Fig 1.
Population FBA methodology with correlated protein sampling.
An isogenic population of yeast is created by correlated sampling of distributions of metabolic proteins obtained from fluorescence microscopy experiments. ρ(x,y) represents Pearson correlation coefficient between the proteins x and y. Assuming Michaelis-Menten kinetics whereby vmax = Ncopy × kcat (where Ncopy is protein copy number and kcat is the turnover number of the protein) the sampled enzyme copy numbers are used to impose upper bounds (vmax) for the possible flux through their associated reactions. The correlations are obtained from microarray expression data. For two representative cells, the black hollow bars represent vmax values imposed on the reactions of an idealized network, while the solid color lines represent the actual flux that would be predicted to flow through the network. In each case, certain reactions, marked with red stars, constrain the flux through the network. Parsimonious Flux Balance Analysis (pFBA) [10] is used to calculate growth rate and flux distributions for each of the member of the population.
Fig 2.
(A) Predicted growth rate distribution from Population FBA analysis of E. coli with correlated sampling of protein distributions. Experimental bulk growth rate marked by black dashed line [34]. (B) Predicted growth rate distributions for 100,000 cells in glucose synthetic defined medium (SD) (blue). Also shown is the experimentally measured growth rate distribution in SD medium and 13C medium [38, 40]. Simulated growth curves have correlated sampling from protein distributions and mRNA microarrays. Growth rate distributions are made by binning growth rates into 50 bins.
Fig 3.
Fluorescence abundance distributions and conversion to protein counts.
(A)Linear fit between ln() values of mean protein counts and mean observed fluorescence abundance. See Methods for the exact values and names of proteins used in the calibration. (B and C) Two examples of fluorescence abundance distributions for different proteins [42], the first set exhibit severe deconvolution problems and were removed from the data set (B), the second set exhibit fluorescence abundances with smooth distributions (C).
Table 1.
Proteins used in conversion from fluorescence abundance to protein counts.
Table 2.
Examples of kcat values from BRENDA and the minimal values required to produce the reaction fluxes measured in 13C fluxomics experiments.
The minimal kcat is obtained by dividing 13C fluxes by mean protein counts using the Gene-Protein-Reaction (GPR) rules. The final kcat is obtained by the doubling procedure to reproduce a mean growth rate of 0.35 hr−1, and the final values of the associated mean vmax values obtained by taking mean vmax over 1000 cells from a population. Factor of 3.0 × 10−7 converts the units from cell−1 s−1 to mmol gDwt−1 hr−1. When more than one enzyme is responsible for a reaction, the GPR rules are used to determine how to process protein counts (sum of subunits in case of ‘or’ and minimum count among the subunits for ‘and’).
Fig 4.
Depiction of yeast central metabolism covering glycolysis, TCA cycle and electron transport chain.
Values next to reactions in the plot represent fluxes through those reactions. Values between parenthesis are derived from our simulations using yeast 7.6 model with (red) and without (black) constraints on acetate (Ac) and glycerol (Gly) secretion, whereas values between brackets (green) were taken from experimental 13C measurements [40]. A mapping between abbreviated reaction names and full names can be found in Table A4 in S1 Text. Constraint on ubiquinole-ferricytochrome c reductase reaction causes the Crabtree effect and is marked by red star.
Fig 5.
Analysis of metabolic fluxes from yeast 7.6 simulations in SD and 13C media.
(A) Glucose uptake, oxygen uptake and ethanol efflux from simulations in SD medium. (B) First PCA component showing fast growing cells performing respiration along with fermentation. (C) Second PCA component showing transport of glycine to mitochondria as part of Serine-Glycine cycle to produce NADH or NADPH which compensates for reduced NADH production due to limited fermentation due to glucose limitation (D) Third PCA component from SD medium simulations shows burning of NADH by mitochondrial alcohol dehydrogenase produced in Serine-Glycine cycle and transport of citric acid to mitochondria, all by fast growing cells.
Fig 6.
Variability in metabolite secretion and uptake among yeast cells.
The plots show a representative selection of reaction fluxes, depicting different types of behavior. All cells depicted here were simulated using the Yeast 7.6 model in SD medium conditions. Glycine efflux plot has negative values which indicate net uptake of glycine.
Fig 7.
Map showing metabolic pathways for cycling of serine and glycine in cytoplasm and mitochondria.
The Serine and Glycine cycle generates NADH, ATP, Succinate and Formate. Average fluxes over the 1,000 cells are shown besides each reaction. Reactions marked with red star were irreversible in previous versions of yeast metabolic model [13]. Letters in parenthesis after metabolite names indicate their location in the cell (c-cytoplasm, m- mitochondria, e-extracellular).
Fig 8.
Bimodality in amino acid utilization.
(A) 2D Histogram of growth rate and threonine uptake rate shows bimodality in threonine uptake among cells growing slower than 0.4 hr−1. (B) Scatter plot showing PDC flux and threonine uptake for slow growing cells (<0.35 hr−1). Whenever GAPDH or PDC flux is bound because of protein constraint (green + and red o respectively), cells take up threonine to fuel the glycine-serine cycle and generate NADH/NADPH and ATP which otherwise would have been generated from glycolysis.
Fig 9.
Growth rate distributions after GA optimizations.
The plots show a comparison between the observed growth rate distribution [38] (black bars) and the distributions obtained after 10 GA optimizations (colored lines) using the Yeast 7.6 model in SD media conditions.
Fig 10.
Analysis of GA replicates for serine glycine cycle usage.
Upon sampling ten thousand cells from each of the 10 GA replicates shown in Fig 9, the fluxes through reactions in the serine glycine cycle occur only in fast growing members of the population. Legend containing color code for the GA replicas can be found in the top left panel.
Fig 11.
Comparison of metabolic fluxes from doubling procedure and independent GA optimizations.
The figure shows a comparison between mean simulated flux through central metabolism after doubling procedure (blue), and the mean flux obtained across 10 GA optimizations (black). All simulations were done using Yeast 7.6 model in SD media conditions.