A method for simultaneous determination of solubility and transfer coefficient of oxygen in aqueous media using off-gas mass spectrometry

A static method was developed that simultaneously determined the solubility of oxygen and the oxygen-transfer coefficient in a stirred bioreactor. It was based on the static method developed by van Sonsbeek et al. to determine the ka in a liquid-impelled loop reactor. Only physical properties of the liquid were used to determine both parameters using a mass spectrometer. Data about the solubility of oxygen in water are available from the literature. Therefore, the solubility of oxygen in water was used to compare our data with published data. Furthermore, the solubility of oxygen in trypticase soy broth was compared to literature data. No significant deviations between our data and literature data could be observed. Our static method and the commonly applied dynamic method to determine the oxygen-transfer coefficient yielded similar results. The effect of temperature on the oxygen-transfer coefficient could be expressed as the activation energy needed for the transition of oxygen from the gas to the water phase. This was verified using the Arrhenius equation. (c) 1994 John Wiley & Sons, Inc.     

A new dynamic model for highly efficient mass transfer in aerated bioreactors and consequences for kLa identification

Gas–liquid mass transfer is often rate‐limiting in laboratory and industrial cultures of aerobic or autotrophic organisms. The volumetric mass transfer coefficient k_La is a crucial characteristic for comparing, optimizing, and upscaling mass transfer efficiency of bioreactors. Reliable dynamic models and resulting methods for parameter identification are needed for quantitative modeling of microbial growth dynamics. We describe a laboratory‐scale stirred tank reactor (STR) with a highly efficient aeration system (k_La ≈ 570 h^?1). The reactor can sustain yeast culture with high cell density and high oxygen uptake rate, leading to a significant drop in gas concentration from inflow to outflow (by 21%). Standard models fail to predict the observed mass transfer dynamics and to identify k_La correctly. In order to capture the concentration gradient in the gas phase, we refine a standard ordinary differential equation (ODE) model and obtain a system of partial integro‐differential equations (PIDE), for which we derive an approximate analytical solution. Specific reactor configurations, in particular a relatively short bubble residence time, allow a quasi steady‐state approximation of the PIDE system by a simpler ODE model which still accounts for the concentration gradient. Moreover, we perform an appropriate scaling of all variables and parameters. In particular, we introduce the dimensionless overall efficiency κ, which is more informative than k_La since it combines the effects of gas inflow, exchange, and solution. Current standard models of mass transfer in laboratory‐scale aerated STRs neglect the gradient in the gas concentration, which arises from highly efficient bubbling systems and high cellular exchange rates. The resulting error in the identification of κ (and hence k_La) increases dramatically with increasing mass transfer efficiency. Notably, the error differs between cell‐free and culture‐based methods of parameter identification, potentially confounding the determination of the “biological enhancement” of mass transfer. Our new model provides an improved theoretical framework that can be readily applied to aerated bioreactors in research and biotechnology. Biotechnol. Bioeng. 2012; 109: 2997–3006. © 2012 Wiley Periodicals, Inc.     

A computational study of invariant I5 in a nearly incompressible transversely isotropic model for white matter

The aligned axonal fiber bundles in white matter make it suitable to be modeled as a transversely isotropic material. Recent experimental studies have shown that a minimal form, nearly incompressible transversely isotropic (MITI) material model, is capable of describing mechanical anisotropy of white matter. Here, we used a finite element (FE) computational approach to demonstrate the significance of the fifth invariant (I₅) when modeling the anisotropic behavior of white matter in the large-strain regime. We first implemented and validated the MITI model in an FE simulation framework for large deformations. Next, we applied the model to a plate-hole structural problem to highlight the significance of the invariant I₅ by comparing with the standard fiber reinforcement (SFR) model. We also compared the two models by fitting the experiment data of asymmetric indentation, shear test, and uniaxial stretch of white matter. Our results demonstrated the significance of I₅ in describing shear deformation/anisotropy, and illustrated the potential of the MITI model to characterize transversely isotropic white matter tissues in the large-strain regime.     

A theoretical model for F-actin remodeling in vascular smooth muscle cells subjected to cyclic stretch

A constrained mixture theory model was developed and used to estimate remodeling of F-actin in vascular smooth muscle cells that were subjected to 10% equibiaxial stretching for up to 30min. The model was based on a synthesis of data on time-dependent changes in atomic force microscopy measured cell stiffness and immunofluorescence measured focal adhesion associated vinculin as well as data on stress fiber stiffness and pre-stretch. Results suggest that an observed acute (after 2min of stretching) increase in cell stiffness is consistent with an increased stretch of the originally present F-actin plus an assembly of new F-actin having nearly homeostatic values of stretch. Moreover, the subsequent (after 30min of stretching) decrease in cell stiffness back towards the baseline value is consistent with a replacement of the overstretched original filaments with the new (reassembled), less stretched filaments. That is, overall cell response is consistent with a recently proposed concept of "tensional homeostasis" whereby cells seek to maintain constant certain mechanical factors via a remodeling of intracellular and transmembrane proteins. Although there is a need to refine the model based on more comprehensive data sets, using multiple experimental approaches, the present results suggest that a constrained mixture theory can capture salient features of the dynamics of F-actin remodeling and that it offers some advantages over many past methods of modeling, particularly those based on classical linearized viscoelasticity.     

A dynamic mass balance model for phosphorus fluxes and concentrations in coastal areas

This paper presents a general, process-based mass balance model (CoastMab) for total phosphorus (TP) in defined coastal areas (at the ecosystem scale). The model is based on ordinary differential equations and calculates inflow, outflow and internal fluxes on a monthly basis. It consists of four compartments: surface water, deep water, erosion/transportation areas for fine sediments and accumulation areas for fine sediments. The separation between surface water and deep water is not done based on water temperature, but on sedimentological criteria instead (from the theoretical wave base). There are algorithms for all major internal TP fluxes (sedimentation, resuspension, diffusion, mixing and burial). Validations were performed using data from 21 different Baltic coastal areas. The results show that the model predicts monthly TP in water and chlorophyll a very well (generally within the uncertainty bands of the empirical data). The model has also been put through sensitivity tests, which show that the most important factor regulating the predictions of the model is generally the TP concentration in the sea beyond the coast. The model is simple to apply, since all driving variables may be accessed from maps or monitoring programs. The driving variables include coastal area, section area (between the defined coastal area and the adjacent sea), mean and maximum depths, latitude (used to predict water temperatures, stratification and mixing), salinity and TP concentration in the sea. Many of the model structures are general and could be used for areas other than those included in this study, e.g., for open coasts, estuaries or tidal coasts, as well as for other substances than phosphorus.     

A structured model for simulation of cultures of the cyanobacterium Spirulina platensis in photobioreactors: I. Coupling between light transfer and growth kinetics

The study of the interactions between physical limitation by light and biological limitations in photobioreactors leads to very complex partial differential equations. Modeling of light transfer and kinetics and the assessment of radiant energy absorded in photoreactors require an equation including two parameters for light absorption and scattering in the culture medium. In this article, a simple model based on the simplified, monodimensional equation of Schuster for radiative transfer is discussed. This approach provides a simple way to determine a working illuminated volume in which growth occurs, therefore allowing indentification of kinetic parameters. These parameters might then be extended to the analysis of more complex geometries such as cylindrical reactors. Moreover, this model allows the behavior of batch or continuous cultures of cyanobacteria under light and mineral limitations to be predicted. (c) 1992 John Wiley & Sons, Inc.     

A model for the study of Wolbachia pipientis Hertig (Rickettsiales: Rickettsiaceae)- induced cytoplasmic incompatibility in arrhenotokous haplodiploid populations: consequences for biological control

Wolbachia is an endocytoplasmic bacterium responsible for various reproductive modifications in arthropods. In several species, Wolbachia induces a phenomenon called cytoplasmic incompatibility (CI), whereby crosses between a Wolbachia-infected male and a healthy female are incompatible. In haplodiploid species reproducing with arrhenotokous parthenogenesis, CI crosses produce only parthenogenetic males, inducing a male-biased sex ratio in the population. Here, we used two modeling approaches to evaluate the respective influences of demographic and biological parameters on Wolbachia fixation probability and on the sex ratio peak occurring during a Wolbachia invasion, and compared these parameters to values reported in the literature. Results suggest that the impact of Wolbachia invasion on population dynamics remains relatively limited, especially for parasitoids with high rates of sib-mating. The consequences for introduction of the parasitoids for biological control are discussed.     

Comparison of solution and crystal structures of maize nonspecific lipid transfer protein: A model for a potential in vivo lipid carrier protein

The three-dimensional solution structure of maize nonspecific lipid transfer protein (nsLTP) obtained by nuclear magnetic resonance (NMR) is compared to the X-ray structure. Although both structures are very similar, some local structural differences are observed in the first and the fourth helices and in several side-chain conformations. These discrepancies arise partly from intermolecular contacts in the crystal lattice. The main characteristic of nsLTP structures is the presence of an internal hydrophobic cavity whose volume was found to vary from 237 to 513 ų without major variations in the 15 solution structures. Comparison of crystal and NMR structures shows the existence of another small hollow at the periphery of the protein containing a water molecule in the X-ray structure, which could play an important structural role. A model of the complexed form of maize nsLTP by α-lysopalmitoylphosphatidylcholine was built by docking the lipid inside the protein cavity of the NMR structure. The main structural feature is a hydrogen bond found also in the X-ray structure of the complex maize nsLTP/palmitate between the hydroxyl of Tyr81 and the carbonyl of the lipid. Comparison of 12 primary sequences of nsLTPs emphasizes that all residues delineating the cavities calculated on solution and X-ray structures are conserved, which suggests that this large cavity is a common feature of all compared plant nsLTPs. Furthermore several conserved basic residues seem to be involved in the stabilization of the protein architecture. Proteins 31:160–171, 1998. © 1998 Wiley-Liss, Inc.