Selected dyes for residence time distribution evaluation in bioreactors

Summary A selection of dyes for tracer studies in bioreactors, specially for wastewater treatment, is presented. Substances that showed no adsorption on air or biomass, stability in time, good solubility and no color change between pH 6.5 to 8.5, were: bromocresol green, bromophenol blue, dextran blue, eosin Y and mordant violet. Consequently they seem to be adequate for common biochemical engineering processes. In addition, dyes that showed some limitations, but may be employed in special cases, were: bromophenol red and phenol red (color change between pH 5.0 to 6.8 and 6.8 to 8.4 respectively) and methylene violet Bernsthen (low spectrophotometric response).     

Wave characterization for mammalian cell culture: residence time distribution

The high dose requirements of biopharmaceutical products led to the development of mammalian cell culture technologies that increase biomanufacturing capacity. The disposable Wave bioreactor is one of the most promising technologies, providing ease of operation and no cross-contamination, and using an innovative undulation movement that ensures good mixing and oxygen transfer without cell damage. However, its recentness demands further characterization. This study evaluated the residence time distribution (RTD) in Wave, allowing the characterization of mixing and flow and the comparison with ideal models and a Stirred tank reactor (STR) used for mammalian cell culture. RTD was determined using methylene blue with pulse input methodology, at three flow rates common in mammalian cell culture (3.3×10(-5)m(3)/h, 7.9×10(-5)m(3)/h, and 1.25×10(-4)m(3)/h) and one typical of microbial culture (5×10(-3)m(3)/h). Samples were taken periodically and the absorbance read at 660nm. It was observed that Wave behavior diverted from ideal models, but was similar to STR. Therefore, the deviations are not related to the particular Wave rocking mechanism, but could be associated with the inadequacy of these reactors to operate in continuous mode or to a possible inability of the theoretical models to properly describe the behavior of reactors designed for mammalian cell culture. Thus, the development of new theoretical models could better characterize the performance of these reactors.     

An approach to the residence time distribution for stochastic multi-compartment models

Stochastic compartmental models are widely used in modeling processes such as drug kinetics in biological systems. This paper considers the distribution of the residence times for stochastic multi-compartment models, especially systems with non-exponential lifetime distributions. The paper first derives the moment generating function of the bivariate residence time distribution for the two-compartment model with general lifetimes and approximates the density of the residence time using the saddlepoint approximation. Then, it extends the distributional approach to the residence time for multi-compartment semi-Markov models combining the cofactor rule for a single destination and the analytic approach to the two-compartment model. This approach provides a complete specification of the residence time distribution based on the moment generating function and thus facilitates an easier calculation of high-order moments than the approach using the coefficient matrix. Applications to drug kinetics demonstrate the simplicity and usefulness of this approach.     

Liquid residence time distributions in immobilized cell bioreactors

Previous work has demonstrated that high ethanol productivities can be achieved using yeast or bacterial cells adsorbed onto the surface of ion exchange resin in vertical packed bed bioreactors. The present work quantitatively characterizes the overall degree of backmixing in such reactors at two scales of operation: 2.0 and 8.0 L. Stimulus-response experiments, using two solvents (2,3-butanediol and 2-ethoxyethanol) as tracers, were performed to measure the liquid phase residence time distribution (RTD) during continuous ethanol fermentations using the yeast Saccharomyces cerevisiae and the bacterium Zymomonas mobilis at the 2-L scale, and with S. cerevisiae at the 8-L scale. In order to separately determine the effects of liquid flow rate and gas evolution on the degree of mixing, stimulus-response experiments were also performed in the systems without microbial cells present. The evolution of CO(2) was found to dramatically increase the extent of mixing; however, the tanks-in-series model for non-ideal flow represented the systems adequately. The packed beds were equivalent to over 70 tanks-in-series during abiotic operation while during fermentations, with similar liquid flow rates, they ranged in equivalence from 35 to 15 tanks-in-series. This increased knowledge of the overall degree of mixing in packed bed, immobilized cell bioreactors will allow for more accurate kinetic modelling and efficient scale up of the process.     

Performance linked to residence time distribution by a novel wool-based bioreactor for tertiary sewage treatment

Laboratory-scale experiments were carried out using up-flow 7 L Submerged Aerated Filter reactors packed with wool fibre or commercial plastic pall rings, Kaldnes, (70% by volume) support media for the tertiary treatment of sewage. The performance of the wool bioreactor was more consistent than that with Kaldnes medium, for both TOC removal (93%) and SS removal (90%). Both plastic and wool-packed bioreactors achieved complete nitrification at the load of about 0.4 kgCOD/m³/day. The sludge yield of the wool bioreactor was almost half that of the bioreactor with Kaldnes suggesting that wool could retain residual organics and particulates. The wool however was degraded and it was concluded that wool would have to be considered as additional sacrificial adsorption capacity rather than an alternative medium. The performance was linked to the residence time distribution studies and these changes in the wool structure. Biomass growth increased the retention of the tracer in the wool reactor by, it was suggested, exposing a greater surface area. Results from the plastic media on the other hand showed increased mixing possibly by increasing the mobility of the plastic. Aeration increased the mixing in both reactors, and patterns were in all cases predominantly well-mixed.     

Effects of residence time on displays during territory establishment in a lizard

We know little about how signals are used during territory establishment, particularly when potential competitors are separated by distances that are typical of those between neighbours. I studied the effects of residence time on the display behaviour of male Anolis sagrei lizards in long- and short-distance contexts. In the long-distance context, the habitat patches of two male lizards were 5 m apart, separating the males by a distance typical of that in territorial neighbourhoods. For the short-distance context, I placed two males in one habitat patch. In both contexts, either 1-day residents were paired with new arrivals, or both individuals were new arrivals. In the long-distance contexts only, I also created situations in which both individuals were 1-day residents. Residence time affected the relative frequencies of headbob displays ('bobbing displays' and 'nodding displays'). However, the direction of the effect depended on opponent proximity. In long-distance contexts, 1-day residents performed fewer bobbing displays relative to nodding displays than did new arrivals; in short-distance contexts 1-day residents performed more bobbing displays relative to nodding displays than did new arrivals. The results suggest that signalling during territory establishment is governed by a qualitatively different set of rules when potential competitors are at short versus long distances. Copyright 2000 The Association for the Study of Animal Behaviour.     

The influence of food concentration and feeding rate on the gut residence time of Daphnia

The gut residence time of Daphnia pulicaria feeding on threedifferent concentrations of Cryptomonas erosa was measured byobserving the passage of small plastic beads through the intestine.Passage times ranged from 4 to 106 min (mean, 27 min), theydecreased with increasing food concentration, and were negativelycorrelated with rates of mandible movement.     

Spatial context influences patch residence time in foraging hierarchies

Understanding responses of organisms to spatial heterogeneity in resources has emerged as a fundamentally important challenge in contemporary ecology. We examined responses of foraging herbivores to multi-scale heterogeneity in plants. We asked the question, “Is the behavior observed at coarse scales in a patch hierarchy the collective outcome of fine scale behaviors or, alternatively, does the spatial context at coarse scales entrain fine scale behavior?” To address this question we created a nested, two-level patch hierarchy. We examined the effects of the spatial context surrounding a patch on the amount of time herbivores resided in the patch. We developed a set of competing models predicting residence time as a function of the mass of plants contained in a patch and the distance between patches and examined the strength of evidence in our observations for these models. Models that included patch mass and inter-patch distance as independent variables successfully predicted observed residence times (bears: r ²=0.67–0.76 and mule deer: r ²=0.33–0.55). Residence times of grizzly bears (Ursus arctos) and mule deer (Odocoileus hemionus) responded to the spatial context surrounding a patch. Evidence ratios of Akaike weights demonstrated that models containing effects of higher levels in the hierarchy on residence time at lower levels received up to 34 times more support in the data than models that failed to consider the higher level context for grizzly bears and up to 48 times more support for mule deer. We conclude that foraging by large herbivores is influenced by more than one level of heterogeneity in patch hierarchies and that simple empirical models offer a viable alternative to optimal foraging models for the prediction of patch residence times.     

The dependence of simple reaction time on temporal patterns of stimuli

Simple reaction time has been measured using various distributions of interstimulus intervals (ISIs), which differed both in the shape of their envelope and in their degree of discretization. For each of 7 such conditions, and for three mean ISIs (2.0, 3.3, and 5.8 s) 600 responses of two subjects have been accumulated.Reaction times depend significantly on the shape of ISI-distributions but also on their degree of discretization. Within an experimental run they depend on single ISIs back to the third before reaction, and on sequences of ISIs. The latter effects are again influenced by the discretization of ISIs. Finally it was found that some learning of the distribution pattern (not the mere mean value) of ISIs takes place.Our results shed some light on existing hypotheses of RT. Some inconsistencies of earlier experimental results can probably be explained by insufficient consideration of the discretization and the learning effects.     

Design methodology accounting for the effects of porous medium heterogeneity on hydraulic residence time and biodegradation in horizontal subsurface flow constructed wetlands

Horizontal flow constructed wetlands are engineered systems capable of eliminating a wide range of pollutants from the aquatic environment. Nevertheless, poor hydrodynamic behavior is commonly found resulting in preferential pathways and variations in both (i) the hydraulic residence time distribution (HRTD) and, consequently, (ii) the wetland's treatment efficiency. The aim of this work was to outline a methodology for wetland design that accounts for the effect of heterogeneous hydraulic properties of the porous substrate on the HRTD and treatment efficiency. Biodegradation of benzene was used to illustrate the influence of hydraulic conductivity heterogeneity on wetland efficiency. Random, spatially correlated hydraulic conductivity fields following a log-normal distribution were generated and then introduced in a subsurface flow numerical model. The results showed that the variance of the distribution and the correlation length in the longitudinal direction are key indicators of the extent of heterogeneity. A reduction of the mean hydraulic residence time was observed as the extent of heterogeneity increased, while the HRTD became broader with increased skewness. At the same time, substrate heterogeneity induced preferential flow paths within the wetland bed resulting in variations of the benzene treatment efficiency. Further to this it was observed that the distribution of biomass within the porous bed became heterogeneous, rising questions on the representativeness of sampling. It was concluded that traditional methods for wetland design based on assumptions such as a homogeneous porous medium and plug flow are not reliable. The alternative design methodology presented here is based on the incorporation of heterogeneity directly during the design phase. The same methodology can also be used to optimize existing systems, where the HRTD has been characterized with tracer experiments.     

Structure-guided residence time optimization of a dabigatran reversal agent

Novel oral anticoagulants are effective and safe alternatives to vitamin-K antagonists for anticoagulation therapy. However, anticoagulation therapy in general is associated with an elevated risk of bleeding. Idarucizumab is a reversal agent for the direct thrombin inhibitor, dabigatran etexilate (Pradaxa®) and is currently in Phase 3 studies. Here, we report data on the antibody fragment aDabi-Fab2, a putative backup molecule for idarucizumab. Although aDabi-Fab2 completely reversed effects of dabigatran in a rat model in vivo, we observed significantly reduced duration of action compared to idarucizumab. Rational protein engineering, based on the X-ray structure of aDabi-Fab2, led to the identification of mutant Y103W. The mutant had optimized shape complementarity to dabigatran while maintaining an energetically favored hydrogen bond. It displayed increased affinity for dabigatran, mainly driven by a slower off-rate. Interestingly, the increased residence time translated into longer duration of action in vivo. It was thus possible to further enhance the efficacy of aDabi-Fab2 based on rational design, giving it the potential to serve as a back-up candidate for idarucizumab.     

Impact of enzyme concentration and residence time on apparent activity recovery in jump dilution analysis

Jump dilution analysis is commonly used to evaluate the reversibility of inhibition and to quantify the residence time of the inhibitor–enzyme complex. During hit and lead characterization, one sometimes observes apparently linear progress curves after jump dilution that display activity recoveries that are intermediate between those expected for fully reversible and irreversible inhibition. Computer simulations of progress curves after jump dilution indicate that seemingly linear progress curves can result when dealing with tight-binding inhibitors if substoichiometric concentrations of inhibitor are preincubated with enzyme. In this situation, the activity recovered is comparable to that expected for instantaneously reversible inhibitors. In addition, simulations demonstrate that intermediate values of activity recovery may be observed for compounds with modestly slow dissociation rates (i.e., residence times >0 min but ?20 min) when the attending curvature of the data is not accounted for. The observation of intermediate values of recovery can, thus, serve as an indication of either modest residence time or a contaminating inactivator within an inhibitor sample, in either case prompting greater scrutiny of the test compound.     

The water residence time in the Mururoa atoll lagoon: sensitivity analysis of a three-dimensional model

 The role of oceanic tide, wind stress, hoa inflow and stratification in the long-term circulation in Mururoa lagoon is investigated using a sensitivity analysis carried out by means of a three-dimensional model. Water renewal time scales are estimated. Wind stress is shown to be the dominant forcing. The hoa inflow slightly increases the turnover time, while stratification enhances the impact of motion in vertical planes parallel to the wind stress. The modelled turnover time is approximately 100 days, and becomes much larger than one year whenever the wind stress is disregarded. Accepted: 25 October 1996     

Interpretation of the gas residence time distributions in large stirred tank reactors

The behaviour of dispersed gas in large aerated stirred tank reactors is modelled by means of a Markov-process, which distinguishes between small recirculation bubbles with stagnant gas content, large rising bubbles with active gas content and exchange of stagnant and active gas contents, the gas exchange region at the impeller. The measurements of the gas residence time distributions (RTDs) in an 1.5 m³ aerated stirred tank reactor with water and Penicillium chrysogenum cultivation medium are interpreted by this model.List of Symbols CPR CO₂ production rate - OTR oxygen transfer rate - PRS pseudo random signal - RTD residence time distribution - V gas volume - recirculation coefficient - mean gas residence time Indices act active gas - ex gas exchange - stagn stagnant gas - tot total gas Dedicated to the 65th birthday of Professor Fritz Wagner.The authors thank Hoechst AG for the strain and the medium components, the GBF for the support of the experiments and H.M. Rüffer thanks the Verband der Chemischen Industrie for a Fond-der-Chemie scholarship.     

Pressure flow patterns in a cylinder with reabsorbing walls

The problem of fluid motion in renal tubules, in contrast to ordinary flow through cylinders with impermeable walls, is complicated by the existence of radial velocities generated by reabsorption processes. As a first approach to this problem, the Navier Stokes equations for axially symmetric, slow flow in an infinite cylinder whose walls reabsorb fluid are integrated. If the rate of reabsorption is constant, the solutions resemble the conventional Poiseuille flow, i.e., the longitudinal velocity profile is parabolic. In addition the drop in mean pressure is proportional to the mean axial flow, the length of tube between reference points, and inversely proportional to the fourth power of the radius. If the rate of reabsorption is a linear function of the distance from the origin, the presence of an additive term alters these relations. If, for example, the gradient in reabsorption is positive, the axial velocity profile tends to flatten and when the gradient is sufficiently large, the maximum velocity moves from the center of the stream toward the periphery, leaving a relative minimum at the center. In passing from the center of the tube to the walls, the radial velocity passes through a miximum, regardless of the reabsorption properties of the wall.     

Patterns of aeration in a solid substrate fermentor through the study of the residence time distribution (RTD) of a volatile tracer

The injection of a volatile tracer in the gas flow allowed to describe the residence time distribution (RTD) in a solid substrate reactor. The chromatographic analysis of Dirac impulses of acetone led to identify the fermentor as a first-order rate system. The evolution of the time constant (lambda) of the system versus the gas flow rate gave a flow rate value that permitted a homogeneous aeration of the fermentor.