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A reaction-diffusion system based on FitzHugh-Nagumo dynamics is used to model the interactions between several neighbouring unmyelinated nerve fibres. A generalization of the idea of contracting blocks is used to establish global existence and stability results.
The three-dimensional (3D) diffusion model of Fogelson, A. L., and R. S. Zucker (1985. Biophys. J. 48: 1003-1017) has been employed as the basis of a refined version of the "Ca theory" for neurotransmitter release. As such, it has been studied here as to its ability to predict the time course of release under various conditions. In particular, conditions were chosen in which the temporal variations in intracellular Ca2+ concentration, the sole factor controlling the release according to the Ca theory, were modified and tested experimentally. The predictions of this model were compared with the experimental results. It is shown that the 3D diffusion model, similarly to earlier simpler versions of the Ca theory, predicts that the time course of release is highly sensitive to both the level of depolarization and the level of the resting concentration of intracellular Ca2+ Moreover, the 3D diffusion model predicts that the time course of release is insensitive to changes in temperature. In contrast, the experimental results show that the time course of release is invariant to the level of depolarization and to the resting level in intracellular Ca2+, but highly sensitive to variations in temperature.
We have systematically investigated the probe size and shape dependence of lateral diffusion in model dimyristoyl phosphatidylcholine membranes. Linear hydrophobic polymers, which differ in length by an order of magnitude, were used to explore the effect on the lateral diffusion coefficient of hydrodynamic restrictions in the bilayer interior. The polymers employed are isoprenoid alcohols--citronellol, solanesol, and dolichol. Tracer lateral diffusion coefficients were measured by fluorescence photobleaching recovery. Despite the large difference in lengths, the nitrobenzoxadiazole labelled alcohols all diffuse at the rate of lipid self-diffusion (5.0 x 10(-12) m2 s-1, 29 degrees C) in the liquid crystal phase. Companion measurements in isotropic polymer solution, in gel phase lipid membranes and with nonpolar fluorescent polyaromatic hydrocarbons, show a marked dependence of the lateral diffusion coefficient on the probe molecule size. Our results in the liquid crystal phase are in accord with free area theory which asserts that lateral diffusion in the membrane is restricted by the surface-free area. Probe molecules which are significantly longer than the host phospholipid, seven times longer in the case of dolichol, are still restricted in their lateral motion by the surface properties of the bilayer in the liquid crystal phase. Fluorescence quenching experiments indicate that the nitrobenzoxadiazole label does not reside at the aqueous interface, although it must reside in close proximity according to the diffusion measurements.
The diffusion model (Ratcliff, 1978) and the leaky competing accumulator model (LCA, Usher & McClelland, 2001) were tested against two-choice data collected from the same subjects with the standard response time procedure and the response signal procedure. In the response signal procedure, a stimulus is presented and then, at one of a number of experimenter-determined times, a signal to respond is presented. The models were fit to the data from the two procedures simultaneously under the assumption that responses in the response signal procedure were based on a mixture of decision processes that had already terminated at response boundaries before the signal and decision processes that had not yet terminated. In the latter case, decisions were based on partial information in one variant of each model or on guessing in a second variant. Both variants of the diffusion model fit the data well and both fit better than either variant of the LCA model, although the differences in numerical goodness-of-fit measures were not large enough to allow decisive selection between the models.
The present work describes a new experimental model of secondary infection which allows, through the recovery of the parasite together with its local in vivo environment, examination of the local nonadaptive immune response of the infected host and the differentiation of the parasite from protoscoleces to cysts. In this model we administered protoscoleces within silicone diffusion chambers, previously implanted into the peritoneal cavities of mice. The process of designing the model involved, first, determination of the optimal time postimplantation to infect the mice and, second, evaluation of the parasite's ability to establish infection within the chambers. The optimal time for infection was considered to be after the inflammation caused by implantation of the chambers had subsided. Our results showed that by day 20 postsurgery, three parameters used as indications of inflammation (complement C3, serum amyloid P protein, and polymorphonuclear cells in the peritoneum and in the chamber contents) had reverted to their normal levels. In our study of parasite differentiation, we found that 2-3% of the total number of parasites inoculated into the chambers were recovered as viable cysts after 100 days. Throughout the infection period, the population of parasites recovered was heterogeneous; certain parasite morphologies that have not been described previously were observed. In conclusion, the use of intraperitoneal diffusion chambers offers a potential tool for investigating the in vivo differentiation process of secondary cysts of Echinococcus granulosus in mice and the early local interactions between host and parasite during this process.
An analysis and a classification of protein disulphide connectivity in a set of distinct sequences are presented. We analyse the number of disulphides per sequence, the number of disulphides per residue and the length of disulphide cross-linked loops. Observed connectivities are classified according to the different possible types of arrangement. In addition, we classify disulphide connectivity by physical models describing the arrangement of multiple disulphides. Firstly, we consider whether the features of native connectivity arrangement are describable by the likelihood of diffusive contact in the unfolded state. This is referred to as the diffusion model, and was originated by Kauzmann. A second model, effectively the inverse of the diffusion model, describes native connectivity arrangement as dominated by the entropic stabilisation effect of cross-linkage. This is referred to as the entropic model. Additionally, we compare the distribution of disulphide cross-linked loops and of loops formed by disulphide-like contacts. For short sequences (less than about 75 residues) native connectivities tend to have entropically more-stabilising arrangement features, whilst for longer sequences (greater than about 200 residues) the diffusion model is appropriate. We introduce the concept of arrangement entropy as a measure of the complexity of a connectivity.
A fundamental problem in developmental biology concerns the proportioning of the developing tissue of a morphallactic system into different cell types in a way that is independent of the overall size of the tissue. The two main models for positional information in pattern formation, the source-sink models and the Turing reaction-diffusion models, have shortcomings that limit their applicability. In a previous paper, we described a model that can produce perfectly scale-invariant spatial patterns and analyzed some of its mathematical properties. In the present paper, we demonstrate some of the shortcomings of the standard reaction-diffusion models and discuss the applicability of our model to developmental systems.
We describe a method to measure protein mass transfer kinetics in ion exchange adsorbents for preparative chromatography based on the use of radioactively labeled protein. The method was developed and evaluated using lysozyme as a test protein with the three commercial strong-acid cation exchangers SP-Sepharose-FF, SP-Sepharose-XL, and S-HyperD. Iodination with 125I was used to label the protein, which was added in trace amounts (approximately 0.1%) to an unlabeled protein solution. The solution was recirculated through a shallow bed of the adsorbent particles and the radioactivity accumulated in the bed measured with a gamma-counter as a function of time. Radiotracer-based kinetics measurements were found to be in good agreement with results obtained with a conventional shallow-bed technique, provided that freshly labeled protein solutions were used. The method has advantages in terms of simplicity, ability to deal with adsorption from complex mixtures, and the potential for measurements under tracer diffusion conditions. Kinetics results obtained for the three different stationary phases were generally consistent with previous studies. Protein mass transfer can be described by a pore diffusion model with a nearly salt-independent pore diffusivity for SP-Sepharose-FF and by a homogeneous diffusion model with a saltindependent adsorbed phase diffusivity for S-HyperD. However, it appears that a more complex model, accounting for parallel pore and surface diffusion, is needed to describe protein mass transfer in SP-Sepharose-XL. The modeling results were found to be correlated with the apparent pore sizes determined by inverse SEC.
Diffuse panbronchiolitis (DPB) is a chronic lower respiratory tract infection commonly associated with persistent late-stage Pseudomonas aeruginosa infection. However, low-dose long-term therapy with certain macrolides is effective in most patients with DPB. The present study was designed to examine the effects of long-term erythromycin (ERY) therapy by using our established murine model of chronic respiratory P. aeruginosa infection. ERY or saline was administered from day 80 after intubation with a P. aeruginosa-precoated tube for the subsequent 10, 20, 40, and 80 days. Bacteriologic and histologic analyses of the murine lungs and electron microscopy of the intubated tube were performed. In the murine model, treatment with ERY for 80 days significantly reduced the number of viable P. aeruginosa organisms in the lungs (P < 0.05). The biofilm formed in situ by P. aeruginosa on the inner wall of the inoculation tube placed into the murine bronchus became significantly thinner after 80 days of ERY treatment. We conclude that the clinical efficacy of macrolides in DPB may be due at least in part to the reduction in P. aeruginosa biofilm formation.
Proteins with complex folding kinetics will be susceptible to misfolding at some stage in the folding process. We simulate this problem by using the diffusion-collision model to study non-native kinetic intermediate misfolding in a four-helix bundle protein. We find a limit on the size of the pairwise hydrophobic area loss in non-native intermediates, such that burying above this limit creates long-lasting non-native kinetic intermediates that would disrupt folding and prevent formation of the native state. Our study of misfolding suggests a method for limiting the production of misfolded kinetic intermediates for helical proteins and could, perhaps, lead to more efficient production of proteins in bulk.
In this paper we consider a diffusive-convective model for the dynamics of a population living in a polluted environment. Threshold results are given concerning the effect of the toxicant on the living population. Some analytic results are proved and numerical experiments give suggestions in more general cases.
The plasmodium of Physarum polycephalum is a large amoeboid organism showing rhythmic contraction everywhere within an organism, and moves by forming spatio-temporal patterns of the rhythmic contraction. We propose a reaction-diffusion-advection model for the pattern formation. This model is constructed under physiological suggestions that the chemical oscillator acts as a clock regulating the rhythmic contraction and interacts spatially not only by diffusion but also by advection of protoplasm. Behavior of the model is studied by numerical calculation, especially the effects of the advection term on a simple reaction-diffusion system. The advection effect reproduces experimentally observed phenomena of fluctuating propagation of the contraction wave. Concept of the reaction-diffusion-advection system is promising for modeling the mechanism of amoeboid behaviour in the Physarum plasmodium. Copyright 1999 Academic Press.
In this paper we report the development of a highly efficient numerical method for determining the principal characteristics (velocity, leading edge width, and peak height) of spatial invasions or epidemics described by deterministic one-dimensiohal reaction-diffusion models whose dynamics include a threshold or Allee effect. We prove that this methodology produces the correct results for single-component models which are generalizations of the Fisher model, and then demonstrate by numerical experimentation that analogous methods work for a wide class of epidemic and invasion models including the S-I and S-E-I epidemic models and the Rosenzweig-McArthur predator-prey model. As examplary application of this approach we consider the atto-fox effect in the classic reaction-diffusion model of rabies in the European fox population and show that the appropriate threshold for this model is within an order of magnitude of the peak disease incidence and thus has potentially significant effects on epidemic properties. We then make a careful re-parameterisation of the model and show that the velocities calculated with realistic thresholds differ surprisingly little from those calculated from threshold-free models. We conclude that an appropriately thresholded reaction-diffusion model provides a robust representation of the initial epidemic wave and thus provides a sound basis on which to begin a properly mechanistic modelling enterprise aimed at understanding the long-term persistence of the disease.
The quantitative influence of viscosity on dissolution kinetics is assessed under laminar flow conditions by utilizing a convective diffusion model for drug dissolution. Functional dependency of three types of viscosity inducing agents is established with respect to the parameters of fluid flow rate, diffusivity, and solubility. Studies of aqueous solutions of sucrose and of glycerol demonstrate that the decrease in dissolution rate of ethyl p-aminobenzoate is related to the decrease in solute diffusivity in these solutions, whereas the solubility change in the glycerol solutions has an additional independent simultaneous effect. Dissolution in hydroxypropyl cellulose solutions remains constant under fixed fluid flow conditions because of the negligible effect of the polymer upon the drug diffusivity. A change in fluid flow rate, however, alters the dissolution rate and correlates quantitatively with the rate of shear in the convective diffusion model. The interpretation of the effect of viscosity on dissolution kinetics with the convective diffusion model explains these phenomena quantitatively in terms of the fundamental mass transport processes.
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The pharmacokinetic performance of a matrix system for transdermal beta-estradiol (E(2)) delivery after multiple consecutive dosing in postmenopausal women undergoing hormone replacement therapy was investigated. The E(2) plasma profiles determined during the third application in 16 postmenopausal women were compared with results obtained in a published clinical study using the same patch in 24 postmenopausal women without E(2) pretreatment; they were compared with a theoretical diffusion/pharmacokinetic model. A conventional theoretical model with constant model parameter (CPM) obtained from in vitro mass balance experiments in a Franz cell type set up described successfully the transdermal E(2) bioavailability parameter AUC(0-96h) (4341.9 +/- 1513.1; calculated 4250.8) and C(average) (45.0 +/- 13.2; calculated 41.2). Also, experimentally, there was no significant drop in E(2) plasma values after patch removal and reapplication; this was corroborated by calculations. Accumulation of E(2) did not occur when several patches were applied consecutively over a period of 3 weeks. Steady state was achieved following application of the first patch. However, the differences between recorded E(2) plasma profiles and theoretical results detected at specific measurement points cannot be explained by the CPM model. Experimentally obtained plasma profiles were always lower in the morning and higher in the evening than predicted on the basis of the model. Measurements of in vivo skin temperature in the postmenopausal women showed oscillating temperature profiles in the form of a cosinor function: The temperature mesor of untreated postmenopausal women was 34.8 degrees C with an acrophase at 17.0 o'clock (95% CI: 14.30-19.30) and an amplitude of +/- 0.4 degrees C (p = 0.1). During the application of the patch the average temperature next to a patch rose 0.3 degrees C, which was statistically significant (p = 0.1). In the skin under the application of the matrix patch a mesor temperature was detected as 35.6 degrees C with an amplitude of +/- 0.5 degrees C with an acrophase at 17.51 o'clock (95% CI: 14.30-21.00) (p = 0.05). The temperature period was 24 h for all measurements and the maximum temperature was observed at about 16.30 h, and a minimum at about 5.00 h. A linear dependency was detected in in vitro experiments between the log of E(2) permeability and the temperature for stripped skin, epidermis/dermis layer, as well as for the matrix. Modeling of E(2) plasma profiles with oscillating diffusion coefficients (ODM1) with a sine wave function results in this equation: D(1) = D(0x) + Da(x).sin(k.t). D(0x) is the diffusion coefficient determined at 35.6 degrees C, k is 1/24 h, D(a) is the diffusion coefficient of the temperature amplitude, h is hour, and x stands for the respective diffusion layer. It was shown that the experimental E(2) plasma profile variations are more pronounced than can simply be explained by skin temperature variations alone (ODM1 model). A simplex fit with an oscillating diffusion coefficient in the form of a sine wave function for the stratum corneum (ODM2 model) resulted in a temperature amplitude of 1.1 degrees C, about twice as high as was determined in the in vivo measurements (ODM2 model). Therefore, other circadian parameterlike blood flow might superimpose the temperature profile. The improvement in data analysis by incorporating oscillating diffusion coefficients (ODM1 and 2) over CPM was judged from a comparison of experimental data with the calculated plasma profiles with the AIC, Akaikes model selection criterion, which allows ranking between models because it is independent of the scaling of the data points. ODM1 and ODM2 improved the data analysis over CPM by allowing better calculation of experimental C(max), t(max), the time to reach to C(max), and the fluctuation, f. No difference between CPM, ODM1, or ODM2 was found for the bioavailability parameter C(average) and AUC(0-96h).
The aim of this study was to develop a new rat model of diffuse brain injury (DBI) associated with acute subdural hemorrhage (SDH). In order to make this model more clinically relevant, we determined whether the varying hematoma volume, severity of DBI, or the presence of hypoxemia could influence the physiological consequence. SDH was made by an autologous blood injection, while DBI was induced using the impact acceleration model (mild, 450 g/1 m, severe, 450 g/2 m). Physiological parameters measured included intracranial pressure (ICP), mean arterial blood pressure (MABP), cerebral blood flow (CBF), and brain tissue water content. In the first series, 23 rats were randomized into the five following groups: Group 1, sham; Group 2, 400 (microL SDH; Group 3, SDH400 + mild DBI; Group 4, SDH400 + severe DBI; and Group 5, SDH300 + severe DBI. Results suggested that SDH300 + severe DBI (Group 5) may be the most suitable model, in which the MABP and CBF temporarily decreased during the SDH induction, but thereafter recovered to the baseline. Conversely, ICP was persistently elevated throughout the experiment. The water content was also significantly higher in both hemispheres compared to that of sham. In the second series, the animal was exposed to a hypoxemic insult (10 or 30 min) in addition to SDH300 + severe DBI (Group 6). The prolonged hypoxemia caused both a severe CBF reduction without recovery and a bilateral brain swelling, whereas the brief hypoxemia showed a gradual CBF recovery from the transient reduction and an increased water content only in the SDH side. These results suggest that these models may be potentially useful to study the combination of DBI and SDH with or without hypoxemia.
We report the measurement of optical transport parameters of pathologically characterized malignant tissues, normal tissues, and different types of benign tumors of the human breast in the visible wavelength region. A spatially resolved steady-state diffuse fluorescence reflectance technique was used to estimate the values for the reduced-scattering coefficient (mu(s)') and the absorption coefficient (mu(a)) of human breast tissues at three wavelengths (530, 550, and 590 nm). Different breast tissues could be well differentiated from one another, and different benign tumors could also be distinguished by their measured transport parameters. A diffusion theory model was developed to describe fluorescence light energy distribution, especially its spatial variation in a turbid and multiply scattering medium such as human tissue. The validity of the model was checked with a Monte Carlo simulation and also with different tissue phantoms prepared with polystyrene microspheres as scatterers, riboflavin as fluorophores, and methylene blue as absorbers.