Flux Variability Analysis (FVA)

Variabilibity in metabolite uptake/production of E. coli

This guide introduces Flux Variability Analysis (FVA) as applied in cobrar to the core metabolic network model of Escherichia coli. Here, FVA is applied to estimate possible flux ranges for metabolite exchanges (positive value = production, negative values = consumption) assuming a minimal media with D-glucose as sole carbon source and under aerobic or anaerobic growth conditions.

For the following example, two packages are required:

library(cobrar)
#> Loading required package: Matrix
#> cobrar uses...
#>  - libSBML (v. 5.19.0)
#>  - glpk (v. 5.0)
library(ggplot2)

Aerobic growth conditions

fpath <- system.file("extdata", "e_coli_core.xml", package="cobrar")
mod <- readSBMLmod(fpath)

fvares <- fva(mod, react = mod@react_id[grepl("^EX_",mod@react_id)],
              opt.factor = seq(0.5, 1, length.out = 61))
fvares$react_name <- mod@react_name[match(fvares$react, mod@react_id)]
fvares$react_name <- gsub(" exchange$","",fvares$react_name)


ggplot(fvares,
       aes(x = react_name)) +
  geom_hline(yintercept = 0, linetype = 3) +
  scale_color_viridis_c() +
  geom_linerange(aes(ymin = min.flux, ymax = max.flux, col = growth.fraction),
                 linewidth = 6) +
  labs(x = "Metabolite exchange",
       y = "mmol / (gDW hr)",
       color = "Growth fraction") +
  theme_bw() +
  theme(axis.text.x = element_text(angle = 60, hjust = 1, vjust = 1))

Anaerobic growth conditions

mod_anero <- changeBounds(mod, "EX_o2_e", lb = 0)

fvares <- fva(mod_anero, react = mod_anero@react_id[grepl("^EX_",mod_anero@react_id)],
              opt.factor = seq(0.5, 1, length.out = 61))
fvares$react_name <- mod_anero@react_name[match(fvares$react, mod_anero@react_id)]
fvares$react_name <- gsub(" exchange$","",fvares$react_name)


ggplot(fvares,
       aes(x = react_name)) +
  geom_hline(yintercept = 0, linetype = 3) +
  scale_color_viridis_c() +
  geom_linerange(aes(ymin = min.flux, ymax = max.flux, col = growth.fraction),
                 linewidth = 6) +
  labs(x = "Metabolite exchange",
       y = "mmol / (gDW hr)",
       color = "Growth fraction") +
  theme_bw() +
  theme(axis.text.x = element_text(angle = 60, hjust = 1, vjust = 1))