Transcript Document 7593453

Engineering of Biological
Processes
Lecture 6: Modeling metabolism
Mark Riley, Associate Professor
Department of Ag and Biosystems
Engineering
The University of Arizona, Tucson, AZ
2007
Objectives: Lecture 6
• Model metabolic reactions to shift
carbon and resources down certain
paths
• Evaluate branch rigidity
Michaelis Menten kinetics
20
r1 = vmax1 S
15
Km1 + S
r
Low Km will be the
path with the higher
flux (all other factors
being equal).
10
5
0
0
10
20
30
40
50
[S]
Low Km also means a
strong interaction
between substrate
and enzyme.
Low Km High Km
These two curves
have the same vmax,
but their Km values
differ by a factor of 2.
Example: Enhancement of ethanol
production
• Want to decrease the cost
• Cheaper substrates
– Greater number of substrates
• Not just glucose
• Higher rates of production
 Yp/s Yield of product per substrate consumed
 Yp/x Yield of product per cell
Species used
• Saccharomyces cerevisiae
– Produces a moderate amount of ethanol
– Narrow substrate specificity (glucose)
• Zymomonas mobilis
– Produces a large amount of ethanol
– Narrow substrate specificity (glucose)
• Escherichia coli
– Broad substrate specificity
– Low ethanol production
– Much is known about its genetics
Goal
Combine the advantages of ZM + EC
Ethanol production
1st attempt: amplify PDC activity
Resulted in accumulation of
acetaldehyde. No significant
increase in EtOH. Increase
in byproducts from
acetaldehyde
2nd attempt:
amplify PDC
activity &
ADH (alcohol
dehydrogenase)
Gave a significant
increase in EtOH
This approach worked because of the large
differences in Km’s
Km = 0.4 mM
Ethanol
Km = 0.4 mM
Acetate
Km = 2.0 mM
Lactate
Km = 7.2 mM
Some definitions
Total flux
Ftot
= vmax1 S
+ vmax2 S
Km1 + S
Km2 + S
Selectivity
vmax1 S
F1
F2
=
Km1 + S
vmax2 S
Km2 + S
Selectivity
r1 vmax 1  Km2  S 



r2 vmax 2  Km1  S 
So, to enhance r1, we want a small value of Km1
Model conversion of pyruvate
d[pyr ]

 v1  v 2  v 3  v 4
dt
v max 1[pyr ]
v1 
K m1  [pyr ]
d[pyr ] v max 1[pyr ]



dt
K m1  [pyr ]
Model conversion of pyruvate
d[pyr ] v max 1[pyr ]
v max 2 [pyr ]
v max 3 [pyr ]
v max 4 [pyr ]





dt
K m1  [pyr ] K m2  [pyr ] K m3  [pyr ] K m 4  [pyr ]
Model production of ethanol
d[ethanol ] v max 4 [pyr ]

dt
K m 4  [pyr ]
v max 4 [pyr ]
[ethanol ]  [ethanol o ] 
dt
K m 4  [pyr ]
Ethanol Km = 0.4 mM
1.7
Eth / TCA
Eth / Lac
Eth / Act
1.6
Ratio of rates
1.5
1.4
1.3
1.2
1.1
1
0.9
0
0.02
0.04
0.06
Time (sec)
0.08
0.1
Ethanol Km = 1 mM
1.6
Eth / TCA
Eth / Lac
Eth / Act
1.5
Ratio of rates
1.4
1.3
1.2
1.1
1
0.9
0
0.02
0.04
0.06
Time (sec)
0.08
0.1
Ethanol Km = 10 mM
1.2
Ratio of rates
1
0.8
0.6
0.4
Eth / TCA
Eth / Lac
Eth / Act
0.2
0
0
0.02
0.04
0.06
Time (sec)
0.08
0.1
Glucose
Glucose 6-Phosphate
2-Keto-3-deoxy-6phosphogluconate
Phosphogluconate
Fructose 6-Phosphate
Fructose 1,6-Bisphosphate
Glyceraldehyde 3-Phosphate
Glyceraldehyde
3-Phosphate
Glyceraldehyde
3-Phosphate
+
Pyruvate
Phosphoenolpyruvate
Acetaldehyde
Lactate
Pyruvate
NADH
Ethanol
Acetate
Acetyl CoA
Citrate
Oxaloacetate
NADH
Isocitrate
Malate
CO2+NADH
a-Ketoglutarate
Fumarate
GTP
Succinate
FADH2
GDP+Pi CO2+NADH
Glucose
Glucose 6-Phosphate
Phosphogluconate
Fructose 6-Phosphate
Fructose 1,6-Bisphosphate
Glyceraldehyde 3-Phosphate
Phosphoenolpyruvate
Pyruvate
Simplified metabolism - upstream end of glycolysis
ATP
Glucose
ADP
ATP
v1
ADP
v2
Glucose 6-Phosphate
v3
Fructose 6-Phosphate
ATP
Additional reactions
ADP
v6
ATP
v4
ADP
ATP
v7
ADP
Fructose 1,6-Bisphosphate
v8
v5
Pyruvate
ATP + AMP
2 ADP
How do you model this?
• What information is needed?
– equations for each v
– initial concentrations of each metabolite
dGluc 6P

dt
dFruc 6P

dt
dFruc1,6P2

dt
dATP

dt
dADP

dt
dAMP

dt
Mass balances
dGluc 6P
Mass balances
 v1  v 2  v3
dt
dFruc 6P
 v3  v 4
dt
dFruc1,6P2
 v 4  v5
dt
dATP
  v1  v 2  v 4  v 6  v 7  v8
dt
dADP
 v1  v 2  v 4  v 6  v 7  2v8
dt
dAMP
  v8
dt
v max,1[ ATP(t)][ Glu cos e]
v1 
[ ATP(t)] [Glu cos e]  [ ATP(t)] [Glu cos e] 
1




K ATP 1
KGlu cos e1
KGlu cos e1 
 K ATP 1
v2  k2 [ ATP(t)][ Gluc 6P]
v max,4 Fruc 6P(t)
v4 
2


ATP
(
t
)


2


KFruc 6P4 1  
  Fruc 6P(t)

AMP(t)  



2
v5  k5 [Fruc1,6P2]
Metabolite profiles
5
4.5
Concentration (mM)
4
Gluc 6P
Fruc 16P2
Fruc 6P
ATP
ADP
AMP
3.5
3
2.5
2
1.5
1
0.5
0
0
0.1
0.2
0.3
Time (min)
0.4
0.5
Rates of reaction
50
Rate of reaction (mM / min)
46
42
38
v1
v2
v3
v4
v5
v6
v7
v8
34
30
26
22
18
14
10
6
2
-2
0
0.1
0.2
0.3
Time (min)
0.4
0.5
Reaction branch nodes
S
Flux of carbon
J1 = J2 + J3
J1
I
J2
P1
J3
P2
Product yields are often a function of the split ratio in branch
points (i.e., 20% / 80% left / right).
Types of reaction branch nodes
(rigidity)
• Flexible nodes
– Flux partitioning can be easily changed
• Weakly rigid nodes
– Flux partitioning is dominated by one branch of the
pathway
• Deregulation of supporting pathway has little effect on flux
• Deregulation of dominant pathway has large effect on flux
• Strongly rigid nodes
– Flux partitioning is tightly controlled
• Highly sensitive to regulation
Types of reaction branch nodes
S
I
P1
P2
Regulation
Negative feedback
Flexible nodes
• The split ratio will depend on the cellular
demands for the 2 products
• Can have substantial changes in the flux
partitioning
Rigid nodes
• Partitioning is strongly regulated by end
product activation and inhibition
• Deregulation of such a node can be very
difficult to perform
S
S
Regulation
Negative feedback
I
P1
-
I
-
P2
P1
Flexible node
I
P1
+ +
+
P2
Weakly rigid node
S
-
-
P2
Strongly rigid node
Regulation
Positive feedback
Branch point effect
Glyoxylate shunt
(cells grown on acetate)
Citrate
For growth on acetate,
Isocitrate = 160 mM
Isocitrate
Lyase (IL)
Km=604 mM
Vmax=389 mM/min
Glyoxylate
Isocitrate
Dehydrogenase (IDH)
Km=8 mM
Vmax=126 mM/min
a-Ketoglutarate
Flux is very sensitive to [isocitrate]
first order in IL, zero order in IDH
Growth on acetate
140
Reaction rate
120
100
80
60
40
160 mM
r (IL)
r (IDH)
20
0
0
When [S] = 50 uM,
r IL = 110 uM/min
r IDH = 20 uM/min
50
100
150
[S] uM
200
250
300
When [S] = 160 uM,
r IL = 120 uM/min
r IDH = 60 uM/min
Branch point effect
Glyoxylate shunt
(cells grown on glucose)
Citrate
For growth on glucose,
Isocitrate = 1 mM
Isocitrate
Lyase (IL)
Km=604 mM
Vmax=389 mM/min
Dehydrogenase (IDH)
Km=8 mM
Vmax=625 mM/min
Vmax had been
=126 mM/min
Glyoxylate
a-Ketoglutarate
Flux is not sensitive to [isocitrate]
first order (but very low) in IL, first order in IDH
Growth on glucose
120
r (IL)
r (IDH)
Reaction rate
100
80
60
40
1 mM
20
0
0
0.5
1
1.5
[S] uM
Note that [S] is much lower than before.
2
Growth on acetate
140
100
80
60
40
r (IL)
r (IDH)
20
0
0
50
100
150
200
250
[S] uM
300
Growth on glucose
120
r (IL)
r (IDH)
100
Reaction rate
Reaction rate
120
80
60
40
20
0
0
0.5
1
[S] uM
1.5
2
Which path controls the branch ratio?
Citrate
Under growth by glucose,
Isocitrate = 1 mM
Glyoxylate shunt
(cells grown on glucose)
Isocitrate
Lyase (IL)
Km=604 mM
Vmax=389 mM/min
Glyoxylate
Dehydrogenase (IDH)
Km=8 mM
Vmax=625 mM/min
a-Ketoglutarate
Which path controls the branch ratio?
• The one that adapts to the available
substrate controls the branch.
• This depends on the values of vmax, Km,
and [S] for each reaction.