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At least 379 records · Page 21Linked to original sources
PubMed2001

The effect of ion pumps on the speed of travelling waves in the fire-diffuse-fire model of Ca2+ release.

The fire-diffuse-fire model provides an idealized model of Ca2+ release within living cells. The effect of calcium pumps, which drive Ca2+ back into internal stores, is often neglected for mathematical simplicity. Here we show how to explicitly analyse such effects by extending the work of Keizer et al. [Keizer, J. E., G. D. Smith, S. Ponce Dawson and J. Pearson (1998). Saltatory propagation of Ca2+ waves by Ca2+ sparks. Biophys. J. 75, 595-600.]. For travelling waves, in which release events occur sequentially, we construct the speed of waves in terms of the time-scale at which pumps operate. An immediate consequence of this analysis is that the inclusion of calcium pumps leads to multiple solutions. A linear stability analysis determines those solution branches in parameter space which are stable. Numerical continuation is used to provide explicit examples of the bifurcation diagrams of the speed of waves as a function of physiologically significant system parameters.

Calcium↗
PubMedDate not supplied

[A diffusion kinetics model of the growth of a cancerous tumor].

Diffusion kinetics model of development of solid tumor has been proposed. This model allows qualitative description of a number of experimental effects, e.g. formation of necrosis zones, change of exponential growth to linear one. Critical parameters for transfer from tumor stabilization mode to its growth have been obtained. Methods of calculation have been elaborated and model calculations have been carried out.

Animals↗
PubMed2006

Mean value and fluctuations in a model of diffusion in porous media.

We consider a stochastic model for the diffusion in a porous media. For a case where the average satisfies an anomalous diffusion equation, we investigate the behavior of the realizations around the mean value. The most relevant result of our work is that, although the concentration corresponding to each realization diffuses normally for large times, it experiences large deviations from the mean value during intermediate times. As a consequence, the experimental measurements will always depart from the average value of the realizations (with respect to the stochastic process) for unpredictable times.

Algorithms↗
PubMed2003

Comparison between mass transfer properties of weak-anion-exchange resins with graft-functionalized polymer layers and traditional ungrafted resins.

Glycidylmethacrylate was grafted to Toyopearl HW-65M and subsequently modified with diethylamine to obtain a weak anion exchanger. The degree of grafting was varied from 11 to 50%. The binding capacity for bovine serum albumin was 11 mg/ml for the lowest degree of grafting and 97 mg/ml for the highest degree of grafting. The maximum binding capacity was observed at 27% degree of grafting. The mass transfer properties of the grafted resins and an ungrafted resin(Toyopearl DEAE 650M) were investigated assuming rectangular isotherms. Simple models for reaction kinetics, pore- and surface diffusion and film diffusion were used to describe the concentration-time data in batch mode. The data were best fitted by a pore diffusion model. The estimated pore diffusion coefficients (D(P)) for bovine serum albumin were fitted by a polynome to the degree of grafting with an maximum value at 27% of D(P) = 1.95-10(-11) m2/s. Compared to published data of other ungrafted resins and to the molecular diffusion coefficient of bovine serum albumin in free solution of D(P) = 5.6 10(-11) m2/s, the diffusion in grafted layers seems to be accelerated. The breakthrough curves for columns packed with various resins showed a decrease in sharpness with increasing degree of grafting which could not be described by a simple pore diffusion model using the calculated transport coefficients from batch mode. The shape of the breakthrough curves could be well described by a combined film and pore diffusion model. For the ungrafted Toyopearl DEAE 650M resin the breakthrough curve is more favorable and the influence of film diffusion to the mass transfer is reduced. It can be concluded that grafting will increase the capacity and the pore diffusion in batch mode but in column operation the grafting layer has a film resistance which plays an important role in the overall mass transfer.

Anion Exchange Resins↗
PubMed1983

On the mechanism of actin monomer-polymer subunit exchange at steady state.

The rate of exchange of G-actin with subunits of F-actin and the rate of hydrolysis of ATP in solutions of F-actin at steady state have been measured simultaneously. Subunit exchange kinetics were analyzed by both a treadmill model and an exchange-diffusion model. The best fit to a treadmill model of the data obtained in 0.5 mM MgCl2 and 0.2 mM ATP at 30 degrees C gave a treadmill efficiency (net monomers incorporated per ATP hydrolyzed) of 0.26, in good agreement with the previously reported s-value of 0.25 (Wegner, A. (1976) J. Mol. Biol. 108, 139-150) for similar ionic conditions. However, in this and other conditions with excess free divalent cations (Ca2+ or Mg2+), the observed exchange kinetics were in better agreement with an exchange-diffusion model than with a treadmilling model over the entire time course of the experiment. In the absence of excess divalent cations (50 mM KCl), exchange was too slow to be analyzed adequately by either model. Using the measured filament length distribution and the observed fit of the exchange-diffusion model to the data in 0.5 mM MgCl2, an on-rate constant of 2.8 x 10(6) M-1 S-1 and an off-rate constant of 5.8 s-1 were calculated. These values, while in good agreement with previously measured pre-steady state polymerization rate constants under different ionic conditions (Pollard, T. D., and Mooseker, M. S. (1981) J. Cell Biol. 88, 654-659), are about 30-fold higher than the rate constants predicted from the rate of ATP hydrolysis at steady state. To rationalize these discrepancies, a model is proposed in which a segment of F-actin subunits at one or both ends of the filament contains bound ATP at steady state.

Actins↗
PubMed1999

In vivo determination of the optical properties of muscle with time-resolved reflectance using a layered model.

We have investigated the possibility of determining the optical coefficients of muscle in the extremities with in vivo time-resolved reflectance measurements using a layered model. A solution of the diffusion equation for two layers was fitted to three-layered Monte Carlo calculations simulating the skin, the subcutaneous fat and the muscle. Relative time-resolved reflectance data at two distances were used to derive the optical coefficients of the layers. We found for skin and subcutaneous fat layer thicknesses (l2) of up to 10 mm that the estimated absorption coefficients of the second layer of the diffusion model have differences of less than 20% compared with those of the muscle layer of the Monte Carlo simulations if the thickness of the first layer of the diffusion model is also fitted. If l2 is known, the differences are less than 5%, whereas the use of a semi-infinite model delivers differences of up to 55%. Even if l2 is only approximately known the absorption coefficient of the muscle can be determined accurately. Experimentally, the time-resolved reflectance was measured on the forearms of volunteers at two distances from the incident beam by means of a streak camera. The thicknesses of the tissues involved were determined by ultrasound. The optical coefficients were derived from these measurements by applying the two-layered diffusion model, and results in accordance with the theoretical studies were observed.

Adipose Tissue↗
PubMed2004

Diffusion-collision model algorithms for protein folding kinetics.

The diffusion-collision model (DCM) of protein folding is described qualitatively and quantitatively. The input parameters required to perform a calculation are explained, and the output data are outlined. Three examples are given of calculating DCM folding kinetics: the Engrailed Homeodomain (a three-helix bundle with three helical microdomains, pdb code 1ENH), protein G (with three microdomains having a beta-hairpin-alpha-helix-beta-hairpin motif, pdb code 1PGA), and apomyoglobin (with eight helices and seven strong microdomain-microdomain pairings).

Algorithms↗
PubMed2005

Adsorption of Acid Red 57 from aqueous solutions onto surfactant-modified sepiolite.

The adsorption of Acid Red 57 (AR57) onto surfactant-modified sepiolite was investigated in aqueous solution in a batch system with respect to contact time, pH and temperature. The surface modification of surfactant-modified sepiolite was controlled using the FTIR technique. The pseudo-first-order, pseudo-second-order kinetic models and the intraparticle diffusion model were used to describe the kinetic data and the rate constants were evaluated. The experimental data fitted very well the pseudo-second-order kinetic model and also followed the intraparticle diffusion model up to 90 min, whereas diffusion is not only the rate controlling step. The Langmuir and Freundlich adsorption models were applied to describe the equilibrium isotherms and the isotherm constants were also determined. The Freundlich model agrees with experimental data well. The activation energy, change of free energy, enthalpy and entropy of adsorption were also evaluated for the adsorption of AR57 onto surfactant-modified sepiolite. The results indicate that surfactant-modified sepiolite could be employed as low-cost material for the removal of textile dyes from effluents.

Adsorption↗
PubMed1995

Radiocesium distribution in undisturbed soil: measurements and diffusion-advection model.

The profile of 137Cs, due to Chernobyl accident, in undisturbed soil was measured experimentally over the years 1987 to 1994 and was found to remain practically fixed in the upper 30 cm of soil since 1987. Total deposition of 137Cs at the site was 20 kBq m-2, and approximately 80% of that is in the upper 10 cm. The profile has two slopes in semilogarythmic scale, i.e., it appears as the sum of two exponentials. The contribution of weapons fallout is found to be negligible. Pure diffusion and diffusion-advection models of cesium migration are investigated. It is found that the pure diffusion model cannot reproduce the double slope, while the diffusion advection model can.

Cesium Radioisotopes↗
PubMed2004

The role of sequence and structure in protein folding kinetics; the diffusion-collision model applied to proteins L and G.

The diffusion-collision model (DCM) is applied to the folding kinetics of protein L and protein G. In the DCM, the two proteins are treated as consisting of two beta-hairpins and one alpha-helix, so that they are isomorphous with the three-helix bundle DCM model. In the absence of sequence dependent factors, both proteins would fold in the same way in the DCM, with the coalescence of the N-terminal hairpin and the helix slightly favored over the C-terminal hairpin and the helix because the former are closer together than the latter. However, sequence dependent factors make the N-terminal hairpin of protein L and the C-terminal hairpin of protein G more stable in the ensemble of unfolded conformations. This difference in the stabilities gives rise to the difference in the calculated folding behavior, in agreement with experiment.

Amino Acid Sequence↗
PubMed1988

Diffusion-collision model for the folding kinetics of myoglobin.

The diffusion-collision model has been used to analyze the folding kinetics of myoglobin. The microdomains, which are the basic units that coalesce during the folding, are identified with the helices and the stabilizing contacts between helices are determined from the native structure. Both association and dissociation reactions are included and a range of stabilization parameters is investigated to determine the variation in overall rate and the relative contributions made by different intermediates during the folding process. In a comparison of folding to the native state and to the midpoint of the folding transition (i.e., 50% native protein at the completion of the reaction) significant differences in the contributing intermediates are found.

Diffusion↗
PubMed2004

Adsorption of acid dyes from aqueous solutions onto acid-activated bentonite.

The adsorption of two dyes, namely, Acid Red 57 (AR57) and Acid Blue 294 (AB294), onto acid-activated bentonite in aqueous solution was studied in a batch system with respect to contact time, pH, and temperature. Acidic pH was favorable for the adsorption of these dyes. The surface characterization of acid-activated bentonite was performed using the FTIR technique. The pseudo-first-order and pseudo-second-order kinetic models and the intraparticle diffusion model were used to describe the kinetic data and the rate constants were evaluated. The dynamic data fitted the pseudo-second-order kinetic model well and also followed the intraparticle diffusion model up to 90 min, but diffusion is not the only rate controlling step. The Langmuir and Freundlich adsorption models were applied to describe the equilibrium isotherms and the isotherm constants were determined. The Freundlich model agrees very well with experimental data. The activation energies of adsorption were also evaluated for the adsorption of AR57 and AB294 onto activated bentonite.

Journal Article↗
PubMed2001

Adsorption of basic dyes on granular activated carbon and natural zeolite.

The adsorption of basic dyes from aqueous solution onto granular activated carbon and natural zeolite has been studied using an agitated batch adsorber. The influence of agitation, initial dye concentration and adsorbent mass has been studied. The parameters of Langmuir and Freundlich adsorption isotherms have been determined using the adsorption data. Homogeneous diffusion model (solid diffusion) combined with external mass transfer resistance is proposed for the kinetic investigation. The dependence of solid diffusion coefficient on initial concentration and mass adsorbent is represented by the simple empirical equations.

Adsorption↗
PubMed2005

Relation between pore sizes of protein crystals and anisotropic solute diffusivities.

The diffusion of a solute, fluorescein, into lysozyme protein crystals with different pore structures was investigated. To determine the diffusion coefficients, three-dimensional solute concentration fields acquired by confocal laser scanning microscopy (CLSM) during diffusion into the crystals were compared with the output of a time-dependent 3-D diffusion model. The diffusion process was found to be anisotropic, and the degree of anisotropy increased in the order: triclinic, tetragonal and orthorhombic crystal morphology. A linear correlation between the pore diffusion coefficients and the pore sizes was established. The maximum size of the solute, deduced from the established correlation of diffusion coefficients and pore size, was 0.73 +/- 0.06 nm, which was in the range of the average diameter of fluorescein (0.69 +/- 0.02 nm). This proves that size exclusion is the key mechanism for solute diffusion in protein crystals. Hence, the origin of solute diffusion anisotropy can be found in the packing of the protein molecules in the crystals, which determines the crystal pore organization.

Anisotropy↗
PubMed1990

Mathematical models of the spatial distribution of retinal oxygen tension and consumption, including changes upon illumination.

To better understand oxygen utilization by the retina, a mathematical model of oxygen diffusion and consumption in the cat outer, avascular retina was developed by analyzing previously recorded profiles of oxygen tension (PO2) as a function of retinal depth. Simple diffusion modelling of the oxygen distribution through the outer retina is possible because the PO2 depends only on diffusion from the choroidal and retinal circulations and on consumption within the tissue. Several different models were evaluated in order to determine the best one from the standpoints of their ability to represent the data and to agree with physiological reality. For the steady state one-dimensional diffusion model adopted (the special three-layer diffusion model), oxygen consumption was constant through the middle layer and zero in the layers near the choroid and near the inner retina. On the average, the oxygen consuming layer, as found by nonlinear regression for each profile, extended from about 75% to 85% of the retinal depth from the vitreous. This is a narrow band through the mid-region of the photoreceptors. Oxygen consumption of the entire avascular retina, determined from fitting eight PO2 profiles measured in light-adapted retinas, averaged 2.7 ml O2(STP)/(100 g tissue.min), while the value determined from fitting thirty-two PO2 profiles measured in dark-adapted retinas averaged 4.4 ml O2(STP)/(100 g tissue.min). Consumption in the light was thus only 60% of that in the dark. This suggests that the outer retina is at greater risk of hypoxic injury in the dark than in the light, a finding of considerable clinical significance.

Animals↗
PubMed2000

Optical tomography in the presence of void regions

There is a growing interest in the use of near-infrared spectroscopy for the noninvasive determination of the oxygenation level within biological tissue. Stemming from this application, there has been further research in the use of this technique for obtaining tomographic images of the neonatal head, with the view of determining the levels of oxygenated and deoxygenated blood within the brain. Owing to computational complexity, methods used for numerical modeling of photon transfer within tissue have usually been limited to the diffusion approximation of the Boltzmann transport equation. The diffusion approximation, however, is not valid in regions of low scatter, such as the cerebrospinal fluid. Methods have been proposed for dealing with nonscattering regions within diffusing materials through the use of a radiosity-diffusion model. Currently, this new model assumes prior knowledge of the void region location; therefore it is instructive to examine the errors introduced in applying a simple diffusion-based reconstruction scheme in cases in which there exists a nonscattering region. We present reconstructed images of objects that contain a nonscattering region within a diffusive material. Here the forward data is calculated with the radiosity-diffusion model, and the inverse problem is solved with either the radiosity-diffusion model or the diffusion-only model. The reconstructed images show that even in the presence of only a thin nonscattering layer, a diffusion-only reconstruction will fail. When a radiosity-diffusion model is used for image reconstruction, together with a priori information about the position of the nonscattering region, the quality of the reconstructed image is considerably improved. The accuracy of the reconstructed images depends largely on the position of the anomaly with respect to the nonscattering region as well as the thickness of the nonscattering region.

Journal Article↗
PubMed2004

Directed percolation in a two-dimensional stochastic fire-diffuse-fire model.

We establish, from extensive numerical experiments, that the two dimensional stochastic fire-diffuse-fire model belongs to the directed percolation universality class. This model is an idealized model of intracellular calcium release that retains both the discrete nature of calcium stores and the stochastic nature of release. It is formed from an array of noisy threshold elements that are coupled only by a diffusing signal. The model supports spontaneous release events that can merge to form spreading circular and spiral waves of activity. The critical level of noise required for the system to exhibit a nonequilibrium phase transition between propagating and nonpropagating waves is obtained by an examination of the local slope delta (t) of the survival probability Pi(t) proportional exp [-delta(t)] for a wave to propagate for a time t .

Action Potentials↗
PubMed2006

Modeling fluid diffusion using the lattice density functional theory approach: counterdiffusion in an external field.

The dependence of the diffusivity on temperature, pressure, and composition is not understood well; consequently, data is preferred significantly over correlations in most practical situations. Even in dilute gases, the contributions of attractions and repulsions to the diffusivity are difficult to understand on a molecular level without performing simulations. We have developed a Lattice Density Functional Theory (LDFT) approach for modeling diffusion to supplement existing methods that are very rigorous but computationally demanding. The LDFT approach is analogous to the van der Waals equation in how it accounts for molecular interactions in that it has first-order corrections to ideal behavior; it is an extension of the Equilibrium LDFT for adsorption and phase behavior. In this work, the LDFT approach is presented and demonstrated by modeling the problem of color counterdiffusion in an externally-applied potential field. This potential field, in combination with the intermolecular potential function, creates a diffusion regime in which repulsions cause oscillations in the density profile. Using the LDFT approach, the oscillations were described and attributed to nearest-neighbor and next nearest-neighbor interactions. The LDFT approach gives qualitative and quantitative agreement with dual control-volume Grand Canonical Molecular Dynamics simulations.

Journal Article↗