Lecture #19 Growth states of cells

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

OBJECTIVE FUNCTIONS Three basic types

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

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

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 Jun 20;82(6): Cone of possible objective functions Measured cellular operating state

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

THE BIOMASS OBJECTIVE FUNCTION (BOF) Cell growth

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 )

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

CORE E. COLI MODEL Start on a small scale

Example: core E. coli growth on glucose CompoundStoichiometry 3pg accoa adp59.81 akg atp coa e4p f6p g3p g6p gln-L glu-L h59.81 h2o nad nadh3.547 nadp nadph oaa pep pi59.81 pyr r5p BOF: core model

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

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

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

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

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

BOF Maintenance Parameters: Quantifying non-metabolic activity mmol ATP gDW-1 hr-1

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

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

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

Growth on other substrates Substrate Growth Rate (UR = -10)Growth Rate (UR = -20)Growth Rate (UR = -30) AerobicAnaerobicAerobicAnaerobicAerobicAnaerobic acetate acetaldehyde α-ketoglutarate ethanol fructose fumarate glucose L-glutamine L-glutamate D-lactate L-malate pyruvate succinate Simulated growth on all 13 biomass producing substrates at different uptake rates, aerobically and anaerobically, with ATPM = 8.39

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

GENOME-SCALE E. COLI MODEL

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

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

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

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

BOF Maintenance Parameters: Quantifying non-metabolic activity mmol ATP gDW-1 hr-1

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

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

UTILIZATION OF THE BIOMASS OBJECTIVE FUNCTION

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)

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%

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

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)

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

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

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