Computational protocol: Parametric studies of metabolic cooperativity in Escherichia coli colonies: Strain and geometric confinement effects

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[…] Three dimensional dynamic flux balance analysis (3DdFBA) is only briefly reviewed here, as it was described rigorously previously []. The method couples a partial differential equation (PDE) description of chemical transport with flux balance analysis (FBA) []. Broadly speaking, the PDE represents the chemical species while FBA represents the cells. Metabolites are consumed and produced by a reaction-diffusion PDE: ∂C→∂t=D∇2C→+R(C→)(1) where C→ is a vector containing the concentrations of metabolites, D encodes the diffusion rates of the metabolites and R(C→) encode the reactive fluxes of the species. R includes any reactions among chemical species, active and passive transport into and out of cell volume and, crucially, exchange fluxes computed via a local dynamic FBA (dFBA) [] simulation (more precisely, fluxes are read from a table of solutions computed via FBA and the solution is used to compute uptake and efflux). Within this study, the reaction diffusion equation is solved on a 3 dimensional regular cubic lattice via a central finite difference scheme []. Dirichlet boundary conditions (constant value) are applied for all chemical species on the boundaries of the simulation volume. Gaseous species are allowed to diffuse anywhere in the simulation domain, while aqueous molecules (acetate, glucose, etc.) are limited to diffusion in lattice sites containing agar and cell mass.Cells, while being represented as a volume fraction (ϕi) on the lattice, are not diffused or actively transported (e.g. via chemotaxis) among lattice points. Rather, as cell growth occurs they are pushed isotropically into neighbouring lattice points (after some maximum volume fraction within the lattice site is achieved, namely ∑i ϕi ≥ 0.65). Volume fraction is related the mass of cells as ϕi=miVρi(2) where mi is the mass of a particular cell type in the lattice site, V is the volume of the lattice site, and ρi = mi,cell/Vcell is the density of a single cell with mi,cell and Vcell taken to be 258 fg and 1 fL [], respectively. Cell mass grows exponentially at the rate set by the local dFBA as dmidt=vbm,imi(3) where vbm is the flux through the biomass equation. An absorbing boundary condition for the cell mass is applied to the boundaries of the simulation volume. Cell mass is prevented from penetrating into the agar substrate. The reaction term in is coupled to the cell mass and the predicted uptake flux as R(C→)=m→·v→C where v→CCOBRApy []. For all simulations, the core E. coli biomass reaction [] was used as the primary objective reaction.When used unmodified, the models were incapable of predicting the correct growth rate and acetate production rate (neither aerobically nor anaerobically) when setting glucose uptake rates to those measured in the chemostat experiments. Therefore, the models were adjusted to minimize errors in acetate production and growth rates under both aerobic and anaerobic conditions. This was accomplished by fitting the maximum oxygen uptake rate and growth associated maintenance (ATP cost for cell growth) to experimental data. The fit parameters, glucose uptake rate, predicted acetate and growth rates, and the associated errors are shown in . In general, growth and aerobic acetate production rates could be fit with little error. The anaerobic acetate production rate was more difficult to capture; over the five strains we found an average error of 16.1%.Two phenotypes of E. coli were considered in the simulations: 1) those growing aerobically on glucose, and 2) those growing aerobically on acetate. Tables of FBA solutions (including uptake and efflux of key metabolites and growth rates) were generated for the phenotypes for all five E. coli strains. Because strain-specific acetate consumption data was not available, the maximal acetate uptake rate used in [] was adopted. FBA tables were generate with 50 (160) divisions between 0 and the maximal glucose (oxygen) uptake rates. […]

Pipeline specifications

Software tools DFBA, COBRApy
Databases BiGG Models
Application Metabolic engineering
Chemicals Glucose, Oxygen