Distribution of differentiated cells in a cell sheet under the lateral inhibition rule of differentiation.

The distribution of differentiated cells among undifferentiated cells was investigated assuming the lateral inhibition hypothesis of cell differentiation. Computer simulations were undertaken in a planar array of polygonal domains in which homogeneous polygons are all competent to differentiate, and immediate neighbors of a differentiated polygon exert lateral inhibition of differentiation. The simulation showed that the average cell number ratio of undifferentiated to differentiated cells is 3.32, when picking a polygon for differentiation at random from a hexagonal pattern. The ratio decreased when using disturbed polygonal patterns instead of a hexagonal one. A non-random sequence of picking polygons also varied cell number ratio values. Our results show that if there is no control system as a whole, the lateral inhibition rule produced cell distributions whose cell number ratio is around 3. Cell number ratios are discussed in regard to observations of epithelial cell sheets.     

Thiessen polygons as a model for animal territory estimation

Thiessen polygons are often used to model territory characteristics. However, information about the quality of Thiessen polygon‐based estimates is currently lacking. We used published data to investigate the match between Thiessen polygons and mapped bird territories regarding territory size, shape and neighbourhood. Although territory sizes and the number of neighbours were strongly correlated between these two methods, both parameters were overestimated by the Thiessen polygons. Therefore, caution is required when Thiessen polygons are used as a model for absolute values and when the assumptions of Thiessen polygons, such as formation of discrete territories and a contiguous study area, are not met.     

POLLEN EXINE SUBSTRUCTURE. I. LILIUM LONGIFLORUM

Acetolyzed exines of Lilium longiflorum partially extracted with hot 2-aminoethanol decrease in size and change from a homogeneous substructure to one with discrete interconnected granules. At first, the granules are arranged in irregular pentagons. As attachments between them are broken, compound polygons result, and with further extraction, the polygons become open at the surface. Granules are angular or ellipsoidal with a diameter of 10 nm or with major and minor axes of 7 and 15 nm. Higher order patterns include clumps of densely packed granules and ladderlike arrangements of adjacent polygons. The size and arrangement of granules and polygons is similar to the structures observed in developing exines of numerous genera.     

Modeling DNA supercoils and knots with B-spline functions

A method is offered to model the complex trajectories of closed circular DNA supercoils and knots. The trajectories are approximated by polygons and analytical expressions of the curves are generated from the polygons with B-spline functions. The resulting curves are used to evaluate the writhe and elastic energy of a series of interrelated supercoils, and to generate detailed atomic models of the deformed double helix.     

Water polygons in high‐resolution protein crystal structures

We have analyzed the interstitial water (ISW) structures in 1500 protein crystal structures deposited in the Protein Data Bank that have greater than 1.5 Å resolution with less than 90% sequence similarity with each other. We observed varieties of polygonal water structures composed of three to eight water molecules. These polygons may represent the time‐ and space‐averaged structures of “stable” water oligomers present in liquid water, and their presence as well as relative population may be relevant in understanding physical properties of liquid water at a given temperature. On an average, 13% of ISWs are localized enough to be visible by X‐ray diffraction. Of those, averages of 78% are water molecules in the first water layer on the protein surface. Of the localized ISWs beyond the first layer, almost half of them form water polygons such as trigons, tetragons, as well as expected pentagons, hexagons, higher polygons, partial dodecahedrons, and disordered networks. Most of the octagons and nanogons are formed by fusion of smaller polygons. The trigons are most commonly observed. We suggest that our observation provides an experimental basis for including these water polygon structures in correlating and predicting various water properties in liquid state.     

Comparing Angular and Curved Shapes in Terms of Implicit Associations and Approach/Avoidance Responses

Most people prefer smoothly curved shapes over more angular shapes. We investigated the origin of this effect using abstract shapes and implicit measures of semantic association and preference. In Experiment 1 we used a multidimensional Implicit Association Test (IAT) to verify the strength of the association of curved and angular polygons with danger (safe vs. danger words), valence (positive vs. negative words) and gender (female vs. male names). Results showed that curved polygons were associated with safe and positive concepts and with female names, whereas angular polygons were associated with danger and negative concepts and with male names. Experiment 2 used a different implicit measure, which avoided any need to categorise the stimuli. Using a revised version of the Stimulus Response Compatibility (SRC) task we tested with a stick figure (i.e., the manikin) approach and avoidance reactions to curved and angular polygons. We found that RTs for approaching vs. avoiding angular polygons did not differ, even in the condition where the angles were more pronounced. By contrast participants were faster and more accurate when moving the manikin towards curved shapes. Experiment 2 suggests that preference for curvature cannot derive entirely from an association of angles with threat. We conclude that smoothly curved contours make these abstract shapes more pleasant. Further studies are needed to clarify the nature of such a preference.     

Calculating the areas of polygons with a smartphone light sensor

This study explores finding the areas of polygons with a smartphone light sensor. A square and an irregular pentagon were chosen as our polygons. During the activity, the LED light was placed at the vertices of our polygons, and the illuminance values of this LED light were detected by the smartphone light sensor. The smartphone was placed on a rotating time-lapse device, and this device was placed at the intersection point of the line segments in the polygons. These line segments were also connected to the vertices of these polygons; therefore, the square was composed of four triangles and the pentagon of five triangles. While the rotating time-lapse device was rotating around itself, it captured the maximum illuminance values of the LED light. Using these maximum illuminance values, we calculated the lengths of the line segments. In addition, we knew the period of the rotating time-lapse device and the duration elapsed between two consecutive maximum illuminance values. Thus, we could calculate the angle between two consecutive line segments. With these values, we could also calculate the areas of the triangles in the polygons. Then, the areas of these triangles were summed to obtain the areas of the square and pentagon.     

The mechanics of heterotypic cell aggregates: insights from computer simulations

Finite element-based computer simulations are used to investigate a number of phenomena, including tissue engulfment, cell sorting, and checkerboard-pattern formation, exhibited by heterotypic cell aggregates. The simulations show that these phenomena can be driven by a single equivalent force, namely a surface (or interfacial) tension, that results from cytoskeletal components and cell-cell adhesions. They also reveal that tissue engulfment, cell sorting, and checkerboard-pattern formation involve several discernible mechanical features or stages. With the aid of analytical arguments, we identify the conditions necessary for each of these phenomena. These findings are consistent with previous experimental investigations and computer simulations, but pose significant challenges to current theories of cell sorting and tissue engulfment.     

Polygons and adhesion plaques and the disassembly and assembly of myofibrils in cardiac myocytes

Successive stages in the disassembly of myofibrils and the subsequent assembly of new myofibrils have been studied in cultures of dissociated chick cardiac myocytes. The myofibrils in trypsinized and dispersed myocytes are sequentially disassembled during the first 3 d of culture. They split longitudinally and then assemble into transitory polygons. Multiples of single sarcomeres, the cardiac polygons, are analogous to the transitory polygonal configurations assumed by stress fibers in spreading fibroblasts. They differ from their counterparts in fibroblasts in that they consist of muscle alpha-actinin vertices and muscle myosin heavy chain struts, rather than of the nonmuscle contractile protein isoforms of stress fiber polygons. EM sections reveal the vertices and struts in cardiac polygons to be typical Z and A bands. Most cardiac polygons are eliminated by day 5 of culture. Concurrent with the disassembly and elimination of the original myofibrils new myofibrils are rapidly assembled elsewhere in the same myocyte. Without exception both distal tips of each nascent myofibril terminate in adhesion plaques. The morphology and composition of the adhesion plaques capping each end of each myofibril are similar to those of the termini of stress fibers in fibroblasts. However, whereas the adhesion complexes involving stress fibers in fibroblasts consist of vinculin/nonmuscle alpha-actinin/beta- and gamma-actins, the analogous structures in myocytes involving myofibrils consist of vinculin/muscle alpha-actinin/alpha-actin. The addition of 1.7-2.0 microns sarcomeres to the distal tips of an elongating myofibril, irrespective of whether the myofibril consists of 1, 10, or several hundred tandem sarcomeres, occurs while the myofibril appears to remain linked to its respective adhesion plaques. The adhesion plaques in vitro are the equivalent of the in vivo intercalated discs, both in terms of their molecular composition and with respect to their functioning as initiating sites for the assembly of new sarcomeres. How 1.7-2.0 microns nascent sarcomeres can be added distally during elongation while the tips of the myofibrils remain inserted into submembranous adhesion plaques is unknown.     

Fundamental physical cellular constraints drive self‐organization of tissues

Morphogenesis is driven by small cell shape changes that modulate tissue organization. Apical surfaces of proliferating epithelial sheets have been particularly well studied. Currently, it is accepted that a stereotyped distribution of cellular polygons is conserved in proliferating tissues among metazoans. In this work, we challenge these previous findings showing that diverse natural packed tissues have very different polygon distributions. We use Voronoi tessellations as a mathematical framework that predicts this diversity. We demonstrate that Voronoi tessellations and the very different tissues analysed share an overriding restriction: the frequency of polygon types correlates with the distribution of cell areas. By altering the balance of tensions and pressures within the packed tissues using disease, genetic or computer model perturbations, we show that as long as packed cells present a balance of forces within tissue, they will be under a physical constraint that limits its organization. Our discoveries establish a new framework to understand tissue architecture in development and disease.     

Isotopic insights into methane production,oxidation, and emissions in Arctic polygon tundra

Arctic wetlands are currently net sources of atmospheric CH₄. Due to their complex biogeochemical controls and high spatial and temporal variability, current net CH₄ emissions and gross CH₄ processes have been difficult to quantify, and their predicted responses to climate change remain uncertain. We investigated CH₄ production, oxidation, and surface emissions in Arctic polygon tundra, across a wet‐to‐dry permafrost degradation gradient from low‐centered (intact) to flat‐ and high‐centered (degraded) polygons. From 3 microtopographic positions (polygon centers, rims, and troughs) along the permafrost degradation gradient, we measured surface CH₄ and CO₂ fluxes, concentrations and stable isotope compositions of CH₄ and DIC at three depths in the soil, and soil moisture and temperature. More degraded sites had lower CH₄ emissions, a different primary methanogenic pathway, and greater CH₄ oxidation than did intact permafrost sites, to a greater degree than soil moisture or temperature could explain. Surface CH₄ flux decreased from 64 nmol m^?2 s^?1 in intact polygons to 7 nmol m^?2 s^?1 in degraded polygons, and stable isotope signatures of CH₄ and DIC showed that acetate cleavage dominated CH₄ production in low‐centered polygons, while CO₂ reduction was the primary pathway in degraded polygons. We see evidence that differences in water flow and vegetation between intact and degraded polygons contributed to these observations. In contrast to many previous studies, these findings document a mechanism whereby permafrost degradation can lead to local decreases in tundra CH₄ emissions.     

Vascular sprout formation entails tissue deformations and VE-cadherin-dependent cell-autonomous motility

Embryonic and fetal vascular sprouts form within constantly expanding tissues. Nevertheless, most biological assays of vascular spouting are conducted in a static mechanical milieu. Here we study embryonic mouse allantoides, which normally give raise to an umbilical artery and vein. However, when placed in culture, allantoides assemble a primary vascular network. Unlike other in vitro assays, allantoic primordial vascular cells are situated on the upper surface of a cellular layer that is engaged in robust spreading motion. Time-lapse imaging allows quantification of primordial vascular cell motility as well as the underlying mesothelial tissue motion. Specifically, we calculate endothelial cell-autonomous motion by subtracting the tissue-level mesothelial motion from the total endothelial cell displacements. Formation of new vascular polygons is hindered by administration of function-blocking VE-cadherin antibodies. Time-lapse recordings reveal that (1) cells at the base of sprouts normally move distally “over” existing sprout cells to form new tip-cells; and (2) loss of VE-cadherin activity prevents this motile behavior. Thus, endothelial cell-cell-adhesion-based motility is required for the advancement of vascular sprouts within a moving tissue environment. To the best of our knowledge, this is the first study that couples endogenous tissue dynamics to assembly of vascular networks in a mammalian system.     

Herbivory simulations in ecological research

Because of the experimental advantages that they offer, mechanical simulations of grazing are more commonly used than true herbivory in ecological studies of the impact of herbivory on plants. However, few studies have explicitly compared plant responses to herbivory and to mechanical simulations. Most such comparisons report differences in plant responses to mechanical versus true herbivory, even though the amounts and types of tissue removed were similar. Moreover, studies that also attempted to mimic the timing of leaf damage report differences in plant responses to the different damage modes. Because a plant's response to herbivory is complex and is activated by more than merely the removal of tissue, exact mechanical simulations may prove difficult.     

SINENVAP: An algorithm that employs kriging to identify optimal spatial interpolation models in polygons

The aim of the SINENVAP algorithm is to facilitate the estimation of spatial interpolations within polygons, by using simple, ordinary, and universal kriging. This algorithm is available as a function of the EcoIndR package, which is available as an RWizard application and an R package on CRAN. The main strengths of this algorithm include: the possibility of using different file formats for polygon variable and coordinate inputs (CSV, EXCEL, RData, shape or ASC), compatibility with UTM or decimal coordinates, estimation of optimal grid cell size, the possibility of selecting only points inside polygons from the entire dataset, the application of a jitter function or to estimate the mean value of the variable for duplicated coordinates, reservation a percentage of data for validation, selection of those grid coordinates nearest the data coordinates reserved for validation, the possibility of fitting 13 different models into the semivariogram, automatic selection of the model that best predicts the data reserved for validation through the use of seven accuracy measures, the possibility of using countries, regions, departments, river basins, or even alpha shape distribution as polygons, and finally, depiction of contour plots with the spatial interpolation of the variable and the error within polygons. The spatial interpolation of the temperature in North America and the distribution of a virtual species are used as examples of this algorithm's potential to perform spatial interpolations on both large and small scales.     

The cyanobacterial community of polygon soils at an inland Antarctic nunatak

Inland Antarctic terrestrial ecosystems and biodiversity are poorly understood in comparison with Antarctic coastal regions. Microorganisms, as primary colonists, are integral to Antarctic soil ecosystem development, essential for pedogenesis and structuring the soil, and providing the nutrients necessary for the subsequent establishment of macroorganisms. This study analysed the microbial communities present in polygon soils of Coal Nunatak (Alexander Island, at the southern limit of the maritime Antarctic). Soils were analysed across three polygons (centre and margins) and at three depths (0–1, 1–2, 2–5 cm). Cyanobacterial communities were characterised using two complementary molecular biological approaches, temperature gradient gel electrophoresis and clone library analysis. The three polygons exhibited conspicuous differences in community composition, both between different polygons and spatially (horizontally and vertically) within a single polygon. Comparison of our data with that from previous studies using classical culture and morphological identification techniques clearly shows the need for more intensive research on patterns of microbial diversity in terrestrial habitats throughout the Antarctic. The majority of the 17 cyanobacterial genera identified at Coal Nunatak are thought to have ubiquitous distributions, while none are known only from the Antarctic. Three of the genera present are also known to be capable of being lichen photobionts.     

Intrusion experiments to measure territory size: development of the method, tests through simulations, and application in the frog Allobates femoralis

Territoriality is a widespread behaviour in animals and its analysis is crucial in several areas of behavioural, ecological and evolutionary research. Commonly, territory size is assessed through territory mapping and the application of simple area estimators such as minimum convex polygons. In the present study we demonstrate that territory size can be determined adequately with an active approach through intrusion experiments, a technique that is commonly used in behavioural research in other contexts. Tests with simulated data indicate that a minimum of twelve trials needs to be performed to establish reliable orders of relative territory size. To estimate absolute territory size, detailed hull techniques are most appropriate when analyzing point patterns of intrusion experiments, while the local convex hull estimator enables the construction of internal utilization distributions based on such point patterns. Additionally we suggest a 'stretch the centre' approach to emphasize the actual process of intrusion experiments in the construction of internal utilization distributions. To demonstrate the utility of the method, we apply all findings from the simulations to data from fieldwork with the model species Allobates femoralis, a territorial aromobatid frog from the lowland rainforest of French Guiana.     

基于1∶100万土壤数据库的中国土壤有机碳密度及储量研究

基于中国1∶100万土壤数据库,利用土壤有机碳储量和碳密度的空间化表达和计算方法研究中国土壤有机碳密度及储量.土壤空间数据库包含926个土壤类型单元,690个土属类型,94 000多个图斑;土壤属性数据库收录了7 292个全国各类型土壤的剖面数据,包括81个土壤属性字段.研究采用“土壤类型GIS连接法”实现土壤剖面有机碳密度与图形图斑连接,通过制图单元碳储量求和得出全国或者区域碳储量,并利用面积平均法计算全国及各类型土壤的有机碳平均密度.结果表明,中国的土壤面积共有928.10×10⁴ km²,有机碳储量为89.14 Pg (1 Pg=10¹⁵ g),土壤平均碳密度9.60 kg·m^-2,是目前与真值最为接近的研究结果.