Quantification of Chemotaxis to Naphthalene by Pseudomonas putida G7

The capillary assay was used to quantify the chemotactic response of Pseudomonas putida G7 to naphthalene. Experiments were conducted in which the cell concentration in the assay chamber, the naphthalene concentration in the capillary, or the incubation time was varied. Data from these experiments were evaluated with a model that accounted for the effect of diffusion on the distribution of substrate and the transport of cells from the chamber through the capillary orifice. By fitting a numerical solution of this model to the data, it was possible to determine the chemotactic sensitivity coefficient, χ₀. The mean of the best-fit values for χ₀ from the three types of experiments was 7.2 × 10⁻⁵ cm²/s. A less computationally intensive model based on earlier approaches that ignore cell transport in the chamber resulted in χ₀ values that were approximately three times higher. The models evaluated in the present study could simulate the results of capillary assays only at low chamber cell concentrations, for which the effect of consumption on the distribution of substrate was negligible. Results from this work suggest that it is possible to use the capillary assay to quantify taxis towards environmentally relevant chemoeffectors that have low aqueous solubility.     

A material-balance approach for modeling bacterial chemotaxis to a consumable substrate in the capillary assay

A mathematical model was developed to simulate the movement of chemotactic bacteria into and within a capillary tube containing a metabolizable chemoattractant. The model was based on a material balance that accounts for the transport of bacteria and chemoattractant as well as consumption of the substrate throughout the capillary assay system. By solving the model with a numerical method, it was possible to predict the concentration of substrate and bacteria at points within the capillary and throughout the chamber. The model was tested for its ability to simulate the results of capillary assay experiments performed with Pseudomonas putida G7 and one of its chemoattractants, naphthalene, under conditions wherein naphthalene consumption was expected to affect the flux of bacteria into the capillary. While variations in the chemotactic responses were evident among different experiments, the model could simulate the accumulation of cells in the capillary using previously determined parameters, including the chemotactic sensitivity and random motility coefficients, chi(0) and mu. In particular, model predictions were consistent with the experimental observation that the chemotactic response in the capillary is diminished under conditions wherein consumption would be expected to be significant.     

Quantitative analysis of experiments on bacterial chemotaxis to naphthalene

A mathematical model was developed to quantify chemotaxis to naphthalene by Pseudomonas putida G7 (PpG7) and its influence on naphthalene degradation. The model was first used to estimate the three transport parameters (coefficients for naphthalene diffusion, random motility, and chemotactic sensitivity) by fitting it to experimental data on naphthalene removal from a discrete source in an aqueous system. The best-fit value of naphthalene diffusivity was close to the value estimated from molecular properties with the Wilke-Chang equation. Simulations applied to a non-chemotactic mutant strain only fit the experimental data well if random motility was negligible, suggesting that motility may be lost rapidly in the absence of substrate or that gravity may influence net random motion in a vertically oriented experimental system. For the chemotactic wild-type strain, random motility and gravity were predicted to have a negligible impact on naphthalene removal relative to the impact of chemotaxis. Based on simulations using the best-fit value of the chemotactic sensitivity coefficient, initial cell concentrations for a non-chemotactic strain would have to be several orders of magnitude higher than for a chemotactic strain to achieve similar rates of naphthalene removal under the experimental conditions we evaluated. The model was also applied to an experimental system representing an adaptation of the conventional capillary assay to evaluate chemotaxis in porous media. Our analysis suggests that it may be possible to quantify chemotaxis in porous media systems by simply adjusting the model's transport parameters to account for tortuosity, as has been suggested by others.     

A simple expression for quantifying bacterial chemotaxis using capillary assay data: application to the analysis of enhanced chemotactic responses from growth-limited cultures.

An individual cell-based mathematical model of Rivero et al. provides a framework for determining values of the chemotactic sensitivity coefficient chi 0, an intrinsic cell population parameter that characterizes the chemotactic response of bacterial populations. This coefficient can theoretically relate the swimming behavior of individual cells to the resulting migration of a bacterial population. When this model is applied to the commonly used capillary assay, an approximate solution can be obtained for a particular range of chemotactic strengths yielding a very simple analytical expression for estimating the value of chi 0, [formula: see text] from measurements of cell accumulation in the capillary, N, when attractant uptake is negligible. A0 and A infinity are the dimensionless attractant concentrations initially present at the mouth of the capillary and far into the capillary, respectively, which are scaled by Kd, the effective dissociation constant for receptor-attractant binding. D is the attractant diffusivity, and mu is the cell random motility coefficient. NRM is the cell accumulation in the capillary in the absence of an attractant gradient, from which mu can be determined independently as mu = (pi/4t)(NRM/pi r2bc)2, with r the capillary tube radius and bc the bacterial density initially in the chamber. When attractant uptake is significant, a slightly more involved procedure requiring a simple numerical integration becomes necessary. As an example, we apply this approach to quantitatively characterize, in terms of the chemotactic sensitivity coefficient chi 0, data from Terracciano indicating enhanced chemotactic responses of Escherichia coli to galactose when cultured under growth-limiting galactose levels in a chemostat.     

Quantification of random motility and chemotaxis bacterial transport coefficients using individual-cell and population-scale assays

A number of individual-cell and population-scale assays have been introduced to quantify bacterial motility and chemotaxis. The transport coefficients reported in the literature, however, span several orders of magnitude, making it difficult to ascertain to what degree variations in bacterial species/strain, growth medium, growth and experimental conditions, and experiment type contribute to the reported differences in coefficient values. We quantified the random motility of Escherichia coli AW405 using the capillary assay, stopped-flow diffusion chamber (SFDC), and tracking microscope. We obtained good agreement for the random motility coefficient between these assays when using the same bacterial strain and consistent growth and experimental conditions. Chemotaxis of E. coli toward the attractant alpha-methylaspartate was quantified using the SFDC and capillary assay. Good agreement for the chemotactic sensitivity coefficient between the SFDC and the capillary assay was obtained across a limited attractant concentration range. Three different mathematical models were considered for analyzing capillary assay data to obtain a chemotactic sensitivity coefficient. These models differed by their treatment of the bacterial concentration in the chamber and the attractant concentration at the mouth. Results from our study indicate that the capillary assay, the most commonly used bacterial random motility and chemotaxis assay, can be used to accurately quantify bacterial transport coefficients over a limited range of attractant concentrations, provided experiments are performed carefully and appropriate mathematical models are used to interpret the experimental data.     

Quantitative relationships between single-cell and cell-population model parameters for chemosensory migration responses of alveolar macrophages to C5a

Phenomenological parameters from a mathematical model of cell motility are used to quantitatively characterize chemosensory migration responses of rat alveolar macrophages migrating to C5a in the linear under-agarose assay, simultaneously at the levels of both single cells and cell populations. This model provides theoretical relationships between single-cell and cell-population motility parameters. Our experiments offer a critical test of these theoretical linking relationships, by comparison of results obtained at the cell population level to results obtained at the single-cell level. Random motility of a cell population is characterized by the random motility coefficient, mu (analogous to a particle diffusion coefficient), whereas single-cell random motility is described by cell speed, s, and persistence time, P (related to the period of time that a cell moves in one direction before changing direction). Population chemotaxis is quantified by the chemotactic sensitivity, chi 0, which provides a measure of the minimum attractant gradient necessary to elicit a specified chemotactic response. Single-cell chemotaxis is characterized by the chemotactic index, CI, which ranges from 0 for purely random motility to 1 for perfectly directed motility. Measurements of cell number versus migration distance were analyzed in conjunction with the phenomenological model to determine the population parameters while paths of individual cells in the same experiment were analyzed in order to determine the single-cell parameters. The parameter mu shows a biphasic dependence on C5a concentration with a maximum of 1.9 x 10(-8) cm2/sec at 10(-11) M C5a and relative minima of 0.86 x 10(-8) cm2/sec at 10(-7) M C5a and 1.1 x 10(-8) cm2/sec in the absence of Ca; s and P remain fairly constant with C5a concentration, with s ranging from 2.1 to 2.5 microns/min and P varying from 22 to 32 min. chi 0 is equal to 1.0 x 10(-6) cm/receptor for all C5a concentrations tested, corresponding to 60% correct orientation for a difference of 500 bound C5a receptors across a 20 microns cell length. The maximum CI measured was 0.2. Values for the population parameters mu and chi 0 were calculated from single-cell parameter values using the aforementioned theoretical linking relationships. The values of mu and chi 0 calculated from single-cell parameters agreed with values of mu and chi 0 determined independently from population migrations, over the full range of C5a concentrations, confirming the validity of the linking equations. Experimental confirmation of such relationships between single-cell and cell-population parameters has not previously been reported.     

Measurement of bacterial random motility and chemotaxis coefficients: I. Stopped-flow diffusion chamber assay

Bacterial chemotaxis, the directed movement of a cell population in response to a chemical gradient, plays a critical role in the distribution and dynamic interaction of bacterial populations in nonmixed systems. Therefore, in order to make reliable predictions about the migratory behavior of bacteria within the environment, a quantitative characterization of the chemotactic response in terms of intrinsic cell properties is needed.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 chemical concentration is imposed on a uniform suspension of bacteria. Once flow is stopped, diffusion causes a transient chemical gradient to develop, and bacteria respond by forming a band of high cell density which travels toward higher concentrations of the attractant. Changes in bacterial spatial distributions observed through light scattering are recorded on photomicrographs during a 10-min period. Computer-aided image analysis converts absorbance of the photographic negatives to a digital representation of bacterial density profiles. A mathematical model (part II) is used to quantitatively characterize these observations in terms of intrinsic cell parameters: a chemotactic sensitivity coefficient, mu(0), from the aggregate cell density accumulated in the band and a random motility coefficient, mu, 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 for Escherichia coli K12 responding to fucose. The values obtained were mu = 1.1 +/- 0. 4 x 10(-5) cm(2)/s and chi(o) = 8 +/- 3 +/- 10(-5) cm(2)/s. We have demonstrated a method capable of determining these parameter values from the now validated mathematical model which will be useful for predicting bacterial migration in application systems.     

Measurement of the chemotaxis coefficient for human neutrophils in the under-agarose migration assay

Clinical and scientific investigations of leukocyte chemotaxis will be greatly aided by an ability to measure quantitative parameters characterizing the intrinsic random motility, chemokinetic, and chemotactic properties of cell populations responding to a given attractant. Quantities typically used at present, such as leading front distances, migrating cell numbers, etc., are unsatisfactory in this regard because their values are affected by many aspects of the assay system unrelated to cell behavioral properties. In this paper we demonstrate the measurement of cell migration parameters that do, in fact, characterize the intrinsic cell chemosensory movement responses using cell density profiles obtained in the linear under-agarose assay. These parameters are the random motility coefficient, mu, and the chemotaxis coefficient, chi, which appear in a theoretical expression for cell population migration. We propose a priori the dependence of chi on attractant concentration, based on an independent experimental correlation of individual cell orientation bias in an attractant gradient with a spatial difference in receptor occupancy. Our under-agarose population migration results are consistent with this proposition, allowing chemotaxis to be reliably characterized by a chemotactic sensitivity constant, chi 0, to which chi is directly proportional. Further, chi 0 has fundamental significance; it represents the reciprocal of the difference in number of bound receptors across cell dimensions required for directional orientation bias. In particular, for the system of human peripheral blood polymorphonuclear neutrophil leukocytes responding to FNLLP, we find that the chemotaxis coefficient is a function of attractant concentration, a following the expression: chi = chi 0NT0 f(a) S(a) Kd/(Kd + a)2 where Kd is the FNLLP-receptor equilibrium dissociation constant and NT0 is the total number of cell surface receptors for FNLLP. f(a) is the fraction of surface receptors remaining after down-regulation, and S(a) is the cell movement speed, both known functions of FNLLP concentration. We find that chi 0NT0 = 0.2 cm; according to a theoretical argument outlined in the Appendix this means that these cells exhibit 75% orientation toward higher attractant concentration when the absolute spatial difference in bound receptors is 0.0025NT0 over 10 micron. (For example, if NT0 = 50,000 this would correspond to a spatial difference of 125 bound receptors over 10 micron.) This result can be compared with estimates obtained from visual studies of individual neutrophils.     

Experimental verification of the behavioral foundation of bacterial transport parameters using microfluidics

We present novel microfluidic experiments to quantify population-scale transport parameters (chemotactic sensitivity χ₀ and random motility μ) of a population of bacteria. Previously, transport parameters have been derived theoretically from single-cell swimming behavior using probabilistic models, yet the mechanistic foundations of this upscaling process have not been verified experimentally. We designed a microfluidic capillary assay to generate and accurately measure gradients of chemoattractant (α-methylaspartate) while simultaneously capturing the swimming trajectories of individual Escherichia coli bacteria using videomicroscopy and cell tracking. By measuring swimming speed and bias in the swimming direction of single cells for a range of chemoattractant concentrations and concentration gradients, we directly computed the chemotactic velocity V_C and the associated chemotactic sensitivity χ₀. We then show how μ can also be readily determined using microfluidics but that a population-scale microfluidic approach is experimentally more convenient than a single-cell analysis in this case. Measured values of both χ₀ [(12.4 ± 2.0) × 10⁻⁴ cm² s⁻¹] and μ [(3.3 ± 0.8) × 10⁻⁶ cm² s⁻¹] are comparable to literature results. This microscale approach to bacterial chemotaxis lends experimental support to theoretical derivations of population-scale transport parameters from single-cell behavior. Furthermore, this study shows that microfluidic platforms can go beyond traditional chemotaxis assays and enable the quantification of bacterial transport parameters.     

Quantification of bacterial chemotaxis by measurement of model parameters using the capillary assay

The capillary assay for quantitative characterization of bacterial motility and chemotaxis is analyzed in terms of a mathematical model for cell population migration, in order to determine values for the cell random motility coefficient, mu and the cell chemotaxis coefficient, chi. The analysis involves both analytical perturbation methods and numerical finite-difference techniques. Transient cell density profiles within the capillary tube are determined as they depend upon mu and chi, providing a means for estimating mu and chi from the common protocol measurements of cell accumulation in the tube at specified observation times. The effects of extraneous factors such as assay geometry, stimulus diffusivity, bacterial density, and observation time are thus separated from the intrinsic cell-stimulus interaction and response. This allows independent population measurements of cell chemosensory movement properties to be extrapolated to situations involving growth and competition of populations, for purposes of better understanding microbial population dynamics in systems of biotechnological and microbial ecological importance.     

Independent prediction of naphthalene transport and biodegradation in soil with a mathematical model.

Experiments were performed to test the ability of a mathematical model to predict naphthalene transport and biodegradation. Pseudomonas putida G7, a model bacterial strain capable of degrading naphthalene, was added to a column packed with the soil that had been pre-equilibrated with naphthalene. Model prediction for transport and degradation were based on predetermined parameters that described naphthalene desorption kinetics and the utilization of naphthalene by the test bacterium. However, initial prediction for naphthalene biodegradation was high, and the formation of cell aggregates is advanced as a plausible explanation. Access of substrate to cells in the interior of an aggregate would be restricted. When the numerical simulation was conducted with a factor to account for cell aggregation, it successfully described the experimental data. Thus, with a single adjustable parameter (an average effectiveness factor), the model predicted macroscopic responses of naphthalene in soil-columns where naphthalene was subject to transport and biodegradation.     

ATP luminescence-based motility-invasion assay

Directional motility and invasion assays are largely based on the use of Boyden chambers or Transwell culture inserts in which porous membranes separate seeded cells from a chemotactic factor supplied in the medium outside the chamber. The major obstaclefor most currently available assays is that they lack a sensitive, easy, and reliable method of quantifying the nonmotile cell populations. Failure to accountfor all cells within the assay chamber prohibits the determination of percentages of migrated cells. Here we describe an ATP luminescence-based motility-invasion (ALMI) assay that circumvents this problem, enabling investigators to quantify directional cell migration or invasiveness easily. The ALMI assay is based on the detection of ATP in viable cells harvested from inert surfaces that do not generate background signals. We demonstrate how the ALMI assay can be used to assess the effects of various experimental conditions such as growth factor stimulation and ethanol exposure on cell migration. In addition, precoating the membranes with extracellular matrix molecules enabled the measurement of the cell invasion. In conclusion, the ALMI assay provides a reliable and flexible method to quantify cell motility and invasiveness using a luminescence microplate reader.     

Chemotaxis of Pseudomonas spp. to the polyaromatic hydrocarbon naphthalene.

Two naphthalene-degrading bacteria, Pseudomonas putida G7 and Pseudomonas sp. strain NCIB 9816-4, were chemotactically attracted to naphthalene in drop assays and modified capillary assays. Growth on naphthalene or salicylate induced the chemotactic response. P. putida G7 was also chemotactic to biphenyl; other polyaromatic hydrocarbons that were tested did not appear to be chemoattractants for either Pseudomonas strain. Strains that were cured of the naphthalene degradation plasmid were not attracted to naphthalene.     

The effect of cell sedimentation on measuring chondrocyte population migration using a Boyden chamber

The Boyden chamber assay provides a convenient method of assessing cell migration and measuring cell motility coefficients at the population level. Previous models of this assay completely ignore cell sedimentation in the suspension, assuming that all cells have already settled on the filter surface before commencing migration within the filter. However, ignoring cell sedimentation could lead to poor data interpretation because the time required for cells to settle through the suspension is close to the incubation period of only a few hours. This study models the Boyden chamber assay by incorporating the cell settling process to account for the cells remaining in the upper well when other cells migrate in the filter. The simulations in this study elucidate the experiments in the literature that test the haptotactic and chemotactic responses of rabbit chondrocytes to type II collagen. This study determines the cell population random motility, as well as the haptotaxis and chemotaxis coefficients, by fitting the experimental data. Results show that the chemotactic motility coefficient is 100 times greater than the haptotactic coefficient, and the equilibrium collagen-receptor dissociation constant is about 10-fold the haptotactic counterpart. Diffusion causes the soluble collagen gradients in the chemotactic case to decline over time, while the coated collagen gradients in the haptotactic assay are likely to remain fixed. As a result, the chemotactic case exhibits a lower number of migrated cells than the haptotactic assay. This study also demonstrates the influences of the dimensionless parameters that control cell behavior in the Boyden assay, providing a reference for future experiment designs.     

Analytical solution to the initial-value problem for traveling bands of chemotactic bacteria

The governing parabolic partial differential equations for the diffusion and chemotactic transport of a distribution of bacteria and for the diffusion and bacterial degradation of a distribution of chemotactic agent are supplemented with boundary and initial conditions that model the recent capillary tube experiments on the formation and propagation of traveling bands of chemotactic bacteria. An iteration procedure that takes the exact solution to the “diffusionless” problem as a first approximation is applied to solve the equations of the complete theoretical model. It is shown that satisfactory agreement with experiment obtains for the analytical results of the first approximation which relate the velocity of propagation and total number of bacteria cells per unit cross-sectional area in a traveling band to the constant parameters in the governing equations and supplementary conditions. The second approximation is shown to yield approximate analytical expressions for the solution functions which are in close correspondence with previously derived traveling band solutions for values of time after the initial period of formation.     

Estimating the efficiency of cell capture and arrest in flow chambers: study of neutrophil binding via E-selectin and ICAM-1

A mathematical model was developed to quantify the efficiency of cell-substrate attachment in the parallel-plate flow chamber. The model decouples the physical features of the system that affect cell-substrate collision rates from the biological features that influence cellular adhesivity. Thus, experimental data on cell rolling and adhesion density are converted into "frequency" parameters that quantify the "efficiency" with which cells in the flow chamber progress from the free stream to rolling, and transition from rolling to firm arrest. The model was partially validated by comparing simulation results with experiments where neutrophils rolled and adhered onto substrates composed of cotransfected cells bearing E-selectin and intercellular adhesion molecule-1 (ICAM-1). Results suggest that: 1) Neutrophils contact the E-selectin substrate on average for 4-8.5s before tethering. This contact duration is insensitive to applied shear stress. 2) At 2 dyn/cm(2), approximately 28% of the collisions between the cells and substrate result in primary capture. Also, approximately 5-7% of collisions between neutrophils in the free stream and previously recruited neutrophils bound on the substrate result in secondary capture. These percentages were higher at lower shears. 3) An adherent cell may influence the flow streams in its vicinity up to a distance of 2.5 cell diameters away. 4) Our estimates of selectin on-rate in cellular systems compare favorably with data from reconstituted systems with immobilized soluble E-selectin. In magnitude, the observed on-rates occur in the order, L-selectin > P-selectin > E-selectin.     

Genetic and biochemical requirements for chemotaxis to L-proline in Escherichia coli.

Chemotaxis to L-proline was examined by the capillary assay, using a set of Escherichia coli strains bearing well-defined defects in the enzymes of proline transport and utilization. Aspartate taxis was measured as a constitutive, control activity whose receptor and transducer requirements are known. Proline chemotaxis showed a pattern of induction more analogous to that of proline dehydrogenase than of that of proline transport, but chemotaxis to proline was eliminated by mutations eliminating either or both of these activities. No response to proline was observed in the absence of a proline concentration gradient or when succinate was provided as an oxidizable carbon source. These data suggest that the chemotactic response to proline results from a direct impact of proline oxidation on the energy metabolism of the cell.     

IGF-I and IGF-II stimulate directed cell migration of bone-marrow-derived human mesenchymal progenitor cells

Insulin-like growth factors (IGFs) are known to be key regulators of bone growth, remodeling, and repair. Since all these processes depend on the recruitment of cells with the potential to be committed to the osteoblastic lineage, we studied possible effects of IGF-I and -II on migration of human mesenchymal progenitor cells (MPC) using a modified Boyden chamber assay. The results were compared to those of primary osteoblasts and in vitro-osteogenic-differentiated MPC. IGF-I and -II stimulated cell migration of all these cell populations in a dose-dependent manner from 1 to 100 ng/mL. The maximal chemotactic index (CI) was 4-5 for MPC and primary osteoblasts and about 3 for in vitro-differentiated MPC. Checkerboard analysis revealed that IGFs stimulated true directed cell migration (chemotaxis) and not simply chemokinesis. Addition of an antibody against the type I IGF receptor (αIR3) completely abolished (MPC) or markedly reduced (primary osteoblasts) the chemotactic effects of each of the IGFs. IGFBP-3 itself had no direct effect, while IGFBP-5 stimulated MPC migration at concentrations of 80 and 160 ng/mL. Parallel application of IGFBP-3 had borderline inhibitory effects while the addition of 40 ng/mL of IGFBP-5 enhanced the chemotactic effect of IGF-I on MPC. In conclusion, our results show that IGF-I and -II are chemotactic factors for MPC and indicate that IGFBP-5 both modulates the IGF-I effect and directly stimulates migration of human mesenchymal progenitor cells.     

A method to select cell populations with enhanced chemotatic activity

Virus-transformed and tumor ceils often show a higher chemotactic activity in comparison to normal cells. Here we show that the blind-well chamber assay is an easy and rapid procedure to select cell populations with enhanced chemotactic activity. Collagen-type-specific antibodies have been applied to analyze the efficiency of cell sorting by the chemotaxis assay.