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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

Interplay of chemotaxis and chemokinesis mechanisms in bacterial dynamics.

Motivated by observations of the dynamics of Myxococcus xanthus, we present a self-interacting random walk model that describes the competition between chemokinesis and chemotaxis. Cells are constrained to move in one dimension, but release a chemical chemoattractant at a steady state. The bacteria sense the chemical that they produce. The probability of direction reversals is modeled as a function of both the absolute level of chemoattractant sensed directly under each cell as well as the gradient sensed across the length of the cell. If the chemical does not degrade or diffuse rapidly, the one-dimensional trajectory depends on the entire past history of the trajectory. We derive the corresponding Fokker-Planck equations, use an iterative mean-field approach that we solve numerically for short times, and perform extensive Monte Carlo simulations of the model. Cell positional distributions and the associated moments are computed in this feedback system. Average drift and mean squared displacements are found. Crossover behaviors among different diffusion regimes are found.

Bacterial Physiological Phenomena↗
PubMed1998

Comparison of alopecia areata in human and nonhuman mammalian species.

Alopecia areata (AA) is a nonscarring form of inflammatory hair loss in humans. AA-like hair loss has also been observed in other species. In recent years the Dundee experimental bald rat and the C3H/HeJ mouse have been put forward as models for human AA. AA in all species presents with a wide range of clinical features from focal, locally extensive, diffuse hair loss, to near universal alopecia. Histologically, all species have dystrophic anagen stage hair follicles associated with a peri- and intrafollicular inflammatory cell infiltrate. Autoantibodies directed against anagen stage hair follicle structures are a consistent finding. Observations on AA pathogenesis suggest nonhuman species can provide excellent models for the human disease. Ultimately, animal models will be used to determine the genetic basis of AA, potential endogenous and/or environmental trigger(s), mechanism(s) of disease initiation and progression, and allow rapid evaluation of new and improved disease treatments.

Alopecia Areata↗
PubMed1973

Kinetics of diffusion and convection in 3.2-A pores. Exact solution by computer simulation.

The kinetics of transport in pores the size postulated for cell membranes has been investigated by direct computer simulation (molecular dynamics). The simulated pore is 11 A long and 3.2 A in radius, and the water molecules are modeled by hard, smooth spheres, 1 A in radius. The balls are given an initial set of positions and velocities (with an average temperature of 313 degrees K) and the computer then calculates their exact paths through the pore. Two different conditions were used at the ends of the pore. In one, the ends are closed and the balls are completely isolated. In the other, the ball density in each end region is fixed so that a pressure difference can be established and a net convective flow produced. The following values were directly measured in the simulated experiments: net and diffusive (oneway) flux; pressure, temperature, and diffusion coefficients in the pore; area available for diffusion; probability distribution of ball positions in the pore; and the interaction between diffusion and convection. The density, viscosity, and diffusion coefficients in the bulk fluid were determined from the theory of hard sphere dense gases. From these values, the "equivalent" pore radius (determined by the same procedure that is used for cell membranes) was computed and compared with the physical pore radius of the simulated pore.

Cell Membrane Permeability↗
PubMed2005

Measurement of the surface concentration for bioassay kinetics in microchannels.

We present a simple and versatile method, based on fluorescence microscopy, to reliably measure the concentration of advected molecules in the vicinity of surfaces in microchannels. This tool is relevant to many microfluidic applications such as immunoassays and single-molecule experiments, where one probes the kinetics of a reaction between an immobilized target and a reactant carried by the bulk flow. The characterization of the surface concentration highlights the dominant role of transverse diffusion, which generates an apparent diffusivity at the surface 3-4 orders of magnitude greater than molecular diffusion alone, even close to the point of injection. We directly measure the effects of the longitudinal position along the channel and of the flow rate on the concentration front and develop a simple analytical model that compares well with the data. Finally, we propose a method to properly account for concentration fronts in single-molecule measurements and use it to directly access the kinetics parameters of protamine-induced condensation of DNA.

Biological Assay↗
PubMed2002

Stable two-dimensional solitary pulses in linearly coupled dissipative Kadomtsev-Petviashvili equations.

We present a two-dimensional (2D) generalization of the stabilized Kuramoto-Sivashinsky system, based on the Kadomtsev-Petviashvili (KP) equation including dissipation of the generic [Newell-Whitehead-Segel (NWS)] type and gain. The system directly applies to the description of gravity-capillary waves on the surface of a liquid layer flowing down an inclined plane, with a surfactant diffusing along the layer's surface. Actually, the model is quite general, offering a simple way to stabilize nonlinear media, combining the weakly 2D dispersion of the KP type with gain and NWS dissipation. Other applications are internal waves in multilayer fluids flowing down an inclined plane, double-front flames in gaseous mixtures, etc. Parallel to this weakly 2D model, we also introduce and study a semiphenomenological one, whose dissipative terms are isotropic, rather than of the NWS type, in order to check if qualitative results are sensitive to the exact form of the lossy terms. The models include an additional linear equation of the advection-diffusion type, linearly coupled to the main KP-NWS equation. The extra equation provides for stability of the zero background in the system, thus opening a way for the existence of stable localized pulses. We focus on the most interesting case, when the dispersive part of the system is of the KP-I type, which corresponds, e.g., to capillary waves, and makes the existence of completely localized 2D pulses possible. Treating the losses and gain as small perturbations and making use of the balance equation for the field momentum, we find that the equilibrium between the gain and losses may select two steady-state solitons from their continuous family existing in the absence of the dissipative terms (the latter family is found in an exact analytical form, and is numerically demonstrated to be stable). The selected soliton with the larger amplitude is expected to be stable. Direct simulations completely corroborate the analytical predictions, for both the physical and phenomenological models.

Journal Article↗
PubMed2003

Unstable trigger waves induce various intricate dynamic regimes in a reaction-diffusion system of blood clotting.

In this work we demonstrate that the unstable trigger waves, connecting stable and unstable spatially uniform steady states, can create intricate dynamic regimes in one-dimensional three-component reaction-diffusion model describing blood clotting. Among the most interesting regimes are the composite and replicating waves running at a constant velocity. The front part of the running composite wave remains constant, while its rear part oscillates in a complex manner. The rear part of the running replicating wave periodically gives rise to new daughter waves, which propagate in the direction opposite the parent wave. The domain of these intricate regimes in parameter space lies in the region of monostability near the region of bistability.

Blood Coagulation↗
PubMed1980

A histochemical model dealing with an immobilized glucose oxidase-peroxidase system. The influence of diffusion limitations on histochemical results.

A histochemical model dealing with an immobilized bienzyme system (glucose oxidase-peroxidase) is presented. The model is an artificial proteic membrane obtained by a previously described co-cross-linking process. The kinetic properties of free and immobilized horseradish peroxidase were studied when 3,3'-diaminobenzidine is used as a hydrogen donor substrate. A new direct method was developed for immobilized enzyme activity measurements. Computer simulation based on experimental kinetic parameters was performed in order to discuss electron microscopy results. By changing diffusion limitations, various profiles of insoluble product were visualized inside the proteic film and no geometrical similarity was seen between enzyme distributions and insoluble osmiophilic product patterns.

Computers↗
PubMed1982

Experimental evidence for an "internal leak" of cat gastric mucosa after stimulation with histamine and carbachol.

Numerous factors are involved in the pathogenesis of gastric ulcer. Possibilities under discussion are acid back diffusion, a reduction in the quality of the gastric mucus, and vascular factors that give rise to local ischemia. One hypothetical model presented for consideration, is based on the notion of an "internal leak", as a result of which acid escapes out of the parietal cells directly into the interstitium. Using the cationic dye acridine orange in cats, it has been possible to show, in particular after prior stimulation with stimulation with histamine and carbachol, but not with pentagastrin, that a microfocal accumulation of the dye in the interstitium can indeed be found. Under conditions of hypoxia, this phenomenon was not observed. In view of the specific properties of the dye, it may be concluded that, under certain conditions, acid substances can indeed diffuse out of the parietal cells into the interstitium. this animal model offers distinct findings compatible with the pathogenetic concept of an "internal leak".

Acridine Orange↗
PubMed1995

Distribution of nerve growth factor following direct delivery to brain interstitium.

Several studies suggest the potential of nerve growth factor (NGF) in the treatment of patients with Alzheimer's disease. To characterize NGF transport within the brain interstitium, we implanted controlled release polymers containing NGF and [125I]NGF into the brains of adult male rats and measured spatial distributions of NGF for up to one week. NGF concentration in the brain was quantified using ELISA, radiation counting, and autoradiography. At 2 days post-implantation, quantities of NGF in excess of 50 pg per section were detected within thick (1 mm) coronal slices of the hemisphere ipsilateral to the site of implantation up to 3 mm rostral and caudal to the edge of the polymer. Lower levels of radioactivity (> 5 pg but < 50 pg NGF per section) could be detected throughout the rest of the brain. Levels were highest in the tissue sections containing the polymer, reaching 9.5 ng per section. Autoradiography of thin (20 microns) coronal sections indicated that local NGF concentrations immediately adjacent to the polymer approached 40 micrograms/ml. Analysis of sequential sections on the autoradiograph confirmed that NGF was transported only 2-3 mm from the polymer in any direction. At one week post-implantation, the pattern of NGF distribution was similar to that seen at 2 days, and concentrations remained high near the site of the implant. Comparison of local NGF concentration profiles to simple models of diffusion with first-order elimination suggests that the NGF moved through the tissue by diffusion through the interstitial space with a half-life on the order of 0.5 h. The limited range of NGF transport in brain tissue indicates that: (i) protein drug agents such as NGF will probably need to be delivered almost directly to the site of action for efficacy; and (ii) toxicities associated with delivery of NGF and other protein agents to non-target cells, as often occurs with systemic delivery of drugs, may be reduced by local, interstitial delivery since therapy can be restricted to a small volume of the brain.

Animals↗
PubMed2006

Impact of extracellular protein binding on passive and active drug transport across Caco-2 cells.

AIM: The objective of the study is to evaluate the mechanism behind alterations in passive and active transport of drugs in the presence of basolaterally applied extracellular protein using the Caco-2 cell model. METHODS: The permeation across Caco-2 monolayers of two groups of compounds, transported either solely by passive diffusion or partly also by active transport in the secretory direction, was studied at two donor concentrations in the absence or presence of bovine serum albumin (BSA, 0-4%). Each group contained compounds with high or low protein binding (PB) capabilities and high or low absorption in humans (fraction absorbed, f(a)). The unbound fraction (f(u)) of each compound was determined by ultrafiltration. RESULTS: The transport rate of the passively permeating compounds was the same in both apical-to-basolateral (absorptive) and basolateral-to-apical (secretory) directions in the absence of BSA. Basolaterally applied BSA increased the transport rate in the absorptive direction and decreased it in the secretory direction for all compounds, in direct proportion to the extent of PB. The efflux ratios for the actively transported compounds were reduced in the presence of BSA. CONCLUSIONS: Basolaterally applied BSA, which mimics in vivo PB, alters both passive and active drug transport in the Caco-2 cell model. Using C(u) in the calculations of transport rate allowed elucidation of the different mechanisms behind these alterations. Our data also suggest that active secretory transport for highly protein-bound compounds might have less effect in vivo than predicted from traditional Caco-2 cell models (without BSA).

Algorithms↗
PubMed1998

An investment appraisal approach to clinical trial design.

In this paper, a general investment appraisal model is presented which shows how pharmaceutical companies could take profit considerations into account when making decisions about the design of randomized controlled trials. A general model is presented based on the net present value method of investment appraisal. The approach is illustrated with a hypothetical example which shows how optimal (net present value maximizing) designs can be determined based on choices about sample size and endpoint measurement. The method could be extended to accommodate considerations about other trial design features, and could be used to determine a portfolio of studies which maximizes the expected return on a given development or trial budget. Furthermore, the approach could be used by pharmaceutical companies to evaluate the incremental costs and benefits of incorporating non-clinical objectives into trials, such as quality of life research and economic evaluation studies. A number of practical difficulties would need to be overcome to utilize the approach. Directions for further research are therefore highlighted centred on the key components of the model: a trial cost function, a product demand function, innovation diffusion processes and Bayesian approaches to trial design.

Bayes Theorem↗
PubMed1991

Electroviscosity of polyelectrolyte solutions.

A theoretical expression for the electroviscous effect in polyelectrolyte solutions, caused by the distortion of counterion-distribution and counterion flow around a polyion under a velocity gradient of solvent flow, was obtained to elucidate the characteristic behaviour of the viscosity of highly charged polyelectrolyte solutions observed at low salt concentration. The derivation of the theory was performed on the basis of the Navier-Stokes-Onsager equation, Poisson equation, and diffusion equations for low molecular ions by the use of a cell model (free-volume model) for a polyion. Energy dissipation was obtained without directly solving these equations. It was found that the derived expression of viscosity explained the experimental results satisfactorily, and that the streaming potential effect caused by the counterion flow played an essential role in the increase in viscosity of polyelectrolyte solutions at finite polymer concentration and low salt concentration ranges.

Journal Article↗
PubMed2005

Self-organisation of nacre in the shells of Pterioida (Bivalvia: Mollusca).

Changes in the morphology and orientation of crystals have been tracked across the nacreous layer in pterioid bivalves, by SEM and X-ray diffraction. Early crystals nucleated on the organic membrane usually covering the outer prismatic layer. They formed polycrystalline aggregates of various shapes, first at prism boundaries and progressively invading the prisms in a centripetal fashion. Their c-axes were perpendicular to the substrate, but the a- and b-axis were variously arranged. As they grew, nacreous crystals became individualized and acquired a common crystallographic orientation also in the a-b plane (with the b-axis in the direction of shell growth). Initial lamellae had well delineated growth fronts, which later changed to diffuse. The increasing orientation was explained by a competition model between nacreous plates within the growing lamellae, which was particularly effective in lamellae with delineated fronts. This competition between adjacent crystals could not take place in gastropod nacre because, contrary to the stepped mode of growth of bivalve nacre, vertical stacking predominated. Our model is an alternative to the heteroepitaxial model where the organic matrix supposedly acted as an orienting template, but is nevertheless compatible with the mineral bridge hypothesis that implied epitaxial growth of stacking nacreous tablets.

Animals↗
PubMed2005

Extracellular diffusivity determines contribution of high-versus low-affinity receptors to neural signaling.

Diffusion-weighted magnetic resonance imaging detects physiological changes in the human brain by highlighting alterations in local diffusivity. However, the causal link between brain tissue diffusivity and neural activity is poorly understood. Synaptic physiology studies in vitro coupled with biophysical modeling have suggested that extracellular diffusion affects the spatial profile of receptor activation during synaptic discharges. Here, we attempt to address this issue more directly, by recording synaptic currents from individual cells in acute brain slices while reducing the bath medium diffusivity by 25-30% (measured with two-photon microscopy) using inert dextran molecules. We find that retarding extracellular diffusion increases the activation of high-affinity NMDA, but not low-affinity AMPA, receptors in response to remote, spontaneous or evoked, synaptic releases of the common excitatory neurotransmitter glutamate. The results suggest that variations in extracellular diffusivity could reflect an altered contribution of higher- versus lower-affinity receptor types to the network activity of synaptic circuits.

Animals↗
PubMedDate not supplied

Nuclear magnetic spin-lattice relaxation of water protons caused by metal cage compounds.

The nuclear magnetic spin-lattice relaxation rates of water protons are reported for solutions of manganese(II), copper(II), and chromium(III) cage complexes of the sarcophagine type. As simple aqueous solutions, the complexes are only modest magnetic relaxation agents, presumably because they lack protons on atoms in the first-coordination-sphere protons that are sufficiently labile to mix the large relaxation rate at the metal complex with that of the bulk solvent. The relaxation is approximately modeled using spectral density functions derived for translational diffusion of the interacting dipole moments with the modification that the electron spin relaxation rate is directly included as a contribution to the correlation time. In all cases studied, the electron spin relaxation rate is sufficiently large that it contributes directly to the water-proton spin relaxation process. The poor relaxation efficiency of the cage compound may, however, be improved dramatically by binding the complex to a protein. The efficiency is improved even further if the rotational motion of the protein is reduced drastically by an intermolecular cross-linking reaction. The relaxation efficiency of the cross-linked protein-cage complexes rivals that of the best first-coordination-sphere relaxation agents like [Gd(DTPA)(H2O)]2- and [Gd(DOTA)(H2O)]-.

Aza Compounds↗
PubMed1991

Orientational distribution of 1,6-diphenyl-1,3,5-hexatriene in phospholipid vesicles as determined by global analysis of frequency domain fluorimetry data.

Polarized differential phase and modulation ratios were obtained for 1,6-diphenyl-1,3,5-hexatriene (DPH) in 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) vesicles by using multifrequency phase fluorometry. Data were analyzed in terms of both empirical sums-of-exponentials modeling and directly in terms of the orientational distribution functions. The orientational analysis model was used to recover the angular distribution of DPH and the rotational diffusion coefficient in the various membrane model systems throughout the phase transition. A global analysis methodology was utilized to obtain an internally consistent set of parameters that fit all of the data simultaneously. The rank order parameters (P2) and (P4) were extracted from the experimental data, and the angular distribution functions of DPH were calculated. When the time-zero anisotropy (r0) of several sets of data taken at various temperatures were linked in a single global analysis, better recovery of the fourth rank order parameter (P4), diffusion constant D, and r0 was obtained with respect to the unlinked analysis. From these recovered values, a detailed picture concerning the orientational distribution of DPH in membranes as a function of temperature was obtained. The results suggest that a single population of DPH molecules was present in the bilayers with their orientational distributions dependent upon the physical state of the membranes in the pure phases. During the phase transition, a superposition of two populations corresponding to the population of the pure phases was present. As the temperature increased in the transition region, one population was increasing at the expense of the other.

Diffusion↗
PubMed2003

Kinetics of reduction of nitrobenzene and carbon tetrachloride at an iron-oxide coated gold electrode.

The rates of reduction of carbon tetrachloride (CT) and nitrobenzene (NB) by iron-oxide coated gold electrodes were studied to gain insight into the processes that control reduction of groundwater contaminants by zerovalent metal permeable reactive barriers. Fe(III)-oxide films were deposited on gold electrodes with a small fraction of the Fe(III) electrochemically reduced to Fe(II) to investigate the role of Fe(II) in the reduction of the CT and NB. Mass transport to the surface of the oxide film was controlled through use of a well-defined flow-through system similar to a wall-jet electrode. The factors affecting the overall reduction rate were investigated by varying the Fe(II) content in the iron-oxide, controlling mass transport of the electroactive species to the oxide surface, and varying the thickness of the oxide film. The rates of reduction of CT and NB were found to be independent of Fe(II) content in the iron-oxide and were only slightly dependent on the rate of transport to the surface of the oxide under a few sets of reaction conditions. Conversely, the rates of reduction were greatly dependent on the thickness of the oxide film, with the reduction rate decreasing as the oxide thickness increased. Evidence suggests that the location of the reduction reaction for CT and NB is at the gold surface and supports a barrier model for the system studied, in which the oxide film physically impedes direct contact of the electroactive species and the gold electrode, increases the diffusion path length, and creates adsorption sites.

Adsorption↗