Flux Balance Analysis and the Evolution of Xylose Fermentation in Yeasts

Growth kinetics follow lag, exponential, and stationary phases, with their transitions marked by drastic changes in biomass growth rates. This may be due to shifts in transcriptional activity, where high substrate concentrations promote increasing ribosome production to support the exponential phase. Under this hypothesis, there are smooth transitions from low to high growth rates on a phenotypically uniform population of cells. However, this is not the case for Clostridium beijerinckii which, when grown in batches, present various phenotypes coexisting. It starts as a vegetative phenotype, where fast substrate consumption is paired by fast biomass growth and production of acidic products. Acidification promotes a fraction of cells to murph into a clostridial phenotype. These are non-dividing cells whose metabolism is geared towards sporulation, a process where glucose and the previously released acidic species in the medium are consumed, producing in turn solvents. Released spores may later germinate into vegetative cells if conditions became favorable.

We propose a kinetic model where all three stages of C beijerinckii are present at any given time. The dynamics between phenotypic states are described by differential equations within dynamic FBA. To model the vegetative-clostrial and spore-vegetative transitions, we used the concentration of acidic species as arguments to a logistic equation whose value can be interpreted as the fraction of the vegetative cells transiting to clostridial state. Likewise, we used a second logistic equation, this time as a function of the concentration of solvents, to model the fraction of clostridial cells that change into spores.

Using public RNA-seq databases we determined divergently expressed genes in each phenotype. We pruned the metabolic network of C beijerinckii accordingly to create phenotype-specific metabolic networks. To train our model we measured changes in substrates, and acidic and solventogenic species along batch cultures of C beijerinckii under various conditions.