Using Kinetic Modelling to Infer Adaptations in Saccharomyces cerevisiae Carbohydrate Storage Metabolism to Dynamic Substrate Conditions

Abstract

Microbial metabolism is strongly dependent on the environmental conditions. While these can be well controlled under laboratory conditions, large-scale bioreactors are characterized by inhomogeneities and consequently dynamic conditions for the organisms. How Saccharomyces cerevisiae response to frequent perturbations in industrial bioreactors is still not understood mechanistically. To study the adjustments to prolonged dynamic conditions, we used published repeated substrate perturbation regime experimental data, extended it with proteomic measurements and used both for modelling approaches. Multiple types of data were combined; including quantitative metabolome, ¹³C enrichment and flux quantification data. Kinetic metabolic modelling was applied to study the relevant intracellular metabolic response dynamics. An existing model of yeast central carbon metabolism was extended, and different subsets of enzymatic kinetic constants were estimated. A novel parameter estimation pipeline based on combinatorial enzyme selection supplemented by regularization was developed to identify and predict the minimum enzyme and parameter adjustments from steady-state to dynamic substrate conditions. This approach predicted proteomic changes in hexose transport and phosphorylation reactions, which were additionally confirmed by proteome measurements. Nevertheless, the modelling also hints at a yet unknown kinetic or regulation phenomenon. Some intracellular fluxes could not be reproduced by mechanistic rate laws, including hexose transport and intracellular trehalase activity during substrate perturbation cycles.

Keywords: Saccharomyces cerevisiae; adaptation; carbon storage metabolism; glucose transport; kinetic modeling; parameter estimation; repeated substrate perturbation regime.

Figure 1

Profile of the experimental feeding regime. After a chemostat phase (reference steady-state) of 50 h, a block-wise feed is applied in a 400 s cycle at the same average substrate supply and dilution rate for another 50 h (adapted from [13]). On the left, a schematic overview of the feed rate during chemostat and repeated substrate perturbation regimes is shown. On the right, the resulting extracellular substrate concentration profile in the fermentation broth is shown.

Figure 2

The protein concentration is presented as a log2 fold change from chemostat to dynamic substrate conditions of selected glycolytic and transporter proteins. Protein concentration fold change was measured by liquid chromatography tandem mass spectrometry (LC-MS/MS).

Figure 3

Kinetic metabolic model with a detailed description of trehalose and glycogen metabolism. Sink reactions account for fluxes towards the TCA, PPP and biomass synthesis. This model was adapted from [29]. The diagram style was adapted from [9]. For a detailed view on model mass balances and reaction kinetics, see Supplementary File S1.

Figure 4

Model simulations in comparison to experimental observations: (A) metabolite concentrations; and (B) reaction rates estimated from 13C enrichment data over one cycle (400 s). Metabolite concentrations and reaction rates are displayed in the y-axis (in mM and mM s⁻¹, respectively) and time in the x-axis; (C) normalized metabolite concentrations during one feeding cycle. Darker colours indicate values closer to the maximum, while brighter ones indicate values closer to the minimum.

Figure 5

Two-step, scaled optimization approach results: (A) fitting the data with different subsets of enzyme parameters; bars show the error between simulation and best fit with the respective combination (upper x-axis). Blue bars highlight the combinations containing the two enzymes HXT and GLK. Red lines show the number of enzymes; (B) implementation of a regularization factor on the estimation of GLK kinetic parameters; the dashed and continuous line; show model and parameter error, respectively. The arrow indicates the chosen regularization factor. Parameters are regularized such that the data is still well reproduced (see Supplementary Figures S3 and S4). (C) change in key GLK parameters identified upon regularization; the deviation between the estimated parameter and the initial value taken from (bioRxiv2022) is shown in the y-axis (in logarithmic scale). Black and empty circles show the estimates prior and post regularization when parameter dependencies are minimized. The x-axis shows specific parameters.

Figure 6

Glucose sensing is needed to explain HXT kinetics: (A) glucose uptake rate at 20 s vs at 400 s; 20 s is the approximate point for the maximum reaction rate. Black data show simulations generated with randomly generated parameter samples when no threshold value is considered. A total of 1000 samples were run within 3 orders of magnitude above and below the estimated parameters. Parameters were randomized for HXT kinetics, and external glucose concentration was fit to the experimental data; (B) visualization of hexose transport rate during the cycle for the abovementioned models; the blue line corresponds to the simulation with the model considering glucose sensing. The grey and black coloured simulations are the ones with the generated models. Only 200 are displayed and some simulations are highlighted in black to ease visualization. The red dots point to the experimental data points. The individual effect of HXT kinetic parameters ($V_{max}$, $K_M$) can be found in Supplementary Figure S5.

Figure 7

Predicted and observed 13C labelling enrichment during substrate perturbation cycles: (A) enrichment of intracellular metabolite (%) vs time; black lines consist of the simulations and red markers to the experimental data points. Feeding phase is shaded in grey. The X-axis is the cycle time, from 0 to 400 s, and the Y-axis is the enrichment percentage, from 0 to 100%; (B) diagram of inflow to cytosolic glucose; (C) fluxes that positively contribute to the cytosolic glucose mass balance (mM s⁻¹) vs. the cycle time (s); red coloured are labelled data, blue coloured, non-labelled; (D) contribution of each flux to the cytosolic glucose mass balance (in %) vs. the cycle time (s); red coloured are labelled data, blue coloured are non-labelled.

Figure 8

Missing regulation on NTH1 could explain excessively low simulated cytosolic trehalose concentrations: (A) NTH1 reaction kinetics; (B) NTH1 reaction rate; (C) cytosolic trehalose; blank lines show simulations, and red dots experimental data.