Mathematical Modeling of Chemotactic Bacterial Transport through a Two-Dimensional Heterogeneous Porous Medium

The impact of bacterial chemotaxis on in situ ground-water bioremediation remains an unanswered question. Although bacteria respond to chemical gradients in aqueous environments and under no-flow conditions, it is unclear whether they can also respond in porous media with advective flow to improve overall contaminant degradation. The effect of chemotaxis is most profound in regions with sharp chemical gradients, most notably around residual nonaqueous phase liquid (NAPL) ganglia and surrounding clay lenses or aquitards with trapped contamination. The purpose of this study is to simulate bacterial transport through a two-dimensional subsurface environment, containing one region of low permeability with trapped contaminant surrounded above and below by two regions of higher permeability. Using mathematical predictions of the effect of pore size on measured bacterial transport parameters, the authors observe a 50% decrease in both motility and chemotaxis in the finer-grained, low-permeability porous medium. The authors simulate how chemotaxis affects bacterial migration to the contaminated region under various flow and initial conditions. Results indicate that bacteria traveling through a high-permeability region with advective flow can successfully migrate toward and accumulate around a contaminant diffusing from a lower permeability region.     

Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis II: Bacterial Populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated.     

Bacterial Motion in Porous Media

The motion of chemotactically different Escherichia coli C600, cheB287, and AW405 cells was studied using a column packed with silica gel. The model chemotaxis of bacteria in porous media seems to be adequate for natural bacterial chemotaxis in soils. The porous structure of silica gel prevents interfering convective flows. Silica gel columns make it possible to separate bacterial cells differing in motility and chemotaxis. Relevant physical phenomena are discussed. The concept of fast and slow chemotaxis is considered.     

Effect of Bacterial Chemotaxis on Biodegradation in a Porous Medium

This research investigates the effect of bacterial chemotaxis on biodegradation rate in an experimental model for in situ bioremediation. The novel experimental methodology of this work has provided for the systematic evaluation of the effect of the chemotaxis phenomenon in a saturated porous medium. The methodology has been developed to measure enhancement of degradation rate of serine, a simulated contaminant and chemoattractant. Escherichia coli RP437 was used as a representative, chemotactic, in situ bacterium, whereas E. coli RP5700, a tsr? mutant strain of RP437 that lacks the serine chemoreceptor, was used as the specifically nonchemotactic control strain. These two strains were highly characterized for this work. Swimming speeds, run lengths, and turn angles were compared using a tracking microscope and were statistically similar, as were serine uptake rates, making this pair of strains an excellent choice for chemotaxis studies. For these experiments, a model aquifer introduces bacteria to serine in saturated sand via a sharp gradient. The aquifer successfully achieved biodegradation at an 18% level; however, the degradation rate of serine was similar for both strains over 21 h, indicating that chemotaxis enhancement did not occur. This result is in agreement with certain prior works which did not detect enhanced chemotactic migration.     

Transport of bacteria in porous media: II. A model for convective Transport and growth

A model is presented for the coupled processes of bacterial growth and convective transport of bacteria has been modeled using a fractional flow approach. The various mechanisms of bacteria retention can be incorporated into the model through selection of an appropriate shape of the fractional flow curve. Permeability reduction due to pore plugging by bacteria was simulated using the effective medium theory. In porous media, the rates of transport and growth of bacteria, the generation of metabolic products, and the consumption of nutrients are strongly coupled processes. Consequently, the set of governing conservation equations form a set of coupled, nonlinear partial differential equations that were solved numerically. Reasonably good agreement between the model and experimental data has been obtained indicating that the physical processes incorporated in the model are adequate. The model has been used to predict the in situ transport and growth of bacteria, nutrient consumption, and metabolite production. It can be particularly useful in simulating laboratory experiments and in scaling microbial-enhanced oil recovery or bioremediation processes to the field. (c) 1994 John Wiley & Sons, Inc.     

Modeling Dicamba Sorption and Transport Through Zoysiagrass Thatch and Soil

The presence of turfgrass thatch complicates the sorption and transport of water soluble pesticides because the surface-applied pesticides must pass through an organic-rich thatch layer prior to entering the soil. The study was conducted (1) to determine the impact of zoysiagrass thatch (Zoy-sia japonica Steud.) on dicamba (3,6-dichloro-2-methoxy benzoic acid) transport through soil columns, and (2) to evaluate the effectiveness of linear equilibrium (LEM), two site nonequilibrium (2SNE) and one site nonequilibrium (1SNE) models to predict dicamba transport through columns containing a surface layer of thatch and columns devoid of thatch. The equilibrium sorption isotherms of ¹⁴C dicamba to homogenized samples of zoysiagrass thatch and a Sassafras loamy sand soil (fine loamy, mixed mesic, Typic Hapludult) were determined. Following the application of bromide to determine transport parameters, 0.56?kg dicamba ha^?1 was surface applied to undisturbed soil columns containing a surface layer of thatch and columns devoid of thatch and leachate samples collected for 12?h under steady-state unsaturated conditions. Zoysiagrass thatch (Kf = 0.82) had a three times greater sorption capacity than the soil (Kf = 0.28) beneath the thatch. Dicamba leaching for columns with thatch layers was ca. 21% less than soil columns devoid of thatch. When dicamba breakthrough curves were fitted to the different forms of the convective dispersive equation, the 2SNE model simulated dicamba transport better than LEM and 1SNE models, indicating the presence of two-site nonequilibrium sorption. Indications are that turfgrass thatch may have significant effects on dicamba leaching that presently used regulatory models based on LEM approach do not adequately consider.     

The Atypical MAP Kinase ErkB Transmits Distinct Chemotactic Signals through a Core Signaling Module

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Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis I: The Single Cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area.     

The Study of Bacterial Chemotaxis to Naphthalene

The chemotaxis of two pseudomonads,Pseudomonas putida AZ (Naph⁺) and P. putida AZ (Naph^–), differing in their ability to metabolize naphthalene was studied by the known capillary method of Adler and the densitometric method devised in our laboratory. The migration of P. putida AZ (Naph⁺) cells toward increasing levels of naphthalene was accompanied by the formation of a migrating front of converted naphthalene. P. putida AZ (Naph^–) cells also exhibited positive chemotaxis to naphthalene, but they did not form the front of converted naphthalene. The analysis of experimental data in terms of a kinetic model of bacterial chemotaxis showed that the densitometric method is a potential tool for studying bacterial chemotaxis to hydrophobic organic substances.     

Mathematical Modeling of a Carrier-Mediated Transport Process in a Liquid Membrane

An analysis of the reaction diffusion in a carrier-mediated transport process through a membrane is presented. A simple approximate analytical expression of concentration profiles is derived in terms of all dimensionless parameters. Furthermore, in this work we employ the homotopy perturbation method to solve the nonlinear reaction–diffusion equations. Moreover, the analytical results have been compared to the numerical simulation using the Matlab program. The simulated results are comparable with the appropriate theories. The results obtained in this work are valid for the entire solution domain.     

Bacterial motility: links to the environment and a driving force for microbial physics

Bacterial motility was recognized 300 years ago. Throughout this history, research into motility has led to advances in microbiology and physics. Thirty years ago, this union helped to make run and tumble chemotaxis the paradigm for bacterial movement. This review highlights how this paradigm has expanded and changed, and emphasizes the following points. The absolute magnitude of swimming speed is ecologically important because it helps determine vulnerability to Brownian motion, sensitivity to gradients, the type of receptors used and the cost of moving, with some bacteria moving at 1 mm s(-1). High costs for high speeds are offset by the benefit of resource translocation across submillimetre redox and other environmental gradients. Much of environmental chemotaxis appears adapted to respond to gradients of micrometres, rather than migrations of centimetres. In such gradients, control of ion pumps is particularly important. Motility, at least in the ocean, is highly intermittent and the speed is variable within a run. Subtleties in flagellar physics provide a variety of reorientation mechanisms. Finally, while careful physical analysis has contributed to our current understanding of bacterial movement, tactic bacteria are increasingly widely used as experimental and theoretical model systems in physics.     

Reactive Transport Modeling of Induced Selective Plugging by Leuconostoc Mesenteroides in Carbonate Formations

A process-based mechanistic reactive transport model was developed to understand how in-situ coupled processes and operational factors affect selective plugging of reactive carbonate formations by the fermenting bacteria Leuconostoc mesenteroides that produces a plugging polymer dextran. The growth and transport of L. mesenteroides and the associated (bio) geochemical reactions were simulated explicitly with enzyme activity at the field scale over spatial extents of hundreds of meters. Simulations were performed to explore controls on selective bioplugging of high permeability zones in a representative carbonate reservoir, a process that can be used to improve oil sweep efficiency through lower permeability layers. Simulation results indicate that dextran production and the effectiveness of plugging can be largely affected by sucrose and bacteria injection rates. Selective plugging of high permeability zones can only be achieved when the injection rates are high compared to the rates of dextran production. Otherwise, plugging only occurs at the vicinity of injection wells. Due to the dependence of enzyme activity on pH and the reactive nature of carbonate formations, the chemistry of the injection and the formation water is also important. The injection of sucrose and L. mesenteroides at the optimum pH for dextran production (5.2) leads to the dissolution of calcite and an increase in pH levels. However, the resulting pH does not suppress plugging with dextran. Lactic acid and CO₂ formed during the growth of L. mesenteroides buffers the pH of water to levels between 5.2 and 7.0 for continued dextran production. At neutral and basic pH levels, induced precipitation of calcite does not significantly modify the permeability profile at carbonate concentrations typically found in oilfield formation waters. This is the first work that examines the controlling parameters that affect selective plugging of carbonate formations at the field scale within the context of enhanced oil recovery. The demonstrated approach can be used to identify optimal operational conditions for enhanced oil recovery and other applications where selective plugging can be beneficial.     

Modeling and Analysis of Unsteady Axisymmetric Squeezing Fluid Flow through Porous Medium Channel with Slip Boundary

The aim of this article is to model and analyze an unsteady axisymmetric flow of non-conducting, Newtonian fluid squeezed between two circular plates passing through porous medium channel with slip boundary condition. A single fourth order nonlinear ordinary differential equation is obtained using similarity transformation. The resulting boundary value problem is solved using Homotopy Perturbation Method (HPM) and fourth order Explicit Runge Kutta Method (RK4). Convergence of HPM solution is verified by obtaining various order approximate solutions along with absolute residuals. Validity of HPM solution is confirmed by comparing analytical and numerical solutions. Furthermore, the effects of various dimensionless parameters on the longitudinal and normal velocity profiles are studied graphically.     

Mechanisms of TonB-catalyzed iron transport through the enteric bacterial cell envelope

The recent solution of enteric bacterial porin structure, and new insights into the mechanism by which outer membrane receptor proteins recognize and internalize specific ligands, advocates the re-evaluation of TonB-dependent transport physiology. In this minireview we discuss the potential structural features of siderophore receptors and TonB, and use this analysis to evaluate both existing and new models of energy and signal transduction from the inner membrane to the outer membrane of gram-negative bacteria.     

Combined Use of Life Cycle Assessment and Groundwater Transport Modeling to Support Contaminated Site Management

The subject of this study is a spent pot lining (SPL) landfill. The aim of this study was to identify the site remediation option, among four alternatives, that minimizes overall environmental impacts based on: 1) a comparative life cycle assessment (LCA); and 2) modeling of contaminant transport in groundwater. The four options were: leaving the landfill in place (Option 1); excavation of the landfill, with on-site disposal of the excavated materials in a secure cell (Option 2); excavation of the landfill, with treatment of the SPL fraction (Option 3); and excavation of the landfill, with incineration of the SPL fraction in a cement kiln (Option 4). The LCA was performed following the guidelines provided by the International Standard Organization (ISO). Furthermore, to improve the relevance of LCA to site remediation sector, impacts caused by residual in-situ contamination were assessed by applying a simulation of contaminant transport in groundwater, using site-specific data. The LCA identified Option 1 as having the least environmental impacts. However, the transport modeling concluded that contaminant concentrations 50 years from the present could be approximately 30 to 40 times the regulatory criteria if this option is retained. In addition, this study demonstrated that LCA can be used as a screening tool to help identify significant environmental issues; the LCA identified acute and chronic water ecotoxicity categories as being the dominant impact categories of the environmental profile and consequently, it is recommended that a complete environmental risk assessment (ERA) be performed for Option 1.     

Transport of bacteria in porous media: I. An experimental investigation

The convective transport of concentrated suspension of bacteria in porous media is of interest for several processes such as microbial enhanced oil recovery and in situ bioremediation. The parameters which affect the transport of the bacterium Bacillus licheniformis JF-2, a candidate microorganism for microbial enhanced oil recovery, were investigated experimentally in sandpacks. Bacteria retention and permeability reduction occurred primarily in the first few centimeters upon entering the porous medium. In downstream sections of the sandpack, the permeability reduction was low, even in cases in which high cell concentrations (10(8) cfu/mL) were detected in the effluent. The effect of (i) addition of a dispersant, (ii) linear velocity of injection, (iii) cell concentration, (iv) salinity (v) temperature, and (vi) the presence of a residual oleic phase were determined experimentally. A lower reduction in permeability and a higher effluent bacterial concentration were obtained in the presence of dispersant, high injection velocities, low salinities, and at a higher temperature. Macroscopic measurements at different linear velocities and in the presence or absence of dispersants suggest that the formation of reversible microaggregates and multiparticle hydrodynamic exclusion may be the primary mechanisms for bacterial retention and permeability reduction. (c) 1994 John Wiley & Sons, Inc.     

Fate and Transport of Trichloroethylene in a Chamber with Alfalfa Plants

Experiments in a laboratory chamber were used to investigate the influence of alfalfa plants on the fate and transport of trichloroethylene (TCE) fed at a concentration of 200 μl/L (~290 mg/L) in the entering groundwater. The dimensions of the chamber were 180 cm in axial length, 35 cm in depth and 10 cm in width. Concentrations of TCE were monitored in the aqueous and gas phases. Evapotranspirational fluxes of TCE from the soil to the headspace of the chamber were also measured. TCE concentration in the solid phase was measured as a function of depth. Mathematical modeling of the fate of TCE was developed assuming rate-independent physical equilibrium partitioning between solid, aqueous, and gas phases. The model included volatilization across a thin atmospheric boundary layer near soil surface. Numerical results were first validated with analytical results for simple cases and then compared with experimental data in the chamber. Results indicated that the water content and air content distributions significantly impact the transport and concentration of TCE in soils.     

Importance of B4 Medium in Determining Organomineralization Potential of Bacterial Environmental Isolates

B4 precipitation medium has been used as the preferred medium for studying mineral precipitation using bacterial strains in vitro since pioneer studies were performed by Boquet and coworkers in 1973. Using this medium, several authors have demonstrated that some environmental isolates were able to precipitate minerals, yet others did not. The main goal of the current study is to understand whether pH and buffer conditions would have a significant effect on mineral precipitation results for environmental isolates grown on B4. For this study, a total of 49 strains isolated from natural environments from Puerto Rico were grown on B4 plates, and their CaCO₃ precipitation potential was investigated. Our findings revealed a strong correlation between a lack of CaCO₃ precipitation and the acidification of the B4 plates by the colonies. The ability to precipitate CaCO₃ could be restored by buffering the B4 medium to a pH of 8.2. Buffering capacity of the medium was proposed to be involved in CaCO₃ precipitation: acid-base titrations conducted on the individual ingredients of B4 showed that yeast extract has a poor buffering capacity between pH 6.5–7.5. This pH range corresponds to the pH of B4 plates [6.87 (±0.05)] prior to the inoculation. This might explain why B4 is such a good precipitation medium: a small variation in the H⁺/OH^? balance during microbial growth and precipitation produces rapid changes in the pH of the medium. Finally, an amorphous matrix was distributed within 90% of the examined crystals generated on B4 medium by the environmental strains. Supplemental materials are available for this article. Go to the publisher's online edition of Geomicrobiology Journal to view the free supplemental file.     

Bacterial cell curvature through mechanical control of cell growth

The cytoskeleton is a key regulator of cell morphogenesis. Crescentin, a bacterial intermediate filament‐like protein, is required for the curved shape of Caulobacter crescentus and localizes to the inner cell curvature. Here, we show that crescentin forms a single filamentous structure that collapses into a helix when detached from the cell membrane, suggesting that it is normally maintained in a stretched configuration. Crescentin causes an elongation rate gradient around the circumference of the sidewall, creating a longitudinal cell length differential and hence curvature. Such curvature can be produced by physical force alone when cells are grown in circular microchambers. Production of crescentin in Escherichia coli is sufficient to generate cell curvature. Our data argue for a model in which physical strain borne by the crescentin structure anisotropically alters the kinetics of cell wall insertion to produce curved growth. Our study suggests that bacteria may use the cytoskeleton for mechanical control of growth to alter morphology.