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.     

Spatio-temporal structure of migrating chemotactic band of Escherichia coli. I. Traveling band profile.

We developed a rapid-scanning, light-scattering densitometer by which extensive measurements of band migration speeds and band profiles of chemotactic bands of Escherichia coli in motility buffer both with and without serine have been made. The purpose is to test the applicability of the phenomenological model proposed by Keller and Segel (J. Theor. Biol. 1971. 30:235) and to determine the motility (mu) and chemotactic (delta) coefficients of the bacteria. We extend the previous analytical solution of the simplified Keller-Segel model by taking into account the substrate diffusion which turns out to be significant in the case of oxygen. We demonstrate that unique sets of values of mu and delta can be obtained for various samples at different stages of migration by comparing the numerical solution of the model equation and the experimental data. The rapid-scanning technique also reveals a hitherto unobserved time-dependent fine structure in the bacterial band. We give a qualitative argument to show that the fine structure is an example of the dissipative structure that arises from a nonlinear coupling between the bacterial density and the oxygen concentration gradient. Implications for a further study of the dissipative structure in testing the Keller-Segel model of chemotaxis are briefly discussed.     

Quasi-elastic light-scattering studies of single skeletal muscle fibers.

Measurements were made of the intensity autocorrelation function, g(2)[tau], of light scattered from intact frog muscle fibers. During the tension plateau of an isometric tenanus, scattered field statistics were approximately Gaussian and intensity fluctuations were quasi-stationary. The half time, tau 1/2, for the decay of g(2)[tau] was typically 70 ms at a scattering angle of 30 degrees. The decay rate, 1/tau 1/2, of g(2)[tau] varied roughly linearly with the projection of the scattering vector on the fiber axis. 1/tau 1/2 was greater during the tension creep phase of tetani of highly stretched fibers, but was roughly independent of sarcomere length during the tension plateau. g(2)[tau] measured during rest or on diffraction pattern maxima during isometric contraction were flat with low amplitudes. These results are consistent with a model of a 200-mu m segment of an isometrically contracting fiber in which scattering material possesses relative axial velocities of 1-2 mu m/s accompanied by relative axial displacements greater than 0.1 mu m. The slow (1-2 mu m/s) motion of one portion of the fiber relative to another observed under the microscope (500X) during isometric contraction is consistent with the light-scattering results. Structural fluctuations on the scale of the myofibrillar sarcomere which may arise from asynchronous cycling of cross-bridges must involve relative axial velocities less than 3 mu m/s or relative axial displacements less than 0.05 mu m.     

Quasielastic light scattering from migrating chemotactic bands of Escherichia coli. II. Analysis of anisotropic bacterial motions.

Chemotactic effects of dissolved oxygen on motions of Escherichia coli in a motility buffer solution have been studied by measurements of quasielastic light scattering. Under conditions where the bacteria form a sharp band in an oxygen concentrations gradient created by their metabolism, components of motions along the direction of the gradient and perpendicular to it were studied separately at each point within the band profile. A theoretical model for bacterial self correlation function based on two-state motions has been developed to extract the mean square speed of run motion and the relative probability of twiddle vs. run at each point of the band profile. A combined novel experimental set-up and new data analysis method allowed us to extract also the mean square displacements at short times along and perpendicular to the direction of the gradient. Parameters extracted from the measured correlation functions have been discussed in the framework of the established picture of bacterial motions under chemotaxis.     

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.     

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.     

Cloning, sequencing, and expression in Escherichia coli of the Clostridium tetanomorphum gene encoding beta-methylaspartase and characterization of the recombinant protein.

The gene encoding methylaspartase (EC 4.3.1.2) from Clostridium tetranomorphum has been cloned, sequenced, and expressed in Escherichia coli. The open reading frame (ORF) codes for a polypeptide of 413 amino acid residues (M(r) 45,539) of which seven are cysteine residues. The size of the ORF indicates that methylaspartase is a homodimer rather than an (AB)2 tetramer. The deduced primary structure of the protein shows no homology to enzymes that catalyze similar reactions or, indeed, any convincing homology with any other characterized protein. The recombinant protein is identical to the enzyme isolated directly from C. tetanomorphum as determined by several criteria. The enzyme is obtained in a highly active form (approximately 70% of the activity of the natural enzyme) and migrates as a single band (M(r) 49,000) in SDS-polyacrylamide gels. The kinetic parameters for the deamination of (2S,3S)-3-methylaspartic acid by the natural and recombinant proteins are very similar, and the proteins display identical potassium ion-dependent primary deuterium isotope effects for V and V/K when (2S,3S)-3-methylaspartic acid is employed as the substrate. In accord with the activity of the natural enzyme, the recombinant protein is able to catalyze the slow formation of (2S,3R)-3-methylaspartic acid, the L-erythro-epimer of the natural substrate, from mesaconic acid and ammonia. Earlier work in which the cysteine residues in the protein were labeled with N-ethylmaleimide had indicated that there were eight cysteine residues per protein monomer. One cysteine residue was protected by substrate. Here evidence is forwarded to suggest that the residue that was protected by the substrate is not a cysteine residue but the translation product of a serine codon. Kinetic data indicate that this serine residue may be modified in the active enzyme. The implications of these findings on the mechanism of catalysis are discussed within the context of a few emerging mode of action for methylaspartate ammonia-lyase.     

Tangent simple systems method applied to a precise study of viscoelastic behaviour of human blood

The tangent simple systems (TSS) method, proposed in (1), is applied in order to study the viscoelastic behaviour of human blood in transient flow for a rectangular low shear rate step. The tangent simple systems which were used are Maxwell liquids. These systems allow one to obtain plots of variations of instantaneous values of viscosity coefficient mu, elasticity modulus G and retardation time tau = mu/G of the studied blood samples, as a function of flow duration. Variations of both parameters mu and G versus time are represented by two exponential functions which involve three couples of parameters (mu o, mu infinity), (Go, G infinity) and (tau mu, tau G). These parameters can be considered as the characteristics of each blood sample. Another representation of the results, called the dual rheogram, is also indicated. The dual rheogram enables one to follow the evolution of the blood structure. Several examples of application of the TSS method to normal blood sample and to suspensions of artificially modified red blood cells (RBC) are given.     

Development of an assay to screen for inhibitors of tau phosphorylation by cdk5

A high-throughput assay for tau phosphorylation by cdk5/p25 is described. Full-length recombinant tau was used as a substrate in the presence of saturating adenosine triphosphate (ATP). Using PHF-1, an antibody directed specifically against 2 tau phosphorylation epitopes (serine 396 and serine 404), an enzyme-linked immunosorbent assay (ELISA)-based colorimetric assay was formatted in 384-well plates. The assay was validated by measuring kinetic parameters for cdk5/p25 catalysis and known inhibitors. Rate constants for the site-specific phosphorylations at the PHF-1 epitopes were determined and suggested preferential phosphorylation at these sites. The performance of this assay in a high-throughput format was demonstrated and used to identify inhibitors of tau phosphorylation at specific epitopes phosphorylated by cdk5/p25.     

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.     

Neutrophil motility in extracellular matrix gels: mesh size and adhesion affect speed of migration.

Polymorphonuclear leukocyte (PMN) migration through tissue extracellular space is an essential step in the inflammatory response, but little is known about the factors influencing PMN migration through gels of extracellular matrix (ECM). In this study, PMN migration within reconstituted gels containing collagen type I or collagen type I supplemented with laminin, fibronectin, or heparin was measured by quantitative direct visualization, resulting in a random motility coefficient (mum a quantitative index for rate of cell dispersion) for the migrating cell population. The random motility coefficient in unsupplemented collagen (0.4 mg/ml) gels was approximately 9 x 10(-9) cm2/s. Supplementing gels with heparin or fibronectin produced a significant decrease in mu, even at the lowest concentrations studied (1 microgram/ml fibronectin or 0.4 microgram/ml heparin). At least 100 micrograms/ml of laminin, or 20% of the total gel protein, was required to produce a similar decrease in mu. Scanning electron microscopy revealed two different gel morphologies: laminin or fibronectin appeared to coat the 150-nm collagen fibers whereas heparin appeared to induce fiber bundle formation and, therefore, larger interstitial spaces. The decrease in mu observed in heparin-supplemented gels correlated with the increased mesh size of the fiber network, but the difference observed in mu for fibronectin- and laminin-supplemented gels did not correlate with either mesh size or the mechanical properties of the gel, as determined by rheological measurements. However, PMNs adhered to fibronectin-coated surfaces in greater numbers than to collagen- or laminin-coated surfaces, suggesting that changes in cell adhesion to protein fibers can also produce significant changes in cell motility within an ECM gel.     

A microscopic model of enzyme kinetics.

Many in vivo enzymatic processes, such as those of the tissue factor pathway of blood coagulation, occur in environments with facilitated substrate delivery or enzymes bound to cellular or lipid surfaces, which are quite different from the ideal fluid environment for which the Michaelis-Menten equation was derived. To describe the kinetics of such reactions, we propose a microscopic model that focuses on the kinetics of a single-enzyme molecule. This model provides the foundation for macroscopic models of the system kinetics of reactions occurring in both ideal and nonideal environments. For ideal reaction systems, the corresponding macroscopic models thus derived are consistent with the Michaelis-Menten equation. It is shown that the apparent Km is in fact a function of the mechanism of substrate delivery and should be interpreted as the substrate level at which the enzyme vacancy time equals the residence time of ES-complexes; it is suggested that our microscopic model parameters characterize more accurately an enzyme and its catalytic efficiency than does the classical Km. This model can also be incorporated into computer simulations of more complex reactions as an alternative to explicit analytical formulation of a macroscopic model.     

Dynamic light-scattering study on polymerization process of muscle actin

Globular actin (G-actin) polymerizes into a fibrous form (F-actin) under physiological salt conditions. The polymerization process of muscle actin was studied by a dynamic light-scattering method. The intensity correlation functions G2(tau) of scattered light from a G-actin solution containing 2 mM Tris-HCl (pH 8.0) and 0.1 mM ATP were analyzed by a cumulant expansion method, and the translational diffusion coefficient was determined to be D = (8.07 +/- 0.10) X 10(-7) cm2/s at 20 degrees C. This D value gave a diameter of 5.3 nm for spherical G-actin including a hydration layer. Polymerization of 1-3 mg/ml G-actin in a solution containing 10 mM Tris-HCl (pH 8.0), 0.2 mM ATP and 60 mM KCl was followed by successive measurements of G2(tau) for a data accumulation period of 60-300 s/run. The time evolution of G2(tau) was analyzed by a least-squares fitting to the field correlation function of a multiexponential form g1(tau) = sigma iAi exp(-gamma i tau) with gamma 1 greater than gamma 2 greater than 3 greater than ..., and the static scattering intensity I(t) = mean value of I as a function of time t after initiation of polymerization was decomposed as I(t) = mean value of I sigma iAi. At the early stage of polymerization, a two-exponential fit gave results indicating that component 1 came from G-actin and component 2 from F-actin growing linearly with t. At the middle stage of polymerization, a three-exponential fit gave the results that component 1 came from G-actin and possibly its small oligomers, component 2 from polymers with a number-average length Ln of about 900 nm which was independent of t, and component 3 from 'ghosts' in dynamic light scattering in a semidilute regime. Component 3 was concluded to arise from restricted motions of polymers with lengths much longer than Ln in cages formed by polymers giving component 2, and a fragmentation-elongation process of F-actin was suggested to start at the middle stage of polymerization, resulting in the size redistribution of F-actin.     

Scaling of tree height and trunk diameter as a function of ring number

 Phipps (1967) showed, in suppressed maples and oaks, that on average the cross-sectional area of successive tree rings is independent of ring number. From that empirical result I argued that mean ring width and mean ring diameter scale as the inverse square root and square root, respectively, of ring number (Prothero 1997). Here I give an illustrative argument as to how macroscopic trunk variables may be related quantitatively to microscopic ring variables. First, evidence is presented consistent with the theory of Greenhill (1881) and the empirical evidence of McMahon (1973) that tree height in a diversity of species scales as about the two-thirds power of trunk diameter. Here I report further evidence bearing on the same question. From these combined results I suggest that tree height, and by implication trunk height, and other parameters governing macroscopic tree trunk proportions, can all be expressed as powers of a microscopic variable, namely ring number, where the scaling exponents are all proper fractions. I suggest that at least one of these relationships is, in principle, non-adaptive. Received: 9 June 1998 / Accepted: 4 February 1999     

Cultivation of E. coli in single- and ten-stage tower-loop reactors

E. Coli was cultivated in batch and continuous operations in the presence of an antifoam agent in stirred-tank and in single- and ten-stage airlift tower reactors with an outer loop. The maximum specific growth rate, mu(m), the substrate yield coefficient, Y(x/s), the respiratory quotient, RQ, substrate conversion, U(s), the volumetric mass transfer coefficient, K(L)a, the specific interfacial area, a, and the specific power input, P/V(L), were measured and compared. If a medium is used with a concentration of complex substrates (extracts) 2.5 times higher than that of glucose, a spectrum of C sources is available and cell regulation influences reactor performance. Both mu(m) and Y(X/S), which were evaluated in batch reactors, cannot be used for continuous reactors or, when measured in stirred-tank reactors, cannot be employed for tower-loop reactors: mu(m) is higher in the stirred-tank batch than in the tower-loop batch reactor, mu(m) and Y(x/s) are higher in the continuous reactor than in the batch single-stage tower-loop reactor. The performance of the single-stage is better than that of the ten-stage reactor due to the inefficient trays employed. A reduction of the medium recirculation rate reduces OTR, U(s), Pr, and Y(X/S) and causes cell sedimentation and flocculation. The volumetric mass transfer coefficient is reduced with increasing cultivation time; the Sauter bubble diameter, d(s), remains constant and does not depend on operational conditions. An increase in the medium recirculation rate reduces k(L)a. The specific power input, P/V(L), for the single-stage tower loop is much lower with the same k(L)a value than for a stirred tank. The relationship k(L)a vs. P/V(L) evaluated for model media in stirred tanks, can also be used for cultivations in these reactors.     

Motility evaluation of bull spermatozoa by photon correlation spectroscopy.

Quasi-elastic light scattering techniques are employed to evaluate motility of bovine spermatozoa. The electric field correlation function CE(k, tau) has two components CE(k, tau) = alphafm+(1-alpha)fd, where fm is the correlation function due to motile cells, fd is due to dead cells and alpha is the fraction of motile cells. A function which is a linear combination of the experimentally measured fd and an empirically determined function fm is fit to the CE(k, tau) data. In this way, alpha and the approximate analytic form of fm are determined. The distribution of swimming speeds P(v) is derived from fm using an inverse Fourier sine transform procedure. Results for the time dependence of motility of bull sperm in Hank's balanced salt solution are presented.     

Protein kinase C mu is negatively regulated by 14-3-3 signal transduction proteins

Recent studies have documented direct interaction between 14-3-3 proteins and key molecules in signal transduction pathways like Ras, Cbl, and protein kinases. In T cells, the 14-3-3tau isoform has been shown to associate with protein kinase C theta and to negatively regulate interleukin-2 secretion. Here we present data that 14-3-3tau interacts with protein kinase C mu (PKCmu), a subtype that differs from other PKC members in structure and activation mechanisms. Specific interaction of PKCmu and 14-3-3tau can be shown in the T cell line Jurkat by immunocoprecipitiation and by pulldown assays of either endogenous or overexpressed proteins using PKCmu-specific antibodies and GST-14-3-3 fusion proteins, respectively. Using PKCmu deletion mutants, the 14-3-3tau binding region is mapped within the regulatory C1 domain. Binding of 14-3-3tau to PKCmu is significantly enhanced upon phorbol ester stimulation of PKCmu kinase activity in Jurkat cells and occurs via a Cbl-like serine containing consensus motif. However, 14-3-3tau is not a substrate of PKCmu. In contrast 14-3-3tau strongly down-regulates PKCmu kinase activity in vitro. Moreover, overexpression of 14-3-3tau significantly reduced phorbol ester induced activation of PKCmu kinase activity in intact cells. We therefore conclude that 14-3-3tau is a negative regulator of PKCmu in T cells.     

Kinetic and structural insight into the mechanism of BphD, a C-C bond hydrolase from the biphenyl degradation pathway

Kinetic and structural analyses of 2-hydroxy-6-oxo-6-phenylhexa-2,4-dienoic acid (HOPDA) hydrolase from Burkholderia xenovorans LB400 (BphD(LB400)) provide insight into the catalytic mechanism of this unusual serine hydrolase. Single turnover stopped-flow analysis at 25 degrees C showed that the enzyme rapidly (1/tau(1) approximately 500 s(-1)) transforms HOPDA (lambda(max) = 434 nm) into a species with electronic absorption maxima at 473 and 492 nm. The absorbance of this enzyme-bound species (E:S) decayed in a biphasic manner (1/tau(2) = 54 s(-1), 1/tau(3) = 6 s(-1) approximately k(cat)) with simultaneous biphasic appearance (48 and 8 s(-1)) of an absorbance band at 270 nm characteristic of one of the products, 2-hydroxypenta-2,4-dienoic acid (HPD). Increasing solution viscosity with glycerol slowed 1/tau(1) and 1/tau(2) but affected neither 1/tau(3) nor k(cat), suggesting that 1/tau(2) may reflect diffusive HPD dissociation, and 1/tau(3) represents an intramolecular event. Product inhibition studies suggested that the other product, benzoate, is released after HPD. Contrary to studies in a related hydrolase, we found no evidence that ketonized HOPDA is partially released prior to hydrolysis, and, therefore, postulate that the biphasic kinetics reflect one of two mechanisms, pending assignment of E:S (lambda(max) = 492 nm). The crystal structures of the wild type, the S112C variant, and S112C incubated with HOPDA were each determined to 1.6 A resolution. The latter reveals interactions between conserved active site residues and the dienoate moiety of the substrate. Most notably, the catalytic residue His265 is hydrogen-bonded to the 2-hydroxy/oxo substituent of HOPDA, consistent with a role in catalyzing ketonization. The data are more consistent with an acyl-enzyme mechanism than with the formation of a gem-diol intermediate.