Water Deficit and Spatial Pattern of Leaf Development. Variability in Responses Can Be Simulated Using a Simple Model of Leaf Development1

We analyzed the effect of short-term water deficits at different periods of sunflower (Helianthus annuus L.) leaf development on the spatial and temporal patterns of tissue expansion and epidermal cell division. Six water-deficit periods were imposed with similar and constant values of soil water content, predawn leaf water potential and [ABA] in the xylem sap, and with negligible reduction of the rate of photosynthesis. Water deficit did not affect the duration of expansion and division. Regardless of their timing, deficits reduced relative expansion rate by 36% and relative cell division rate by 39% (cells blocked at the G0-G1 phase) in all positions within the leaf. However, reductions in final leaf area and cell number in a given zone of the leaf largely differed with the timing of deficit, with a maximum effect for earliest deficits. Individual cell area was only affected during the periods when division slowed down. These behaviors could be simulated in all leaf zones and for all timings by assuming that water deficit affects relative cell division rate and relative expansion rate independently, and that leaf development in each zone follows a stable three-phase pattern in which duration of each phase is stable if expressed in thermal time (C. Granier and F. Tardieu [1998b] Plant Cell Environ 21: 695–703).

Spatial and Temporal Analyses of Expansion and Cell Cycle in Sunflower Leaves1 : A Common Pattern of Development for All Zones of a Leaf and Different Leaves of a Plant

We have investigated the spatial distributions of expansion and cell cycle in sunflower (Helianthus annuus L.) leaves located at two positions on the stem, from leaf initiation to the end of expansion. Relative expansion rate (RER) was analyzed by following the deformation of a grid drawn on the lamina; relative division rate (RDR) and flow-cytometry data were obtained in four zones perpendicular to the midrib. Calculations for determining in situ durations of the cell cycle and of S-G2-M in the epidermis are proposed. Area and cell number of a given leaf zone increased exponentially during the first two-thirds of the development duration. RER and RDR were constant and similar in all zones of a leaf and in all studied leaves during this period. Reduction in RER occurred afterward with a tip-to-base gradient and lagged behind that of RDR by 4 to 5 d in all zones. After a long period of constancy, cell-cycle duration increased rapidly and simultaneously within a leaf zone, with cells blocked in the G0-G1 phase of the cycle. Cells that began their cycle after the end of the period with exponential increase in cell number could not finish it, suggesting that they abruptly lost their competence to cross a critical step of the cycle. Differences in area and in cell number among zones of a leaf and among leaves of a plant essentially depended on the timing of two events, cessation of exponential expansion and of exponential division.

The spatial pattern of child growth in Papua New Guinea

Child growth in PNG shows strong regional differences, with highlands children being generally shorter but stockier than those from lowland areas. Differences in diet, socioeconomic status and local subsistence agriculture were found to be important predictors of child growth. All variables indicating higher socioeconomic status were correlated with better growth, as was a high consumption of imported and local high quality foods such as cereals, legumes, tinned fish or meat and fresh fish. Differences in subsistence explained between 25% and 50% of the geographical variation in growth. Child growth was better in systems based on cassava and sweet potato, and worse in those where banana, sago and taro are staples. The cultivation of all major cash crops and sales of fish and food crops improved child growth. Birth weights show similar patterns to those observed in child growth. The implications of these findings for possible interventions are discussed.

The spatial pattern of the vacuolation ('spongiform change') in the cerebral cortex in variant Creutzfeldt-Jakob disease (vCJD)

The spatial pattern of the vacuolation ('spongiform change') was studied in areas of the cerebral cortex in 11 cases of variant Creutzfeldt-Jakob disease (vCJD). The vacuoles were evenly distributed along the cortex in 40/106 (38%) areas studied and randomly distributed in 6/106 (5.6%) areas. In 22/106 (21%) areas, the vacuoles were aggregated into clusters, 50 - 1600 μm in diameter and which were distributed in a regular pattern parallel to the pia mater. In 38/106 (36%) areas, large clusters of vacuoles, at least 1600 μm in diameter, were present. No significant differences in spatial patterns were observed between the different cortical regions or between the upper and lower laminae. In addition, age at onset and duration of the disease had no significant affect on spatial patterns. The spatial distribution of the vacuolation contrasts with that reported in sporadic CJD (sCJD) suggesting a different pattern of cortical degeneration in vCJD.

Spatial pattern of prion protein deposits in patients with sporadic Creutzfeldt–Jakob disease

The spatial pattern of the prion protein (PrP) deposits was studied in the cerebral cortex and cerebellum in 10 patients with sporadic Creutzfeldt–Jakob disease (CJD). In all patients the PrP deposits were aggregated into clusters and, in 90% of cortical areas and in 50% of cerebellar sections, the clusters exhibited a regular periodicity parallel to the tissue boundary; a spatial pattern also exhibited by ß-amyloid (Aß) deposits in Alzheimer's disease (AD). In the cerebral cortex, the incidence of regular clustering of the PrP deposits was similar in the upper and lower cortical laminae. The sizes of the PrP clusters in the upper and lower cortex were uncorrelated. No significant differences in mean cluster size of the PrP deposits were observed between brain regions. The size, location and distribution of the PrP deposit clusters suggest that PrP deposition occurs in relation to specific anatomical pathways and supports the hypothesis that prion pathology spreads through the brain via such pathways. In addition, the data suggest that there are similarities in the pathogenesis of extracellular protein deposits in prion disease and in AD.

The spatial pattern of senile plaques, neurofibrillary tangles and A4 deposits in Alzheimer's disease

The spatial patterns of senile plaques (SP) and neurofibrillary tangles (NFT) as visualised using the Gallyas stain and of discrete A4 protein deposits were determined in coronal serial sections from a variety of brain regions in six elderly patients with Alzheimer's disease (AD). These lesions showed clustering in virtually all tissues examined with many of the clusters being regularly spaced. These spatial patterns were compared with the clustering observed for SP and NFT stained by the Glees and Marsland method in the same tissues. The data suggest that on average, while the regular clusters of A4 deposits and NFT were of approximately the same mean diameter (3600 microns), clusters of both Glees and Gallyas SP were approximately half this diameter (1800 - 2000 microns). If SP develop in local areas of the brain where both A4 deposition and neurofibrillary changes have occurred, the data suggest that the SP clusters would represent the region of overlap of the A4 deposits and neurofibrillary changes. Various hypothese are advocated to explain the regular clsuetring of the A4 deposits.

Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd.

The spatial pattern of the vacuolation in patients with sporadic Creutzfeldt-Jakob disease

The spatial pattern of the vacuolation ('spongiform change') was studied in the upper and lower laminae of the cerebral cortex, the CA1/CA2 sectors of the hippocampus and the molecular layer of the cerebellum in 11 cases of sporadic Creutzfeldt-Jakob disease (CJD). Individual vacuoles were grouped into clusters, 50 to >1600 μm in diameter and, in the majority of tissue sections, the vacuole clusters were distributed with regular periodicity parallel to the tissue boundary. The size of the vacuole clusters was positively correlated with patient age in the lower laminae of the occipital cortex and the inferior temporal gyrus (ITG) and negatively correlated with age in the hippocampus. In addition, the size of the vacuole clusters was positively correlated with disease duration in the upper laminae of the ITG. The size and distribution of the vacuole clusters suggests that the vacuolation in CJD reflects the degeneration of specific brain pathways and supports the hypothesis that prion pathology may spread through the brain along well defined anatomical pathways. (C) 2000 Elsevier Science Ireland Ltd.

The spatial pattern of discrete beta-amyloid deposits in Alzheimer's disease reflects synaptic disconnection

The spatial pattern of discrete beta-amyloid (A beta) deposits was studied in the superficial laminae of cortical fields of different types and in the hippocampus in 6 cases of Alzheimer's disease (AD). In 41/42 tissues examined, discrete A beta deposits were aggregated into clusters and in 34/41 tissues (25/34 of the cortical tissues), there was evidence for a regular periodicity of the A beta deposit clusters parallel to the tissue boundary. The dimensions of the clusters varied from 400 to > 12,800 microns in different tissues. Although the A beta deposit clusters were larger than predicted, the regular periodicity suggests that they develop in relation to groups of cells associated with specific projections. This would be consistent with the hypothesis that the distribution of discrete A beta deposits in AD could reflect progressive synaptic disconnection along interconnected neuronal pathways. This implies that amyloid deposition could be a response to, rather than a cause of, synaptic disconnection in AD.

Spatial pattern analysis of beta-amyloid (A beta) deposits in Alzheimer disease by linear regression

The spatial patterns of discrete beta-amyloid (Abeta) deposits in brain tissue from patients with Alzheimer disease (AD) were studied using a statistical method based on linear regression, the results being compared with the more conventional variance/mean (V/M) method. Both methods suggested that Abeta deposits occurred in clusters (400 to <12,800 mu m in diameter) in all but 1 of the 42 tissues examined. In many tissues, a regular periodicity of the Abeta deposit clusters parallel to the tissue boundary was observed. In 23 of 42 (55%) tissues, the two methods revealed essentially the same spatial patterns of Abeta deposits; in 15 of 42 (36%), the regression method indicated the presence of clusters at a scale not revealed by the V/M method; and in 4 of 42 (9%), there was no agreement between the two methods. Perceived advantages of the regression method are that there is a greater probability of detecting clustering at multiple scales, the dimension of larger Abeta clusters can be estimated more accurately, and the spacing between the clusters may be estimated. However, both methods may be useful, with the regression method providing greater resolution and the V/M method providing greater simplicity and ease of interpretation. Estimates of the distance between regularly spaced Abeta clusters were in the range 2,200-11,800 mu m, depending on tissue and cluster size. The regular periodicity of Abeta deposit clusters in many tissues would be consistent with their development in relation to clusters of neurons that give rise to specific neuronal projections.

The spatial pattern of beta-amyloid (Abeta) deposits in Alzheimer’s disease patients is related to apolipoprotein genotype

The spatial patterns of the diffuse, primitive, and classic beta-amyloid (Abeta) deposits was studied in the frontal and temporal cortex in cases of Alzheimer’s disease (AD) expressing different apolipoprotein (Apo E) genotypes. No significant differences in the density of the three Abeta deposit subtypes were observed in individuals expressing genotypes e2/3 and e3/3 compared with those expressing e3/4 and e4/4. In all patients, Abeta deposit subtypes occurred in the tissue in clusters. Chi-square contingency analyses of the data suggested that the cluster size of the diffuse and classic Abeta deposits was unrelated to Apo E genotype. However, the primitive (‘neuritic’) type Abeta deposits occurred more frequently in smaller, denser clusters in individuals expressing genotypes e3/4 and e4/4 compared with those expressing e2/3 and e3/3. Hence, the presence of the e4 allele may be associated with a more specific pattern of neuronal degeneration in the frontal and temporal cortex in AD.

The usefulness of spatial pattern analysis in understanding the pathogenesis of neurodegenerative disorders, with particular reference to plaque formation in Alzheimer's disease

Discrete, microscopic lesions are developed in the brain in a number of neurodegenerative diseases. These lesions may not be randomly distributed in the tissue but exhibit a spatial pattern, i.e., a departure from randomness towards regularlity or clustering. The spatial pattern of a lesion may reflect its development in relation to other brain lesions or to neuroanatomical structures. Hence, a study of spatial pattern may help to elucidate the pathogenesis of a lesion. A number of statistical methods can be used to study the spatial patterns of brain lesions. They range from simple tests of whether the distribution of a lesion departs from random to more complex methods which can detect clustering and the size, distribution and spacing of clusters. This paper reviews the uses and limitations of these methods as applied to neurodegenerative disorders, and in particular to senile plaque formation in Alzheimer's disease.