Dynamics of populations with individual variation in dispersal on bounded domains

Most classical models for the movement of organisms assume that all individuals have the same patterns and rates of movement (for example, diffusion with a fixed diffusion coefficient) but there is empirical evidence that movement rates and patterns may vary among different individuals. A simple way to capture variation in dispersal that has been suggested in the ecological literature is to allow individuals to switch between two distinct dispersal modes. We study models for populations whose members can switch between two different nonzero rates of diffusion and whose local population dynamics are subject to density dependence of logistic type. The resulting models are reaction–diffusion systems that can be cooperative at some population densities and competitive at others. We assume that the focal population inhabits a bounded region and study how its overall dynamics depend on the parameters describing switching rates and local population dynamics. (Traveling waves and spread rates have been studied for similar models in the context of biological invasions.) The analytic methods include ideas and results from reaction–diffusion theory, semi-dynamical systems, and bifurcation/continuation theory.     

Rotating wave solutions of the FitzHugh–Nagumo equations

This paper will treat the bifurcation and numerical simulation of rotating wave (RW) solutions of the FitzHugh-Nagumo (FHN) equations. These equations are often used as a simple mathematical model of excitable media. The dependence of the solutions on a uniformly applied current, and also on the diffusion coefficients or domain size will be studied. Ranges of applied current and/or diffusion coefficients in which RW solutions are observed will be described using bifurcation theory and continuation methods. The bifurcation of time-periodic solutions of these FHN equations without diffusion is described first. Similar methods are then used to find RW solutions on a circular ring and numerical simulations are described. These results are then extended to investigate RW solutions on annular rings of finite cross-section. Scaling arguments are used to show how the existence of solutions depends on either the diffusion coefficient or on the size of the region.     

Formation of a regular dissipative structure: a bifurcation and non-linear analysis.

A non-linear reaction diffusion model of a negative feedback epigenetic control system is presented. The model involves synthesis of the mitotic inducing and inhibiting proteins, simultaneously with intercellular self-diffusion and cross-diffusion of the latter only. The importance of negative cross-diffusion for creating a regular dissipative structure is shown. A bifurcation analysis of the non-linear diffusive system has been performed and it is concluded that bifurcation is supercritical. Lastly, using Liapunov's direct method, it is shown that the pattern evolved by the system is globally asymptotically stable.     

Diffusion of lysozyme chloride in water and aqueous potassium chloride solutions.

The diffusion of lysozyme chloride in aqueous solution has been studied at 25 degrees C using the Goüy interferometric technique. The concentration dependence of the diffusion coefficient in water has been measured over the concentration range 1.1599-9.1556 gcm-3 and the results suggest a value of D 25, w at infinite dilution of 5.838 x 10(-6) cm2s-1. The variation in diffusion coefficient with ionic strength has also been considered by following the diffusion of 0.45% lysozyme chloride in a series of potassium chloride solutions. The value of D in 0.15 M KCl has been found to be approximately one quarter of that in water alone an the diffusion coefficient has been shown to increase markedly as the KCl concentration is reduced below 0.05 M. Interpretation of these observations involves consideration of solution electrostatic effects.     

Estimation of hematocrit profile symmetry recovery length downstream from a bifurcation

Downstream from a microvascular bifurcation the distribution of blood cells in the vessel lumen is not symmetric. A diffusion process is used to model the rearrangement of red cells as blood flows between junctions in the microcirculation. A Fourier series approach is used to solve the model diffusion convection equation in slit geometry. Both flat and parabolic velocity profiles are considered. The eigenvalues, found using the Rayleigh-Ritz method, are used to find an upper bound on distance required for a symmetric red cell distribution to be obtained. The method has also been applied to cylindrical geometry and the computed symmetry recovery lengths are compared to distances between bifurcations measured in vivo. These estimates indicate that red cell distributions are frequently asymmetric in the microcirculation. Such asymmetries can have a strong effect on plasma skimming and material balance calculations.     

Lateral diffusion of saturated phosphatidylcholines in cholesterol-containing bilayers

Lateral diffusion in oriented bilayers of saturated cholesterol-containing phosphatidylcholines, dipalmitoylphosphatidylcholine and dimyrilstoylphosphatidylcholine upon their limiting hydration has been studied by NMR with impulse gradient of magnetic field. For both systems, similar dependences of the coefficient of lateral diffusion on temperature and cholesterol concentration were observed, which agree with the phase diagram showing the presence of regions of ordered and unordered liquid-crystalline phases and a two-phase region. Under similar conditions, the coefficient of lateral diffusion for dipalmytoylphosphatidylcholine has lower values, which is in qualitative agreement with its greater molecular mass. A comparison of data for dipalmytoylphosphatidylcholine with the results obtained earlier for dipalmytoylsphyngomyelin/cholesterol under the same conditions shows, despite a similarity in phase diagrams, greater (two- to threefold) differences in the values of the coefficient of lateral diffusion and a different mode of dependence of the coefficient on cholesterol concentration. A comparison of data for dimyrilstoylphosphatidylcholine with the results obtained previously shows that the values of the coefficient of lateral diffusion and the mode of its dependence on cholesterol concentration coincide in the region of higher concentrations (more than 15 mole %) and differ in the region of lower concentrations (below 15 mole %). The discrepancies may be explained by different contents of water in the systems during the measurements. At a limiting hydration (more than 35%) of water, the coefficient of lateral diffusion decreases with increasing cholesterol concentration. If the content of water is about 25% (as a result of equilibrium hydration from vapors), the coefficient of lateral diffusion of phosphatidylcholine is probably independent of cholesterol concentration. This results from a denser packing of molecules in the bilayer at a lower water concentration, an effect that competes with the ordering effect of cholesterol.     

Electric field-induced concentration gradients in planar supported bilayers.

A simple method of generating electric field-induced concentration gradients in planar supported bilayers has been developed. Gradients of charged, fluorescently labeled probes were visualized by epifluorescence microscopy and could be observed at field strengths as low as 1 V/cm. Steady-state concentration gradients can be described by a simple competition between random diffusion and electric field-induced drift. A model based on this principle has been used to determine the diffusion coefficient of the fluorescent probes. This technique achieves a degree of electrical manipulation of supported bilayers that offers a variety of possibilities for the development of new molecular architectures and the study of biological membranes.     

Lateral diffusion of cholesterol in monolayers.

The surface diffusion coefficient of cholesterol in cholesterol monolayers has been measured as a function of cholesterol surface concentration. Two different radiochemical methods, one integral and the other differential, were developed which gave comparable results. In the integral method two cholesterol monolayers, one of which is radioactive, are isolated on inert hydrophilic supports and then brought into contact. After some time the supports are separated and the radioactivity of the supports is measured. The differential method is an autoradiographic experiment. Two cholesterol monolayers, one of which is radioactive, are separated by means of a thin barrier. Upon removal of the barrier and at later times, an autoradiographic plate is brought to within a fraction of a mm from the aqueous surface and exposed. The plates are developed and analysed. The data show that the cholesterol surface diffusion coefficient in the dilute monolayers is approximately 10(-6)cm2/s and is nearly independent of surface concentration up to a concentration corresponding to an area of 40 A2/molecule. As the monolayer becomes compressed beyond this surface concentration, the diffusion coefficient decreases ubruptly with the deeply decreasing surface tension to about 10(-7) cm2/s, when a fully condensed surface layer of 38 A2/molecule is reached. This diffusion coefficient is of the same order of magnitude as the diffusion coefficients measured in lipid bilayers and in membranes.     

Lecithin translational diffusion studied by pulsed nuclear magnetic resonance.

The translational diffusion coefficient of egg yolk and dilauroyl lecithin in optically isotropic phases containing sodium cholate has been measured using the pulsed NMR magnetic field gradient method. After a correction for geometrical factors the measured diffusion coefficient is found to agree well with previous determinations in phospholipid systems. The experimental data imply that the cubic mesophase of the lecithin-sodium cholate-water system contains continuous lipid aggregates. A possible model of the arrangement of the different amphiphile molecules in the cubic phase is discussed.     

Analysis of acetylene reduction rates of soybean nodules at low acetylene concentrations

It has been previously proposed that acetylene reduction data at subsaturating acetylene concentrations could be interpreted by use of the Michaelis-Menten equation, based on the acetylene concentration external to the nodules. One difficulty of this view is that the assumption that the system is not diffusion limited is violated when studying intact nodules. The presence of a gas diffusion barrier in the nodule cortex leads to an alternate expression for the gas exchange rates at subsaturating gas concentrations. A theoretical comparison of the `apparent' Michaelis-Menten model and diffusion model illustrated the difficulties observed in the former model of overestimating the Michaelis-Menten coefficient and yielding a correlation between the Michaelis-Menten coefficient and the maximum rate. On the other hand, use of a diffusion model resulted in (a) estimates of the Michaelis-Menten coefficient consistent with enzyme studies, (b) stability of the estimates of the Michaelis-Menten coefficient independent of treatment, and (c) a sensitivity of the diffusion barrier conductance to plant drought stress. It was concluded that all studies of nodule gas exchange need to consider possible effects caused by the presence of a diffusion barrier.     

Transient state isoelectric focusing. Experimental determination of apparent diffusion coefficients in polyacrylamide gels

A photoelectric scanning assembly utilizing uv absorption optics and an on-line digital data acquisition and processing system has been used to follow kinetically zone spreading during the defocusing stage (absence of electric field) of transient state isoelectric focusing (TRANSIF) in polyacrylamide gels. Measurement of the variance (σ²) of a diffusing zone as a function of time yields a linear relationship, the slope of which corresponds to the apparent diffusion coefficient (D) of the protein. A linear relationship is also obtained when the logarithm of the apparent diffusion coefficients (logD) are plotted vs acrylamide concentration (T). This relationship can be used to extrapolate D to zero gel concentration. The apparent diffusion coefficient measured in this way is significantly larger than the true diffusion coefficient. The slope of the plot logD vs T, designated C_R, is expected to be a measure of molecular size related to the retardation coefficient in polyacrylamide gel electrophoresis.     

Lateral diffusion of cholesterol and dimyristoylphosphatidylcholine in a lipid bilayer measured by pulsed field gradient NMR spectroscopy

The pulsed field gradient NMR method for measuring self-diffusion has been used for a direct determination of the lateral diffusion coefficient of cholesterol, fluorine labeled at the 6-position, for an oriented lamellar liquid-crystalline phase of dimyristoylphosphatidylcholine (DMPC)/cholesterol/water. It is found that the diffusion coefficients of DMPC and cholesterol are equal over a large temperature interval. The apparent energy of activation for the diffusion process (58 kJ/mol) is about the same as for a lamellar phase of DMPC/water, whereas the phospholipid lateral diffusion coefficient is approximately four times smaller in the presence of cholesterol.     

Regionalization and lateral diffusion of membrane proteins in unfertilized and fertilized mouse eggs

The unfertilized mouse egg has a round and highly villated main body and a "nipple" that is unvillated and buds off on fertilization to form the second polar body. Fluorescent markers stain the body more intensely than the nipple, which has been assumed to result from surface amplification due to microvilli. Using fluorescence recovery after photobleaching and microfluorescence photometry, we have measured the membrane protein diffusion and concentration on the main body and nipple region of unfertilized and on fertilized CD-1 mouse eggs. Two general membrane protein labels were used: rhodamine-labeled succinylated concanavalin A and trinitrobenzene sulfonate visualized with a rhodamine Fab fragment of a sheep anti-trinitrophenyl. We found that while the diffusion coefficient was the same on the nipple and main body, considerably higher recovery was observed on the nipple for both probes. The ratio of intensity of fluorescence on the nipple to main body was significantly lower for the concanavalin A stain than for the trinitrophenyl stain, indicating that true concentration gradients exist beyond those that result from surface amplification. The effect of fertilization was not general. No effect was observed for the concanavalin A stain for either diffusion coefficient or percent recovery. For the trinitrophenyl stain, percent recovery decreased approximately twofold while diffusion coefficient increased approximately threefold.     

具有食饵自身抑制作用的Volterra方程的极限环解

一、引言 在捕食者与食饵相互作用的生态数学模型中,比较典型的是Volterra模型(E.C.皮洛,1978)     

Diffusion measurements of water, ubiquinone and lipid bilayer inside a cylindrical nanoporous support: a stimulated echo pulsed-field gradient MAS-NMR investigation

Stimulated echo pulsed-field gradient 1H magic angle spinning NMR has been used to investigate the mobility of water, ubiquinone and tethered phospholipids, components of a biomimetic model membrane. The diffusion constant of water corresponds to an isotropic motion in a cylinder. When the lipid bilayer is obtained after the fusion of small unilamellar vesicles, the extracted value of lipid diffusion indicates unrestricted motion. The cylindrical arrangement of the lipids permits a simplification of data analysis since the normal bilayer is perpendicular to the gradient axis. This feature leads to a linear relation between the logarithm of the attenuation of the signal intensity and a factor depending on the gradient strength, for lipids covering the inner wall of aluminium oxide nanopores as well as for lipids adsorbed on a polymer sheet rolled into a cylinder. The effect of the bilayer formation on water diffusion has also been observed. The lateral diffusion coefficient of ubiquinone is in the same order of magnitude as the lipid lateral diffusion coefficient, in agreement with its localization within the bilayer.     

Diffusion of methylene blue in the human maxillary sinus mucosa

The coefficient of diffusion of methylene blue in pathologically changed human maxillary sinus mucosa in vitro has been estimated for the first time. The mean value of the diffusion coefficient is (4.8 +/- 2.9) x 10(-7) cm2/s. The method is based on the registration of the dynamics of reflectance of tissue samples under the action of the dye. The diffusion coefficient has been estimated by approximation of experimental data in the framework of the model presented.     

Permeability of lysozyme tetragonal crystals to water

Diffusion of water within cross-linked tetragonal crystals of hen egg-white lysozyme has been measured and simulated on a computer using the X-ray structure of water-filled channels within the crystal lattice. Relative to the self-diffusion coefficient of bulk water molecules, the experimental diffusion coefficient of water within the crystal was found to be 13 times reduced in the (001) crystallographic plane and 5 times reduced in the [001] direction. Comparison of the experimental and computer simulated diffusion coefficients shows that steric limitations for water diffusion are mostly responsible for this reduction of the water diffusion in the crystal, with the self-diffusion coefficient of intracrystalline water reduced by no more than 30–40% as compared to that of bulk water.     

Physical characteristics of ribosomal protein S4 from Escherichia coli

A hydrodynamic study of protein S4 from Escherichia coli 30 S ribosomal subunits indicates that this protein is moderately asymmetric. A sedimentation coefficient of 1.69 S and a diffusion coefficient of 7.58 X 10(-7) cm2/s suggest that S4 has an axial ratio of about 5:1 using a prolate ellipsoidal model. This structure should give a radius of gyration of about 29-30 A from small-angle neutron or small-angle x-ray scattering studies. This study has utilized quasi-elastic light scattering as an analytical tool to obtain a diffusion coefficient as well as a method to monitor sample quality. Using quasi-elastic light scattering in this manner allows an assessment of problems associated with protein purity which may be responsible for the many disparate results reported for ribosomal proteins and especially protein S4.