Comparison of dynamic oxygen electrode methods for the measurement of KLa

The dynamic oxygen electrode method for measuring K_L a requires the use of a dynamic process model. Six models from the literature are described and compared with respect to their accuracy and ease of use. It is shown theoretically that for sufficient accuracy K_L a should be less than the inverse electrode response time. Experimental measurements demonstrate their application to viscous and nonviscous systems. The liquid diffusion film is shown to cause an important measurement lag that can be accounted for by a first-order time delay. Investigation on the influence of the experimental starting conditions show the importance of the gas and hold-up dynamics. A new method is proposed to simplify the K_L a calculation and to eliminate errors caused by starting conditions. This method, which accounts for gas, film, and electrode dynamical effects, requires only a simple semilog plot of the response data.     

Bubble-column design for growth of fragile insect cells

A mathematical model for the design of bubble-columns for growth of shear-sensitive insect cells is presented. The model is based on two assumptions. First, the loss of cell viability as a result of aeration is a first-order process. Second, a hypothetical volume X, in which all viable cells are killed, is associated with each air bubble during its lifetime. The model merely consists of an equation for k _d, the first-order death-rate constant, and A _min, the minimum specific surface area of the air bubbles to supply sufficient oxygen. In addition to X, the equation for k _d contains the air flow F, the air-bubble diameter d _b, the diameter D and the height H of the bubble column. This equation has been experimentally validated. Comparison of the equations for k _d and A _min shows that especially H is the key parameter to manipulate in bubble-column design in order to meet the demands set by A _min and k _dg, the first-order growth-rate constant. It is concluded that net growth of cells is enhanced as size and height of the bubble column increase.     

CO2 in large-scale and high-density CHO cell perfusion culture

Productivity in a CHO perfusion culture reactor was maximized when pCO₂ was maintained in the range of 30–76 mm Hg. Higher levels of pCO₂ (> 150 mm Hg) resulted in CHO cell growth inhibition and dramatic reduction in productivity. We measured the oxygen utilization and CO₂ production rates for CHO cells in perfusion culture at 5.55×10^-17 mol cell^-1 sec^-1 and 5.36×10^-17 mol cell^-1 sec^-1 respectively. A simple method to directly measure the mass transfer coefficients for oxygen and carbon dioxide was also developed. For a 500 L bioreactor using pure oxygen sparge at 0.002 VVM from a microporous frit sparger, the overall apparent transfer rates (k_La+k_AA) for oxygen and carbon dioxide were 0.07264 min^-1 and 0.002962 min^-1 respectively. Thus, while a very low flow rate of pure oxygen microbubbles would be adequate to meet oxygen supply requirements for up to 2.1×10⁷ cells/mL, the low CO₂ removal efficiency would limit culture density to only 2.4×10⁶ cells/mL. An additional model was developed to predict the effect of bubble size on oxygen and CO₂ transfer rates. If pure oxygen is used in both the headspace and sparge, then the sparging rate can be minimized by the use of bubbles in the size range of 2–3 mm. For bubbles in this size range, the ratio of oxygen supply to carbon dioxide removal rates is matched to the ratio of metabolic oxygen utilization and carbon dioxide generation rates. Using this strategy in the 500 L reactor, we predict that dissolved oxygen and CO₂ levels can be maintained in the range to support maximum productivity (40% DO, 76 mm Hg pCO₂) for a culture at 10⁷ cells/mL, and with a minimum sparge rate of 0.006 vessel volumes per minute.A = volumetric agitated gas-liquid interfacial area at the top of the liquid, 1/mB = cell broth bleeding rate from the vessel, L/minCER = carbon dioxide evolution rate in the bioreactor, mol/min[CO₂] = dissolved CO₂ concentration in liquid, M[CO₂]^* = CO₂ concentration in equilibrium with sparger gas, M[CO₂]^** = CO₂ concentration in equilibrium with headspace gas, MCO₂(1) = dissolved carbon dioxide molecule in water[C_T] = total carbonic species concentration in bioreactor medium, M[C_T]_F = total carbonic species concentration in feed medium, MD = bioreactor diameter, mD_I = impeller diameter, mD_b = the initial delivered bubble diameter, mF = fresh medium feeding rate, L/minH_L = liquid height in the vessel, mk_A = carbon dioxide transfer coefficient at liquid surface, m/mink _infA ^supO = oxygen transfer coefficient at liquid surface, m/minNomenclature     

Feed-forward activation in a theoretical first-order biochemical pathway which contains an anticipatory model

This paper explores the consequences of the theoretical forward activation enzymatic pathway A ₀ A ₁ A ₂ A ₃ where E ₁ convents A ₀ to A ₁, E ₂ converts A ₁ to A ₂ and E ₃ converts A ₂ to A ₃. A ₀, which is environmentally determined, also serves to activate (or modulate) the activity of E ₃ in such a way as to keep the concentration of A ₂ ([A ₂]) constant at a particular set-point value. For mathematical simplicity, first order rate kinetics are used where k ₁, k ₂ and k ₃ are the rate constants for E ₁, E ₂, and E ₃ respectively. It is shown that if k ₃ is modulated appropriately so as keep [A ₂] at the setpoint value with a changing upstream [A ₀], then the modulation of k ₃ must be anticipatory of the dynamics of the biochemical pathway. In other words, the rate of change of k ₃, will be a function of [A ₀], k ₁, k ₂, k ₃, and the set-point value of [A ₂]. If the modulation of k ₃ does not perfectly model (anticipate) the reaction pathway of which it is a part, then the actual [A ₂] will deviate from the set-point value. This type of anticipatory feed-forward activation may represent an important aspect of biological organization.     

Application of a novel method for age estimation of a baleen whale and a porpoise

Eyeballs from 121 fin whales (Balaenoptera physalus) and 83 harbor porpoises (Phocoena phocoena) were used for age estimation using the aspartic acid racemization (AAR) technique. The racemization rate (k_Asp) for fin whales was established from 15 fetuses (age 0) and 15 adult whales where age was estimated by reading growth layer groups (GLGs) in the earplugs. The (k_Asp) for harbor porpoises was derived from 15 porpoises (two calves and 13 > 1 yr old) age‐estimated by counting GLGs in the teeth and two calves classified to age based on length. The (k_Asp) values were estimated by regression of GLGs against D/L ratios. For the fin whales an (k_Asp) of 1.15 × 10^?3/yr (SE ± 0.00005) and a D/L ratio at birth [(D/L)₀] of 0.028 (SE ± 0.0012) were estimated, which is in agreement with rates for other mysticeti. For the harbor porpoises a (k_Asp) of 3.10 × 10^?3/yr (SE ± 0.0004) and a (D/L)₀ value of 0.023 (SE ± 0.0018) were estimated, which is considerably higher than found for other cetaceans. Correlation between chosen age estimates from AAR and GLG counts indicated that AAR might be an alternative method for estimating age in marine mammals.     

Absorption of oxygen in highly viscous newtonian and non-Newtonian fermentation model media in bubble column bioreactors

Summary Mean relative gas holdup, slip velocity, bubble size distribution, mean specific interfacial area, and volumetric mass transfer coefficient of oxygen were estimated in sparged columns 14 cm in diameter and 380 and/or 390 cm high with two different aerator types (porous plate and injector nozzle) in highly viscous Newtonian (glycerol solutions) and non-Newtonian (CMC solutions) fluids.For the Newtonian liquids the above properties were estimated as function of the viscosity of the liquid. For the non-Newtonian liquids they were determined as function of the fluid consistency index and flow behavior index. Significant differences between Newtonian and non-Newtonian systems appear. In Newtonian medium k_L a drops with increasing viscosity and already approaches a constant value at =40 cP. In pseudoplastic medium k_L a varies with the fluid consistency and flow behavior indexes in the entire investigated range.In both of these systems the primary bubble population changes into two or three populations along the reactor: the medium bubbles gradually disappear and small and large bubbles are formed.     

Age estimates based on aspartic acid racemization for bowhead whales (Balaena mysticetus) harvested in 1998–2000 and the relationship between racemization rate and body temperature

Fifty‐two eyes were collected and analyzed to estimate ages of 42 bowhead whales using the aspartic acid racemization aging technique. Between‐eye and within‐eye variance components for the ratio of the D and L optical isomers (D/L ratio) were estimated via analysis of variance using multiple measurements from nine whales with both eyes sampled and analyzed. For whales with more than one (D/L)_act value, an inverse variance weighted average of the values was used as (D/L)_act for the whale. Racemization rate (k_Asp) and D/L ratio at birth (D/L)₀ were estimated using (D/L)_act from 27 bowhead whales with age estimates based on baleen or ovarian corpora data and two term fetuses. The estimates were k_Asp = 0.977 × 10^?3/yr and (D/L)₀ = 0.0250. The nonlinear least squares analysis that produced these estimates also estimated female age at sexual maturity as ASM = 25.86 yr. SE(age) was estimated via a bootstrap that took into account the SE of (D/L)_act and the variances and covariance of k_Asp and (D/L)₀. One male exceeded 100 yr of age; the oldest female was 88. A strong linear relationship between k_Asp and body temperature was estimated by combining bowhead data with independent data from studies of humans and fin whales. Using this relationship, we estimated k_Asp and ASM for North Atlantic minke whales.     

A kLa identification technique for a dynamic model of the coupled system: Air-lift fermenter — oxygen probes

The time delay of oxygen probe response to the signal from a fermenter makes identification of the volumetric oxygen transfer coefficient k_La by the dynamic method more complicated. A coupled model involving the transient-state oxygen balance of the fermenter together with the dynamic model of the oxygen probe must be then formulated, solved and identified. In this paper two simple models of air-lift loop fermenters have been proposed and a coupled mathematical model of the fermenter – oxygen probe system has been developed. The identification procedure was used to estimate k_La values in the fermenter with internal circulation flow on the basis of experimental measurements. A comparison of evaluated and experimental indications of the probes placed at various heights of the column proves that the model presented gives a possibility of the first-step approximation of k_La in loop fermenters.     

On-line estimation of kLa by an analog computer

A new method was developed for estimating the volumetric oxygen transfer coefficient, k_La, in a fermentor. Various methods were investigated for the on-line estimation of k_La with an analog computer employing a steepest-descent calculation technique. The method by which k_La is estimated (by minimizing the error residue of the model) was found to be very applicable. A method for the simultaneous estimation of the volumetric oxygen transfer coefficient and respiration rate in biological systems is also presented.     

Mixing and oxygen transfer characteristics of a microplate bioreactor with surface-attached microposts

Bioprocess optimization for cell-based therapies is a resource heavy activity. To reduce the associated cost and time, process development may be carried out in small volume systems, with the caveat that such systems be predictive for process scale-up. The transport of oxygen from the gas phase into the culture medium, characterized using the volumetric mass transfer coefficient, k_La, has been identified as a critical parameter for predictive process scale-up. Here, we describe the development of a 96-well microplate with integrated Redbud Posts to provide mixing and enhanced k_La. Mixing in the microplate is characterized by observation of dyes and analyzed using the relative mixing index (RMI). The k_La is measured via dynamic gassing out method. Actuating Redbud Posts are shown to increase rate of planar homogeneity (2 min) verse diffusion alone (120 min) and increase oxygenation, with increasing stirrer speed (3500-9000 rpm) and decreasing fill volume (150-350 μL) leading to an increase in k_La (4-88 h⁻¹). Significant increase in Chinese Hamster Ovary growth in Redbud Labs vessel (580,000 cells mL^-1) versus the control (420,000 cells mL^-1); t(12.814) = 8.3678, p ≤ .001), and CD4⁺ Naïve cell growth in the microbioreactor indicates the potential for this technology in early stage bioprocess development and optimization.     

Vergleich von Messungen des kLa-Wertes nach der stationären und der dynamischen Methode bei der Fermentation von L-Lysin und Turimycin

The calculation and scale-up of fermentation processes need k_La as one of the most important engineering data. There are two methods to determine k_La depending on power input, aeration rate and the properties of the fermentation broth: static with a balance between air supply and exit, dynamic gassing out with following the changes of dissolved oxygen concentration during periods of air off and a following air on. Within early intervals of fermentation time the data from both methods agree well, while for later time intervals the dynamic method always gives much lower values for k_La than static. The only explanations for this phenomenon are quick changes in the oxygen metabolism or an enzymatic storage of oxygen. For both gassing out and saturation period it is possible to calculate the same absolute amounts of this additional oxygen.     

Dynamic measurement of the volumetric oxygen transfer coefficient in fermentation systems

A rapid and internally consistent technique has been developed to measure the volumetric oxygen transfer coefficient, k_La, in fermentation systems. The method consists of tracing the dissolved O₂ concentration of the fermentation broth during a short interruption of the aeration. The O₂ concentration trace thus obtained can be analyzed to determine the values of k_La. Additional experiments on prolonged O₂ starvation, carried out to find the limitation of the technique, suggest that O₂ uptake rate will vary if a prolonged (2–10 min.) O₂ starvation occurs.     

Studies on Oxygen Transfer in Submerged Fermentations

Using gas analysis method, comparative studies were made between sulfite solutions and the biological systems in relation to their behavior to oxygen. It was found that sulfite oxidation method did not always give a maximum rate of oxygen transfer that could take place into the growing cell suspensions. Sulfite solution was different from the biological systems in some respects especially in K_La values, and these differences might be due to the variation of the sizes of air bubbles. For a measure of a eration effectiveness, oxygen transfer rate in biological systems seemed to be preferable.     

Determination of oxygen-transfer coefficients in viscous streptomycete fermentations

Two types of steam-sterilizable dissolved-oxygen probs were evaluated for use in fermentations. A galvanic-cell probe was selected over a polarographic probe because of its demonstrated ruggedness and dependability. Various methods for determining k_La in fermentors were compared and the oxygen balance method selected for use in viscous streptomycete fermentations. Rheological data are presented to identify a range of mash viscosity where many k_La measurement methods are not applicable. Oxygen transfer data are presented for streptomycete fermentations pilot fermentors.     

Two-compartment method for determination of the oxygen transfer rate with electrochemical sensors based on sulfite oxidation

The dissolved oxygen concentration is a crucial parameter in aerobic bioprocesses due to the low solubility of oxygen in water. The present study describes a new method for determining the oxygen transfer rate (OTR) in shaken-culture systems based on the sodium sulfite method in combination with an electrochemical oxygen sensor. The method replaces the laborious titration of the remaining sulfite by an on-line detection of the end point of the reaction. This method is a two-step procedure that can be applied in arbitrary flasks that do not allow the insertion of electrodes. The method does not therefore depend on the type of vessel in which the OTR is detected. The concept is demonstrated by determination of the OTR for standard baffled 1-L shake flasks and for opaque Ultra Yield™ flasks. Under typical shaking conditions, k_La values in the standard baffled flasks reached values up to 220 h^-1, whereas the k_La values of the Ultra Yield flasks were significantly higher (up to 422 h^-1).     

Enhancement factor for oxygen absorption into fermentation broth

Values of the enhancement factor for oxygen absorption into fermentation broth, i.e., the ratio of the liquid phase mass transfer coefficients for oxygen absorption for both cases with and without respiration of microorganisms were predicted theoretically on the assumption of various cell concentration distributions. Calculations indicate that in the usual case the enhancement factor is only slightly or negligibly larger than unity, even when accumulation of microorganisms at or near the gas-liquid interface is assumed. Results of experiments with sparged-stirred fermentors on oxygen absorption into fermentation broths containing resting and growing cells of Candida tropicalis confirmed the theoretical prediction. Except for extreme cases, the effect of respiration of microorganisms on k_La, values can practically be ignored.     

Dynamic measurement of the volumetric mass transfer coefficient in agitated vessels: Effect of the start-up period on the response of an oxygen electrode

The response of a polarographic oxygen electrode to a step change and to an exponential change in bulk oxygen concentration was studied theoretically and experimentally for the case where there is a significant liquid film resistance at the outerside of the membrane-covered electrode. The probe response has been described considering the start-up period of the concentration changes (the period of time that will elapse before the new concentration level is established and/or before the volumetric mass transfer coefficient k_La regains its steady-state value after the gas supply is opened to the fermentor). A linear change of the pertinent characteristics is assumed during this start-up period. It is shown that a substantial error could be introduced by neglecting the start-up period for cases frequently occurring in practice. In addition, the dependences of the probe response on the direct contact of bubbles with an electrode and on the fluid flow field around it were discussed.     

Determination of specific oxygen uptake rate of Photorhabdus luminescens during submerged culture in lab scale bioreactor

Photorhabdus luminescens, a bacterial symbiont of entomoparasitic nematodes, was cultured in a 10 L bioreactor. Cellular density and bioluminescence were recorded and volumetric oxygen transfer coefficient (k_La) and specific oxygen transfer rates were determined during the batch process. Exponential phase of the bacterium lasted for 20 h, showing a maximum specific growth rate of 0.339 h^?1 in a defined medium. Bioluminescence peaked within 21h, and was maintained until the end of the batch process (48 h). The specific oxygen uptake rate (SOUR) was high during both lag and early exponential phase, and eventually reached a stable value of 0.33 mmol g^?1 h^?1 during stationary phase. Maintenance of 200 rpm agitation and 1.4 volume of air per volume of medium per minute (vvm) aeration, gave rise to a k_La value of 39.5 h^?1. This k_La value was sufficient to meet the oxygen demand of 14.4 g L^?1 (DCW) biomass. This research is particularly relevant since there are no reports available on SOURs of symbiotic bacteria or their nematode partners. The insight gained through this study will be useful during the development of a submerged monoxenic culture of Heterorhabditis bacteriophora and its symbiotic bacterium P. luminescens in bioreactors.     

Use of glucose oxidase system in measuring aeration capacity of fermentors. Comparison of the dynamic and steady-state methods of kla measurement

A steady-state method for k_la determination has been presented using the Michaelis–Menten two-substrate kinetic equation for oxidation of glucose in the presence of the enzymes glucose oxidase and excess catalase. The conditions have been specified where spontaneous hydrolysis of lactone is sufficiently rapid, thus eliminating inhibitory action of lactone on the oxidation. In glucose oxidase-free batches, the k_la values were determined using various modification of the dynamic method. The dynamic methods in which gas interchange was effected without interrupting aeration and agitation of the batch yielded erroneously lower k_la values as compared to the results of steady-state methods if the measured k_la value was higher than 0.03 s^?1. The values yielded by the dynamic method in which the gas interchange was effected at the same time with turning on aeration and agitation of the batch agreed with values resulting from the steady-state method provided that the measured k_la values were lower than 0.08^?1 and the simultaneous interfacial transport of nitrogen and oxygen had been taken into account in the evaluation. At k_la values higher than 0.08 ^?1, this modification of the dynamic method also yielded lower k_la values as compared with the outcome of the steady-state method. The experiments performed do not, however, allow one to decide unambiguously on the whether these lower k_la values are due to failure of the adopted model to describe adequately the dynamic behavior of the system or whether they are true values differing from those yielded by the steady-state method on account of different physical properties of compared batches.     

Enhancement of oxygen absorption into sodium sulfite solutions

Oxygen absorption enhancement in a sodium sulfite solution was studied in the absence and presence of copper catalyst both for absorption across the liquid surface in a stirred cell and for absorption from individual bubbles rising through a turbulent liquid. The enhancement factor was determined from the ratio of oxygen and argon mass transfer coefficients, measured under identical experimental conditions in the same batch of liquid. It has been found that the oxygen absorption is not chemically enhanced, as long as the mass transfer coefficient, k_L⁰, is high enough, i.e., higher than the value 1.4 × 10^?4 m sec^?1 for the sulfite solution we used. An analysis of our data as well as literature data indicates that the sulfite system is poorly suited for studies of the volumetric mass transfer coefficient of physical absorption (k_L⁰a) in fermentors, inasmuch as oxygen absorption can be chemically enhanced while the degree of enhancement depends on the operating conditions of batch aeration, as well as on the concentration of trace impurities with catalytic effects upon the sulfite solution used.