Biological Network Analysis: Metabolic Optimization Methods

1. Biological Network Analysis:Metabolic Optimization Methods Tomer Shlomi Winter 2008

2. Linear Programming • c, l, A, b, α, β are parameters • Problem may be either feasible or infeasible • If the problem has an unique optimal value: • It may either have a single optimal solution • Or a space of optimal solutions • Alternatively, the problem may be unbounded

3. CBM Example (I)

4. CBM Example (II)

5. CBM Example (III)

6. Flux Balance Analysis • Searches for a steady-state flux distribution v: S∙v=0 • Satisfying thermodynamic and capacity constraints: vmin≤v ≤vmax • With maximal growth rate Max vbiomass

7. Lecture Outline 1. Growth rate predictions Phenotypic Phase Plane (PPP) analysis 2. Gene knockout lethality predictions FBA Minimization of Metabolic Adjustment (MOMA) Regulatory On/Off Minimization (ROOM) 3. Predicting knockout strategy for metabolic production OptKnock OptStrain 4. Gene function prediction

8. 1. Growth rate predictions

9. Flux Balance Analysis (reminder) • Searches for a steady-state flux distribution v with maximal growth rate: Max vbiomass S∙v=0 vmin≤v ≤vmax • Requires bounds on metabolite uptake rates (b1)

10. Phenotype Phase Planes (PPP) (I) X axis – Succinate uptake rate Y axis – Oxygene uptake rate Z axis - Growth rate (maximal value of the objective function as function of succinate and oxygen uptake) Line of optimality

11. Phenotype Phase Planes (PPP) (II) Schilling 2001 • Observations: • Metabolic network is unable to utilize succinate as sole carbon source in anaerobic conditinos. • Region 1: oxygen excess – this region is wasteful – (less carbon is available for biomass production since it is oxidized to eliminate the excess oxygen.) Growth rate Oxygene Succinate • Region 3- the uptake of additional succinate has a negative effect. Cellular resources are required to eliminate excessive succinate.

12. Does E. coli behave according to Phenotype Phase Planes? (I) • E. coli was grown with malate as sole carbon source. • A range of substrate concentrations and temperatures were used in order to vary the malate uptake rate (MUR). • Oxygen uptake rate (OUR) and growth rate were measured

13. Does E. coli behave according to Phenotype Phase Planes? (II) Malate/oxygen PPP The experimentally determined growth rate were on the line of optimality of the PPP ! Ibarra et al., Nature 2002

14. Does E. coli behave according to Phenotype Phase Planes? (III) Same experiments were made using glycerol as sole carbon source Day 0 – Sub optimal growth Why? Day 1-40 – evolution toward optimal growth Day 40 –optimal growth Day 60 –optimal growth (no change)

15. 2. Gene Knockout Lethality

16. Predicting Knockout Lethality (I) • A gene knockout is simulated by setting the flux through the corresponding reaction to zero • The corresponding reactions are identified by evaluating the Boolean gene-to-reaction mapping in the model

17. Predicting Knockout Lethality (II) • A gene is predicted essential if it’s knockout yields a significant drop in the maximal possible growth rate • v1 is essential for growth • v6 is not essential for growth

18. Gene knockout lethality:E. coli in glycerol minimal media • In total, 819 out of the 896 mutants (91%) showed growth behaviors in glycerol minimal medium in agreement with computational predictions • 69% correct prediction out of the experimental essential genes

19. Gene knockout lethality:Resolving Discrepancies (I) 2. Gene essentiality prediction

20. Gene knockout lethality:Resolving Discrepancies (II)

21. Gene knockout lethality:Resolving Discrepancies (II)

22. 3. MOMA and ROOM

23. Minimization of Metabolic Adjustment (MOMA) (I) • FBA assumes optimality of growth for wild type – evolution drives the growth rate towards optimality • This assumption is not necessarily correct following a gene knockout! • What other objective can capture the • biological essence of these mutations? (hint – the title of this slide)

24. Minimization of Metabolic Adjustment (MOMA) (II) • Assumption: following the knockout, the mutant remains as close as possible to the wild-type strain • The flux distribution of mutant should also satisfy all constraints as in FBA

25. w v Minimization of Metabolic Adjustment (MOMA) (III) Formally: w – the wild-type optimal growth vector (obtained via FBA). v – a vector in mutant flux space. Find Vm which minimizes the Euclidian distance to Vwt : • Min (w-v)², - minimize Euclidian distance • s.t • S∙v = 0, - mass balance constraints • vmin v vmax - capacity constraints • vj = 0, jG - knockout constraints Solved using Quadratic Programming (QP)

26. Validating MOMA: Gene essentiality prediction

27. Validating MOMA: Experimental fluxes

28. Regulatory On/Off Minimization (ROOM) (I) • Assumption: The organism adapts by minimizing the set of flux changes (via the regulatory system) • Search for a feasible flux distribution with minimal number of changes from the wild-type byp Wild-type solution A B C E Knockout solution cof cof byp D

29. Regulatory On/Off Minimization (ROOM) (II) • Integer variables are required to track the ‘number of changes in flux’ from the wild-type • Use Boolean auxiliary variables y to reflect changes in flux between the wild-type and mutant • yi=0 if and only if vi =wi • Formulate a MILP problem to find a pair of v and y with a minimal sum of yi’s. Min yi - minimize changes s.t v – y ( vmax - w)  w - distance constraints v – y ( vmin - w)  w - distance constraints • S∙v = 0, - mass balance constraints • vj = 0, jG - knockout constraints

30. Validating ROOM: Alternative pathways • ROOM identifies short alternative pathways to re-route metabolic flux following a gene knockout, in accordance with experimental data

31. Validating ROOM: Experimental fluxes (I) • Intracellular fluxes measurements in E. coli central carbon metabolism • Obtainedusing NMR spectroscopy in C labelling experiments • Knockouts: pyk, pgi, zwf, and gnd in Glycolysis and Pentose Phosphate pathways • Glucose limited and Ammonia limited medias • FBA wild-type predictions above 90% accuracy 13 Emmerling, M. et al. (2002), Hua, Q. et al. (2003), Jiao, Z et al. (2003) (*) Based on a figure from Jiao, Z., et al.

32. Validating ROOM: Experimental fluxes (II) • ROOM flux predictions are significantly more accurate than MOMA and FBA in 4 out of 8 experiments • ROOM growth rate predictions are significantly more accurate than MOMA

33. 4. Metabolite Production

34. Constraint-based Modeling:Biotechnological Applications • Design bacteria that produces chemicals of interest Vanillin The major compound in Vanilla Bacteria Objective: Grow Fast Bioengineering Objective: Produce Vanillin Bioengineering Objective Produce Vanillin

35. OptKnock • Designing microbial organisms for efficient production of metabolites • Finds reactions whose removal increases the production of metabolite of interest

36. OptKnock: Optimization problem (I) • A nested (bi-level) optimization problem is needed

37. OptKnock: Optimization problem (I) • A nested (bi-level) optimization problem is needed Reactions to remove Cells have to grow Removed reactions have zero flux The max number of reactions to remove

39. Succinate Production Strains

40. OptStrain • An integrated framework for redesigning microbial production systems Step 1: Creation of universal reactions DB Step 2: Compute maximal theoretical metabolite production yield Step 3: Identifying the minimal number of required to be added to an organism to achieve the maximal production yield. Step 4: Adding the identified reactions and finding gene deletions that ensure metabolite secretion (OptKnock)

41. OptStrain: Step 1 • Creation of universal reactions DB • Download set of known reactions from KEGG (Kyoto Encyclopedia of Genes and Genomes) • Validate reaction data consistency – remove unbalanced reaction • Define a universal stoichiometric matrix S.

42. OptStrain: Step 2 • Determination of maximal theoretical yield of a metabolite of interest • Yield – metabolite production rate per unit of substrate uptake • Use LP to find the maximal yield for different substrates, denoted R

43. OptStrain: Step 3 • Identification of minimum number of non-native reactions for a host organism • MILP formulation – yi represented whether reaction i should be added to the organism

44. OptStrain: Step 4 • Incorporating the non-native reactions into the host organism’s stoichiometric model • Eliminate genes such that biomass production is coupled with the production of the metabolite of interest • OptKnock

45. Case study: Hydrogen production • The highest hydrogen yield (0.126 g/g substrate consumed) is obtained for methanol

46. Case study: Hydrogen production (I) • Testing E. coli on glucose media • Step 3 reveals that new reactions are needed for E. coli on glucose

47. Case study: Hydrogen production (II) • C. acetobutylicum - the "Weizmann Organism", after Chaim Weizmann, who in 1916 helped discover how C. acetobutylicum culture could be used to produce acetone, butanol, and ethanol from starch • The knockout of 2 reactions tightly couple biomass production and metabolite hydrogen secretion

48. Case study: Vanillin production (I) • Vanillin is an important flavor and aroma molecule (found in vanilla pods) • Maximal theoretical production rate: 0.63 (g/g glucose) • E. coli needs 3 new reactions to achieve this vanillin yield • Previous bioengineering experiments have already involved the extraction of these 3 reactions from Neurospora crassa and their addition to E. coli • However, the resulting vanillin production rate was only 0.15

49. Case study: Vanillin production (II) • OptStrain predicts knockout sets that provide a vanillin yield of 0.57 (g vanillin/g glucose) in E. coli • This is close to the maximal theoretical production rate

50. 4. Gene function prediction