Gas absorption in pulmonary airways at low Peclet number

A mathematical model is presented that investigates the mass transport of a diffusible and soluble gas contaminant through a liquid-lined tube when the Peclet number is small. The transport is determined by four dimensionless parameters: lambda, the tube aspect ratio; d, the relative difference in end concentrations; gamma, the radial transport coefficient; and Pe, the Peclet number. The problem is formulated for arbitrary gamma, but in the case of ozone and nitrous oxides the value of gamma is small. An asymptotic analysis for Pe much less than 1 and gamma much less than 1 is presented which yields the concentration field and transport characteristics we seek. It also provides a low Peclet number analysis for the conjugate problem of mass and heat transfer that is not currently available in the literature. The application to transport in the small airways of the lung is discussed, particularly the radial absorption differences in inspiratory and expiratory flow. Depending on the relative sizes of gamma and Pe, fractional uptake decreases with increasing Pe during inspiration but can increase during expiration.     

Mass transfer correlations for rotating drum bioreactors

Evaporative cooling is extremely important for large-scale operation of rotating drum bioreactors (RDBs). Outlet water vapour concentrations were measured for a RDB containing wet wheat bran with the aim of determining the mass transfer coefficient for evaporation from the bran bed to the headspace. Mass transfer was expressed as the mass transfer coefficient times the area for transfer per unit volume of void space in the drum. Values of ka' were determined under combinations of aeration superficial velocities ranging from 0.006 to 0.017 ms(-1) and rotation rates ranging from 0 to 9 rpm. Mass transfer coefficients were evaluated using a variety of residence time distributions (RTDs) for flow in the gas phase including plug flow and well-mixed and a Central Jet RTD based on RTD studies. If plug flow is assumed, the degree of holdup at low effective Peclet (Pe(eff)) numbers gives an apparent under-estimate of ka' compared with empirical correlations. Values of ka' calculated using the Central Jet RTD agree well with values of ka' from literature correlations. There was a linear relationship between ka' and effective Peclet number: ka' = 2.32 x 10(-3)Pe(eff).     

Neural network designs for poly- β-hydroxybutyrate production optimization under simulated industrial conditions

Improvement of the fermentation efficiency of poly--hydroxybutyrate (PHB) may make it competitive with chemically synthesized petroleum-based polymers. One step toward this is optimization of fluid dispersion and the feed rates to a fed-batch bioreactor. In a recent study using a fermentation model, dispersion corresponding to a Peclet number of 20 was shown to maximize the productivity of PHB. Here further improvement has been investigated using neural optimization. A comparison of seven neural topologies has shown that while feed-forward and radial basis neural networks are computationally efficient, recurrent networks generate higher concentrations of PHB. All networks enhanced the productivity by 16–93% over model-based optimization.     

An analysis of pollutant gas transport and absorption in pulmonary airways

A mathematical model of ozone absorption, or for any soluble gas that has similar transport properties, is developed for a branching network of liquid-lined cylinders. In particular, we investigate specific flow regimes for finite length tubes where boundary layer phenomena and entrance effects exist in high Reynolds and Peclet (Pe) number airways. The smaller airways which have lower Reynolds and Peclet number flows are modelled by incorporating the detailed analysis found in [10] and modifying it for airways which have alveolated surfaces. We also consider a reacting gas and treat specific regimes where the reaction front is located at the air-liquid interface, within the liquid or at the liquid-tissue interface. Asymptotic methods are used in regions of the tracheobronchial tree where Pe much less than 1 and Pe much greater than 1. In addition, the fact that the radial transport parameter gamma much less than 1 for this toxin, and others such as nitrous oxides, is employed to simplify the analysis. The ozone concentrations, airway absorption and tissue dose are examined as a function of airway generation for several values of the governing parameters. The general result is a maximal dosing in airway generations 17 to 18 that is much larger (up to an order of magnitude) than the predictions of previous theories.     

Axial dispersion in respiratory bronchioles and alveolar ducts

The mixing of gases in the pulmonary acinus was characterized by analyzing axial gas dispersion during steady flow in models of respiratory bronchioles and alveolar ducts. An analysis (method of moments) developed for addressing dispersion in porous media was used to derive an integral expression for the axial dispersion coefficient (D*). Evaluation of D* required solving the Navier-Stokes equations for the flow field and a convection-diffusion type equation arising from the analysis. D* was strongly dependent on alveolar volume per central duct volume, the aperture size through which the alveoli communicate with the central duct, and the Péclet number (Pe). At smaller Pe (flow rate) D* was substantially smaller than the molecular diffusion coefficient, whereas at larger Pe (flow rate) D* was much greater than the Taylor-Aris result for flow-enhanced dispersion in straight tubes. Also, flow-enhanced dispersion became appreciable at smaller Pe than indicated by the Taylor-Aris result. These behaviors transcend both the lower and upper limits established previously for gas mixing in the pulmonary acinus.     

Neural and Hybrid Optimizations of the Fed-Batch Synthesis of Poly-β-Hydroxybutyrate by Ralstonia eutropha in a Nonideal Bioreactor

Poly-β-hydroxybutyrate (PHB) is synthesized by some microorganisms under stressful conditions. Despite its properties being comparable to those of synthetic polymers, and its biocompatibility and biodegradability, low productivities have dampened commercial interest in microbial PHB production. To increase production efficiency, a fed-batch fermentation with Ralstonia eutropha was optimized recently through a neural-cum-dispersion model (D-model) incorporating incomplete dispersion and noise in the feed streams. The approach described in the work has been improved in two ways: first by a model comprising neural networks only (N-model) and then by a hybrid neural model (H-model) with a mathematical component. At optimum dispersion, PHB production through the N-model optimization was 35% more than by the D-model, and this was enhanced by a further 58% using hybrid optimization. Recognizing that the D-model itself more than doubled the PHB production compared to a noise-free fully dispersed bioreactor, the present results establish hybrid neural optimization as a viable method for PHB production improvement under realistic conditions.     

Optimization of microbial poly(3-hydroxybutyrate) recover using dispersions of sodium hypochlorite solution and chloroform

Optimization was carried out for the recovery of microbiol poly(3-hydroxybutyrate) (PHB) from Alcaligenes eutrophus. This process involved the use of a dispersion made of sodium hypochlorite solution and chloroform. The dispersion enabled us to take advantage of both differential digestion by hypochlorite and solvent extraction by chloroform. The PHB recovery (%) from cell powder was maximized using a 30% hypochlorite concentration, a 90-min treatment time, and a 1:1 (v/v) chloroform-to-aqueous-phase ratio. Under these optimal conditions, the recovery was about 91% and the purity of recovered PHB was higher than 97%. The number average molecular weight, M(n) of recovered PHB was about 300,000 and the weight average molecular weight M(w) was about 1,020,000, compared to the original M(n) of 530,000 and M(w) of 1,272,000. The moderate decrease in both M(n) and M(w) might be ascribed to the shielding effect of chloroform. In addition, the relatively small decrease in M(w) probably resulted from the loss of short PHB chains which might be water soluble. The crystallinity of recovered PHB was in the range of 60 to 65%although a slightly higher crystallinity was observed when the dispersion was used. (c) 1994 John Wiley & Sons, Inc.     

Modelling of the chromatographic separation of xylose-mannose in ion-exchange resin columns

A mathematical model was proposed for the chromatographic separation of xylose and mannose on an ion-exchange resin in the Pb form: dispersion in the mobile phase, external mass transfer around the particles and internal diffusion were taken into account. Small-scale experiments provided an evaluation of the different parameters. Dispersion in the mobile phase was found to be the predominant phenomenon. The Peclet numbers were calculated by identification in the Laplace domain of the elution profiles. Influence of temperature and initial concentration of the sample were studied.     

Further considerations in a theoretical description of gas transport in lung airways

A discrete one-dimensional model of convection-diffusion in branching alveolar ducts is described and it is shown that, for a suitable choice of effective axial dispersion, the solution closely approximates that for an axially symmetric representation, at least for Peclet numbers Pe<1. Following earlier work a composite model of a uniform lung is formed by matching such a respiratory pathway (now having the more convenient one-dimensional form) onto a trumpet representation of the conducting airways. Enhanced mixing due to heart action, and isotropic volume changes of trumpet (in addition to the pathway) during breathing are additional factors included. Calculations are made of O₂ concentrations during steady-state breathing and of the concentration of inert gas during single breath wash-out of a gas mixture containing it. Predicted alveolar levels in each case agree extremely well with published data, although no alveolar slope is obtained for the inert gas.     

Thrombin Flux and Wall Shear Rate Regulate Fibrin Fiber Deposition State during Polymerization under Flow

Thrombin is released as a soluble enzyme from the surface of platelets and tissue-factor-bearing cells to trigger fibrin polymerization during thrombosis under flow conditions. Although isotropic fibrin polymerization under static conditions involves protofibril extension and lateral aggregation leading to a gel, factors regulating fiber growth are poorly quantified under hemodynamic flow due to the difficulty of setting thrombin fluxes. A membrane microfluidic device allowed combined control of both thrombin wall flux (10⁻¹³ to 10⁻¹¹ nmol/μm² s) and the wall shear rate (10-100 s⁻¹) of a flowing fibrinogen solution. At a thrombin flux of 10⁻¹² nmol/μm² s, both fibrin deposition and fiber thickness decreased as the wall shear rate increased from 10 to 100 s⁻¹. Direct measurement and transport-reaction simulations at 12 different thrombin flux-wall shear rate conditions demonstrated that two dimensionless numbers, the Peclet number (Pe) and the Damkohler number (Da), defined a state diagram to predict fibrin morphology. For Da < 10, we only observed thin films at all Pe. For 10 < Da < 900, we observed either mat fibers or gels, depending on the Pe. For Da > 900 and Pe < 100, we observed three-dimensional gels. These results indicate that increases in wall shear rate quench first lateral aggregation and then protofibril extension.     

Peroxisomal polyhydroxyalkanoate biosynthesis is a promising strategy for bioplastic production in high biomass crops

Polyhydroxyalkanoates (PHAs) are bacterial carbon storage polymers with diverse plastic‐like properties. PHA biosynthesis in transgenic plants is being developed as a way to reduce the cost and increase the sustainability of industrial PHA production. The homopolymer polyhydroxybutyrate (PHB) is the simplest form of these biodegradable polyesters. Plant peroxisomes contain the substrate molecules and necessary reducing power for PHB biosynthesis, but peroxisomal PHB production has not been explored in whole soil‐grown transgenic plants to date. We generated transgenic sugarcane (Saccharum sp.) with the three‐enzyme Ralstonia eutropha PHA biosynthetic pathway targeted to peroxisomes. We also introduced the pathway into Arabidopsis thaliana, as a model system for studying and manipulating peroxisomal PHB production. PHB, at levels up to 1.6%–1.8% dry weight, accumulated in sugarcane leaves and A. thaliana seedlings, respectively. In sugarcane, PHB accumulated throughout most leaf cell types in both peroxisomes and vacuoles. A small percentage of total polymer was also identified as the copolymer poly (3‐hydroxybutyrate‐co‐3‐hydroxyvalerate) in both plant species. No obvious deleterious effect was observed on plant growth because of peroxisomal PHA biosynthesis at these levels. This study highlights how using peroxisomal metabolism for PHA biosynthesis could significantly contribute to reaching commercial production levels of PHAs in crop plants.     

Metabolic pathway analysis of a recombinant yeast for rational strain development

Elementary mode analysis has been used to study a metabolic pathway model of a recombinant Saccharomyces cerevisiae system that was genetically engineered to produce the bacterial storage compound poly-beta-hydroxybutyrate (PHB). The model includes biochemical reactions from the intermediary metabolism and takes into account cellular compartmentalization as well as the reversibility/irreversibility of the reactions. The reaction network connects the production and/or consumption of eight external metabolites including glucose, acetate, glycerol, ethanol, PHB, CO(2), succinate, and adenosine triphosphate (ATP). Elementary mode analysis of the wild-type S. cerevisiae system reveals 241 unique reaction combinations that balance the eight external metabolites. When the recombinant PHB pathway is included, and when the reaction model is altered to simulate the experimental conditions when PHB accumulates, the analysis reveals 20 unique elementary modes. Of these 20 modes, 7 produce PHB with the optimal mode having a theoretical PHB carbon yield of 0.67. Elementary mode analysis was also used to analyze the possible effects of biochemical network modifications and altered culturing conditions. When the natively absent ATP citrate-lyase activity is added to the recombinant reaction network, the number of unique modes increases from 20 to 496, with 314 of these modes producing PHB. With this topological modification, the maximum theoretical PHB carbon yield increases from 0.67 to 0.83. Adding a transhydrogenase reaction to the model also improves the theoretical conversion of substrate into PHB. The recombinant system with the transhydrogenase reaction but without the ATP citrate-lyase reaction has an increase in PHB carbon yield from 0.67 to 0.71. When the model includes both the ATP citrate-lyase reaction and the transhydrogenase reaction, the maximum theoretical carbon yield increases to 0.84. The reaction model was also used to explore the possibility of producing PHB under anaerobic conditions. In the absence of oxygen, the recombinant reaction network possesses two elementary modes capable of producing PHB. Interestingly, both modes also produce ethanol. Elementary mode analysis provides a means of deconstructing complex metabolic networks into their basic functional units. This information can be used for analyzing existing pathways and for the rational design of further modifications that could improve the system's conversion of substrate into product.     

Recovery of poly(3-hydroxybutyrate) from coagulated Ralstonia eutropha using a chemical digestion method

For economic recovery of poly(3-hydroxybutyrate) (PHB) from culture broths of Ralstonia eutropha containing PHB, Al-based and Fe-based coagulants were used in the pretreatment step. The coagulated cells were then separated by centrifugation, and PHB was extracted by chemical digestion with a sodium hypochlorite/chloroform dispersion solution. The practical upper limits of dosage were found to be 1, 500 mg-Al/L and 1,000 mg-Fe/L, respectively, for Al- and Fe-based coagulants. When the harvested cells were treated with a 50% sodium hypochlorite/chloroform dispersion solution, PHB recovery and purity were 90-94% and 98-99%, respectively. The influence of the use of coagulants on the PHB recovery process was found to be insignificant. Despite the residual Al and Fe in the recovered PHB (less than 450 mg-Al/kg-PHB and 750 mg-Fe/kg-PHB, respectively), no detectable amounts of Al and Fe were leached from films made of the recovered PHB under acidic conditions. The use of Fe-based coagulants is less recommended because the Fe impurity can cause an unwanted colorization problem in the final product.     

High level production of supra molecular weight poly (3-hydroxybutyrate) by metabolically engineered<Emphasis Type="Italic">Escherichia coli</Emphasis>

The supra molecular weight poly ([R]-3-hydroxybutyrate) (PHB), having a molecular weight greater than 2 million Da, has recently been found to possess improved mechanical properties compared with the normal molecular weight PHB, which has a molecular weight of less than 1 million Da. However, applications for this PHB have been hampered due to the difficulty of its production. Reported here, is the development of a new metabolically engineeredEscherichia coli strain and its fermentation for high level production of supra molecular weight PHB. RecombinantE. coli strains, harboring plasmids of different copy numbers containing theAlcaligenes latus PHB biosynthesis genes, were cultured and the molecular weights of the accumulated PHB were compared. When the recombinantE. coli XL 1-Blue, harboring a medium-copy-number pJC2 containing theA. latus PHB biosynthesis genes, was cultivated by fed-batch culture at pH 6.0, supra molecular weight PHB could be produced at up to 89.8 g/L with a productivity of 2.07 g PHB/L-h. The molecular weight of PHB obtained under these conditions was as high as 22 MDa, exceeding by an order of magnitude the molecular weight of PHB typically produced inRalstonia eutropha or recombinantE. coli     

Poly(3-hydroxybutyrate) granules at the early stages of formation are localized close to the cytoplasmic membrane in Caryophanon latum

Localization of newly synthesized poly(3hydroxybutyrate) (PHB) granules was determined by confocal laser scanning fluorescence microscopy of Nile red-stained cells and by transmission electron microscopy (TEM). PHB granules of Nile red-stained living cells of Caryophanon latum at the early stages of PHB accumulation were frequently found at or close to the cytoplasmic membrane. TEM analysis of the same culture revealed electron-translucent globular structures resembling PHB granules that were nonrandomly distributed in the cell lumen but were frequently found at or close to the cytoplasmic membrane. Immunogold labeling using PHB-specific antiserum confirmed that the electron-translucent structures represented PHB granules. Electron microscopy examination of PHB granules after cell lysis revealed that PHB granules were often associated with membrane vesicles. Nonrandom localization of PHB granules was also found in Beijerinckia indica. Cells of this species harbored one PHB granule at each cell pole. Our results show that newly synthesized PHB granules often are close to or even in physical contact with the cytoplasmic membrane. Possible explanations for this unexpected finding and a hypothetical model of PHB granule formation in C. latum are discussed.     

Theory of spatial patterns of intracellular organelles

Here we report on a generalized theory of spatial patterns of intracellular organelles, which are controlled by cells using cytoskeleton-based movements powered by molecular motors. The theory reveals that organelles exhibit one of the four distinct, stable patterns, namely aggregation, hyperdispersion, radial dispersion, and areal dispersion. Existence of specific patterns is determined by the contributions from three transport mechanisms, characterized by two Peclet numbers. The predicted patterns compare well with experimental data. This study provides a firm theoretical ground for classification of spatial patterns of organelles and understanding their regulation by cells.     

Removal of endotoxin during purification of poly(3-hydroxybutyrate) from gram-negative bacteria.

Poly(3-hydroxybutyrate) (PHB) was produced by cultivating several gram-negative bacteria, including Ralstonia eutropha, Alcaligenes latus, and recombinant Escherichia coli. PHB was recovered from these bacteria by two different methods, and the endotoxin levels were determined. When PHB was recovered by the chloroform extraction method, the endotoxin level was less than 10 endotoxin units (EU) per g of PHB irrespective of the bacterial strains employed and the PHB content in the cell. The NaOH digestion method, which was particularly effective for the recovery of PHB from recombinant E. coli, was also examined for endotoxin removal. The endotoxin level present in PHB recovered by 0.2 N NaOH digestion for 1 h at 30 degrees C was higher than 10(4) EU/g of PHB. Increasing the digestion time or NaOH concentration reduced the endotoxin level to less than 1 EU/g of PHB. It was concluded that PHB with a low endotoxin level, which can be used for various biomedical applications, could be produced by chloroform extraction. Furthermore, PHB with a much lower endotoxin level could be produced from recombinant E. coli by simple NaOH digestion.     

Connection between poly-beta-hydroxybutyrate biosynthesis and growth on C(1) and C(2) compounds in the methylotroph Methylobacterium extorquens AM1

Several DNA regions containing genes involved in poly-beta-hydroxybutyrate (PHB) biosynthesis and degradation and also in fatty acid degradation were identified from genomic sequence data and have been characterized in the serine cycle facultative methylotroph Methylobacterium extorquens AM1. Genes involved in PHB biosynthesis include those encoding beta-ketothiolase (phaA), NADPH-linked acetoacetyl coenzyme A (acetyl-CoA) reductase (phaB), and PHB synthase (phaC). phaA and phaB are closely linked on the chromosome together with a third gene with identity to a regulator of PHB granule-associated protein, referred to as orf3. phaC was unlinked to phaA and phaB. Genes involved in PHB degradation include two unlinked genes predicted to encode intracellular PHB depolymerases (depA and depB). These genes show a high level of identity with each other at both DNA and amino acid levels. In addition, a gene encoding beta-hydroxybutyrate dehydrogenase (hbd) was identified. Insertion mutations were introduced into depA, depB, phaA, phaB, phaC, and hbd and also in a gene predicted to encode crotonase (croA), which is involved in fatty acid degradation, to investigate their role in PHB cycling. Mutants in depA, depB, hbd, and croA all produced normal levels of PHB, and the only growth phenotype observed was the inability of the hbd mutant to grow on beta-hydroxybutyrate. However, the phaA, phaB, and phaC mutants all showed defects in PHB synthesis. Surprisingly, these mutants also showed defects in growth on C(1) and C(2) compounds and, for phaB, these defects were rescued by glyoxylate supplementation. These results suggest that beta-hydroxybutyryl-CoA is an intermediate in the unknown pathway that converts acetyl-CoA to glyoxylate in methylotrophs and Streptomyces spp.     

Comparison of two mathematical models for correlating the organic matter removal efficiency with hydraulic retention time in a hybrid anaerobic baffled reactor treating molasses

A modelling of the anaerobic digestion process of molasses was conducted in a 70-L multistage anaerobic biofilm reactor or hybrid anaerobic baffled reactor with six compartments at an operating temperature of 26 °C. Five hydraulic retention times (6, 16, 24, 72 and 120 h) were studied at a constant influent COD concentration of 10,000 mg/L. Two different kinetic models (one was based on a dispersion model with first-order kinetics for substrate consumption and the other based on a modification of the Young equation) were evaluated and compared to predict the organic matter removal efficiency or fractional conversion. The first-order kinetic constant obtained with the dispersion model was 0.28 h⁻¹, the Peclet dispersion number being 45, with a mean relative error of 2%. The model based on the Young equation predicted the behaviour of the reactor more accurately showing deviations lower than 10% between the theoretical and experimental values of the fractional conversion, the mean relative error being 0.9% in this case.