Fractal analysis of STM images of photochemical polymer of coniferyl alcohol

Fractal analysis was applied to images of photochemical lignin polymer obtained using scanning tunneling microscope. We studied the polymer obtained in vitro by ionic mechanism through UV radiation--induced polymerization. The analysis showed the regularity of the lignin-like polymer at different levels of organization. At the 95% confidence level, there was no significant difference in the fractal dimension between images representing different organizational levels of photochemical lignin. That means that lignin produced in in vitro conditions by photochemical mechanism of synthesis, has a fractal structural organization. The obtained values of the fractal dimension are in good agreement with the theoretically predicted value for the polyaddition and polycondensation mechanism of polymerization, known as the bulk model.     

Determination of the fractal dimension of membrane protein aggregates using fluorescence energy transfer.

It is demonstrated that fluorescence resonance energy transfer may be used to determine the fractal dimension of aggregates of membrane-bound proteins. Theoretical and experimental results are presented for two different experimental designs: energy transfer between proteins and energy transfer from lipids to proteins. For energy transfer between proteins the lattice spacing must be known independently for a fractal dimension to be uniquely determined, and this represents a disadvantage to this experimental design. Results are presented for the calcium ATPase and a fractal dimension of 1.9 is estimated for ATPase aggregates by assuming a lattice spacing of 50 A. Energy transfer from lipids to protein provides a means of estimating the length of the "coast-line" of the aggregate. In this case the fractal dimension is uniquely determined from a log-log plot. An analysis of data for bacteriohodopsin reconstituted in phospholipid vesicles gives a fractal dimension of 1.6. The structural basis of the value for the fractal dimension is discussed for these two systems. These techniques provide a means of assessing the nature of protein-protein interactions in membranous systems.     

Current insights into chromatin structure organization

This review summarizes current insights into organization of chromatin structure at different levels of DNA compaction. Analysis of available experimental data allowed concluding that only nucleosomal level of structural organization was sufficiently investigated, whereas structure of a 30-nm chromatin fiber remains an open issue. The data on the chromatin structure obtained at the level of the nucleus speak in favor of a biphasic fractal organization of chromatin.     

The role of of laccase in lignification

The enzymatic mechanism of monolignol polymerization in lignin biosynthesis is not known, although it has been the subject of significant interest for more than 60 years. Peroxidase had been considered to be the exclusive plant enzyme involved in the oxidative polymerization of lignin precursors. Recently, laccase and laccase-like oxidase activities have been associated with lignification. Laccase is bound to lignifying plant cell walls and can polymerize lignin precursors in vitro . Strong circumstantial evidence from different species implicates this enzyme in the polymerization of lignin precursors. Lignin has a complex structure and it has been difficult to analyze the heterogeneity of lignin by chemical and physical techniques. If lignin precursors are polymerized by enzymes that differ in their catalytic properties, then lignin heterogeneity could be produced by differential expression of multiple enzymes during plant development. When laccase genes are correctly identified, these ideas can be tested in genetic experiments where gain or loss of function can be predicted by the presence or absence of the functional gene.     

The Quasi-Fractal Structure of Fish Brain Neurons

The box-counting method for calculating the fractal dimension (D) with the ImageJ 1.20s software is used as a tool for quantitative analysis of the neuronal morphology in the fish brain. The fractal dimension was determined for several types of neurons in the brain of two teleost species, Pholidapus dybowskii and Oncorhynchus keta. These results were compared with those obtained for some neurons of the human brain. The fractal (fractional) dimension (D), as a quantitative index of filling of two-dimensional space by the black and white image of a cell, is shown to vary from 1.22 to 1.72 depending on the type of neuron. The fractal dimension reaches its maximum in less specialized neurons that carry out a number of different functions. On the other hand, highly specialized neurons display a relatively low fractal dimension. Thus, the fractal dimension serves as a numerical measure of the spatial complexity of the neuron and correlates with the morphofunctional organization of the cell.     

山东泰山地区景观结构变化及其分形分析

将泰山风景区划分为 8个区域 11个基本景观类型 ,包括松林、栎林、刺槐林、侧柏林、针阔叶混交林、经济林、灌丛、裸岩、荒地、水体、建筑。在此基础上 ,利用 3S技术和分形理论对各个景观要素进行了分析 ,并讨论了景观特性及其变化的分形性质。结果表明 :(1)分维值的大小反映了景观斑块面积、斑块数量和平均斑块面积等因素的相互作用 ,在一定尺度下分维的大小反映了区域内景观斑块的不规则程度和复杂程度 ,斑块越不规则、越复杂 ,其分维越大 ,反之亦然。在泰山地区 ,自 1986年至 2 0 0 1年 ,刺槐林一直保持着较高的分维值 ,其它景观类型的分维值则差别不大 ,而针阔叶混交林的分维值变化较大 ;(2 )森林景观受多种因子的影响 ,在高海拔区域主要受垂直地带性规律影响为主 ,在旅游区主要受人类活动的影响为主 ,15 a来各个区域分形维数的总体变化趋势相似 ;(3)大部分区域在 2 0 0 1年的景观多样性、破碎度高于 1986年的 ,而景观优势度则略为下降     

A Fractal Nature for Polymerized Laminin

Polylaminin (polyLM) is a non-covalent acid-induced nano- and micro-structured polymer of the protein laminin displaying distinguished biological properties. Polylaminin stimulates neuritogenesis beyond the levels achieved by ordinary laminin and has been shown to promote axonal regeneration in animal models of spinal cord injury. Here we used confocal fluorescence microscopy (CFM), scanning electron microscopy (SEM) and atomic force microscopy (AFM) to characterize its three-dimensional structure. Renderization of confocal optical slices of immunostained polyLM revealed the aspect of a loose flocculated meshwork, which was homogeneously stained by the antibody. On the other hand, an ordinary matrix obtained upon adsorption of laminin in neutral pH (LM) was constituted of bulky protein aggregates whose interior was not accessible to the same anti-laminin antibody. SEM and AFM analyses revealed that the seed unit of polyLM was a flat polygon formed in solution whereas the seed structure of LM was highly heterogeneous, intercalating rod-like, spherical and thin spread lamellar deposits. As polyLM was visualized at progressively increasing magnifications, we observed that the morphology of the polymer was alike independently of the magnification used for the observation. A search for the Hausdorff dimension in images of the two matrices showed that polyLM, but not LM, presented fractal dimensions of 1.55, 1.62 and 1.70 after 1, 8 and 12 hours of adsorption, respectively. Data in the present work suggest that the intrinsic fractal nature of polymerized laminin can be the structural basis for the fractal-like organization of basement membranes in the neurogenic niches of the central nervous system.     

Fractal analysis of the uterine contractions.

The fractal dimension D may be calculated in many ways, since its strict definition, the Hausdorff definition is too complicated for practical estimation. In this paper we perform a comparative study often methods of fractal analysis of time series. In Benoit, a commercial program for fractal analysis, five methods of computing fractal dimension of time series (rescaled range analysis, power spectral analysis, roughness-length, variogram methods and wavelet method) are available. We have implemented some other algorithms for calculating D: Higuchi's fractal dimension, relative dispersion analysis, running fractal dimension, method based on mathematical morphology and method based on intensity differences. For biomedical signals results obtained by means of different algorithms are different, but consistent.     

Automated image segmentation by fractal grey tone functions

A new image segmentation method is presented. It is based on mathematical derivations stemming from both mathematical morphology and fractal geometry. Structures of different nature are most often characterized by a fractal grey tone function, in a certain range of resolutions, with a particular value of the fractal dimension. Our method allows the isolation of such structures. It only requires a series of dilated and eroded grey tone images.     

Microstructural characterization of chitosan and alginate films by microscopy techniques and texture image analysis

The aim of this work is to characterize the microstructure of chitosan and alginate edible films by microscopy techniques and texture image analysis. Edible films were obtained by solution casting and solvent evaporation. The microscopy techniques used in this work were: light, environmental scanning electron and atomic force microscopy. Textural features and fractal dimension were extracted from the images. Entropy and fractal dimension were more useful to evaluate the complexity and roughness of films. The highest values of entropy and fractal dimension corresponded to alginate/chitosan, followed of alginate and chitosan films. An entropy/fractal dimension ratio, proposed here, was useful to characterize the degree of image complexity and roughness of edible films at different magnifications. It was possible to postulate that microscopy techniques combined with texture image analysis are efficient tools to quantitatively evaluate the surface morphology of edible films made of chitosan and alginate.     

Power-law species richness accumulation as manifestation of the fractal community structure

Applications of the fractal to describing the species structure of communities are discussed. Fundamental notions of fractal geometry are explained in the first part. The problem of applying the concept of fractal to describe the spatial allocation of particular species and of community as a whole is reviewed in the second part. In the final part, the usage of the selfsimirity principle for analyzing community organization is substantiated, and evidence of the fractal structure of biocenoses is presented according to Whittaker's concept of alpha diversity. It is shown that community is characterized, as a fractal object, by scale invariance, by power function relationship between the number of structural elements of the community (individuals, populations, species) and the scale (sampling effort), and, finally, by fractional value of the power (fractal dimension). Power function is the formula the takes into account the share of rare species, or species represented by a single individual. providing for no saturation of the function f(x). This formula also does not contradict the A.P. Levich's "rule of ecological non-additivity" and, lastly, allows the application of fractal formalism to characterize the species structure of a community. It is concluded that the mathematical image of species richness is a monofractal, i.e., a set characterised by only one parameter, fractal dimension. Thus, the species structure of a community (as well as the pattern of its spatial allocation) displays self-similarity and is a fractal.     

Fractal Organization of Cultivated in vitro Spiculogenous Cells and Larval Spicules of the Sea Urchin Strongylocentrotus nudus

The morphological patterns of the cultivated cells of primary mesenchyme and the spicules of the larval skeleton of the sea urchin Strongylocentrotus nudus were quantified, and the value of their fractal dimensions (D) was determined with ImageJ 1.20s software. It was shown that during cytodifferentiation, the values of D in the fractal (fractional) dimension, which reflects the complex spatial organization of the spiculogenous mesenchyme elements in two-dimensional space, increase to values close to 1.7. The invertible treatment with cytochalasin, which destroys the system of the actin filaments, suppresses the normal control of biomineralization and causes a complex form of spicules, the fractal dimension of which varies within 1.5–1.6. Thus, the determination of the fractal dimension value serves as evidence of the fractional essence of the patterns studied, quantifies the spatially complex organization of cells and their assemblies during morphogenesis, and allows us to estimate the variation in the spicule morphology after cytochalasin treatment.     

Spectroscopic properties of oxidation species generated in the lignin of wood fibers by a laccase catalyzed treatment: electronic hole state migration and stabilization in the lignin matrix

A laccase catalyzed oxidative treatment of wood pulp fibers has been found to induce unusual modifications of these fibers that are qualitatively different from those encountered when more severely degraded fibers are subjected to similar enzymatically catalyzed oxidative treatments. These results suggest that the physical/conformational state of the lignin of wood fibers determines which oxidation pathways dominate in a given oxidative treatment, leading to different lignin modifications depending on both the chemical and the physical structure of the lignin polymer. Spectroscopic measurements (ESR, IR, UV-Vis and fluorescence) show that the laccase treatment results in the formation of two different species in the dried fibers: one is interpreted as chemically transformed (via oxygen) lignin products, and the other as initial oxidation radicals which have gained stabilization against transformation into the first mentioned products via a migration mechanism. It is argued that these initial radicals may likely be cation radical (or hole state) parts in lignin. The migration mechanism is identified with site-to-site transfer or 'hopping' via electron transfer and it is postulated that this mechanism 'carries' cation radical parts of the lignin, produced at the surface of the fiber, into parts of the lignin where chemical transformation pathways are suppressed due to the lignin conformational state. The possible existence of such a migration mechanism, the relative dominance of which should depend sensitively on the polymer conformational state, may have implications for the biogeneration and biodegradation of lignin as well as for oxidative treatments of non-natural conjugated polymers.     

江河源区高寒草甸退化序列土壤粒径分布及其分形维数

江河源区高寒草甸退化日益严重,恢复治理已进行了大量工作,但收效甚微,主要是对退化机理认识不清.为阐明退化草地的形成机制,
本文以江河源区高寒草甸为对象,分析退化序列土壤粒径的分布特征、分形维数,以及分形维数与土壤侵蚀模数的关系.结果表明: 随着高寒草甸退化加剧,土壤的黏粒百分含量呈增加趋势,粉砂和极细砂呈减小趋势;退化序列土壤粒径分形维数与黏粒百分含量呈显著正相关,与极细砂和粉砂呈显著负相关;各粒级土壤侵蚀模数与分形维数呈二次函数关系,分形维数2.81为土壤侵蚀发生的阈值.以土壤粒径分形维数2.81作为草地恢复指标,选择使分形维数小于2.81的相应措施,是恢复退化草地的有力保证.     

王港潮滩重金属Pb、Zn和Cu的积累特征

对15a来王港潮滩重金属积累规律和污染状况进行了研究,第1次测到了王港地区210Pb的本底值为1.16dpm/g,校正了前人对王港地区沉积速率的研究。尝试性地把分形理论引入到环境压力的定量研究中。研究表明,王港潮滩现代平均沉积速率为4.13cm/a;从重金属相关性分析得出:王港潮滩Fe、Zn与Li相关系数非常显著,归一化后,Cu、Zn的归一化值在15a内相对稳定,其中Cu的波动范围在0.4～2之间,Zn在1.5～2.6之间狭小的范围内波动。分形回归分析结果表明,王港潮滩重金属Cu、Zn归一化值的信息维数高,系统的结构松散,自组织程度低。Cu的分维值范围在5～6.5,平均值为5.8085,Zn的分维值范围在在3～6.5,平均值为4.68。王港潮滩重金属的人为污染较轻,主要受地球化学元素的控制;同时,Pb的归一化值的分维值较低,其分维值范围在2～5.5,平均值为3.608,自组织程度较高,说明存在一定程度的Pb污染。     

Quantitative method to study the network formation of endothelial cells in response to tumor angiogenic factors

To study the network formation of endothelial cells (ECs) in an extracellular matrix (ECM) environment, we have devised an EC aggregation-type model based on a diffusion limited cluster aggregation model (DLCA), where clusters of particles diffuse and stick together upon contact. We use this model to quantify EC differentiation into cord-like structures by comparing experimental and simulation data. Approximations made with the DLCA model, when combined with experimental kinetics and cell concentration results, not only allow us to quantify cell differentiation by a pseudo diffusion coefficient, but also measure the effects of tumor angiogenic factors (TAFs) on the formation of cord-like structures by ECs. We have tested our model by using an in vitro assay, where we record EC aggregation by analysing time-lapse images that provide us with the evolution of the fractal dimension measure through time. We performed these experiments for various cell concentrations and TAFs (e.g. EVG, FGF-b, and VEGF). During the first six hours of an experiment, ECs aggregate quickly. The value of the measured fractal dimension decreases with time until reaching an asymptotic value that depends solely on the EC concentration. In contrast, the kinetics depend on the nature of TAFs. The experimental and simulation results correlate with each other in regards to the fractal dimension and kinetics, allowing us to quantify the influence of each TAF by a pseudo diffusion coefficient. We have shown that the shape, kinetic aggregation, and fractal dimension of the EC aggregates fit into an in vitro model capable of reproducing the first stage of angiogenesis. We conclude that the DLCA model, combined with experimental results, is a highly effective assay for the quantification of the kinetics and network characteristics of ECs embedded in ECM proteins. Finally, we present a new method that can be used for studying the effect of angiogenic drugs in in vitro assays.     

Fractal dimension in human cerebellum measured by magnetic resonance imaging

Fractal dimension has been used to quantify the structures of a wide range of objects in biology and medicine. We measured fractal dimension of human cerebellum (CB) in magnetic resonance images of 24 healthy young subjects (12 men and 12 women). CB images were resampled to a series of image sets with different 3D resolutions. At each resolution, the skeleton of the CB white matter was obtained and the number of pixels belonging to the skeleton was determined. Fractal dimension of the CB skeleton was calculated using the box-counting method. The results indicated that the CB skeleton is a highly fractal structure, with a fractal dimension of 2.57 +/- 0.01. No significant difference in the CB fractal dimension was observed between men and women.     

Aggregation during coniferyl alcohol polymerization in pectin solution: a biomimetic approach of the first steps of lignification

Coniferyl alcohol was polymerized in pectin solution in order to mimic the lignification that is the final step of biosynthesis of plant cell wall. Dehydrogenated polymers (DHP = coniferyl alcohol polymers = synthetic lignin) interact with pectin to form hydrophobic clusters as monitored by pyrene fluorescence spectroscopy. The structure of these clusters was studied during the polymerization of synthetic lignin by static and quasielastic light scattering and small angle neutron scattering experiments. We show that synthetic lignin and pectin contribute to the same clusters, but the inner structure of these clusters is very heterogeneous and displays three phases. One observes a segregation between well separated pectin and lignin rich phases at length scales below approximately 30 nm. As a corollary of this segregation, clusters embody a large amount of solvent. On average, the density of the polymer rich phase (lignin plus pectin) inside clusters increases while its specific surface area decreases throughout the polymerization process. These results are discussed with respect to in vivo lignification of the plant cell wall.