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Results for “Spatial heterogeneity”

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PubMed2004

Spatially heterogeneous dynamics and dynamic facilitation in a model of viscous silica.

We perform molecular dynamics simulations to study the structural relaxation dynamics of a model of viscous silica, the prototype of a strong glass former. We find that the melt dynamics are spatially heterogeneous regardless of whether the bulk relaxation is non-Arrhenius or Arrhenius, and cannot be understood as a statistical bondbreaking process. Further, we show that stringlike motion is suppressed by the covalent bondings, yet high particle mobility propagates continuously, supporting the concept of dynamic facilitation emphasized in recent theoretical work.

Journal Article↗

PubMed2002

Spatial heterogeneity in the heart: recent insights and open questions.

Within the left ventricular myocardium and despite its rather homogeneous structure, local myocardial perfusion varies substantially. Areas of low and high local flow differ with regard to substrate uptake, energy turnover, and demand. This spatial heterogeneity is related to distinct differences in local protein expression, forming the basis of a novel homeostatic mechanism.

Animals↗

PubMed1999

Blissful Ignorance? Departure Rules for Migrants in a Spatially Heterogeneous Environment.

Incomplete knowledge of the variation in site quality to be encountered during migration may make it necessary for birds to base their departure decisions on behavioural rules of thumb. Here I analyse four such rules for time-minimizers and show how they perform in spatially heterogeneous, autocorrelated environments. The first rule projects the currently experienced fuelling rate onto all the future sites, the second rule is based on a fixed expected rate along the route, the third rule assumes that the expected rate at sites nearby is close to the value currently experienced and the fourth rule uses the experienced values to form an expectation during migration. Simulations demonstrate that a global update rule which uses the current experience and interprets it as the global value to be expected at all the future sites is outperforming the second rule, which is based on fixed expectations, in nearly all circumstances and that it is very robust with respect to spatial autocorrelation and the degree of variability in fuelling rates. This rule leads to the repeatedly observed pattern of a shallow relationship between departure fuel load and fuel deposition rate. A third rule shows its best performance under the assumption that the quality of sites only changes little with distance and therefore comes close to the global update rule. The fourth departure rule, a modified version of the global update rule, which allows some adjustments of the expected value through all the experienced values so far, leads only to small increases in performance. Copyright 1999 Academic Press.

Journal Article↗

PubMed1985

Digital imaging fluorescence microscopy: spatial heterogeneity of photobleaching rate constants in individual cells.

Photobleaching and related photochemical processes are recognized experimental barriers to quantification of fluorescence by microscopy. We have measured the kinetics of photobleaching of fluorophores in living and fixed cells and in microemulsions, and have demonstrated the spatial variability of these processes within individual cells. An inverted fluorescence microscope and a high-sensitivity camera, together with high-speed data acquisition by a computer-controlled image processor, have been used to control precisely exposure time to excitation light and to record images. To improve the signal-to-noise ratio, 32 digital images were integrated. After correction for spatial variations in camera sensitivity and background fluorescence, the images of the relative fluorescence intensities for 0.065 micron2 areas in the object plane were obtained. To evaluate photobleaching objectively, an algorithm was developed to fit a three-parameter exponential equation to 20 images recorded from the same microscope field as a function of illumination time. The results of this analysis demonstrated that the photobleaching process followed first-order reaction kinetics with rate constants that were spatially heterogeneous and varied, within the same cell, between 2- and 65-fold, depending on the fluorophore. The photobleaching rate constants increased proportionally with increasing excitation intensity and, for benzo(a)pyrene, were independent of probe concentration over three orders of magnitude (1.25 microM to 1.25 mM). The propensity to photobleach was different with each fluorophore. Under the cellular conditions used in these studies, the average rates of photobleaching decreased in this order: N-(7-nitrobenz-2-oxa-1,3-diazole)-23,24-dinor-5-cholen-22-amine-3 beta-ol greater than acridine orange greater than rhodamine-123 greater than benzo(a)pyrene greater than fluorescein greater than tetramethylrhodamine greater than 1,1'dioctadecyl-3,3,3',3'-tetramethylindocarbocyanine. The photobleaching appears to be an oxidation reaction, in that the addition of saturated solutions of Na2S2O5 to mineral oil microemulsions eliminated photobleaching of N-(7-nitrobenz-2-oxa-1,3-diazole)-23,24-dinor-5-cholen-22-amine-3 beta-ol or benzo(a)pyrene. We identified experimental conditions to observe, without detectable photobleaching, fluorophores in living cells, which can not be studied anaerobically. Useful images were obtained when excitation light was reduced to eliminate photobleaching, as determined from zero-time images calculated from the exponential fit routine.(ABSTRACT TRUNCATED AT 400 WORDS)

4-Chloro-7-nitrobenzofurazan↗

PubMed2001

Spatial heterogeneity and critical patch size: Area effects via diffusion in closed environments.

We describe a class of mathematical models for critical patch size in which the mechanisms inducing area effects are based on source-sink population dynamics arising from dispersal throughout a closed, finite, but spatially heterogeneous environment. Our models are reaction-diffusion equations, but unlike classical KISS models for area effects they do not assume that there is dispersal across the boundary of the environment into a hostile exterior. We observe that simple rescaling has the same effects in our models as in KISS models and hence predicts the same sort of area effects, but that other sorts of rescaling may not predict area effects. The models considered here provide an alternative to the KISS models used in our previous work on species-area relationships in island biogeography.

Animals↗

PubMed1996

Competition in a spatially heterogeneous environment: modelling the risk of spread of a genetically engineered population.

In recent years regulations have been developed to address the risks of releasing genetically engineered organisms into the natural environment. These risks are generally considered to be proportional to the exposure multiplied by the hazard. Exposure is, in part, determined by the spatial spread of the organisms, a component of risk suited to mathematical analysis. In this paper we exampine a mathematical model describing the spread of organisms introduced into a hetereogeneous environment, focusing on the risk of spread and plausibility of containment strategies. Two competing populations are assumed, one the natural species and the other an engineered species or strain, both of which move randomly in a spatially heterogenous environment consisting of alternating favourable and unfavourable patches. The classical Lotka-Volterra competition model with diffusion is used. Analyses of the possible spread and invasion of engineered organisms are thus reduced to finding periodic travelling wave solutions to the model equations. We focus on whether a very small number of engineered organisms can spatially invade a natural population. Initially we investigate the problem for spatially periodic diffusion coefficients and demonstrate that, under the right circumstances and a large enough unfavourable patch, invasion does not succeed. However, if spatially periodic carrying capacities are assumed along with spatially varying diffusion rates, the situation is far more complex. In this case containment of the engineered species is no longer only a simple function of the unfavourable patch length. By using perturbation solutions to the nonuniform steady states, approximate invasion conditions are obtained.

DNA, Recombinant↗

PubMed2005

Unique spatial heterogeneity in ionic liquids.

A multiscale coarse-graining model for ionic liquids has been extended to investigate the unique aggregation of cations in ionic liquids through computer simulation. It has been found that, with sufficiently long side chains, the tail groups of cations aggregate to form spatially heterogeneous domains, while headgroups of the cations and the anions distribute as uniformly as possible. This is understood as the result of competition between the charged electrostatic interactions between headgroups and anions and the collective short-range interactions between the neutral tail groups. This aggregation can help to explain a number of experimentally observed physical phenomena in ionic liquids.

Journal Article↗

PubMed2004

Numerical approximations for an age-structured model of a population dispersing in a spatially heterogeneous environment.

As ecological information on life history and habitat characteristics has become more sophisticated, models have become more realistic, and simulation methodology has become more important. The numerical analysis of simulation models, especially those of complex structured ecological systems, is generally lacking. The numerical analysis techniques developed here are to help form a systematic basis for a simulation theory for physiologically structured, individual-based population models in a spatially heterogeneous habitat. The major thrust of this paper is to develop and analyse a finite-difference-finite-element numerical approximation scheme for a mathematical model of an age-structured population dispersing in a bounded spatial environment in Rn. The numerical scheme applies a characteristic finite-difference discretization for the time-age domain and a finite-element discretization with numerical integral modifications for the spatial domain. The scheme not only provides optimal error estimates from the numerical analysis perspective but also produces biologically reasonable approximate solutions in that the solutions remain non-negative. The existence and boundedness of the non-negative approximate solution are shown, and the optimal error estimate is proved.

Animals↗

PubMed2005

Spatially heterogeneous dynamics and the Adam-Gibbs relation in the Dzugutov liquid.

We perform molecular dynamics simulations of a one-component glass-forming liquid and use the inherent structure formalism to test the predictions of the Adam-Gibbs (AG) theory and to explore the possible connection between these predictions and spatially heterogeneous dynamics. We calculate the temperature dependence of the average potential energy of the equilibrium liquid and show that it obeys the Rosenfeld-Tarazona T(3/5) law for low temperature T, while the average inherent structure energy is found to be inversely proportional to temperature at low T, consistent with a Gaussian distribution of potential energy minima. We investigate the shape of the basins around the local minima in configuration space via the average basin vibrational frequency and show that the basins become slightly broader upon cooling. We evaluate the configurational entropy S(conf), a measure of the multiplicity of potential energy minima sampled by the system, and test the validity of the AG relation between S(conf) and the bulk dynamics. We quantify the dynamically heterogeneous motion by analyzing the motion of particles that are mobile on short and intermediate time scales relative to the characteristic bulk relaxation time. These mobile particles move in one-dimensional "strings", and these strings form clusters with a well-defined average cluster size. The AG approach predicts that the minimum size of cooperatively rearranging regions (CRR) of molecules is inversely proportional to S(conf), and recently (Phys. Rev. Lett. 2003, 90, 085506) it has been shown that the mobile-particle clusters are consistent with the CRR envisaged by Adam and Gibbs. We test the possibility that the mobile-particle strings, rather than clusters, may describe the CRR of the Adam-Gibbs approach. We find that the strings also follow a nearly inverse relation with S(conf). We further show that the logarithm of the time when the strings and clusters are maximum, which occurs in the late-beta-relaxation regime of the intermediate scattering function, follows a linear relationship with 1/TS(conf), in agreement with the AG prediction for the relationship between the configurational entropy and the characteristic time for the liquid to undergo a transition to a new configuration. Since strings are the basic elements of the clusters, we propose that strings are a more appropriate measure of the minimum size of a CRR that leads to configurational transitions. That the cluster size also has an inverse relationship with S(conf) may be a consequence of the fact that the clusters are composed of strings.

Journal Article↗

PubMed2001

Spatial heterogeneity of the nonlinear dynamics in the FMRI BOLD response.

Recent studies of blood oxygenation level dependent (BOLD) signal responses averaged over a region of interest have demonstrated that the response is nonlinear with respect to stimulus duration. Specifically, shorter duration stimuli produce signal changes larger than expected from a linear system. The focus of this study is to characterize the spatial heterogeneity of this nonlinear effect. A series of MR images of the visual and motor cortexes were acquired during visual stimulation and finger tapping, respectively, at five different stimulus durations (SD). The nonlinearity was assessed by fitting ideal linear responses to the responses at each SD. This amplitude, which is constant for different SD in a linear system, was normalized by the amplitude of the response to a blocked design, thus describing the amount by which the stimulus is larger than predicted from a linear extrapolation of the response to the long duration stimulus. The amplitude of the BOLD response showed a nonlinear behavior that varied considerably and consistently over space, ranging from almost linear to 10 times larger than a linear prediction at short SD. In the motor cortex different nonlinear behavior was found in the primary and supplementary motor cortexes.

Adult↗

PubMedDate not supplied

[Some problems of studying spatial heterogeneity of animal communities].

The efficiency of different techniques of data collection and processing was considered by the example of bird communities. Accounted variance of the coefficients of bird complex similarity was used as the measure. Annual censuses in different sites proved more expedient than a long-term census in a single key site to study medium- and small-scale spatial heterogeneity of bird communities. Averaging and generalization of data collected in different years and sites yielded satisfactory results. Estimated informativeness in this case proved closer to the real one compared to averaged long-term data since the included representation errors in space and time.

Animals↗

PubMed2002

Lung albumin accumulation is spatially heterogeneous but not correlated with regional pulmonary perfusion.

The contribution of pulmonary perfusion heterogeneity to the development of regional differences in lung injury and edema is unknown. To test whether regional differences in pulmonary perfusion are associated with regional differences in microvascular function during lung injury, pigs were mechanically ventilated in the prone position and infused with endotoxin (Escherichia coli 055:B5, 0.15 microg. kg(-1). h(-1); n = 8) or saline (n = 4) for 4 h. Extravascular albumin accumulation and perfusion were measured in multiple approximately 0.7-ml lung regions by injecting pigs with radiolabeled albumin and radioactive microspheres, respectively. Extravascular albumin accumulation was spatially heterogeneous but not correlated with regional perfusion. Extravascular albumin accumulation was greater in dorsal than ventral regions, and regions with similar albumin accumulation were spatially clustered. This spatial organization was less evident in endotoxemic than control pigs. We conclude that there are regional differences in lung albumin accumulation that are spatially organized but not mediated by regional differences in pulmonary perfusion. We speculate that regional differences in microvascular pressure or endothelial function may account for the observed distribution of extravascular albumin accumulation.

Albumins↗

PubMed2006

Nitrogen spatial heterogeneity influences diversity following restoration in a ponderosa pine forest, Montana.

The resource heterogeneity hypothesis (RHH) is frequently cited in the ecological literature as an important mechanism for maintaining species diversity. The RHH has rarely been evaluated in the context of restoration ecology in which a commonly cited goal is to restore diversity. In this study we focused on the spatial heterogeneity of total inorganic nitrogen (TIN) following restoration treatments in a ponderosa pine (Pinus ponderosa)/Douglas-fir (Pseudotsuga menziesii) forest in western Montana, USA. Our objective was to evaluate relationships between understory species richness and TIN heterogeneity following mechanical thinning (thin-only), prescribed burning (burn-only), and mechanical thinning with prescribed burning (thin/burn) to discern the ecological and management implications of these restoration approaches. We employed a randomized block design, with three 9-ha replicates of each treatment and an untreated control. Within each treatment, we randomly established a 20 x 50 m (1000 m2) plot in which we measured species richness across the entire plot and in 12 1-m(2) quadrats randomly placed within each larger plot. Additionally, we measured TIN from a grid consisting of 112 soil samples (0-5 cm) in each plot and computed standard deviations as a measure of heterogeneity. We found a correlation between the net increase in species richness and the TIN standard deviations one and two years following restoration treatments, supporting RHH. Using nonmetric multidimensional scaling ordination and chi-squared analysis, we found that high and low TIN quadrats contained different understory communities in 2003 and 2004, further supporting RHH. A comparison of restoration treatments demonstrated that thin/burn and burn-only treatments created higher N heterogeneity relative to the control. We also found that within prescribed burn treatments, TIN heterogeneity was positively correlated with fine-fuel consumption, a variable reflecting burn severity. These findings may lead to more informed restoration decisions that consider treatment effects on understory diversity in ponderosa pine/Douglas-fir ecosystems.

Biodiversity↗

PubMed1996

Spatially heterogeneous discrete waves in predator-prey communities over a patchy environment.

A model motivated by the earlier work of J. D. Murray and D. Stirzaker is proposed to describe the dynamics of predator-prey communities over a patchy environment. The model is a system of delay differential equations. It is shown that if only one time lag is incorporated into the model, then a branch of spatially homogeneous periodic solutions occur as a primary Hopf bifurcation. However, if two time lags are used to measure different delayed factors in the process of growth, decay, and predator consumption of the prey population, then stable spatially heterogeneous periodic solutions (discrete waves or phase-locked oscillations) may exist. The utilized method is based on center manifold, normal form, and equivariant Hopf bifurcation theory.

Animals↗

PubMed2002

Metapopulation dynamics and spatial heterogeneity in cancer.

With the advent of drugs targeting specific molecular defects in cancerous cells [Gorre, M. E., et al. (2001) Science 293, 876-880], it is important to understand the degree of genetic heterogeneity present in tumor cell populations and the rules that govern microdiversity in human cancer. Here, we first show that populations with different genotypes in genes influencing cell growth and programmed cell death coexist in advanced malignant tumors of the colon, exhibiting microsatellite instability. Detailed, physical mapping of the diverse populations shows them to be arranged in small, intermingling areas, resulting in a variegated pattern of diversity. Using computational modeling of the experimental data, we find that the coexistence between similar competitors is enhanced, instead of deterred, by spatial dynamics [Hanski, I. (1999) Metapopulation Dynamics (Oxford Univ. Press, New York)]. The model suggests a simple and plausible scenario for the generation of spatial heterogeneity during tumor progression. The emergence and persistence of the patterns of diversity encountered in the tumors can be generated without a need to invoke differences in mutation rates, neutrality of interactions, or separated time scales. We posit that the rules that apply to spatial ecology and explain the maintenance of diversity are also at work in tumors and may underlie tumor microheterogeneity.

Adenocarcinoma↗

PubMed2005

Spatial heterogeneity of daphniid parasitism within lakes.

Spatially explicit models show that local interactions of hosts and parasites can strongly influence invasion and persistence of parasites and can create lasting spatial patchiness of parasite distributions. These predictions have been supported by experiments conducted in two-dimensional landscapes. Yet, three-dimensional systems, such as lakes, ponds, and oceans, have received comparatively little attention from epidemiologists. Freshwater zooplankton hosts often aggregate horizontally and vertically in lakes, potentially leading to local host-parasite interactions in one-, two-, or three-dimensions. To evaluate the potential spatial component of daphniid parasitism driven by these local interactions (patchiness), we surveyed vertical and horizontal heterogeneity of pelagic Daphnia infected with multiple microparasites in several north temperate lakes. These surveys uncovered little evidence for persistent vertical patchiness of parasitism, since the prevalence of two parasites showed little consistent trend with depth in four lakes (but more heterogeneity during day than at night). On a horizontal scale of tens of meters, we found little systematic evidence of strong aggregation and spatial patterning of daphniid hosts and parasites. Yet, we observed broad-scale, basin-wide patterns of parasite prevalence. These patterns suggest that nearshore offshore gradients, rather than local-scale interactions, could play a role in governing epidemiology of this open water host-parasite system.

Animals↗

PubMedDate not supplied

Hairy root culture in a liquid-dispersed bioreactor: characterization of spatial heterogeneity.

A liquid-dispersed reactor equipped with a vertical mesh cylinder for inoculum support was developed for culture of Atropa belladonna hairy roots. The working volume of the culture vessel was 4.4 L with an aspect ratio of 1.7. Medium was dispersed as a spray onto the top of the root bed, and the roots grew radially outward from the central mesh cylinder to the vessel wall. Significant benefits in terms of liquid drainage and reduced interstitial liquid holdup were obtained using a vertical rather than horizontal support structure for the biomass and by operating the reactor with cocurrent air and liquid flow. With root growth, a pattern of spatial heterogeneity developed in the vessel. Higher local biomass densities, lower volumes of interstitial liquid, lower sugar concentrations, and higher root atropine contents were found in the upper sections of the root bed compared with the lower sections, suggesting a greater level of metabolic activity toward the top of the reactor. Although gas-liquid oxygen transfer to the spray droplets was very rapid, there was evidence of significant oxygen limitations in the reactor. Substantial volumes of non-free-draining interstitial liquid accumulated in the root bed. Roots near the bottom of the vessel trapped up to 3-4 times their own weight in liquid, thus eliminating the advantages of improved contact with the gas phase offered by liquid-dispersed culture systems. Local nutrient and product concentrations in the non-free-draining liquid were significantly different from those in the bulk medium, indicating poor liquid mixing within the root bed. Oxygen enrichment of the gas phase improved neither growth nor atropine production, highlighting the greater importance of liquid-solid compared with gas-liquid oxygen transfer resistance. The absence of mechanical or pneumatic agitation and the tendency of the root bed to accumulate liquid and impede drainage were identified as the major limitations to reactor performance. Improved reactor operating strategies and selection or development of root lines offering minimal resistance to liquid flow and low liquid retention characteristics are possible solutions to these problems.

Atropa belladonna↗

PubMed2006

Spatial heterogeneity in oligodendrocyte lineage maturation and not cerebral blood flow predicts fetal ovine periventricular white matter injury.

Although periventricular white matter injury (PWMI) is the leading cause of chronic neurological disability and cerebral palsy in survivors of premature birth, the cellular-molecular mechanisms by which ischemia-reperfusion contributes to the pathogenesis of PWMI are not well defined. To define pathophysiologic relationships among ischemia, acute cerebral white matter damage, and vulnerable target populations, we used a global cerebral ischemia-reperfusion model in the instrumented 0.65 gestation fetal sheep. We developed a novel method to make repeated measurements of cerebral blood flow using fluorescently labeled microspheres to resolve the spatial heterogeneity of flow in situ in three-dimensional space. Basal flow in the periventricular white matter (PVWM) was significantly lower than in the cerebral cortex. During global cerebral ischemia induced by carotid occlusion, flow to all regions was reduced by nearly 90%. Ischemia of 30 or 37 min duration generated selective graded injury to frontal and parietal PVWM, two regions of predilection for human PWMI. Injury was proportional to the duration of ischemia and increased markedly with 45 min of ischemia to extensively damage cortical and subcortical gray matter. Surprisingly, the distribution of PVWM damage was not uniform and not explained by heterogeneity in the degree of white matter ischemia. Rather, the extent of white matter damage coincided with the presence of a susceptible population of late oligodendrocyte progenitors. These data support that although ischemia is necessary to generate PWMI, the presence of susceptible populations of oligodendrocyte progenitors underlies regional predilection to injury.

Animals↗