The wild-type S. stipitis strain NRRL Y-7124 (ATCC 58376) was used in this study. S. cerevisiae 311 (ATCC 42511), a mutant that was created by treating a wild-type strain with ethidium bromide , was chosen as the respiratory-deficient S. cerevisiae strain. Stocks of the two yeasts were stored at 4°C on YM agar slants.
All pure and mixed cultures were performed in a synthetic yeast minimal medium . The composition per liter of water was 1.00 g MgSO4 ·7 H2O, 1.10 g/L KCl, 0.15 g CaCl2 · 2 H2O, 1.00 g (NH4)2HPO4, 8.75 g/L (NH4)2SO4, 60.3 mg myo-inositol, 30.0 mg Ca-panthothenate, 6.0 mg thiamine-HCl, 1.5 mg pyridoxine-HCl, 0.03 mg biotin, 10.6 mg MnSO4 · H2O, 9.0 mg ZnSO4 · 7 H2O, 5.0 mg FeSO4 · 7 H2O, and 2.4 mg CuSO4 · 2 H2O. Pre-cultures in media containing 20 g/L glucose and 20 g/L xylose for S. cerevisiae and S. stipitis, respectively, were grown at 30°C for 36 hours on a shake table set at 175 RPM. The inoculum concentration for each experiment was determined by calculating the volume of preculture required to obtain the target initial concentration of each cell type using the measured biomass concentration in the shake flask media.
All fermentations were performed in a HEL BioX array of 4 250 mL vessels situated in a shared block that provided both electric heat and independent magnetic agitation (HEL Group Ltd., Barnet, UK). Electrochemical probes monitored the dissolved oxygen and pH in each vessel, while individual thermocouples recorded the media temperatures. Bioreactor cultivations were performed at a constant temperature of 30°C and pH of 5, the optimal growth conditions for each yeast species . The pH in each vessel was controlled by the automatic addition of 1 N sulfuric acid or 2 N NaOH. Glucose and xylose were autoclaved separately and added to the growth media in the amounts indicated for each experiment. Antifoam A was added to the reactors as necessary to prevent foaming.
Aeration of culture media was found to be a crucial operating variable. The agitation speed was held constant at 500 RPM for both pure and mixed culture fermentations. The gas flow rate into each reactor was altered according to the aeration level required for each experiment. A linear relationship between the gas sparge rate and the gas–liquid oxygen mass transfer coefficient (k
a) was determined using the static gassing out method . Purely aerobic cultures were aerated with pure oxygen, while microaerobic fermentations were aerated with house air passed through a HEPA-VENT filter (Whatman Ltd., Kent, UK).
Total cell weight was measured using a correlation between OD595 measured on a WPA UV1101 Biotech Photometer (Biochrom Ltd., Cambridge, UK) and dry cell weight. Cell counts of S. cerevisiae and S. stipitis in co-culture were performed on a hemacytometer in triplicate and averaged. A typical cell count considered approximately 50 S. cerevisiae cells and 200 S. stipitis cells. Conversion factors between dry cell weight and number of cells were found by drying pure culture samples of each yeast after cell counts had been performed. These factors were found to be 0.006943 gdw/L for S. cerevisiae and 0.001944 gdw/L for S. stipitis. Ethanol, glucose and xylose concentrations were measured by YSI 2700 SELECT biochemistry analyzers (YSI Inc., Yellow Springs, OH) configured with the enzyme-bound membranes specified for each metabolite. Raw readings were interpreted by 2700 Xylose PC Software (YSI Inc., Yellow Springs, OH) to resolve cross-talk between the xylose and glucose specific membranes.
The most comprehensive S. cerevisiae metabolic reconstruction currently available, iMM904 , was used for pure and mixed culture simulations. The fully compartmentalized network was reconstructed from 904 genes and accounts for 1228 metabolites and 1412 reactions. S. stipitis metabolism was simulated with iBB814 , the first published genome-scale reconstruction for this organism. This model accounts for 814 genes, 971 metabolites and 1371 reactions that are compartmentalized in the cytoplasm, mitochondria, and extracellular space. Following the publication of iBB814, a slightly more detailed S. stipitis metabolic reconstruction was developed . We do not anticipate that the use of this alternative reconstruction would significantly alter the results reported in this paper.
The S. cerevisiae
co-culture model was constructed by combining the iMM904 and iBB814 stoichiometric matrices into a single matrix [56
]. Flux distributions for S. cerevisiae
) and S. stipitis
) were calculated by solving the following linear program based on the assumption that the two species attempted to maximize their individual growth rates:
where the subscript i represents the species, A
is the matrix of stoichiometric coefficients, v
is the vector of reaction fluxes including exchange fluxes, v
i,min and v
i,max are vectors of lower and upper flux bounds, μ
is the growth rate, and w
are vectors of experimentally determined weights that represent the contribution of each flux to biomass formation in S. cerevisiae and S. stipitis, respectively. Other than competing for the common substrate glucose, the two yeasts were assumed to grow independently without species interactions. Therefore the co-culture objective function μ was assumed to be the sum of the individual species growth rates, and the inclusion of multi-level objective functions  was deemed unnecessary. The co-culture model was also used to simulate pure cultures of S. cerevisiae and S. stipitis by constraining all fluxes of the unmodeled organism to zero.
The steady-state flux balance model (2) was extended to a dynamic model through the addition of the following extracellular mass balance equations:
are the biomass concentrations of S. cerevisiae and S. stipitis, respectively, G, Z, and E are the concentrations of glucose, xylose, and ethanol, respectively, v
e,c and v
e,s are ethanol exchange fluxes, v
is the glucose uptake rate for S. cerevisiae, and v
are the glucose and xylose uptake rates, respectively, for S. stipitis. An equation for the dissolved oxygen concentration (O) was necessary to accurately describe microaerobic growth of S. stipitis (see results). In this equation (8), v
are oxygen exchange fluxes, k
a is the volumetric mass transfer coefficient of oxygen from sparged gas to the culture medium, and O* is the saturation concentration of oxygen. For all simulations, O* was taken to be 0.24 mM, the saturation concentration for water at 30°C and 1 atm.
The following substrate uptake expressions were used to calculate upper bounds on the actual sugar and oxygen uptake rates:
are the maximum uptake rates of each substrate, K
are corresponding saturation constants, K
are ethanol inhibition constants, and K
is a glucose inhibition constant. The glucose (9) and xylose (10) uptake rates were assumed to follow Michaelis-Menten kinetics with an additional inhibitory term that reflects growth rate suppression at high ethanol concentrations . The glucose inhibition term added to the xylose uptake kinetics accounted for diauxic growth where S. stipitis favors glucose over xylose as the carbon source. The oxygen uptake rate was calculated from a Michaelis-Menten expression based on the dissolved oxygen content of the medium .
Pure and mixed culture dynamic flux balance models were solved using the Mosek optimization toolbox (Mosek ApS, Denmark) to resolve the linear program for intracellular metabolism within Matlab (Mathworks, Natick, MA) . Because S. cerevisiae could not meet the non-growth associated ATP maintenance demand during the xylose-only consumption phase, the maintenance flux was constrained to zero after glucose depletion to prevent the LP solver from returning zero fluxes for the S. stipitis network. Due to time-scale differences between the sugar and oxygen consumption rates, the differential equation system (3)--(8) exhibited a high degree of stiffness. To reduce the time required to generate large numbers of DFBA simulations for parameter fitting and in silico culture optimization, Matlab stiff ODE solvers ode15s and ode23tb were used to obtain approximate solutions. An ODE solver with greater accuracy, ode23, was used to generate model predictions once parameters had been estimated or an optimum had been determined. A typical co-culture batch simulation that was solved in two minutes with ode15s required five hours with ode23.