Engineering of Biological Processes

Lecture 6: Modeling metabolism

Mark Riley, Associate ProfessorDepartment of Ag and Biosystems

EngineeringThe University of Arizona, Tucson, AZ

2007

Objectives: Lecture 6

• Model metabolic reactions to shift carbon and resources down certain paths

• Evaluate branch rigidity

These two curves have the same vmax, but their Km values

differ by a factor of 2.

0

5

10

15

20

0 10 20 30 40 50

[S]

r

Low Km High Km

r1 = vmax1 S

Km1 + S

Low Km will be the path with the higher flux (all other factorsbeing equal).

Low Km also means a strong interaction between substrate and enzyme.

Michaelis Menten kinetics

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 activityResulted 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

EthanolKm = 0.4 mM

AcetateKm = 2.0 mM

LactateKm = 7.2 mM

Km = 0.4 mM

This approach worked because of the large differences in Km’s

Some definitions

Ftot = vmax1 S

Km1 + S

+ vmax2 S

Km2 + S

Total flux

Selectivity

F1

F2 vmax2 S

Km2 + S

vmax1 S

Km1 + S=

Selectivity

SK

SK

vmax

vmax

r

r

m1

m2

2

1

2

1

So, to enhance r1, we want a small value of Km1

Model conversion of pyruvate

]pyr[K

]pyr[vv

1m

1max1

]pyr[K

]pyr[v

dt

]pyr[d

1m

1max

4321 vvvvdt

]pyr[d

Model conversion of pyruvate

]pyr[K

]pyr[v

]pyr[K

]pyr[v

]pyr[K

]pyr[v

]pyr[K

]pyr[v

dt

]pyr[d

4m

4max

3m

3max

2m

2max

1m

1max

Model production of ethanol

]pyr[K

]pyr[v

dt

]ethanol[d

4m

4max

dt]pyr[K

]pyr[v]ethanol[]ethanol[

4m

4maxo

Ethanol Km = 0.4 mM

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

0 0.02 0.04 0.06 0.08 0.1

Time (sec)

Ra

tio

of

rate

s

Eth / TCA

Eth / Lac

Eth / Act

Ethanol Km = 1 mM

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

0 0.02 0.04 0.06 0.08 0.1

Time (sec)

Ra

tio

of

rate

s

Eth / TCA

Eth / Lac

Eth / Act

Ethanol Km = 10 mM

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1

Time (sec)

Ra

tio

of

rate

s

Eth / TCA

Eth / Lac

Eth / Act

Glucose Glucose 6-Phosphate

Fructose 6-Phosphate

Fructose 1,6-Bisphosphate

Glyceraldehyde 3-Phosphate

Pyruvate

Acetate Acetyl CoA

Citrate

-Ketoglutarate

Succinate

Fumarate

Oxaloacetate

Phosphogluconate

Glyceraldehyde 3-Phosphate

Acetaldehyde

2-Keto-3-deoxy-6-phosphogluconate

Glyceraldehyde 3-Phosphate

+Pyruvate

Lactate

Ethanol

MalateIsocitrate

CO2+NADHFADH2

CO2+NADH

NADH

NADH

GTP

GDP+Pi

Phosphoenolpyruvate

Glucose Glucose 6-Phosphate

Fructose 6-Phosphate

Fructose 1,6-Bisphosphate

Glyceraldehyde 3-Phosphate

Pyruvate

Phosphogluconate

Phosphoenolpyruvate

Glucose Glucose 6-Phosphate

Fructose 6-Phosphate

Fructose 1,6-Bisphosphate

Pyruvate

Simplified metabolism - upstream end of glycolysis

ATP ADPv1

ATP ADPv2

v3

ATP

ADP

v4

v5

ATPADPv6

ADPATPv7

2 ADPATP + AMPv8

Additional reactions

How do you model this?

• What information is needed? – equations for each v– initial concentrations of each metabolite

Mass balances

dt

dAMPdt

dADPdt

dATPdt

2P6,1dFrucdt

P6dFrucdt

P6dGluc

Mass balances

8vdt

dAMP

8v27v6v4v2v1vdt

dADP

8v7v6v4v2v1vdt

dATP

5v4vdt

2P6,1dFruc

4v3vdt

P6dFruc

3v2v1vdt

P6dGluc

1ecosGlu1ATP1ecosGlu1ATP

1max,

K]ecosGlu[

K)]t(ATP[

K]ecosGlu[

K)]t(ATP[

1

]ecosGlu)][t(ATP[v1v

]P6Gluc)][t(ATP[k2v 2

]2P6,1Fruc[k5v 5

22

24max,

)t(P6Fruc)t(AMP)t(ATP

14P6KFruc

)t(P6Frucvv4

Metabolite profiles

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.1 0.2 0.3 0.4 0.5

Time (min)

Co

nc

en

tra

tio

n (

mM

) Gluc 6PFruc 16P2Fruc 6PATPADPAMP

Rates of reaction

-2

2

6

10

14

18

22

26

30

34

38

42

46

50

0 0.1 0.2 0.3 0.4 0.5

Time (min)

Ra

te o

f re

ac

tio

n (

mM

/ m

in)

v1

v2

v3

v4

v5

v6

v7

v8

Reaction branch nodes

P1 P2

I

S

J1

J2 J3

J1 = J2 + J3

Flux of carbon

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

P1 P2

I

S

- -

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

P1 P2

I

S

- -

Flexible node

P1 P2

I

S

- -

++

Strongly rigid node

P1 P2

I

S

- -

+

Weakly rigid node

RegulationNegative feedback

RegulationPositive feedback

Branch point effect

Citrate

Glyoxylate -Ketoglutarate

IsocitrateLyase (IL)Km=604 MVmax=389 mM/min

IsocitrateDehydrogenase (IDH)Km=8 MVmax=126 mM/min

Glyoxylate shunt(cells grown on acetate) For growth on acetate,

Isocitrate = 160 M

Growth on acetate

0

20

40

60

80

100

120

140

0 50 100 150 200 250 300

[S] uM

Rea

ctio

n r

ate

r (IL)

r (IDH)

Flux is very sensitive to [isocitrate] first order in IL, zero order in IDH

160 M

When [S] = 50 uM, r IL = 110 uM/minr IDH = 20 uM/min

When [S] = 160 uM, r IL = 120 uM/minr IDH = 60 uM/min

Branch point effect

Citrate

Glyoxylate -Ketoglutarate

IsocitrateLyase (IL)Km=604 MVmax=389 mM/min

Dehydrogenase (IDH)Km=8 MVmax=625 mM/min

Glyoxylate shunt(cells grown on glucose) For growth on glucose,

Isocitrate = 1 M

Vmax had been=126 mM/min

Growth on glucose

0

20

40

60

80

100

120

0 0.5 1 1.5 2

[S] uM

Rea

ctio

n r

ate

r (IL)

r (IDH)

Flux is not sensitive to [isocitrate] first order (but very low) in IL, first order in IDH

1 M

Note that [S] is much lower than before.

Growth on glucose

0

20

40

60

80

100

120

0 0.5 1 1.5 2

[S] uM

Rea

ctio

n r

ate

r (IL)

r (IDH)

Growth on acetate

0

20

40

60

80

100

120

140

0 50 100 150 200 250 300

[S] uM

Rea

ctio

n r

ate

r (IL)

r (IDH)

Which path controls the branch ratio?

Citrate

Glyoxylate -Ketoglutarate

IsocitrateLyase (IL)Km=604 MVmax=389 mM/min

Dehydrogenase (IDH)Km=8 MVmax=625 mM/min

Glyoxylate shunt(cells grown on glucose)

Under growth by glucose,Isocitrate = 1 M

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.