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Modern European cranial variables and blood polymorphisms show comparable spatial patterns.

Spatial patterns in cranial traits for modern European populations are compared with patterns described by Sokal et al. (1989) for blood polymorphisms. Spatial patterns in these variables are described from both one-dimensional and directional autocorrelation correlograms. Manhattan distances computed among one-dimensional correlograms are used (1) to cluster variables with similar patterns and (2) to test the hypothesis that these clusters are to some extent accounted for by the type of variable. The one-dimensional correlograms for cranial traits do not show a significant contrast with either red cell antigens or the set of blood polymorphisms that excludes HLA. The only contrast that accounts for any of the cluster structure among one-dimensional correlograms is that between HLA and non-HLA variables. A cluster analysis of the directional correlograms demonstrates that cranial traits reflect patterns comparable to those for blood polymorphisms. This finding implies that patterns in cranial variables can be accounted for by the same, or similar, population processes as those inferred from patterns in blood polymorphisms. The implications of this finding for the likely origin of the northwest-southeast cline seen in some modern blood polymorphisms and modern cranial variables, but not in Neolithic cranial variables, are discussed.

Antigens

Dissecting spatial patterning and signaling with directional diffusion in spatial multi-omics.

Spatial multi-omics sequencing enables the simultaneous profiling of transcriptomics, proteomics, and epigenomics at a spatial resolution, offering insights into complex tissue organization and molecular regulation. However, the effective integration of multiple omics modalities in a spatial context remains a major challenge. Here, we present SpaDDM, a spatial multi-omics integration framework based on directional diffusion models (DDMs), which supports spatial pattern identification, cross-omics alignment, and inter-and intracellular signaling flow analysis. SpaDDM employs DDM-based graph networks to learn omics-specific representations by jointly incorporating spatial coordinates and molecular measurements within each modality, followed by an attention mechanism to align features across modalities. We benchmarked SpaDDM on diverse spatial multi-omics datasets, including transcriptomics-epigenomics and transcriptomics-proteomics combinations across multiple tissues and species. SpaDDM consistently outperformed existing methods by more accurately deciphering spatial tissue patterns and effectively reducing the boundary noise between spatial regions. Moreover, the learned low-dimensional coembedded representations of individual cells serve as integral mediators for inferring the signaling flows that underlie spatial patterning. Finally, we demonstrated that SpaDDM alignment of complementary information across multi-omics layers facilitates cross-omics translation and significantly improves the prediction of cell state alignments.

Multiomics

Spatial patterns of human gene frequencies in Europe.

The aims of this study of spatial patterns of human gene frequencies in Europe are twofold. One is to present new methodology developed for the analysis of such data. The other is to report on the diversity of spatial patterns observed in Europe and their interpretation as evidence of population processes. Spatial variation in 59 allele and haplotype frequencies (26 genetic systems) for polymorphisms in blood antigens, enzymes, and proteins is analyzed for an aggregate of 3,384 localities, using homogeneity tests, one-dimensional and directional spatial correlograms, and SYMAP interpolated surfaces. The data matrices are reduced to reveal the principal patterns by clustering techniques. The findings of this study can be summarized as follows: 1) There is significant heterogeneity in allele frequencies among the localities for all but one genetic system. 2) There are significant spatial patterns for most allele frequencies. 3) There is a substantial minority of clinal patterns in these populations. Clinal trends are found more frequently in HLA alleles than for other variables. North-south and northwest-southwest gradients predominate. 4) There is a strong decline in overall genetic similarity with geographic distance for most variables. 5) There are few, if any, appreciable correlations in pairs of allele frequencies over the continent, and there is little interesting correlation structure in the resulting correlation matrix. 6) Few spatial correlograms are markedly similar to each other, yet they form well-defined clusters. Spatial variation patterns, therefore, differ among allele frequencies. Patterns of human gene frequencies in modern Europe are diverse and complex. No single model suffices for interpretation of the observed genetic structure. Some clinal patterns reported here support the Neolithic demic-expansion hypothesis, others suggest latitudinal selection. Most of the clinal patterns are in HLA alleles, but there is also evidence from ABO for east-west migration diffusion. The majority of patterns are patchy, consistent with hypotheses of isolation by distance or of settlement of genetically differing, subsequently expanding ethnic groups. While undoubtedly there has been an ongoing stochastic process of differentiation consistent with the isolation-by-distance model, this has not obscured the directional patterns caused by migration (demic diffusion), and has perhaps only reinforced the contribution from settlement of ethnic units to patterns of genetic variation. However, the impact of the latter is most difficult to discern and requires further methodological developments.

ABO Blood-Group System

Rapid detection of spatial pattern by Fourier analysis.

Fast Fourier transform analysis can be used to accurately and rapidly detect pattern in large two-dimensional arrangements of points, such as the locations of cells in culture or plants in a unit square. We present here a sample study of pattern in spatial random point processes. This is evidently the first time that Fourier transform-based cross-correlation techniques have been applied to the analysis of point processes of biological origin. Radial profiles of the power spectra and autocorrelation estimates revealed a nearly constant interpore distance of 0.49 +/- 0.04 mm in the locations of eccrine gland pores on the surface of human skin. Additionally, gland-free areas may exist near hair follicles.

Algorithms

Spatial patterns underlying population differences in the background EEG.

A method is described which can be used to extract common spatial patterns underlying the EEGs from two human populations. These spatial patterns account, in the least-squares sense, maximally for the variance in the EEGs from one population and minimally for the variance in the other population and therefore would seem to be optimal for quantitatively discriminating between the individual EEGs in the two populations. By using this method, it is suggested that the problems associated with the more common approach to discriminating EEGs, significance probability mapping, can be avoided. The method is tested using EEGs from a population of normal subjects and using the EEGs from a population of patients with neurologic disorders. The results in most cases are excellent and the misclassification which occurs in some cases is attributed to the nonhomogeneity of the patient population particularly. The advantages of the method for feature selection, for automatically classifying the clinical EEG, and with respect to the reference-free nature of the selected features are discussed.

Adolescent

Spatial patterns of reflex evoked by pressure stimulation of the foot pads in cats.

1. The spatial patterns of reflexes elicited by localized pressure stimulation of the foot skin were analysed by recording electromyographic activities of various hindlimb muscles or muscle nerve discharges in cats anaesthetized with sodium pentobarbitone. 2. Reflex discharges evoked by stimulation of the central pad occurred mainly in physiological toe extensors located in the foot. Stimulus-response relationships of single motor units revealed characteristically wide ranges of graded response and recruitment. 3. Within the central pad, the strongest excitation was evoked from the central lobe and was distributed to extensors of all four toes. Excitation from the medial and the lateral lobes was usually asymmetrical and weaker in toe muscles of the stimulated side. It is suggested that the weakness was in part due to concomitant inhibition. 4. Stimulation of a toe pad caused marked suppression of central pad-evoked activity of toe extensors with a highly specific spatial pattern. The inhibition was strongest in extensors of its own toe, and gradually weaker in the more distant toes. Weak excitation was occasionally evoked in extensors of the most medial or lateral toes, when the most lateral or the most medial toe-pad, respectively, was stimulated. 5. A similar pattern of relfex to that from the toe pad was evoked from the claw base and the hairy toe dorsum of each digit. 6. Reflex effects, both inhibitory and excitatory, from the central and toe pads, claw bases and toe dorsum were maintained during prolonged stimuli, indicating that slowly adapting receptors contributed to these reflexes. 7. It is concluded that stimulation of localized skin areas of the foot, particularly the pads, evokes highly specialized reflexes, which may be important in controlling movements of individual digits.

Animals

Spatial patterns of cells in dividing epithelia.

The spatial patterns of cell boundaries in a view of the apical surface of a dividing epithelium are explored by constructing a hypothetical cell pattern of an epithelium of dividing cells. The two elements specified in the hypothetical pattern are the orientation of division planes and the separation between the division planes in neighbouring cells. The orientations of division planes in one generation are all the same but are orthogonal to those in the preceding generation. The division-plane orientations follow in an orthogonal succession, as happens in early embryos. The division planes in neighbouring cells are offset. The contractions of division planes that would occur during cytokinesis distort existing boundaries creating various types of cell shapes. The patterns generated resemble cell patterns found in life. The hypothetical pattern is regenerative and shows how epithelial cell patterns where cells divide might arise. It has enabled the putative identification of sister cells and first cousins in the embryonic chick chorion.

Animals

Spatial patterns produced by a reaction-diffusion system in primary hair follicles.

This paper is the third in a series examining the role of a reaction-diffusion (RD) system as the principal mechanism providing spatial information for cell differentiation during hair follicle initiation and development and hair fibre formation. A theoretical mechanism is described by which the RD system supplies positional information during hair follicle development. Solutions of the RD system within the primordial follicle are described as well as the sequence of spatial patterns provides the follicle/epidermis boundary conditions required to account for the density and grouping of follicles during initiation. At the same time the spatial patterns are also shown to be capable of providing the positional information which determines various geometrical aspects of follicle development; in particular the development of follicles at an angle to the skin surface and the initiation and location of sweat glands and sebaceous glands on the follicle.

Animals

Steady-state spatial patterns in a cell-chemotaxis model.

We investigate a simple cell-chemotaxis model for the generation of spatial patterns in cell aggregations. For simple boundary-value problems, we analyse the local and global bifurcation of spatially heterogeneous patterns away from the uniform equilibria as the total number of cells is varied. We also discuss the existence of periodic spatially structured solutions for the cells and chemoattractant in the infinite domain.

Animals

Temporal and spatial patterns of expression of laminin, chondroitin sulphate proteoglycan and HNK-1 immunoreactivity during regeneration in the goldfish optic nerve.

Current views suggest that the extracellular environment is critically important for successful axonal regeneration in the CNS. The goldfish optic nerve readily regenerates, indicating the presence of an environment that supports regeneration. An analysis of changes that occur during regeneration in this model may help identify those molecules that contribute to a favourable environment for axonal regrowth. We examined the distribution and expression of two extracellular matrix molecules, laminin and chondroitin sulphate proteoglycan, and a carbohydrate epitope shared by a family of adhesion molecules (HNK-1), using immunocytochemical detection in sections from the normal adult goldfish optic nerve and in nerves from one hour to five months following optic nerve crush. We also used in vitro preparations to determine if neurites in retinal explants could express these same molecules. The linear distributions of laminin and chondroitin sulphate proteoglycan immunoreactivity in control optic nerves are co-extensive with the glia limitans, suggesting both are expressed by non-neuronal components surrounding the axon fascicles. Between one and three weeks postoperatively when axons elongate and reach their target, laminin and chondroitin sulphate proteoglycan immunoreactivity increases around the crush site and distally. At six weeks postoperatively the pattern of immunoreactivity has returned to normal. While the temporal pattern of changes in immunoreactivity is similar, the spatial pattern of these two extracellular proteins in the regenerating nerve differs. Chondroitin sulphate proteoglycan immunoreactivity is organized in discrete columns associated with regenerating axons while laminin immunoreactivity is more diffusely distributed. Examination of retinal explants reveals growing neurites express chondroitin sulphate proteoglycan but not laminin. Our results suggest that laminin is only associated with non-neuronal cells, while chondroitin sulphate proteoglycan is associated with axons as well as non-neuronal cells. HNK-1 immunoreactivity is co-extensive with both the glia limitans and axon fascicles and is more extensively distributed in the intact nerve than either laminin or chondroitin sulphate proteoglycan immunoreactivity. In contrast to laminin and chondroitin sulphate proteoglycan, HNK-1 immunoreactivity is substantially decreased at the crush site within one week following optic nerve crush. HNK-1 immunoreactivity reappears through the crush site during the next several weeks, although non-immunoreactive regions, co-extensive with areas predominantly containing non-neuronal cells, persist both proximal and distal to the crush, up to six weeks postoperatively. The pattern suggests that HNK-1 epitope expression by these non-neuronal cells is decreased during axonal regeneration.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals

Spatial patterns and ESS's.

The classical idea of an evolutionarily stable strategy (ESS) does not involve any spatial dependence. An evolution equation for analyzing games in a region is suggested and the possibility of spatial patterns is investigated. It is shown that an ESS is so stable that it forbids any spatial dependence but that other equilibria may have patterns associated with them if the dispersion rates are suitably chosen.

Biological Evolution

Spatial patterns of spinal cord [14C]-2-deoxyglucose metabolic activity in a rat model of painful peripheral mononeuropathy.

Spatial patterns of spinal cord glucose metabolic activity were examined in unanesthetized rats with painful peripheral mononeuropathy produced by sciatic nerve ligation (chronic constrictive injury, CCI). Spinal cord metabolic activity was assessed 10 days after nerve ligation by using the fully quantitative [14C]2-deoxyglucose technique. This technique allows simultaneous examination of both neural activity inferred from local glucose utilization and its spatial distribution in multiple spinal regions previously implicated in nociceptive processing. Rats used in the experiment exhibited thermal hyperalgesia to radiant heat applied to the hind paw ipsilateral to nerve ligation and behaviors indicative of spontaneous pain. Sciatic nerve ligation produced a significant increase in spinal cord metabolic activity in four sampling regions (laminae I-IV, V-VI, VII and VIII-IX) of lumbar segments compared to sham-operated rats. The pattern of altered metabolic activity in CCI rats presented 3 distinct features. (1) The spinal cord grey matter both ipsilateral and contralateral to nerve ligation exhibited substantial increases in metabolic activity compared to sham-operated rats. (2) This increase in metabolic activity was somatotopically specific, i.e., higher metabolic rates were observed on the side ipsilateral to nerve ligation than on the contralateral side, and higher metabolic rates were seen in the medial portion of the ipsilateral spinal cord dorsal horn than in the lateral portion. The peak metabolic activity occurred in laminae V-VI of CCI rats, a region involved in nociceptive processing. (3) The increase in spinal cord metabolic activity of CCI rats extended from lumbar segment L1 to L5 in all 4 sampling regions. The substantial increase in metabolic activity in both the ipsilateral and contralateral spinal cord that occurs over an extensive rostro-caudal area in CCI rats may represent a unique pattern of spinal cord metabolic activity distinct from that observed in rats exposed to acute thermal pain. This pattern of spinal cord neural activity in CCI rats may reflect possible radiation of neuropathic pain. In addition, the procedure of curare-induced paralysis in a separate group of CCI rats did not change the extent and patterns of metabolic activity seen in non-paralyzed CCI rats, reflecting a minimal influence of the afferent feedback from flexor motor reflexes on spinal cord metabolic activity following sciatic nerve ligation. This chronic increase in spinal cord neural activity in the absence of overt peripheral stimulation suggests a spinal cord hyperactive state and may account for behaviors suggestive of spontaneous pain in CCI rats.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals

[Spatial pattern and consequences of demographic aging processes for regional planning].

The spatial dimension of man-environment interactions in old age is analyzed within urban, suburban, and rural residential environments of the German Rhine-Main-Agglomeration. By comparing the three levels of organization, utilization, and interpretation, housing conditions as well as geographical distribution and redistribution (migrations) our outside-home-activities and environmental perception show a fundamental influence on the everyday lives of the 750 elderly who were interviewed. The majority of the target population and, especially, the rural elderly is characterized by traditional patterns of spatial organization and distribution, mobility, regional attachment, and a concern about preserving the stability of their current residential environment from changes. The suburban and urban seniors, however, exhibit a greater amount of locational flexibility and utility-oriented behavior patterns. These spatial variations are induced by specific regional values and intensity of local and regional identification. They might be interpreted as different stages in the process of modernization within postindustrial societies. Reflecting, however, the paradigms of planning for the elderly, these different patterns are not systematically considered to the necessary and sufficient extent. Instead of promoting regional or local networks that are favored by senior citizens, agencies usually prefer comprehensive approaches on a macrolevel. First steps to improve this situation and to combine life- and system-world demands have been taken by the federal government, which implemented a neighborhood-related research program on housing for the elderly. As a result of this, further research on environmental aspects on aging should pay more methodological attention to the hitherto neglected regional and local level, and also for the transfer of its findings into planning policy.

Aged

Spatial patterning of response to odors in the peripheral olfactory system.

The low odor specificities of the olfactory receptors suggest that odor recognition depends on the simultaneous activity in an ensemble of receptor neurons. This ensemble could conceivably code quality without reference to the point of origin of each input on the receptor sheet. However, the nose-to-bulb projection appears sufficiently precise to provide the bulb with a topographical map of the receptor sheet although it is poorly delineated in the anteroposterior plane. (It is also known that the morphological changes that follow prolonged exposure to odors are more differentiated in the coronal than in the anteroposterior plane.) Furthermore, it is clear from work at both epithelial and bulbar levels that a spatiotemporal pattern of excitation is generated by odor stimulation of the receptor sheet and that this pattern differs for different odors. This evidence, then, supports the view that there is a spatial component to odor quality coding. This spatial pattern has two elements. One is imposed and depends (at least in part) on differences in the retentivity of different odorants by the mucous sheet, which has powerful sorptive properties. It effectiveness seems particularly weak for odorants with relatively long retention times. The second component is inherent and depends on the tendency of receptors with similar peak odor specificities to aggregate in the same region (or regions) of the epithelium. Different odors or groups of odors maximally excite different regions, which may overlap. The imposed component could not, in itself, provide an adequate mechanism for odor recognition, partly because many compounds have comparable or even identical mean retention times (e.g., enantiomeric isomers). The inherent component, on the other hand, possesses this potential. However, either or both forms of patterning may cooperate with a third nonspatial mechanism (based on differential responsiveness of receptors to different odors) in coding odor quality.

Animals

Capillary spatial pattern and muscle fiber geometry in three hamster striated muscles.

Since most oxygen exchange in muscle is thought to occur by diffusion across the walls of capillaries, it is important to determine the spatial relationship between capillaries and muscle fibers. We have extended the work of Kayar et al. (Microvasc. Res 24: 326-341, 1982) to include other statistical tests that allow one to make stronger statements regarding the spatial pattern. Data for hamsters were obtained from two sartorius, three retractor, and five soleus muscle sections. Distances between all pairs of capillaries, distances between a capillary and its first nearest neighbor for all capillaries, and distances between random tissue sample points and the closest capillary were used to test the spatial arrangement of capillaries. The null hypothesis tested of complete spatial randomness of capillary locations was rejected in favor of a regular alternative in one each of the sartorius and retractor fields and in all five soleus fields. We formulated a geometric model, composed of a space-filling array of identical hexagonal muscle fibers with capillaries placed randomly at the juncture of three fibers or between two fibers, according to the observed relative probability of those occurrences. The model simulations of muscle fibers and capillaries were then analyzed by the same statistical tests used on the histological sections. The findings were similar in both cases, providing confidence that the assumptions of the model were sufficient approximations. The results of this study provide a basis for the placement of capillaries around muscle fibers in mathematical models of oxygen transport in capillary networks.

Animals

High reliability rates of spatial pattern analysis by vectorcardiogram in assessing the severity of eccentric left ventricular hypertrophy.

In 33 patients, including 12 control subjects and 21 with eccentric LVH, LV mass determined by angiocardiogram was correlated to 26 VCG measurements (Frank system) calculated from the scalar X, Y, and Z leads. The results demonstrated that the most reliable indices of VCG in assessing the severity of eccentric LVH determined by angiocardiogram were the magnitude of the spatial mean QRS vector and the time of the spatial maximal QRS vector ("spatial VAT"), of which correlation coefficients were 0.93 and 0.93, respectively. Such high correlation coefficients have never been obtained with the usual ECG analysis. These findings strongly suggest that (1) increased QRS voltage and usual prolonged QRS duration in eccentric LVH are due to an increase in LV mass, and (2) prolonged VAT observed in eccentric LVH is closely related to an anatomic alteration, namely, the greater distance of intra-ventricular conducting pathways as the result of LV dilatation, as an increase in LV mass is usually paralleled by the grade of the chamber enlargement in this type of LVH. Regarding the T loop, correlations between the LV mass and the VCG measurements were less as compared to those of the QRS loop. In general, T changes in moderate or severe LVH may be also related to a certain altered cardiac muscle state, in addition to an increase in LV mass. Angiocardiographic and light microscopic findings of a patient with eccentric LVH in whom a widened QRS-T angle was demonstrated to an extent much more than that expected with an increase in LV mass are presented and discussed. The spatial pattern analysis by VCG is very useful and reliable in assessing the severity of eccentric LVH.

Adolescent

The spatial pattern of the synaptic vesicular apparatus as a correlate of transmitter storage models.

A statistical stereological approach which allows one to derive a three-dimensional pattern of synaptic vesicle accumulation in relation to the active zone from an analysis of electron micrograms (random sections) of synapses is described. This approach is illustrated with a study of presynaptic terminals from the dorsal horn of the cat spinal cord, based on the morphometrical treatment of 105 micrographs containing 5190 synaptic vesicles. The spatial pattern obtained was found to have a bimodal shape, which can be considered a possible structural correlate of the two-pool model of transmitter storage. The connection of similar quantitative estimates with physiological data is discussed.

Animals