0 0 0 -1
rcalc rmeas 0
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T=
T2
0 0 0 0 0.667
0 0 0.667 0 0
0.12 0 0.333 0 0.333
0 0 0 1 0
-1.12 -1 0 -1 0
1 0 0 0 0
0.15 0.333 -0.333 -0.333 0
-2.42 0.333 0 -0.333 00 1 -1 0 -1
T2-1 =
0 1 0 0 0
-0.5 3.0736 0 1.5015 0
0 7.7177 -3.003 3.003 0
-0.5 -4.1936 0 -1.5015 0
-0.5 -4.6441 3.003 -1.5015 -1
xs
xs
x
xs
x
rr
rr
r
rr
r
6441.45.0
1936.45.0
7177.7
0736.35.0
5
4
3
2
1
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-0.3335 -3.0976 2.0030 -1.0015 -0.6670
0.0000 5.1477 -2.0030 2.0030 0.0000
-0.1665 1.1435 0 0.5000 -0.3330
-0.5000 -4.1936 0.0000 -1.5015 -0.0000
T1 * T2-1 =
xs
xs
x
xs
glyc
c
e
a
rr
rr
r
rr
r
r
r
r
1936.40.5-
1435.10.1665-
147.5
0976.30.333-
Now it is easy to see that re is proportional to rx
Assume no acetaldehyde excretion
xs rr5.0
6441.405
Given this assumption all yield coefficients can be calculated!
108.0288.9
x
x
s
xsx
r
r
r
rY
554.0288.9
147.5
x
x
s
ese
r
r
r
rY
290.0288.9
)1435.1288.91665.0(
x
x
s
csc
r
r
r
rY
C-mol/C-mol
048.0...sgY
C-mol/C-mol
C-mol/C-mol
C-mol/C-mol
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Lactic acid bacteria (revisited)
Glucose
NADH
Pyruvate
CO2
ATP
Lactate
Acet yl-
CoA
FormateNADH
Acet yl-P
Acetate
Acet aldehy de
Ethanol
NADH
ATP
NADH
NADH
v1v2
v4
v3
v5 v6
Biomass
ATP
ATP
CO2 + NADHSink for ATP (or ratherthe reason for ATP
synthesis)
7
0 0 0 0 0 0 1
0 1 0 0 0 0 0
0 0 0 0.3333 0 0 01 -1 -1 -1 0 0 0
0 0 0.6667 0.6667 -1 -1 0
0.3333 -0.3333 0.3333 0 0 -1 0.1
0.3333 0 0 0 0.5 0 -2
T2 =
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6.1500 0.0000 -1.5000 0.5000 1.5000 -1.5000 3.0000
0 1.0000 0 0 0 0 0
6.1500 -1.0000 -4.5000 -0.5000 1.5000 -1.5000 3.0000
-0.0000 0.0000 3.0000 -0.0000 -0.0000 0.0000 -0.0000
-0.1000 -0.0000 1.0000 -0.3333 -1.0000 1.0000 0.0000
4.2000 -0.6667 -2.0000 0.0000 1.0000 -2.0000 2.0000
1.0000 0 0 0 0 0 0
T2-1 =
1,3-propanediolProblem 5.5
Terephtalic acid and 1,3-propanediol (3G) can form the
polyester Sorona
(If you exchange 3G for ethylene glycol you get PET!)
1,3-propanediol can be produced by recombinant E. coli
(a process developed by Du Pont/Genencor)
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Glycerol utilization by Klebsiella
DHAP G-3-P Glycerol
NAD+NADH
Pyruvate
Acet yl-CoA
Acetyl-P Acetaldehyde
Ethanol
Formic acid
CO2
+ H2
Acet ic acid
ADPATP
Lactic acid
NADHNAD+
NADHNAD+
(1)(3)
(4) (6)
(5) NADHNAD+
(7)
Biomass
3G
NADNADHATP
2 ATP+NADH
Undesired consumption ofNADH
Stoichiometry1. Anaerobic fermentation
2. Product formation
3. Biomass formation
- CH8/3O + 2/3 CH2O (=HAc) + 1/3(H2+CO2(or HCOOH)) + 2/3 NADH +2/3 ATP = 0- CH8/3O + CH8/3O2/3 1/3 NADH =0
- 1.1 CH8/3O + X + 0.1 CO2+ 0.467 NADH 2.42 ATP =0
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mc rTTTr1
211
0 0 1.0000
0.6667 -0.3333 0.4670
0.6667 0 -2.4200
T2=
-1.0000 -1.0000 -1.1000
0.6667 0 0
0.3333 0 0
0 0 0.1000
0 1.0000 0
T1=
-13.3910 3.0000 -4.5000
2.4200 0 1.0000
1.2100 0 0.50000.1000 0 0
8.6610 -3.0000 3.0000
121TT
x
x
x
x
x
G
CO
HCOOH
HAc
s
r
r
r
r
r
r
r
r
r
r
66.8
1.0
21.1
42.2
39.13
3
2
647.039.13
66.833
x
x
s
G
Gsr
r
r
rY
The yield of 3G (under the most favorable fermentation route) is thus obtained as
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StoichiometryE. coli case
ATPO
P
ONADHv
ATPNADHCOOCHv
ATPNADHOCHOCHv
ATPNADHCOXOCHv
24
223
3
2
3
822
221
2
1
:
3
12:
3
1
3
2:
42.21.01.01.1:
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