Steady-state flux optima

A BRA

x1

x2

RB

D

C

Feasible fluxdistributions

x1

x2

Max Z=3 at (x2=1, x1=0)

RC

RD

Flux Balance Constraints:

RA < 1 molecule/sec (external)RA = RB (because no net increase)

x1 + x2 < 1 (mass conservation) x1 >0 (positive rates)

x2 > 0

Z = 3RD + RC

(But what if we really wanted to select for a fixed ratio of 3:1?)

FBA - Linear Program

• For growth, define a growth flux where a linear combination of monomer (M) fluxes reflects the known ratios (d) of the monomers in the final cell polymers.

• A linear programming finds a solution to the equations below, while minimizing an objective function (Z).

Typically Z= growth (or production of a key compound).

• i reactions

biomassMd growthv

allMM

ii

iii

i

Xv

v

v

0

bvS

0 5 10 15 20 25 30 35 40 4510

-6

10-4

10-2

100

102

ACCOA

COA

ATP

FAD

GLY

NADH

LEU

SUCCOA

metabolites

coef

f. in

gro

wth

rea

ctio

nBiomass Composition

Flux ratios at each branch point yields optimal polymer composition for replication

x,y are two of the 100s of flux dimensions

Minimization of Metabolic Adjustment

(MoMA)

Flux Data

0 50 100 150 2000

20

40

60

80

100

120

140

160

180

200

1

2

3

456

78

9

10

11121314

15

16

17 18

-50 0 50 100 150 200 250-50

0

50

100

150

200

250

1

2

3456

78

910

11121314

1516

17

18

Experimental Fluxes

Pre

dic

ted

Flu

xes

-50 0 50 100 150 200 250-50

0

50

100

150

200

250

1

2

3

456

78

910

111213

14

15

16

1718

pyk (LP)

WT (LP)

Experimental Fluxes

Pre

dic

ted

Flu

xes

Experimental Fluxes

Pre

dic

ted

Flu

xes

pyk (QP)

=0.91p=8e-8

=-0.06p=6e-1

=0.56P=7e-3

C009-limited

Competitive growth data: reproducibility

Correlation between two selection experiments

Badarinarayana, et al. Nature Biotech.19: 1060

Essential 142 80 62Reduced growth 46 24 22

Non essential 299 119 180 p = 4∙10-3

Essential 162 96 66Reduced growth 44 19 25

Non essential 281 108 173 p = 10-5

MOMA

FBA

Competitive growth data

2 p-values

4x10-3

1x10-5

Position effects Novel redundancies

On minimal media

negative small selection effect

Hypothesis: next optima are achieved by regulation of activities.

LP

QP

Lab evolution optimization

C.ph Tolonen Alcohol resistanceE.co Reppas/Lin Trp/Tyr exchangeE.co Lenski Citrate utilizationE.co Palsson Glycerol utilizationE.co Edwards Radiation resistanceE.co Ingram Lactate productionE.co Stephanopoulos Ethanol resistanceE.co Marliere ThermotoleranceM.tb J&J Diarylquinoline

resistanceE.co DuPont 1,3-propanediol

production

Non-optimal evolves to optimal

Ibarra et al. Nature. 2002 Nov 14;420(6912):186-9. Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth.

Cross-feeding symbiotic systems:aphids & Buchnera

• obligate mutualism• nutritional interactions: amino acids and vitamins• established 200-250 million years ago• close relative of E. coli with tiny genome (641kb)

Aphids

Internal view of the aphid. (by T. Sasaki)

Bacteriocyte

(Photo by T.

Fukatsu)

Buchnera (Photo by

M. Morioka)

http://buchnera.gsc.riken.go.jphttp://buchnera.gsc.riken.go.jp

Shigenobu et al. Genome sequence of the endocellular bacterial symbiont of aphids Buchnera sp.APS. Nature

407, 81-86 (2000).

14

Trp & Tyr (key pharma precursors)

Cross-feeding

synthetic ecosystem

(syntrophic co-culture)

trp/tyrA pair of genomes shows the best co-growth

Reppas, Lin & Church ; Shendure et al. Accurate Multiplex Polony Sequencing of an Evolved Bacterial Genome(2005) Science 309:1728

SecondPassage

First Passage

Covariance in lab evolution

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

# of passages

Do

ub

lin

g t

ime

(h

r)

Q1

Q3

Q2-1

Q2-2

EcNR1

Sequence monitoring of evolution(optimize transport & drug resistance)

Sequence

Reppas, Lin & Church

17

Evolved syntrophic strain pairs

Trp

Tyr

18

Reading lab-evolved genomessequenced across time & within each time-point

Independent lines of Trp & Tyr co-culture

5 OmpF: (pore: large,hydrophilic > small)

42R-> G,L,C, 113 D->V, 117 E->A

2 Promoter: (cis-regulator) -12A->C, -35 C->A

5 Lrp: (trans-regulator) 1b, 9b, 8b, IS2 insert, R->L in

DBD.

Reppas, Shendure, Porecca -12 -11 -10 -9 -8 -7 -6

At late times Tyr becomes prototrophic!

19

Resynthesis of mutant

combinations---

Additive effects insensitive to

order of mutation