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PubMed2000

Biased diffusion in anisotropic disordered systems

We investigate a diffusion process into an anisotropic disordered medium in the presence of a bias. The medium is modeled by a two-dimensional square lattice in which the anisotropic disorder is represented by a bond percolation model with different occupation probabilities on each direction. The biased diffusion process is mapped by a random walk with unequal transition probabilities along and against the field (in the [1,1] direction) by performing Monte Carlo simulations. We observe a transition from pure to drift diffusion when the bias reaches a threshold B(c). In order to estimate this B(c), an effective exponentis used to characterize the diffusion process. This B(c) is also compared with another estimation for the critical field.

Journal Article↗
PubMed1993

Percutaneous absorption: a single-layer model.

In vitro percutaneous permeation of betamethasone 17-valerate through excised human skin was studied. Pressure-sensitive silicone adhesive containing betamethasone 17-valerate in suspension was used as a vehicle. Steady-state flux through the split-thickness skin was similar to that through the isolated epidermis. However, the lag-time and half-life after removal of the vehicle were longer for the split-thickness skin than from epidermis. At steady state, 37% of the drug in the split-thickness skin was partitioned in dermis. When the kinetic parameters of a simple single-layer model are defined to specify the permeability coefficient and the drug amount in skin at steady state, this model can predict the longer half-life observed for the split-thickness skin sample compared with that for epidermis. The difference between the observed and theoretical values of the half-life after removal of the vehicle was within 23%. On the other hand, the lag-time had a large variation and the simple diffusion model failed to be predictive. A single-layer model described by two or three kinetic parameters may be able to describe percutaneous permeation kinetics even when the processes after the compound permeation through stratum corneum are not negligible. However, it is stressed that none of the kinetic parameters inherent in this simple model directly represents one of the single physicochemical parameters, such as diffusion and partition coefficients and path length of each skin layer.

Betamethasone Valerate↗
PubMed2005

Modeling biofilm and floc diffusion processes based on analytical solution of reaction-diffusion equations.

Biofilm modeling is often considered as a complex mathematical subject. This paper evaluates simple equations to describe the basic processes in a biofilm system with the main aim to show several interesting applications. To avoid mathematical complexity the simulations are carried out in a simple spreadsheet. Frequently, only the solution for zero-order reaction kinetics of the reaction-diffusion equation is used (better known as half-order kinetics). A weighted average of the analytical solutions for zero- and first-order reactions is proposed as basic and useful model to describe steady-state (in biofilm composition) biofilm reactors. This approach is compared with several modeling approaches, such as the simple solution for zero-order reaction and more complex ones (i) direct numerical solution for the diffusion equations, (ii) 1-D AQUASIM and (iii) 2-D modeling. The systems evaluated are single and multiple species biofilms. It is shown that for describing conversions in biofilm reactors, the zero-order solution is generally sufficient; however, for design purposes large deviations of the correct solution can occur. Additionally, the role of diffusion in flocculated and granular sludge systems is discussed. The relation between the measured (apparent) substrate affinity constant and diffusion processes is outlined.

Biofilms↗
PubMed2005

Acquiring linear subspaces for face recognition under variable lighting.

Previous work has demonstrated that the image variation of many objects (human faces in particular) under variable lighting can be effectively modeled by low-dimensional linear spaces, even when there are multiple light sources and shadowing. Basis images spanning this space are usually obtained in one of three ways: A large set of images of the object under different lighting conditions is acquired, and principal component analysis (PCA) is used to estimate a subspace. Alternatively, synthetic images are rendered from a 3D model (perhaps reconstructed from images) under point sources and, again, PCA is used to estimate a subspace. Finally, images rendered from a 3D model under diffuse lighting based on spherical harmonics are directly used as basis images. In this paper, we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low-dimensional linear space and that this subspace is close to those acquired by the other methods. More specifically, there exist configurations of k point light source directions, with k typically ranging from 5 to 9, such that, by taking k images of an object under these single sources, the resulting subspace is an effective representation for recognition under a wide range of lighting conditions. Since the subspace is generated directly from real images, potentially complex and/or brittle intermediate steps such as 3D reconstruction can be completely avoided; nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse (harmonic) light fields. We validate the use of subspaces constructed in this fashion within the context of face recognition.

Algorithms↗
PubMed1990

Ethanol diffuses across the gastric muscle wall.

Ethanol inhibits the electrical and mechanical activities of gastric smooth muscle, but only at concentrations higher than can be provided by serum delivery. We speculated that the ethanol concentration in the gastric wall may exceed plasma levels by direct diffusion across the mucosa and through the muscle layers. A model of acute ethanol ingestion was created by partitioning the stomachs of three dogs with a surgical stapling device and instilling carbon 14 (14C)-labeled ethanol into the proximal segments. The flux of ethanol was traced by counting 14C in serial sections of the gastric wall. A mucosa-to-serosa gradient of 14C activity was established. The data indicate that direct diffusion from the mucosal surface will produce dramatically higher concentrations of ethanol in gastric muscle than would be anticipated from serum levels alone.

Animals↗
PubMed1994

Direct imaging of reptation for semiflexible actin filaments.

According to the reptation model of polymer diffusion, a polymer chain exhibits snake-like motion through the entangled mesh of surrounding molecules, in which the undulations of the chain are restricted to a tube-like region. The reptation model can account for many of the dynamic properties of entangled polymer solutions and melts, and has received support from observations of block copolymer diffusion across an interface; but reptative motion has not previously been imaged directly. Here we report such a direct observation of reptation, obtained by video microscopy of fluorescently labelled single, semiflexible filaments of actin in a solution of unlabelled actin filaments. From the restricted thermal undulations of these filaments we can measure the diameter of the confining tube, and we also observe the characteristic thermally excited sliding of the filament out of the end of the tube. We find that the chain self-diffusion coefficient decreases approximately linearly as the filament length increases, in agreement with the reptation model.

Actins↗
PubMed2005

A two-dimensional mathematical model of non-linear dual-sorption of percutaneous drug absorption.

BACKGROUND: Certain drugs, for example scopolamine and timolol, show non-linear kinetic behavior during permeation process. This non-linear kinetic behavior is due to two mechanisms; the first mechanism being a simple dissolution producing mobile and freely diffusible molecules and the second being an adsorption process producing non-mobile molecules that do not participate in the diffusion process. When such a drug is applied on the skin surface, the concentration of the drug accumulated in the skin and the amount of the drug eliminated into the blood vessel depend on the value of a parameter, C, the donor concentration. The present paper studies the effect of the parameter value, C, when the region of the contact of the skin with drug, is a line segment on the skin surface. To confirm that dual-sorption process gives an explanation to non-linear kinetic behavior, the characteristic features that are used in one-dimensional models are (1) prolongation of half-life if the plot of flux versus time are straight lines soon after the vehicle removal, (2) the decrease in half-life with increase in donor concentration. This paper introduces another feature as a characteristic to confirm that dual-sorption model gives an explanation to the non-linear kinetic behavior of the drug. This new feature is "the prolongation of half-life is not a necessary feature if the plots of drug flux versus time is a non-linear curve, soon after the vehicle removal". METHODS: From biological point of view, a drug absorption model is said to be nonlinear if the sorption isotherm is non-linear. When a model is non-linear the relationship between lag-time and donor concentration is non-linear and the lag time decreases with increase in donor concentration. A two-dimensional dual-sorption model is developed for percutaneous absorption of a drug, which shows non-linear kinetic behavior in the permeation process. This model may be used when the diffusion of the drug in the direction parallel to the skin surface must be examined, as well as in the direction into the skin, examined in one-dimensional models. The dual-sorption model is an initial/boundary value problem which consists of (1) one non-linear, two-dimensional, second-order parabolic equation, (2) boundary conditions, (3) one initial condition. Note that, the number of boundary conditions are, six and four, respectively, if the permeation process under consideration is, during the application of the vehicle and during the removal of the vehicle. Adopting the approach of method of lines, the initial/boundary value problem is transformed into an initial-value problem, which consists of (1) a system of non-linear ordinary differential equations, (2) one initial condition. The system of non-linear ordinary differential equations contains time-dependent non-homogeneous terms, if the permeation process under consideration is, during the application of the vehicle. To solve this initial-value problem, an eight-stage sequential algorithm which is second-order accurate, and requires only tri-diagonal solvers, is developed. RESULTS: Simulation of the numerical methods described is carried out with various values of the parameter C. The illustrations are given in the form of figures. The concentration profiles are viewed as parabolas along the mesh lines parallel to x-axis or y-axis. The flow rates in different subregions of the skin-region are studied. The shapes of the concentration profiles are examined before and after the steady-state concentration is reached. The concentration reaches steady-state when the flux reaches the steady state. The plots of flux versus time and cumulative amount of drug eliminated into the receptor cell versus time are given. CONCLUSION: Based on the various values of the parameter, C, conclusions are drawn about (1) flow rate of the drug in different regions of the skin, (2) shape of the concentration profiles, (3) the time required to reach the steady-state value of the concentration, (4) concentration of the drug in different regions of the skin, when steady-state value of the concentration is reached, (5) the time required to reach the steady-state value of the flux, (6) time required to reach the steady-state value of the concentration of the drug, (7) half-life of the concentration of the drug and (8) lag-time. A comparison, between this two-dimensional model and the one-dimensional non-linear dual-sorption model that exists in the literature, is done based on (1) the shape of the concentration profiles at various time levels, (2) the time required to reach the steady-state value of the concentration, (3) lag-time and (4) half-life.

Administration, Topical↗
PubMed1989

Spatial patterns of human gene frequencies in Europe.

The aims of this study of spatial patterns of human gene frequencies in Europe are twofold. One is to present new methodology developed for the analysis of such data. The other is to report on the diversity of spatial patterns observed in Europe and their interpretation as evidence of population processes. Spatial variation in 59 allele and haplotype frequencies (26 genetic systems) for polymorphisms in blood antigens, enzymes, and proteins is analyzed for an aggregate of 3,384 localities, using homogeneity tests, one-dimensional and directional spatial correlograms, and SYMAP interpolated surfaces. The data matrices are reduced to reveal the principal patterns by clustering techniques. The findings of this study can be summarized as follows: 1) There is significant heterogeneity in allele frequencies among the localities for all but one genetic system. 2) There are significant spatial patterns for most allele frequencies. 3) There is a substantial minority of clinal patterns in these populations. Clinal trends are found more frequently in HLA alleles than for other variables. North-south and northwest-southwest gradients predominate. 4) There is a strong decline in overall genetic similarity with geographic distance for most variables. 5) There are few, if any, appreciable correlations in pairs of allele frequencies over the continent, and there is little interesting correlation structure in the resulting correlation matrix. 6) Few spatial correlograms are markedly similar to each other, yet they form well-defined clusters. Spatial variation patterns, therefore, differ among allele frequencies. Patterns of human gene frequencies in modern Europe are diverse and complex. No single model suffices for interpretation of the observed genetic structure. Some clinal patterns reported here support the Neolithic demic-expansion hypothesis, others suggest latitudinal selection. Most of the clinal patterns are in HLA alleles, but there is also evidence from ABO for east-west migration diffusion. The majority of patterns are patchy, consistent with hypotheses of isolation by distance or of settlement of genetically differing, subsequently expanding ethnic groups. While undoubtedly there has been an ongoing stochastic process of differentiation consistent with the isolation-by-distance model, this has not obscured the directional patterns caused by migration (demic diffusion), and has perhaps only reinforced the contribution from settlement of ethnic units to patterns of genetic variation. However, the impact of the latter is most difficult to discern and requires further methodological developments.

ABO Blood-Group System↗
PubMed2006

Steady-state directional diffuse reflectance and fluorescence of human skin.

We present numerical simulations predicting the directional diffuse reflectance and autofluorescence from human skin. Skin is modeled as a seven-layered medium, with each layer having its own optical properties and fluorophore concentrations. Both collimated and diffuse monochromatic excitation at 442 nm are considered. In addition, the effect of an index-matching cream used to eliminate total internal reflection within the skin is assessed. We compute the intensity distributions of the excitation and fluorescence light in the skin by solving the radiative transfer equation using the modified method of characteristics. It was found that the use of an index-matching cream reduces the directional fluorescence signal while increasing the directional diffuse reflectance from the skin for collimated excitation. On the other hand, both the fluorescence and diffuse reflectance increase for diffuse excitation with an index-matching cream. Moreover, the directional fluorescence intensity obtained by use of collimated excitation is larger than that obtained by use of diffuse excitation light. This computational tool could be valuable in designing optical devices for biomedical applications.

Algorithms↗
PubMed2007

Structure and release behavior of PMMA/silica composite drug delivery system.

The preparation, characterization, and in vitro release of aspirin from polymethylmethacrylate (PMMA)/silica composites prepared via a sol-gel route are reported. The in vitro drug release test revealed that the release rate of aspirin in PBS increased with the silica content in the composites; on the contrary, the increase of the content of 3-(trimethoxysilyl) propyl methacrylate (MSMA), a coupling agent, decreased the drug release rate. The drug release rate/composite structure relationship was studied using Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), and swelling ratio (SR) measurement. The results indicated that the interface between polymer matrix and inorganic fillers has significant influence on the drug release behavior of the composite materials. In addition, models of mass transfer based on Fickian diffusion law at constant temperature and pressure were employed to analyze the results of the in vitro drug release experiments. The drug release behaviors of the composite samples fitted well with the Fickian diffusion model. The values of k, which is in direct proportion to drug release rate, increased with the increasing content of silica while decreased with that of MSMA in the composite samples.

Aspirin↗
PubMed2005

Mechanism of flavin transfer and oxygen activation by the two-component flavoenzyme styrene monooxygenase.

Styrene monooxygenase (SMO) from Pseudomonas putida S12 is a two-component flavoenzyme composed of the NADH-specific flavin reductase, SMOB, and FAD-specific styrene epoxidase, SMOA. Here, we report the cloning, and expression of native and histidine-tagged versions of SMOA and SMOB and studies of the flavin transfer and styrene oxygenation reactions. In the reductive half-reaction, SMOB catalyzes the two-electron reduction of FAD with a turnover number of 3200 s(-1). Single turnover studies of the reaction of reduced SMOA with substrates indicate the formation of a stable oxygen intermediate with the absorbance characteristics of a flavin hydroperoxide. Based on the results of numerical simulations of the steady-state mechanism of SMO, we find that the observed coupling of NADH and styrene oxidation can be best explained by a model, which includes both the direct transfer and passive diffusion of reduced FAD from SMOB to SMOA.

Benzene↗
PubMed2004

Low-density releases of Neoseiulus fallacis provide for rapid dispersal and control of Tetranychus urticae (Acari: Phytoseiidae, Tetranychidae) on apple seedlings.

Releases of Neoseiulus fallacis (Garman) at 1500--6000 per ha when prey were at 0.1-0.3 per leaf provided seasonal control of Tetranychus urticae Koch (all stages) at 1-2 per leaf in an apple seedling rootstock nursery. Predaceous mites (all stages) increased to 0.3-0.4 per leaf after releases and predator prey ratios of < or = 1:3-7 provided pest regulation thereafter. Such low-density releases were thought to be effective because multiple dispersal bouts allowed predators to locate widely distributed spider mites (on 2-6% of leaves). A random-diffusion model simulating predator dispersal (incorporating wind speed and direction parameters) adequately explained movement and pest control patterns. An upright, dense, uniform planting of apple seedlings was an effective producer and recipient for dispersing predators and these attributes seemed to explain why biological control was so effective. Low-density releases of N. fallacis for control of T. urticae are predicted to be less effective on other crops with less prominent profiles and soil coverage.

Animals↗
PubMed1998

Brownian dynamics simulations of protein folding: access to milliseconds time scale and beyond.

Protein folding occurs on a time scale ranging from milliseconds to minutes for a majority of proteins. Computer simulation of protein folding, from a random configuration to the native structure, is nontrivial owing to the large disparity between the simulation and folding time scales. As an effort to overcome this limitation, simple models with idealized protein subdomains, e.g., the diffusion-collision model of Karplus and Weaver, have gained some popularity. We present here new results for the folding of a four-helix bundle within the framework of the diffusion-collision model. Even with such simplifying assumptions, a direct application of standard Brownian dynamics methods would consume 10,000 processor-years on current supercomputers. We circumvent this difficulty by invoking a special Brownian dynamics simulation. The method features the calculation of the mean passage time of an event from the flux overpopulation method and the sampling of events that lead to productive collisions even if their probability is extremely small (because of large free-energy barriers that separate them from the higher probability events). Using these developments, we demonstrate that a coarse-grained model of the four-helix bundle can be simulated in several days on current supercomputers. Furthermore, such simulations yield folding times that are in the range of time scales observed in experiments.

Biophysics↗
PubMed2000

Localization-delocalization transition in non-hermitian disordered systems

Using the supersymmetry technique, we study the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems with a direction. In contrast to chains, our model captures the diffusive character of carriers' motion at short distances. We calculate the joint probability of complex eigenvalues and some other correlation functions. We find that the transition is abrupt and it is due to an interplay between two saddle points in the free energy functional.

Journal Article↗
PubMed2002

Modeling the cell's guidance system.

Cell locomotion can be directed by external gradients of diffusible substances leading to chemotaxis. Recently, the mechanisms of gradient sensing, the cell guidance system, came under scrutiny both in experimental analysis and computational modeling. Here, we review several recent computational models of gradient sensing in eukaryotic cells, demonstrating why some of them predict little sensitivity to changes in the gradient and response "locking," whereas others predict high gradient sensitivity at the expense of signal gain. We also propose a way to view chemotaxis regulation as a highly coupled combination of semi-independent control modules, leading to simplifying modeling of this complex cellular behavior.

Animals↗
PubMed2004

A mechanism for polar protein localization in bacteria.

We investigate a mechanism for the polar localization of proteins in bacteria. We focus on the MinCD/DivIVA system regulating division site placement in the rod-shaped bacterium Bacillus subtilis. Our model relies on a combination of geometric effects and reaction-diffusion dynamics to direct proteins to both cell poles, where division is then blocked. We discuss similarities and differences with related division models in Escherichia coli and also develop extensions of the model to asymmetric polar protein localization. We propose that our mechanism for polar localization may be employed more widely in bacteria, especially in outgrowing spores, which do not possess any pre-existing polar division apparatus from prior division events.

Adenosine Triphosphatases↗
PubMed1990

Model for drug uptake by brain tumors: effects of osmotic treatment and of diffusion in brain.

A mathematical model describing drug uptake into brain tumors, directly from blood and indirectly from neighboring tissue, is presented. The model quantitatively describes uptake into tumor, brain surrounding tumor (BST), and normal brain and uptake following reversible osmotic blood-brain barrier (BBB) and blood-tumor barrier disruption. It employs published data on the time course for reclosure of the BBB following osmotic treatment and on the brain and tumor uptake of [14C]alpha-aminoisobutyric acid by Walker 256 carcinomas and C6 gliomas implanted into the rat brain. Constant infusion and bolus injection infusion schedules are considered. In untreated brain, the BST acts as a sink, reducing the integrated exposure of the adjacent tumor to the drug, whereas following osmotic treatment, tumor exposure to drug is enhanced, not only by increased delivery from blood but also by diffusion (and bulk flow) from neighboring brain. The model provides a quantitative framework for examining the efficacy of osmotic treatment to enhance chemotherapy of brain tumors.

Aminoisobutyric Acids↗