A sufficiency analysis of asymptotic stability in continuous recombinant fermentation with auxotrophic mutants
Abstract Fermentations employing genetically modified microorganisms are sensitive to the disturbances likely in large bioreactors. Since these disturbances may affect the competition between recombinant cells and plasmid-free cells, with consequent effects on plasmid stability and reactor stability, it is useful to identify regions of asymptotic stability (RAS) which do not vary with shifts in the operating condition. Using a model for continuous fermentation with auxotrophic mutants, sufficient conditions have been derived for such operationally invariant RAS. Plots for Saccharomyces cerevisiae containing the pBR322 plasmid show that improving the segregational stability makes the fermentation more vulnerable to disturbances. Thus, real reactor operation must balance both kinds of stability.
In this paper we study the multivariate ANOVA decomposition for $1$-periodic functions on the torus. In particular we use the integral projection operator that leads to the classical ANOVA decomposition. Relationships between the Fourier coefficients of the function and its ANOVA terms lead to special frequency index sets and give an understanding of the decomposition working in the frequency domain. Moreover, we consider the truncated ANOVA decomposition and provide error bounds for approximation in $\mathrm{L}_\infty$ and $\mathrm{L}_2$. We present an approximation method based on the truncated decomposition with regard to a superposition dimension $d_s$.