Application of In-Situ and Soft-Sensors for Estimation of Recombinant P. pastoris GS115 Biomass Concentration: A Case Analysis of HBcAg (Mut+) and HBsAg (MutS) Production Processes under Varying Conditions

Microbial biomass concentration is a key bioprocess parameter, estimated using various labor, operator and process cross-sensitive techniques, analyzed in a broad context and therefore the subject of correct interpretation. In this paper, the authors present the results of P. pastoris cell density estimation based on off-line (optical density, wet/dry cell weight concentration), in-situ (turbidity, permittivity), and soft-sensor (off-gas O2/CO2, alkali consumption) techniques. Cultivations were performed in a 5 L oxygen-enriched stirred tank bioreactor. The experimental plan determined varying aeration rates/levels, glycerol or methanol substrates, residual methanol levels, and temperature. In total, results from 13 up to 150 g (dry cell weight)/L cultivation runs were analyzed. Linear and exponential correlation models were identified for the turbidity sensor signal and dry cell weight concentration (DCW). Evaluated linear correlation between permittivity and DCW in the glycerol consumption phase (<60 g/L) and medium (for Mut+ strain) to significant (for MutS strain) linearity decline for methanol consumption phase. DCW and permittivity-based biomass estimates used for soft-sensor parameters identification. Dataset consisting from 4 Mut+ strain cultivation experiments used for estimation quality (expressed in NRMSE) comparison for turbidity-based (8%), permittivity-based (11%), O2 uptake-based (10%), CO2 production-based (13%), and alkali consumption-based (8%) biomass estimates. Additionally, the authors present a novel solution (algorithm) for uncommon in-situ turbidity and permittivity sensor signal shift (caused by the intensive stirrer rate change and antifoam agent addition) on-line identification and minimization. The sensor signal filtering method leads to about 5-fold and 2-fold minimized biomass estimate drifts for turbidity- and permittivity-based biomass estimates, respectively.


Introduction
Pichia pastoris (Komagataella pastoris) is a yeast culture widely used in biotechnology and is capable of expressing various types of recombinant proteins, under submerged bioreactor cultivation conditions, that are of major importance [1,2]. Hepatitis B core-(HBcAg) [3,4] and surface-(HBsAg) [5,6] antigens are recombinant protein examples being investigated for improved vaccines and agents used in biomedicine development. Hepatitis B antigens can be also used in biosensing development for clinical assays [1]. Under optimal process conditions, the process productivity depends on the overall number of microorganisms and fraction of those which are in active target product production-, the reviewed process disturbances and cross sensitivity to parameters like anti-foam agent addition or rapid stirrer rate change influence on biomass estimation accuracy.
Application of various standard off-line (OD/WCW/DCW), in-situ (turbidity/permittivity) and soft-sensor-based (off-gas O 2 /CO 2 ; alkali consumption) methods for 13 high cell density P. pastoris cultivations is presented in this contribution. For the different process stages and biomass levels, simple approximation models were identified and used. Biomass estimation results, in the context of varying process conditions, were analyzed. Aspects of the practical implementation and interpretation of the applied methods are discussed. A practical example for the oxygen uptake rate calculation for the bioprocess with oxygen enrichment and one O 2 off-gas analyzer is demonstrated. Finally, a novel solution (algorithm) for uncommon in-situ turbidity and permittivity sensor signal shifting, caused by intensive stirrer rate change and antifoam agent addition, was implemented and tested experimentally.

Cultivation Conditions
Cultivation of both HBcAg (Mut + ) and HBsAg (Mut S ) recombinant Pichia pastoris GS115 strains was performed in a series of experiments in a 5 L fully automated bench-top bioreactor system EDF-5.4 (Biotehniskais Centrs AS, Riga, Latvia). In general, cultivation conditions corresponded to the Invitrogen corporation cultivation guidelines for Mut + and Mut S strains, respectively. However, some parameters (see Table 1) varied due to recombinant protein production screening or technical reasons, namely, residual methanol levels (0.01-5 g/L) during the protein production phase, process temperature (throughout the whole process) (30 ± 0.1 or 24 ± 0.1 • C), dissolved oxygen (DO) level (1-40%) and aeration rate (1.7 or 3.0 slpm). Inv., Mut S 30 3.0 no 1.5-2.5 1-2; 20-35 1 The letters indicate specific strain cultivated-'c' HBcAg obtainment processes and 's' HBsAg obtainment processes. 2 Residual methanolan indicative methanol concentration range in the methanol consumption (induction) phase. On-line and off-line methanol analysis is available in Appendix A, Figure A3. 3 Some of the online process parameters are indicated in Appendix A, Figure A1.
Additional Mut S strain cultivation under conditions proposed by Gurramkonda et al. [50] was performed, and two different residual methanol set-points 2 and 6 g/L were tested. The main differences between the Invitrogen's and Gurramkonda's protocols were related to the DO and excess methanol levels, as well as some differences in the batch and fed-batch media nutritional content.
Before the start of the cultivation process, the culture medium pH was adjusted to 5.0 ± 0.1 (Invitrogen protocol) or 5.6 ± 0.1 (Gurramkonda's protocol) using a 28% NH 4 OH solution, which was also used to control the set pH value during the cultivation (peristaltic pump: WP10-S 3/16 L4-B, Welco, Tokyo, Japan; tubing: inner diameter 3.2 mm, outer diameter 6.4 mm). DO set-point of 30 ± 5% was controlled by automatically adjusting the stirrer rotational speed (200-1000 rpm) or additional inlet air enrichment with O 2 regarding Table 1.
As it is indicated in the Table 1, in some experiments DO level insignificantly differed from the set-point. The aeration and O 2 enrichment procedure is described in the further subsections of this chapter. An outlet gas condenser was used for humidity condensing from the exhaust gas to minimize evaporation and the water content in the off-gas. Off-gas drying through glycerol concentrate and silica gel was used. The foam level was controlled by the addition of antifoam 204 (Sigma).
Four datasets characterizing a set of experiments to be calibrated to different models or set of experiments, in which biomass measurements are available for specific method or process comparison, are introduced. Dataset 1 (experiments 3c, 4c, 5c, 6c, 1s, 2s, 4s, 5s, 6s and 7s) and Dataset 2 (experiments 1c and 2c) are used for different calibration model evaluation for the turbidity measurement. Dataset 3 (experiments 3c, 4c, 5c and 6c) forms a set of 4 experiments from which the performance of used in-situ turbidity/permittivity and soft-sensor techniques can be compared for the case of using constant soft-sensor parameters. Finally, Dataset 4 (experiments 1s, 2s, 3s and 6s) consists of Mut S strain cultivation experiments with permittivity measurement available as well.
The bioreactor setup consists of a glass vessel and a stainless steel upper and bottom lid (see Figure 1). The reactor has a working volume of 2-4 L, two standard Rushton turbines, and an outlet gas condenser. The process controller (PLC) has 3 DI/DO, 4 AI/AO and 1 relay input unit (Siemens AG, Germany). The process analytical tools of the off-gas O 2 and CO 2 measurement (Bluesens, Herten, Germany; BlueInOneFerm; measurement ranges for O 2 and CO 2 , respectively, were up to 50 and 25 vol.%), culture turbidity (ASD19-EB-01, Optek, Essen, Germany; light absorption (transmission) measurement within 840-910 nm wavelength range; optical path length 10 mm) and permittivity (Hamilton, Bonaduz, Switzerland, Incyte) were connected to the PLC and utilized for process monitoring. PC (SCADA) was connected to the PLC through a router via Ethernet link. Programming in Matlab (R2019a, Mathworks, Natick, MA, USA) .m code was used for implementation of the proposed biomass estimation and on-line sensor filtering algorithms. The data exchange of the process and control variables between the control algorithms (Matlab) and SCADA (programmed in the software platform of PcVue Solutions, Ltd., Sèvres, France) was implemented every 1 s through an OPC server. Detailed information on the reactor vessel and control system configuration can be found in the research published earlier [52].

Off-Line Measurements
Cell growth was monitored by off-line measurements of the optical density (OD) at a wavelength of 590 nm (GRANAT, KFK-2, St. Petersburg, Russia). Wet cell weight (WCW) and dry cell weight (DCW) concentration measurements were determined gravimetrically. Biomass samples were placed in pre-weighted Eppendorf tubes ® and centrifuged at 13,200 RPM for 5 min. Afterwards, the supernatant was discarded, and the cells were resuspended in distilled water and centrifuged once more. The liquid phase was discarded, and the remaining wet cell biomass was weighted. Afterwards, the samples were dried at 105 • C until a constant weight was reached, and the dry cell biomass was determined.
Off-line methanol was measured using gas chromatography (6890 N GC Agilent, Santa Clara, CA, USA).
All yield parameters calculated attributing them to dry cell weights.
1 Figure 1. Schematic diagram of the bioreactor and controls architecture.

Turbidity and Permitivitty Signal Acquisition and Filtering
Turbidity sensor signal recording was made every 60 s. Signal preprocessing parameters were chosen to provide stable sensor readings (symmetric signal damping and 60 s as an integration time for signal damping). Permittivity was measured and calculated by the Incyte 'Frequency Scan' mode with 17 simultaneous measurements across a frequency range of 0.3-10 MHz. Permittivity measurements were made every 2 s and integrated, creating a moving average over a defined period. These acquisition periods varied in experiments 3c, 4c, 5c, 6c, 1s, 2s, 3s, and 4s; their respective values in seconds were 60, 60, 60, 60, 60, 720, 360, and 60.
The turbidity and permittivity signal filtering technique was implemented for sudden signal jumps and drops initiated by sudden stirrer rotational speed changes and antifoam agent addition. The concept of the filtering method is based on sensor signal change rate analysis allowing to count rapid sensor signal shifts, which are uncharacteristic for common biomass growth or cell lysis behavior. Counting such uncommon sensor signal shifts allows for subtraction of accumulated shifts from the actual sensor readings. The filtering algorithm is presented in Figure 2.
Further the filtering algorithm main execution steps are described. The actual sensor signal is read (E i ) at the time moment t i (Step 1). As the filter algorithm uses a median calculation over a time period of τ med = 30 min ahead of each iteration (procedure described further), execution of the main filtering loop could take place when the sensor signal sampling time or t process is equal or exceeds τ med (Step 2). Initially, in Step 3, the following parameters are calculated: time difference between the sensor signal sampling events (signal sampling frequency ∆t = 1 min): sampled sensor signal difference: sensor signal change rate sum at the moment of a new sensor signal reading: where τ sum indicates the amount of the last RS E samples to be summed if the sensor signal sampling frequency is 1 min. In this research, τ sum = 5 min was used for both turbidity and permittivity probe signal filtering. Summing of R E allows to obtain less noisy and extended height peaks of uncommon signal change rate, therefore it is easier to identify them. From the results presented in the Results section, it can be seen that explicit RS E shifts from zero (RS E zero-baseline shift) are observable for turbidity measurement within the process 10-30 h (for permittivity-based measurement, this deviation is practically negligible). The median of RS E calculation (Equation (5)) and its subtraction from RS E , are performed for signal normalization ( Step 3) to exclude the RS E zero-baseline shift phenomenon. The median of the sensor signal change rate sum at the time moment t i : where τ med indicates the amount of the last RS E samples to be used for RS E median value calculation, if the sampling frequency is 1 min. In this research, τ med = 30 min was used for both turbidity and permittivity probe signal filtering. Normalized sensor signal change rate sum at the time moment t i : Further the filtering algorithm main execution steps are described. The actual sensor signal is read (Ei) at the time moment ti (Step 1). As the filter algorithm uses a median calculation over a time period of τmed = 30 min ahead of each iteration (procedure described further), execution of the main filtering loop could take place when the sensor signal sampling time or tprocess is equal or exceeds τmed (Step 2). Initially, in Step 3, the following parameters are calculated: time difference between the sensor signal sampling events (signal Normalized RS E,i (nRS E,i ) then is compared with the allowed preset minimum and maximum limit values of RS E,min and RS E,max (Step 4) (identified RS E,min and RS E,max shown in the Results section). If nRS E exceeds the preset minimum or maximum bounds, then the algorithm considers the inappropriate behavior of the biomass concentration increment/decrement, and substitutes the sensor signal reading with the last output from the filter (E i,out = E i-1,out ) (Step 6). The filter accounts for the difference between the actual and previous raw sensor signal readings, and sums it to the cumulative shift parameter (E i,shift ) that accounts for all the registered shifts from a particular process. E i,shift can be positive or negative and is subtracted from the raw E i (E i,out = E i − E i,shift ) each time when no pre-set inappropriate behavior of the biomass concentration increment/decrement occurs (Step 5). E i,out is used in biomass estimation (Step 7).

Turbidity Signal Approximation to DCW
Two datasets of experiments, Dataset 1 and Dataset 2, representing two aeration regimes 3.0 slpm and 1.7 slpm used respectively, were identified for different representation of DCW and E turb relationship in the high cell density region (calibration data and identified models shown in Figure 3 and Table 2 respectively).
where τmed indicates the amount of the last RSE samples to be used for RSE median value calculation, if the sampling frequency is 1 min. In this research, τmed = 30 min was used for both turbidity and permittivity probe signal filtering. Normalized sensor signal change rate sum at the time moment ti: Normalized RSE,i (nRSE,i) then is compared with the allowed preset minimum and maximum limit values of RSE,min and RSE,max (Step 4) (identified RSE,min and RSE,max shown in the Results section). If nRSE exceeds the preset minimum or maximum bounds, then the algorithm considers the inappropriate behavior of the biomass concentration increment/decrement, and substitutes the sensor signal reading with the last output from the filter (Ei,out = Ei-1,out) (Step 6). The filter accounts for the difference between the actual and previous raw sensor signal readings, and sums it to the cumulative shift parameter (Ei,shift) that accounts for all the registered shifts from a particular process. Ei,shift can be positive or negative and is subtracted from the raw Ei (Ei,out = Ei − Ei,shift) each time when no pre-set inappropriate behavior of the biomass concentration increment/decrement occurs (Step 5). Ei,out is used in biomass estimation (Step 7).

Turbidity Signal Approximation to DCW
Two datasets of experiments, Dataset 1 and Dataset 2, representing two aeration regimes 3.0 slpm and 1.7 slpm used respectively, were identified for different representation of DCW and Eturb relationship in the high cell density region (calibration data and identified models shown in Figure 3 and Table 2 respectively). In-situ turbidity signal (Eturb) approximation to DCW. Sparse points of the Eturb from the processes with aeration Qair = 3.0 slpm (black plus, Dataset 1) and Qair = 1.7 slpm (red plus, Dataset 2); solid and dashed lines, respectively, represent the fitted models Exponential 1 and Linear shown in Table 2. Table 2. Identified in-situ turbidity sensor biomass estimation approximation models and their parameters for two aeration regimes.

Aeration (slpm) Fit Interval Model Name Model Parameters
Dataset 1: 3.0 Whole region Exponential 1 (Equation (7)) a = 1.547, b = 2.85 Figure 3. In-situ turbidity signal (E turb ) approximation to DCW. Sparse points of the E turb from the processes with aeration Qair = 3.0 slpm (black plus, Dataset 1) and Qair = 1.7 slpm (red plus, Dataset 2); solid and dashed lines, respectively, represent the fitted models Exponential 1 and Linear shown in Table 2. Table 2. Identified in-situ turbidity sensor biomass estimation approximation models and their parameters for two aeration regimes.

Datasets of Experiments
Sensors 2021, 21, 1268 9 of 34 was identified, approximating DCW measurements in the whole turbidity measurement range of 0-1.55 CU. For the Dataset 2 experiments, Exponential 2 model: was identified, approximating DCW measurements in the turbidity measurement range of 0-1.40 CU. However, the model Exponential 2 has a parabolic-like curvature with a narrow maximum within 1.40-1.45 CU, and a sharp spike. The same correlation quality for Dataset 2 was obtained by the Linear model: for the two measurement ranges of E turb ≤ 0.72 and E turb > 0.72, each having its own set of model parameters. Identified Exponential 1 and Linear models were used for in-situ turbidity-based biomass estimation for Dataset 1 and Dataset 2 experiments respectively, presented in the Results section.

Permittivity Signal Approximation to DCW
For biomass concentration (X perm ) estimation from the permittivity signal (E perm ), a linear relationship (Equation (10)) was used: Fitting the experimental permittivity signal data to off-line DCW measurements (Dataset 3 experiments 3c, 4c, 5c, 6c; and experiments 1s, 2s, 3s, 4s) from glycerol batch and fed-batch phases, when cell viability is close to 100%, the correlation between the X perm and CF X parameters can be considered linear (calibration data enclosed in Appendix E, Figure A13). Experimental data showed that the pre-induction permittivity measurement correlation to DCW did not significantly differ for different experiments. The cell factor CF X = 4.04 g/L/pF/cm was identified and used to calculate permittivity-based biomass concentration estimates for both glycerol and methanol consumption phases presented in this research. A similar approach to determine CF X is presented by Horta et al. [29]; however, they analyzed this correlation for dry biomass values only up to approx. 7 g/L. After methanol induction, which can be accompanied by physiochemical or morphological changes in the cell [39], the E perm correlation to DCW is no longer linear. As it appears from the results shown further, in the methanol consumption phase, the use the same correlation cell factor identified for glycerol phase (4.04 g/L/pF) lead to a varying-quality fit for DCW measurements even for the experiments performed under similar conditions. The possible reasons for this phenomenon are discussed further.

OUR and CPR Calculation
Information from the culture oxygen uptake rate (OUR) and carbon dioxide production rate (CPR) can be used for biomass concentration quantification. In steady-state conditions, the oxygen uptake rate (OUR) can be assumed to be equal to the oxygen transfer rate (OTR), OUR = OTR. For online OUR and CPR calculation, information about O 2 and CO 2 concentrations in the bioreactor inlet and outlet gas lines, along with the gas flow rates in these lines, is required. The estimation precision depends on identification and the control precision of the previously mentioned parameter. In the majority of the conducted experiments, inlet air enrichment with O 2 was used to follow the guidance from Invitrogen Co. cultivation protocols, according to the requirement of the relatively high dissolved oxygen (DO) level control. Air and O 2 enrichment flows were controlled with separate rotameters and automatic valves for both gases (system configuration enclosed in Appendix C, Figure A7). Extra oxygen was added by the means of oxygen pulses. During these oxygen pulses (oxygen valve 'open') the air valve is closed simultaneously. At the end of oxygen pulses, (oxygen valve 'close'), the air valve opens. The inlet gas flow rate was organized to have the same rotameter set-point for both gases (Qair,rot = QO 2 ,rot). That leads to a constant overall flow rate (Q air + Q O2,enr = const) of 1.7 or 3.0 slpm regarding the experimental plan as indicated in Table 1. This principle has been explained in detail in another research [53]. In this case, different inlet air O 2 enrichment levels were achieved by manipulating the oxygen valve open times: τ O2,enr = n O2,% ·τ O2,period /100 (11) where τ O2, period was 30 s, and n O2 , % -oxygen valve percentage controlled by the PLC PID algorithm while maintaining the set DO level.
Enriching the inlet air with O 2 and having one O 2 gas analyzer at the exhaust gas line, inlet O 2 concentration calculation is required. For this purpose, 'inlet gas O 2 calibration' was made in a water environment to assess the O 2 concentration in the inlet gas under different n O2 , % and when no oxygen consumption was present. Set calibration percentages (n O2_calibr,% ) and the corresponding O 2 concentrations in the output (c O2_calibr,% ) were: The mathematical expressions of the necessary parameters for OUR and CPR calculation are described below. Pure oxygen flow rate at the moment of oxygen pulse (in L/min): Q O2,enr = n O2,% ·Q O2, rot /100 (12) inlet air flow rate during an open air valve (L/min): correction factor taking into account the gas dilution by N 2 : CorF = C N2,air ·Q air (Q air + Q O2,enr )·(100 − C O2,air − C CO2,air )·100 (14) concentration of O 2 in the inlet gas (vol. %): total flow rate of O 2 in the bioreactor (L/min): oxygen transfer rate (g/kg/h): carbon dioxide production (evolution) rate (g/kg/h):

Estimation of Biomass Concentration from OUR, CPR and BCR
In most aerobic cultivations, the relationship between the biomass concentration (X) and the OUR and CPR in a bioreactor can be modeled by means of Luedeking/Piret-type relationships [38,54]: where R X is the biomass growth rate of the cellular system, g/kg/h; X is the biomass concentration, g/kg; and /h] are model parameters related to biomass maintenance as Y mXO quantifies the growth-independent part of the oxygen uptake rate and Y mXC quantifies the growth-independent part of the CPR. A similar equations can be formulated for the amonia or sodium hydroxide consumption rate during the cultivation [54] and for taking into account the influence of feed solution addition on the pH change [38]: ] is a parameter related to the feeding (characterize the pH change due to substrate addition), and F s is the substrate feeding rate, kg/h; W is the culture mass (or volume in L if the culture broth density ≈1 kg/L), kg. The rate of W(t) change can be defined as: where F b is the base addition rate, kg/h; F af is the anti-foam solution addition rate, kg/h; F smp is the sampling rate, kg/h; F CO2 is the carbon lost rate related to CO 2 production/evolution, kg/h. As W(t) can be calculated online, the biomass balance in the reactor (Equation (23)) can be formulated by the ordinary differential Equations (24)-(26). Ordinary differential equations can be solved if the initial biomass X 0 as well as the coef- , and Y rXB2 are known. The six coefficients can be identified independently of the data records W(t), OUR(t), CPR(t), BCR(t), and X(t) previously measured in the process under consideration using standard nonlinear parameter optimization techniques [54]: Soft-sensor yield coefficients Y rXO , Y mXO , Y rXC , Y mXC , Y rXB1 , and Y rXB2 , used in the estimations, were determined using MATLAB's fminsearch function minimizing RMSE between reference and soft-sensor output. Off-gas (O 2 /CO 2 concentrations) and alkali consumption data available for all experiments presented in this research, was used to identify a set of individual soft-sensor parameter (Y rXO , Y mXO , Y rXC , Y mXC , Y rXB1 , and Y rXB2 ) for correlation to DCW (results included in Appendix D). Off-gas analysis-based soft-sensors were fitted to the process data from both glycerol and methanol consumption phases. One set of alkali consumption-based soft-sensor parameters was identified for both substrate consumption phases, as during the initial process stage (corresponding to glycerol phase), alkali consumption dynamics had a weak correlation to biomass growth dynamics.
Obtained parameter sets were analyzed in context with the specific growth rate (Appendix D, Figure A10), as the soft-sensor yield and rate parameter dependency of specific growth rate was discussed in the Introduction section. However, strong correlation between the soft-sensor parameter sets from the experiments with similar growth rates (like for exps. 3c and 4c) or process conditions (like for exps. 4c and 5c) cannot be identified. The possible reason of this might be the posed inaccuracies due to OUR, CER or BCR calculation and varying cell metabolism in similarly propagating cultures under varying process conditions. As the scope of this research is to demonstrate model-free soft-sensor application possibilities under particular experimental conditions, techniques, like Kalman or Particle filtering are avoided. Soft-sensor yield parameter reconciliation procedures using first-principle (elemental balancing) constraints, leaving the soft-sensor techniques as simple as possible, are also avoided. Instead, a decision was made to include Mut + strain cultivation experiments 3c, 4c, 5c and 6c, that have similar experimental conditions and consistent measurements available, in Dataset 3 for comparison reasons. The reference parameters from literature and the mean values of identified soft-sensor parameters for Dataset 3 experiments for both glycerol and methanol phases are presented in Table 3. The soft-sensor parameters obtained from Gamisans et al. research [43] (see Table 3), correspond to the specific biomass growth rate range of 0.035-0.150 1/h and 0.035-0.100 1/h for glycerol and methanol consumption phases, respectively.  Figure A11); average parameters from 3c exp. were excluded, as they significantly differ from the reference for the methanol phase. 2 Total yield also includes consumed oxygen or produced CO 2 due to culture maintenance requirement. 3 Parameters calculated from Y mOX = m ATP · Y O2/ATP · M O2 and Y mOX = m ATP · Y O2/ATP · M O2 equations for O 2 uptake and CO 2 production cases respectively (m ATP 2.51 mmol(ATP)/g(X)/h and 0.44 mmol(ATP)/g(X)/h for glycerol and methanol consumption phases respectively taken from Gamisans et al. research [43]); stoichiometric yield coefficients Y O2/ATP = 0.5/1.53 = 0.33 g(O 2 )/g(ATP) and Y CO2/ATP = 3/2 = 1.5 g(CO 2 )/g(ATP) for glycerol and Y O2/ATP = 0.5/2.01 = 0.25 g(O 2 )/g(ATP) and Y CO2/ATP =3/2 = 1.5 g(CO 2 )/g(ATP) for methanol consumption cases respectively adapted from Niu et al. research [55]. 4 Calculated using the available range from the reviewed maintenance rate coefficients 0.016-0.030 g(S)/g(X)/h [56] and Y O2/S = 1.5 g(O 2 )/g(S) [17].
Soft-sensor parameters for Dataset 3 experiments were also identified for permittivitybased reference biomass estimates, as this was found to be valuable for comparison reasons, assuming a more similar soft-sensor and permittivity measurement relation to the culture physiology in opposite to gravimetric DCW measurement. The identified soft-sensor parameters for both reference biomass measurements for Dataset 3 experiments and sole glycerol and methanol substrates are shown in Figure 4.

Estimation Quality Analysis
Estimation quality was analyzed by mean of normalized root mean square error attributed to the measurement range (NRMSE) and expressed in percent's. Root mean square error expressed as: and NRMSE: NRMSE = RMSE X max − X min ·100% (28) where X i is the ith reference biomass measurement,X i is the biomass estimate, X min and X max are the minimum and maximum values of reference X i . NRMSE values, obtained in this research are calculated for the samples taken along the duration of the process (t 0 − t end ).

Estimation Quality Analysis
Estimation quality was analyzed by mean of normalized root mean square error attributed to the measurement range (NRMSE) and expressed in percent's. Root mean square error expressed as: and NRMSE: where is the ith reference biomass measurement, is the biomass estimate, and are the minimum and maximum values of reference . NRMSE values, obtained in this research are calculated for the samples taken along the duration of the process (t0 − tend).

Results
Four datasets were used for the evaluation of the presented biomass concentration estimation method. Datasets consist of 13 cultivation experiments performed under various conditions, from which six were Mut + (HBcAg production) and seven were Mut S (HBsAg production) processes. The main results of the method implementation are presented further.

Biomass Concentration Determined Off-Line
Reliability of the off-line biomass optical density (OD), wet cell weight (WCW) and dry cell weight (DCW) concentration measurements can be evaluated on the basis of how these parameters correlate between each other. Information on the correlation between DCW, WCW and OD is important when recalculation from one to another measurement is necessary (for comparison reasons, yield calculations etc.). The results further described in detail are obtained from Dataset 1 and Dataset 2 off-line data included in Appendix A ( Figure A2), where the method of correlation appears in a brief context of some of the varying process parameters indicated in Table 1 (some of the on-line parameters are available in Appendix A, Figure A1). The results indicates a more consistent and linear correlation of DCW~WCW compared to more disperse and less linear correlations of DCW~OD and WCW~OD ( Figure A2 (27) and (28), the ∆WCW average measurement error of 0.7 DCW is about 30% lower than the measured ∆DCW. Despite this, the DCW concentration measurement was chosen to be correlated to the instrumental methods described further. This is due to the mathematical calculations used further, where DCW concentration is commonly used to represent specific yield and kinetic expressions.

Biomass Estimates from In-Situ Turbidity and Permittivity Sensors
As it was discussed in the Introduction chapter, sudden stirrer rate changes and antifoam agent addition may cause significant changes in the turbidity and permittivity signals and a respective shift in biomass estimates. Particular cross-sensitivity is presented in the example enclosed in Figure 5.
For, example, well observable simultaneous negative turbidity and positive permittivity signal shifts ( Figure 5, panel A) happen when the addition of an anti-foam agent takes place at around process 42 h ( Figure 5, plot on the top of panel B). In the same example within process 44-45 h, a sudden stirrer rate decrease and an increase caused significant permittivity signal and minor turbidity signal shifts. As it can be seen from the supplementary data included in Appendix B (Table A1 and Figures A4-A6), a strong correlation of the shift actuator (stirrer rate or anti-foam addition rate change) and shift actuator signal height to the height of sensor signal shift or specific measurement (turbidity or permittivity), is not observable. This means, that the sensor signal should be analyzed directly for uncommon shifts that account for un-typical biomass growth/lysis. From the data presented in Figure 5 panel B, the nRS turb and nRS perm filtering criteria response to the shift actuators can be evaluated. Optimal (safe) filter parameters that are appropriate for accounting and filtering of the major turbidity and permittivity signal disturbances in Dataset 1/Dataset 2 and Dataset 3/Dataset 4 experiments respectively, were identified (Table 4) and the improvement for biomass concentration estimation quality, represented by X permFiltr and X turbFiltr results, can be visually observed in Figure 6. For, example, well observable simultaneous negative turbidity and positive permittivity signal shifts ( Figure 5, panel A) happen when the addition of an anti-foam agent takes place at around process 42 h ( Figure 5, plot on the top of panel B). In the same example within process 44-45 h, a sudden stirrer rate decrease and an increase caused significant permittivity signal and minor turbidity signal shifts. As it can be seen from the supplementary data included in Appendix B (Table A1 and Figures A4-A6), a strong correlation of the shift actuator (stirrer rate or anti-foam addition rate change) and shift actuator signal height to the height of sensor signal shift or specific measurement (turbidity or permittivity), is not observable. This means, that the sensor signal should be analyzed directly for uncommon shifts that account for un-typical biomass growth/lysis. From the data presented in Figure 5 panel B, the nRSturb and nRSperm filtering criteria response to the shift actuators can be evaluated. Optimal (safe) filter parameters that are appropriate for accounting and filtering of the major turbidity and permittivity signal disturbances in Dataset 1/Dataset 2 and Dataset 3/Dataset 4 experiments respectively, were identified (Table  4) and the improvement for biomass concentration estimation quality, represented by   Figure 6. In-situ turbidity and permittivity sensor XDCW estimation results.
As it can be observed from the results of experiment no. 6c ( Figure 5, panel A, 42 h; or Figure 6, 42 h) and experiment no. 2s ( Figure 6, ~75 h), the filter did not completely eliminate the sudden permittivity signal shifts. It would be possible to eliminate these sudden jump to a higher extent by narrowing the permittivity signal nRSE,max and nRSE,min bounds, although that would lead to signal over-filtration in some other explorative examples included in this research. Signal over-filtration is a result of the biomass increment/decrement-related sensor response 'freezing' in a no changing state (Figure 2, place in the algorithm where the actual sensor output is equalized to one-step-ahead measurement, Ei,out = Ei-1,out). For example, some over-filtration can be observed for the turbidity signal at the end of experiment no. 6s and starting from the middle of experiment no. 7s. Over-filtration of the permittivity signal is not observable in such extent.
A total of six experiments (1c, 3, 5c, 6c, 1s and 4s), representing the average tendency of uncommon signal shifting frequency and range per experiment, were analyzed in detail, and the raw results are included in Appendix B. From 12 shift cases analyzed in detail, seven occurred due to the intensive change of the stirrer rotational speed, three resulted from the mixed stirrer/a-foam addition interaction, and two cases occurred purely because of anti-foam addition. In these analyzed examples, XturbRaw shifted by 10% on average, and the filter minimized this shift to 1.8%, but for XpermRaw, it was 51.0% and 19.0%, respectively.  Figure 6,~75 h), the filter did not completely eliminate the sudden permittivity signal shifts. It would be possible to eliminate these sudden jump to a higher extent by narrowing the permittivity signal nRS E,max and nRS E,min bounds, although that would lead to signal over-filtration in some other explorative examples included in this research. Signal over-filtration is a result of the biomass increment/decrement-related sensor response 'freezing' in a no changing state (Figure 2, place in the algorithm where the actual sensor output is equalized to one-step-ahead measurement, E i,out = E i-1,out ). For example, some over-filtration can be observed for the turbidity signal at the end of experiment no. 6s and starting from the middle of experiment no. 7s. Over-filtration of the permittivity signal is not observable in such extent.
A total of six experiments (1c, 3, 5c, 6c, 1s and 4s), representing the average tendency of uncommon signal shifting frequency and range per experiment, were analyzed in detail, and the raw results are included in Appendix B. From 12 shift cases analyzed in detail, seven occurred due to the intensive change of the stirrer rotational speed, three resulted from the mixed stirrer/a-foam addition interaction, and two cases occurred purely because of anti-foam addition. In these analyzed examples, X turbRaw shifted by 10% on average, and the filter minimized this shift to 1.8%, but for X permRaw , it was 51.0% and 19.0%, respectively. From these results, an average filtering efficiency of the single shifts can be evaluated-for the turbidity measurement shifts, the error was reduced 5 times but for the permittivity measurement, this indicator was reduced twice.
A good X turbFiltr (for Dataset 1 and Dataset 2 experiments) and X permFiltr (for Dataset 3 and Dataset 4 experiments) estimation quality in the glycerol phase (average RMSE's 5.0 and 2.7, respectively) and a notably lower estimation quality in the methanol phase (average RSME's 12.3 and 28.5, respectively) was achieved. Normalized root mean square errors (NRSME) of 7% and 8% were calculated from Dataset 1/Dataset 2 and Dataset 3 X turbFiltr fit to DCW respectively. NRMSE of 11% was calculated from Dataset 3 X permFiltr fit to DCW. Calculated NRMSEs for in-situ and soft-sensors are compared in Table 5. Other results characterizing the soft-sensor performance, are presented in the next section. Fit to X permFiltr for Dataset 3 --11 14 10 Both methods showed a lower biomass estimation quality for the methanol consumption phase. Such behavior for X turb estimates can be explained by the application of the method based on limited optical characteristics under rather high cell density conditions. It should also be mentioned that, during the glycerol consumption phase, fewer off-line biomass samples were analyzed, therefore, having an impact on the estimation error calculated for this phase.

Biomass Estimation from OUR, CER and BCR Data
As it was shown in the soft-sensor development procedure in the Materials and Methods section, off-gas analysis-based soft-sensor yield (conversion) parameters for methylotrophic P. pastoris may depend on specific biomass growth rate. A strong correlation between the soft-sensor parameter sets from the experiments with similar growth rates (like for exps. 3c and 4c) or process conditions (like for exps. 4c and 5c) was not identified.
Dataset 3 experiments with similar experimental conditions were selected for softsensor performance evaluation. Specific growth rates for Dataset 3 experiments were comparably similar, e.g., µ glyc = [0.09 0.10 0.14 0.14] 1/h for glycerol and µ meth = [0.015 0.015 0.030 0.010] 1/h for methanol consumption phase, respectively. The identified and reference yield and yield-rate parameter values are compared in Table 3. The identified model parameters were used for biomass estimation (results included in Figure 7).
As can be extracted from the available reference sources [39,43], O 2 and CO 2 yield parameters also include part of the consumed/produced O 2 /CO 2 due to maintenance requirements. For comparison reasons, the integration of consumed O 2 and produced CO 2 per mass of biomass was done (data included in Appendix D, Figure A11). The mean yield coefficients Y OX_total and Y CX_total , representing the total yield ratio of consumed oxygen and produced carbon dioxide per mass of biomass, were in accordance or comparably close to the indicated reference values for those parameters identified for the methanol consumption phase. The Y CX_total parameter for glycerol consumption phase is also close to the reference sources, however it partly declines, indicating an unclosing C-balance. As it appears from the carbon mass balance for the methanol consumption phase ( Figure A12 enclosed in the Appendix D), for the majority of reference DCW measurements, a C imbalance is lower than 10%, indicating for a closing C elemental balance that was also proposed elsewhere [39]. The findings above indicate a comparably accurate CER calculation. At the same time, a comparably higher OUR-based yield coefficient deviation from reference sources indicate for inaccuracies in OUR calculations. Such inaccuracies may occur due to O 2 off-gas measurement calibration shifts and/or an insufficiently accurate method utilized for oxygen concentration calculation in oxygen enriched inlet air.
With the identified set of Dataset 3 mean parameters, DCW estimation error (NRMSE) for X OUR , X CPR and X BCR was 10%, 13% and 8%, respectively. The soft-sensor parameters for fitting to the reference permittivity (X permFiltr ) measurement, identified for the same dataset, did not lead to an improved estimation quality for any of the observed methods. The estimation quality between the used methods is compared in the Table 5. 1 Dataset 3 experiments with similar experimental conditions were selected for soft-sensor performance evaluation. Specific growth rates for Dataset 3 experiments were comparably similar, e.g., μglyc = [0.09 0.10 0.14 0.14] 1/h for glycerol and μmeth = [0.015 0.015 0.030 0.010] 1/h for methanol consumption phase, respectively. The identified and reference yield and yield-rate parameter values are compared in Table 3. The identified model parameters were used for biomass estimation (results included in Figure 7).  Table 3. The identified model parameters were used for biomass estimation (results included in Figure 7).

Discussion
Various biomass estimation methods were applied in up to 135 DCW high cell density P. pastoris cultivations under varying process conditions. A high number of cultivations (13 exp.) were analyzed. This forms an extensive overview of the method reproducibility and applicability under particular or similar experimental conditions. As the glycerol or methanol consumption leads to different cell physiological behavior, separate soft-sensor parameters were fit for each of the substrate consumption phases. Below, the major findings are summarized, and a discussion on the result interpretation is extended.

Off-Line Biomass Detection Methods
For cell densities up to 60 DCW, the photometric OD measurements suitably correlate to the DCW (RMSE 4.2 g/L). For higher DCW densities, the OD measurement fails to sufficiently represent the biomass dynamics. The above-mentioned is true because of the cross-sensitivity of the well-known UV/NIR method to culture constituents, such as cell debris, by-products or other matters added to the bioreactor. The aforementioned is illustrated in an obvious way elsewhere [27], where the same in-situ turbidity signal at different process stages corresponds to about 2 times different DCW levels. Statistical and instrumental errors of ±0.98 DCW and ±2.33 WCW obtained for DCW and WCW measurements respectively, indicate a suitable accuracy for reference biomass concentration measurement methods.

DCW Estimation with the In-Situ Turbidity Sensor
Biomass densities of 50 DCW were achieved up until the start of the methanol consumption (induction) phase. For biomass densities up to 50 DCW, the in-situ turbidity method performed well for DCW estimation (RMSE 5.0 g/L). For the higher biomass densities of 50-135 g/L, an estimation accuracy about two times lower was observed (RMSE 12.3 g/L). Few research results are available, where turbidity probe applications are demonstrated at such high cell densities (≥90 DCW). In the research conducted by Goldfeld and co-authors [30], at-line NIR turbidity measurement was used for high cell density P. pastoris biomass monitoring. A similar correlation quality up to about 90 DCW (300 WCW) can be observed for the turbidity related biomass estimation method [30]. However, for the 90-165 DCW (300-550 WCW) interval, the average deviation between off-line (WCW) and on-line measurements fit either poorly or even not at all [30]. From the available measurement data [30], a rough estimate of at least 1.5 times better X turbFiltr~D CW fit for the 90-130 DCW range, comprehensively examined in the current research, can be evaluated for the current contribution. Another research is available, where successful S. cerevisiae monitoring for up to 90 DCW [23] is presented. However, in this example, a long-lasting (45 days) continuous membrane filtrated culture under constant mixing and aeration conditions was investigated. As one of the discussed reference examples had a lower turbidity-based biomass estimate correlation quality to DCW [30], but the other one [23] lacked an investigation in the biomass density region above 90 DCW, the particular contribution can be addressed as one of the rare examples, where the turbiditybased biomass estimation results above 90 DCW are demonstrated with comparably higher accuracy. Moreover, a new region of high cell densities for the in-situ turbidity technique is investigated. Turbidity measurement demonstrated one of the highest accuracies of 8% (NRMSE) in comparison to other investigated methods.

In-Situ Permittivity (X permFiltr ) Based Biomass Estimates
For the glycerol consumption phase (<25-30 h), permittivity-based biomass estimates fit well to DCW. Starting from the very beginning of the methanol consumption phase, within 1-2 h, X permFiltr declined in all cultivations by about 10-20 g/L. This change in the culture dielectric properties under new conditions is a characteristic behavior as adaptation to another substrate and start of recombinant protein synthesis occurs [57]. The X permFiltr behavior within the methanol consumption phase differed between Mut + and Mut S strains. In the majority of Mut + processes (3c, 4c and 5c), X permFiltr closely followed the DCW dynamics. At the same time, in the Mut S processes, X permFiltr remained at the same level (1s and 3s) or increased slowly (2s and 4s). Similar permittivity-based biomass estimates and DCW dynamics are observable also in the research conducted by Goldfeld et al. [30].
The reason for such X permFiltr and DCW shifts in the comparably similar processes (like for the Dataset 3 experiments) can be caused by the varying permittivity of cell population caused by changes in the cell size and/or intracellular conductivity [57]. If one assumes that the intracellular conductivity remains unchanged for the morphologically different cell clusters, the varying dynamics of the cell population size could lead to differences between X permFiltr and DCW. Vanz et al. [49] studied the morphological changes of P. pastoris under high yield HBsAg production. From the presented data, one can extract that, during the induction phase (120 h) for 40% of the cell population, the diameter increased by about 50% leading to about 3-fold increased cell volume for this population. Particular changes at the end lead to the cell volume increase of the whole system by about 20%. At the same time, the number of apoptotic cells in the induction phase increased by 10%. Overall, that would lead to a viable cell volume increase by 10%. Under circumstances introduced earlier, the permittivity-based biomass estimate should, accordingly, increase by 10%. Raschmanová et al. [31] extensively studied the morphological changes of several P. pastoris strains under different growth rates, synthesizing extracellular proteins. The results indicate the extended range for the apoptotic (impaired viability) cells to form 10 to 30% of the population depending on the strain used and the specific biomass growth rate. Moreover, the populations of larger cells appeared to grow under medium biomass growth rates (µ methanol = 0.16 1/h), and with a trend to decrease at low (µ methanol = 0.08 1/h) and high (µ methanol = 0.32 1/h) biomass growth rates.
The findings above show that the P. pastoris culture morphology and viability significantly change over the methanol induction phase. Moreover, the dynamics of these changes vary under different biomass-specific growth rates (excess methanol levels), influencing also the permittivity-based biomass estimate correlation to DCW. This could be the case of the varied X permFiltr and DCW correlation for Mut + cultivations presented here, as the protein yield and accumulation dynamics were similar in these processes (yet unpublished results). Despite the varied cultivation conditions in Mut S cultivations, a significant decline in X permFiltr against DCW was noted. Due to the poor HBsAg biosynthesis, the obtainment of purified product was possible from only one experiment (yet unpublished results). This leads to the conclusion that in the Mut S processes, less viable, low-size and low-productivity cell populations dominated in comparison to Mut + processes.
A number of permittivity measurements showed an average DCW fit quality of 11% (NRMSE) for Dataset 3 using fixed parameter sets for glycerol and methanol consumption phases. Above-described permittivity measurement performance lead to the conclusion, that there is some interpretation gap, regarding permittivity correlation to methylotrophic P. pastoris DCW biomass during induction phase. Therefore, for the in-depth investigation of permittivity/DCW correlation, analysis of the cell morphology change would be necessary.

Soft-Sensor-Based Biomass Estimates
Evaluated off-gas and alkali consumption-based soft-sensor estimation accuracies for Dataset 3 experiments are 10%, 13% and 8% for oxygen-uptake-based, carbon-productionbased and alkali-consumption-based biomass estimators, respectively. As the scope of this research was to demonstrate a model-free soft-sensor development that is as simple as possible, the obtained results still could be improved by means of the methods discussed in the introduction. Taking into account the differences between some of the identified and reference yield parameters for oxygen consumption and, in a lesser extent, for carbon dioxide production, one should state that the possible reasons for this could be related to the imprecisions in O 2 /CO 2 off-gas sensor calibration, airflow adjustment etc. For oxygen consumption-based yield parameters, these differences may also occur due to an insufficiently accurate method utilized for oxygen concentration calculation in oxygenenriched inlet air.
The alkali consumption-based estimator shows similar performance to turbidity measurement. Knowing that the turbidity measurement better performs in the first part of the process (<50 DCW), but alkali-based biomass estimator indicates better results starting from the end of the glycerol batch phase (>25 DCW), a combination of both measurements would lead to a superior, reliable and non-complex biomass estimation procedure.

In-Situ Turbidity and Permittivity Signal Filter
The in-situ sensor signal filtering method lead to about 5-fold and 2-fold minimized biomass estimate drifts for turbidity-and permittivity-based biomass estimates, respectively. As the method was verified in a sufficiently high number of experiments (for turbidity 12 exps. and for permittivity 8 exps.), it is applicable in process on-line monitoring. Considering filtering performance, e.g., some of the shifts may be filtered only partly or some overfiltration is possible, the method is applicable for decision making in bioprocess control. Some examples of unfiltered permittivity signal peaks, analyzed in detail, are added to the supplementary material (Appendix B, Figures A4-A6). From this data, one can observe that unfiltrated shift nRS E does not exceed preset reference nRS E,max and nRS E,min bounds, but the nRS E peak has a wider area compared to neighbor peaks not related to the signal uncommon shift. Therefore, identifying uncommon shift nRS E peak threshold area and selecting it as a filtering criterium, might lead to improved filtering accuracy.

Concluding Remarks
Despite the inert implementation of the process analytical tools for decision-making in biopharma's process control, the future cybernetical-physical systems (i.e., interconnected systems of physical machines that are controlled by soft-sensor and algorithms) are likely to become autonomous units, being able to function without manual interventions, and delivering quality by design [58]. For that purpose, reliable and well interpretable realtime biomass sensor data acquisition will be of major importance. Due to this reason, the contribution authors expect to enhance the development of biomass monitoring.

Acknowledgments:
The authors would like to acknowledge the contribution of colleagues from the Latvian Biomedicine Research and Study Centre -Andris Kazaks for supplying both recombinant P. pastoris strains and Inara Akopjana for preparing seed inoculation cultures for bioreactor processes. The authors also would like to acknowledge Rita Skerbaka for the off-line methanol analysis.

Conflicts of Interest:
The authors declare no conflict of interests. Appendix A Figure A1. Some of the process variables regarding the process control strategy applied from Table 1. Legend description the same as for Figure A2.  Table 1); (B) HBsAg processes under different cultivation protocols and cultivation temperature (the legend indicates the abbreviation of the cultivation protocol and process temperature, respectively; information according to Table 1); and (C) comparison of panels A and B (HBc and HBs are short abbreviations of HBcAg and HBsAg, respectively). Figure A1. Some of the process variables regarding the process control strategy applied from Table 1. Legend description the same as for Figure A2.  Table 1); (B) HBsAg processes under different cultivation protocols and cultivation temperature (the legend indicates the abbreviation of the cultivation protocol and process temperature, respectively; information according to Table 1); and (C) comparison of panels A and B (HBc and HBs are short abbreviations of HBcAg and HBsAg, respectively).  Table 1); (B) HBsAg processes under different cultivation protocols and cultivation temperature (the legend indicates the abbreviation of the cultivation protocol and process temperature, respectively; information according to Table 1); and (C) comparison of panels A and B (HBc and HBs are short abbreviations of HBcAg and HBsAg, respectively). Appendix B Table A1. In-situ turbidity and permittivity sensor signal filtering quality parameter evaluation overview for a part of the presented experiments.   (3) Maximum addition rate of the anti-foam agent reached in approximately 2 to 3 min starting from the time indicated in column 1 or reached in the time indicated in parentheses (from the right of the parameter); (4) Maximum RSn of the turbidity signal reached in approximately 2 to 3 min starting from the time indicated in column 1; (5) Influence of the raw sensor signal shift of DCW biomass estimate, where: X turbRaw0 biomass estimate from the raw turbidity sensor signal just before the signal's uncommon shift; X turbRaw1 biomass estimate from the raw turbidity sensor signal immediately after the signal uncommon shift; diff. in % (parameter in parentheses) = ABS(X turbRaw1 − X turbRaw0 )*100%/X turbRaw0 ; for columns (6), (8) and (9) analogic description as for column (5) using appropriate parameters of X turbFiltr , X permRaw and X permFiltr ; (7) maximum RSn of the permittivity signal reached in approximately 2 to 3 min starting from time indicated in column 1.     Appendix C Figure A7. Flow chart of the used gas mixing system and exhaust gas line for gas analysis.

Appendix B
Volume of gas mixing chamber ≈1 L.  Volume of gas mixing chamber ≈1 L.
Exhaust gass filter cloging happen in experiment 7s. This may explain bad X OTR and X CPR estimation results in experiment 7s.     Appendix E Figure A13. Permittivity signal correlation to DCW (fitted to Dataset 3 and 1s, 2s and 3s experiments). Figure A12. Carbon balance for the methanol consumption phase. Carbon balance calculated as a ratio of car-bon_accumulated_lost / carbon_supplied. carbon_accumulated_lost, consisted of carbon utilized for biomass formation and carbon lost due to CO 2 evolution; carbon_supplied consisted of carbon supplied due to methanol feed.

Appendix E
Sensors 2021, 21, x FOR PROOF 31 of 34 (B) Figure A11. Total yield coefficients of O2 consumption (YOX_total) (panel A) and CO2 production (YCX_total) (panel B) for glycerol (squares) and methanol (circles) phases. In each subplot, average values from available measurement points for glycerol (g) and methanol (m) phases are indicated. Figure A12. Carbon balance for the methanol consumption phase. Carbon balance calculated as a ratio of carbon_accumu-lated_lost / carbon_supplied. carbon_accumulated_lost, consisted of carbon utilized for biomass formation and carbon lost due to CO2 evolution; carbon_supplied consisted of carbon supplied due to methanol feed.