Steadystate flux optima Flux Balance Constraints x 1
Steady-state flux optima Flux Balance Constraints: x 1 C RC RB R A RA < 1 molecule/sec (external) A B RA = R B (because no net increase) x 2 D x 1 + x 2 < 1 (mass conservation) RD x 1 >0 (positive rates) x 2 > 0 Max Z=3 at (x 2=1, x 1=0) Feasible flux Z = 3 RD + RC distributions (But what if we really wanted to select for a fixed ratio of 3: 1? ) x 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= ngrowth (or production of a key compound). • i reactions
Biomass Composition coeff. in growth reaction ATP GLY ACCOA LEU NADH COA FAD SUCCOA metabolites
Flux ratios at each branch point yields optimal polymer composition for replication x, y are two of the 100 s of flux dimensions
Minimization of Metabolic Adjustment (Mo. MA)
Flux Data
Predicted Fluxes C 009 -limited 200 180 160 140 120 100 80 60 40 20 0 WT (LP) 9 10 1 6 17 1545 0 250 18 150 8 2 7 9 100 14 5 46 3 r=-0. 06 p=6 e-1 10 13 11 12 Predicted Fluxes 200 50 250 Dpyk (LP) 200 15 17 2 141311 312 r=0. 91 p=8 e-8 16 18 50 100 150 Experimental Fluxes 8 150 100 14 10 9 13 11 31 12 50 0 200 Dpyk (QP) 7 16 0 7 8 r=0. 56 P=7 e-3 16 15 62 5 4 18 17 1 -50 -50 0 50 100 150 200 250 Experimental Fluxes
Competitive growth data: reproducibility Correlation between two selection experiments Badarinarayana, et al. Nature Biotech. 19: 1060
Competitive growth data On minimal media negative selection LP small effect C 2 p-values 4 x 10 -3 QP 1 x 10 -5 Position effects Novel redundancies Hypothesis: next optima are achieved by regulation of activities.
Lab evolution optimization C. ph E. co E. co M. tb E. co Tolonen Reppas/Lin Lenski Palsson Edwards Ingram Stephanopoulos Marliere J&J Du. Pont Alcohol resistance Trp/Tyr exchange Citrate utilization Glycerol utilization Radiation resistance Lactate production Ethanol resistance Thermotolerance Diarylquinoline resistance 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 (641 kb) Internal view of the aphid. (by T. Sasaki) Bacteriocyt e (Photo by T. Fukatsu) Aphids http: //buchnera. gsc. riken. go. jp Buchnera (Photo by M. Morioka)
Shigenobu et al. Genome sequence of the endocellular bacterial symbiont of aphids Buchnera sp. APS. Nature 407, 81 -86 (2000).
Trp & Tyr (key pharma precursors) Crossfeeding synthetic ecosystem (syntrophic co-culture) 14
Covariance in lab evolution First Passage Second Passage trp/ tyr. A 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
Sequence monitoring of evolution (optimize transport & drug resistance) Sequence Reppas, Lin & Church
Evolved syntrophic strain pairs Trp D Tyr D 17
Reading lab-evolved genomes sequenced across time & within each time-point Independent lines of Trp. D & Tyr. D co-culture 5 Omp. F: (pore: large, hydrophilic > small) 42 R-> G, L, C, 113 D->V, 117 E->A 2 Promoter: (cis-regulator) -12 A->C, -35 C->A 5 Lrp: (trans-regulator) 1 b. D, 9 b. D, 8 b. D, IS 2 insert, R->L in DBD. At late times Tyr. D becomes prototrophic! Reppas, Shendure, Porecca -12 -11 -10 -9 18 -8 -7 -6
Resynthesis of mutant combinations --Additive effects insensitive to order of mutation 19
- Slides: 19