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PubMed2006

Modelling radionuclide transport for time varying flow in a channel network.

Water flowrates and flow directions may change over time in the subsurface for a number of reasons. In fractured rocks flow takes place in channels within fractures. Solutes are carried by the advective flow. In addition, solutes may diffuse in and out of stagnant waters in the rock matrix and other stagnant water regions. Sorbing species may sorb on fracture surfaces and on the micropore surfaces in the rock matrix. We present a method by which solute particles can be traced in flowing water undergoing changes in flowrate and direction in a complex channel network where the solutes can also interact with the rock by diffusion in the rock matrix. The novelty of this paper is handling of diffusion in the rock matrix under transient flow conditions. The diffusive processes are stochastic and it is not possible to follow a particle deterministically. The method therefore utilises the properties of a probability distribution function for a tracer moving in a fracture where matrix diffusion is active. The method is incorporated in a three dimensional channel network model. Particle tracking is used to trace out a multitude of flowpaths, each of which consists of a large number of channels within fractures. Along each channel the aperture and velocity as well as the matrix sorption properties can vary. An efficient method is presented whereby a particle can be followed along the variable property flowpath. For stationary flow conditions and a network of channels with advective flow and matrix diffusion, a simple analytical solution for the residence time distribution along each pathway can be used. Only two parameter groups need to be integrated along each path. For transient flow conditions, a time stepping procedure that incorporates a stochastic Monte-Carlo like method to follow the particles along the paths when flow conditions change is used. The method is fast and an example is used for illustrative purposes. It is exemplified by a case where land rises due to glacial rebound. It is shown that the effects of changing flowrates and directions can be considerable and that the diffusive migration in the matrix can have a dominating effect on the results.

Computer Simulation↗
PubMed2003

Three-component competitive adsorption model for flow-through PAC systems. 1. Model development and verification with a PAC/membrane system.

Natural organic matter (NOM) interferes with the adsorption of trace organic compounds on porous adsorbents such as powdered activated carbon (PAC) by pore blockage and direct competition for adsorption sites. The competitive effect of NOM in flow-through systems in which the retention time of the PAC is greater than the hydraulic retention time of the system can be magnified because NOM from the influent water can continue to adsorb on the PAC retained in the system. As a result, the adsorption capacity and the diffusion coefficient of trace compounds can decrease as NOM from the influent water accumulates. In this study, a dynamic three-component adsorption model was developed to quantitatively describe the removal of a trace compound from water in flow-through PAC processes. The system was simplified by using p-dichlorobenzene (p-DCB) to represent the NOM fraction that competes directly with the target trace organic atrazine for adsorption sites and by using poly(styrene sulfonate) (PSS-1.8k) to represent large, pore-blocking NOM. The model was based on the homogeneous surface diffusion assumption with the adsorption capacity of atrazine being gradually adjusted using a simplified version of the ideal adsorbed solution theory model developed in this study. The surface diffusion coefficients of atrazine and p-DCB were modeled as a function of the surface concentration of the pore-blocking compound, PSS-1.8k. The model was verified experimentally with a PAC/microfiltration (MF) system. The use of single-solute adsorption parameters obtained from batch isotherm and kinetic tests resulted in good model predictions for the adsorption of atrazine and the two model compounds under operating conditions typical of PAC/MF systems. The model will be applied to study various operating conditions and other system parameters of PAC/membrane systems in part 2 of this study.

Adsorption↗
PubMed1998

Magnetic resonance myocardial fiber-orientation mapping with direct histological correlation.

Functional properties of the myocardium are mediated by the tissue structure. Consequently, proper physiological studies and modeling necessitate a precise knowledge of the fiber orientation. Magnetic resonance (MR) diffusion tensor imaging techniques have been used as a nondestructive means to characterize tissue fiber structure; however, the descriptions so far have been mostly qualitative. This study presents a direct, quantitative comparison of high-resolution MR fiber mapping and histology measurements in a block of excised canine myocardium. Results show an excellent correspondence of the measured fiber angles not only on a point-by-point basis (average difference of -2.30 +/- 0.98 degrees, n = 239) but also in the transmural rotation of the helix angles (average correlation coefficient of 0.942 +/- 0.008 with average false-positive probability of 0.004 +/- 0.001, n = 24). These data strongly support the hypothesis that the eigenvector of the largest MR diffusion tensor eigenvalue coincides with the orientation of the local myocardial fibers and underscore the potential of MR imaging as a noninvasive, three-dimensional modality to characterize tissue fiber architecture.

Animals↗
PubMed1997

Mechanistic roles of neutral surfactants on concurrent polarized and passive membrane transport of a model peptide in Caco-2 cells.

The transport of the model peptide Acf(NMef)2NH2 across Caco-2 cell monolayers was studied in the apical (AP) to basolateral (BL) and the BL to AP direction in the presence of Polysorbate 80 or Cremophore EL in the AP compartment. Increasing surfactant concentrations resulted in increasing AP-->BL peptide permeability and decreasing BL-->AP permeability. In either direction, limiting permeabilities were achieved at concentrations less than the critical micellar concentrations (cmc's) of the surfactants, and remained constant at much higher concentrations. These plateau permeabilities were not equivalent in the two directions. This residual assymetry was abolished by increasing the peptide concentration. Altogether, the observations support the presence of at least two pumps in Caco-2 cells for this peptide, polarized in the BL-->AP direction. These experimental results were analyzed within the context of a quantitative biophysical model incorporating concurrent passive diffusion across the AP and BL membranes accompanied by surfactant-inhibitable active polarized efflux across the AP membrane. The model was also used to locate the additional transport activity at the BL membrane as an uptake pump. Under conditions of complete inhibition, the intrinsic passive diffusional permeability of Acf(NMef)2NH2 was found to be 13 x 10(-6) cm/s, essentially identical with results reported earlier with this peptide utilizing verapamil as an inhibitor. With respect to the mechanism of surfactant inhibition of the apical efflux transport, the monomeric species was found to be responsible with no contribution from micelles. Modeling the mode of inhibition as a noncompetitive Michaelis-Menten process gave identical Kis of 0.5 microM for the two surfactants. Finally, increase of either surfactant beyond 750 microM resulted in a decrease of peptide permeability in the AP-->BL direction. This was attributed to weak association of the peptide with micelles in the AP compartment, which effectively decreased the thermodynamic activity of the peptide at surfactant concentrations greater than 20 times their cmc. Both the experimental approach and accompanying theoretical model demonstrated in this work will allow for further characterization of the inhibitory potencies of surfactants for the nonpassive efflux pathway in vitro and in vivo.

Biological Transport↗
PubMed2005

Modeling the signaling endosome hypothesis: why a drive to the nucleus is better than a (random) walk.

BACKGROUND: Information transfer from the plasma membrane to the nucleus is a universal cell biological property. Such information is generally encoded in the form of post-translationally modified protein messengers. Textbook signaling models typically depend upon the diffusion of molecular signals from the site of initiation at the plasma membrane to the site of effector function within the nucleus. However, such models fail to consider several critical constraints placed upon diffusion by the cellular milieu, including the likelihood of signal termination by dephosphorylation. In contrast, signaling associated with retrogradely transported membrane-bounded organelles such as endosomes provides a dephosphorylation-resistant mechanism for the vectorial transmission of molecular signals. We explore the relative efficiencies of signal diffusion versus retrograde transport of signaling endosomes. RESULTS: Using large-scale Monte Carlo simulations of diffusing STAT-3 molecules coupled with probabilistic modeling of dephosphorylation kinetics we found that predicted theoretical measures of STAT-3 diffusion likely overestimate the effective range of this signal. Compared to the inherently nucleus-directed movement of retrogradely transported signaling endosomes, diffusion of STAT-3 becomes less efficient at information transfer in spatial domains greater than 200 nanometers from the plasma membrane. CONCLUSION: Our model suggests that cells might utilize two distinct information transmission paradigms: 1) fast local signaling via diffusion over spatial domains on the order of less than 200 nanometers; 2) long-distance signaling via information packets associated with the cytoskeletal transport apparatus. Our model supports previous observations suggesting that the signaling endosome hypothesis is a subset of a more general hypothesis that the most efficient mechanism for intracellular signaling-at-a-distance involves the association of signaling molecules with molecular motors that move along the cytoskeleton. Importantly, however, cytoskeletal association of membrane-bounded complexes containing ligand-occupied transmembrane receptors and downstream effector molecules provides the ability to regenerate signals at any point along the transmission path. We conclude that signaling endosomes provide unique information transmission properties relevant to all cell architectures, and we propose that the majority of relevant information transmitted from the plasma membrane to the nucleus will be found in association with organelles of endocytic origin.

Animals↗
PubMed1992

Paracrine control of photomembrane removal.

Photomembrane turnover in vertebrate photoreceptors is regulated by light. Rod outer segments (ROS) shed membrane filled tips at light onset, during the coexistence of two light modulated processes: a dark priming factor and a light induction event. Transduction of these two signals is not direct but appears to involve the neural retina and diffusible paracrine molecules. I propose a model wherein three paracrines control this ROS tip shedding. Melatonin, a lipid soluble dark priming molecule, is synthesized in the dark by all photoreceptor cells, diffusing freely and separating the ROS disk membranes. A second paracrine, dopamine is released from the inner retina whenever light is absorbed by the 502 nm-cones, inhibiting melatonin synthesis. Third, a proposed trophic paracrine, "rostrophin", is released in the dark from internal horizontal cells, and stabilizes the photomembrane. Shedding occurs as rostrophin decreases in the presence melatonin; briefly at light onset or continuously in red or dim white light.

Animals↗
PubMed1991

Determination of glucose diffusion coefficients in biofilms with micro-electrodes.

A glucose micro-electrode was developed for direct measurements inside biofilms, and applied for the determination of effective diffusion coefficients in a model system of agar beads containing immobilized yeast cells. Two methods were used, one based on concentration gradients present at the liquid/solid interface of an active biofilm under steady-state conditions, the other based on the rate of glucose redistribution in an inactivated biofilm under transient-state conditions. Additional measurements with pH and oxygen micro-electrodes were performed and thus allowed for in-situ correction of the glucose electrode signal. From the micro-electrode measurements in the model system it was concluded that the glucose micro-sensor is a useful tool with which to obtain effective diffusion coefficients in biofilms.

Agar↗
PubMed2004

Brownian dynamics study of cytochrome f interactions with cytochrome c6 and plastocyanin in Chlamydomonas reinhardtii plastocyanin, and cytochrome c6 mutants.

Using Brownian dynamics simulations, all of the charged residues in Chlamydomonas reinhardtii cytochrome c(6) (cyt c(6)) and plastocyanin (PC) were mutated to alanine and their interactions with cytochrome f (cyt f) were modeled. Systematic mutation of charged residues on both PC and cyt c(6) confirmed that electrostatic interactions (at least in vitro) play an important role in bringing these proteins sufficiently close to cyt f to allow hydrophobic and van der Waals interactions to form the final electron transfer-active complex. The charged residue mutants on PC and cyt c(6) displayed similar inhibition classes. Our results indicate a difference between the two acidic clusters on PC. Mutations D44A and E43A of the lower cluster showed greater inhibition than do any of the mutations of the upper cluster residues. Replacement of acidic residues on cyt c(6) that correspond to the PC's lower cluster, particularly E70 and E69, was observed to be more inhibitory than those corresponding to the upper cluster. In PC residues D42, E43, D44, D53, D59, D61, and E85, and in cyt c(6) residues D2, E54, K57, D65, R66, E70, E71, and the heme had significant electrostatic contacts with cyt f charged residues. PC and cyt c(6) showed different binding sites and orientations on cyt f. As there are no experimental cyt c(6) mutation data available for algae, our results could serve as a good guide for future experimental work on this protein. The comparison between computational values and the available experimental data (for PC-cyt f interactions) showed overall good agreement, which supports the predictive power of Brownian dynamics simulations in mutagenesis studies.

Amino Acid Substitution↗
PubMed2001

Visual filling-in for computing perceptual surface properties.

The visual system is constantly confronted with the problem of integrating local signals into more global arrangements. This arises from the nature of early cell responses, whether they signal localized measures of luminance, motion, retinal position differences, or discontinuities. Consequently, from sparse, local measurements, the visual system must somehow generate the most likely hypothesis that is consistent with them. In this paper, we study the problem of determining achromatic surface properties, namely brightness. Mechanisms of brightness filling-in have been described by qualitative as well as quantitative models, such as by the one proposed by Cohen and Grossberg. We demonstrate that filling-in from contrast estimates leads to a regularized solution for the computational problem of generating brightness representations from sparse estimates. This provides deeper insights into the nature of filling-in processes and the underlying objective function one wishes to compute. This particularly guided the proposal of a new modified version of filling-in, namely confidence-based filling-in which generates more robust brightness representations. Our investigation relates the modeling of perceptual data for biological vision to the mathematical frameworks of regularization theory and linear spatially variant diffusion. It therefore unifies different research directions that have so far coexisted in different scientific communities.

Animals↗
PubMed1998

Derivation of unstirred-layer transport number equations from the Nernst-Planck flux equations.

Since the late 1960s it has been known that the passage of current across a membrane can give rise to local changes in salt concentration in unstirred layers or regions adjacent to that membrane, which in turn give rise to the development of slow transient diffusion potentials and osmotic flows across those membranes. These effects have been successfully explained in terms of transport number discontinuities at the membrane-solution interface, the transport number of an ion reflecting the proportion of current carried by that ion. Using the standard definitions for transport numbers and the regular diffusion equations, these polarization or transport number effects have been analyzed and modeled in a number of papers. Recently, the validity of these equations has been questioned. This paper has demonstrated that, by going back to the Nernst-Planck flux equations, exactly the same resultant equations can be derived and therefore that the equations derived directly from the transport number definitions and standard diffusion equations are indeed valid.

Diffusion↗
PubMed2005

Surface viscosity, diffusion, and intermonolayer friction: simulating sheared amphiphilic bilayers.

The flow properties of an amphiphilic bilayer are studied in molecular dynamics simulations, by exposing a coarse grained model bilayer to two shear flows directed along the bilayer surface. The first field, with a vorticity perpendicular to the bilayer, induces a regular shear deformation, allowing a direct calculation of the surface viscosity. In experiments this property is measured indirectly, by relating it to the diffusion coefficient of a tracer particle through the Saffman-Einstein expression. The current calculations provide an independent test of this relation. The second flow field, with a vorticity parallel to the bilayer, causes the two constituent monolayers to slide past one another, yielding the interlayer friction coefficient.

Computer Simulation↗
PubMed1999

Diffusion models for population dynamics incorporating individual behavior at boundaries: applications to refuge design.

We construct models for dispersal of a population which incorporate the response of individuals to interfaces between habitat types. The models are based on random walks where there may be a bias in the direction an individual moves when it encounters an interface. This sort of dispersal process is called skew Brownian motion. Our models take the form of diffusion equations with matching conditions across the interface between regions for population densities and fluxes. We combine the dispersal models with linear population growth models which assume that the population growth rate differs between regions of different habitat types. We use those models to study issues of refuge design. We specifically consider how the effectiveness of buffer zones depends on their size, quality, and the population's response to the interface between the buffer zone and the refuge.

Animals↗
PubMed1985

Lithium stimulation of granulopoiesis in diffusion chambers--a model of a humoral, indirect stimulation of stem cell proliferation.

Lithium has been recognized as a stimulator of granulopoiesis both in vivo and in vitro. The mechanism by which lithium provokes this stimulation is unclear, with previous data focusing on such divergent causes as direct effects on progenitor cells v elevations in granulocyte macrophage colony-stimulating activity (GM-CSA) production. In the present study, we used a model system of granulopoiesis in diffusion chambers to study this stimulation of granulopoiesis. Lithium pretreatment of mice followed by a rest period to allow for excretion of the lithium (confirmed by serum assays) revealed a stimulation of progenitor cell growth within the diffusion chambers. No changes in the serum and chamber fluid GM-CSA levels were discernible between the control host mice and the lithium-pretreated mice. These data indicate that lithium stimulates granulopoiesis by an indirect mechanism that does not appear to involve GM-CSA.

Animals↗
PubMed2005

A multi-scale stochastic drug release model for polymer-coated targeted drug delivery systems.

A multi-scale mathematical model for drug release of oral targeted drug delivery systems was developed and applied to a commercially available delayed release tablet (Asacol) that delivers 5-aminosalicyclic acid (5-ASA) to the colon. Underlying physical and biochemical principles governing the involved processes (diffusion and dissolution) were employed to develop the mathematical description. Finite element formulation was used to numerically solve the model equations. Molecular dynamics (MD) simulations were used to predict macro-scale transport properties of the drug and the biologic fluid. The effect of pH variability in the gastrointestinal tract environment on the dissolution of the polymeric enteric coating was investigated using the Monte Carlo method. The direct coupling method employed (MD) predicted a sufficiently accurate diffusion coefficient (5.7x10(-6) cm2 s-1) of the drug molecules in reasonable (3 h) computation times. The model was validated using experimental data from in vitro dissolution experiments and provided accurate prediction of the drug release from the delivery system (root mean square error of 5%). The amount of drug entering the systemic circulation, computed from the predicted drug release in varying pH environments in the small bowel, was 15-24%. This range was in good agreement with clinical in vivo data (13-36%) obtained from literature. This research shows that in silico experiments using mechanistic models and stochastic approaches can be used for drug design and optimization and as a decision making tool for physicians.

Administration, Oral↗
PubMed2003

A mathematical model of single target site location by Brownian movement in subcellular compartments.

The location of distinct sites is mandatory for many cellular processes. In the subcompartments of the cell nucleus, only very small numbers of diffusing macromolecules and specific target sites of some types may be present. In this case, we are faced with the Brownian movement of individual macromolecules and their "random search" for single/few specific target sites, rather than bulk-averaged diffusion and multiple sites. In this article, I consider the location of a distant central target site, e.g. a globular protein, by individual macromolecules executing unbiased (i.e. drift-free) random walks in a spherical compartment. For this walk-and-capture model, the closed-form analytic solution of the first passage time probability density function (p.d.f.) has been obtained as well as the first and second moment. In the limit of a large ratio of the radii of the spherical diffusion space and central target, well-known relations for the variance and the first two moments for the exponential p.d.f. were found to hold with high accuracy. These calculations reinforce earlier numerical results and Monte Carlo simulations. A major implication derivable from the model is that non-directed random movement is an effective means for locating single sites in submicron-sized compartments, even when the diffusion coefficients are comparatively small and the diffusing species are present in one copy only. These theoretical conclusions are underscored numerically for effective diffusion constants ranging from 0.5 to 10.0 microm(2) s(-1), which have been reported for a couple of nuclear proteins in their physiological environment. Spherical compartments of submicron size are, for example, the Cajal bodies (size: 0.1-1.0 microm), which are present in 1-5 copies in the cell nucleus. Within a small Cajal body of radius 0.1 microm a single diffusing protein molecule (with D=0.5 microm(2) s(-1)) would encounter a medium-sized protein of radius 2.5 nm within 1 s with a probability near certainty (p=0.98).

Animals↗
PubMed1976

Numerical determination of intestinal membrane diffusing constants by a gradient method.

Optimisation problems arising in the identification of kinetic parameters of intestinal membranes are here considered. The dynamic behaviour of the membrane is described by means of a linear compartmental model. Using optimisation techniques of a gradient type, the intestinal kinetic parameters are identified, minimising a quadratic criterion between experimental data of D-histidine transport and model prediction. Numerical results are reported and their physiological implications discussed. The quantitative assessment of the asymmetry of diffusion constants with respect to diffusion direction seems to be an important result of this work.

Biological Transport↗
PubMed2002

Diffusive permeability of rabbit peritoneum for small solutes in vitro: effect of gentamicin and insulin.

The purpose of the in vitro study was to compare the diffusive transport of creatinine, uric acid and glucose, directed from the interstitial (I) to the mesothelial (M) side of the peritoneum and in the opposite direction, before (15-60min) and after (75-120min) application of gentamicin and insulin. The experiments were undertaken on the rabbit parietal peritoneum in a modified Ussing chamber. A mathematical model was used to calculate a diffusive permeability coefficient P (in cm/s) and a diffusive mass transport coefficient KH (in mL/min). In the basic experimental series without drugs, the dynamics of peritoneal transport for examined solutes remained constant and there were no differences between transport directions (I--> M and M--> I). Mean values of P+/-SEM (KH+/-SEM) were 3.06+/-0.32 (321.1+/-33.5), 2.09+/-0.29 (219.2+/-30.7) and 2.73+/-0.47 (286.7+/-49.6) for creatinine, uric acid and glucose, respectively. The introduction of gentamicin decreased glucose transport directed from the mesothelial to the interstitial side of the membrane by about 12%. After insulin application we observed the increase of creatinine and glucose peritoneal transport rate. For creatinine, the above augmentation was by about 31% for I--> M and 83% for M--> I direction. In these conditions, the glucose transport directed from the interstitial to the mesothelial side of membrane increased by about 24%. Generally, in vitro gentamicin decreases, but insulin increases the diffusive permeability of the peritoneum for some small solutes. We suppose that these findings may be important for the efficiency of peritoneal dialysis.

Animals↗