The influence of temperature on the dynamics of protein precrystallization clusters,studied by photon correlation spectroscopy

Hen-egg white lysozyme was used for studying the influence of temperature on crystallization. The reaction was initiated at variable temperatures, covering the range between 5–50 °C, and was monitored with photon correlation spectroscopy. When aggregation was induced by addition of NaCl, the clusters formed exhibited diffusion limited aggregation behavior and crystals appeared in less than two days. In contrast, (NH₄)₂SO₄ induced aggregation took place mostly in the cross-over regime. In this case, solutions either remained transparent and void of crystals or formed gels within a few weeks. In both cases the kinetics could be dynamically scaled into master curves indicating that the precrystallization formed aggregates are fractals resulting from different collision processes.     

Protein sequences as random fractals

The analysis of primary sequences from a protein sequence data base suggests that the sequences can be considered as examples of constrained random fractals. Fractal dimensions of the positional distributions of the 20 residues along the chain have been calculated. These fractal dimensions can be used as indices of intrinsic preferences of various residues.     

Fractal properties of forest spatial structure

The definition of fractal dimension of natural objects, which enables to deal with scale dependence of fractal dimension is discussed. Abrupt changes of fractal dimension of spatial structure of terrestrial ecosystems are considered in the context of hierarchical paradigm. On this ground the procedure is proposed for segmentation of a territory, which takes into account the scale dependence of spatial variability of ecological parameters. Using remotely sensed data — normalized difference vegetation index (NDVI) and thermal radiation in the infrared band — fractal dimensions and critical scales are evaluated for different forest types with the help of software, developed for this purpose. The results obtained corroborate the potentialities of fractal approach in ecology. These methods and results can be used for discrimination of remotely sensed data; but further investigations, including detailed comparison of fractal characteristics of remotely sensed forest images with results of on-site field studies are necessary to validate them.     

外显子与内含子序列分维的双碱基研究

引入碱基间的关联,研究了外显子和内含子序列以双碱基为单位的分维,我们发现在这种情况下,外显子和内显子序列在短程和中程存在自相似性并分别定义了这两个区域的分维。结果表明,短程的分维值Ｄｇ一般比中程的Ｄｍ大,外显子的两个分维值比内含子大。我们改变双联体的位相而分维却不变,这反映出在双联体基础上,外显子的不规则性大于内含子,短程的不规则性大于中程,外显子和内含子序列对以２为周期的结构没有位相的特异性。     

The influence of polystyrene nanoparticles on the fractal kinetics of lactate dehydrogenase

Plastics are ubiquitous in the aquatic environment and their degradation of fragments down to the nanoscale level have raised concerns given their ability to pervade cells. The accumulation of nanoparticles could lead to molecular crowding which can alter the normal functioning of enzymes. The purpose of this study was to examine the influence of polystyrene nanoparticles (NPs) on the fractal kinetics of the lactate dehydrogenase reaction: pyruvate + NADH ? lactate + NAD⁺. The influence of NPs on LDH activity was examined first in vitro to highlight specific effects and secondly in mussels exposed to NPs in vivo for 24h at 15 °C. The reaction rates of LDH were determined with increasing concentrations of pyruvate to reach saturation at circa 1 mM pyruvate. The addition of F-actin, a known binding template for LDH, revealed a characteristic change in reaction rates associated with fractal organization. The addition of 50 and 100 nm transparent NPs also produced these changes. The fractal dimension was determined and revealed that both F-actin and NPs reduced the fractal dimension of the LDH reaction. The addition of viscosity sensor probe in the reaction media revealed viscosity waves during the reaction at low substrate concentrations thought to be associated to synchronized switching between the relaxed and tensed states of LDH. The amplitude and the frequency of viscosity waves were increased by both NPs and F-actin which were associated with increased reaction rates. In mussels exposed to NPs, the isolation of digestive gland subcellular fraction revealed that LDH activity was significantly influenced by the fractal dimension of the LDH reaction where a loss of affinity (high fractal K_M) was detected in mussels exposed to the high concentrations of NPs. It is concluded that polystyrene NPs could change the biophysical properties of the cytoplasm such as the fractal organization of the intracellular environment during the LDH reaction.     

A fractal analysis of analyte-estrogen receptor binding and dissociation kinetics using biosensors: environmental and biomedical effects

A fractal analysis is used to model the binding and dissociation kinetics between analytes in solution and estrogen receptors (ERs) immobilized on a sensor chip of a surface plasmon resonance (SPR) biosensor. The influence of different ligands is also analyzed. A better understanding of the kinetics provides physical insights into the interactions, and suggests means by which appropriate interactions (to promote correct signaling) and inappropriate interactions such as with xenoestrogens (to minimize inappropriate and deleterious to health signaling) may be better controlled. The fractal approach is applied to analyte–ER interaction data available in the literature. The units for the different parameters (rate coefficients and affinities) in fractal-type kinetics are different from those obtained in classical kinetics. Numerical values obtained for the binding and the dissociation rate coefficients are linked to the degree of roughness or heterogeneity (fractal dimension, D_f) present on the biosensor chip surface. In general, the binding and the dissociation rate coefficients are very sensitive to the degree of heterogeneity on the surface. A single-fractal analysis is adequate in some cases. In others (that exhibit complexities in the binding or the dissociation curves) a dual-fractal analysis is required to obtain a better fit. This has biomedical and environmental implications in that the dissociation (and the binding) rate coefficient may be used to alleviate (deleterious effects) or enhance (beneficial effects) by selective modulation of the surface. The affinity values obtained in the analysis are consistent with the numbers required to (a) promote signaling between the correct analyte and the estrogen receptor, and (b) minimize the signaling between xenoestrogens and the estrogen receptor.     

Path tortuosity of Eurasian badgers (<Emphasis Type="Italic">Meles meles</Emphasis>) in a heterogeneous Mediterranean landscape

Movement is the process by which individual organisms are displaced over time to eat, reproduce and defend resources. Fractal analysis is a technique used to study animal movement that measures spatial complexity of path tortuosity; here, we apply it to characterize the movement patterns of the Eurasian badger (Meles meles) in a Mediterranean landscape. We calculated path tortuosity overall and seasonally, and for individuals of different sexes and social groups. The influence of variables related to badgers’ resources (food, shelter, water), human infra-structures and weather conditions were analysed with respect to the tortuosity of each badger’s path. A total of 55 search paths from six badgers were considered for this study. Although badgers generally displayed convoluted movement, there were two exceptions: (a) males overall and (b) all badgers in summer; for both, movements had a lower fractal value, i.e. were less tortuous. The convoluted movement pattern generally observed is probably adapted to the clumped distribution of food in the study area. Nevertheless, our results suggest that the use of dens and latrines were the principal determinants of tortuosity of badgers’ paths while foraging.     

Fractal dimension analysis and mathematical morphology of structural changes in actin filaments imaged by electron microscopy

In this work, we examined structural changes of actin filaments interacting with myosin visualized by quick freeze deep-etch replica electron microscopy (EM) by using a new method of image processing/analysis based on mathematical morphology.In order to quantify the degree of structural changes, two characteristic patterns were extracted from the EM images. One is the winding pattern of the filament shape (WP) reflecting flexibility of the filament, and the other is the surface pattern of the filament (SP) reflecting intra-molecular domain-mobility of actin monomers constituting the filament. EM images were processed by morphological filtering followed by box-counting to calculate the fractal dimensions for WP (D_WP) and SP (D_SP). The result indicates that D_WP was larger than D_SP irrespective of the state of the filament (myosin-free or bound) and that both parameters for myosin-bound filaments were significantly larger than those for myosin-free filaments. Overall, this work provides the first quantitative insight into how conformational disorder of actin monomers is correlated with the myosin-induced increase in flexibility of actin filaments along their length as suggested by earlier studies with different techniques. Our method is yet to be improved in details, but promising as a powerful tool for studying the structural change of protein molecules and their assemblies, which can potentially be applied to a wide range of biological and biomedical images.     

Fractal analysis of plant spatial patterns: a monitoring tool for vegetation transition shifts

Spatial heterogeneity, like species diversity, is an important ecosystem property. We examine the effects of land use on the diversity and spatial distribution of plants in five semi-arid communities of eastern Spain using non-linear methods to assess the spatialtemporal dynamics of plant populations. Specifically, we are interested in detecting long-term structural changes or drift in an ecosystem before it is too late to prevent irreversible degradation. Fractal analysis is used to characterize the complexity of plant spatial patterns and Information Theory indices are used to measure change in information flow with land use changes and soil substrate. We found that grazing favored diversity and heterogeneity of species distribution on the impoverished gypsum and saline substrate community, as opposed to the detrimental effect of grazing in the Alpha steppe community. Indeed, old-field succession after 30 years of abandonment showed a recovery of species diversity but not the spatial structure of the vegetation. Further, Information Fractal Dimension, representing the unpredictability of plant spatial patterns in the landscape, increased as we moved from a highly diverse to a less diverse community, revealing the change to a more scattered and homogeneous spatial plant distribution. The Information Fractal Dimension is a good estimator of ecosystem disturbance, independent of scale, and thus can be used to monitor ecosystem dynamics.