Modelling applicability of fractal analysis to efficiency of soil exploration by roots

BACKGROUND AND AIMS: Fractal analysis allows calculation of fractal dimension, fractal abundance and lacunarity. Fractal analysis of plant roots has revealed correlations of fractal dimension with age, topology or genotypic variation, while fractal abundance has been associated with root length. Lacunarity is associated with heterogeneity of distribution, and has yet to be utilized in analysis of roots. In this study, fractal analysis was applied to the study of root architecture and acquisition of diffusion-limited nutrients. The hypothesis that soil depletion and root competition are more closely correlated with a combination of fractal parameters than by any one alone was tested. MODEL: The geometric simulation model SimRoot was used to dynamically model roots of various architectures growing for up to 16 d in three soil types with contrasting nutrient mobility. Fractal parameters were calculated for whole roots, projections of roots and vertical slices of roots taken at 0, 2.5 and 5 cm from the root origin. Nutrient depletion volumes, competition volumes, and relative competition were regressed against fractal parameters and root length. KEY RESULTS: Root length was correlated with depletion volume, competition volume and relative competition at all times. In analysis of three-dimensional, projected roots and 0 cm slices, log(fractal abundance) was highly correlated with log(depletion volume) when times were pooled. Other than this, multiple regression yielded better correlations than regression with single fractal parameters. Correlations decreased with age of roots and distance of vertical slices from the root origin. Field data were also examined to see if fractal dimension, fractal abundance and lacunarity can be used to distinguish common bean genotypes in field situations. There were significant differences in fractal dimension and fractal abundance, but not in lacunarity. CONCLUSIONS: These results suggest that applying fractal analysis to research of soil exploration by root systems should include fractal abundance, and possibly lacunarity, along with fractal dimension.     

The use of fractal features from the periphery of cell nuclei as a classification tool.

A polygonization-based method is used to estimate the fractal dimension and several new scalar lacunarity features from digitized transmission electron micrographs (TEM) of mouse liver cell nuclei. The fractal features have been estimated in different segments of 1D curves obtained by scanning the 2D cell nuclei in a spiral-like fashion called "peel-off scanning". This is a venue to separate estimates of fractal features in the center and periphery of a cell nucleus. Our aim was to see if a small set of fractal features could discriminate between samples from normal liver, hyperplastic nodules and hepatocellular carcinomas. The Bhattacharyya distance was used to evaluate the features. Bayesian classification with pooled co-variance matrix and equal prior probabilities was used as the rule for classification. Several single fractal features estimated from the periphery of the cell nuclei discriminated samples from the hyperplastic nodules and hepatocellular carcinomas from normal ones. The outer 25-30% of the cell nuclei contained important texture information about the differences between the classes. The polygonization-based method was also used as an analysis tool to relate the differences between the classes to differences in the chromatin structure.     

Lacunarity Analysis: A Promising Method for the Automated Assessment of Melanocytic Naevi and Melanoma

The early diagnosis of melanoma is critical to achieving reduced mortality and increased survival. Although clinical examination is currently the method of choice for melanocytic lesion assessment, there is a growing interest among clinicians regarding the potential diagnostic utility of computerised image analysis. Recognising that there exist significant shortcomings in currently available algorithms, we are motivated to investigate the utility of lacunarity, a simple statistical measure previously used in geology and other fields for the analysis of fractal and multi-scaled images, in the automated assessment of melanocytic naevi and melanoma. Digitised dermoscopic images of 111 benign melanocytic naevi, 99 dysplastic naevi and 102 melanomas were obtained over the period 2003 to 2008, and subject to lacunarity analysis. We found the lacunarity algorithm could accurately distinguish melanoma from benign melanocytic naevi or non-melanoma without introducing many of the limitations associated with other previously reported diagnostic algorithms. Lacunarity analysis suggests an ordering of irregularity in melanocytic lesions, and we suggest the clinical application of this ordering may have utility in the naked-eye dermoscopic diagnosis of early melanoma.     

Quantifying the branching frequency of virtual filamentous microbes using fractal analysis

The productivity of an industrial fermentation process involving a filamentous microbe is heavily dependent on the morphological form adopted by the organism. The development of systems capable of rapidly and accurately characterizing morphology within a given process represents a significant challenge, as the complex phenotypes that are manifested are not easily quantified. Conventional parameters employed in these analyses are often of limited value, as they reveal little about the branching behavior of the organism; an important consideration given the demonstrated link between branching frequency and metabolite production. In this study, the influence of branching behavior on the spatial distribution of mycelia grown in silico is examined through fractal analysis. It is demonstrated that fractal dimension, quantified based on the frequency distribution of parameterized boundary curves, and lacunarity act as robust estimators of branching behavior. The analysis can, in theory, be applied to any morphological form, providing universally applicable process parameters for more complete data acquisition. Biotechnol. Bioeng. 2013; 110: 437–447. © 2012 Wiley Periodicals, Inc.     

Nano- and microscale mechanical properties of erythrocytes in hereditary spherocytosis

Hereditary spherocytosis (HS), an erythrocyte membranopathy, is a heterogeneous disease, even at the level of the erythrocyte population. The paper aims at studying the mechanical properties (the Young’s modulus, median and RMS roughness of friction force maps; fractal dimension, lacunarity and spatial distribution parameters of lateral force maps) of the cell surface layer of the erythrocytes of two different morphologies (discocytes and spherocytes) in HS using atomic force microscopy. The results of spatial-spectral and fractal analysis showed that the mechanical property maps of the HS spherocyte surface were more structurally homogeneous compared to the maps of HS discocytes. HS spherocytes also had a reduced RMS roughness and lacunarity of the mechanical property maps. The Young’s modulus and averaged friction forces over the microscale HS spherocyte surface regions were approximately 20% higher than that of HS discocytes. The revealed significant difference at the nano- and microscales in the structural and mechanical properties of main (discoidal and spheroidal) morphological types of HS erythrocytes can potentially cause blood flow disturbance in the vascular system in HS.     

基于样带的唐古特白刺灌丛沙包空间格局尺度研究

黄河河岸与库布齐沙漠之间生态过渡带上的唐古特白刺(Nitraria Tangutorum)灌丛沙包由于遭受到不同程度的破坏而表现出一定程度的退化,空间格局尺度从一定程度上表征了其破碎化程度。我们分别应用样方方差法,小波分析,分维,谱分析以及空隙度分析等方法对鄂尔多斯高原北缘唐古特白刺灌丛沙包的空间格局尺度进行了比较研究,旨在选出适合分析干旱半干旱区白刺灌丛沙包空间格局尺度的方法,并确定研究区内唐古特白刺灌丛沙包的空间格局尺度,为保护唐古特白刺灌丛沙包提供科学依据。结果表明:(1)TTLQV法得到的格局尺度过大,而小波分析得到的格局尺度过小,分维分析得到的格局尺度除了相对较小之外,趋势也不明显,因此都不适合分析干旱半干旱区白刺灌丛沙包的空间格局尺度;(2)而3TLQV,tQV,谱分析和空隙度分析所得到的结果则相对容易接受,其大小顺序是:3TLQV>tQV>空隙度分析>谱分析;(3)独贵塔拉、呼和木独和巴拉贡唐古特白刺灌丛沙包的空间格局尺度分别为16.7～27.1m,10.2～25.0m和8.8～17.0m,这一结果将有助于在今后的研究中合理地确定研究范围和尺度。     

Metapopulations in multifractal landscapes: on the role of spatial aggregation

The use of fractals in ecology is currently pervasive over many areas. However, very few studies have linked fractal properties of landscapes to generating ecological mechanisms and dynamics. In this study I show that lacunarity (a measure of the landscape texture) is a well suited ecologically scaled landscape index that can be explicitly incorporated in metapopulation models such as the classical Levins equation. I show that the average lacunarity of an aggregated landscape is linearly correlated to the habitat that a species with local spatial processed information may perceive. Lacunarity is a computationally feasible index to measure, and is related to the metapopulation capacity of landscapes. A general approach to multifractal landscapes has been conceived, and some analytical results for self-similar landscapes are outlined, including the specific effect of landscape heterogeneity, decoupled from that of contagion by dispersal. Spatially explicit simulations show agreement with the semi-implicit method presented.     

A New Cell-Selective Three-Dimensional Microincubator Based on Silicon Photonic Crystals

In this work, we show that vertical, high aspect-ratio (HAR) photonic crystals (PhCs), consisting of periodic arrays of 5 µm wide gaps with depth of 50 µm separated by 3 µm thick silicon walls, fabricated by electrochemical micromachining, can be used as three-dimensional microincubators, allowing cell lines to be selectively grown into the gaps. Silicon micromachined dice incorporating regions with different surface profiles, namely flat silicon and deeply etched PhC, were used as microincubators for culturing adherent cell lines with different morphology and adhesion properties. We extensively investigated and compared the proliferative behavior on HAR PhCs of eight human cell models, with different origins, such as the epithelial (SW613-B3; HeLa; SW480; HCT116; HT29) and the mesenchymal (MRC-5V1; CF; HT1080). We also verified the contribution of cell sedimentation into the silicon gaps. Fluorescence microscopy analysis highlights that only cell lines that exhibit, in the tested culture condition, the behavior typical of the mesenchymal phenotype are able to penetrate into the gaps of the PhC, extending their body deeply in the narrow gaps between adjacent silicon walls, and to grow adherent to the vertical surfaces of silicon. Results reported in this work, confirmed in various experiments, strongly support our statement that such three-dimensional microstructures have selection capabilities with regard to the cell lines that can actively populate the narrow gaps. Cells with a mesenchymal phenotype could be exploited in the next future as bioreceptors, in combination with HAR PhC optical transducers, e.g., for label-free optical detection of cellular activities involving changes in cell adhesion and/or morphology (e.g., apoptosis) in a three-dimensional microenvironment.     

On the Fractal Geometry of DNA by the Binary Image Analysis

The multifractal analysis of binary images of DNA is studied in order to define a methodological approach to the classification of DNA sequences. This method is based on the computation of some multifractality parameters on a suitable binary image of DNA, which takes into account the nucleotide distribution. The binary image of DNA is obtained by a dot-plot (recurrence plot) of the indicator matrix. The fractal geometry of these images is characterized by fractal dimension (FD), lacunarity, and succolarity. These parameters are compared with some other coefficients such as complexity and Shannon information entropy. It will be shown that the complexity parameters are more or less equivalent to FD, while the parameters of multifractality have different values in the sense that sequences with higher FD might have lower lacunarity and/or succolarity. In particular, the genome of Drosophila melanogaster has been considered by focusing on the chromosome 3r, which shows the highest fractality with a corresponding higher level of complexity. We will single out some results on the nucleotide distribution in 3r with respect to complexity and fractality. In particular, we will show that sequences with higher FD also have a higher frequency distribution of guanine, while low FD is characterized by the higher presence of adenine.     

Foliage randomness and light interception in 3-D digitized trees: an analysis from multiscale discretization of the canopy

Light models for vegetation canopies based on the turbid medium analogy are usually limited by the basic assumption of random foliage dispersion in the canopy space. The objective of this paper was to assess the effect of three possible sources of non-randomness in tree canopies on light interception properties. For this purpose, four three-dimensional (3-D) digitized trees and four theoretical canopies – one random and three built from fractal rules – were used to compute canopy structure parameters and light interception, namely the sky-vault averaged STAR (Silhouette to Total Area Ratio). STAR values were computed from (1) images of the 3-D plants, and (2) from a 3-D turbid medium model using space discretization at different scales. For all trees, departure from randomness was mainly due to the spatial variations in leaf area density within the canopy volume. Indeed STAR estimations, based on turbid medium assumption, using the finest space discretization were very close to STAR values computed from the plant images. At this finest scale, foliage dispersion was slightly clumped, except one theoretical fractal canopy, which showed a marked regular dispersion. Taking into account a non-infinitely small leaf size, whose effect is theoretically to shorten self-shading, had a minor effect on STAR computations. STAR values computed from the 3-D turbid medium were very sensitive to plant lacunarity, a parameter introduced in the context of fractal studies to characterize the distribution of gaps in porous media at different scales. This study shows that 3-D turbid medium models based on space discretization are able to give correct estimation of light interception by 3-D isolated trees, provided that the 3-D grid is properly defined, that is, discretization maximizes plant lacunarity.     

Adapting lacunarity techniques for gradient-based analyses of landscape surfaces

Typically, landscapes are modeled in the form of categorical map patterns, i.e. as mosaics made up of basic elements which are presumed to possess sharp and well-defined boundary lines. Many landscape ecological concepts are based upon this perception. In reality, however, the spatial value progressions of environmental parameters tend to be “gradual” rather than “abrupt”. Therefore, gradient approaches have shifted to the forefront of scientific interest recently. Appropriate methods are needed for the implementation of such approaches. Lacunarity analysis may provide a suitable starting point in this context. We propose adapted versions of standard lacunarity techniques for analyzing ecological gradients in general and the heterogeneity of physical landscape surfaces in particular. A simple way of customizing lacunarity analysis for quantifying the heterogeneity of digital elevation models is to use the value range for defining the box mass used in the calculation process. Furthermore, we demonstrate how lacunarity analysis can be combined with metrics derived from surface metrology, such as the “Average Surface Roughness”. Finally, the “classical” lacunarity approach is used in combination with simple landform indices. The methods are tested using different data sets, including high-resolution digital elevation models. In summary, lacunarity analysis is adopted in order to establish a gradient-based approach for terrain analysis and proves to be a valuable concept for comparing three-dimensional surface patterns in terms of their degree of “heterogeneity”. The proposed developments are meant to serve as a stimulus for making increased use of this simple but effective technique in landscape ecology. They offer a large potential for expanding the methodical spectrum of landscape structure analysis towards gradient-based approaches. Methods like lacunarity analysis are promising, since they do not rely on predefined landscape units or patches and thus enable ecologists to effectively deal with the complexity of natural systems.     

A Reproducible Colonial Morphology Formed by Individual Pluripotent Embryonal Carcinoma Cells in Culture and Selection of Variants

Embryonal carcinoma cells are stem cells equivalent to those of the early embryo which can be grown in vitro and which under certain conditions can differentiate into many cell types. Events in this differentiation process are numerous and complex, thus a system for the analysis of clonal differentiation is essential. In this paper I report that individual pluripotent embryonal carcinoma cells can each give rise to colonies, in the absence of a feeder layer but in the presence of β-mercaptoethanol, that show a distinctive and reproducible gross morphology. Embryonal carcinoma cell lines can be derived from the stem cells in these colonies. Furthermore, variant cell lines can be derived from those colonies showing an altered gross morphology. These lines when cloned as above give rise to colonies showing a gross colonial morphology different to that of wild-type. These variant lines have been shown to be embryonal carcinoma cell lines. These findings indicate that genetic and cell lineage analysis of embryonal carcinoma cell differentiation might be possible.     

Analysis of fractal dimension of O2A glial cells differentiating in vitro

Fractal dimension is a quantitative measure of morphological complexity. Glial cells of the oligodendrocyte-type 2 astrocyte (O2A) lineage exhibit increasing morphological complexity as they differentiate in vitro. Enriched populations of O2A progenitor cells isolated from neonatal rat cerebral hemispheres or optic nerves were allowed to differentiate in vitro, and their fractal dimensions were measured over time. The fractal dimensions of the maturing cells correlated with perceived complexity; cells with elaborate process branching had larger fractal dimensions than cells with a simpler morphology. An analysis of changes in fractal dimension revealed distinct rates of growth for both oligodendrocytes and type 2 astrocytes. The fractal dimension remained constant over a 10-fold range in optical magnification, demonstrating that cultured O2A glial cells exhibit self-similarity, a defining characteristic of fractal objects. These results illustrate that fractal dimension analysis of maturing cell populations is a useful method for quantitatively describing the process of cell differentiation.     

Enhanced expression of cellular prion protein gene by insulin or nerve growth factor in immortalized mouse neuronal precursor cell lines

In order to understand the fundamental and putative roles of PrP(c) in the central nervous system, neuronal cell lines were established. Cells were immortalized by recombinant retrovirus vector-mediated transduction of SV40 T-antigen gene. Among these, two cell lines were selected based on their RT-PCR expressions of neuron-specific neurofilament (NF-H, NF-M) and cell morphology. These cell lines showed the properties of neuronal progenitor cells in antigenicity, morphology and responses to differentiating agents. Expression of PrP(c) was detected by immunocytochemical analysis. These cell lines responded to differentiating agents such as dibutyl cyclic AMP (dcAMP) and phorbol 12-myristate 13-acetate (PMA) before developing into neuronal-like cells. Neurite extensions were observed 20 min after incubation with the differentiating agents. Treatment with nerve growth factor (NGF) and insulin induced cell differentiation and enhanced expression of PrP gene (Prnp) mRNA and protein. The latter phenomenon was not inhibited by wortmannin, which is a specific inhibitor of phosphatidylinositol 3-kinase. These results suggest that PrP(c) plays an important role in the differentiation-mediated classic signaling pathway of neuronal cell.     

Cell adhesion molecule uvomorulin expression in human breast cancer cell lines: relationship to morphology and invasive capacities.

Loss of cell-cell adhesion in carcinoma cells may be an important step in the acquisition of an invasive, metastatic phenotype. We have examined the expression of the epithelial-specific cell adhesion molecule uvomorulin (E-cadherin, cell-CAM 120/80, L-CAM) in human breast cancer cell lines. We find that fibroblastoid, highly invasive, vimentin-expressing breast cancer cell lines do not express uvomorulin. Of the more epithelial-appearing, less invasive, keratin-expressing breast cancer cell lines, some express uvomorulin, and some do not. We examined the morphologies of the cell lines in the reconstituted basement membrane matrix Matrigel and measured the ability of the cells to traverse a Matrigel-coated filter as in vitro models for detachment of carcinoma cells from neighboring cells and invasion through basement membrane into surrounding tissue. Colonies of uvomorulin-positive cells have a characteristic fused appearance in Matrigel, whereas uvomorulin-negative cells appear detached. Cells which are uvomorulin negative and vimentin positive have a stellate morphology in Matrigel. We show that uvomorulin is responsible for the fused colony morphology in Matrigel since treatment of uvomorulin-positive MCF-7 cells with an antibody to uvomorulin caused the cells to detach from one another but did not induce invasiveness in these cells, as measured by their ability to cross a Matrigel-coated polycarbonate filter in a modified Boyden chamber assay. Two uvomorulin-negative, vimentin-negative cell lines are also not highly invasive as measured by this assay. We suggest that loss of uvomorulin-mediated cell-cell adhesion may be one of many changes involved in the progression of a carcinoma cell to an invasive phenotype.     

Ultra High Content Image Analysis and Phenotype Profiling of 3D Cultured Micro-Tissues

In many situations, 3D cell cultures mimic the natural organization of tissues more closely than 2D cultures. Conventional methods for phenotyping such 3D cultures use either single or multiple simple parameters based on morphology and fluorescence staining intensity. However, due to their simplicity many details are not taken into account which limits system-level study of phenotype characteristics. Here, we have developed a new image analysis platform to automatically profile 3D cell phenotypes with 598 parameters including morphology, topology, and texture parameters such as wavelet and image moments. As proof of concept, we analyzed mouse breast cancer cells (4T1 cells) in a 384-well plate format following exposure to a diverse set of compounds at different concentrations. The result showed concentration dependent phenotypic trajectories for different biologically active compounds that could be used to classify compounds based on their biological target. To demonstrate the wider applicability of our method, we analyzed the phenotypes of a collection of 44 human breast cancer cell lines cultured in 3D and showed that our method correctly distinguished basal-A, basal-B, luminal and ERBB2+ cell lines in a supervised nearest neighbor classification method.     

Changes in leaf tissue of <Emphasis Type="Italic">Carica papaya</Emphasis> during single and mixed infections with <Emphasis Type="Italic">Papaya ringspot virus</Emphasis> and <Emphasis Type="Italic">Papaya mosaic virus</Emphasis>

Papaya (Carica papaya L.) is susceptible to viral diseases caused by Papaya mosaic virus (PapMV) and Papaya ringspot virus (PRSV), which limit fruit production and affect economic yield. The symptoms produced by both the viruses are similar in early stages of infection and include vein and leaf chlorosis, which develop into mosaic at later stages of infection when leaf lamina can get reduced in size and distorted with a shoe-string aspect. Digital image analyses, such as fractal dimension (FD) and lacunarity (λ) were used here to examine papaya tissue after single and mixed infections of PRSV and PapMV. Morphological changes, such as hypoplasia, hyperplasia, and neoplasia are described in tissues with viral infections. Furthermore, we quantified these changes and suggest three ranges of tissue damage according to their λ values in rank 1 (0.01 to 0.39), rank 2 (0.4 to 0.79), and rank 3 (0.8 to 1). Our analyses suggest that in synergism and antagonism there is a competition of both viruses to occupy the same mesophyll cells, as indicated by their intermediate values of lacunarity.     

木本植物对喀斯特石质生境岩石形态结构的适应性

为弄清植物对喀斯特岩石形态结构的适应性,选择3种岩石类型及7种木本群落为研究对象,基于分形、空间句法理论研究岩石结构面孔裂隙形态结构及其与群落特征的关系。结果表明:石灰岩结构面孔裂隙间隙度大、白云岩居中、白云质砂岩小,分维数则反之;白云质砂岩结构面孔裂隙整合度、控制值、密度值大,白云岩居中,石灰岩小;白云岩生境下群落物种多样性及优势种碳、氮含量高、白云质砂岩次之、石灰岩低;分形与空间句法指数间呈显著相关关系,两者能较好的揭示岩石形态结构;总体上3种岩性生境下物种多样性及优势种碳、氮含量与岩石结构面孔裂隙分形及空间句法指数具较强相关关系;大致相同的环境下白云岩形态结构适宜植物生长、白云质砂岩次之、石灰岩差;研究岩石形态结构对喀斯特植被恢复具有重要意义。     

An in vitro model that recapitulates the epithelial to mesenchymal transition (EMT) in human breast cancer

The epithelial to mesenchymal transition (EMT) is a developmental program in which epithelial cells down-regulate their cell-cell junctions, acquire spindle cell morphology and exhibit cellular motility. In human breast cancer, invasion into surrounding tissue is the first step in metastatic progression. Here, we devised an in vitro model using selected cell lines, which recapitulates many features of EMT as observed in human breast cancer. By comparing the gene expression profiles of claudin-low breast cancers with the experimental model, we identified a 9-gene signature characteristic of EMT. This signature was found to distinguish a series of breast cancer cell lines that have demonstrable, classical EMT hallmarks, including loss of E-cadherin protein and acquisition of N-cadherin and vimentin expression. We subsequently developed a three-dimensional model to recapitulate the process of EMT with these cell lines. The cells maintain epithelial morphology when encapsulated in a reconstituted basement membrane, but undergo spontaneous EMT and invade into surrounding collagen in the absence of exogenous cues. Collectively, this model of EMT in vitro reveals the behaviour of breast cancer cells beyond the basement membrane breach and recapitulates the in vivo context for further investigation into EMT and drugs that may interfere with it.     

Multicolor karyotype analyses of mouse embryonic stem cells

Summary The manipulation of embryonic stem (ES) cells to introduce directional genetic changes into the genome of mice has become an important tool in biomedical research. Monitoring of cell morphology before and after DNA manipulation and special culture conditions are a prerequisite to preserve the pluripotent properties of ES cells and thus their ability to generate chimera and effective germline transmission (GLT). It has been reported that prolonged cell culturing may affect the diploid chromosomal composition of cells and therefore the percentage of chimerism and GLT. Herein, we report multicolor-fluorescence in situ hybridization (M-FISH) analysis of four different ES cell lines/clones. Although the morphology of all four ES cell lines/clones appeared normal and all four expressed the early markers Oct-3/4 and Nanog, two cell lines presented consistent numerical and structural chromosome aberrations. We demonstrate that M-FISH is a sensitive and accurate method for a comprehensive karyotype analysis of ES cells and may minimize time, costs, and disappointment due to inadequate ES cell sources. Both authors contributed equally to this work.