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In this paper a periodic delay differential equation with spatial spread is investigated. This equation can be used to model the growth of malaria which is transmitted by a mosquito. Using monotone techniques, it is shown that the following bifurcation holds: either the disease dies out or the density of infectious people tends to a spatially homogeneous, time periodic and positive solution.
The effects of spatial movements of infected and susceptible individuals on disease dynamics is not well understood. Empirical studies on the spatial spread of disease and behaviour of infected individuals are few and theoretical studies may be useful to explore different scenarios. Hence due to lack of detail in empirical studies, theoretical models have become necessary tools in investigating the disease influence in host-pathogen systems. In this paper we developed and analysed a spatially explicit model of two interacting social groups of animals of the same species. We investigated how the movement scenarios of susceptible and infected individuals together with the between-group contact parameter affect the survival rate of susceptible individuals in each group. This work can easily be applied to various host-pathogen systems. We define bounds on the number of susceptibles which avoid infection once the disease has died out as a function of the initial conditions and other model parameters. For example, once disease has passed through the populations, a larger diffusion coefficient for each group can result in higher population levels when there is no between-group interaction but in lower levels when there is between-group interaction. Numerical simulations are used to demonstrate these bounds and behaviours and to describe the different outcomes in ecological terms.
The generation of the surface electromyogram (sEMG) is described with regard to the properties of the single muscle fiber action potential as source, the physical aspects of volume conduction and recording configuration, and the properties and firing pattern of motor units (MUs). The spatial aspect of the motor unit action potential (MUP) is emphasized in relation to the results of high-density, multichannel sEMG measurements. The endplate zone, depth, size, and position of MUs can be estimated. The use of muscle fiber conduction velocity measurements in channelopathies and the changes in pathological fatigue are described. Using the unique patterns of spatial spread of MUPs over the skin (MU fingerprint), MU classification and the determination of firing moments is done noninvasively. Clinical applications of high-density sEMG measurements are reviewed. Emerging possibilities provided by MUP size and fingerprint measurements in neuromuscular disease and motor control are discussed. We conclude that multichannel sEMG adds unique, and sometimes indispensable, spatial information to our knowledge of the motor unit.
An SEI metapopulation model is developed for the spread of an infectious agent by migration. The model portrays two age classes on a number of patches connected by migration routes which are used as host animals mature. A feature of this model is that the basic reproduction ratio may be computed directly, using a scheme that separates topography, demography, and epidemiology. We also provide formulas for individual patch basic reproduction numbers and discuss their connection with the basic reproduction ratio for the system. The model is applied to the problem of spatial spread of bovine tuberculosis in a possum population. The temporal dynamics of infection are investigated for some generic networks of migration links, and the basic reproduction ratio is computed-its value is not greatly different from that for a homogeneous model. Three scenarios are considered for the control of bovine tuberculosis in possums where the spatial aspect is shown to be crucial for the design of disease management operations.
Tracking spectral changes of rapidly varying signals is a demanding task. In this study, we explore on Monte Carlo-simulated glutamate-activated AMPA patch and synaptic currents whether a wavelet analysis offers such a possibility. Unlike Fourier methods that determine only the frequency content of a signal, the wavelet analysis determines both the frequency and the time. This is owing to the nature of the basis functions, which are infinite for Fourier transforms (sines and cosines are infinite), but are finite for wavelet analysis (wavelets are localized waves). In agreement with previous reports, the frequency of the stationary patch current fluctuations is higher for larger currents, whereas the mean-variance plots are parabolic. The spectra of the current fluctuations and mean-variance plots are close to the theoretically predicted values. The median frequency of the synaptic and nonstationary patch currents is, however, time dependent, though at the peak of synaptic currents, the median frequency is insensitive to the number of glutamate molecules released. Such time dependence demonstrates that the "composite spectra" of the current fluctuations gathered over the whole duration of synaptic currents cannot be used to assess the mean open time or effective mean open time of AMPA channels. The current (patch or synaptic) versus median frequency plots show hysteresis. The median frequency is thus not a simple reflection of the overall receptor saturation levels and is greater during the rise phase for the same saturation level. The hysteresis is due to the higher occupancy of the doubly bound state during the rise phase and not due to the spatial spread of the saturation disk, which remains remarkably constant. Albeit time dependent, the variance of the synaptic and nonstationary patch currents can be accurately determined. Nevertheless the evaluation of the number of AMPA channels and their single current from the mean-variance plots of patch or synaptic currents is not highly accurate owing to the varying number of the activatable AMPA channels caused by desensitization. The spatial nonuniformity of open, bound, and desensitized AMPA channels, and the time dependence and spatial nonuniformity of the glutamate concentration in the synaptic cleft, further reduce the accuracy of estimates of the number of AMPA channels from synaptic currents. In conclusion, wavelet analysis of nonstationary fluctuations of patch and synaptic currents expands our ability to determine accurately the variance and frequency of current fluctuations, demonstrates the limits of applicability of techniques currently used to evaluate the single channel current and number of AMPA channels, and offers new insights into the mechanisms involved in the generation of unitary quantal events at excitatory central synapses.
A three dimensional (3D) model of Ca(2+) diffusion and binding within a sarcomere of a myofibril, including Ca(2+) binding sites troponin, parvalbumin, sarcoplasmic reticulum Ca(2+) pump, and fluorescent Ca(2+)-indicator dye (fluo-3), was developed to numerically simulate laser scanning confocal microscope images of Ca(2+) "sparks" in skeletal muscle. Diffusion of free dye (D), calcium dye (CaD), and Ca(2+) were included in the model. The Ca(2+) release current was assumed to last 8 ms, to arise within 4 x 10(-5) microm(3) at the triad and to be constant during release. Line scan confocal fluorescence images of Ca(2+) sparks were simulated by 3D convolution of the calculated distribution of CaD with a Gaussian kernel approximating the point spread function of the microscope. Our results indicate that the amplitude of the simulated spark is proportional to the Ca(2+) release current if all other model parameters are constant. For a given release current, the kinetic properties and concentrations of the binding sites and the diffusion parameters of D, CaD, and Ca(2+) all have significant effects on the simulated Ca(2+) sparks. The simulated sparks exhibited similar amplitudes and temporal properties, but less spatial spread than experimentally observed sparks.
1. We sought to evaluate the contribution of the sarcoplasmic reticulum (SR) Ca2+ pump (vs. diffusion) to the kinetics of [Ca24]i decline during Ca2+ sparks, which are due to spontaneous local SR Ca2+ release, in isolated rat ventricular myocytes measured using fluo-3 and laser scanning confocal microscopy. 2. Resting Ca2+ sparks were compared before (control) and after the SR Ca2(+)-ATPase was either completely blocked by 5 microM thapsigargin (TG) or stimulated by isoprenaline. Na(+)-Ca2+ exchange was blocked using Na(+)-free, Ca(2+)-free solution (0 Na+, O Ca2+) and conditions were arranged so that the SR Ca2+ content was the same under all conditions when Ca2+ sparks were measured. 3. The control Ca2+ spark amplitude (281 +/- 13 nM) was not changed by TG (270 +/- 21 nM) or isoprenaline (302 +/- 10 nM). However, the time constant of [Ca2+]i decline was significantly slower in the presence of TG (29.3 +/- 4.3 ms) compared with control (21.6 +/- 1.5 ms) and faster with isoprenaline (14.5 +/- 0.9 ms), but in all cases was much faster than the global [Ca2+]i decline during a control twitch (177 +/- 10 ms). 4. The spatial spread of Ca2+ during the Ca2+ spark was also influenced by the SR Ca2+ pump. The apparent 'space constant' of the Ca2+ sparks was longest when the SR Ca2+ pump was blocked, intermediate in control and shortest with isoprenaline. 5. We conclude that while Ca2+ diffusion from the source of Ca2+ release is the dominant process in local [Ca2+]i decline during the Ca2+ spark, Ca2+ transport by the SR contributes significantly to both the kinetics and spatial distribution of [Ca2+]i during the Ca2+ spark.
The mRNA encoding the cloned substance K receptor was microinjected into Xenopus laevis oocytes. After expression of the mRNA, Ca2+ was imaged in the oocytes with a digital imaging fluorescence microscopy system using the Ca2(+)-sensitive dyes fura-2 and fluo-3. Application of substance K caused a dose-related wave of Ca2+ mobilization to spread from a focus and to elevate the Ca2+ concentration in the oocyte. Activation of endogenous muscarinic or angiotensin II receptors in noninjected oocytes evoked a similar response. The Ca2+ rise in oocytes induced by substance K was due to internal Ca2+ mobilization and was independent of external Ca2+, since it occurred in Ca2(+)-free medium fortified with 2 mM EGTA. The Ca2+ imaging was well correlated with ion current measurements of voltage-clamped oocytes. Imaging, in addition to detecting the spatial spread of Ca2+ across the cell, was at least as sensitive as voltage clamping and much faster when screening oocytes for the expression of receptor mRNAs that stimulate Ca2+ mobilization. While it is known that fertilization of Xenopus eggs causes a spreading wave of Ca2+ mobilization, we found that activation of either native or newly expressed receptors in oocytes causes a similar change in Ca2+ distribution.
Localized Ca(2+)-release signals (puffs) and propagated Ca(2+) waves were characterized in rat ureteric myocytes by confocal microscopy. Ca(2+) puffs were evoked by photorelease of low concentrations of Ins(1,4,5)P(3) from a caged precursor and by low concentrations of acetylcholine; they were also observed spontaneously in Ca(2+)-overloaded myocytes. Ca(2+) puffs showed some variability in amplitude, time course and spatial spread, suggesting that Ins(1,4,5)P(3)-gated channels exist in clusters containing variable numbers of channels and that within these clusters a variable number of channels can be recruited. Immunodetection of Ins(1,4,5)P(3) receptors revealed the existence of several spots of fluorescence in the confocal cell sections, supporting the existence of clusters of Ins(1,4,5)P(3) receptors. Strong Ins(1,4,5)P(3) photorelease and high concentrations of acetylcholine induced Ca(2+) waves that originated from an initiation site and propagated in the whole cell by spatial recruitment of neighbouring Ca(2+)-release sites. Both Ca(2+) puffs and Ca(2+) waves were blocked selectively by intracellular applications of heparin and an anti-Ins(1,4,5)P(3)-receptor antibody, but were unaffected by ryanodine and intracellular application of an anti-ryanodine receptor antibody. mRNAs encoding for the three subtypes of Ins(1,4,5)P(3) receptor and subtype 3 of ryanodine receptor were detected in these myocytes, and the maximal binding capacity of [(3)H]Ins(1,4,5)P(3) was 10- to 12-fold higher than that of [(3)H]ryanodine. These results suggest that Ins(1,4,5)P(3)-gated channels mediate a continuum of Ca(2+) signalling in smooth-muscle cells expressing a high level of Ins(1,4,5)P(3) receptors and no subtypes 1 and 2 of ryanodine receptors.
The small brown planthopper, Laodelphax striatellus, immigrates annually into Japan over the East China Sea from the Asian mainland. It is not known whether this long-distance dispersal has any effect on the genetic structure of Japanese L. striatellus populations. The dispersal of L. striatellus is suspected to be relevant to the population dynamics of infection with the parasitic bacterium Wolbachia, which causes cytoplasmic incompatibility in L. striatellus. Wolbachia infection has spread within and among Japanese L. striatellus populations due to this cytoplasmic incompatibility. In the present study, the geographic differences among II L. striatellus populations from Japan and Taiwan was investigated using allozyme polymorphism. FST values on three enzyme loci (GPI, PGM, and AK) indicated a geographically differentiated population structure. Significant differentiation was found even among populations located along the course of the long-distance dispersal. The results indicated that long-range dispersal of L. striatellus does not occur regularly over the main islands of Japan and that it does not have a large effect on the population structure of L. striatellus. This conclusion is in agreement with the geographically variable life history of L. striatellus adapted to local climates. The short-term rice stripe epidemic, which is vectored by L. striatellus, in northwestern Kyushu, Japan, during 1985 and 1986 corresponds to these results. Based on the present findings, short-distance dispersal was considered to drive the spatial spread of Wolbachia infection among L. striatellus populations.
The TATA element is a well-known example of a DNA promoter sequence recognized by the TATA box binding protein (TBP) through its intrinsic motion and deformability. Although TBP recognizes the TATA element octamer unusually (through the minor groove, which lacks the distinctive features of the major groove), single base-pair replacements alter transcriptional activity. Recent crystallographic experiments have suggested that TATA/TBP complexes differing by a single base pair retain substantial structural similarity despite their functional differences in activating transcription. To investigate the subtle role of sequence-dependent motion within the TATA element and certain aspects of its effect on assembly of the transcriptional complex, we examine 5-ns dynamics trajectories of 13 variant TATA/TBP complexes differing from each other by a single base pair. They include the wild-type (WT) adenovirus 2 major late promoter (AdMLP) TATA element, TATAAAAG (the octamer specifies positions -31 to -24 with respect to the transcription initiation site), and the variants A31 (i.e., AATAAAAG), T30, A29, C29, G28, T28, T27, G26, T26, C25, T25, and T24. Our simulated TATA/TBP complexes develop sequence-dependent structure and motion trends that may lead to favorable orientations for high-activity variants (with respect to binding TFIIA, TFIIB, and other transcription factors), while conversely, accelerate dissociation of low-activity TATA/TBP complexes. The motions that promote favorable geometries for preinitiation complexes include small rotations between TBP's N- and C-terminal domains, sense strand DNA backbone "slithering," and rotations in TBP's H2 and H2' helices. Low-activity variants tend to translate the H1 and H1' helices and withdraw the intercalating phenylalanines. These cumulative DNA and protein motions lead to a spatial spread of complex orientations up to 4 A; this is associated with an overall bend of the variant TATA/TBP complexes that spans 93 degrees to 110 degrees (107 degrees for the crystal reference). Taken together, our analyses imply larger differences when these local structural and bending changes are extended to longer DNA (upstream and downstream) and suggest that specific local TATA/TBP motions (e.g., shifts in TBP helices and TATA bases and backbone) play a role in modulating the formation and maintenance of the transcription initiation complex.
This article reviews how the uptake of neurotransmitter by glial amino acid transporters limits the spatial spread of transmitter to preserve the independent operation of nearby synapses, temporally shapes postsynaptic currents, and regulates the effects of tonic transmitter release. We demonstrate the importance of amino acid uptake and recycling mechanisms for preventing the loss of energetically costly neurotransmitter from the brain, and also examine the suggestion that glutamate uptake into glia plays a key role in regulating the energy production of the brain. Finally, we assess the role of glial amino acid transporters in transmitter recycling pathways.
A model has been formulated in to describe the spatial spread of an epidemic involving n types of individuals, when triggered by the introduction of infectives from outside. Wave solutions for such a model have been investigated in and have been shown only to exist at certain speeds. This paper establishes that the asymptotic speed of propagation, as defined in Aronson and Weinberger, of such an epidemic is in fact c0, the minimum speed at which wave solutions exist. This extends the known result for the one-type and host-vector epidemics.
A model is formulated to describe the spatial spread of an epidemic involving n types of individual. This encompasses the measles, host-vector and carrier-borne epidemics, and in addition rabies involving several species of animal. The existence, uniqueness and non-existence of wave solutions for different speeds are established for this model.
The flow mapping procedure has been developed in parallel to the standard pulsed Doppler procedure. It has a different purpose--picking up flow signals at the site of lesions rather than calibrating velocities--and has its own methodology, developed within the last six years. On the basis of invasive correlations performed in 267 cases of valvular heart disease, we review the three-fold purpose of the flow mapping technique: diagnosing lesions, relying on the presence of flow anomalies; assessing their severity, relying on the spatial spreading of these flow signals; and identifying the site of the lesion, which is a specific advantage, relying on the anatomical location of these flow signals and/or on the direction of the jets. For example, using this technique, it is now possible to easily differentiate a cusp tear from a leak of a bioprosthesis, to measure the size of the leaks, and to reconstruct the image of aortic or mitral stenotic areas. These optimal results are only obtained using an appropriate methodology which mainly includes a) the selection of adequate two-dimensional short axis planes in order to explore the diseased valve in its entirety, because of frequent assymetrical orifices, and to pick up the jets at their starting point, b) measurements of the abnormal areas, c) when jets are studied, a three dimensional approach is required in order to cope with the three dimensional nature of the jet and to make available the calculation of three dimensional indices of severity.(ABSTRACT TRUNCATED AT 250 WORDS)
Dye transfer between lens fiber cells and between lens epithelial cells and underlying fiber cells was studied using a wide dynamic range-cooled CCD camera, H2O immersion objectives and image analysis techniques. Each lens was decapsulated by a new technique which leaves the epithelial cells adherent to the lens fiber mass. Lucifer Yellow CH was injected into either single epithelial cells or single fiber cells using the standard whole cell configuration of the patch voltage clamp technique. The results demonstrate extensive dye communication between fiber cells at the lens posterior surface, anterior surface, and equatorial surface. Dye transfer between deep fiber cells was also observed. Dye transfer between approximately 10% of epithelial cells and their underlying fiber cells was apparent when care was taken to yield wide dynamic range images. This was required because the relatively high concentration of dye in the epithelial cell masks the presence of much lower dye concentrations in the underlying fiber cell. A mathematical model which includes dye concentration, time, and spatial spread suggests that those epithelial cells that are coupled to an underlying fiber cell are about as well dye coupled as the epithelial cells themselves. The relatively low dye concentration in a fiber cell is due to its larger volume and diffusion of the dye along the axis of the fiber away from the fiber/epithelial junction.
This paper describes a model for the spatial spread of an epidemic in which the latent period has a Gamma distribution with arbitrary mean and variance while the infected and uninfected may have different diffusion coefficients. Using a variant of the "linear chain trick" we derive a simple algorithm for the propagation speed of the infection front. By way of verification, we show that, with suitably matched parameters, the algorithm agrees closely with speeds obtained numerically from the corresponding model in which the latent period is a constant.
We measured spike rates in parallel with visually induced oscillations of multi-unit activity (MUA) and local field potentials (LFP) from cortical areas 17 and 18 of anesthetized cats. Variations in the three response types were systematically correlated with stimulus size and placement. Oscillation amplitudes of both MUA and LFP were on average low with stimuli covering just the receptive field and they increased progressively with larger stimuli, whereas average spike rates rather decreased monotonically with stimulus sizes beyond the receptive field (area 18) or reached a plateau with stimuli in the far surround (area 17). Thus, spike rates and oscillation amplitudes follow different rules of spatial summation. Since the spatial spread of the synchronized components of oscillations roughly matches the horizontal divergence zone of the pyramidal cells' axonal collaterals in area 17 and 18, the interconnected system of neighbouring columns seems to constitute a functional unit, within which the oscillations could exert their functional role.