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PubMedDate not supplied

Use of a diffusion model for mono- and bicomponent anion-exchange of two isoenzymes of glucoamylase from Aspergillus niger in a fixed bed.

The adsorption of glucoamylases I and II (GA I and GA II, respectively) from Aspergillus niger on the anion exchanger DEAE-Toyopearl 650 was studied in fixed-bed experiments, and the effect of temperature, flowrate, inlet concentration, bed length, and particle size on the process was characterized. The anion exchanger showed a higher adsorption capacity for the more active isoenzyme GA I in all experimental conditions studied. A mathematical model accounting for external and pore diffusion and nonlinear equilibrium isotherm (for GA I) was used to fit the experimental breakthrough curves, showing very accurate fittings in all of the operating conditions. The values of the pore diffusion coefficient at 15, 20, and 25 degrees C were, respectively, 1.25 x 10(-)(11), 1.46 x 10(-)(11) and 1.83 x 10(-)(11) (for GA I) and 1.82 x 10(-)(11), 2.44 x 10(-)(11) and 2.73 x 10(-)(11) (for GA II) m(2)/s. Bicomponent adsorption experiments showed no significant interference effects between GA I and GA II, and so the mathematical model was again used to fit these experiments, yielding very satisfactory results.

Adsorption↗
PubMed1986

Pattern sensitivity to boundary and initial conditions in reaction-diffusion models.

We consider Turing-type reaction-diffusion equations and study (via computer simulations) how the relationship between initial conditions and the asymptotic steady state solutions varies as a function of the boundary conditions. The results indicate that boundary conditions which are nonhomogeneous with respect to the kinetic steady state give rise to spatial patterns which are much less sensitive to variations in the initial conditions than those obtained with homogeneous boundary conditions, such as zero flux conditions. We also compare linear pattern predictions with the numerical solutions of the full nonlinear problem.

Animals↗
PubMed1975

Systems approach to study of solute transport across membranes using suspension cultures of mammalian cells III: steady-state diffusion models.

General physical models are derived for the diffusional transport of drugs across membranes of mammalian cells in culture suspension. These models represent different sets of possible physical processes taking place during the transport of a drug molecule. Once the diffusing species reaches the cell barrier, it may gain entrance to the cell kinetically by one of the principal quasisteady-state mechanisms, all of which assume the cell membrane to be an integral part of the total barrier.

Biological Transport↗
PubMed2006

A bioreaction-diffusion model for growth of marine sponge explants in bioreactors.

Marine sponges are sources of high-value bioactives. Engineering aspects of in vitro culture of sponges from cuttings (explants) are poorly understood. This work develops a diffusion-controlled growth model for sponge explants. The model assumes that the explant growth is controlled by diffusive transport of at least some nutrients from the surrounding medium into the explant that generally has a poorly developed aquiferous system for internal irrigation during early stages of growth. Growth is assumed to obey Monod-type kinetics. The model is shown to satisfactorily explain the measured growth behavior of the marine sponge Crambe crambe in two different growth media. In addition, the model is generally consistent with published data for growth of explants of the sponges Disidea avara and Hemimycale columella. The model predicted that nutrient concentration profiles for nutrients, such as dissolved oxygen within the explant, are consistent with data published by independent researchers. In view of the proposed model's ability to explain available data for growth of several species of sponge explants, diffusive transport does play a controlling role in explant growth at least until a fully developed aquiferous system has become established. According to the model and experimental observations, the instantaneous growth rate depends on the size of the explant and all those factors that influence the diffusion of critical nutrients within the explant. Growth follows a hyperbolic profile that is consistent with the Monod kinetics.

Animals↗
PubMed2005

Extending logistic regression to model diffuse interactions.

In an observational study focussed on association between a health outcome and numerous explanatory variables, the question of interactions can be problematic. Commonly, logistic regression of the outcome on the explanatory variables might be employed. Such modelling often includes an attempt to select some pairwise product interaction terms, from amongst the many such possible pairs. For several reasons, however, this can be unsatisfying. Here we consider a different approach based on a parsimonious extension of a logistic regression model without interaction terms. This extension permits an overall synergism or antagonism in how the explanatory variables combine to associate with the outcome, without any attempt to identify specific variables which give rise to interactive behaviour. We call this diffuse interaction. We elucidate some simple properties of the diffuse interaction model, and give an example of its application to epidemiological data. We also consider asymptotic behaviour in a restricted case of the model, to gain some insight into how well this kind of interaction can be detected from data.

Analysis of Variance↗
PubMed2006

Traveling waves in coupled reaction-diffusion models with degenerate sources.

We consider a general system of coupled nonlinear diffusion equations that are characterized by having degenerate source terms and thereby not having isolated rest states. Using a general form of physically relevant source terms, we derive conditions that are required to trigger traveling waves when a stable uniform steady-state solution is perturbed by a highly localized disturbance. We show that the degeneracy in the source terms implies that traveling waves have a number of surprising properties that are not present for systems with nondegenerate source terms. We also show that such systems can lead to a pair of waves that initially propagate outwards from the disturbance, slow down, and reverse direction before ultimately colliding and annihilating each other.

Action Potentials↗
PubMed2003

Reaction-diffusion models of growing plant tips: bifurcations on hemispheres.

We study two chemical models for pattern formation in growing plant tips. For hemisphere radius and parameter values together optimal for spherical surface harmonic patterns of index l = 3, the Brusselator model gives an 84% probability of dichotomous branching pattern and 16% of annular pattern, while the hyperchirality model gives 88% probability of dichotomous branching and 12% of annular pattern. The models are two-morphogen reaction-diffusion systems on the surface of a hemispherical shell, with Dirichlet boundary conditions. Bifurcation analysis shows that both models give possible mechanisms for dichotomous branching of the growing tips. Symmetries of the models are used in the analysis.

Models, Biological↗
PubMed2001

Film-pore diffusion modeling for the sorption of metal ions from aqueous effluents onto peat.

The sorption of three metal ions, namely, copper, nickel and lead onto sphagnum peat moss has been studied using an agitated batch sorber system. The equilibrium isotherms were determined and kinetic runs were performed over a range of concentrations for each metal ion. A film-pore diffusion mass transfer model has been developed based on a single effective diffusion coefficient for each system. Error analysis of the experimental and theoretical data indicated relatively large errors at low initial metal ion concentrations. Therefore the model was modified to introduce a surface coverage concentration dependent effective diffusivity to account for a contribution from surface diffusion.

Adsorption↗
PubMed2006

Ion diffusion modelling of Fricke-agarose dosemeter gels.

In Fricke-agarose gels, an accurate determination of the spatial dose distribution is hindered by the diffusion of ferric ions. In this work, a model was developed to describe the diffusion process within gel samples of finite length and, thus, permit the reconstruction of the initial spatial distribution of the ferric ions. The temporal evolution of the ion concentration as a function of the initial concentration is derived by solving Fick's second law of diffusion in two dimensions with boundary reflections. The model was applied to magnetic resonance imaging data acquired at high spatial resolution (0.3 mm) and was found to describe accurately the observed diffusion effects.

Computer Simulation↗
PubMed1991

Diffusion models for chemotaxis: a statistical analysis of noninteractive unicellular movement.

A program is developed for applying stochastic differential equations to models for chemotaxis. First a few of the experimental and theoretical models for chemotaxis both for swimming bacteria and for cells migrating along a substrate are reviewed. In physical and biological models of deterministic systems, finite difference equations are often replaced by a limiting differential equation in order to take advantage of the ease in the use of calculus. A similar but more intricate methodology is developed here for stochastic models for chemotaxis. This exposition is possible because recent work in probability theory gives ease in the use of the stochastic calculus for diffusions and broad applicability in the convergence of stochastic difference equations to a stochastic differential equation. Stochastic differential equations suggest useful data for the model and provide statistical tests. We begin with phenomenological considerations as we analyze a one-dimensional model proposed by Boyarsky, Noble, and Peterson in their study of human granulocytes. In this context, a theoretical model consists in identifying which diffusion best approximates a model for cell movement based upon theoretical considerations of cell physiology. Such a diffusion approximation theorem is presented along with discussion of the relationship between autocovariance and persistence. Both the stochastic calculus and the diffusion approximation theorem are described in one dimension. Finally, these tools are extended to multidimensional models and applied to a three-dimensional experimental setup of spherical symmetry.

Chemotaxis↗
PubMed1996

The diffusion model for migration and selection in a dioecious population.

The diffusion approximation is derived for migration and selection at a multiallelic locus in a dioecious population subdivided into a lattice of panmictic colonies. Generations are discrete and nonoverlapping; autosomal and X-linked loci are analyzed. The relation between juvenile and adult subpopulation numbers is very general and includes both soft and hard selection; the zygotic sex ratio is the same in every colony. All the results hold for both adult and juvenile migration. If ploidy-weighted average selection, drift, and diffusion coefficients are used, then the ploidy-weighted average allelic frequencies satisfy the corresponding partial differential equation for a monoecious population. The boundary conditions and the unidimensional transition conditions for coincident discontinuities in the carrying capacity and migration rate extend identically. The previous unidimensional formulation and analysis of symmetric, nearest-neighbor migration of a monoecious population across a geographical barrier is generalized to symmetric migration of arbitrary finite range, and the transition conditions are shown to hold for a dioecious population. Thus, the entire theory of clines and of the wave of advance of favorable alleles is applicable to dioecious populations.

Animals↗
PubMed1977

A diffusion model for mesoderm induction in amphibian embryos.

In this paper we try to answer the question whether diffusion is a possible mechanism to explain mesoderm induction in Amphibians. First the embryological data are discussed and a hypothesis for mesoderm formation is set forth. The blastula being essentially a hollow sphere, we assume that the induction mechanism in an embryo at the blastula stage can be simulated by diffusion-reaction processes on spherical surfaces. A model is constructed for the simple case when the source is held constant with respect to time, the decay proportional to the concentration and the diffusion coefficient a constant. From simulation we find a (best) value for the decay constant to be 6 x 10(-5)/sec and for the diffusion constant to be 0.24 x 10(-6) cm2/sec. The relation between the parameters is derived from an analytic solution for the diffusion process on a spherical surface with a continuously producing point source and the concentration proportional to the decay. The form and regulative properties of the steady concentration gradient are discussed.

Amphibians↗
PubMed1978

Estimation of dissolution rate of salicylamide in complexing media using a theoretical diffusion model.

Dissolution rates of salicylamide in water and caffeine solutions under perfect sink conditions were predicted by theoretical diffusion equations applicable to dissolution in complexing media. Experimental dissolution rates were measured using a compartmentalized rotating-basket apparatus under two sets of conditions. Agreement was found between experimental and predicted rates. Use of the theoretical equation for estimating dissolution rates involves simple calculations of diffusion coefficients and diffusion layer thickness under the operative dissolution conditions. The increase in dissolution rate caused by addition of the complexant can be calculated for diffusion-controlled dissolution directly if the stability constant and the drug solubility in water are known or measured.

Caffeine↗