Fractal geometry of mosaic pattern demonstrates liver regeneration is a self-similar process.

Partial hepatectomy causes compensatory, nonneoplastic growth and regeneration in mammalian liver. Compensatory liver growth can be used to examine aspects of patterns of cell division in regenerating tissue. Chimeric animals provide markers of cell lineage which are independent of growth and can be used to follow cell division patterns. Previous experimental evidence suggests that compensatory liver growth is uniform, without focal centers of proliferation. In this study we have extended that observation to include genes important in regeneration and cell cycle control in order to establish that nascent growth centers are not present in regenerating liver. There is a uniform spatial distribution of expression of these genes which is not related to mosaic pattern in the chimeras. While these genes may help regulate hepatocyte proliferation they do not appear to regulate patch pattern in the chimeras. With this information confirming uniform growth it was possible to use fractal analysis to test various hypothesized patterns of regenerative growth in the liver. The results of this analysis indicate that mosaic pattern does not change substantially during the regenerative process. Patch area and perimeter (the area occupied by or perimeter around cells of like lineage) increase during compensatory liver growth in chimeric rats without alteration of the geometric complexity of patch boundaries (boundaries around cells of like lineage). These tissue findings are consistent with previously reported computer models of growth in which repetitive application of simple decisions assuming uniform growth created complex mosaic patterns. They support the notion that an iterating (repeating), self-similar (a pattern in which parts are representative of, but not identical to the whole) cell division program is sufficient for the regeneration of liver tissue following partial hepatectomy. Iterating, self-similar cell division programs are important because they suggest a way in which complex patterns (or morphogenesis) can be efficiently created from a small amount of stored information.     

TrappedAcetobacter in membrane bioreactor: Fractal interpretation of a compatible population

Summary Acetobacter localisation within membrane porosity and cell release in permeate stream were investigated. Predictions by a model based on the fractal nature of membranes were compared with the data obtained from pilot plant running tests. The results indicate possibilities for application in studies to help and control the process.     

Fractal geometry: a tool for describing spatial patterns of plant communities

Vegetation is a fractal because it exhibits variation over a continuum of scales. The spatial structure of sandrim, bryophyte, pocosin, suburban lawn, forest tree, and forest understory communities was analyzed with a combination of ordination and geostatistical methods. The results either suggest appropriate quadrat sizes and spacings for vegetation research, or they reveal that a sampling design compatible with classical statistics is impossible. The fractal dimensions obtained from these analyses are generally close to 2, implying weak spatial dependence. The fractal dimension is not a constant function of scale, implying that patterns of spatial variation at one scale cannot be extrapolated to other scales.     

Wheel-running activity: a new interpretation

The wheel-running activity of caged mammals has been misinterpreted for many years as a measure of 'general activity'. A review of the literature and recent experimental evidence suggests that this behaviour has a far more specific function for the animal, and that its major and invaluable experimental use lies as both a field and laboratory tool for the studies of particular forms of migration. This new interpretation allows a greater understanding of the motivations underlying this widely-monitored behaviour.

Summary

It is apparent that the nature of the response to an activity-wheel has been greatly misunderstood for many years. The behaviour appears to be far more specific than previously thought, reflecting a type of inherent response which is not evident when activity is recorded by other methods. This report indicates that the wheel is used by a caged animal when the individual is motivated to reach an unattainable resource. This results in an urge to travel, either to remove itself from the immediate area, or to search for specific resources. It is proposed that when the goal is perceptually not present, the activity wheel is a specific monitor of 'exploratory migration', and reflects the urge to collect information about the location of resources. It implies, therefore, that the use of the activity-wheel as a simple measure of 'general activity' should cease; the major future uses of this particular activity recording device should be in the studies of the daily, ontogenetic and seasonal variation in the incidence of exploratory migration, and the influence upon it of other environ- mental factors, as well as a method of investigating goal-orientation, both in the field and the laboratory. This new interpretation provides a more precise explanation of what is being measured in wheel-running experiments, and should result in a more specific use of wheel-activity in experimentation.     

Fractal geometry of a complex plumage trait reveals bird's quality

Animal coloration is key in natural and sexual selection, playing significant roles in intra- and interspecific communication because of its linkage to individual behaviour, genetics and physiology. Simple animal traits such as the area or the colour intensity of homogeneous patches have been profusely studied. More complex patterns are widespread in nature, but they escape our understanding because their variation is difficult to capture effectively by standard, simple measures. Here, we used fractal geometry to quantify inter-individual variation in the expression of a complex plumage trait, the heterogeneous black bib of the red-legged partridge (Alectoris rufa). We show that a higher bib fractal dimension (FD) predicted better individual body condition, as well as immune responsiveness, which is condition-dependent in our study species. Moreover, when food intake was experimentally reduced during moult as a means to reduce body condition, the bib''s FD significantly decreased. Fractal geometry therefore provides new opportunities for the study of complex animal colour patterns and their roles in animal communication.     

Woody Polygonaceae from Brazil: new species and a new interpretation

Three new species, Ruprechtia maracaensis, Ruprechtia nitida , and Triplaris matogrossensis are described. Ruprechtia glauca is a poorly known species from the state of Bahia. Its relationship with R. laxiflora is discussed.     

Floret position in Costularia (Cyperaceae): a new interpretation

The spikelet of Costularia has been interpreted as comprising proximal, sterile glumes followed by two larger fertile glumes that subtend respectively, a lower male and an upper bisexual floret. The terminal uppermost glume, with two keels and therefore resembling a prophyll, was empty. Studies of developmental stages of spikelets from Zimbabwe (Chimanimani Mts.) have revealed that the terminal glume envelops the bisexual floret and becomes empty only with maturation of the ovary.     

Fractal geometry of bean root systems: correlations between spatial and fractal dimension

An obstacle to the study of root architecture is the difficulty of measuring and quantifying the three-dimensional configuration of roots in soil. The objective of this work was to determine if fractal geometry might be useful in estimating the three-dimensional complexity of root architecture from more accessible measurements. A set of results called projection theorems predict that the fractal dimension (FD) of a projection of a root system should be identical to the FD of roots in three-dimensional space (three-dimensional FD). To test this prediction we employed SimRoot, an explicit geometric simulation model of root growth derived from empirical measurements of common bean (Phaseolus vulgaris L.). We computed the three-dimensional FD, FD of horizontal plane intercepts (planar FD), FD of vertical line intercepts (linear FD), and FD of orthogonal projections onto planes (projected FD). Three-dimensional FD was found to differ from corresponding projected FD, suggesting that the analysis of roots grown in a narrow space or excavated and flattened prior to analysis is problematic. A log-linear relationship was found between FD of roots and spatial dimension. This log-linear relationship suggests that the three-dimensional FD of root systems may be accurately estimated from excavations and tracing of root intersections on exposed planes.     

Fractal geometry and root system structures of heterogeneous plant communities

Above-ground plant growth is widely known in terms of structural diversity. Likewise, the below-ground growth presents a mosaic of heterogeneous structures of differing complexity. In this study, root system structures of heterogeneous plant communities were recorded as integral systems by using the trench profile method. Fractal dimensions of the root images were calculated from image files by the box-counting method. This method allows the structural complexity of such associations to be compared between plant communities, with regard to their potentials for soil resource acquisition and utilization. Distinct and partly significant differences are found (fractal dimension between 1.46±0.09 and 1.71±0.05) in the below-ground structural complexity of plant communities, belonging to different biotope types. The size of the heterogeneous plant community to be examined has an crucial influence on the fractal dimension of the root system structures. The structural heterogeneity becomes particularly evident (fractal dimensions between 1.32 and 1.77) when analysing many small units of a complex root system association. In larger plant communities, a broad variety of below-ground structures is recorded in its entirety, integrating the specific features of single sub-structures. In that way, extreme fractal dimensions are lost and the diversity decreases. Therefore, the analysis of larger units of root system associations provides a general knowledge of the complexity of root system structures for heterogeneous plant communities.     

Genetic interpretation of polytene chromosomes banding pattern

This mini-review covers new data regarding the problem of the functional organization of polytene chromosomes: The localization of RNA synthesis in the polytene chromosome puffs, diffuse bands and interbands; The relative stability of banding pattern and its functional value; The informational content of bands.     

Community pattern analysis: A method for quantifying community mosaic structure

A method of quantifying community spatial patterns, community pattern analysis, is described. It is proposed that ordination analysis is used to obtain an integrated score for each quadrat from transect data. For the data presented here, separate ordinations were made of both floristic and environmental (soils) data. The ordination axis scores are then analysed using two or three-term local variance analysis to quantify the scales of community pattern. Correlation analyses allow the relationship between the vegetation and soils data (as represented by ordination axis scores), and other environmental data to be investigated at defined scales. The advantages of this method, that employs the joint application of conventional methods, are that it includes the influence of all species in the analysis, and that multiple uncorrelated scales of pattern within a community are identified.     

Muscle contraction: a new interpretation of the transient behaviour of muscle

Piazzesi et al. [G. Piazzesi, L. Lucii, V. Lombardi, J. Physiol. 545 (2002) 145–151] made a study on the muscle transients due to step changes in force using improved time resolution and recorded filament movement and shortening velocities in the four phases. They point to Phase 2 and to Phase 4 (working muscle) and claim that their results do not contradict the swinging-cross-bridge (SCB) model which has a much-quoted constant power stroke of about 150 Å (their value of 70 Å was smaller). Siding with the SCB model, they nevertheless record that the power stroke decreases with load. We are pleased with this experimental result as it conforms to our theory, published in 1996, of an impulsive model with a much smaller step-size distance z (≈20 Å). Using their data we obtain precise interval times and estimates of filament movement in Phase 2 and in working muscle. Our first result is that the time frames (interval times) for Phase 2 are the same as in working muscle. Moreover, we demonstrate that the authors’ data verify the correctness of our calculated z values. There are eight active ATP events in Phase 2 in time frame t compared to one in working muscle in the same time frame t. This gives, for the first time, precise numbers for contractile events. We show that the SCB model is incorrect and our analysis supports the impulsive model with a much smaller filament (zero-load) motion, ≈20 Å per ATP split.