1. Lecture #19 Growth states of cells

2. Outline Objective functions The BOF The core E. coli model The genome-scale E. coli model Using BOF

3. OBJECTIVE FUNCTIONS Three basic types

4. Types of objective functions For basic exploration and probing of solution space – lecture #20 To represent likely physiological objectives – this lecture To represent bioengineering design objectives – lecture #31

5. Inferring the objective function Back calculate it from a known functional state – Burgard AP, Maranas CD. Biotechnol Bioeng. 2003 Jun 20;82(6):670-7. Guess at multiple objectives and find the one that fits best – Savinell JM, Palsson BO. J Theor Biol. 1992 Mar 21;155(2):215-42. – Schuetz R, Kuepfer L, Sauer U. Mol Syst Biol. 2007;3:119.

6. Identifying Candidate Cellular Objectives Calculating the cone of possible objective functions Defined Cellular Objective Mathematics Biological Significance: Given an experimentally measured cell state, calculates range of possible objectives for which the cell could be optimizing Example: Calculating potential objectives for Escherichia coli led to showed that optimal growth was a candidate objective function [Burgard and Maranas] References Burgard AP, Maranas CD. Biotechnol Bioeng. 2003 Jun 20;82(6):670-7. Cone of possible objective functions Measured cellular operating state

7. Objective Functions: fit to data Schuetz R, Kuepfer L, Sauer U. Mol Syst Biol. 2007;3:119.

8. THE BIOMASS OBJECTIVE FUNCTION (BOF) Cell growth

9. Properties of the BOF Quantifiable – Simultaneous demands on the metabolic network – Measurements needed: Dry Cell Weight Composition – Obtainable through standard assays Macromolecular breakdown – Drill-drown biochemical assays – Moving towards High-throughput measurements Can select for cells which display an optimal biomass formation – Adaptive Evolution enables experimental selection of cells with optimal biomass formation (max v BOF )

10. Conceptual Basis: The Biomass Objective Function Quantifying Macromolecular Content of a cell Quantifying Building Blocks of Macromolecules

11. CORE E. COLI MODEL Start on a small scale

12. Example: core E. coli growth on glucose CompoundStoichiometry 3pg-1.496 accoa-3.7478 adp59.81 akg4.1182 atp-59.81 coa3.7478 e4p-0.361 f6p-0.0709 g3p-0.129 g6p-0.205 gln-L-0.2557 glu-L-4.9414 h59.81 h2o-59.81 nad-3.547 nadh3.547 nadp13.0279 nadph-13.0279 oaa-1.7867 pep-0.5191 pi59.81 pyr-2.8328 r5p-0.8977 BOF: core model

13. Metabolic requirements to produce 1 g cells Scaled shadow prices (σ) of metabolites Yield of metabolite Growth yield Shadow price of metabolite Scaled shadow price: a dimensionless measure of the relative importance of a metabolite for producing biomass

14. Aerobic growth with no ATP maintenance Biomass yield: 0.0917 gDW/g Glc

15. Sensitivity of Biomass Yield Effect of varying flux through the pentose phosphate shunt on biomass yield

16. P/O ratio Can vary the P/O ratio by altering the NADH dehydrogenase (NADH16) or ATP synthase (ATPS4r) Standard P/O ratio in core model: 1.25 Set NADH16 to export 0 protons, P/O ratio = 0.5 Set ATPS4r to import 10 protons per ATP, P/O ratio = 0.5 Set ATPS4r to import 2.5 protons per ATP, P/O ratio = 2.0

17. Effects of Altering P/O Ratio The biomass yield is slightly more sensitive to changes in NADH transhydrogenase than in ATP synthase The scaled shadow price of ATP is lower when the P/O ratio is lower

18. BOF Maintenance Parameters: Quantifying non-metabolic activity 0 8.39 59.81 mmol ATP gDW-1 hr-1

19. ATP Maintenance Requirements Set nonzero lower bounds on ATPM reaction to simulate non-growth associated consumption of ATP Effects of maintenance requirement on use of pentose phosphate shunt: Yield sensitivity at 3 different ATPM req. Optimal PPS flux vs. ATPM req. Max biomass vs. ATPM req. Max ATP yield = 17.5

20. ATP Maintenance Requirements Effects of ATPM on NADPH yield and shadow price The discontinuity occurs because optimal pathway use for production of biomass shifts NADPH shadow price NADPH yield NADPH scaled shadow price

21. Effect of Precursor Drain Drain PEP from the system and maximize biomass Several discontinuities occur, each at a change in the flux distribution At a PEP drain of above 1.9, excess ATP and NADPH are produced, so their shadow prices are 0

22. Growth on other substrates Substrate Growth Rate (UR = -10)Growth Rate (UR = -20)Growth Rate (UR = -30) AerobicAnaerobicAerobicAnaerobicAerobicAnaerobic acetate0.173300.389300.60530 acetaldehyde0.284200.607300.93030 α-ketoglutarate0.528701.098201.66760 ethanol0.330400.669601.06870 fructose0.87390.21161.79060.51632.70720.8208 fumarate0.370700.786501.20220.0358 glucose0.87390.21161.79060.51632.70720.8208 L-glutamine0.559201.163601.76790 L-glutamate0.598701.242501.88620 D-lactate0.350300.740301.13030.0289 L-malate0.370700.786501.20220.0358 pyruvate0.291200.62210.06550.9530.1399 succinate0.397500.840101.28270 Simulated growth on all 13 biomass producing substrates at different uptake rates, aerobically and anaerobically, with ATPM = 8.39

23. Example: Growth on acetate, aerobic Acetate uptake rate = 10 mmol gDW -1 hr -1 Growth rate = 0.1733 hr -1

24. GENOME-SCALE E. COLI MODEL

25. The Biomass Objective Function: Genome-scale Quantifying Macromolecular Content of a cell Quantifying Building Blocks of Macromolecules

26. Procedure to Generate a Detailed Biomass Objective Function 23 BOF WT BOF CORE

27. BOF: Average and Essential Cellular Composition Define components of average cell Analysis of essential biomass components – Biomass objective function Core Upgrades BOF WT = Core + Upgrades BOF CORE = Core

28. Non-metabolic costs for cellular activity exist – Protein Synthesis and Breakdown – RNA/DNA polymerization – Membrane Leakage Non-metabolic costs – Approximated through ATP usage – Experimental growth data necessary to quantify – Two types: Growth and Non-Growth Associated BOF Maintenance Parameters: Accounting for non-metabolic activity Energy Cost: ATP + H 2 O  ADP + H + P i

29. BOF Maintenance Parameters: Quantifying non-metabolic activity 0 8.39 59.81 mmol ATP gDW-1 hr-1

30. Biomass Objective Function of E. coli Black – always essential Blue – have minimal component(s) Red – non-essential BOFwt = All BOFcore = Black + Blue

31. E. coli Reconstruction – iAF1261 Calculation and organization of data: Equation should be easily adjustable

32. UTILIZATION OF THE BIOMASS OBJECTIVE FUNCTION

33. Reconstruction to Predictive Model: How the BOF gets used (Panels D & E) Key biological factors to consider when using a reconstruction as a predictive model (A – D) Prediction of physiological behavior (E)

34. Which Parameters Matter?: Sensitivity Analysis on BOF Components Examining the key parameters associated with optimal growth predictions – Protein, RNA, Lipid content – P/O ratio – Maintenance parameters NGAM – non-growth associated maintenance GAM - non-growth associated maintenance Condition specific ? – Substrate conditions – Evolutionarily stable 50–80%10–25% 7–15%1.0–2.7 50%

35. Reaction Essentiality in Generating Biomass Precursors Black - Essential Gray - Nonessential but Influential White – No Affect

36. Application: Gene Deletions & Production Deficiencies H. Influenzae Central MetabolismH. Influenzae Central Metabolism 50 Biomass Requirements Genes of Central Metabolism Minimal Substrate Conditions (fructose) Carbon-supplemented Conditions (fructose, glucose, glycerol, galactose, fucose, ribose, and sialic acid) Production Capabilities Under Two Environmental Conditions: 1. “in vitro” Minimal Media (fructose) 1. “in vitro” Minimal Media (fructose) 2. “in vivo” Complete Conditions (multiple carbon sources) 2. “in vivo” Complete Conditions (multiple carbon sources)

37. Analysis of alternate growth conditions: BOF enabled prediction of phenotypes Examined all 300 different exchange reactions for their ability to support growth Compared results to Biolog ® Data for E. coli validation regulation errors discovery targets parallel concept

38. Summary Growth is enabled by the balanced production of all the compounds necessary for growth For a core metabolic model, growth can be represented by the balanced production of the 12 biosynthetic precursors Maintenance parameters are needed for metabolic demands other than the stoichiometric requirement for growth Model can be interrogated for many parameters: the glycolysis/ppp split, the P/O ratio, maintenance parameters, substrates, etc At the genome-scale several complicating factors appear: BOF=core + upgrades, variable P/O, etc

39. The end