## 3 Results and Discussion
### Selection of Spectral Ranges for MLR and PLS Models
In contrast to MIR spectroscopy, ethanol exhibits an intensive Raman peak at 880 cm\({}^{-1}\), originating from the high polarizability of the C-C bond [32; 33; 34]. For the evaluation of Raman spectra by MLR, the measurement channel for ethanol (S3) was set to the range from 868-888 cm\({}^{-1}\), overlapping with this peak. Additionally, intensive peaks can be observed at 1060 cm\({}^{-1}\) and 1125 cm\({}^{-1}\) for glucose [22; 31] and at 1045 cm\({}^{-1}\) and 1090 cm\({}^{-1}\) for ethanol due to the excitation of C-O stretching vibrations [22; 32]. The intensive peak in the range from 1112-1132 cm\({}^{-1}\) was selected as a measurement channel for glucose (S1). As reference channels (S2, S4), spectral ranges without interfering Raman peaks in the neighboring area of the measurement channels were chosen (see Table 1 and Figure 3). For the PLS evaluation of Raman spectra, the complete spectral range from 800-1400 cm\({}^{-1}\) was used. In contrast to the offset-corrected spectra in Figure 3, the measured Raman spectra were superimposed by a pronounced fluorescence background, which was rising from higher to smaller Raman shifts, as shown in Figure 4.  
Figure 3: Raman spectra obtained during yeast fermentation and selected spectral regions (S1–S4) used for the MLR models. The spectra were corrected against the culture medium and inoculum without the initial carbon source glucose and offset-corrected by subtraction of a straight line. Top left: Raman spectra of 30 g L\({}^{-1}\) glucose and 10 g L\({}^{-1}\) ethanol in deionized water for comparison (background against deionized water). The fluorescence background, mainly caused by biomass growth, was increasing during the fermentation. Since the fluorescence intensity in reference channel S4 (825-845 cm\({}^{-1}\)) was increasing faster than the intensity in reference channel S2 (1165-1185 cm\({}^{-1}\)), the difference of these two channels could be correlated to the biomass growth in the corresponding MLR model (see Equation (4)). Prediction of Temporal Concentration Courses Using MLR and PLS Evaluation of Raman and MIR-ATR Spectra  
The measured Raman intensity spectra and the MIR absorption spectra were converted into the corresponding analyte concentrations using the developed MLR and PLS models. For model building, the data of three fermentations were used. Applying the four models (2D MLR, 4D MLR, PLS without PP, PLS with PP) to the Raman intensity and MIR-ATR absorption spectra, the temporal concentration courses of glucose, ethanol, and biomass during a fourth fermentation were predicted (Figure 5). Figure 4: Uncorrected Raman spectra recorded during batch fermentation of _S. cerevisiae._ The fluorescence background is rising from higher to smaller Raman shifts and is increasing during the yeast fermentation. During the first phase of the yeast fermentation, most of the carbon source glucose is metabolized into ethanol, biomass, and carbon dioxide [30]. Due to the high glucose concentration, the metabolism follows an oxidative-reductive metabolism (Crabtree effect) [35], enabling the formation of ethanol during an aerobic fermentation. As can be seen in Figure 5, the initial glucose concentration of 30 g L\({}^{-1}\) was transformed within 2.5 h into an ethanol concentration of approximately 10 g L\({}^{-1}\) and 5 g L\({}^{-1}\) of dry yeast biomass. After the medium is depleted of glucose, an enzymatic adaption of the yeast cells with the aim to use the previously-formed ethanol as a new carbon substrate is observed [30]. In this phase of fermentation, the ethanol is converted into biomass and carbon dioxide [29; 30]. Thereby the concentration of produced biomass increased to 10 g L\({}^{-1}\) (biomass concentration including inoculum: 15 g L\({}^{-1}\)). Such a two-phase metabolism (first phase: growth on glucose, second phase: growth on ethanol) is termed diauxie and is based on the mechanism of catabolite repression [36; 37]. The fermentations were stopped after 10 h, when the carbon source ethanol had been consumed.