Flux Balance Analysis

Author(s): Ronan M.T. Fleming, Leiden University

Reviewer(s):

Table of Contents

Author(s): Ronan M.T. Fleming, Leiden University Reviewer(s): INTRODUCTION TIMING E. coli core model MATERIALS - EQUIPMENT SETUP PROCEDURE Load E. coli core model Checking the non-trivial constraints on a model What are the default constraints on the model? Hint: printConstraints Example 1: Calculating growth rates What is the growth rate of E. coli on glucose (uptake rate = 18.5 mmol/gDW/h) under aerobic conditions? Hint: changeRxnBounds, changeObjective, optimizeCbModel, printFluxVector What are the main fields to check in the FBAsolution structure? Hint: help optimizeCbModel What does FBAsolution.stat mean? Example 2: Display an optimal flux vector on a metabolic map Which reactions/pathways are in use (look at the flux vector and flux map)? Hint: drawFlux Example 3: Anerobic growth What is the optimal growth rate under anaerobic conditions? Hint: changeRxnBounds What reactions of oxidative phosphorylation are active in anaerobic conditions? Hint: printFluxVector drawFlux Example 3: Growth on alternate substrates What is the growth rate of E. coli on succinate? Hint: changeRxnBounds REFERENCES

INTRODUCTION

In this practical, the use of Flux Balance Analysis (FBA) is introduced using the E. coli core model, with functions in the COBRA Toolbox v3.0 [2].

Flux balance analysis is a solution to the optimisation problem

where c is a vector of linear objective coefficients, S is an m times n matrix of stoichiometric coefficients for m molecular species involved in n reactions.

are n times 1 vectors that are the lower and upper bounds on the n times 1 variable vector

of reaction rates (fluxes). The optimal objective value is

is always unique, but the optimal vector

is usually not unique.

In summary, the data is {c,S,l,u} and the variable being optimised is v.

TIMING

< 1 hrs

E. coli core model

A map of the E. coli core model is shown in Figure 1.

Figure 1 Map of the core E. coli metabolic network. Orange circles represent cytosolic metabolites, yellow circles represent extracellular metabolites, and the blue arrows represent reactions. Reaction name abbreviations are uppercase (blue) and metabolite name abbreviations are lowercase (rust colour). This flux map was drawn using SimPheny and edited for clarity with Adobe Illustrator.

MATERIALS - EQUIPMENT SETUP

Please ensure that all the required dependencies (e.g. , git and curl) of The COBRA Toolbox have been properly installed by following the installation guide here. Please ensure that the COBRA Toolbox has been initialised (tutorial_initialize.mlx) and verify that the pre-packaged LP and QP solvers are functional (tutorial_verify.mlx).

PROCEDURE

Load E. coli core model

The most appropriate way to load a model into The COBRA Toolbox is to use the readCbModel function.

fileName = 'ecoli_core_model.mat';
if ~exist('modelOri','var')
    modelOri = readCbModel(fileName);
end
%backward compatibility with primer requires relaxation of upper bound on
%ATPM
modelOri = changeRxnBounds(modelOri,'ATPM',1000,'u');
model = modelOri;

The meaning of each field in a standard model is defined in the standard COBRA model field definition.

In general, the following fields should always be present:

S, the stoichiometric matrix
mets, the identifiers of the metabolites
b, Accumulation (positive) or depletion (negative) of the corresponding metabolites. 0 Indicates no concentration change.
csense, indicator whether the b vector is a lower bound ('G'), upper bound ('L'), or hard constraint 'E' for the metabolites.
rxns, the identifiers of the reactions
lb, the lower bounds of the reactions
ub, the upper bounds of the reactions
c, the linear objective
genes, the list of genes in your model
rules, the Gene-protein-reaction rules in a computer readable format present in your model.
osenseStr, the objective sense either 'max' for maximisation or 'min' for minimisation

Checking the non-trivial constraints on a model

What are the default constraints on the model?

Hint: printConstraints

Example 1: Calculating growth rates

Growth of E. coli on glucose can be simulated under aerobic conditions.

What is the growth rate of E. coli on glucose (uptake rate = 18.5 mmol/gDW/h) under aerobic conditions?

Hint: changeRxnBounds, changeObjective, optimizeCbModel, printFluxVector

What are the main fields to check in the FBAsolution structure?

Hint: help optimizeCbModel

What does FBAsolution.stat mean?

Example 2: Display an optimal flux vector on a metabolic map

Which reactions/pathways are in use (look at the flux vector and flux map)?

Hint: drawFlux

if exist('FBAsolution','var')
    outputFormatOK = changeCbMapOutput('matlab');
    map=readCbMap('ecoli_core_map');
    options.zeroFluxWidth = 0.1;
    options.rxnDirMultiplier = 10;
    drawFlux(map, model, FBAsolution.v, options);
end

Example 3: Anerobic growth

Growth of E. coli on glucose can be simulated under anaerobic conditions.

What is the optimal growth rate under anaerobic conditions?

Hint: changeRxnBounds

What reactions of oxidative phosphorylation are active in anaerobic conditions?

Hint: printFluxVector drawFlux

Example 3: Growth on alternate substrates

Just as FBA was used to calculate growth rates of E. coli on glucose, it can also be used to simulate growth on other substrates. The core E. coli model contains exchange reactions for 13 different organic compounds, each of which can be used as the sole carbon source under aerobic conditions.

What is the growth rate of E. coli on succinate?

Hint: changeRxnBounds

REFERENCES

1. Orth, J.D., Fleming, R.M. & Palsson, B.O. in EcoSal - Escherichia coli and Salmonella Cellular and Molecular Biology. (ed. P.D. Karp) (ASM Press, Washington D.C.; 2009).

2. Varma, A. & Palsson, B.O. Metabolic capabilities of Escherichia coli: I. Synthesis of biosynthetic precursors and cofactors. Journal of Theoretical Biology 165, 477-502 (1993).

3. Laurent Heirendt & Sylvain Arreckx, Thomas Pfau, Sebastian N. Mendoza, Anne Richelle, Almut Heinken, Hulda S. Haraldsdottir, Jacek Wachowiak, Sarah M. Keating, Vanja Vlasov, Stefania Magnusdottir, Chiam Yu Ng, German Preciat, Alise Zagare, Siu H.J. Chan, Maike K. Aurich, Catherine M. Clancy, Jennifer Modamio, John T. Sauls, Alberto Noronha, Aarash Bordbar, Benjamin Cousins, Diana C. El Assal, Luis V. Valcarcel, Inigo Apaolaza, Susan Ghaderi, Masoud Ahookhosh, Marouen Ben Guebila, Andrejs Kostromins, Nicolas Sompairac, Hoai M. Le, Ding Ma, Yuekai Sun, Lin Wang, James T. Yurkovich, Miguel A.P. Oliveira, Phan T. Vuong, Lemmer P. El Assal, Inna Kuperstein, Andrei Zinovyev, H. Scott Hinton, William A. Bryant, Francisco J. Aragon Artacho, Francisco J. Planes, Egils Stalidzans, Alejandro Maass, Santosh Vempala, Michael Hucka, Michael A. Saunders, Costas D. Maranas, Nathan E. Lewis, Thomas Sauter, Bernhard Ø. Palsson, Ines Thiele, Ronan M.T. Fleming, Creation and analysis of biochemical constraint-based models: the COBRA Toolbox v3.0, Nature Protocols, volume 14, pages 639–702, 2019 doi.org/10.1038/s41596-018-0098-2.