Fractals in the Neurosciences, Part I: General Principles and Basic Neurosciences.

The natural complexity of the brain, its hierarchical structure, and the sophisticated topological architecture of the neurons organized in micronetworks and macronetworks are all factors contributing to the limits of the application of Euclidean geometry and linear dynamics to the neurosciences. The introduction of fractal geometry for the quantitative analysis and description of the geometric complexity of natural systems has been a major paradigm shift in the last decades. Nowadays, modern neurosciences admit the prevalence of fractal properties such as self-similarity in the brain at various levels of observation, from the microscale to the macroscale, in molecular, anatomic, functional, and pathological perspectives.

The fractal geometry of life.

The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms (Weibel [1991]). Fractals fulfil a certain number of theoretical and methodological criteria including a high level of organization, shape irregularity, functional and morphological self-similarity, scale invariance, iterative pathways and a peculiar non-integer fractal dimension [FD].

Nuclear patterns of human breast cancer cells during apoptosis: characterisation by fractal dimension and co-occurrence matrix statistics.

An analytical strategy combining fractal geometry and grey-level co-occurrence matrix (GLCM) statistics was devised to investigate ultrastructural changes in oestrogen-insensitive SK-BR3 human breast cancer cells undergoing apoptosis in vitro. Apoptosis was induced by 1 microM calcimycin (A23187 Ca(2+) ionophore) and assessed by measuring conventional cellular parameters during the culture period. SK-BR3 cells entered the early stage of apoptosis within 24 h of treatment with calcimycin, which induced detectable changes in nuclear components, as documented by increased values of most GLCM parameters and by the general reduction of the fractal dimensions.

Fractal organization of feline oocyte cytoplasm.

The present study aimed at verifying whether immature cat oocytes with morphologic irregular cytoplasm display self-similar features which can be analytically described by fractal analysis. Original images of oocytes collected by ovariectomy were acquired at a final magnification of 400x with a CCD video camera connected to an optic microscope. After greyscale thresholding segmentation of cytoplasm, image profiles were submitted to fractal analysis using FANAL++, a program which provided an analytical standard procedure for determining the fractal dimension (FD).

Apoptosis and oxidative status in peripheral blood mononuclear cells of diabetic patients.

We have compared the concentrations of intracellular glutathione (GSH), glutathione-dependent antioxidative enzymes, the cell death rate and immunophenotype profile of peripheral blood mononuclear cells (PBMC) from healthy donors and from patients with insulin-dependent type II (NIDDM) diabetes mellitus. The IDDM and NIDDM patients had above-normal absolute lymphocyte counts, whereas the percentages of CD3, CD4 adn CD8 T lymphocytes were significantly reduced. In contrast, the absolute number and percentage of B lymphocytes was higher in diabetic patients than in healthy donors.

Calcium Dobesilate protects human peripheral blood mononuclear cells from oxidation and apoptosis.

The antioxidant effects of Calcium Dobesilate (CD, Doxium) were investigated in relation to the oxidative status, apoptosis and in vitro proliferation of human peripheral blood mononuclear cells (PBMC) isolated from healthy donors. CD alone did not modify cell growth in vitrountil 10 microM. This molecule counteracted oxidative damages generated by the high reducing sugar dR and was shown to reduce apoptosis by delaying both membrane permeability changes and DNA fragmentation.

Resveratrol modulates apoptosis and oxidation in human blood mononuclear cells.

Background: We examined the effect of resveratrol (RS), a nonflavonoid polyphenolic phytoalexin found in grapes and red wine, and RS coincubated with the oxidant 2-deoxy-D-ribose (dR), on apoptosis and on the oxidative metabolic status of normal human peripheral blood mononuclear cells (PBMNCs) isolated ex vivo from healthy donors.

Material And Methods: Apoptosis was measured by changes of membrane permeability to propidium iodide (PI), plasma membrane exposure of phosphatidylserine (PS) and intracellular caspase activity. Oxidative status was assessed by recording the intracellular glutathione concentration (GSH), the activities of the enzymes y-glutamyltransferase (y-GT) and glutathione-S-transferase (GST), and intracellular lipid peroxidation (MDA).

Fractal morphometry of cell complexity.

Irregularity and self-similarity under scale changes are the main attributes of the morphological complexity of both normal and abnormal cells and tissues. In other words, the shape of a self-similar object does not change when the scale of measurement changes, because each part of it looks similar to the original object. However, the size and geometrical parameters of an irregular object do differ when it is examined at increasing resolution, which reveals more details.

Ultrastructural complexity of nuclear components during early apoptotic phases in breast cancer cells.

Fractal morphometry was used to investigate the ultrastructural features of the plasma membrane, perinuclear membrane and nuclear chromatin in SK-BR-3 human breast cancer cells undergoing apoptosis. Cells were incubated with 1 microM calcimycin (A23187) for 24 h. Cells in the early stage of apoptosis had fractal dimension (FD) values indicating that their plasma membranes were less rough (lower FD) than those of control cells, while their perinuclear membranes were unaffected.

Spontaneous apoptosis, oxidative status and immunophenotype markers in blood lymphocytes of AIDS patients.

Peripheral blood mononuclear cells (PBMC) from 251 HIV-positive drug abusers of known clinical stage and from 40 healthy donors were tested for conventional immunologic markers (CD3, CD4, CD8, CD19, CD14, CD16/CD56, CD45 and HLA-DR). Additional cell parameters and the occurrence of spontaneous apoptosis (programmed cell death) were investigated on freshly isolated PBMC by flow cytometric measurement of either annexin-V bound to plasma membrane phosphatidylserine or propidium iodide uptake. The activity of gamma-glutamyltransferase (gamma-GT), an ectoenzyme contributing to the synthesis of the intracellular antioxidant glutathione (GSH) and involved in early apoptosis, was also determined in these cells.

Effects of steroid hormones on nuclear membrane and membrane-bound heterochromatin from breast cancer cells evaluated by fractal morphometry.

Objective: To evaluate the effect of steroid hormones on the ultrastructure of nuclear heterochromatin and perinuclear membranes in human MCF-7 breast cancer cells.

Study Design: MCF-7 cells were cultured briefly (five minutes) in the presence of 10(-9) M estrogen 17 beta-estradiol, a stimulator of cell proliferation and/or 10(-9) M glucocorticoid dexamethasone. Changes in the morphologic complexity of nuclear membrane-bound heterochromatin (NMBHC) and nuclear membranes (ENM) were assessed by means of the fractal capacity dimension, D, a noneuclidean geometric descriptor of complex, irregular bodies.

Prevention of Oxidation and Apoptosis in Human Peripheral Blood Mononuclear Cells Exposed to Calcium Dobesilate.

The antioxidant effects of calcium dobesilate (CD) (Doxium(R)) were investigated in relation to the oxidative status, apoptosis, and in vitro proliferation of human peripheral blood mononuclear cells (PBMC) isolated from healthy donors. Calcium dobesilate alone did not modify cell growth in vitro until it reached 10 µM. This molecule counteracted oxidative damage generated by the highly reducing sugar 2-deoxy-D-ribose (dR) and was shown to reduce apoptosis by delaying both membrane permeability changes and DNA fragmentation.

Steroid hormones modify nuclear heterochromatin structure and plasma membrane enzyme of MCF-7 cells. A combined fractal, electron microscopical and enzymatic analysis.

Ultrastructural features of the nuclear membrane envelope (ENM) and the nuclear membrane-bound heterochromatin (NMBHC) were investigated in MCF-7 human breast cancer cells by fractal morphometry. The fractal dimension D established by the box counting method proved to be effective for quantifying nuclear changes in MCF-7 cells treated with steroid hormones, namely the estrogen 17 beta-estradiol, which stimulates cell proliferation, and the glucocorticoid dexamethasone. When MCF-7 cells were briefly (5 min) cultured in the presence of 17 beta-estradiol (10(-9) M), the irregularity of the NMBHC outline was increased as documented by the increased fractal dimension D.

Apoptotic cell death and the proliferative capacity of human breast cancers.

The proliferative capacity (%S-phase fraction), DNA ploidy, apoptosis frequency (DNA fragmentation) and steroid hormone receptor status (estrogen receptor, ER; progesterone receptor, PR) of 110 samples of human breast tissues with ductal invasive carcinoma were measured using biochemical and cytofluorimetric procedures. The DNA fragmentation had a left-skewed frequency distribution and an overall median value of 1.64%, whilst the median %S-phase fraction was 8%.

Self-similarity and fractal irregularity in pathologic tissues.

The irregularity and self-similarity under scale changes are the main attributes of the morphologic complexity of cells and tissues, either normal or pathologic. In other words, the shape of a self-similar object does not change when scales of measure change because any part of it might be similar to the original object. Size and geometric parameters of an irregular object, however, differ when inspected at increasing resolution, which reveals more details.

Changes in membrane enzymes and glycosphingolipids in lymphocytes from HIV-1--infected and noninfected intravenous drug users.

The amounts of cell-surface glycosphingolipids and plasma membrane enzymes produced on the peripheral blood mononuclear cells (PBMNCs) isolated from 101 intravenous drug users (IDUs), of whom 91 were HIV-1 seropositive, were examined. Seronegative IDUs and age-matched healthy donors served as controls. The numbers of circulating CD3+, CD4+, and CD8+ T lymphocytes decreased during the advanced stages of the infection.

Enzymatic, biophysical and ultrastructural changes of plasma membranes in chemical-induced rat hepatoma.

Plasma membranes from liver of control rats or from chemical-induced hepatoma were prepared. The basal activity of adenylate cyclase was increased significantly in the rat plasma membranes of DEN-induced hepatoma compared to normal tissue. The glucagon-induced response on the cellular effector systems via guanine nucleotide-binding regulatory proteins (G proteins) was inhibited in hepatoma plasma membranes.

Apoptosis in human lymphoblastoid cells induced by acivicin, a specific gamma-glutamyltransferase inhibitor.

We examined the effects of acivicin, a specific inhibitor of the ectoenzyme gamma-glutamyltransferase (gamma-GT), on gamma-GT activity and apoptosis in 2 human T-lymphoblastoid CEM cell lines, CCRF and VBL-100. In both cell lines, acivicin was found to cause morphological and biochemical changes of apoptosis in a dose-dependent manner. There was a close correlation between inhibition of gamma-GT activity and the emergence of apoptotic cells.

Fractals in pathology: are they really useful?

Through several examples selected from functional and pathological cells and tissues, including surface, cytoplasmic and nuclear membranes one will focus on the application of the fractal approach to measuring irregular and complex structures, on the importance of evaluating real morphology and on its potential role in understanding of tumor biology.

Changes in the activities of signal transduction and transport membrane enzymes in CEM lymphoblastoid cells by glucocorticoid-induced apoptosis.

The behaviour of the membrane enzymes PIP2-phospholipase C (PLC), that modulates the extracellular signals, and gamma-glutamyltransferase (gamma-GT), involved in metabolite transport, was followed during the early and active phases of apoptosis induced in CCRF-CEM cells by glucocorticoid (10(-6) M dexamethasone, DEX). The activities of gamma-GT and PLC increased significantly at 15 and 30 s after dexamethasone addition. Both activities decreased to the control level after 2 min but increased again at 5 min.

Digital image analysis of self-similar cell profiles.

Many biological objects appear to have self-similar structures which can be characterized by their fractal dimension D. However, applications of the concept of fractal geometry are rather scarce in cell and tissue biology. Here we adapt and analyse critically 3 methods of digital image analysis to measure D of cellular profiles.

Effect of cocaine and morphine on neutral endopeptidase activity of human peripheral blood mononuclear cells cultured with lectins.

We have tested the effect of alkaloids (cocaine, morphine) and enkephalins on neutral endopeptidase of peripheral blood mononuclear cells activated by lectins. When treated with concanavalin A and cocaine, peripheral blood mononuclear cells showed an enhanced activity (+110 per cent) of the membrane neutral endopeptidase, which was not related to the expression of the common acute lymphoblastic leukemia antigen at the cell surface, although both molecules have the identical amino acid sequence. Phytohemagglutinin-P, morphine and synthetic enkephalins did not induce the activity of neutral endopeptidase nor the expression of common acute lymphoblastic leukemia antigen.

Sulfated proteoglycans in the extracellular matrix of human breast tissues with infiltrating carcinoma.

The size, content and distribution of sulfated proteoglycans, constituents of the extracellular matrix, were investigated in non-neoplastic human breast tissues and in tissues with infiltrating carcinoma. Sulfated proteoglycans were identified as cuprolinic-blue-positive elements on electron microscopy preparations by the method of the critical electrolyte concentration. Morphometric data indicated that the numerical density of PG per surface area (NA) in normal tissues was about 2 to 7 times higher respectively in dense or loose connective zone then that found in the corresponding zones of malignant tissues.