Analytical solutions for distributions of chemotactic bacteria

This paper reports general and specialized results on analytical solutions to the governing phenomenological equations for chemotactic redistribution and population growth of motile bacteria. It is shown that the number of bacteria cells per unit volume,b, is proportional to a certain prescribed function ofs, the concentration of the critical substrate chemotactic agent, for steady-state solutions through an arbitrary spatial region with a boundary that is impermeable to bacteria cell transport. Moreover, it is demonstrated that the steady-state solution forb ands is unique for a prescribed total number of bacteria cells in the spatial region and a generic Robin boundary condition ons. The latter solution can be approximated to desired accuracy in terms of the Poisson-Green's function associated with the spatial region. Also, as shown by example, closed-form exact steady-state solutions are obtainable for certain consumption rate functions and geometrically symmetric spatial regions. A solutional procedure is formulated for the initialvalue problem in cases for which significant population growth is present and bacteria cell redistribution due to motility and chemotactic flow proceeds slowly relative to the diffusion of the chemoattractant substrate. Finally, a remarkably simple exact analytical solution is reported for a stradily propagating plane-wave which features motility, chemotactic motion and bacteria population growth regulated by substrate diffusion.     

Localized bacterial infection in a distributed model for tissue inflammation

Phagocyte motility and chemotaxis are included in a distributed mathematical model for the inflammatory response to bacterial invasion of tissue. Both uniform and non-uniform steady state solutions may occur for the model equations governing bacteria and phagocyte densities in a macroscopic tissue region. The non-uniform states appear to be more dangerous because they allow large bacteria densities concentrated in local foci, and in some cases greater total bacteria and phagocyte populations. Using a linear stability analysis, it is shown that a phagocyte chemotactic response smaller than a critical value can lead to a non-uniform state, while a chemotactic response greater than this critical value stabilizes the uniform state. This result is the opposite of that found for the role of chemotaxis in aggregation of slimemold amoebae because, in the inflammatory response, the chemotactic population serves as an inhibitor rather than an activator. We speculate that these non-uniform steady states could be related to the localized cell aggregation seen in chronic granulomatous inflammation. The formation of non-uniform states is not necessarily a consequence of defective phagocyte chemotaxis, however. Rather, certain values of the kinetic parameters can yield values for the critical chemotactic response which are greater than the normal response.Numerical computations of the transient inflammatory response to bacterial challenge are presented, using parameter values estimated from the experimental literature wherever possible.     

Chemotaxis by Naegleria fowleri for Bacteria1

Naegleria fowleri amebae demonstrated a chemotactic and chemokinetic response toward live cells and extracts of Escherichia coli and other bacterial species when experiments were performed using a blind-well chemotaxis chamber. The peptide N-formyl-methionyl-leucyl-phenylalanine acted as a chemokinetic rather than a chemotactic factor for N. fowleri amebae. Competition experiments in which nerve cell extracts or bacteria were placed on either side of the filter in chemotaxis chambers resulted in increased movement towards bacteria. A scanning electron microscopy study of the interaction of N. fowleri with different bacterial species confirmed that when the amebae were near ingestible bacteria they moved toward the bacteria by pseudopod formation. Naegleria fowleri appeared to respond to bacteria by three interrelated but distinct processes: (a) chemokinesis, (b) chemotaxis, and (c) formation of food cups.     

Relation between chemotaxis and consumption of amino acids in bacteria

Chemotaxis enables bacteria to navigate chemical gradients in their environment, accumulating toward high concentrations of attractants and avoiding high concentrations of repellents. Although finding nutrients is likely to be an important function of bacterial chemotaxis, not all characterized attractants are nutrients. Moreover, even for potential nutrients, the exact relation between the metabolic value of chemicals and their efficiency as chemoattractants has not been systematically explored. Here we compare the chemotactic response of amino acids with their use by bacteria for two well‐established models of chemotactic behavior, Escherichia coli and Bacillus subtilis. We demonstrate that in E. coli chemotaxis toward amino acids indeed strongly correlates with their utilization. However, no such correlation is observed for B. subtilis, suggesting that in this case, the amino acids are not followed because of their nutritional value but rather as environmental cues.     

Chemical characterization of root exudates from rice (Oryza sativa) and their effects on the chemotactic response of endophytic bacteria

Root exudates represent an important source of nutrients for microorganisms in the rhizosphere and seem to participate in early colonization inducing chemotactic responses of rhizospheric bacteria. We characterized the root exudates collected from rice plantlets cultured under hydroponic conditions and assessed their effects on the chemotaxis of two strains of endophytic bacteria, Corynebacterium flavescens and Bacillus pumilus, collected from the rice rhizosphere. We compared these chemotactic effects on endophytic bacteria with those on two strains of plant-growth-promoting bacteria, Azospirillum brasilense (isolated from the corn rhizosphere) and Bacillus sp. (from the rice rhizosphere). The root exudates were collected at different time intervals. The highest concentration and diversity of amino acids and carbohydrates were found during the first 2 weeks after seeding. Histidine, proline, valine, alanine, and glycine were the main amino acid residues identified during the 4 weeks of culture. The main carbohydrates identified were glucose, arabinose, mannose, galactose, and glucuronic acid. The chemotactic responses of the analyzed endophytic bacteria to root exudates were 3.9 to 5.1 times higher than those of A. brasilense and 2.2 to 2.8 times higher than Bacillus sp. Our results indicate that rice exudates may induce a higher chemotactic response for endophytic bacteria than for other bacterial strains present in the rice rhizosphere.     

Chemosensory Responses of Acanthamoeba castellanii: Visual Analysis of Random Movement and Responses to Chemical Signals

A visual assay slide chamber was used in conjunction with time-lapse videomicroscopy to analyze chemotactic behavior of axenically grown Acanthamoeba castellanii. Data were collected and analyzed as vector scatter diagrams and cell tracks. Amebas responded to a variety of bacterial products or potential bacterial products by moving actively toward the attractant. Responses to the chemotactic peptide formyl-methionyl-leucyl-phenylalanine (fMLP), lipopolysaccharide, and lipid A were statistically significant (P≤ 0.03), as was the response to fMLP benzylamide (P≤ 0.05). Significant responses to cyclic AMP, lipoteichoic acid, and N-acetyl glucosamine were also found. Chemotactic peptide antagonists, mannose, mannosylated bovine serum albumin, and N-acetyl muramic acid all yielded nonsignificant responses (P > 0.05). There was no single optimal concentration for response to any of the attractants tested, and amebas responded equally over the range of concentrations tested. Pretreatment of amebas with chemotactic peptides, bacterial products, and bacteria reduced the directional response to attractants. Amebas that had been grown in the presence of bacteria appeared more responsive to chemotactic peptides. Treatment of amebas with trypsin reduced the response of cells to chemotactic peptides, though sensitivity was restored within a couple of hours. This suggests the ameba membrane may have receptors, sensitive to these bacterial substances, which are different from the mannose receptors involved in binding bacteria to the membrane during phagocytosis. The rate of movement was relatively constant (ca. 0.40 μm/s), indicating that the locomotor response to these signals is a taxis, or possibly a klinokinesis, but not an orthokinesis. Studies of the population diffusion rate in the absence of signals indicate that the basic population motility follows the pattern of a Levy walk, rather than the more familiar Gaussian diffusion. This suggests that the usual mathematical models of ameboid dispersion may need to be modified.     

Growth rate effects on fundamental transport properties of bacterial populations

In many natural environments, bacterial populations experience suboptimal growth due to the competition with other microorganisms for limited resources. The chemotactic response provides a mechanism by which bacterial populations can improve their situation by migrating toward more favorable growth conditions. For bacteria cultured under suboptimal growth conditions, evidence for an enhanced chemotactic response has been observed previously. In this article, for the first time, we have quantitatively characterized this behavior in terms of two macroscopic transport coefficients, the random motility and chemotactic sensitivity coefficients, measured in the stopped-flow diffusion chamber assay. Escherichia coli cultured over a range of growth rates in a chemostat exhibits a dramatic increase in the chemotactic sensitivity coefficient for D-fucose at low growth rates, while the random motility coefficient remains relatively constant by comparison. The change in the chemotactic sensitivity coefficient is accounted for by an independently measured increase in the number of galactose-binding proteins which mediate the chemotactic signal. This result is consistent with the relationship between macroscopic and microscopic parameters for chemotaxis, which was proposed in the mathematical model of Rivero and co-workers. (c) 1993 John Wiley & Sons, Inc.     

Stopped-flow chamber and image analysis system for quantitative characterization of bacterial population migration: Motility and chemotaxis ofEscherichia coli K12 to fucose

The directed movement of a bacterial population in response to a chemical gradient is known as bacterial chemotaxis and plays a critical role in the distribution and dynamic interaction of bacterial populations. A quantitative characterization of the chemotactic response in terms of intrinsic cell properties is necessary for making reliable predictions about the migratory behavior of bacterial populations within the environment. The design of the stopped-flow diffusion chamber (SFDC) provides a well-characterized chemical gradient and reliable method for measuring bacterial migration behavior. During flow through the chamber a step change in the chemical concentration is imposed on a uniform suspension of bacteria. Once flow is stopped a transient chemical gradient forms due to diffusion; bacteria respond by forming a band of high cell density that travels toward higher concentrations of the attractant. Sequential observations of bacterial spatial distributions over a period of about ten minutes are recorded on photomicrographs. Computer-aided image analysis of the photographic negatives converts light-scattering information to a digital representation of the bacterial density profiles. A mathematical model is used to quantitatively characterize these observations in terms of intrinsic cell parameters: a chemotactic sensitivity coefficient, χ₀, from the aggregate cell density accumulated in the band and a random motility coefficient, μ₀, from population dispersion in the absence of a chemical gradient. Using the SFDC assay and an individual cell-based mathematical model we successfully determined values for both of these population parameters forEscherichia coli K12 responding to fucose. The values we obtained were μ₀=1.1 ± 0.4 x 10^-5 cm²/sec and χ₀=8 ± 3 x 10^-5 cm²/sec. These parameters will be useful for predicting population behavior in application systems such as biofilm development, population dynamics of genetically-engineered bacteria released into the environment, and in situ bioremediation technologies.     

Bacterial chemotaxis transverse to axial flow in a microfluidic channel

Swimming bacteria sense and respond to chemical signals in their environment. Chemotaxis is the directed migration of a bacterial population toward increasing concentrations of a chemical that they perceive to be beneficial to their survival. Bacteria that are indigenous to groundwater environments exhibit chemotaxis toward chemical contaminants such as hydrocarbons, which they are also able to degrade. This phenomenon may facilitate bioremediation processes by bringing bacteria into closer proximity to these contaminants. A microfluidic device was assembled to study chemotaxis transverse to advective flow. Using a T-shaped channel design (T-sensor), two fluid streams were brought into contact by impinging flow. They then flowed adjacent to each other along a transparent channel. An advantage to this design is that it allows real-time visualization of bacterial distributions within the channel. Under laminar flow conditions a chemotactic driving force was created perpendicular to the direction of flow by diffusion of the chemical attractant from one input stream to the other. A comparison of the chemotactic band behavior in the absence and presence of flow showed that fluid velocity did not significantly impede chemotactic migration in the transverse direction.     

Chemotaxis increases vertical migration and apparent transverse dispersion of bacteria in a bench-scale microcosm

The success of in situ bioremediation is often limited by the inability to bring bacteria in contact with the pollutant, which they will degrade. A bench-scale model aquifer was used to evaluate the impact of chemotaxis on the migration of bacteria toward the source of a chemical pollutant. The model was packed with sand and aqueous media was pumped across horizontally, simulating groundwater flow in a homogenous aquifer. A vertical gradient in chemoattractant was created by either a continuous injection of sodium benzoate or a pulse injection of sodium acetate. A pulse of chemotactic Pseudomonas putida F1 or a non-chemotactic mutant of the same species was injected below the attractant. The eluent was sampled at the microcosm outlet to generate vertical concentration profiles of the bacteria and chemoattractant. Moment analysis was used to determine the center and variance of the bacterial profiles. The center of the chemotactic bacterial population was located at an average of 0.74 ± 0.07 cm closer to the level at which the chemoattractant was injected than its non-chemotactic mutant in benzoate experiments (P < 0.015) and 0.4 ± 0.2 cm closer in acetate experiments (P < 0.05). The transverse dispersivity of the chemotactic bacteria was 4 ± 1 × 10(-3) cm higher in benzoate experiments than the transverse dispersivity of the non-chemotactic mutant and 1 ± 2 × 10(-3) cm higher in acetate experiments. These results underscore the contribution of chemotaxis to improve transport of bacteria to contaminant sources, potentially enhancing the effectiveness of in situ bioremediation.     

Flagellin phase‐dependent swimming on epithelial cell surfaces contributes to productive Salmonella gut colonisation

The flagellum is a sophisticated nanomachine and an important virulence factor of many pathogenic bacteria. Flagellar motility enables directed movements towards host cells in a chemotactic process, and near‐surface swimming on cell surfaces is crucial for selection of permissive entry sites. The long external flagellar filament is made of tens of thousands subunits of a single protein, flagellin, and many Salmonella serovars alternate expression of antigenically distinct flagellin proteins, FliC and FljB. However, the role of the different flagellin variants during gut colonisation and host cell invasion remains elusive. Here, we demonstrate that flagella made of different flagellin variants display structural differences and affect Salmonella's swimming behaviour on host cell surfaces. We observed a distinct advantage of bacteria expressing FliC‐flagella to identify target sites on host cell surfaces and to invade epithelial cells. FliC‐expressing bacteria outcompeted FljB‐expressing bacteria for intestinal tissue colonisation in the gastroenteritis and typhoid murine infection models. Intracellular survival and responses of the host immune system were not altered. We conclude that structural properties of flagella modulate the swimming behaviour on host cell surfaces, which facilitates the search for invasion sites and might constitute a general mechanism for productive host cell invasion of flagellated bacteria.     

Chemotaxis of Ralstonia sp. SJ98 towards p-nitrophenol in soil

Bioremediation of contaminated sites has been accepted as an efficient and cheaper alternative to physicochemical means of remediation in several cases. Although chemotactic behaviour of many bacteria has been studied earlier and assays have been developed to study bacterial chemotaxis in semi-solid media, this phenomenon has never been demonstrated in soil. For bioremediation application it is important to know whether bacteria actually migrate through the heterogenous soil medium towards a gradient of a particular chemoattractant. In the present study we have successfully demonstrated bacterial chemotaxis of a Ralstonia sp. SJ98 in soil microcosm using qualitative and quantitative plate and tray assays. The migration of bacteria has been established using several methods such as plate counting, vital staining and flow cytometry and slot blot hybridization. A non-chemotactic p-nitrophenol utilizing strain Burkholderia cepacia RKJ200 has been used as negative control. Our work clearly substantiates the hypothesis that chemotactic bacteria may enhance in situ bioremediation of toxic pollutants from soils and sediments.     

Response of Bdellovibrio and Like Organisms (BALOs) to the Migration of Naturally Occurring Bacteria to Chemoattractants

A dual culture-based and non–culture-based approach was applied to characterize predator bacterial groups in surface water samples collected from Apalachicola Bay, Florida. Chemotaxis drop assays were performed on concentrated samples in an effort to isolate predator bacteria by their chemotactic ability. Yeast extract (YE) and casamino acids (CA) proved to be strong chemoattractants and resulted in three visibly distinct bands; however, dextrose, succinate, pyruvate, and concentrated cells of Vibrio parahaemolyticus P5 as prey did not elicit any response. The three distinct bands from YE and CA were separately collected to identify the chemotactic microbial assemblages. Plaque-forming unit assays from different chemotaxis bands with P5 as prey indicated 5- (CA) to 10-fold (YE) higher numbers of predator bacteria in the outermost chemotactic bands. Polymerase chain reaction–restriction fragment length polymorphism and 16S rDNA sequencing of clones from different chemotaxis bands resulted in identification of Pseudoalteromonas spp., Marinomonas spp., and Vibrio spp., with their numbers inversely proportional to the numbers of predators—i.e., Bdellovibrio spp. and Bacteriovorax spp—in the chemotaxis bands. This study indicates that predatorial bacteria potentially respond to high densities of microbial biomass in aquatic ecosystems and that chemotaxis drop assay may be an alternate culture-independent method to characterize predatorial bacterial guilds from the environment.     

Bacterial chemotaxis toward a NAPL source within a pore-scale microfluidic chamber

Chemotaxis toward chemical pollutants provides a mechanism for bacteria to migrate to locations of high contamination, which may improve the effectiveness of bioremediation. A microfluidic device was designed to mimic the dissolution of an organic-phase contaminant from a single pore into a larger macropore representing a preferred pathway for microorganisms that are carried along by groundwater flow. The glass windows of the microfluidic device allowed direct image analysis of bacterial distributions within the vicinity of the organic contaminant. Concentrations of chemotactic bacteria P. putida F1 near the organic/aqueous interface were 25% greater than those of a nonchemotactic mutant in the vicinity of toluene for a fluid velocity of 0.5 m/d. For E. coli responding to phenol, the bacterial concentrations were 60% greater than the controls, also at a velocity of 0.5 m/d. Velocities in the macropore were varied over a range from 0.5 to 10 m/d, the lower end of which is typical of groundwater velocities. The accumulation of chemotactic bacteria near the NAPL chemoattractant source decreased as the fluid velocity increased. Good agreement between computer-based simulations, generated using reasonable values of the model parameters, and the experimental data for P. putida strains confirmed the contribution due to chemotaxis. The experimental data for E. coli required a larger chemotactic sensitivity coefficient than that for P. putida, which was consistent with parameter values reported in the literature.     

Cell balance equation for chemotactic bacteria with a biphasic tumbling frequency

Alts three-dimensional cell balance equation characterizing the chemotactic bacteria was analyzed under the presence of one-dimensional spatial chemoattractant gradients. Our work differs from that of others who have developed rather general models for chemotaxis in the use of a non-smooth anisotropic tumbling frequency function that responds biphasically to the combined temporal and spatial chemoattractant gradients. General three-dimensional expressions for the bacterial transport parameters were derived for chemotactic bacteria, followed by a perturbation analysis under the planar geometry. The bacterial random motility and chemotaxis were summarized by a motility tensor and a chemotactic velocity vector, respectively. The consequence of invoking the diffusion-approximation assumption and using intrinsic one-dimensional models with modified cellular swimming speeds was investigated by numerical simulations. Characterizing the bacterial random orientation after tumbles by a turn angle probability distribution function, we found that only the first-order angular moment of this turn angle probability distribution is important in influencing the bacterial long-term transport. Mathematics Subject Classification (2000):60G05, 60J60, 82A70     

Finite time blow-up in some models of chemotaxis

We consider a class of models of chemotactic bacterial populations, introduced by Keller-Segel. For those models, we investigate the possibility of chemotactic collapse, in other words, the possibility that in finite time the population of predators aggregates to form a delta-function. To study this phenomenon, we construct self-similar solutions, which may or may not blow-up (in finite time), depending on the relative strength of three mechanisms in competition: (i) the chemotactic attraction of bacteria towards regions of high concentration in substrate (ii) the rate of consumption of the substrate by the bacteria and (iii) (possibly) the diffusion of bacteria. The solutions we construct are radially symmetric, and therefore have no relation with the classical traveling wave solutions. Our scaling can be justified by a dimensional analysis. We give some evidence of numerical stability.     

Mathematical model for characterization of bacterial migration through sand cores

The migration of chemotactic bacteria in liquid media has previously been characterized in terms of two fundamental transport coefficients-the random motility coefficient and the chemotactic sensitivity coefficient. For modeling migration in porous media, we have shown that these coefficients which appear in macroscopic balance equations can be replaced by effective values that reflect the impact of the porous media on the swimming behavior of individual bacteria. Explicit relationships between values of the coefficients in porous and liquid media were derived. This type of quantitative analysis of bacterial migration is necessary for predicting bacterial population distributions in subsurface environments for applications such as in situ bioremediation in which bacteria respond chemotactically to the pollutants that they degrade.We analyzed bacterial penetration times through sand columns from two different experimental studies reported in the literature within the context of our mathematical model to evaluate the effective transport coefficients. Our results indicated that the presence of the porous medium reduced the random motility of the bacterial population by a factor comparable to the theoretical prediction. We were unable to determine the effect of the porous medium on the chemotactic sensitivity coefficient because no chemotactic response was observed in the experimental studies. However, the mathematical model was instrumental in developing a plausible explanation for why no chemotactic response was observed. The chemical gradients may have been too shallow over most of the sand core to elicit a measurable response. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 53: 487-496, 1997.     

A Note on the Possible Ecological Significance of Chemotaxis in Certain Ciliated Protozoa1

ABSTRACT. A heat-stable chemoattractant has been isolated from bacterial cultures. This component has a molecular weight in the range of 500–1000 daltons, is produced by both Gram-positive and Gram-negative bacteria, and serves equally well as an attractant for both the bacterial feeding Paramecium and for its natural predator, Didinium. Aspects of the ecological relationship between bacterial feeding ciliates and their ciliate predators are briefly discussed with respect to responses of both predator and prey to such a common chemotactic bacterial factor.