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.

Transformations in flagellar structure of Rhodobacter sphaeroides and possible relationship to changes in swimming speed.

Rhodobacter sphaeroides is a photosynthetic bacterium which swims by rotating a single flagellum in one direction, periodically stopping, and reorienting during these stops. Free-swimming R. sphaeroides was examined by both differential interference contrast (DIC) microscopy, which allows the flagella of swimming cells to be seen in vivo, and tracking microscopy, which tracks swimming patterns in three dimensions. DIC microscopy showed that when rotation stopped, the helical flagellum relaxed into a high-amplitude, short-wavelength coiled form, confirming previous observations. However, DIC microscopy also revealed that the coiled filament could rotate slowly, reorienting the cell before a transition back to the functional helix. The time taken to reform a functional helix depended on the rate of rotation of the helix and the length of the filament. In addition to these coiled and helical forms, a third conformation was observed: a rapidly rotating, apparently straight form. This form took shape from the cell body out and was seen to form directly from flagella that were initially in either the coiled or the helical conformation. This form was always significantly longer than the coiled or helical form from which it was derived. The resolution of DIC microscopy made it impossible to identify whether this form was genuinely in a straight conformation or was a low-amplitude, long-wavelength helix. Examination of the three-dimensional swimming pattern showed that R. sphaeroides changed speed while swimming, sometimes doubling the swimming speed between stops. The rate of acceleration out of stops was also variable. The transformations in waveform are assumed to be torsionally driven and may be related to the changes in speed measured in free-swimming cells. The roles of and mechanisms that may be involved in the transformations of filament conformations and changes in swimming speed are discussed.

Temperature-sensitive motility of Sulfolobus acidocaldarius influences population distribution in extreme environments.

A three-dimensional tracking microscope was used to quantify the effects of temperature (50 to 80 degrees C) and pH (2 to 4) on the motility of Sulfolobus acidocaldarius, a thermoacidophilic archaeon. Swimming speed and run time increased with temperature but remained relatively unchanged with increasing pH. These results were consistent with reported changes in the rate of respiration of S. acidocaldarius as a function of temperature and pH. Cells exhibited a forward-biased turn angle distribution with a mean of 54 degrees. Cell trajectories during a run were in the shape of right-handed helices. A cellular dynamics simulation was used to test the hypothesis that a population of S. acidocaldarius cells could distribute preferentially in a spatial temperature gradient due to variation in swimming speed. Simulation results showed that a population of cells could migrate from a higher to a lower temperature in the presence of sharp temperature gradients. This simulation result was achieved without incorporating the ability of cells to sense a temporal thermal gradient; thus, the response was not thermotactic. We postulate that this temperature-sensitive motility is one survival mechanism of S. acidocaldarius that allows this organism to move away from lethal hot spots in its hydrothermal environment.

Mathematical models for motile bacterial transport in cylindrical tubes.

Mathematical models considering motile bacterial transport within a geometrically restrictive cylindrical tube were developed. Two macroscopic transport parameters, the random motility coefficient as a self-diffusion coefficient of the cell population and the chemotactic velocity as a chemical-induced velocity, were derived. The three-dimensional cell balance equation was reduced to forms similar to Segel's one-dimensional phenomenological cell balance equations with additional modifications for bacteria-wall interactions. Two conceptually different approaches accounting for such interactions were presented. The first approach parallels treatments in the gas kinetic theory by viewing bacterial interactions with walls as collisions and subsequent diffusive/specular reflections, which led to the Bosanquet formula for the bacterial diffusion coefficient. Based on the experimental observation that bacterial swimming motion is guided by a straight tube, the second approach considered modifications in the bacterial swimming orientation as a consequence of various long-range interactions with the tube surface. A phenomenological turning model capable of aligning bacterial motion along a tube axis was proposed. The model predicts that under the geometrical restriction of a small cylindrical tube, the macroscopic bacterial transport resulting from the proposed turning model can exhibit behavior that ranges from dimensionally reduced diffusion to pure wave propagation, depending on the influence of the tube diameter on the reversal probability in the bacterial swimming motion. Our theoretical model provides explicit equations that explain how such a transition can occur. The predicted results were then qualitatively compared with experimental data from the literature. As a preliminary comparison, we concluded that bacterial transport in cylindrical tubes of diameter 10 micrometers remains in the mode of a dimensionally reduced diffusion, and shifts to a wave motion when the tube diameter decreases to 6 micrometers.

The global turning probability density function for motile bacteria and its applications.

The angular turning probability density distribution for motile bacteria is usually measured in local coordinates and is therefore inconvenient for global analyses of the chemotactic bacterial migration. In this paper we present analytical derivations that convert the local angular turning probability density distribution into a global one. The explicit expression of a reduced global turning probability density function for motile bacteria was derived and its relevant properties were investigated. Depending on the angle variable being intergrated and the integration range, three types of cosine moments were separately defined and studied. Some statistical indices and parameters such as the directional persistence, persistence number, and one-dimensional reversal probability were found to be embedded in the various moments of the reduced global turning probability density function. Applications of the reduced global turning probability and its integrated moments to a three-dimensional cell balance equation in an axisymmetric system were also discussed.

Residence time calculation for chemotactic bacteria within porous media.

Local chemical gradients can have a significant impact on bacterial population distributions within subsurface environments by evoking chemotactic responses. These local gradients may be created by consumption of a slowly diffusing nutrient, generation of a local food source from cell lysis, or dissolution of nonaqueous phase liquids trapped within the interstices of a soil matrix. We used a random walk simulation algorithm to study the effect of a local microscopic gradient on the swimming behavior of bacteria in a porous medium. The model porous medium was constructed using molecular dynamics simulations applied to a fluid of equal-sized spheres. The chemoattractant gradient was approximated with spherical symmetry, and the parameters for the swimming behavior of soil bacterium Pseudomonas putida were based on literature values. Two different mechanisms for bacterial chemotaxis, one in which the bacteria responded to both positive and negative gradients, and the other in which they responded only to positive gradients, were compared. The results of the computer simulations showed that chemotaxis can increase migration through a porous medium in response to microscopic-scale gradients. The simulation results also suggested that a more significant role of chemotaxis may be to increase the residence time of the bacteria in the vicinity of an attractant source.

Interactions between motile Escherichia coli and glass in media with various ionic strengths, as observed with a three-dimensional-tracking microscope.

Escherichia coli bacteria have been observed to swim along a glass surface for several minutes at a time. Settling velocities of nonmotile cells and a computer simulation of motile cells confirmed that an attractive force kept the bacteria near the surface. The goal of this study was to evaluate whether this attractive force could be explained by reversible adhesion of E. coli to the surface in the secondary energy minimum, according to the theory of Derjaguin, Landan, Verwey, and Overbeek (DLVO theory). This theory describes interactions between colloidal particles by combining attractive van der Waals forces with repulsive electrostatic forces. A three-dimensional-tracking microscope was used to follow both wild-type and smooth-swimming E. coli bacteria as they interacted with a glass coverslip in media of increasing ionic strengths, which corresponded to increasing depths of the secondary energy minimum. We found no quantifiable changes with ionic strength for either the tendencies of individual bacteria to approach the surface or the overall times bacteria spent near the surface. One change in bacterial behavior which was observed with the change in ionic strength was that the diameters of the circles which the smooth-swimming bacteria traced out on the glass increased in low-ionic-strength solution.

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.

Turn angle and run time distributions characterize swimming behavior for Pseudomonas putida.

The swimming behavior of Pseudomonas putida was analyzed with a tracking microscope to quantify its run time and turn angle distributions. Monte Carlo computer simulations illustrated that the bimodal turn angle distribution of P. putida reduced collisions with obstacles in porous media in comparison to the unimodal distribution of Escherichia coli.

Implementing therapist-driven protocols.

In January of 1993, as part of a hospital-wide cost-reduction strategy, the University of California San Diego (UCSD) Medical Center Respiratory Care Department implemented a patient-driven protocol program designed to utilize the assessment skills and judgments of respiratory care staff, within physician-approved guidelines. This program produced a 60% reduction in the use of hand-held nebulizer therapy and chest physical therapy in the institution, with a substantial decrease in operational expenses. This article describes key elements of the implementation of protocol-driven programs, provides examples from the UCSD experience, and offers insights gained from others who have been successful agents of change. It describes patient-driven protocols, how they can be implemented, the barriers to and promoters of such protocols, and what the results can be for a respiratory care department.

Determination of effective transport coefficients for bacterial migration in sand columns.

A well-characterized experimental system was designed to evaluate the effect of porous media on macroscopic transport coefficients which are used to characterize the migration of bacterial populations. Bacterial density profiles of Pseudomonas putida PRS2000 were determined in the presence and absence of a chemical attractant (3-chlorobenzoate) gradient within sand columns having a narrow distribution of particle diameters. These experimental profiles were compared with theoretical predictions to evaluate the macroscopic transport coefficients. The effective random motility coefficient, used to quantify migration due to a random process in a porous medium, decreased nearly 20-fold as grain size in the columns decreased from 800 to 80 (mu)m. The effective random motility coefficient (mu)(infeff) was related to the random motility coefficient (mu), measured in a bulk aqueous system, according to (mu)(infeff) = ((epsilon)/(tau))(mu) with porosity (epsilon) and tortuosity (tau). Over the times and distances examined in these experiments, bacterial density profiles were unaffected by the presence of an attractant gradient. Theoretical profiles with the aqueous phase value of the chemotactic sensitivity coefficient (used to quantify migration due to a directed process) were consistent with this result and suggested that any chemotactic effect on bacterial migration was below the detection limits of our assay.

Three-dimensional tracking of motile bacteria near a solid planar surface.

Knowing how motile bacteria move near and along a solid surface is crucial to understanding such diverse phenomena as the migration of infectious bacteria along a catheter, biofilm growth, and the movement of bacteria through the pore spaces of saturated soil, a critical step in the in situ bioremediation of contaminated aquifers. In this study, a tracking microscope is used to record the three-dimensional motion of Escherichia coli near a planar glass surface. Data from the tracking microscope are analyzed to quantify the effects of bacteria-surface interactions on the swimming behavior of bacteria. The speed of cells approaching the surface is found to decrease in agreement with the mathematical model of Ramia et al. [Ramia, M., Tullock, D. L. & Phan-Tien, N. (1993) Biophys J. 65,755-778], which represents the bacteria as spheres with a single polar flagellum rotating at a constant rate. The tendency of cells to swim adjacent to the surface is shown in computer-generated reproductions of cell traces. The attractive interaction potential between the cells and the solid surface is offered as one of several possible explanations for this tendency.

Random walk calculations for bacterial migration in porous media.

Bacterial migration is important in understanding many practical problems ranging from disease pathogenesis to the bioremediation of hazardous waste in the environment. Our laboratory has been successful in quantifying bacterial migration in fluid media through experiment and the use of population balance equations and cellular level simulations that incorporate parameters based on a fundamental description of the microscopic motion of bacteria. The present work is part of an effort to extend these results to bacterial migration in porous media. Random walk algorithms have been used successfully to date in nonbiological contexts to obtain the diffusion coefficient for disordered continuum problems. This approach has been used here to describe bacterial motility. We have generated model porous media using molecular dynamics simulations applied to a fluid with equal sized spheres. The porosity is varied by allowing different degrees of sphere overlap. A random walk algorithm is applied to simulate bacterial migration, and the Einstein relation is used to calculate the effective bacterial diffusion coefficient. The tortuosity as a function of particle size is calculated and compared with available experimental results of migration of Pseudomonas putida in sand columns. Tortuosity increases with decreasing obstacle diameter, which is in agreement with the experimental results.

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.

Comparison of cytology and cervicography in screening a high risk Australian population for cervical human papillomavirus and cervical intraepithelial neoplasia.

Two different screening methods, the Papanicolaou (Pap) smear and cervigram were compared in screening 245 Sydney women over a 6-month period in 1988 at a city sexually transmitted diseases (STD) centre, for cervical human papillomavirus (HPV), cervical intraepithelial neoplasia (CIN) and cervical cancer. The Pap smear through the identification of cytologically abnormal cells correctly detected 54% of cases of histologically proven CIN and 39.2% of cases of HPV. The cervigram through the identification of acetowhite epithelium and/or abnormal vessels on the cervix correctly detected 64% of cases of histologically proven CIN and 70.6% of cases of HPV. However, when both tests were used together, 92% of CIN lesions and 82.4% of HPV lesions were correctly identified. Histology of a colposcopically directed biopsy was used as the 'gold standard'. The sensitivity and specificity of the Pap smear after correction for verification bias was 46% and 78% respectively, and for the cervigram was 49% and 60% respectively. Hence neither screening test appears adequate on its own, at least in an STD population.

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.

Diagnosis and treatment of ossification of the posterior longitudinal ligament of the spine: report of eight cases and literature review.

PURPOSE: Ossification of the posterior longitudinal ligament (OPLL) is a common, well-recognized cause of spinal stenosis and myelopathy in Japan. Although also common in whites, especially among the elderly, it has received little scientific attention. We wish to increase awareness of this important cause of myelopathy, and to determine if the clinical characteristics of OPLL are similar in non-Japanese and Japanese patients. PATIENTS AND METHODS: The clinical and radiologic features of eight cases of OPLL are presented. These cases combined with 73 non-Japanese cases gathered from the English literature are contrasted with 2,125 Japanese cases of OPLL. RESULTS: Similarities among non-Japanese and Japanese cases included: (1) male predominance; (2) peak age at onset of symptoms in the sixth decade; (3) clinical presentation, which ranged from asymptomatic to quadriplegia, with progressive or acute onset of neurologic deterioration; (4) greater than 95% localization to the cervical spine, spastic quadriparesis being the most common neurologic presentation; (5) an association with several rheumatic conditions including diffuse idiopathic skeletal hyperostosis (DISH), spondylosis, and ankylosing spondylitis; and (6) neurologic improvement with either conservative or surgical treatment in a significant proportion of patients. Differences between the two groups were minimal and included a higher mean age at onset (although onset in both groups occurred within the sixth decade) and a greater proportion of patients with DISH and with the continuous type of OPLL in the non-Japanese group. CONCLUSION: The clinical characteristics of OPLL are similar in Japanese and non-Japanese patient populations. Increased awareness of this condition, which has potentially devastating neurologic complications, will favorably influence diagnosis, treatment, and outcome.