1. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Robustness Analysis & Phenotype Phase Plane Analysis

2. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Learning Objectives Explain the capabilities of robustness analysis Explain how shadow prices can be used in metabolic modeling Explain how reduced costs can be used in metabolic modeling Explain the capabilities of phenotype phase plane analysis

3. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Lesson Outline Robustness Analysis Shadow Prices Reduced Costs Phenotype Phase Plane Analysis

4. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis ROBUSTNESS ANALYSIS The flux through one reaction is varied and the optimal objective value is calculated as a function of this flux. This reveals how sensitive the objective is to a particular reaction. Example: Determine the effect of varying glucose uptake on growth Clear; % Input model model=readCbModel('ecoli_textbook'); % Set oxygen uptake rate model = changeRxnBounds(model,'EX_o2(e)',-17,'l'); % Set the upper bound for glucose uptake model = changeRxnBounds(model,'EX_glc(e)',-18.5,'l'); % Set optimization objective model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); % Use robustnessAnalysis for glucose uptake rate robustnessAnalysis(model,'EX_glc(e)',100); AerobicGlucoseBioMassRA.m

5. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Robustness Analysis Example Impact of Increasing Glucose Growth remains at 0 hr -1 until a glucose uptake rate of about 0.48 mmol gDW -1 hr -1, because with such a small amount of glucose, the system cannot make 8.39 mmol gDW -1 hr -1 of ATP needed to meet the default lower bound of the ATP maintenance reaction (ATPM) Oxygen uptake limits growth! Excess glucose cannot be fully oxidized, so the acetate fermentation pathways is used. X X AerobicGlucoseBioMassRA.m

6. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Robustness Analysis Example Maps (AerobicGlucoseBioMassRA.m) EX_glc(e) =-7 mmol gDW -1 hr -1 EX_glc(e) =-10 mmol gDW -1 hr -1

7. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Robustness Analysis Example Impact of Increasing Oxygen At an oxygen uptake of about 21.80 mmol gDW -1 hr -1, growth actually begins to decrease as oxygen uptake increases. This is because glucose becomes limiting at this point, and glucose that would have been used to produce biomass must instead be used to reduce excess oxygen. EX_glc(e) is set at -10 mmol gDW -1 hr -1 AerobicGlucoseBioMassRA.m X X

8. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Robustness Analysis Example Maps Impact of Increasing Oxygen EX_o2(e) = -20EX_o2(e) = -25 AerobicGlucoseBioMassRA_Map.m

9. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Maximum Anaerobic Ethanol Production AnaerobicEthanolRA.m % AnaerobicEthanolRA.m clear; % Input the E.coli core model model=readCbModel('ecoli_textbook'); % Set uptake rates model = changeRxnBounds(model,'EX_glc(e)',-10,‘b'); model = changeRxnBounds(model,'EX_o2(e)',-0,'b'); % Set optimization objective to Biomass_Ecoli_core_N(w/GAM)_Nmet2 model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); % Using robustnessAnalysis, plot the objective function as a function % of the ethanol secretion rate [controlFlux, objFlux] = robustnessAnalysis(model,'EX_etoh(e)',100); Maximum Growth Rate (8.283, 0.2117) Maximum Ethanol Production Fix Glucose and Oxygen Uptake Rates

10. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Ethanol Production Phenotypes AnaerobicEthanolRA.m & AnaerobicEthanolRA_Maps.m % Draw a map of the different production phenotypes clear; model=readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_glc(e)',-10,'b'); model = changeRxnBounds(model,'EX_o2(e)',-0,'b'); model = changeRxnBounds(model,'EX_etoh(e)',4.242,'b'); % Low %model = changeRxnBounds(model,'EX_etoh(e)',12.53,'b'); % Medium %model = changeRxnBounds(model,'EX_etoh(e)',18.38,'b'); % High model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); FBAsolution = optimizeCbModel(model,'max',0,0) map=readCbMap('ecoli_Textbook_ExportMap'); options.zeroFluxWidth = 0.1; options.rxnDirMultiplier = 10; drawFlux(map, model, FBAsolution.x, options); printFluxVector(model, FBAsolution.x, true) Low Production (4.242, 0.1757) High Production (18.38, 0.1063) Medium Production (12.53, 0.2002)

11. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Ethanol Production Phenotype Maps AnaerobicEthanolRA_Maps.m Low Production Medium Production High Production

12. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Lesson Outline Robustness Analysis Shadow Prices Reduced Costs Phenotype Phase Plane Analysis

13. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Shadow Prices: Metabolites Shadow prices, π i, are the derivative of the objective function, Z, with respect to the flux, b i, of a metabolite. The shadow prices define the incremental change in the objective function if a constraining flux is incrementally changed. The sensitivity of an FBA solution is indicated by shadow prices. They indicate how much the addition of a given metabolite will increase or decrease the objective. In the COBRA Toolbox, shadow prices can be calculated by optimizeCbModel. The vector of y shadow prices is solution.y (glpk solver) -0.0360 -0.0325 -0.0230 +0.0229 ShadowPricesExampleO2.m EX_glc(e) = -10

14. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Shadow Prices Since If the objective is set to maximize cell growth rate ( Z GR ), and the shadow price ( π i ), of oxygen ( b EX_o2(e) ) is -0.0230, it means that an additional flux unit of oxygen, within the EX_o2(e) uptake region of -15 and -21, will increase the growth rate by 0.0230. Each steady state solution (phenotype) will have different shadow prices. This example is based on EX_glc(e) = -10 (AerobicGlucoseBioMassShadowPrices.m) 1 unit of flux of b NADH -0.0360 -0.0325 -0.0230 +0.0229 EX_glc(e) = -10 ShadowPricesExampleO2.m

15. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Shadow Prices for Growth on Glucose (ShadowPricesAerobicGrowthRateData.m) clear; model=readCbModel('ecoli_textbook'); changeCobraSolver('glpk'); % Use Matlab solver % Set the lower bounds for oxygen and glucose uptake model = changeRxnBounds(model,'EX_o2(e)',-20,‘b '); model = changeRxnBounds(model,'EX_glc(e)',-10,'l'); % Set optimization objective to Biomass_Ecoli_core_N(w/GAM)_Nmet2 model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); % Optimize objective function FBAsolution = optimizeCbModel(model,'max'); % Must allow loops % Print flux values printFluxVector(model, FBAsolution.x, true) % Print shadow prices 'Shadow prices' printShadowPriceVector(model, FBAsolution.y, true) clear; model=readCbModel('ecoli_textbook'); changeCobraSolver('glpk'); % Use Matlab solver % Set the lower bounds for oxygen and glucose uptake model = changeRxnBounds(model,'EX_o2(e)',-20,‘b '); model = changeRxnBounds(model,'EX_glc(e)',-10,'l'); % Set optimization objective to Biomass_Ecoli_core_N(w/GAM)_Nmet2 model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); % Optimize objective function FBAsolution = optimizeCbModel(model,'max'); % Must allow loops % Print flux values printFluxVector(model, FBAsolution.x, true) % Print shadow prices 'Shadow prices' printShadowPriceVector(model, FBAsolution.y, true) MetaboliteSP 13dpg[c]-0.037 2pg[c]-0.027 3pg[c]-0.027 6pgc[c]-0.057 6pgl[c]-0.055 ac[c]-0.003 acald[c]-0.011 acald[e]-0.011 acon-C[c]-0.040 actp[c]-0.013 akg[c]-0.033 akg[e]-0.031 amp[c]0.010 atp[c]-0.010 cit[c]-0.040 coa[c]0.010 dhap[c]-0.036 e4p[c]-0.043 etoh[c]-0.013 etoh[e]-0.010 f6p[c]-0.059 fdp[c]-0.071 for[c]-0.004 for[e]-0.004 fru[e]-0.046 fum[c]-0.028 fum[e]-0.023 g3p[c]-0.036 g6p[c]-0.059 MetaboliteSP glc-D[e]-0.046 gln-L[c]-0.047 gln-L[e]-0.037 glu-L[c]-0.037 glu-L[e]-0.034 glx[c]-0.015 h[c]0.003 icit[c]-0.040 lac-D[c]-0.015 lac-D[e]-0.013 mal-L[c]-0.028 mal-L[e]-0.023 nadh[c]-0.004 nadph[c]-0.006 o2[c]-0.023 o2[e]-0.023 oaa[c]-0.027 pep[c]-0.027 pi[c]-0.003 pyr[c]-0.014 pyr[e]-0.011 q8h2[c]0.006 r5p[c]-0.051 ru5p-D[c]-0.051 s7p[c]-0.066 succ[c]-0.022 succ[e]-0.024 succoa[c]-0.019 xu5p-D[c]-0.051

16. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Glucose Shadow Prices: Aerobic Growth Rate Example (ShadowPricesAerobicGrowthRate_glc.m) If the objective is set to maximize cell growth rate ( Z GR ), and the shadow price ( π glc-D[e] ), of glucose is -0.046 when EX_o2(e) = -20, it means that an additional molecule of glucose will increase the growth rate by 0.046. clear; model=readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_o2(e)',-20,‘b '); model = changeRxnBounds(model,'EX_glc(e)',-10,‘b '); model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); FBAsolution = optimizeCbModel(model,'max') printFluxVector(model, FBAsolution.x, true) clear; model=readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_o2(e)',-20,‘b '); model = changeRxnBounds(model,'EX_glc(e)',-10,‘b '); model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); FBAsolution = optimizeCbModel(model,'max') printFluxVector(model, FBAsolution.x, true) Biomass (EX_glc(e) = -10) 0.8320.878 Biomass (EX_glc(e) = -11)ΔBiomass 0.046 -0.046 -0.137 -0.033 Change between -10 & -11

17. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Lesson Outline Robustness Analysis Shadow Prices Reduced Costs Phenotype Phase Plane Analysis

18. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Reduced Costs: Reactions Reduced costs are the derivatives of the objective function ( Z ) with respect to an internal reaction ( v i ) with 0 flux. Reduced costs indicate how much each particular reaction affects the objective. The reduced costs are associated with each flux (v i ) and signify the amount by which the objective function is decreased if v i is increased. For instance, if the input flux of glucose shows a reduced cost of -x, it means that increasing that flux by one unit will increase of the objective function by x units. In the COBRA Toolbox, reduced costs can be calculated by optimizeCbModel. The vector of reduced costs is FBAsolution.w (glpk solver) 1 unit of flux EX_glc(e) = -10 +0.0229 -0.0230 -0.0325 -0.0360 ReducedCostsExampleO2.m

19. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Glucose Reduced Costs: Aerobic Growth Rate Example (ReducedCostsAerobicGrowthRate_glc.m) If the objective is set to maximize cell growth rate ( Z GR ), and the reduced costs ( ρ EX_glc(e) ), of glucose ( EX_glc(e) ) is -0.046, it means that an additional unit of glucose will increase the growth rate by 0.046. clear; model=readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_o2(e)',-20,‘b '); model = changeRxnBounds(model,'EX_glc(e)',-10,‘b '); model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); FBAsolution = optimizeCbModel(model,'max') printFluxVector(model, FBAsolution.x, true) clear; model=readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_o2(e)',-20,‘b '); model = changeRxnBounds(model,'EX_glc(e)',-10,‘b '); model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); FBAsolution = optimizeCbModel(model,'max') printFluxVector(model, FBAsolution.x, true) Biomass (EX_glc(e) = -10) 0. 8320. 878 Biomass (EX_glc(e) = -11) Δ Biomass 0.046 -0.046 -0.137 -0.033 Change between -10 & -11

20. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Lesson Outline Robustness Analysis Shadow Prices Reduced Costs Phenotype Phase Plane Analysis

21. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Price, N. D., J. L. Reed, et al. (2004). "Genome-scale models of microbial cells: evaluating the consequences of constraints." Nature reviews. Microbiology 2(11): 886-897.

22. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis It is also possible to vary two parameters simultaneously and plot the results as a phenotypic phase plane. These plots can reveal the interactions between two reactions. Matlab Cobra function: phenotypePhasePlane(model, ‘rxn1’,’rxn2’) Phenotype Phase PlaneShadow Prices of rxn1Shadow Prices of rxn2

23. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example AerobicGlucoseBioMassPPP.m % Input model model=readCbModel('ecoli_textbook'); % Set oxygen and glucose uptake rates model = changeRxnBounds(model,'EX_o2(e)',-20,'l'); model = changeRxnBounds(model,'EX_glc(e)',-20,'l'); % Set optimization objective model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); % Phenotype phase plane analysis phenotypePhasePlane(model,'EX_glc(e)', 'EX_o2(e)‘);

24. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (II) Variables: EX_o2(e) & EX_glc(e) Phase 1 Phase 3 Phase 2 Phase 4 Phase 5 AerobicGlucoseBioMassPPP.m

25. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (Phase 1) >> AerobicGlucoseBioMassPhase1 FBAsolution = f: 0 x: [] stat: -1 origStat: 110 solver: 'glpk' time: 0.0210 >> AerobicGlucoseBioMassPhase1 FBAsolution = f: 0 x: [] stat: -1 origStat: 110 solver: 'glpk' time: 0.0210 No Growth No growth; not enough glucose AerobicGlucoseBioMassPhase1.m EX_glc(e)= 1 EX_o2(e)= 10 Ferm TCA PPP Glyc Ana OxP

26. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (Phase 2) ACONTa3.41586 ACONTb3.41586 AKGDH2.69395 ATPM8.39 ATPS4r21.278 Biomass0.183018 CO2t-10.2116 CS3.41586 CYTBD20 ENO5.23969 EX_co2(e)10.2116 EX_glc(e)-3 EX_h2o(e)11.5448 EX_h(e)3.67134 EX_nh4(e)-0.997959 EX_o2(e)-10 EX_pi(e)-0.673268 AerobicGlucoseBioMassPhase2.m EX_glc(e) Growth is limited by excess oxygen; not enough glucose to reduce all the oxygen and produce biomass optimally FBA2.81795 FUM3.2184 GAPD5.51348 GLCpts3 GLNS9.47587 GLUDy-0.951162 GLUN9.42907 H2Ot-11.5448 ICDHyr2.89141 ICL0.524456 MALS0.524456 MDH3.74286 NADH1616.7816 NH4t0.997959 O2t10 PDH4.62623 PFK2.81795 EX_glc(e)= -3 EX_o2(e)= -10 PGI2.96248 PGK-5.51348 PGM-5.23969 PIt2r0.673268 PYK2.14468 RPE-0.131553 RPI-0.131553 SUCDi3.2184 SUCOAS-2.69395 TALA-0.032741 THD20.444093 TKT1-0.032741 TKT2-0.098811 TPI2.81795 Ferm TCA PPP Glyc Ana OxP

27. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (Phase 3) ACKr-1.83668 ACONTa2.106 ACONTb2.106 ACt2r-1.83668 AKGDH1.70302 ATPM8.39 ATPS4r21.5061 Biomass0.373508 CO2t-10.4318 CS2.106 CYTBD20 ENO7.66481 EX_ac(e)1.83668 EX_co2(e)10.4318 EX_glc(e)-5 EX_h2o(e)13.1526 EX_h(e)9.32925 AerobicGlucoseBioMassPhase3.m EX_nh4(e)-2.03666 EX_o2(e)-10 EX_pi(e)-1.37402 FBA3.84494 FUM1.70302 G6PDH2r2.35059 GAPD8.22357 GLCpts5 GLNS0.095506 GLUDy-1.94116 GND2.35059 H2Ot-13.1526 ICDHyr2.106 MDH1.70302 NADH1618.297 NH4t2.03666 O2t10 PDH5.34252 PFK3.84494 PGI2.57284 PGK-8.22357 PGL2.35059 PGM-7.66481 PIt2r1.37402 PPC1.07032 PTAr1.83668 PYK1.40059 RPE1.29858 RPI-1.05201 SUCDi1.70302 SUCOAS-1.70302 TALA0.71671 TKT10.71671 TKT20.581873 TPI3.84494 EX_glc(e) EX_glc(e)= -3 EX_o2(e)= -10 EX_glc(e) Ferm TCA PPP Glyc Ana OxP Not enough oxygen to fully oxidize glucose; acetate produced through fermentation EX_glc(e)= -5 EX_o2(e)= -10

28. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (Phase 4) ACKr-9.90568 ACONTa0.60316 ACONTb0.60316 ACt2r-9.90568 ATPM8.39 ATPS4r18.8064 Biomass0.559051 CO2t-4.89467 CS0.60316 CYTBD20 ENO16.0799 EX_ac(e)9.90568 EX_co2(e)4.89467 EX_for(e)11.5033 EX_glc(e)-10 EX_h2o(e)8.96702 EX_h(e)32.6235 EX_nh4(e)-3.04839 AerobicGlucoseBioMassPhase4.m EX_o2(e)-10 EX_pi(e)-2.05658 FBA7.84632 FORti11.5033 G6PDH2r4.79277 GAPD16.9163 GLCpts10 GLNS0.142949 GLUDy-2.90544 GND4.79277 H2Ot-8.96702 ICDHyr0.60316 NADH1620 NH4t3.04839 O2t10 PDH1.10076 PFK7.84632 PFL11.5033 PGI5.09263 PGK-16.9163 PGL4.79277 PGM-16.0799 PIt2r2.05658 PPC1.60202 PTAr9.90568 PYK4.18773 RPE2.79333 RPI-1.99944 TALA1.49758 TKT11.49758 TKT21.29576 TPI7.84632 EX_glc(e) Ferm TCA PPP Glyc Ana OxP EX_glc(e)= -10 EX_o2(e)= -10 Not enough oxygen to fully oxidize glucose; acetate and formate are produced and secreted

29. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (Phase 5) ACALD-2.12502 ACKr-23.0206 ACONTa0.912497 ACONTb0.912497 ACt2r-23.0206 ALCD2x-2.12502 ATPM8.39 ATPS4r5.95415 Biomass0.845766 CO2t1.51113 CS0.912497 CYTBD20 ENO34.4864 ETOHt2r-2.12502 EX_ac(e)23.0206 EX_co2(e)-1.51113 EX_etoh(e)2.12502 EX_for(e)29.2279 AerobicGlucoseBioMassPhase5.m EX_glc(e)-19 EX_h2o(e)2.52474 EX_h(e)69.2146 EX_nh4(e)-4.61179 EX_o2(e)-10 EX_pi(e)-3.11132 FBA18.1587 FORti29.2279 GAPD35.7517 GLCpts19 GLNS0.216262 GLUDy-4.39553 H2Ot-2.52474 ICDHyr0.912497 NADH1620 NH4t4.61179 O2t10 PFK18.1587 PFL29.2279 PGI18.8266 PGK-35.7517 PGM-34.4864 PIt2r3.11132 PPC2.42363 PTAr23.0206 PYK12.6238 RPE-0.607936 RPI-0.607936 TALA-0.151307 THD214.5016 TKT1-0.151307 TKT2-0.456629 TPI18.1587 EX_glc(e) Ferm TCA PPP Glyc Ana OxP EX_glc(e)= -19 EX_o2(e)= -10 Not enough oxygen to fully oxidize glucose; acetate, formate and ethanol are produced and secreted.

30. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (VI) Variables: EX_o2(e) & EX_glc(e) Phase 1 Phase 3 Phase 2 Phase 4 Phase 5 No growth; not enough glucose Growth is limited by excess oxygen; not enough glucose to reduce all the oxygen and produce biomass optimally Not enough oxygen to fully oxidize glucose; acetate produced through fermentation Not enough oxygen to fully oxidize glucose; acetate and formate are produced and secreted Not enough oxygen to fully oxidize glucose; acetate, formate and ethanol are produced and secreted. AerobicGlucoseBioMassPPP.m

31. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (VII) There is a different phenotype for each phase region Phase 1 Phase 2 Phase 3 Phase 4 Phase 5 +0.02290.00-0.0230-0.0325 -0.0581-0.0360 Oxygen Shadow Prices Phase 1 Phase 2 Phase 3 Phase 4 Phase 5 -0.13730.00-0.0459-0.0325 -0.0305 Glucose Shadow Prices

32. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (VIII) (Robustness Analysis setting O 2 = -5 mmol/g DW-hr) There is a different phenotype for each phase region Given: O 2 = -5 mmol/g DW-hr Phase Boundaries Robustness Analysis Phase 1 Phase 2 Phase 3 Phase 4 Phase 5 -0.13730.0000-0.0459-0.0325 -0.0305 Glucose Shadow Prices

33. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (IX) (Robustness Analysis setting O 2 = -15 mmol/g DW-hr) There is a different phenotype for each phase region Given: O 2 = -15 mmol/g DW-hr Phase Boundaries Robustness Analysis Phase 1 Phase 2 Phase 3 Phase 4 Phase 5 -0.13730.00-0.0459-0.0325 -0.0305 Glucose Shadow Prices

34. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (X) (Robustness Analysis setting O 2 = 10 mmol/g DW-hr) There is a different phenotype for each phase region Given: O 2 = 10 mmol/g DW-hr Phase Boundaries Robustness Analysis Phase 1 Phase 2 Phase 3 Phase 4 Phase 5 -0.13730.00-0.0459-0.0325 -0.0305 Glucose Shadow Prices

35. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Line of Optimality The line of optimality (LO) is defined as a line representing the optimal relation between the two metabolic fluxes used to create a phenotype phase plane. The line of optimality is determined by specifying an uptake rate of the substrate along the x-axis and then allowing any value for the flux along the y-axis. Linear Programming can then be used to calculate the optimal value of the objective as a function of the y-axis flux. Once the objective is determined, the corresponding flux value for the y-axis is used to plot the line of optimality (LO). The LO defines the optimal utilization of the metabolic pathways without limitations on the availability of the substrates. LO

36. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (XI) (Robustness Analysis setting Glucose = -2.5 mmol/gDW-hr) Phase 1 Phase 2 Phase 3 Phase 4 Phase 5 -0.13730.0000-0.0459-0.0325 -0.0305 There is a different phenotype for each phase region Given: Glucose = -2.5 mmol/gDW-hr Phase Boundaries Robustness Analysis LO Glucose Shadow Prices

37. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (XII) (Robustness Analysis setting Glucose = -5 mmol/gDW-hr) There is a different phenotype for each phase region Given: Glucose = -5 mmol/gDW-hr Phase Boundaries Robustness Analysis LO Phase 1 Phase 2 Phase 3 Phase 4 Phase 5 -0.13730.0000-0.0459-0.0325 -0.0305 LO Glucose Shadow Prices

38. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (XIII) Variables: EX_o2(e) & EX_glc(e) Phase 1 Phase 3 Phase 2 Phase 4 Phase 5 No growth; not enough glucose Growth is limited by excess oxygen; not enough glucose to reduce all the oxygen and produce biomass optimally Not enough oxygen to fully oxidize glucose; acetate produced through fermentation Not enough oxygen to fully oxidize glucose; acetate and formate are produced and secreted Not enough oxygen to fully oxidize glucose; acetate, formate and ethanol are produced and secreted. Line of Optimality (LO) AerobicGlucoseBioMassPPP.m

39. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Adaptive Laboratory Evolution A phenotypic phase plane is a representation of how two fluxes in a metabolic network relate to each other and affect in silico-predicted optimal growth. Distinct planes are represented by several colors. Here, the line of optimality (LO, yellow) defines the ratio of glycerol uptake rate to oxygen uptake rate (OUR) that leads to optimal biomass production. On glycerol, wild-type E. coli initially has a phenotype that maps to a suboptimal region of the portrait. After a growing for several hundred generations on glycerol, the E. coli phenotype migrates to the line of optimality. (Conrad, T. M., N. E. Lewis, et al. (2011). "Microbial laboratory evolution in the era of genome-scale science." Molecular Systems Biology 7: 509.)

40. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Lesson Outline Robustness Analysis Shadow Prices Reduced Costs Phenotype Phase Plane Analysis

41. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Extra Slides

42. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (III) EX_glc(e) = -1 mmol/g DW-hr Phase 1 EX_glc(e) Ferm TCA PPP Glyc Ana OxP No growth; not enough glucose EX_glc(e) = -3 mmol/g DW-hr Phase 2 EX_glc(e) Ferm TCA PPP Glyc Ana OxP Growth is limited by excess oxygen; not enough glucose to reduce all the oxygen and produce biomass optimally

43. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (IV) Phase 3 EX_glc(e) = -5 mmol/g DW-hr EX_glc(e) Ferm TCA PPP Glyc Ana OxP Not enough oxygen to fully oxidize glucose; acetate produced through fermentation Phase 4 EX_glc(e) = -10 mmol/g DW-hr EX_glc(e) Ferm TCA PPP Glyc Ana OxP Not enough oxygen to fully oxidize glucose; acetate and formate are produced and secreted

44. © 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (V) Phase 5 EX_glc(e) = -19 mmol/g DW-hr EX_glc(e) Ferm TCA PPP Glyc Ana OxP Not enough oxygen to fully oxidize glucose; acetate, formate and ethanol are produced and secreted.