A supervision and control tool based on artificial intelligence for high cell density cultivations

PROCESS SYSTEMS ENGINEERING

A supervision and control tool based on artificial intelligence for high cell density cultivations

A. C. L. Horta^I,II,*; A. J. Silva^II; C. R. Sargo^II; A. M. Velez^II; M. C. Gonzaga^II; R. C. Giordano^II; V. M. Gonçalves^III; T. C. Zangirolami^II

^IUniversidade Federal de Goiás, Instituto de Química, Phone: + (55) (62) 3521-1097, Ext: 209, Fax: + (55) (62) 3521-1167, P.O. Box 131, Zip Code: 74001-970, Goiânia - GO, Brazil. E-mail: [e-mail]

^IIUniversidade Federal de São Carlos, Departamento de Engenharia Química, São Carlos - SP, Brazil. E-mail: [e-mail]

^IIIInstituto Butantan, Centro de Biotecnologia, São Paulo - SP, Brazil. E-mail: [e-mail]

ABSTRACT

High cell density cultivations of recombinant E. coli have been increasingly used for the production of heterologous proteins. However, it is a challenge to maintain these cultivations within the desired conditions, given that some variables such as dissolved oxygen concentration (DOC) and feed flow rate are difficult to control. This paper describes the software SUPERSYS_HCDC, a tool developed to supervise fed-batch cultures of rE. coli with biomass concentrations up to 150 g_DCW/L and cell productivities up to 9 g_DCW.L^-1.h^-1. The tool includes automatic control of the DOC by integrated action of the stirrer speed as well as of the air and oxygen flow rates; automatic start-up of the feed flow of fresh medium (system based on a neural network committee); and automatic slowdown of feeding when oxygen consumption exceeds the maximum capacity of the oxygen supply.

Keywords: High cell density cultivations; Monitoring and control system; Recombinant E. coli; Fed-batch; Artificial intelligence.

INTRODUCTION

Fed-batch cultivations of recombinant Escherichia coli (rE. coli) are used in the production of numerous products of the pharmaceutical industry like insulin, growth hormones, vaccines and interferons (Liljeqvist and Stahl, 1999; Eiteman and Altman, 2006; Tripathi et al., 2009). Regardless of the product of interest, the cultures are carried out with the initial goal of achieving high cell density and then proceed to the induction of the synthesis of the desired protein.

The operation mode most widely employed in high cell density cultivations (HCDC) of rE. coli is fed-batch culture with exponentially increasing feed flow rate (Shiloach and Fass, 2005). However, when running a HCDC, operational difficulties are commonly found in both the growth and protein production phases. Throughout the cultivation, the substrate concentration must be kept at the desired level, because its accumulation can cause inhibition of cell growth and protein production. On the other hand, an excessive shortage of substrate supply can hamper growth and protein synthesis. Furthermore, it can lead to decreased viability and even to cell death if the rate of carbon supplied is not enough to meet the maintenance requirements (Silva, 2011). For these reasons, a precise control of the feed flow rate of supplementary medium (F) is required and F must be adjusted to the demand at every stage of cultivation, which can vary considerably after the induction of protein synthesis due to metabolic stress associated to the expression of heterologous genes involved in the production of recombinant proteins (Dabros et al., 2010).

Besides preventing substrate accumulation, F should restrict the growth rate in order to avoid the formation of metabolic by-products (Lee, 1996; Kilikian et al., 2000). The formation of acetate, the main by-product of E. coli metabolism, is triggered either by the so-called overflow metabolism or by oxygen depletion. The mechanism known as overflow occurs mainly in cultures with glucose as carbon source, when growth is maintained above the critical specific growth rate (µ_C) and a rapid assimilation of the carbon source takes place (Rocha, 2003). In order to avoid overflow metabolism, the specific growth rate is limited below a critical value limiting the replenishment of the carbon source (Rocha, 2003; Demain and Vaishnav, 2009). This procedure ensures no accumulation of substrate or acetate. In turn, however, it decreases the productivity of the process by limiting the growth rate.

Other problems can occur frequently in HCDC conducted under conditions of exponential growth, such as temperature build-up, dissolved oxygen tension below the desirable levels, early (or late) startup of the feed pump, foam formation, and overpressure, among others.

Due to all the above mentioned reasons, an advanced monitoring and control tool is required to achieve the desired bioreactor performance during HCD cultivations. Some commercial products (AFS-BioCommand Bioprocessing Software^® from New Brunswick Scientific; DASGIP Control 4.0^® from Dasgip AG; BioeXpert^® from Applikon Biotechnology; Iris^® from Infors HT) perform basic tasks, such as data acquisition as well as control of pH, flow rates (air, nitrogen, oxygen, feed supply, base or acid solution) and dissolved oxygen concentration. They also include special features, like remote access and open-configuration by the users. However, they are expensive and bioreactor-specific embedded softwares. The objective of this study was to develop, test and validate an artificial intelligence based tool called SUPERSYS_HCDC, a free and open access supervisory system for monitoring and control of rE. coli HCDC. In previously published works, specific functionalities of SUPERSYS_HCDC, namely automatic start-up of the feeding pump (Horta et al., 2011a) and a model-based adaptive control of the feeding flow rate using on-line permittivity data provided by a biomass sensor (Horta et al., 2012), were addressed. Here, a complete overview of the supervisory system set-up is presented and specially selected results that exemplify its potential are highlighted. In addition, the novel approach developed to control the dissolved oxygen concentration, which combines the usual manipulated variables (stirring speed, gas flow rate and oxygen enrichment) with automatic restriction of feeding flow rate, is detailed.

MATERIALS AND METHODS

Microorganisms

Five recombinant E. coli BL21(DE3) strains, modified with the following plasmids, were cultivated under the supervision of SUPERSYS_HCDC: a) pET37b+/PspA3 and PspA4Pro, kindly provided by Dr. Eliane Miyaji (Centro de Biotecnologia, Instituto Butantan, São Paulo, Brazil), and pET37b+/ PspA245, provided by Dr. Luciana Leite (Centro de Biotecnologia, Instituto Butantan, São Paulo, Brazil), all three clones expressing a fragment of the surface protein A of Streptococcus pneumoniae (Barazzone et al., 2011; Carvalho et al., 2012); b) pET28a/SpaA, producing a recombinant fragment of the SpaA protein from Erysipelothrix rhusiopathiae (Silva et al., 2012); c) pT101/D-TOPO, kindly donated by Laboratório de Biocatálisis, ICP-CSIC-Madri, Spain, with pac gene codifying for penicillin G acylase (PGA) production (Montes et al., 2007).

Medium

All the cultivations were carried out in fed-batch mode. A modified HDF medium composition (Seeger et al., 1995; Sargo, 2011), a chemically defined medium containing glycerol as carbon source, was used in 17 cultures of rE. coli strains pET37b+/PspA3, PspA245, PspA4Pro and pT101/D-TOPO. Five cultures of rE. coli strains pT101/D-TOPO and pET28a/SpaA were performed using modified complex media (Silva, 2011), based on LB or ZYM-50552 auto-induction media compositions (Studier, 2005), containing glucose, glycerol or a mixture of both as main carbon sources and yeast extract and tryptone as nutrients.

Bioreactor Operation and Instrumentation

The twenty-two fed-batch cultures were carried out in a 5.0 L home-made bioreactor and monitored by SUPERSYS_HCDC^®(Horta et al., 2011c). The complete experimental set-up is shown in Figure 1. The pH was controlled (on/off) at 6.7 (pHmeter GLI PRO) by addition of NH₄OH (30%) in the batch phase and at 6.9 in the feeding phase. The upward shift in the pH was to ensure an adequate nitrogen supply for the growing cell population and avoid the possibility that growth and heterologous protein production would become limited by nitrogen shortage (Seeger et al., 1995; Korz et al., 1995; Lee, 1996; Babaeipour et al., 2007; Carvalho et al., 2012; Tripathi et al., 2009). Temperature was set at 25, 30, 35 or 37 ºC (depending on the strain being cultivated). The dissolved oxygen concentration (DOC) was monitored using a dissolved oxygen sensor (Mettler Toledo Inpro 6800 probe, connected to a CE O2 4050 transmitter), and maintained at 30% by a hybrid controller (PID + Heuristic), which automatically changed both agitation speed (between 200 and 900 rpm) and the composition of the gas stream supplied to the bioreactor (by mixing pure oxygen with air). The total gas flow rate was maintained at 4 -6 L/min by two mass flow controllers (GFC AALBORG). The broth permittivity and conductivity were monitored by a Biomass Sensor (FOGALE^® Nanotech), with data acquisition via compact field point (cFP). The exhaust gas composition was assessed by a Sick/Maihak S.710 CO₂ and O₂ analyzer. On-line data acquisition, as well as monitoring/control of all instruments via a cFP-2020 (National Instruments), was performed by the software SuperSys_HCDC^R developed in LabView^®. Supplementary feed flow rate was controlled by SuperSys_HCDC^R to match the growth requirements through on-line estimation of the specific growth rate based on permittivity data (Horta et al., 2011c). All listed instruments presented data acquisition in real time, with acquisition intervals selected by the user, which was every 10s for the experiments described here.

Main control loops and their respective signal and mass fluxes are also indicated in Figure 1. A more detailed description of the control loops is given in the following.

For all experiments, the exponential feeding flow rate was calculated using Equation (1) (Nielsen et al., 2002) and was automatically controlled by the supervisory system.

In Equation (1), F (Lh^-1) is the feed flow rate, µSET (h^-1) is the desired specific growth, Y_XS (g_DCW g_glycerol^-1) is the biomass yield coefficient based on glycerol, m (g_DCW g_glycerol^-1 h^-1) is the maintenance coefficient, C_X0 [g_DCW L^-1] and V₀ (L) correspond to the cellular concentration and volume, respectively, at the beginning of the fed-batch phase, C_S0 (g_glycerol L^-1) is the carbon source concentration in the supplementary medium and C_SR (g_glycerol L^-1) represents the residual glycerol concentration.

Equation (1) controls the feed flow rate of fresh substrate and contain 6 variables (µ, µ_set, Yxs, m, C_x0, V₀) and 2 constants (C_s0, C_sr), which are specified by the user. The strategy for controlling the exponential feed flow rate changed according to the cultivation (Silva, 2011; Sargo, 2011). It evolved from the classical control strategy, where µ_SET, Yxs and m are taken as constants, to a more sophisticated approach, where µ and µ_set were continuously retuned at each 10 min interval using the values of µ obtained online from the permittivity measurements provided by the capacitance biomass sensor (Horta et al., 2012). Concerning Yxs and m, usually they are taken as constant parameters. But, in fact, they can vary significantly throughout the cultivation, reflecting the metabolic changes in different culture phases. SUPERSYS_HCDC^R contains an option that enables the estimation of these parameters for each sample, using a fitting algorithm such as Levenberg-Marquardt to adjust the parametric model (Monod) to the at-line measured data, like optical density and substrate concentration (Horta et al., 2011b; Horta et al., 2012).

Analytical Procedures

Cell growth was followed by the culture broth optical density reading (OD, λ = 600 nm), dry cell weight measurements (g_DCW.L^-1), counting CFU.mL^-1 and on-line estimation by measuring broth permittivity (pF.cm^-1).

Metabolite concentrations were assessed by HPLC (Waters Corp. system), using an Aminex HPX-87H column (Bio-Rad) and 5 mM sulfuric acid solution as mobile phase (flow rate of 0.6 mL min^-1), at 60 ºC. Organic acids were detected at 210 nm (Waters 486 UV detector), while glycerol, glucose, lactose and galactose were measured with a refractive index detector (Waters 410).

Supervisory and Control Tool

The SUPERSYS_HCDC software comprises modules that perform basic functions as well as real time inference of important variables. Carbon dioxide evolution rate (CER), oxygen uptake rate (OUR) and respiratory quotient (RQ) are calculated taking into account the on-line molar fractions of CO₂ (Y_CO2) and O ₂ (Y_O2) in the exhaust gas and the air (Q_air) and oxygen (Q_O2) inlet flow rates (Equations (2), (3) and (4)).

In Equations (2) to (4), R is the ideal gas constant, P the atmospheric pressure and T the temperature, both at standard temperature and pressure (STP).

On-line cell concentration (Cx_perm) data were generated after treating the permittivity signal with a smoothed moving average (SMA) filter. Cx_perm was further used for inference of the growth rate (r_x) and specific growth rate (µ), as described in Horta et al. (2012). Bioreactor volume (Vn, in L) was also continuously updated as a function of sample withdrawal (V_sample) and feeding medium supplied as described by Equation (5).

where V(n-1) is the volume of the previous step and the term (C₁/C₂)[exp(C₂(t(n)-t_bat))-exp(C₂(t(n-1)-t_bat))] represents the volume of fresh medium added (meaning of C₁ and C₂ is given at Figure 2).

The on-line estimated µ values enabled the implementation of an automatic control of the feeding flow rate (F) defined by Equation (1) through the dynamical updating of the specific growth rate. For this purpose, every 10 minutes µ_SET was replaced by µ_DYN, which was obtained after processing a vector containing 50 instances with the SMA filter (Horta et al., 2012).

To cope with the changes in cell metabolism taking place after induction, which strongly impact the specific growth rate as well as the maintenance and biomass yield coefficients, a module for automatic fitting of Yxs and m to Equation (1) was set-up and integrated to the control program. The parametric fitting system is based on the global (Simulated Annealing, Particle Swarm, Differential Evolution) and local search (Levenberg-Marquadt) algorithms to estimate, inside a confidence region, the optimal values for Yxs and m (Horta et al., 2012).

Besides the automatic updating of key parameters in Equation (1), the feed flow rate control also incorporated a modulation of the growth rate to maintain DOC at the desired set-point. Thus, F control only followed Equation (1) if the DOC was ~ 30 % of saturation. When OUR exceeded the maximum bioreactor oxygen transfer rate (OTR), at the maximum stirring speed and maximum oxygen flow rate, the F control combined Equation (1) to the logic described in Figure 2, preventing oxygen depletion and the formation of undesirable metabolic by-products, such as acetic acid.

To complete the automation of feed supply, a special module for automatic start-up of the feed pump was developed and implemented. The identification of the end of the batch phase was performed by a neural network based softsensor, which produced a command signal to start the feed pump (Horta et al., 2011a). The neural network (nn) was trained offline, using data from real experiments. The nn committee structure guaranteed that a new nn generated from a new experiment could be added to the committee without loss of knowledge from the previous experiments.

To match the typically high OUR of E. coli HCDC, the DOC control was accomplished by developing a hybrid system, which combined the classical PID (proportional, integral and derivative) controller directly acting on the stirrer speed to a heuristic algorithm modulating the flow rates of air and oxygen. The PID controller is described in Figure 3, where "Agit" refers to the stirrer speed (rpm), "Kc" to the proportional constant, "Td" the derivative constant, "Ti" to the integral constant, "SetP" to the DOC set-point and "t" to time (s).

The control of air (Q_AIR) and oxygen (Q_O2) flow rates is performed by an independent algorithm based on the heuristic logics presented at Figure 4.

Another important feature developed and implemented in SUPERSYS_HCDC is a set of specific alarms for fault detection and warning and its pseudocode is given in Figure 5. The alarm system warns the operator via the computer loudspeakers, as well as by sending text messages via SMS.

RESULTS AND DISCUSSION

SUPERSYS_HCDC was upgraded, tested and validated by using it as the supervisory and control system in 22 fed-batch cultures of recombinant E. coli, 19 of them being high cell density cultures (final biomass concentration over 50 g_DCW/L). The results showing the performance of the developed supervisory system concerning the dynamic control of the supplementary medium flow rate and the automatic start-up of the feed pump have already been detailed (Horta et al., 2011a,b, 2012). The results concerning the on-line estimation of CER, OUR and RQ, as well as the DOC control, are highlighted in the followings.

On-Line Estimation of CER, OUR, RQ and µ

Figure 6 shows the results of an example of an auto-induction experiment in which cells were exposed to the inducer (lactose) from the beginning, but protein expression was actually intensified 4h after the onset of cultivation when the glucose present in the batch medium was totally consumed. Figure 6 (a) shows that the on-line signs (perm and CER) and the off-line (Cx) showed similar increasing profiles within ~ 4 h of culture. Figure 6(b) exhibits the results of CER, OUR and RQ on-line calculation from the gas analyzer measurements of C_O2 and O₂ mole fractions in the exhaust gas leaving the bioreactor (Equations (2), (3) and (4)). These data can be compared to the trends in permittivity signal, biomass concentration experimental points and µ inferred from the biomass sensor, which are displayed in Figures 6 (a), (b), (c).

After induction intensification, while the measures of Cx (Fig. 6(a)) indicated that growth continued at a slow specific growth rate (decreasing from ~ 0.1 to 0.05h^-1), CER, OUR, RQ and permittivity on-line data (Fig. 6(b)) suggested severe growth stagnation and even a decline in metabolism, following closely the UFC/mL counts. This mismatch happens because optical density readings or dry cell weight measurements do not distinguish viable from non-viable cells. Conversely, permittivity data reflect the polarization of the cell membrane when submitted to low radio frequencies (0.1-20 MHz). Hence, the dielectric permittivity is directly proportional to the viable biomass concentration, since dead cells do not present polarization in their membranes (Matanguihan et al., 1994; Markx and Davey, 1999; Tibayrenc et al., 2011). Similarly, CO2 production as well as O2 uptake is also strongly influenced by the physiological state of the cells. Thus, CER, OUR and permittivity data described the metabolic burden imposed by the impacts of prolonged induction on cell viability, leading to the growth cessation after 10 h of cultivation (Figures 6(a), (b)). These changes in growth profile were correctly reproduced by the specific growth rate estimated from permittivity data (Figure 6(c)). The same approach, i.e., the use of on-line permittivity data for real time inference of growth rate for different organisms, has been reported elsewhere (Davey et al., 1996; Henry et al., 2007; Dabros et al., 2010).

These results highlight the importance of permittivity, CER and OUR data for physiological state identification, as well as for setting up suitable control strategies of feed supply. This is particularly true for cultivations of genetically modified organisms, because the production of the recombinant protein impairs cell viability, leading to reduced growth and substrate uptake rates. In addition, it has been shown that biomass yield and maintenance coefficients underwent expressive changes throughout the induction phase to correctly describe the metabolic shift associated with protein synthesis (Horta et al., 2012). Thus, to properly tackle such a complex problem, an integrated supervision environment, as provided by SUPERSYS_HCDC^® or alike, is required.

Hybrid Controller of DOC

E. coli cultures are characterized by their high oxygen demand. Kuprijanov et al. (2009) emphasized the importance of fine controlling the DOC and proposed a very efficient feedforward/feedback controller based on a gain schedule approach. This controller was set-up with the air flow rate and stirring speed as manipulated variables and validated in fermentations of rE. coli releasing a green fluorescent protein.

However, to meet the OUR requirements, the control strategy must include not only the usual actuators (stirrer speed and total gas flow rate), but also be combined with new actuators (oxygen and air flow rates) to promote the gradual oxygen enrichment of inlet air. For this purpose, a hybrid controller acting on the stirrer speed, air and oxygen flow rates was implemented as described in Figures 3 and 4. The performance of the DOC hybrid controller can be seen in Figure 7 (a), which shows that the desired levels of DOC were kept throughout the cultivation. As expected, the stirrer speed and air flow rate remained as main actuators within the first 12 h of culture. When both reached their upper limits, air enrichment with pure oxygen automatically started to take place. From this moment on, the air flow rate decreased from 4 to 1.7 L/min, while the oxygen flow rate increased gradually from 0 to 2.3 L/min. Just before 30 h of culture, a new event (substrate shortage followed by the inducer pulse - data not shown) led to a reduction of growth and oxygen uptake rates. Again, the hybrid controller showed an efficient response, automatically cutting down the oxygen supply and returning the air flow rate to 4 L/min.

The occasional oscillations observed in the DOC data are due to the variations in the air and oxygen flow rates, which are related to the mass flow controller operation ranges. Mass flow controllers specified to operate at maximum flow rates of ~ 5 L/min have accuracy limits in the range of ± 0.3 L/min. The accuracy of the flow rates supplied by the mass flow controllers was also affected by the head loss increase due to the biomass build-up in the broth that also led to higher viscosity.

DOC Control by Growth Rate Modulation

Actually, the maximum achievable biomass concentration in a fed-batch culture is limited by the highest oxygen transfer rate (OTR) that can be supplied by the bioreactor system. For rE. coli HCDC special care must be taken to prevent carbon source accumulation, which can easily happen if growth is limited by OTR. Furthermore, when OUR exceeds OTR, low levels of DOC are established, driving cell metabolism towards the production of undesirable fermentative products. Thus, an additional module was included in the DOC controller so that the feeding flow rate was manipulated to keep the DOC at the set point in which the bioreactor was operated at its maximum OTR.

Figure 8 shows the performance of the DOC controller when the modulation by the feeding flow rate was activated. Shortly before 18 h of cultivation, Figures 8(a) and 8(c) show that both the oxygen flow rate and the stirring speed were at their upper limits. In spite of this, the DOC (Fig. 8(d)) presented a decreasing profile. At this moment, the controller automatically reduced the feeding flow rate to decrease the growth rate and, consequently, oxygen consumption. The effects of the control action can also be seen in Figures 8(h) and 8(j): substrate and acetate accumulation profiles (between 14 and 18 h) were reverted after the feeding was slowed down. The combined controller performance was satisfactory and DOC was kept between 10 and 40 % of saturation throughout the cultivation.

Looking at Figure 8(f), we observe that the permittivity estimated concentration matched perfectly to the off-line biomass concentration points (dry weight measurements) up to the moment of induction. After the inducer is added, the viability decrease was depicted by the permittivity data, but not by the off-line biomass concentration measurements, as discussed previously. The cumulative alkali consumption (Fig. 8(i)) for pH control also showed a close correlation with biomass concentration. The pH remained at the desired set-point throughout the experiment, with slightly higher values after induction (Figure 8e).

Concerning the specific growth rate (µ) estimated from permittivity data (Figure 8(g)), the oscillatory behavior registered up to ~ 7.5 h was related mainly to the low resolution of the permittivity measurements (Horta et al., 2012). After the induction, a sharp decrease of µ and a gradual increase of substrate concentration were observed as consequences of the cell metabolic effort to produce the heterologous protein.

SuperSys_HCDC and Overall Process Performance

The cultivation performance was influenced by the software functions. Table 1 shows some of the key indicators, such as maximum biomass concentration, productivity, protein production and acetic acid concentration, together with the tools available in the software at different evolution stages.

As can be seen in Table 1, the software was validated for cultivations carried out with different medium formulations (complex/defined), inducers (IPTG/lactose) and inducing strategies (pulse/continuous). Increasing biomass productivity with software evolution was observed. In addition, more advanced strategies (1 to 4) helped to reduce the formation of acetate. There was also an increase in the production of recombinant protein, mainly due to implementation of a feed flow rate control matching the actual cell growth rate (Horta et al., 2012).

CONCLUSIONS

The adequate control, monitoring and supervision of a bioprocess is an important step to achieve batch to batch reproducibility and quality control high standards, as well as more robust and cost effective processes, less prone to human errors. These issues are crucial for the production of biopharmaceuticals and are present in both FDA and GMP regulations.

In this work, the development of the automatic supervision and control tool SUPERSYS_HCDC is presented and discussed. The tool includes several up-to-date functionalities, such as: automatic combined control of the DOC; automatic start-up of the feed pump; remote access and warning system by voice alarms or SMS messages. It was set-up in the LabView environment, enabling a user-friendly interface, with flexibility of choices by the operator for all tasks. Its modular structure also facilitates the inclusion of new functionalities. In the latest version (St5 - not included here), growth rate modulation for DOC control can also be performed by automatic temperature reduction. Furthermore, a new version of the tool (St6) for supervision and control of airlift bioreactors is under development.

The tool was designed to be used as support in HCDC of rE. coli and, so far, it has been extensively tested in 22 fed-batch cultures of 5 different recombinant strains of this bacterium. But it has also been used to supervise batch and fed-batch cultures of other industrially important microorganisms like Pichia pastoris, Bacillus subtilis, Bacillus megaterium and Saccharomyces cerevisiae.

The tool proved to be extremely useful for correctly running long lasting (~ 40 h) HCDC, when the bioreactor was operated by several users with different practice skills. Important decisions such as the right moment for starting the feed pump, the oxygen and air flow rates to be used, and suitable feeding profiles could be left to the tool.

In the specific case of HCD cultures of rE. coli, the tool showed a reliable performance when controlling the DOC and the nutrient supply, even considering the high level of difficulty imposed by the high biomass concentrations and the metabolic drifts triggered by heterologous protein synthesis. It certainly contributed to achieve a biomass concentration of 155 g_DCW/L in only 17 h of culture, leading to a maximum cell productivity of 9.2 g_DCW.L^-1.h^-1.

The SUPERSYS_HCDC tool will be available as free software at www.ladabio.deq.ufscar.br.

ACKNOWLEDGEMENTS

The authors would like to thank the São Paulo Research Foundation (FAPESP) and Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES) for funding this work, and Tiago Martins Pereira and Amadeus Gomes de Azevedo for technical support.

NOMENCLATURE

C_S Substrate concentration g/L C_S0 Substrate concentration in the feeding medium g/L C_SR Residual substrate concentration g/L C_X Cellular concentration C_X0 Cellular concentration (g/L) in the beginning of the feeding stage F Feeding rate L/h m Maintenance coefficient g_X/g_S.h t Time T Temperature ºC or K V₀ Volume of cultivation medium at the beginning of feeding stage L Y_XS Yield coefficient g_X/g_S Greek Letters µ_DYN Dynamic specific growth rate on-line estimated h^-1 µ or mi Specific growth rate h^-1 µ_CRIT Critical specific growth rate h^-1 µ_MAX Critical specific growth rate h^-1 µ_SET Specific growth rate limited by the fed flow rate h^-1 Abbreviations AI Artificial Intelligence HCDC High Cell Density Cultivation SMA Smoothed Moving Average OD Optical Density 600 nm DCW Dry Cell Weight DOC Dissolved Oxygen Concentration % of saturation

(Submitted: September 26, 2012; Revised: April 4, 2013; Accepted: June 24, 2013)

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*

To whom correspondence should be addressed

Publication Dates

• Publication in this collection
  07 July 2014
• Date of issue
  June 2014

History

• Accepted
  24 June 2013
• Reviewed
  04 Apr 2013
• Received
  26 Sept 2012