Mathematical Model of Growth and Heterologous Hantavirus Protein Production of the Recombinant Yeast Saccharomyces cerevisiae

A segregated mathematical model was developed for the analysis and interpretation of cultivation data of growth of the recombinant yeast Saccharomyces cerevisiae on multiple substrates (glucose, maltose, pyruvate, ethanol, acetate, and galactose). The model accounts for substrate consumption, plasmid stability, and production level of a model protein, a modified nucleocapsid protein of the Puumala virus. Recombinant nucleocapsid proteins from different Hantaviruses have previously been demonstrated as suitable antigens for diagnostics as well as for sero‐epidemiological studies. The model is based on a system of 10 nonlinear ordinary differential equations and accounts for the influence of various factors, e.g., selective pressure for enhancing plasmid stability by formaldehyde or the toxic effects of the intracellular accumulation of the heterologous protein on cell growth and product yield. The model allows the growth of two populations of cells to be simulated: plasmid‐bearing and plasmid‐free yeast cells, which have lost the plasmid during cultivation. Based on the model, sensitivity studies in respect to parameter changes were performed. These enabled, for example, the evaluation of the impact of an increase in the initial concentration of nutrients and growth factors (e.g., vitamins, microelements, etc.) on the biomass yield and the heterologous protein production level. As expected, the productivity of the heterologous protein in S. cerevisiae is closely correlated with plasmid stability. The 25 free model parameters, including the yield coefficients for different growth stages and dynamic constants, were estimated by nonlinear techniques, and the model was validated against a data set not used for parameter estimation. The simulation results were found to be in good agreement with the experimental data.