Nonlinear observation of specific growth rate in aerobic fermentation processes

Simple nonlinear observers for the on-line estimation of the specific growth rate from presently attainable real-time measurements are presented. The proposed observers do not assume or require any model for the specific growth rate and they are very successful in accurately estimating this parameter. Moreover, they are very easy to implement and to calibrate. Indeed, due to the particular structure of their gain, their tuning is reduced to the calibration of a single parameter. Simulation results obtained under different operating conditions are given in order to highlight the performances of the proposed estimators.     

Inferential control of the specific growth rate in fed-batch cultivation processes

Inferential control algorithms and systems for set-point control of the specific growth rate in fed-batch cultivation processes are presented. Realization of the proposed control systems does not require mathematical model and a priori knowledge of the culture of microorganisms under control. Feed-back signal in PID control loops of the investigated systems is based on measurements of the O₂ concentration in exhaust gas and the air supply rate, however, measurements of the other technological parameters related to the culture growth dynamics can also be applied.     

Knowledge-based control of fermentation processes

A decade has passed since the first applications of a knowledge-based approach to the control of bioprocesses were reported. During this period, both the development and application of intelligent control in biotechnology have undergone remarkable evolution in terms of concepts, objectives, and tools. Stimulated by rapid progress in the field of real-time expert systems, knowledge-based methodology for the control of fermentation processes has now reached a more mature phase. A growing interest among the biotechnology community and intensive, realistic, and fruitful research being undertaken both in universities and in industry suggest that large-scale application of knowledge-based systems for the control of bioprocesses is inevitable. This article provides a concise summary of the main achievements in this new area and discusses recent trends, porblems, and perspectives.     

Evaluation of the maximum specific growth rate of a yeast indicating non-linear growth trends in batch culture

The maximum specific growth rate (μ_max) of an ethanolic D-xylose-fermenting yeast, Pichia stipitis, showing non-linear growth trends in batch culture, was calculated using the rate equation μ₂ = (1/Δt) ln(x ₂/x ₁). The absolute error Δμ, affecting μ₂, was derived using an equation given by Borzani (1994). Based on the assumption of linearity of growth curves between two closest time points, the relation between the two rate formulae, μ₁ = (1/xˉ)dx _t /dt and μ₂ = (1/Δt) ln(x ₂/x ₁) was established. In a particular condition, when μ₁ = μ₂, an equation has been developed, the roots of which are the specific growth rates at different time points. This revised version was published online in July 2006 with corrections to the Cover Date.     

A general equation for the evaluation of the error that affects the value of the maximum specific growth rate

A general equation is proposed to evaluate the absolute error that affects the maximum specific growth rate calculated from batch or continuous experiments. This error depends on the relative errors of the cell concentration measurements and on the duration of the test.Nomenclature X ₁ Cell concentration at the beginning of the exponential growth phase or of the washing-out period - X ₁ Lowest value of X ₁ due to experimental errors - X ₁ Highest value of X ₁ due to experimental errors - X ₂ Cell concentration at the end of the exponential growth phse or of the washing-out period - X ₂ Lowest value of X ₂ due to experimental errors - X ₂ Highest value of X ₂ due to experiment errors - Relative error that affects X ₁ - Relative error that affects X ₂ - t Exponential growth stage or washing-out duration - Asolute error that affects - Maximum specific growth rate - ₁ Lowest value of due to experimental errors - ₂ Highest value of due to experimental errors The author is with the Instituto Mauá de Technologia, Estrada das Lágrimas 2035, 09580-900, São Caetano do Sul, SP, Brazil     

Simultaneous identification of growth law and estimation of its rate parameter for biological growth data: a new approach

Scientific formalizations of the notion of growth and measurement of the rate of growth in living organisms are age-old problems. The most frequently used metric, “Average Relative Growth Rate” is invariant under the choice of the underlying growth model. Theoretically, the estimated rate parameter and relative growth rate remain constant for all mutually exclusive and exhaustive time intervals if the underlying law is exponential but not for other common growth laws (e.g., logistic, Gompertz, power, general logistic). We propose a new growth metric specific to a particular growth law and show that it is capable of identifying the underlying growth model. The metric remains constant over different time intervals if the underlying law is true, while the extent of its variation reflects the departure of the assumed model from the true one. We propose a new estimator of the relative growth rate, which is more sensitive to the true underlying model than the existing one. The advantage of using this is that it can detect crucial intervals where the growth process is erratic and unusual. It may help experimental scientists to study more closely the effect of the parameters responsible for the growth of the organism/population under study.     

Clonal variation in maximum specific growth rate and susceptibility towards antimicrobials

AIMS: To examine associations between growth rate within bacterial populations and survival patterns following treatment with antimicrobial agents. METHODS AND RESULTS: Time survival data were generated for the inactivation of Escherichia coli populations, grown as batch and continuous cultures, exposed to ciprofloxacin, benzalkonium chloride and tetracycline. Time-survivor plots were biphasic. Surviving cells were collected and immediately re-exposed to agent or were regrown and then re-exposed. Survivors were resistant to immediate challenge with any of the treatment agents. This resistance was lost on regrowth suggesting that survival reflects an expressed phenotype within a subset of the culture (persisters) rather than individual resistant clones or nonspecific quenching of the test agent. The fraction of persisters increased with decreasing growth rate when cultures were prepared in continuous culture. CONCLUSIONS: Clonal growth rates within populations were determined by culture of individual cells within microtitre plate wells. The fraction of clones, in batch cultures, growing maximally at rates below the apparent threshold for susceptibility to the test agents was sufficient to explain the results of continuous culture experiments. SIGNIFICANCE AND IMPACT OF THE STUDY: The presence of persisters in populations of bacteria relate to small subset of cells that are growing only slowly or are metabolically quiescent.     

Adaptive on-line model for aerobic Saccharomyces cerevisiae fermentation

In order to study and control fermentation processes, indirect on-tine measurements and mathematical models can be used. In this article we present a mathematical on-line model for fermentation processes. The model is based on atom and partial mass balances as well as on equations describing the acid-base system. The model is brought into an adaptive form by including transport equations for mass transfer and unstructured expressions for the fermentation kinetics. The state of the process, i.e., the concentrations of biomass, substrate, and products, can be estimated on-line using the balance part of the model completed with measurement equations for the input and output flows of the process. Adaptivity is realized by means of on-line estimation of parameters in the transport and kinetic expressions using recursive regression analysis. These expressions can thus be used in the model as valid equations enabling prediction of the process. This makes model-based automation of the process and testing of the validity of the measurement variables possible. The model and the on-line principles are applied to a 3.5-L laboratory tormentor in which Saccharomyces cerevisiae is cultivated. The experimental results show that the model-based estimation of the state and the predictions of the process correlate closely with high-performance liquid chromatography (HPLC) analyses. (c) 1995 John Wiley & Sons, Inc.     

Decrease of proteolytic degradation of recombinant hirudin produced by Pichia pastoris by controlling the specific growth rate

The effects of the specific growth rate and methanol concentration on the degradation of hirudin produced by recombinant Pichia pastoris were investigated. When a methanol-limited state and the specific growth rate of 0.02 h^–1 were maintained during the fermentation, a minimum degradation of hirudin and a maximum specific hirudin production rate were achieved. By this strategy, the production of intact recombinant hirudin Hir65 reached 0.7 g l^–1 in fed-batch fermentation. Its proportion was 35% to all forms of hirudin.     

Control of IgG glycosylation by in situ and real-time estimation of specific growth rate of CHO cells cultured in bioreactor

The cell-specific growth rate (µ) is a critical process parameter for antibody production processes performed by animal cell cultures, as it describes the cell growth and reflects the cell physiological state. When there are changes in these parameters, which are indicated by variations of µ, the synthesis and the quality of antibodies are often affected. Therefore, it is essential to monitor and control the variations of µto assure the antibody production and achieve high product quality. In this study, a novel approach for on-line estimation of µ was developed based on the process analytical technology initiative by using an in situ dielectric spectroscopy. Critical moments, such as significant µ decreases, were successfully detected by this method, in association with changes in cell physiology as well as with an accumulation of nonglycosylated antibodies. Thus, this method was used to perform medium renewals at the appropriate time points, maintaining the values of µ close to its maximum. Using this method, we demonstrated that the physiological state of cells remained stable, the quantity and the glycosylation quality of antibodies were assured at the same time, leading to better process performances compared with the reference feed-harvest cell cultures carried out by using off-line nutrient measurements.     

Multirate state and parameter estimation in an antibiotic fermentation with delayed measurements

This article discusses issues related to estimation and monitoring of fermentation processes that exhibit endogenous metabolism and time-varying maintenance activity. Such culture-related activities hamper the use of traditional, software sensor-based algorithms, such as the extended kalman filter (EKF). In the approach presented here, the individual effects of the endogenous decay and the true maintenance processes have been lumped to represent a modified maintenance coefficient, m(c). Model equations that relate measurable process outputs, such as the carbon dioxide evolution rate (CER) and biomass, to the observable process parameters (such as net specific growth rate and the modified maintenance coefficient) are proposed. These model equations are used in an estimator that can formally accommodate delayed, infrequent measurements of the culture states (such as the biomass) as well as frequent, culture-related secondary measurements (such as the CER). The resulting multirate software sensor-based estimation strategy is used to monitor biomass profiles as well as profiles of critical fermentation parameters, such as the specific growth for a fed-batch fermentation of Streptomyces clavuligerus. (c) 1994 John Wiley & Sons, Inc.     

Evaluation of expected absolute error affecting the maximum specific growth rate for random relative error of cell concentration

Borzani's [(1994) World Journal of Microbiology and Biotechnology 10, 475–476] idea of evaluation of absolute error affecting the 'maximum specific growth rate' (ESGR), calculated on the basis of the first and the last time points of the entire experimental time period, is generalized to the real-life situations where the relative errors of cell concentration cannot be assumed to be constant during the experiment. Visualizing the entire experimental time period as to comprise of several successive, mutually exclusive and exhaustive time intervals, we compute specific growth rates (SGRs) for each of these time intervals. Defining maximum of these SGR values as MSGR in contrast to Borzani's ESGR our aim is to study the effect of the expected absolute error on SGRs of different intervals. This will reveal the discrepancy between the true and observed MSGRs. Assuming the relative error distribution on (0,1) to be rectangular and symmetric truncated normal with mean at 0.5 and suitable variance, the expected values of the absolute errors are evaluated and numerically tabulated using the software packages MATHEMATICA and S-PLUS. Our results thus hold for situations involving varying relative errors where Borzani's results cannot be applied. A discussion with a concrete numerical example on the misidentification of the MSGR interval due to the effect of the random relative measuremental errors reveals to an experimental biologist that ignorance of this fact may lead to his/her entire experiment being futile.     

Improving bioreactor production of a recombinant glycoprotein in Escherichia coli: Effect of specific growth rate on protein glycosylation and specific productivity

In the last decades bacterial glycoengineering emerged as a new field as the result of the ability to transfer the Campylobacter jejuni N- glycosylation machinery into Escherichia coli for the production of recombinant glycoproteins that can be used as antigens for diagnosis, vaccines, and therapeutics. However, the identification of critical parameters implicated in the production process and its optimization to jump to a productive scale is still required. In this study, we developed a dual expression glycosylation vector for the production of the recombinant glycoprotein AcrA-O157, a novel antigen that allows the serodiagnosis of the infection with enterohemorrhagic E. coli O157 in humans. Volumetric productivity was studied in different culture media and found that 2xYP had 6.9-fold higher productivity than the extensively used LB. Subsequently, bioreactor batch and exponential-fed-batch cultures were designed to determine the influence of the specific growth rate (μ) on AcrA-O157 glycosylation efficiency, production kinetics, and specific productivity. At μ_max, AcrA glycosylation with O157-polysaccharide and the specific synthesis rate were maximal, constituting the optimal physiological condition for AcrA-O157 production. Our findings should be considered for the design, optimization, and scaling up of AcrA-O157 production and other recombinant glycoproteins attractive for industrial applications.     

The effect of specific growth rates on the recovery of amino acids

Three specific growth rates, 0.23, 0.45 and 0.51 h^–1, were used to cultivate Corynebacterium glutamicum in a pH-auxostat. The specific formation rates of most amino acids increased by raising the specific growth rates. The highest specific growth rate, 0.51 h^–1, favors the production of LEU; whereas the highest production yield for ALA and GLU were at = 0.23 h^–1. A correlation among specific growth rates, glucose consumption rate, and production yields of amino acids was obtained.     

补料分批发酵过程中两阶段发酵生产1,3-丙二醇

在补料分批发酵过程中提高比生长速率不仅减少乙醇、甲酸的生成,而且提高1,3-丙二醇的得率和比生产速率.发酵后期甘油的浓度在15～26 g/L时有利于提高1,3-丙二醇的生产.采取在发酵前期控制菌体较高比生长速率和发酵后期控制适宜甘油浓度相结合的策略,有效地提高了1,3-丙二醇的生产,降低副产物乳酸和乙醇的生成.     

高通量快速测定致病性及非致病性副溶血性弧菌最大比生长速率

【目的】比较15 °C、20 °C和25 °C时, 9株不同致病性与非致病性副溶血性弧菌菌株在TSB (3% NaCl, pH 8.0)中的最大比生长速率之间的差异。【方法】应用Bioscreen C全自动微生物生长曲线分析仪测定副溶血性弧菌的最大比生长速率。【结果】15 °C、 20 °C和25 °C时, 9株副溶血性弧菌菌株间最大比生长速率的变异系数分别为20.72%、17.5%和15.98%。不同副溶血性弧菌最大比生长速率之间的差异随着温度的降低而增加。【结论】在进行定量微生物风险评估时, 应用仅基于一株菌建立的生长预测模型会给预测结果带来较大的不确定性。需建立可描述不同副溶血性弧菌菌株的最大比生长速率的随机模型来为定量微生物风险评估提供更准确有效的预测模型。     

Performances of aseptic sampling devices for on-line monitoring of fermentation processes

Two liquid sampling systems, which are set in the bioreactor and can be sterilized in place, are described. They are composed primarily of an inorganic membrane filter which is either stationary or is set in a rotating motion. These systems have been tested during three types of fermentation processes (ethanol, lactic acid, and polysaccharide productions). The rotating system gave better filtration performances than the stationary sampler which can be used only in alcoholic fermentation. The rotating sampler was coupled with a high-pressure liquid chromatograph for the on-line quantitation of the major compounds present in the filtrate. The results are in good agreement with those obtained from off-line analysis on samples taken manually. (c) 1992 John Wiley & Sons, Inc.