Steady-state flux optima

1
Steady-state flux optima
RC
Flux Balance Constraints RA lt 1 molecule/sec
(external) RA RB (because no net
increase) x1 x2 lt 1 (mass conservation) x1 gt0
(positive rates) x2 gt 0
C
x1
RB
RA
A
B
x2
D
RD
x2
Max Z3 at (x21, x10)
Feasible flux distributions
Z 3RD RC (But what if we really
wanted to select for a fixed ratio of 31?)
x1
2
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 ngrowth (or
  production of a key compound).
• i reactions

3
Biomass Composition
ATP
GLY
LEU
coeff. in growth reaction
ACCOA
NADH
FAD
SUCCOA
COA
metabolites
4
Flux ratios at each branch point yields optimal
polymer composition for replication
x,y are two of the 100s of flux dimensions
5
Minimization of Metabolic Adjustment (MoMA)
6
Flux Data
7
C009-limited
200
WT (LP)
180
7
8
160
140
9
120
10
Predicted Fluxes
100
r0.91 p8e-8
11
13
14
12
3
1
80
60
40
16
20
2
5
6
4
15
17
18
0
0
50
100
150
200
Experimental Fluxes
250
250
Dpyk (LP)
Dpyk (QP)
200
200
18
7
r0.56 P7e-3
8
150
r-0.06 p6e-1
150
7
8
2
Predicted Fluxes
Predicted Fluxes
10
100
9
13
100
9
11
12
3
1
14
10
11
13
14
12
3
50
50
5
6
4
16
16
2
15
5
6
0
15
17
0
17
18
4
1
-50
-50
-50
0
50
100
150
200
250
-50
0
50
100
150
200
250
Experimental Fluxes
Experimental Fluxes
8
Competitive growth data reproducibility
Correlation between two selection experiments
Badarinarayana, et al. Nature Biotech.19 1060
9
Competitive growth data
On minimal media
negative small

selection effect
C 2 p-values 4x10-3 1x10-5
LP QP
Novel redundancies
Position effects
Hypothesis next optima are achieved by
regulation of activities.
10
Lab evolution optimization
C.ph Tolonen Alcohol resistance E.co Reppas/Lin
Trp/Tyr exchange E.co Lenski Citrate
utilization E.co Palsson Glycerol
utilization E.co Edwards Radiation
resistance E.co Ingram Lactate
production E.co Stephanopoulos Ethanol
resistance E.co Marliere Thermotolerance M.tb JJ
Diarylquinoline resistance E.co DuPont 1,3-pro
panediol production
11
Non-optimal evolves to optimal
Ibarra et al. Nature. 2002 Nov
14420(6912)186-9. Escherichia coli K-12
undergoes adaptive evolution to achieve in silico
predicted optimal growth.
12
Cross-feeding symbiotic systemsaphids Buchnera

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

Internal view of the aphid. (by T. Sasaki)
Bacteriocyte (Photo by T. Fukatsu)
Buchnera (Photo by M. Morioka)
Aphids
http//buchnera.gsc.riken.go.jp
13
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)
15
Covariance in lab evolution
Second Passage
First Passage
?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 3091728
16
Sequence monitoring of evolution(optimize
transport drug resistance)
Sequence
Reppas, Lin Church
17
Evolved syntrophic strain pairs
Trp D
Tyr D
18
Reading lab-evolved genomessequenced across time
within each time-point

• Independent lines of
• TrpD TyrD co-culture
• 5 OmpF (pore large,hydrophilic gt small)
• 42R-gt G,L,C, 113 D-gtV, 117 E-gtA
• 2 Promoter (cis-regulator)
• -12A-gtC, -35 C-gtA
• 5 Lrp (trans-regulator)
• 1bD, 9bD, 8bD, IS2 insert, R-gtL in DBD.

At late times TyrD becomes prototrophic!
Reppas, Shendure, Porecca
19
Resynthesis of mutant combinations---Additive
effects insensitive to order of mutation