Modeling Biofilms on Gas-Permeable Supports: Flux Limitations

A computer model is used to investigate the microbial uptake of oxygen and a carbon-source substrate for biofilms growing on gas-permeable, hollow-fiber membranes and impermeable solid supports of similar geometry. Substrate and oxygen fluxes are predicted for different biofilm thicknesses as a function of fluid velocity and substrate concentration. Under conditions of oxygen limitation, low water velocities, and moderate to high bulk liquid substrate concentration, the membranes have a clear advantage and outperform solid supports. This improvement in performance stems from the ability of the membrane to deliver high oxygen concentrations (8–20 mg∕L) directly to the biofilm, whereas it is difficult to maintain bulk dissolved oxygen concentrations much above 4 mg∕L in wastewater treatment. The growth of an active biofilm can actually increase the flux of oxygen across the membrane dramatically; however, the presence of a biofilm always reduces the ability of a membrane to oxygenate the surrounding wastewater. This drop in oxygen transfer performance is caused by the fact that the active biofilm consumes oxygen and impedes diffusion of the oxygen into the bulk water. In thick biofilms the oxygen flux can drop to zero so that the external regions of the biofilm and the external wastewater become anaerobic. This may cause some operating problems, but it may also facilitate nitrification-denitrification. Additional aeration of the external wastewater could improve biofilm performance and assist in controlling biofilm growth.     

Quantitative Cellular Automaton Model for Biofilms

A fully quantitative cellular automaton (CA) biofilm model was developed. The model describes substrate and biomass as discrete particles existing and interacting in a specified physical domain. Substrate particles move by random walks, simulating molecular diffusion. Microbial particles grow attached to a surface or to other microbial particles, consume substrate particles, and duplicate if a sufficient amount of substrate is consumed. The dynamics of the system are simulated using stochastic processes that represent the occurrence of specific events, such as substrate diffusion, substrate utilization, biofilm growth, and biofilm decay and detachment. The ability of the CA model to predict substrate gradients and fluxes was evaluated by comparing model simulations to predictions from a traditional differential equations model. One and 2D CA models were evaluated. In general, CA model predictions of steady-state flux, biofilm thickness, and substrate gradients inside the biofilm fitted well the differential equations model results; the 2D model had a better agreement at high substrate concentrations. Fully quantitative CA biofilm models offer an alternative approach to simulate biofilm activity and development. Specific advantages of CA modeling include the ability to simulate growth of heterogeneous biofilms with irregular boundary conditions, and the possibility of developing computationally efficient parallel processing algorithms for the quantitative simulation of biofilms in two and three dimensions.     

Verification of Anaerobic Biofilm Model for Phenol Degradation with Sulfate Reduction

A mathematical model was developed to describe phenol degradation with sulfate reduction in an anaerobic biofilm process. The model incorporates the mechanisms of diffusive mass transport and Monod kinetics. The model was solved using a combination of the orthogonal collocation method and Gear's method. A pilot-scale column reactor was conducted to verify the model. The batch kinetic tests were independently conducted to determine nine biokinetic coefficients used in the model while shear loss and initial thickness of the biofilm were assumed so that the model simulated the substrate concentration results very well. The removal efficiencies for phenol and sulfate are 98 and 88%, respectively. At a steady-state condition, the experimental data of phenol and sulfate concentrations were higher than those obtained from the model. The reason was that the effect of shear loss became significant as the biofilm grew thicker. The higher shear loss resulted in the more-suspended biomass. The suspended biomass decomposed and released soluble microbial products which increased the substrate effluent concentrations. The procedures presented in this paper could be employed for the design of anaerobic biofilm reactor systems for the biodegradation of multiple substrates.     

Growth kinetics of suspended microbial cells: from single-substrate-controlled growth to mixed-substrate kinetics

Growth kinetics, i.e., the relationship between specific growth rate and the concentration of a substrate, is one of the basic tools in microbiology. However, despite more than half a century of research, many fundamental questions about the validity and application of growth kinetics as observed in the laboratory to environmental growth conditions are still unanswered. For pure cultures growing with single substrates, enormous inconsistencies exist in the growth kinetic data reported. The low quality of experimental data has so far hampered the comparison and validation of the different growth models proposed, and only recently have data collected from nutrient-controlled chemostat cultures allowed us to compare different kinetic models on a statistical basis. The problems are mainly due to (i) the analytical difficulty in measuring substrates at growth-controlling concentrations and (ii) the fact that during a kinetic experiment, particularly in batch systems, microorganisms alter their kinetic properties because of adaptation to the changing environment. For example, for Escherichia coli growing with glucose, a physiological long-term adaptation results in a change in KS for glucose from some 5 mg liter-1 to ca. 30 microg liter-1. The data suggest that a dilemma exists, namely, that either "intrinsic" KS (under substrate-controlled conditions in chemostat culture) or micromax (under substrate-excess conditions in batch culture) can be measured but both cannot be determined at the same time. The above-described conventional growth kinetics derived from single-substrate-controlled laboratory experiments have invariably been used for describing both growth and substrate utilization in ecosystems. However, in nature, microbial cells are exposed to a wide spectrum of potential substrates, many of which they utilize simultaneously (in particular carbon sources). The kinetic data available to date for growth of pure cultures in carbon-controlled continuous culture with defined mixtures of two or more carbon sources (including pollutants) clearly demonstrate that simultaneous utilization results in lowered residual steady-state concentrations of all substrates. This should result in a competitive advantage of a cell capable of mixed-substrate growth because it can grow much faster at low substrate concentrations than one would expect from single-substrate kinetics. Additionally, the relevance of the kinetic principles obtained from defined culture systems with single, mixed, or multicomponent substrates to the kinetics of pollutant degradation as it occurs in the presence of alternative carbon sources in complex environmental systems is discussed. The presented overview indicates that many of the environmentally relevant apects in growth kinetics are still waiting to be discovered, established, and exploited.     

Efficacy of Biofilms under Toxic Conditions

Response of biofilms to toxic compounds has been modeled using Monod-type inhibition kinetics. Biofilm inhibition due to substrate, secondary substrate, and product is considered. For biofilm inhibition due to substrate and secondary substrate with high inhibitory substances, the model predicted the biofilm effectiveness factor to be higher than unity. On the other hand, for slightly inhibitory substances, substrate limitations within the biofilm due to mass transfer resistance resulted in a reduction in biofilm effectiveness factor as its thickness increased. In case of product inhibition, the effectiveness factor of the biofilm was always lower than one due to accumulation of product leading to higher concentrations within the biofilm than in the bulk. The generalized models developed for effectiveness factors under various conditions of inhibition can be used as a predictive tool in design of wastewater treatment systems.     

Simultaneous Removal of Organic Matter and Nitrogen Compounds in Autoaerated Biofilms

This paper describes the simultaneous removal of organic matter and nitrogen compounds carried out using an autoaerated multispecies biofilm growing on gas-permeable hollow-fiber membranes. In order to perform the aerobic heterotrophic oxidation and nitrification processes, the biofilm absorbs atmospheric oxygen through the inside walls of hollow fibers and consumes substrate from the bulk liquid. A mass balance calculated the consumed oxygen. Depending on the removed organic and nitrification rates, the oxygen flux through the hollow fibers can reach up to 90% of the total oxygen consumed, whereas the remaining 10% pertains to the dissolved oxygen from the influent wastewater. Without the biofilm the oxygen transfer rate through clean hollow fibers is 3.5?g?m?2?day?1, whereas the oxygen transfer rate through the biomembrane (hollow fiber+biofilm) achieves a maximum value of 25?g?m?2?day?1. The enhanced oxygen transfer using the biological pathway may be attributed, among many other factors, to the mobility of the microorganisms generating microturbulence, which produces more active bioturbulent diffusiveness than the molecular diffusion in the biofilm. It has also shown that the oxygen utilization efficiency was affected by the substrate utilization rate.     

Analytical steady-state solution to the rapid buffering approximation near an open Ca2+ channel

We derive an analytical steady-state solution for the Ca2+ profile near an open Ca2+ channel based on a transport equation which describes the buffered diffusion of Ca2+ in the presence of rapid stationary and mobile Ca2+ buffers (Wagner and Keizer, 1994). This steady-state rapid buffering approximation gives an upper bound on local Ca2+ elevations such as Ca2+ puffs or sparks when conditions for the validity of the rapid buffering approximation are met and is an alternative to approximations that assume that mobile buffers are unsaturable. This result also provides an analytical estimate of the cytosolic Ca2+ domain concentration ([Ca2+]d) near a channel pore and shows the dependence of [Ca2+]d on moderate concentrations of endogenous mobile buffer, Ca2+ indicator dye, and bulk cytosolic Ca2+. Assuming a simple relationship between [Ca2+]d and the lumenal depletion domain of an intracellular Ca2+ channel, lumenal and cytosolic Ca2+ profiles are matched to give an implicit analytical expression for the effect of bulk lumenal Ca2+ on [Ca2+]d.     

Modeling Biofilms on Gas-Permeable Supports: Concentration and Activity Profiles

Several investigators have shown that membrane oxygenation provides a number of advantages in biological treatment. These include operational flexibility, reduced energy requirements, and less stripping of volatile compounds. Membranes have also been observed to provide a support surface for microbial growth. This steady-state model study investigates the microbial uptake of oxygen and a carbon-source substrate for aerobic, heterotrophic biofilms on gas permeable membrane- and impermeable solid-supported surfaces. The model predictions indicate that very different concentration and activity profiles may be found in biofilms grown on solid surfaces and gas permeable membranes. For a solid-supported biofilm the highest concentrations of oxygen and substrate and the greatest microbial activity are located on the outside of the biofilm. For a membrane-supported film, the oxygen and substrate are never present at the same location in their maximum concentrations, and the location of maximum biological activity in the biofilm can occur at other locations within the film. These differences may lead to significant differences in the microbial ecology and populations of biofilms and, in turn, in biofilm morphology.     

Bitwise Implementation of a Two-Dimensional Cellular Automata Biofilm Model

Mathematical modeling using the cellular automata (CA) approach is an attractive alternative to models based on partial differential equations when the domains to be simulated have complex boundary conditions. The computational efficiency of CA models is readily observed when using parallel processors, but implementations in personal computers are, although feasible, not quite efficient. In an effort to improve the computational efficiency of CA implementations in personal computers, we introduce in this paper a bitwise implementation based on the use of each bit as a different CA cell. Thus, in a 32-bit processor, each computer word stores information about 32 different CA cells. We illustrate the bitwise implementation with a biofilm model that simulates substrate diffusion and microbial growth of a single-species, single-substrate, structurally heterogeneous biofilm. The efficiency of the bitwise implementation was evaluated by comparing the computational time of equivalent CA biofilm models that used more common low-level implementations, namely, if-then operators and look-up tables. The processing speed of the bitwise implementation was over an order of magnitude higher than the processing speed of the other two implementations. Regarding the biofilm simulations, the CA model exhibited self-organization of the biofilm morphology as a function of kinetic and physical parameters.     

Analysis of Overall Perchlorate Removal Rates in Packed-Bed Bioreactors

Perchlorate (ClO?4) can be used as a terminal electron acceptor by some bacteria for cell respiration during the oxidation of substrates. Packed-bed biofilm reactors have been used to treat perchlorate-contaminated waters with rates varying over six orders of magnitude (0.0007 to 20 mg∕L-min). While this range implies large differences in treatment efficiencies, it is demonstrated in this report that these rates are correlated to concentrations of perchlorate in the reactor. Overall perchlorate reduction rates obeyed first-order kinetics for reactors using organic substrates as electron donors (acetate or a complex high-protein medium). Higher reaction rates appear possible in hydrogen-gas feed reactors rather than in organic-feed reactors, although additional work is necessary to confirm this preliminary result. Findings of first-order perchlorate kinetics will help engineers design packed-bed reactors for the remediation of perchlorate-contaminated waters.     

Cultivation of Escherichia coli with mixtures of 3-phenylpropionic acid and glucose: steady-state growth kinetics

The fate of pollutants in the environment is affected by the presence of easily degradable carbon sources. As a step towards understanding these complex interactions, a model system was explored: the degradation of mixtures of glucose (i.e., an easily degradable substrate) and 3-phenylpropionic acid (3ppa) (a model pollutant) by Escherichia coli ML 30 was studied systematically in carbon-limited continuous culture. The two substrates were always consumed simultaneously regardless of the dilution rate applied. Even at dilution rates higher than the maximum specific growth rate for 3ppa (0.35 +/- 0.05 h-1), the two carbon substrates were utilized together. When cells were grown at a constant dilution rate with different mixtures of 3ppa and glucose, in which 3ppa contributed between 5 and 90% of carbon substrate in the feed medium, the steady-state concentrations of 3ppa and glucose were approximately proportional to the ratio of the two substrates in the feed medium. When cells were cultivated at different dilution rates with a 1:1 mixture (based on carbon) of glucose and 3ppa, an overall maximum specific growth rate of 0.90 +/- 0.05 h-1 and a Monod substrate saturation constant for 3ppa (Ks) of 600 to 700 micrograms liter-1, similar to that measured during growth with 3ppa alone, fitted the experimentally determined steady-state 3ppa concentrations. However, due to the highly differing substrate affinity constants for 3ppa and glucose (Ks approximately 30 to 70 micrograms liter-1), the total steady-state carbon concentration in the culture at a constant dilution rate was determined mainly by the steady-state 3ppa carbon concentration, and it increased with increasing proportions of 3ppa in the feed medium.     

Modeling Substrate Interactions during Aerobic Biodegradation of Mixtures of Vinyl Chloride and Ethene

Ethene (ETH) is often associated with vinyl chloride (VC) in contaminated groundwater, as it is formed along with vinyl chloride during reductive dechlorination of higher chloroethenes (e.g., perchloroethylene and trichloroethylene). In the present study the interaction between VC and ETH during their aerobic biodegradation by enrichment cultures was investigated. The cultures were able to use both compounds as growth substrates. In mixture experiments, the degradation rate of one substrate was affected by the presence of the other. A biokinetic model based on competitive inhibition described well the observed substrate interactions over a range of initial VC (0–144 μmol?L?1) and ETH (0–37.5 μmol?L?1) concentrations, using parameters estimated from single-substrate experiments. Notably, half-velocity coefficients could be used as competitive inhibition coefficients. This finding shows the importance of obtaining accurate measurements of half-velocity coefficients in order model competitive inhibition processes. Simulation results showed that when the initial ETH concentration was raised from 0 to 30 μmol?L?1, the apparent half-velocity coefficient for VC (KVCAPP) increased by nearly three times, from 12.9 to 35.4 μmol?L?1. This finding has strong environmental implications because a low half-velocity coefficient for VC is regarded as the major prerequisite for achieving efficient and complete VC degradation. Moreover, the effect of ETH on the efficiency of VC removal is strongly dependent on the KVC/KETH ratio, consequently determination of KETH for VC-degrading microbes is important when biodegradation (or bioaugmentation) is considered for clean up of VC-contaminated sites. Additional model simulations, using the ratio of KVC to KETH for previously characterized VC- and ETH-utilizing microorganisms (values ranged from 0.06 to 1.2) showed that their ability to degrade VC in the presence of ETH may differ significantly.     

Mathematical Model for the Biofilm–Activated Sludge Reactor

A steady state mathematical model is developed for describing the completely mixed biofilm–activated sludge reactor (hybrid reactor). The model is derived by simultaneously considering Monod kinetics expressions and Fickian’s diffusion theory for substrate in biofilm. In addition, it includes the basic concepts, which describe both culture (suspended and attached) and the competition between them for limiting substrate. By using this model the suspended biomass concentration can be obtained for this system. Subsequently, the other remaining parameters of the system can be computed. Therefore it helps to design and operate the hybrid reactor under different conditions for any given set of kinetic parameters. The utility of the model has been explained for a given set of data and verified by comparing with another solution. It is found that for the same set of data, the model is accurate in the results. The model has been presented in more than one form, each form having an explicit solution of the system. Compared with other solutions of such a system, the model provides a good tool for describing such a system based on fundamental principles.     

A freshwater anaerobe coupling acetate oxidation to tetrachloroethylene dehalogenation

Strain TT4B has been isolated from anaerobic sediments known to be contaminated with a variety of organic solvents. It is a gram-negative, rod-shaped bacterium and grew anaerobically with acetate as the electron donor and tetrachloroethylene as the electron acceptor in a mineral medium. cis-Dichloroethylene was the halogenated product. This strain did not grow fermentatively and used only acetate or pyruvate as electron donors. Tetrachloroethylene and trichloroethylene were used as electron acceptors, as were ferric nitriloacetate and fumarate. Nitrogen and sulfur oxyanions were not able to substitute as the electron acceptor for this organism. Modest growth occurred in a two-phase system with 1 ml of hexadecane containing 50 to 200 mM tetrachloroethylene (aqueous concentrations, 25 to 100 microM) and 10 ml of anaerobic mineral solution with Na2S as the reducing agent. Growth was completely inhibited at tetrachloroethylene levels above 100 microM.     

Simultaneous Removal of Phenol and Nitrate in an Anaerobic Bioreactor

Phenol and nitrate are two major pollutants simultaneously occurring in several industrial wastewaters. In this study, a 110-day gradual enrichment of an anaerobic culture has been carried out at 25°C in an anaerobic bioreactor for continuously treating a synthetic wastewater containing 600?mg/L phenol and 430?mg/L?NO3?–N. The results showed that the enriched culture can utilize phenol as a sole electron donor and nitrate as a sole electron acceptor. At the end of the enrichment (on Day 110), 93.3% of phenol and 98.0% of NO3?–N were simultaneously removed at a hydraulic retention time of 20.25?h in the anaerobic bioreactor. The removal of 1?g?NO3?–N required about 3.19?g chemical oxygen demand as the electron donor. Batch tests further revealed that cresol, nitrophenol, and monochlorinated phenol (MCP) could exert detrimental influences on the treatment abilities of the enriched culture. However, the inhibitory effects of cresol were impermanent, as compared to those of nitrophenol and MCP. In order to operate the anaerobic bioreactor steadily, high concentrations of cresol should be diluted before being fed while the existence of nitrophenol and MCP in the bioreactor should be avoided.     

Effect of substance P and receptor antagonists on secretion of lingual lipase and amylase from rat von Ebner''s gland

Electron donor acceptor gels based on cyanocarbons have been tested for human serum protein adsorption in the absence of salt-promotion by water-structuring salt. This phenomenon was compared with a normal adsorption process in the presence of salt. The tricyanoaminopropene-divinyl sulfone-agarose displayed unusual protein adsorption properties as binding could occur both independently or dependently of the salt-promotion. The absence of hydrophobic or ionic character of the salt-independent interaction suggests an electron donor acceptor adsorption mechanism which is shown, for the first time, to occur independently of salt-promotion in aqueous solution. Study of the protein adsorption specificity showed similar protein selectivity for the fractions adsorbed in both conditions.     

Systematic Approach for Modeling Tetrachloroethene Biodegradation

The anaerobic biodegradation of tetrachloroethene (PCE) is a reasonably well understood process. Specific organisms capable of using PCE as an electron acceptor for growth require the addition of an electron donor to remove PCE from contaminated ground waters. However, competition from other anaerobic microorganisms for added electron donor will influence the rate and completeness of PCE degradation. The approach developed here allows for the explicit modeling of PCE and byproduct biodegradation as a function of electron donor and byproduct concentrations, and the microbiological ecology of the system. The approach is general and can be easily modified for ready use with in situ ground-water models or ex situ reactor models. Simulations conducted with models developed from this approach show the sensitivity of PCE biodegradation to input parameter values, in particular initial biomass concentrations. Additionally, the dechlorination rate will be strongly influenced by the microbial ecology of the system. Finally, comparison with experimental acclimation results indicates that existing kinetic constants may not be generally applicable. Better techniques for measuring the biomass of specific organism groups in mixed systems are required.     

Expression and function of recombination activating genes in mature B cells

An analysis of the effects of external and internal metabolites on the steady-state behavior of linear pathways comprising a sequence of three Michaelis-Menten-type reactions with and without a simple feedback inhibition (i.e. an interaction of an internal metabolite with the pathway) is performed with respect to the transit time tau by its formulation as rectangular-hyperbolic functions of the flux J, instead of direct expressions in terms of the external metabolite concentrations. For a given concentration of the external metabolite M1 (substrate of the pathway) or M4 (product of the pathway), the flux J has a lower value in the pathway with feedback inhibition than in the pathway without feedback inhibition. With variation in the M1 concentration the transit time tau shows a concave relationship with the flux J which is virtually identical for both pathways, yielding a minimum at a certain value of J. With variation in the M4 concentration the transit time tau monotonously decreases with higher value of J, and for a given value of J the feedback inhibition allows a lower transit time. This effect is enhanced with stronger feedback inhibition, and is in turn greatly reduced with higher values of total concentration and rate constants for the first enzyme in the pathway.     

Influence of Hydrodynamics on the Performance of a Biofilm Airlift Suspension Reactor

Five biofilm airlift suspension (BAS) reactors filled with ceramic materials as biocarriers were used to investigate the hydrodynamics, liquid mixing, and biofilm detachment kinetics in the BAS reactor. A mathematical model was developed to describe the internal liquid circulation within the BAS reactor. The Froude number was introduced to correlate the relationship between the Froude number and superficial gas velocity at different biocarrier concentrations. The validity of the empirical model was verified over a wide range of experimental conditions and the result shows that the internal liquid circulation velocity was proportional to the square root of the reactor height and the superficial gas velocity. Because the internal liquid circulation flow rate was much larger than influent flow rate, the BAS reactor had a strong capacity to resist shock loading caused by the change in influent organic matter concentration. Shock loading resistance increased with the height of a BAS reactor. Although biofilm detachment was a very complicated process which involved many mechanisms, dimensional analysis was employed to successfully analyze the biofilm detachment kinetics. It was found that the biofilm detachment rate was proportional to the first power of the superficial gas velocity and biofilm thickness, and to the 2/3 power of the number of biocarriers in the reactor, respectively. Use of the Froude number and dimensional analysis provide an effective and accurate method to study the characteristics of the BAS reactor.     

Effect of surface diffusion on the creep of thin films and sintered arrays of particles

An analysis is presented that illustrates the effect of surface diffusion on the creep of a uniform, sintered array of cylinders. The analysis is also appropriate for describing the creep of thin films bonded to substrates when there is no interfacial diffusion. The first part of the paper presents an analytical solution which can be obtained when it is assumed that a constant flux of matter out of the grain boundary is maintained. This solution illustrates the important physical phenomenon behind the problem in that a finite surface diffusivity causes a back stress to be developed owing to the enhanced surface curvatures in the region of the grain boundary. In the latter portion of the paper, this analytical solution is used to generate numerical solutions for more practical boundary conditions, and to illustrate the effects of finite boundary lengths.