*2.2. Pathway-Scale Kinetic Model of Substrate Uptake* 2.2.1. Structure of the Model

A kinetic ordinary differential equation (ODE)-based model of *C. cohnii*, including metabolic reactions that connect glucose, ethanol and glycerol uptake and the Krebs cycle with the production of Acetyl-CoA, the precursor of DHA, was developed. The model is organized into three compartments (extracellular, cytosol and mitochondria). The model contains 35 reactions and 36 metabolites (Figure 4).

The model structure was developed based on research by Zhang's group on transcriptomics [31] and the 13C metabolic flux analysis [32] of DHA production in the case of glucose consumption. This kinetic model structure is similar to the structure proposed in Cui et al. [32]; however, the pentose phosphate pathway and glutamate dehydrogenase reactions were removed to make the kinetic model simpler and because the fluxes through these reactions were relatively small. The model does not include energy and redox cofactor moieties. The kinetic equations and some parameters of the reactions were obtained from the following databases: *Brenda* [33], *SABIO-RK* [34] and *UniProt* [35].

The tricarboxylic acid cycle reaction parameters were adapted from [36]. The equilibrium constant of reactions was assessed using *Equilibrator* [37] and the NIST database (https://randr.nist.gov/enzyme/, accessed on 3 January 2022). The unit used for the reaction fluxes in the model is mmol·L−1·min<sup>−</sup>1.

**Figure 4.** Metabolic network scope of the kinetic model. Dashed lines show transport reactions. Abbreviated metabolites—ExtGlucose: external glucose; ExtGlycerol: external glycerol; ExtEthanol: external ethanol; Glu6P: glucose 6-phosphate; Fru6p: fructose 6-phosphate; Fru1,6P: fructose 1,6 bisphosphate; DHAP: dihydroxyacetone phosphate; Gra3P: glyceraldehyde-3-phopshate; Gri1,3P: glycerate-1,3-biphosphate; Gri3P: glycerate-2-phosphate; Gri2P: Glycerate-2-phosphate; PEP: phosphoenolpyruvate; Acetyl-CoA: acetyl coenzyme-A. (Enzymes: HK: hexokinase; PGI: Phosphoglucose isomerase; PFK: Phosphofuctokinase; ALD: Fructosebiphosphate aldolase; TPI: Triosephosphate isomerase; Gra3PDH: Glyceraldehyde phosphate dehydrogenase; PGK: 3-phosphoglycerate kinase; PGM: Phosphoglycerolmutase; ENO: Phosphopyruvate hydratase; PYK: Pyruvate kinase; PDH: pyruvate dehydrogenase; PYC: pyruvate carboxylase; CS: citrate synthase; ACO: aconitate hydratase; IDE: isocitrate dehydrogenase; OGDH: 2-oxoglutarate dehydrogenase; SS: succinyl-CoA synthetase; SDE: succinate dehydrogenase; FUH: fumarate hydratase; MDE: malate dehydrogenase; ACL: ATPdependent citrate lyase; ME: malic enzyme; ADH: alcohol dehydrogenase; ALDH: acetaldehyde dehydrogenase; AcA LIG: acetate CoA ligase).

#### 2.2.2. Parameter Estimation Results

Three experimental parameter sets have been developed for the kinetic model to account for different substrate uptakes: glucose, glycerol and ethanol. The most detailed published dataset available corresponds to the consumption of glucose based on 13C metabolic flux analysis [32] with a glucose consumption rate of 3.58 mmoL·min−1·L−<sup>1</sup> and reaction rates, including the Krebs cycle and Acetyl-CoA production. For modeling purposes, a single, concentration-independent substrate uptake rate for glycerol and ethanol was derived from the cultivation experiments described in Section 2.1.

During the parameter estimation, it became clear that a single set of model parameters could not describe all three examined substrates. The same parameter set of kinetic models could be used for glucose and glycerol experiments. This could be expected because of the common pathway of glucose and glycerol from Gra3P to pyruvate, which then enters the mitochondria, serving as the precursor for both mitochondrial oxaloacetate (reaction PYC) and mitochondrial Acetyl-CoA (reaction PDH). It turned out that, in the case of ethanol that enters the Krebs cycle via Acetyl-CoA, the PDH reaction rate had to be close to zero to facilitate all of the mitochondrial pyruvate flux towards mitochondrial oxaloacetate.

As a result, we developed two structurally identical kinetic models that were able to simulate the experimentally observed data. Both models were deposited in the BioModels [38] database in SBML (level 2 version 4) and COPASI formats: (1) glucose and glycerol consumption model (Biomodels ID: MODEL2112280001) with a Vmax of PDH being 907 mmoL·min−1·L−<sup>1</sup> (Supplementary Files S1 and S2) ethanol consumption model (Biomodels ID: MODEL2112290001) with a low Vmax of PDH 1e-6 mmol·min−1·L−<sup>1</sup> (Supplementary File S2). The parameters of the models are summarized in Supplementary File S3.

#### 2.2.3. Simulation Results

The simulations of the glucose/glycerol model confirm the experimentally determined production flux of cellular Acetyl-CoA at 3.87 mmoL·min−1·L−<sup>1</sup> when consuming glucose at 3.58 mmoL·min−1·L−<sup>1</sup> (Table 1). The same model predicts the cellular Acetyl-CoA production flux at 1.44 mmoL·min−1·L−<sup>1</sup> when consuming glycerol at 2.42 mmoL·min−1·L<sup>−</sup>1. The ethanol model predicts a cellular Acetyl-CoA production flux of 4.76 mmol·min−1·L−<sup>1</sup> when consuming ethanol at 7.76 mmoL·min−1·L−1. This means that the percentage of substrate that undergoes carbon transformation into two carbon atoms of Acetyl-CoA is 36, 40 and 61% for glucose, glycerol and ethanol, respectively. The most efficient substrate in terms of carbon uptake (C1 moles) at the experimentally observed uptake rate is glucose (21.46 mmoL·min−1·L<sup>−</sup>1) followed by ethanol (15.52 mmoL·min−1·L<sup>−</sup>1) and glycerol (7.27 mmoL·min−1·L<sup>−</sup>1).


**Table 1.** Some simulated flux rates for different substrates.

#### *2.3. Medium-Scale Stoichiometric Model of DHA Production*
