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PubMed2006

Receptor-based models with hysteresis for pattern formation in hydra.

In this paper, we propose a new receptor-based model for pattern formation and regulation in a fresh-water polyp, namely hydra. The model is defined in the form of a system of reaction-diffusion equations with zero-flux boundary conditions coupled with a system of ordinary differential equations. The production of diffusible biochemical molecules has a hysteretic dependence on the density of these molecules and is modeled by additional ordinary differential equations. We study the hysteresis-driven mechanism of pattern formation and we demonstrate the advantages and constraints of its ability to explain different aspects of pattern formation and regulation in hydra. The properties of the model demonstrate a range of stationary and oscillatory spatially heterogeneous patterns, arising from multiple spatially homogeneous steady states and switches in the production rates.

Algorithms↗

PubMed2006

An integrated computational/experimental model of tumor invasion.

The intracellular and extracellular dynamics that govern tumor growth and invasiveness in vivo remain poorly understood. Cell genotype and phenotype, and nutrient, oxygen, and growth factor concentrations are key variables. In previous work, using a reaction-diffusion mathematical model based on variables that directly describe tumor cell cycle and biology, we formulated the hypothesis that tumor morphology is determined by the competition between heterogeneous cell proliferation caused by spatial diffusion gradients, e.g., of cell nutrients, driving shape instability and invasive tumor morphologies, and stabilizing mechanical forces, e.g., cell-to-cell and cell-to-matrix adhesion. To test this hypothesis, we here obtain variable-based statistics for input to the mathematical model from in vitro human and rat glioblastoma cultures. A linear stability analysis of the model predicts that glioma spheroid morphology is marginally stable. In agreement with this prediction, for a range of variable values, unbounded growth of the tumor mass and invasion of the environment are observed in vitro. The mechanism of invasion is recursive subspheroid component development at the tumor viable rim and separation from the parent spheroid. Results of computer simulations of the mathematical model closely resemble the morphologies and spatial arrangement of tumor cells from the in vitro model. We propose that tumor morphogenesis in vivo may be a function of marginally stable environmental conditions caused by spatial variations in cell nutrients, oxygen, and growth factors, and that controlling these conditions by decreasing spatial gradients could benefit treatment outcomes, whereas current treatment, and especially antiangiogenic therapy, may trigger spatial heterogeneity (e.g., local hypoxia), thus causing invasive instability.

Animals↗

PubMed2004

Accounting for regional background and population size in the detection of spatial clusters and outliers using geostatistical filtering and spatial neutral models: the case of lung cancer in Long Island, New York.

BACKGROUND: Complete Spatial Randomness (CSR) is the null hypothesis employed by many statistical tests for spatial pattern, such as local cluster or boundary analysis. CSR is however not a relevant null hypothesis for highly complex and organized systems such as those encountered in the environmental and health sciences in which underlying spatial pattern is present. This paper presents a geostatistical approach to filter the noise caused by spatially varying population size and to generate spatially correlated neutral models that account for regional background obtained by geostatistical smoothing of observed mortality rates. These neutral models were used in conjunction with the local Moran statistics to identify spatial clusters and outliers in the geographical distribution of male and female lung cancer in Nassau, Queens, and Suffolk counties, New York, USA. RESULTS: We developed a typology of neutral models that progressively relaxes the assumptions of null hypotheses, allowing for the presence of spatial autocorrelation, non-uniform risk, and incorporation of spatially heterogeneous population sizes. Incorporation of spatial autocorrelation led to fewer significant ZIP codes than found in previous studies, confirming earlier claims that CSR can lead to over-identification of the number of significant spatial clusters or outliers. Accounting for population size through geostatistical filtering increased the size of clusters while removing most of the spatial outliers. Integration of regional background into the neutral models yielded substantially different spatial clusters and outliers, leading to the identification of ZIP codes where SMR values significantly depart from their regional background. CONCLUSION: The approach presented in this paper enables researchers to assess geographic relationships using appropriate null hypotheses that account for the background variation extant in real-world systems. In particular, this new methodology allows one to identify geographic pattern above and beyond background variation. The implementation of this approach in spatial statistical software will facilitate the detection of spatial disparities in mortality rates, establishing the rationale for targeted cancer control interventions, including consideration of health services needs, and resource allocation for screening and diagnostic testing. It will allow researchers to systematically evaluate how sensitive their results are to assumptions implicit under alternative null hypotheses.

Journal Article↗

PubMed1994

Functional architecture of vestibular primary afferents from the posterior semicircular canal of a turtle, Pseudemys (Trachemys) scripta elegans.

Physiological studies in many vertebrates indicate that vestibular primary afferents are not a homogeneous population. Such data raise the question of what structural mechanisms underlie these physiological differences and what functional role is played by afferents of each type. We have begun to answer these questions by characterizing the architecture of 110 afferents innervating the posterior canal of Pseudemys scripta. We emphasize their spatial organization because experimental evidence suggests that afferent physiological properties exhibit significant spatial heterogeneity. The sensory surface of the posterior canal comprises paired, triangular hemicristae, which are innervated by two afferent types. Bouton afferents (66% of total afferents) are found over the entire sensory surface. They differ significantly in the shape and size of their collecting areas, number of boutons, soma size, and axon diameter; this morphological variation is systematically related to the afferent's spatial position. In addition, multivariate analyses suggest that bouton afferents may comprise two subtypes: alpha afferents have delicate processes and are found throughout the crista; beta afferents are more robust and are concentrated preferentially toward the canal center. Calyx-bearing afferents comprise two morphological subtypes: dimorphs (13% of total afferents) bear calyceal and bouton endings; calyceal afferents (21%) bear calyceal endings only. Both types occur exclusively in an elliptical region near the center of each hemicrista; their morphology varies with radial distance from the center of this elliptical region. Our data provide evidence that in Pseudemys: (1) the classical vestibular afferent types (bouton, calyx, dimorph) are structurally heterogeneous, and (2) their spatial sampling characteristics are highly structured and distinctive for each type. These spatial patterns may shed light on regional differences in physiological profiles of vestibular afferents, and they raise questions about the role of this spatial heterogeneity in signaling head movement.

Animals↗

PubMed2005

Heterogeneous model of schistosomiasis transmission and long-term control: the combined influence of spatial variation and age-dependent factors on optimal allocation of drug therapy.

Prior field studies and modelling analyses have individually highlighted the importance of age-specific and spatial heterogeneities on the risk for schistosomiasis in human populations. As long-term, large-scale drug treatment programs for schistosomiasis are initiated in subSaharan Africa and elsewhere, optimal strategies for timing and distribution of therapy have yet to be fully defined on the working, district-level scale, where strong heterogeneities are often observed among sublocations. Based on transmission estimates from recent field studies, we develop an extended model of heterogeneous schistosome transmission for distributed human and snail population clusters and age-dependent behaviour, based on a 'mean worm burden + snail infection prevalence' formulation. We analyse its equilibria and basic reproduction patterns and their dependence on the underlying transmission parameters. Our model allows the exploration of chemotherapy-based control strategies targeted at high-risk behavioural groups and localities, and the approach to an optimal design in terms of cost. Efficacy of the approach is demonstrated for a model environment having linked, but spatially-distributed, populations and transmission sites.

Adolescent↗

PubMed2003

Spatial and temporal heterogeneity of Anopheles mosquitoes and Plasmodium falciparum transmission along the Kenyan coast.

The seasonal dynamics and spatial distributions of Anopheles mosquitoes and Plasmodium falciparum parasites were studied for one year at 30 villages in Malindi, Kilifi, and Kwale Districts along the coast of Kenya. Anopheline mosquitoes were sampled inside houses at each site once every two months and malaria parasite prevalence in local school children was determined at the end of the entomologic survey. A total of 5,476 Anopheles gambiae s.l. and 3,461 An. funestus were collected. Species in the An. gambiae complex, identified by a polymerase chain reaction, included 81.9% An. gambiae s.s., 12.8% An. arabiensis, and 5.3% An. merus. Anopheles gambiae s.s. contributed most to the transmission of P. falciparum along the coast as a whole, while An. funestus accounted for more than 50% of all transmission in Kwale District. Large spatial heterogeneity of transmission intensity (< 1 up to 120 infective bites per person per year) resulted in correspondingly large and significantly related variations in parasite prevalence (range = 38-83%). Thirty-two percent of the sites (7 of 22 sites) with malaria prevalences ranging from 38% to 70% had annual entomologic inoculation rates (EIR) less than five infective bites per person per year. Anopheles gambiae s.l. and An. funestus densities in Kwale were not significantly influenced by rainfall. However, both were positively correlated with rainfall one and three months previously in Malindi and Kilifi Districts, respectively. These unexpected variations in the relationship between mosquito populations and rainfall suggest environmental heterogeneity in the predominant aquatic habitats in each district. One important conclusion is that the highly non-linear relationship between EIRs and prevalence indicates that the consistent pattern of high prevalence might be governed by substantial variation in transmission intensity measured by entomologic surveys. The field-based estimate of entomologic parameters on a district level does not provide a sensitive indicator of transmission intensity in this study.

Animals↗

PubMedDate not supplied

Descriptive spatial analysis of BSE in western France.

The spatial heterogeneity of Bovine Spongiform Encephalopathy (BSE) was analysed on the 84 cases confirmed in western France (WF) between August and December 2000, when both the Mandatory Reporting System and an active surveillance on cattle at risk were running. Ninety-four percent of these cases were born between June 1993 and June 1996, and we analysed the location at birth. One disease mapping and two clustering methods (Scan of Kulldorff and the method of Besag and Newell) were used. In order to attenuate the contrasts artificially created by the standard disease mapping method (over-dispersion), we estimated the Standard Incidence Ratio (SIR) with a Bayesian method (Poisson-Gamma model) allowing a smoothing of the estimators. The geographical location of interest was the "canton", that divided the total area into 526 geographical units. The background population (2.6 million cattle) was obtained from the Agricultural Census 2000. We tested the hypothesis of a homogenous spatial distribution of the BSE risk where the expected number of BSE cases per unit area was obtained by applying the overall BSE rate in WF to each "canton", standardised on the type of breed, dairy versus beef suckler. The SIR ranged from 0.80 to 2.18 and the spatial distribution of BSE cases was significantly heterogeneous. Two spatial clusters were detected with the spatial scan statistics of Kulldorff and the method of Besag and Newell (18 to 20 observed BSE-cases per cluster with a radius of 45 km) centred on the "département" of Côtes-d'Armor and Mayenne. Another cluster was detected with the method of Besag and Newell (9 observed BSE-cases) in the "département" of Finistère. The results proved that the risk of BSE is linked to the geographical location in the area of the study.

Animals↗

PubMed2001

Texture analysis of fluorescence lifetime images of nuclear DNA with effect of fluorescence resonance energy transfer.

BACKGROUND: Fluorescence lifetime imaging microscopy (FLIM) is becoming an important tool in cellular imaging. In FLIM, the image contrast is concentration insensitive, whereas it is sensitive to the local environment and interactions of fluorophores such as fluorescence resonance energy transfer (RET). METHODS: Fluorescence microscopy, lifetime imaging, and texture analysis were used to study the spatial distribution of fluorophores bound to nuclear DNA. 3T3-Swiss albino mice fibroblast nuclei were labeled with Hoechst 33258 (Ho), an AT-specific dye, and 7-aminoactinomycin D (7-AAD), a GC-specific dye. Ho is a RET donor to the 7-AAD acceptor. RESULTS: Texture analysis of 50 alcohol-fixed nuclei quantitatively showed changes of spatial distribution of apparent donor lifetimes. RET increased the spatial heterogeneity in the phase and modulation lifetime images. In most of the doubly stained cells (about 80%), the phase and modulation lifetime distributions were spatially homogeneous. In about 20% of the cells, we noticed that lower phase and modulation lifetimes caused by RET were correlated with regions of high Ho intensity in the nuclei. CONCLUSIONS: The spatial lifetime heterogeneity of Ho in presence of 7-AAD seems to be caused by RET between closely spaced strands in the three dimensionally condensed regions of DNA.

3T3 Cells↗

PubMed2005

The unexpected importance of mosquito oviposition behaviour for malaria: non-productive larval habitats can be sources for malaria transmission.

BACKGROUND: Mosquitoes commute between blood-meal hosts and water. Thus, heterogeneity in human biting reflects underlying spatial heterogeneity in the distribution and suitability of larval habitat as well as inherent differences in the attractiveness, suitability and distribution of blood-meal hosts. One of the possible strategies of malaria control is to identify local vector species and then attack water bodies that contain their larvae. METHODS: Biting and host seeking, not oviposition, have been the focus of most previous studies of mosquitoes and malaria transmission. This study presents a mathematical model that incorporates mosquito oviposition behaviour. RESULTS: The model demonstrates that oviposition is one potential factor explaining heterogeneous biting and vector distribution in a landscape with a heterogeneous distribution of larval habitat. Adult female mosquitoes tend to aggregate around places where they oviposit, thereby increasing the risk of malaria, regardless of the suitability of the habitat for larval development. Thus, a water body may be unsuitable for adult mosquito emergence, but simultaneously, be a source for human malaria. CONCLUSION: Larval density may be a misleading indicator of a habitat's importance for malaria control. Even if mosquitoes could be lured to oviposit in sprayed larval habitats, this would not necessarily mitigate -- and might aggravate -- the risk of malaria transmission. Forcing mosquitoes to fly away from humans in search of larval habitat may be a more efficient way to reduce the risk of malaria than killing larvae. Thus, draining, fouling, or filling standing water where mosquitoes oviposit can be more effective than applying larvicide.

Animals↗

PubMed2003

Temporal heterogeneity in oxygen tension in human melanoma xenografts.

The spatial heterogeneity of the oxygen tension (pO(2)) in human and experimental tumours has been studied extensively, whereas studies of the temporal heterogeneity in pO(2) are sparse. In the work reported here, pO(2) was measured continuously over periods of at least 60 min in A-07 human melanoma xenografts by using the OxyLite fibre-optic oxygen-sensing device. The main purpose of the work was to establish the usefulness of the OxyLite system in measuring the temporal heterogeneity in pO(2) in tissues and to characterise the fluctuations in tissue pO(2) in A-07 tumours. The OxyLite device was found to be suitable for studies of the temporal heterogeneity in pO(2) in tumours. However, potential pitfalls were identified, and reliable pO(2) measurements require that precautions are taken to avoid these pitfalls, that is, erroneous pO(2) readings caused by tissue trauma induced by the probe, probe movements induced by reflex actions of the host mouse and occasional probe drift. Significant fluctuations in pO(2) were detected in the majority of the 70 tumour regions subjected to measurement. The fluctuations in different regions of the same tumour were in general temporally independent, implying that they were caused primarily by redistribution of the tumour perfusion rather than fluctuations in global perfusion. Fourier analysis of the pO(2) traces showed that the pO(2) usually fluctuated at frequencies lower than 1.5-2.0 mHz, corresponding to less than 0.1 cycle min(-1). Haemodynamic effects may cause pO(2) fluctuations in this frequency range, and hence, the redistribution of the perfusion could have been caused by morphological abnormalities of the tumour microvasculature. Moreover, acute hypoxia, that is, pO(2) fluctuations around 10 or 5 mmHg, was detected in 20 of 70 regions, that is, 29% (10 mmHg), or 27 of 70 regions, that is, 39% (5 mmHg). The median fraction of the time these regions were acutely hypoxic was 73% (10 mmHg) or 53% (5 mmHg). Consequently, if A-07 tumours are adequate models of tumours in man, acute hypoxia may be a commonly occurring phenomenon in neoplastic tissues, and hence, acute hypoxia is likely to cause resistance to radiation therapy and promote tumour aggressiveness.

Animals↗

PubMed2002

Simple model for heterogeneous flows of yield stress fluids.

Various experiments evidence spatial heterogeneities in sheared yield stress fluids. To account for heterogeneities in the velocity gradient direction, we use a simple model corresponding to a nonmonotonic local flow curve and study a simple shear geometry. Different types of boundary conditions are considered. Under controlled macroscopic shear stress Sigma, we find homogeneous flow in the bulk and a hysteretic macroscopic stress-shear-rate curve. Under controlled macroscopic shear rate Gamma;, shear banding is predicted within a range of values of Gamma;. For small shear rates, stick-slip can also be observed. These qualitative behaviors are robust to changes in the boundary conditions.

Journal Article↗

PubMed1985

Heterotrophic bacteria in water distribution systems. I. Spatial and temporal variation.

The drinking water distribution system of the city of Metz in France was sampled intensively during six, monthly surveys which were designed to determine the spatial and temporal distribution of total heterotrophic bacteria in the network. A non-hierarchical nearest-centroid clustering method was used for dividing the water distribution system into zones corresponding to different levels of bacterial density. The general pattern of the spatial heterogeneity showed a high degree of reproducibility. Since the frequency distribution of total heterotrophic bacteria within the zones was compatible with the negative binomial distribution, the water distribution system studied may be considered as being composed of several heterogeneous subsystems. The consistency of this structured spatial dispersion pattern of bacteria in light of some physical and chemical characteristics of the system is evident. In consideration of the principal features of flow in the system relevant to the layout of water mains, the location of zones of highest bacterial concentrations have been attributed to lower levels of chlorine residuals and prolonged retention time of the water in the network, especially in the storage units, before reaching the various distribution areas. Although the monthly variation in the bacterial concentration of the entire system showed a marked increase which was concomitant with warmest water temperatures, the zones were subject to noticeable discrepancies in the range of temporal variation.

Bacteria↗

PubMed2001

Protozoan community structure in a fractal soil environment.

Protozoan abundance was quantified, and 365 protozoan species were recorded, in 150 soil samples from an upland grassland in Scotland. Across the entire size range (2-200 pm) protozoan species richness varied by a factor of two, whereas abundance increased by a factor of 20 with decreasing body size. As the soil had fractal structure, the relatively flat species curve can be explained if spatial heterogeneity determines species number--for in a fractal environment, heterogeneity will be the same at all spatial scales. Community structure appeared to approach a temporary steady-state about six days after re-hydration of dried soil. A simple model based on combining the fractal character of increasing habitat area at smaller spatial scales, with the weight-specific energy requirements of protozoa, provided theoretical curves of abundance and biovolume on body size which provide a reasonable fit to real data. We suggest two possibilities--that the apparent competence of the theoretical model is fortuitous and the product of poorly understood dynamic elements of the trophic structure in the community; or that key elements of protozoan community structure in a fractal soil environment may be largely explained in terms of habitat space and energy requirements.

Animals↗

PubMed2004

The maintenance (or not) of polygenic variation by soft selection in heterogeneous environments.

On the basis of single-locus models, spatial heterogeneity of the environment coupled with strong population regulation within each habitat (soft selection) is considered an important mechanism maintaining genetic variation. We studied the capacity of soft selection to maintain polygenic variation for a trait determined by several additive loci, selected in opposite directions in two habitats connected by dispersal. We found three main types of stable equilibria. Extreme equilibria are characterized by extreme specialization to one habitat and loss of polymorphism. They are analogous to monomorphic equilibria in singe-locus models and are favored by similar factors: high dispersal, weak selection, and low marginal average fitness of intermediate genotypes. At the remaining two types of equilibria the population mean is intermediate but variance is very different. At fully polymorphic equilibria all loci are polymorphic, whereas at low-variance equilibria at most one locus remains polymorphic. For most parameters only one type of equilibrium is stable; the transition between the domains of fully polymorphic and low-variance equilibria is typically sharp. Low-variance equilibria are favored by high marginal average fitness of intermediate genotypes, in contrast to single-locus models, in which marginal overdominance is particularly favorable for maintenance of polymorphism. The capacity of soft selection to maintain polygenic variation is thus more limited than extrapolation from single-locus models would suggest, in particular if dispersal is high and selection weak. This is because in a polygenic model, variance can evolve independently of the mean, whereas in the single-locus two-allele case, selection for an intermediate mean automatically leads to maintenance of polymorphism.

Animals↗

PubMed2003

[Research progress on hydrological scaling].

With the development of hydrology and the extending effect of mankind on environment, scale issue has become a great challenge to many hydrologists due to the stochasticism and complexity of hydrological phenomena and natural catchments. More and more concern has been given to the scaling issues to gain a large-scale (or small-scale) hydrological characteristic from a certain known catchments, but hasn't been solved successfully. The first part of this paper introduced some concepts about hydrological scale, scale issue and scaling. The key problem is the spatial heterogeneity of catchments and the temporal and spatial variability of hydrological fluxes. Three approaches to scale were put forward in the third part, which were distributed modeling, fractal theory and statistical self similarity analyses. Existing problems and future research directions were proposed in the last part.

Models, Theoretical↗

PubMed2026

Toxoplasma gondii IgG seroprevalence in Mauritanian dromedary camels: First multi-regional survey.

Toxoplasma gondii is a globally distributed zoonotic parasite, and dromedary camels are important intermediate hosts in arid and semi-arid regions. However, information on T. gondii exposure in camels is lacking in Mauritania, which harbors one of the largest camel populations in West Africa. This study reports the first multi-regional seroepidemiological survey to estimate T. gondii seroprevalence and identify associated risk factors in Mauritanian dromedaries. Between 2023 and 2024, serum samples were collected from 953 camels across eight climatically distinct regions. Anti-T. gondii IgG antibodies were detected using the Modified Agglutination Test (MAT; cutoff≥1:20). Risk factors investigated included geographical region, sex, age group, and season of sampling, using multivariable logistic regression and a mixed-effects linear probability model accounting for regional clustering. The overall seroprevalence was 15.0% (143/953). Exposure varied markedly across regions, ranging from 0% in the hyper-arid northern regions of Adrar and Tagant to 41.7% in the southern Sahelian region of Guidimakha. This pronounced spatial gradient is consistent with contrasting climatic and ecological conditions, as higher rainfall and humidity in the south are hypothesized to favor environmental oocyst survival compared to the extreme aridity of the north. Geographical region and age were independent predictors of seropositivity. Compared with camels from Nouakchott, those from Guidimakha had higher odds of exposure (aOR = 2.63), whereas camels from Trarza had a markedly lower risk (aOR = 0.09). Camels older than 6 years were more than twice as likely to be seropositive as those aged 3-5 years, whereas sex and season were not associated with seropositivity. These findings indicate that T. gondii exposure is widespread in Mauritanian dromedaries and that ecological conditions may influence exposure patterns. The marked spatial heterogeneity supports targeted surveillance and One Health interventions to reduce the potential zoonotic risk associated with camel-derived food products.

Animals↗

PubMed1998

Spatial structure, environmental heterogeneity, and population dynamics: analysis of the coupled logistic map.

Spatial extent can have two important consequences for population dynamics: It can generate spatial structure, in which individuals interact more intensely with neighbors than with more distant conspecifics, and it allows for environmental heterogeneity, in which habitat quality varies spatially. Studies of these features are difficult to interpret because the models are complex and sometimes idiosyncratic. Here we analyze one of the simplest possible spatial population models, to understand the mathematical basis for the observed patterns: two patches coupled by dispersal, with dynamics in each patch governed by the logistic map. With suitable choices of parameters, this model can represent spatial structure, environmental heterogeneity, or both in combination. We synthesize previous work and new analyses on this model, with two goals: to provide a comprehensive baseline to aid our understanding of more complex spatial models, and to generate predictions about the effects of spatial structure and environmental heterogeneity on population dynamics. Spatial structure alone can generate positive, negative, or zero spatial correlations between patches when dispersal rates are high, medium, or low relative to the complexity of the local dynamics. It can also lead to quasiperiodicity and hyperchaos, which are not present in the nonspatial model. With density-independent dispersal, spatial structure cannot destabilize equilibria or periodic orbits that would be stable in the absence of space. When densities in the two patches are uncorrelated, the probability that the population in a patch reaches extreme low densities is reduced relative to the same patch in isolation; this "rescue effect" would reduce the probability of metapopulation extinction beyond the simple effect of spreading of risk. Pure environmental heterogeneity always produces positive spatial correlations. The dynamics of the entire population is approximated by a nonspatial model with mean patch characteristics. This approximation worsens as the difference between the patches increases and the dispersal rate decreases: Under extreme conditions, destabilization of equilibria and periodic orbits occurs at mean parameter values lower than those predicted by the mean parameters. Apparent within-patch dynamics are distorted: The local population appears to have the wrong growth parameter and a constant number of immigrants (or emigrants) per generation. Adding environmental heterogeneity to spatial structure increases the occurrence of spatially correlated population dynamics, but the resulting temporal dynamics are more complex than would be predicted by the mean parameter values. The three classes of spatial pattern (positive, negative, and zero correlation), while still mathematically distinct, become increasingly similar phenomenologically.

Animals↗

PubMed1994

Distinct spatiotemporal distributions of the N-methyl-D-aspartate receptor channel subunit mRNAs in the mouse cervical cord.

The distribution of five N-methyl-D-aspartate (NMDA) receptor channel subunit mRNAs in the mouse spinal cord from embryonic day 13 (E13) through postnatal day 56 (P56) was semiquantitatively examined at the cervical level via in situ hybridization with subunit-specific oligonucleotide probes. Signals for the epsilon 1 subunit mRNA were restricted to the most ventral portion of the spinal cord during embryonic stages. They extended to all laminae of the spinal cord except for the lamina 2 (substantia gelatinosa) during postnatal development. A wide expression of the epsilon 2 subunit mRNA was found in the spinal gray matter from E13 through neonatal stages, but the signals became restricted to the lamina 2 by P21. No significant signals for the epsilon 3 subunit mRNA were detected in the spinal cord at any developmental stages. The epsilon 4 subunit mRNA was distributed widely in the spinal cord during embryonic and early postnatal periods but decreased nearly to background levels by P21. In contrast to the differential distribution of the epsilon subunit mRNAs, the zeta 1 subunit mRNA was found ubiquitously at each developmental stage examined. These findings suggest that the molecular organization of the epsilon subunits may be different between the dorsal horn and the remaining regions in the mature spinal cord, which provides a molecular basis for functional heterogeneity of the NMDA receptor channel. Moreover, this spatial heterogeneity might be generated through drastic alterations in the subunit composition of the channel complex during spinal cord development.

Animals↗