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  • 1
    Electronic Resource
    Electronic Resource
    Analysis of chemotactic bacterial distributions in population migration assays using a mathematical model applicable to steep or shallow attractant gradients (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 721-749 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The mathematical model developed by Riveroet al. (1989,Chem. Engng Sci. 44, 2881–2897) is applied to literature data measuring chemotactic bacterial population distributions in response to steep as well as shallow attractant gradients. This model is based on a fundamental picture of the sensing and response mechanisms of individual bacterial cells, and thus relates individual cell properties such as swimming speed and tumbling frequency to population parameters such as the random motility coefficient and the chemotactic sensitivity coefficient. Numerical solution of the model equations generates predicted bacterial density and attractant concentration profiles for any given experimental assay. We have previously validated the mathematical model from experimental work involving a step-change in the attractant gradient (Fordet al., 1991Biotechnol. Bioengng.37, 647–660; For and Lauffenburger, 1991,Biotechnol. Bioengng,37, 661–672). Within the context of this experimental assay, effects of attractant diffusion and consumption, random motility, and chemotactic sensitivity on the shape of the profiles are explored to enhance our understanding of this complex phenomenon. We have applied this model to various other types of gradients with successful intepretation of data reported by Dalquistet al. (1972,Nature New Biol. 236, 120–123) forSalmonella typhimurum validating the mathematical model and supportin the involvement of high and low affinity receptors for serine chemotaxis by these cells.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461551
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  • 2
    Electronic Resource
    Electronic Resource
    Mathematical model for characterization of bacterial migration through sand cores (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 53 (1997), S. 487-496 
    Details
    ISSN: 0006-3592
    Keywords: bacterial chemotaxis ; Escherichia coli ; random motility ; mathematical model ; sand core ; porous media ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: 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. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 53: 487-496, 1997.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Analysis of bacterial swimming speed approaching a solid-liquid interface (1997)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 43 (1997), S. 1341-1347 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Previous experimental studies have found that surface interactions significantly affect the transport of motile bacteria through small tubes, along solid surfaces, and through porous media. However, the role that hydrodynamic forces play in the interactions between solid surfaces and motile bacteria remains unclear. In this study, the swimming speeds of populations of Escherichia coli bacteria were measured near (〈 10 μm) and far (〉10 μm) from a flat glass surface at four ranges of orientations to the surface (0°-45°, 45°-90°, 90°-135°, and 135°-180°). Populations of bacteria close to the surface and moving in the orientation range most perpendicular (0-45°) to the surface experienced the greatest change in the swimming speed when compared to the population in the same orientation range located far from the surface. The decrease in swimming speed experienced by this population was on the same order as that predicted by hydrodynamic models of bacterial swimming near surfaces.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690430523
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  • 4
    Electronic Resource
    Electronic Resource
    Measurement of bacterial random motility and chemotaxis coefficients: II. Application of single-cell-based mathematical model (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 37 (1991), S. 661-672 
    Details
    ISSN: 0006-3592
    Keywords: bacterial chemotaxis ; Escherichia coli ; random motility ; diffusion chamber assay ; mathematical model ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A quantitative description of bacterial chemotaxis is necessary for making predictions about the migratory behavior of bacterial populations in applications such as biofilm development, release of genetically engineered bacteria into the environment, and in situ bioremediation technologies. The bacterial chemotactic response is characterized by a mathematical model which relates individual cell properties such as swimming speed and tumbling frequency to population parameters, specifically the random motility coefficient and the chemotactic sensitivity coefficient. Our model includes a nonlinear dependence of the chemotactic velocity on the attractant gradient as well as a dependence of the random motility coefficient on the temporal and spatial attractant gradients, both of which previous analyses have neglected. As we will show, these aspects are critical for interpreting the results from experiments like those performed in the stopped-flow diffusion chamber (SFDC) because the initial temporal and spatial gradients are very steep. Our analysis demonstrates that values for the random motility coefficient and chemotactic sensitivity coefficient can be obtained from experimental plots of net cell redistribution from initial conditions versus the square root of time. Values for these parameters are determined from experimental measurements of bacterial population distributions in the SFDC as described in the companion article. Using parameter values determined from independent experiments, μ = 1.1 ± 0.4 ± 10-5 cm2/s and χ0 = 8 ± 3 ± 10-5 cm2/s, excellent agreement is found between theoretically predicted bacterial density profiles and actual experimental profiles for Escherichia coli K12 responding to fucose over two orders of magnitude in initial attractant concentration. Thus, our model captures the concentration dependence of this behavioral response satisfactorily in terms of cell population parameters which are derived from individual cell properties and will therefore be useful for making predictions about the migratory behavior of bacterial populations in the environment.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bit.260370708
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  • 5
    Electronic Resource
    Electronic Resource
    Analysis of bacterial migration: I. Numerical solution of balance equation (1994)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 40 (1994), S. 704-715 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Chemotaxis describes the ability of motile bacteria to bias their motion in the direction of increasing gradients of chemicals, usually energy sources, known as attractants. In experimental studies of the migration of chemotactic bacteria, 1-D phenomenological cell balance equations (Rivero et al., 1989) have been used to quantitatively analyze experimental observations (Ford et al., 1991; Ford and Lauffenburger, 1991). While attractive for their simplicity and the ease of solution, they are limited in the strict mathematical sense to the situation in which individual bacteria are confined to motion in one dimension and respond to attractant gradients in one dimension only. Recently, Ford and Cummings (1992) reduced the general 3-D cell balance equation of Alt (1980) to obtain an equation describing the migration of a bacterial population in response to a 1-D attractant gradient. Solutions of this equation for single gradients of attractants are compared to those of 1-D balance equations, results from cellular dynamics simulations (Frymier et al., 1993), and experimental data from our laboratory for E. coli responding to α-methylaspartate. We also investigate two aspects of the experimentally derived expression for the tumbling probability: the effect of different models for the down-gradient swimming behavior of the bacteria and the validity of ignoring the temporal derivative of the attractant concentration.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690400413
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  • 6
    Electronic Resource
    Electronic Resource
    Growth rate effects on fundamental transport properties of bacterial populations (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 42 (1993), S. 1277-1286 
    Details
    ISSN: 0006-3592
    Keywords: chemotaxis ; growth rate ; migration ; bacteria ; transport coefficients ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: 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. © 1993 John Wiley & Sons, Inc.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bit.260421104
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  • 7
    Electronic Resource
    Electronic Resource
    Analysis of bacterial migration: II. Studies with multiple attractant gradients (1995)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 41 (1995), S. 402-414 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Many motile bacteria exhibit chemotaxis, the ability to bias their random motion to ward or away from increasing concentrations of chemical substances which benefit or inhibit their survival, respectively. Since bacteria encounter numerous chemical concentration gradients simulatneously in natural surroundings, it is necessary to know quantitatively how a bacterial population responds in the presence of more than one chemical stimulus to develop predictive mathematical models describing bacterial migration in natural systems. This work evaluates three hypothetical models describing the integration of chemical signals from multiple stimuli: high sensitivity, maximum signal, and simple additivity. An expression for the tumbling probability for individual stimuli (Brown and Berg, 1974) is modified according to the proposed models and incorporated into the cell balance equation for a 1-D attractant gradient (Ford and Cummings, 1992). Random motility and chemotactic sensitivity coefficients, required input parameters for the model, are measured for single stimulus responses. Theoretical predictions with the three signal integration models are compared to the net chemotactic response of Escherichia coli to co- and antidirectional gradients of D-fucose and α-methylaspartate in the stopped-flow diffusion chamber assay. Results eliminate the high-sensitivity model and favor the simple additivity over the maximum signal. None of the simple models, however, accurately predict the observed behavior, suggesting a more complex model with more steps in the signal processing mechanism is required to predict responses to multiple stimuli.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690410221
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  • 8
    Electronic Resource
    Electronic Resource
    Measurement of bacterial random motility and chemotaxis coefficients: I. Stopped-flow diffusion chamber assay (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 37 (1991), S. 647-660 
    Details
    ISSN: 0006-3592
    Keywords: bacterial chemotaxis ; Escherichia coli ; motility, random ; diffusion chamber assay ; mathematical model ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: 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, μ0, from the aggregate cell density accumulated in the band and a random motility coefficient, μ, 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 μ = 1.1 ± 0. 4 × 10-5 cm2/s and χo = 8 ± 3 ± 10-5 cm2/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.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bit.260370707
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