*4.3. Development of the Constraint-Based Medium-Scale Stoichiometric Model*

A constraint-based, medium-scale stoichiometric model [57] of central carbon metabolism, biomass production and pathways to DHA was developed, extending the scope of the kinetic model. Reactions were included in the model based on the results of transcriptomics [31] and on the reactions from the genome annotation of the *Symbiodinium minutum* genome, which is a phylogenetically close relative of *C. cohnii*. The specific growth rate was calculated by an exponential approximation of the growth curve. It is assumed that DHA production is constant during the growth period.

The model was built and optimized using COBRA Toolbox v3.0 [58] and RAVEN 2.0 [59] functionality. The model was visualized by Paint4Net [60], Escher [61] and IM-FLer [62] software.

The model was validated using the experimental data generated during this study and those found in the literature.

## **5. Conclusions**

Kinetic and stoichiometric modeling-based analysis demonstrates the attractiveness of glycerol as a substrate for DHA (main fraction of PUFA [30]) production by *C. cohnii*, along with established substrates, such as ethanol and glucose. This is proven experimentally and analyzed mathematically by mechanistic models of *C. cohnii* metabolism. The promising results on the applicability of crude glycerol [12] increase the attractivity of glycerol even further.

The iterative application of the pathway-scale kinetic model and constraint-based stoichiometric model combines the accuracy of the kinetic model of the main productforming pathways with the large-scale stoichiometric model's ability to determine if the pathways addressed by the kinetic model could be supplied with all of the necessary molecular components. Simultaneously, biomass could be produced by the metabolic network of the organism of interest. This approach is important for improving the understanding of metabolic network functionality and increasing the predictability and efficiency of metabolic engineering efforts.

Our experiments, in combination with modeling, supported the potential of glycerol as another renewable substrate of *C. cohnii* for the production of DHA. Despite a lower consumption rate and lower specific growth rate, the PUFA content and efficiency of carbon transformation into biomass are better with glycerol than with glucose. Therefore, the sustainability parameters [63] of DHA production from glycerol are expected to be better than in the case of glucose and ethanol.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/ 10.3390/md20020115/s1, File S1: Kinetic model for Acetyl-CoA production from glucose and glycerol by *C. cohnii*, File S2: Kinetic model for Acetyl-CoA production from ethanol by *C. cohnii*, File S3: Parameters of kinetic models for Acetyl-CoA production from glucose, glycerol and ethanol by *C. cohnii*, File S4: Constraint-based stoichiometric model of central metabolism of *C. cohnii*, File S5: Flux distribution of kinetic models for Acetyl-CoA production from glucose, glycerol and ethanol (columns A–C and F). The supplementary information includes also flux values adapted for stoichiometric model simulations (columns D and E). Reactions marked by yellow are reactions, which are set to zero in stoichiometric model. Reactions marked by green are set to default upper and lower bounds (1000 and −1000 respectivelly).

**Author Contributions:** Conceptualization, E.S., D.P., A.P., V.G., K.B. and U.K.; methodology, E.S. and U.K.; software, R.M., S.P. and K.B.; validation, R.M., M.R.B. and K.B.; formal analysis, K.S., E.S. and U.K.; investigation, I.S., S.P., R.M., M.R.B., K.S., M.G. and K.B.; resources, I.S., M.G. and U.K.; data curation, S.P., K.B. and M.G.; writing—original draft preparation, R.M., K.B., M.G., E.S. and U.K.; writing—review and editing, R.M., M.R.B., E.S., D.P., A.P., V.G. and U.K.; visualization, R.M. and E.S.; supervision, E.S. and U.K.; project administration, E.S.; funding acquisition, A.P., E.S. and U.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the Latvian ERDF project 1.1.1.1/18/A/022. R.M., M.R.B. and A.P. were supported by University of Latvia under project "Climate change and its impacts on sustainability of natural resources" (Nr. Y5-AZ20-ZF-N-270).

**Institutional Review Board Statement:** Not applicable.

**Data Availability Statement:** Data is contained within the article or supplementary material.

**Conflicts of Interest:** The authors declare no conflict of interest.
