Irreversible enzyme-shuttle immunoassay

The concept of a competitive enzyme immunoassay that utilizes simultaneously the bound and the free analyte-enzyme conjugate (heterobifunctional conjugate) for signal generation in response to varying analyte concentrations in samples has been investigated. Two antigenic sites of the heterobifunctional conjugate are used in the assay for binding to immunoglobulins: the analyte derivative binds to an immobilized antibody, Ab(1), and the enzyme component binds to a spatially separated immobilized antibody, Ab(2). The analytical system is set up such that in the absence of analyte, the conjugate is predominantly bound in the compartment that contains Ab(1). With increasing concentration of native analyte in samples, an increasing concentration of native analyte in samples, an increasing amount of conjugate migrates to the second compartment that contains Ab(2). The enzyme bound in each compartment is used for signal generation. Mathematical models have been developed to determine the optimal conditions and to predict the performance of such dual-antibody systems. The theoretical predictions are supported by experimental results. The dual-antibody system has been compared with a conventional competitive enzyme immunoassay using the same reagents.     

Effect of hydrogen sulfide on growth of sulfate reducing bacteria

A culture of sulfate reducing bacteria (SRB) growing on lactate and sulfate was incubated at different pH values in the range of 5.8-7.0. The effect of pH on growth rate was determined in this pH range; the highest growth rate was observed at pH 6.7. Hydrogen sulfide produced from sulfate reduction was found to have a direct and reversible toxicity effect on the SRB. A hydrogen sulfide Concentration of 547 mg/L (16.1 mM) completely inhibited the culture growth. Comparison between acetic acid and hydrogen sulfide inhibition is presented and the concomitant inhibition kinetics are mathematically described. (c) 1992 John Wiley & Sons, Inc.     

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.     

A model for light-limited continuous cultures: growth, shading, and maintenance

Light-limited growth in continuous cultures of phototrophic organisms is modeled. It is assumed that light energy up-take rate depends hyperbolically on light intensity and that the maintenance costs are proportional to biomass. Modeling the light distribution caused by shading within the vessel is necessary to explain the existence of steady state in light-limited chemostats. The model fits well to experimental data from literature on light-limited chemostats and turbidostats. Attention is given to the implications of the model for the estimation of the specific maintenance rate constant in light-limited continuous cultures.     

Competitive exclusion through reproductive interference

A simple differential equation model was developed to describe the competitive interaction that may occur between species through reproductive interference. The model has the form comparable to Volterra's competition equations, and the graphical analysis of the outcome of the two-species interaction based on its zero-growth isoclines proved that: (1) The possible outcome in this model, as in usual models of resource competition, is either stable coexistence of both species or gradual exclusion of one species by the other, depending critically upon the values of the activity overlapping coefficient c_ij; (2) but, for the same c_ij-values, competitive exclusion is much more ready to occur here than in resource competition; (3) and moreover, the final result of the competition is always dependent on the initial-condition due to its non-linear isoclines, i.e., even under the parameter condition that generally allows both species to coexist, an extreme bias in intial density to one species can readily cause subsequent complete exclusion of its counterparts. Thus, it may follow that the reproductive interference is likely to be working in nature as an efficient mechanism to bring about habitat partitioning in either time or space between some closely related species in insect communities, even though they inhabit heterogeneous habitats where resource competition rarely occurs so that they could otherwise attain steady coexistence.     

The random walk description for isotope exchange in a polypeptide

Isotope exchange in a polypeptide is considered from the point of view in which the boundary point between helix and coil regions of a polypeptide behaves like a weakly asymmetric random walker. We assume that the boundary point is reflected completely at the ends of a polypeptide. The equilibrium fraction of helix region is obtained under this assumption, and this is also confirmed by computer simulation. The experimental results of isotope exchange can be explained in this situation. On the other hand. the rate constant of exchange of a residue given by experiments can also be explained by another assumption, as considered before (M. Fujiwara and N. Saitô, Polym. J. 9 (1977) 625.), in which the nucleations of coil states take place in the helix region. Which of the two is of major importance is left to further studies.     

Age-dependent population diffusion with external constraint

We present a simple model for age dependent population diffusion when the dynamics is submitted to external constraints. Existence, uniqueness and dependence on the parameters of the solution are discussed.This work has been done within the framework of the cultural agreement between the Universities of Bordeaux and Rome     

Seed dispersal in a patchy environment with global age dependence

A model of seed population dynamics proposed by S. A. Levin, A. Hastings, and D. Cohen is presented and analyzed. With the environment considered as a mosaic of patches, patch age is used along with time as an independent variable. Local dynamics depend not only on the local state, but also on the global environment via dispersal modelled by an integral over all patch ages. Basic technical properties of the time varying solutions are examined; necessary and sufficient conditions for nontrivial steady states are given; and general sufficient conditions for global asymptotic stability of these steady states are established. Primary tools of analysis include a hybrid Picard iteration, fixed point methods, monotonicity of solution structure, and upper and lower solutions for differential equations.This work was supported in part by National Science Foundation Grants MCS-7903497 and MCS-790349701