Co-immobilized Nitrosomonas europaea and Nitrobacter agilis cells: validation of a dynamic model for simultaneous substrate conversion and growth in kappa-carrageenan gel beads

A dynamic model for two microbial species immobilized in a gel matrix is presented and validated with experiments. The model characterizes the nitrification of ammonia with Nitrosomonas europaea and Nitrobacter agilis co-immobilized in K-carrageenan gel beads. The model consists of kinetic equations for the microorganisms and mass transfer equations for the substrates and products inside and outside the gel beads. The model predicts reactor bulk concentrations together with the substrate consumption rate, product formation, and biomass growth inside the gel beads as a function of time. A 50-day experiment with immobilized cells in a 3.3-dm(3) air-lift loop reactor was carried out to validate the model. The parameter values for the model were obtained from literature and separate experiments. The experimentally determined reactor bulk concentrations and the biomass distribution of the two microorganisms in the gel beads were well predicted by the model. A sensitivity analysis of the model for the given initial values indicated the most relevant parameters to be the maximum specific growth rate of the microorganisms, the diffusion coefficient of oxygen, and the radius of the beads. The dynamic model provides a useful tool for further study and possible control of the nitrification process. (c) 1994 John Wiley & Sons, Inc.     

Three-dimensional dynamic simulation of total knee replacement motion during a step-up task.

A three-dimensional dynamic model of the tibiofemoral and patellofemoral articulations was developed to predict the motions of knee implants during a step-up activity. Patterns of muscle activity, initial joint angles and velocities, and kinematics of the hip and tinkle were measured experimentally and used as inputs to the simulation. Prosthetic knee kinematics were determined by integration of dynamic equations of motion subject to forces generated by muscles, ligaments, and contact at both the tibiofemoral and patellofemoral articulations. The modeling of contacts between implants did not rely upon explicit constraint equations; thus, changes in the number of contact points were allowed without modification to the model formulation. The simulation reproduced experimentally measured flexion-extension angle of the knee (within one standard deviation), but translations at the tibiofemoral articulations were larger during the simulated step-up task than those reported for patients with total knee replacements.     

Modelling for waste water treatment by Rhodopseudomonas palustris Y6 immobilized on fibre in a columnar bioreactor

A kinetic model of continuous treatment of waste water by Rhodopseudomonas palustris Y6 immobilized on soft fibre in a columnar bioreaction system was established. Good agreement was found between the model prediction and the experimental data from continuous operation [initial chemical oxygen demand (COD) concentration = 29.700 g/l] of the system. The optimum operational conditions for the maximum COD reduction capacity were investigated from the model prediction and the experimental data. The waste water treatment process may significantly increase the waste reduction capacity because a large amount of active biomass for COD reduction is immobilized in the system, resulting in operation stability. The results presented here provide a useful basis for further scaling up and efficient operation of waste water treatment processes.     

Experimental optimization of a step aeration waste treatment process

Evolutionary operation (EVOP) was used to experimentally investigate the optimum steady state operating conditions for a step aeration activated sludge waste treatment process. A laboratory scale two tank step aeration activated sludge unit with fixed total volume, total influent flow rate, recycle flow rate, and sludge wasting rate was employed. The volume ratio and flow rate ratio which minimized effluent chemical oxygen demand were determined. The results indicate that EVOP is a useful technique for improving the performance of biological processes.     

Use of a mathematical model of erythropoiesis to study the recovery process in mice exposed to acute x-ray irradiation]

The model described in the preceding paper was used (after introducing several further presumptions of a radiobiological nature) for the interpretation of the dynamics of erythropoietic recovery, experimentally studied by the authors in mice after acute X-irradiation. The solution of equations in the model was carried out by a digital computer, finding some (not yet experimentally determined) quantitative characteristics of the system by trial and error. A satisfactory degree of agreement in the behaviour of the model with the experimentally determined course of recovery seems to indicate the validity of the basic assumptions of the model, esp. the existence of the negative feedback between erythroid populations of the bone marrow and spleen.     

Multi-strand β-sheet of Alzheimer Aβ(1–40) folds to β-strip helix: implication for protofilament formation

X-ray fiber diffraction experiments on Alzheimer Aβ(1–40) fibrils formed in an assembly process thought to simulate a portion of the pathophysiological process in Alzheimer's disease, indicated protofilaments with tilted β-strands rather than strands oriented perpendicular to the fibril axis as is usually interpreted from cross-β patterns. The protofilament width and tilt angle determined by these experiments were used to predict a β-strip helix model – a β-helix-like structure in which multiple identical polypeptide molecules assemble in-register to form a helical sheet structure such that the outer strands 1 and m join with a register shift t – with m = 11 and t = 22. Starting from untwisted β-sheets comprising 10, 11, and 12 strands, multiple explicit solvent molecular dynamics (MD) simulations were performed to determine whether the sheets form β-strip helices matching the dimensions of the experimentally measured protofilament. In the simulations, the predicted 11-strand sheets curled up to form a closed β-strip helix-like structure with dimensions matching experimental values, whereas the 10- and 12-strand sheets did not form a closed helical structure. The 12-strand structure did, however, show similarity to a cross-β structure determined by a solid-state NMR experiment. The 11-strand β-strip helix resembles a trans-membrane β-barrel which could explain the ability of small oligomers of Aβ(1–40) to form toxic ion channels. A further consequence of opposite sides of the 11-strand strip coming together at a register shift of 22 is end-to-end joins between neighboring β-strip helices, resulting in a protofilament that keeps growing in both directions.

Communicated by Ramaswamy H. Sarma     

Maintenance of heterocyst patterning in a filamentous cyanobacterium

In the absence of sufficient combined nitrogen, some filamentous cyanobacteria differentiate nitrogen-fixing heterocysts at approximately every 10th cell position. As cells between heterocysts grow and divide, this initial pattern is maintained by the differentiation of a single cell approximately midway between existing heterocysts. This paper introduces a mathematical model for the maintenance of the periodic pattern of heterocysts differentiated by Anabaena sp. strain PCC 7120 based on the current experimental knowledge of the system. The model equations describe a non-diffusing activator (HetR) and two inhibitors (PatS and HetN) that undergo diffusion in a growing one-dimensional domain. The inhibitors in this model have distinct diffusion rates and temporal expression patterns. These unique aspects of the model reflect recent experimental findings regarding the molecular interactions that regulate patterning in Anabaena. Output from the model is in good agreement with both the temporal and spatial characteristics of the pattern maintenance process observed experimentally.     

Kinetic modeling of a multiple immobilized enzyme system. I. Development and testing of the model

A kinetic model for the reaction sequence catalyzed by coimmobilized invertase and glucose oxidase with a sucrose substrate in a tubular reactor has been developed. The computerized mathematical model employs and orthogonal collection technique for solving oxidase were coimmobilized in poly(2-hydroxyethlmethacrylate) gels and used in a continuous flow packed-bed tubular reactor system. In addition to describing the development of the kinetic model, this article compares experimentally determined reactor effluent concentrations for various sucrose feed solutions to those predicted by the model. Variations between experimental and predicted reactor effluent concentrations were found to be on the micromolar level for sucrose feed concentrations as low as 1.38mM.     

Spontaneous Movements in Plants Studied as a Random Walk Process

A theory to describe spontaneous curvatures performed by different plant materials on the clinostat is put forward. The movements are proposed to follow the assumptions of a random walk process (statistically randomly distributed movements) and thus to give curvatures following the equations E(α) = 0 V(α) = constant * time where α is the curvature from the starting direction, E(α) is the expectation of α and V(α) is the variance ofα. These equations are experimentally shown to be valid for Lepidium roots and Helianthus hypocotyls. Results for roots reported in the literature are recalculated and are shown to support the theory.     

The Suitability of Jatropha Seed Press Cake as a Biosorbent for Removal of Hexavalent Chromium from Aqueous Solutions

Jatropha seed press cake (JPC), a biodeisel waste, was investigated for its use as biosorbent for Cr(VI) removal from wastewater. The acid-pretreated biomass exhibited 1.9-fold higher biosorption efficiency for Cr(VI). The Cr(VI) biosorption efficiency was found to increase with decrease in pH of aqueous medium. The adsorption capacity of biosorbent for Cr(VI) increased with increasing concentration of Cr(VI). The biosorption of Cr(VI) by acid-treated JPC followed a pseudo-second-order kinetics. The results of equilibrium studies showed that the biosorption process fitted the Langmuir isotherm model, with a maximum adsorption capacity of 22.727 mg of Cr(VI)/g of biosorbent at 30°C. The activation energy was found to be 27.114 kJ/mol, suggesting that the adsorption process was mainly a physical process. The important thermodynamic parameters of adsorption (ΔG, ΔH, andΔS) were determined, which indicated that the Cr(VI) sorption by JPC is a spontaneous and endothermic process.     

Design and application of a pre-composting test step to determine the effect of high fat food wastes on an industrial scale in-vessel composting system

The high fat content in food wastes was suspected to inhibit an industrial in-vessel composting process from reaching the European Union Animal By-Product Regulation (composting temperature >70 °C for 1 h). The aim of this study was to design a test step to guide the mixing ratio of food waste to green waste to meet the regulation. A 15-compartment composting unit was designed to contain the compost mixes. Sausage and cheese wastes were mixed with green waste at 1:1; 1:2; 1:3 and 1:4 ratios by wet weight volume. Only the sausage waste mix ratio of 1:4 gave an average temperature of 70 °C for at least 1 h after 2 days of composting (fat content - 17%; C: N ratio - 8.6). All the cheese waste mixes did not reach 70 °C after 15 days of composting. This study demonstrated that using a simple pre-composting test step could reduce the chances of process failure during industrial composting. Although both sausage and cheese wastes are high in fat, they performed very differently in the composting process. Two linear equations were fitted to model the impact of these wastes on the maximum composting temperature.     

Simple and rapid methods to evaluate methane potential and biomass yield for a range of mixed solid wastes

This paper describes rapid techniques to evaluate the methane potential and biomass yield of solid wastes. A number of solid wastes were mixed to provide a range of C:N ratios. Empirical formulae were calculated for each waste based on the results of chemical analysis and these formulae were used to estimate the COD equivalent and stoichiometric methane potential (SMP). The actual COD and biochemical methane potential (BMP) were determined experimentally for each waste and for both parameters there was a good agreement between the empirical and experimental values. The potential of adenosine triphosphate (ATP) to act as an indicator of biomass yield (mg VSS mg(-1) COD removed) was determined during the anaerobic digestion process. The biomass yield determined from ATP analysis was in the range 0.01-0.25mg VSS mg(-1) COD removed which corroborated well with previously reported studies. Empirical formula based SMP together with ATP measurement were shown to provide rapid methods to replace or augment the traditional BMP and VSS measurements and are useful for evaluating the bioenergy and biomass potential of solid wastes for anaerobic digestion.     

Production of biosurfactants and antibiotics by fluorescent pseudomonads isolated from a closed hydroponic system equipped with a slow filter

The presence of antibiotic- and biosurfactant-producing strains of fluorescent pseudomonads in a closed hydroponic system equipped with a slow filter was investigated. A total of 271 strains of pseudomonads were isolated before the filter, from the filter skin and from the effluent. Production of biosurfactants was determined using the drop-collapse method. The ability of the strains to inhibit the growth of the plant pathogens Pythium ultimum, Phytophthora cryptogea and Fusarium oxysporum was determined using dual culture plating. The influence of carbon sources on production was determined for selected strains, which also were identified to species level. Production of antibiotics or biosurfactants was observed to be a common trait among the fluorescent pseudomonads within the closed hydroponic system and it was affected by the filter. Pythium ultimum was the pathogen that was most sensitive to antibiotics produced by the fluorescent pseudomonads. The results indicated a strong influence of nutritional resources on antibiotic and biosurfactant production.     

A Derivative Matching Approach to Moment Closure for the Stochastic Logistic Model

Continuous-time birth-death Markov processes serve as useful models in population biology. When the birth-death rates are nonlinear, the time evolution of the first n order moments of the population is not closed, in the sense that it depends on moments of order higher than n. For analysis purposes, the time evolution of the first n order moments is often made to be closed by approximating these higher order moments as a nonlinear function of moments up to order n, which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model. We obtain the moment closure function by first assuming a certain separable form for it, and then matching time derivatives of the exact (not closed) moment equations with that of the approximate (closed) equations for some initial time and set of initial conditions. The separable structure ensures that the steady-state solutions for the approximate equations are unique, real and positive, while the derivative matching guarantees a good approximation, at least locally in time. Explicit formulas to construct these moment closure functions for arbitrary order of truncation n are provided with higher values of n leading to better approximations of the actual moment dynamics. A host of other moment closure functions previously proposed in the literature are also investigated. Among these we show that only the ones that achieve derivative matching provide a close approximation to the exact solution. Moreover, we improve the accuracy of several previously proposed moment closure functions by forcing derivative matching.     

The effect of scallop dredging on Irish Sea benthos: experiments using a closed area

A 2 km² area off the southwest coast of the Isle of Man (Irish Sea) has been closed to commercial fishing with mobile gear since March 1989. This area was heavily fished for Pecten maximus (Linnaeus, 1758) prior to closure, and the seabed immediately surrounding the closed area is still one of the most heavily dredged in the Irish Sea. Two methods have been used to study the effect of scallop dredging on the benthos in this closed area and adjacent fished areas. Firstly, twice-yearly grab sampling of experimental plots inside and outside the closed area since 1995 has enabled comparisons of the benthic infauna and epifauna of experimentally dredged plots, undredged control plots and plots exposed to commercial dredging. Secondly, divers have carried out visual transect surveys of P. maximus numbers regularly since closure. Communities of experimentally disturbed plots have become less similar to adjacent undisturbed control areas and more similar to commercially dredged areas. At each sampling date, similarity between dredged samples was greater than between undredged samples. Since 1989, there have been increases in the mean numbers of P. maximus in the closed area. The age structure of the closed area P. maximus population is also different to that outside, with a higher mean age due to the presence of large, old individuals.These results present strong evidence that scallop dredging alters benthic communities and suggest that the closure of areas to commercial dredging may allow the development of more heterogeneous communities and permit the populations of some species to increase. A common problem with studying fishing disturbance is the lack of good control sites and this work also demonstrates the value of closed areas to scientific studies of demersal fishing.     

Characterization of polychlorinated alkane mixtures—a Monte Carlo modeling approach

A Monte Carlo model was developed to characterize the molecular composition of polychlorinated alkane mixtures. The model is based upon a simulation of the free-radical chlorination process by which polychlorinated alkane mixtures are produced industrially from n-alkanes. In the model, the free-radical chlorination reaction was simulated by randomly selecting a position on a partially converted alkane molecule for target by chlorine free-radical attack. The relative reactivities of the hydrogen atoms on the alkane chain towards chlorine free-radical substitution were either determined experimentally or extrapolated from experimental results and incorporated into the model. The result of the simulation is the prediction of the detailed molecular composition of any PCA mixture. Good agreement was found when comparing the distribution of molecules predicted by the model to analytically determined distributions of real PCA mixtures. Results from the model were then coupled with rules describing the action of biological enzymes to estimate the upper limit possible for the aerobic biodegradation of PCA mixtures.     

A multigroup model for predator-prey interactions

The predator-prey interactions between the protozoan Tetrahymena pyriformis and the bacterium Aerobacter aerogenes have been studied experimentally and mathematically. A mathematical model for the ciliates defines the mass distribution of cells within the population. The resulting model equations are solved by the use of multigroup theory. Experimental data from batch and continuous flow reactors are compared with the results of the numerical integration.     

Fate of three bioluminescent pathogenic bacteria fed through a cascade of urine microbial fuel cells

Microbial fuel cell (MFC) technology is currently gaining recognition as one of the most promising bioenergy technologies of the future. One aspect of this technology that has received little attention is the disinfection of effluents and the fate of pathogenic organisms that find their way into the waste stream. In this study, three independent trials were carried out to evaluate the fate of three bioluminescent pathogenic bacteria (Salmonella enterica serovar Typhimurium, Pseudomonas aeruginosa and Staphylococcus aureus) introduced into the anodic chamber of a urine-fed cascade of 9 MFCs with matured, electroactive biofilms. These are common examples of enteric human pathogens, which could contaminate urine or waste streams. The results showed that the average power generation in the closed circuit cascade reached 754 ± 16 µW, with an average pathogen log-fold reduction of 6.24 ± 0.63 compared to 2.01 ± 0.26 for the open circuit cascade for all three pathogens. The results suggest that the bio-electrochemical reactions associated with electricity generation were the primary driving force for the inactivation of the introduced pathogens. These findings show that pathogenic organisms introduced into waste streams could be inactivated by the power-generating process within the MFC cascade system, thereby preventing propagation and thus rendering the effluent safer for possible reuse.

     

Evaluation of an electrochemical model of erythrocyte pH buffering using 31P nuclear magnetic resonance data

When erythrocytes are suspended in a solution of known composition the resultant values of such basic cell parameters as volume and pH are difficult to predict. To facilitate such predictions, we developed a mathematical model describing the passive transmembrane distribution of permeant species; three simultaneous equations were produced. Certain essential data required for the model were determined experimentally; these included the pH dependence of the charge on the hemoglobin molecule and the variation of the osmotic coefficient of hemoglobin with cell volume. Finally, cells were added to various solutions, and then titrated to produce a wide pH range (pH 6-8). We measured the resultant cell volume, cellular and extracellular pH using both conventional and 31P NMR methods. The expected equilibrium values of these electrochemical parameters were also calculated by solving (numerically) the three model equations. The accuracy of the model simulations was evaluated by direct comparison of calculated and experimentally determined values.